PolymerSpectroscopy

Polymer Spectroscopy

Edited by

ALLAN H. FAWCETTThe Queens University of Belfast,Belfast, Northern Ireland, UK

JOHN WILEY & SONSChichester • New York • Brisbane • Toronto • Singapore

Copyright © 1996 by John Wiley & Sons Ltd,Baffins Lane, Chichester,West Sussex PO19 IUD, England

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LIST OF CONTRIBUTORS

Gordon G. CameronDepartment of Chemistry, University of Aberdeen, Meeston Walk, Old AberdeenAB92UE, Scotland, UK

Michelle CareyDepartment of Chemistry, Imperial College of Science, Technology and Medicine,South Kensington, London SWl'2AY, UK

Trudy G. CarswellChemistry Department, University of Queensland, Brisbane, QLD 4072, Australia

Francesco CiardelliDipartimento di Chimica e Chimica Industriale, Universita of Pisa, ViaRisorgimento 35, 56126 Pisa, Italy

Iain G. DavidsonDepartment of Chemistry, University of Aberdeen, Meeston Walk, Old AberdeenAB9 2UE, Scotland, UK

Christine DuchChemistry Department, University of Wales, Swansea, Singleton Park, SwanseaSA2 8PP, Wales, UK

Allan H. FawcettSchool of Chemistry, The Queen's University of Belfast, Belfast BT95AG, North-ern Ireland, UK

Adriano Fissi, CNRInstitute of Biophysics, University of Pisa, Via Risorgimento 35,56126 Pisa, Italy

Jerome FournierChemistry Department, University of Wales, Swansea, Singleton Park, SwanseaSA2 8PP, Wales, UK

R. Wayne GarrettChemistry Department, University of Queensland, Brisbane, QLD 4072, Australia

J. G. HamiltonSchool of Chemistry, The Queens University of Belfast, Belfast BT95AG,Northern Ireland, UK

Robin K. HarrisDepartment of Chemistry, University of Durham, Science Laboratories, SouthRoad, Durham DHl 3LE, UK

James R. HaydenChemistry Department, University of Wales, Swansea, Singleton Park, SwanseaSA28PP,Wales,UK

Patrick J. HendraDepartment of Chemistry, University of Southampton, Highfield, SouthamptonSO95NH, UK

Ian R. HerbertDepartment of Chemistry, University of Durham, Science Laboratories, SouthRoad, Durham DHl 3LE, UK

David J. T. HillChemistry Department, University of Queensland, Brisbane, QLD 4072, Australia

Oliver W. HowarthCentre for Nuclear Magnetic Resonance, Department of Chemistry, University ofWarwick, Coventry CV4IAL, UK

Roger N. IbbettDepartment of Chemistry, University of Durham, Science Laboratories, SouthRoad, Durham DHl 3LE, UK

Jack L. KoenigDepartment of Macromolecular Science, Case Western Reserve University, 10900Euclid Avenue, Cleveland, OH 44106-7202, USA

W.F.Maddams,Department of Chemistry, University of Southampton, Highfield, SouthamptonSO95NH,UK

James H. O'DonnellChemistry Department, University of Queensland, Brisbane, QLD 4072, Australia(Deceased)

David PhillipsDepartment of Chemistry, Imperial College of Science, Technology and Medicine,South Kensington, London SW72AY, UK

Osvaldo PieroniDipartimento di Chimica e Chimica Industriale, and CNR, Institute of Biophysics,Universita di Pisa, Via Risorgimemto 35, 56126 Pisa, Italy

Peter J. PomeryChemistry Department, University of Queensland, Brisbane, QLD 4072, Australia

Adrian R. RenniePolymers and Colloids Group, Cavendish Laboratory, University of Cambridge,Madingley Road, Cambridge CB3 OHE, UK

R. W. RichardsDepartment of Chemistry, University of Durham, Durham DHl 3LE, UK

J. J. RooneySchool of Chemistry, The Queen's University of Belfast, Belfast BT9 5AG,Northern Ireland, UK

H.W.SpiessMax-Planck-Institute fur Polymerforschung, Postfach 3148, D-55021 Mainz,Germany

Alan E. TonelliFiber and Polymer Science Program, College of Textiles, North Carolina StateUniversity, PO Box 8301, Raleigh, NC 27695-8301, USA

Graham WilliamsChemistry Department, University of Wales, Swansea, Singleton Park, SwanseaSA2 8PP, Wales, UK

Mark A. WhiskensDepartment of Chemistry, University of Durham, Science Laboratories, SouthRoad, Durham DHl 3LE, UK

Catherine L. WinzorChemistry of Department University of Queensland, Brisbane, QLD 4072, Australia

Robert J. YoungManchester Materials Science Centre, University of Manchester, GrosvenorStreet, Manchester Ml 7HS, UK

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Contents

List of Contributors ............................................................. xiii

Introduction to Polymer Spectroscopy .......................... 1

1. NMR Characterisation of Macromolecules in Solution ....................................................................... 7 1.1 Introduction ................................................................... 7 1.2 Branched Molecules: Polyethylene and a

Polyester System .......................................................... 9 1.3 The Microstructure of Linear Chains ............................ 15 1.4 The Participation of a Charge-Transfer Complex in

a Free Radical Polymerization Reaction ...................... 22 1.5 The Polymerization of Dienes ...................................... 25 1.6 Ring-Opening-Metathesis Polymerizations .................. 30

1.6.1 Stereoselectivity in ROMP ......................... 32 1.6.2 Distribution of trans Double Bonds in

High cis Poly(Norbornene) ......................... 36 1.6.3 Regioselectivity in ROMP .......................... 41 1.6.4 Direct Observation of Tacticity ................... 45

1.7 References ................................................................... 52

2. Conformation: the Connection between the NMR Spectra and the Microstructures of Polymers ......... 55 2.1 Introduction ................................................................... 55 2.2 Substituent Effects on 13C Chemical Shifts .................. 56

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2.3 γ-Gauche Effect Method of Predicting NMR Chemical Shifts ............................................................. 60

2.4 Applications of γ-Gauche Effect Analysis of Polymer Microstructures ............................................... 64 2.4.1 Polypropylene (PP) .................................... 64 2.4.2 Propylene-Vinyl Chloride Copolymers

(P-VC) ........................................................ 67 2.4.3 Poly(Propylene Oxide) (PPO) .................... 68 2.4.4 Poly(Vinylidene Fluoride) (PVF2) ................ 81

2.5 NMR Spectroscopy as a Means to Probe Polymer Conformations .............................................................. 84 2.5.1 Styrene-Methyl Methacrylate

Copolymers (S-MM) ................................... 84 2.5.2 Ethylene-Vinyl Acetate (E-VAc)

Copolymers ................................................ 88 2.6 NMR Observation of Rigid Polymer

Conformations .............................................................. 92 2.7 References ................................................................... 93

3. ‘Model-Free’ RIS Statistical Weight Parameters from 13C NMR Data ..................................................... 97 3.1 Introduction ................................................................... 97 3.2 Methods ........................................................................ 100 3.3 Some Calculation Details ............................................. 101 3.4 Individual Polymers ...................................................... 102 3.5 The Calculated RIS Parameters .................................. 109 3.6 β-Gauche Effects .......................................................... 111 3.7 Coupling Constants ...................................................... 111 3.8 Characteristic Ratios .................................................... 113 3.9 Conclusions .................................................................. 114

Contents vii


3.10 Acknowledgement ........................................................ 115 3.11 References ................................................................... 115

4. NMR Studies of Solid Polymers ................................ 117 4.1 Introduction ................................................................... 117 4.2 The Techniques ............................................................ 118 4.3 High-Resolution Carbon-13 NMR of Polymers ............ 121 4.4 Proton Spin Relaxation ................................................. 125 4.5 Discrimination in Carbon-13 Spectra ........................... 128 4.6 Spectra of Abundant Spins ........................................... 131 4.7 Conclusion .................................................................... 132 4.8 Acknowledgements ...................................................... 132 4.9 References ................................................................... 133

5. Multidimensional Solid-State NMR of Polymers ...... 135 5.1 Introduction ................................................................... 135 5.2 Multidimensional Solid-State NMR Spectra ................. 137 5.3 Examples ...................................................................... 138

5.3.1 Increase of Spectral Resolution ................. 138 5.3.2 Separated Local Field NMR ....................... 140 5.3.3 Wideline Separation Experiments .............. 141 5.3.4 2D and 3D Exchange NMR ........................ 142 5.3.5 Chain Alignment from 2D and 3D NMR ...... 144 5.3.6 Domain Sizes from Spin Diffusion

Experiments ............................................... 146 5.3.7 Spatially Resolved Solid State NMR .......... 146

5.4 Conclusion .................................................................... 148 5.5 Acknowledgements ...................................................... 149 5.6 References ................................................................... 149

viii Contents


6. NMR Imaging of Polymers ......................................... 151 6.1 Introduction ................................................................... 151

6.1.1 Basis of NMR Imaging ............................... 151 6.1.2 Relaxation Parameters in NMR Imaging .... 153 6.1.3 Resolution in NMR Imaging ....................... 155 6.1.4 Utility of NMRI ............................................ 155 6.1.5 Image Processing ...................................... 156

6.2 Advanced Imaging Techniques .................................... 156 6.2.1 Chemical Shift Imaging .............................. 156

6.3 Applications of NMRI to Polymers ................................ 159 6.3.1 Detection of Voids in Composites .............. 159 6.3.2 Detection of Nonuniform Dispersion of

Filler ........................................................... 161 6.3.3 NMRI of Physical Aging ............................. 161 6.3.4 NMRI Studies of Diffusion in Polymers ...... 162 6.3.5 Desorption of Liquids from Polymers ......... 165 6.3.6 Multicomponent Diffusion as Studied by

NMRI ......................................................... 167 6.3.7 Absorption-Desorption Cycling of

Liquids in Polymers .................................... 169 6.4 Acknowledgements ...................................................... 171 6.5 References ................................................................... 171

7. Fourier Transform Infrared and Raman Spectroscopies in the Study of Polymer Orientation .................................................................. 173 7.1 Introduction ................................................................... 173

7.1.1 The Basis of Orientation Measurements by Infrared Spectroscopy ........................... 174

Contents ix


7.1.2 The Basis of Orientation Measurements by Raman Spectroscopy ............................ 176

7.2 ........................................................................................ 177 7.2.1 Experimental Techniques on Static

Samples ..................................................... 177 7.2.2 Infrared Spectroscopic Studies on

Oriented Polymers ..................................... 180 7.2.3 Raman Spectroscopic Studies on

Oriented Polymers ..................................... 182 7.3 Time Resolved Measurements .................................... 185

7.3.1 The Response of a Viscoelastic System to Sinusoidal Stress ................................... 185

7.3.2 Experimental .............................................. 187 7.3.3 Some Examples of Dynamic Linear

Dichroic Infrared Studies ............................ 192 7.4 Elastomers Under Stress ............................................. 198 7.5 Conclusion .................................................................... 200 7.6 References ................................................................... 201

8. Deformation Studies of Polymers using Raman Spectroscopy ............................................................. 203 8.1 Introduction ................................................................... 203

8.1.1 Polydiacetylene Single Crystals ................. 204 8.1.2 Extension of the Technique to Other

Materials .................................................... 206 8.2 High-Performance Polymer Fibres ............................... 206

8.2.1 Aromatic Polyamide Fibres ........................ 206 8.2.2 Polyethylene Fibres ................................... 210

8.3 Isotropic Polymers ........................................................ 214 8.3.1 Urethane-Diacetylene Copolymers ............ 214

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8.3.2 Deformation Studies .................................. 217 8.4 Composites ................................................................... 221

8.4.1 Single-Fibre Composites ............................ 221 8.4.2 Interfacial Micromechanics ......................... 224

8.5 Conclusions .................................................................. 227 8.6 Acknowledgements ...................................................... 228 8.7 References ................................................................... 228

9. Spin-Label Studies of Heterogeneous Polymer Systems ...................................................................... 231 9.1 Introduction ................................................................... 231

9.1.1 Synthesis of Spin Labels ............................ 232 9.2 Theoretical Background ............................................... 235

9.2.1 Correlation Times ...................................... 235 9.2.1.1 Fast Motion ................................... 239 9.2.1.2 Slow Motion ................................... 240

9.2.2 The Glass Transition and T50G ................... 240 9.3 Heterogeneous Systems .............................................. 242 9.4 Polymer Blends ............................................................. 245 9.5 References ................................................................... 251

10. The Use of ESR Spectroscopy for Studying Polymerization and Polymer Degradation Reactions .................................................................... 253 10.1 Introduction ................................................................... 253 10.2 Experimental ................................................................. 254 10.3 Results and Discussion ................................................ 255

10.3.1 Free Radical Polymerization ...................... 255 10.3.1.1 Identification of the Radicals in

the ESR Spectrum ........................ 255

Contents xi


10.3.1.2 Measurement of Radical Concentration ................................ 256

10.3.1.3 Monomer Concentration during Polymerization ............................... 256

10.3.1.4 Radical Concentration during Polymerization ............................... 257

10.3.1.5 Correction for Changing Sensitivity of the Spectrometer ..... 259

10.3.1.6 Kinetic Analysis ............................. 260 10.3.1.7 Crosslinking Methacrylate

Monomers ..................................... 261 10.3.2 Polymer Degradation by High-Energy

Radiation ................................................... 263 10.3.2.1 Poly(Methyl Methacrylate) ............. 263 10.3.2.2 Polystyrene ................................... 267 10.3.2.3 Random Copolymers of Methyl

Methacrylate and Styrene ............. 268 10.3.2.4 ESR and the Mechanism of

Radiolysis ...................................... 269 10.4 Conclusions .................................................................. 273 10.5 Acknowledgements ...................................................... 273 10.6 References ................................................................... 273

11. Dynamics of Bulk Polymers and Polymerizing Systems as Studied Using Dielectric Relaxation Spectroscopy ............................................................. 275 11.1 Introduction ................................................................... 275 11.2 Amorphous Polymers: Phenomenological and

Molecular Aspects ........................................................ 276 11.3 Crystalline Polymers ..................................................... 280

xii Contents


11.4 Liquid Crystalline (LC) Polymers .................................. 282 11.5 Real-Time Studies of Chemical and Physical

Changes ....................................................................... 288 11.6 Conclusions and Future Prospects .............................. 293 11.7 Acknowledgements ...................................................... 294 11.8 References ................................................................... 294

12. Light Scattering from Polymer Systems .................. 297 12.1 Introduction ................................................................... 297 12.2 Small Angle Light Scattering (SALS) ........................... 298

12.2.1 Semi-Crystalline Polymers ......................... 298 12.2.2 Phase-Separating Polymer Mixtures .......... 305

12.3 Quasi-Elastic Light Scattering (QELS) ......................... 309 12.3.1 Dilute Polymer Solutions ............................ 309 12.3.2 Gels ........................................................... 311 12.3.3 Semi-Dilute Solutions and Trapped

Chains ....................................................... 313 12.3.4 Surface Quasi-Elastic Light Scattering

(SQELS) .................................................... 316 12.4 Conclusions .................................................................. 321 12.5 References ................................................................... 321

13. Neutron Scattering from Polymers ........................... 325 13.1 Introduction ................................................................... 325 13.2 The Principles of Neutron Scattering ........................... 325 13.3 Neutron Experiments .................................................... 329

13.3.1 Studies of Polymer Dimensions: Small Angle Scattering ........................................ 330

13.3.2 Polymers at Surfaces-Reflection ................ 333

Contents xiii


13.3.3 Polymer Dynamics-Quasi-Elastic Scattering .................................................. 334

13.4 Some Examples of Recent Progress ........................... 336 13.4.1 Studies of Copolymers ............................... 336 13.4.2 Adsorption at Surfaces ............................... 339 13.4.3 Kinetics and Polymer Motion ...................... 341

13.5 Final Remarks ............................................................... 342 13.6 References ................................................................... 342

14. Optical Activity and the Structure of Macromolecules ......................................................... 347 14.1 Introduction ................................................................... 347

14.1.1 Origin of Optical Activity in Macromolecules ......................................... 347

14.1.2 Objective .................................................... 350 14.2 Chiroptical Properties of Photochromic

Polypeptides ................................................................. 351 14.2.1 Polypeptides Photoresponsive to UV

Light ........................................................... 351 14.2.1.1 Azobenzene-Containing

Polypeptides .................................. 351 14.2.1.2 Light-Induced Conformational

Changes ........................................ 352 14.2.1.3 Photosimulated Aggregation-

Disaggregation Effects .................. 355 14.2.2 Photomodulation of Polypeptide

Conformation by Sunlight ........................... 357 14.2.2.1 Spiropyran-Containing

Polypeptides .................................. 357

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14.2.2.2 Photomodulation of Conformation ................................. 360

14.2.2.3 Photoinduced Variations of Viscosity ........................................ 366

14.3 References ................................................................... 367

15. Polymer Luminescence and Photophysics ............. 369 15.1 Introduction ................................................................... 369 15.2 Probes of Order in Polymers ........................................ 370 15.3 Probes of Sub-Group Motions ...................................... 372 15.4 Photochemistry in Polymers ......................................... 372 15.5 Excimer-Forming Polymers .......................................... 374 15.6 Dynamics of Luminescence ......................................... 376 15.7 Fluorescence Decay in Vinyl Aromatic Polymers ........ 377

15.7.1 Diffusional Models ..................................... 379 15.7.1.1 Random Walk Migration, Evenly

Spaced Chromophores ................. 380 15.7.1.2 Random Water, Random

Distribution Chromophores ........... 380 15.7.1.3 Multiple Trap Energies .................. 381 15.7.1.4 Reversible Excimer Formation ...... 381 15.7.1.5 Diffusion of Energy and

Chromophore ................................ 381 15.7.1.6 Fluorescence Anisotrophy

Measurements .............................. 385 15.8 Conclusion .................................................................... 387 15.9 Acknowledgements ...................................................... 388 15.10 References ................................................................... 388

Index .................................................................................. 391

1 NMR CHARACTERISATIONOF MACROMOLECULESIN SOLUTIONA. H. FAWCETT, J. G. HAMILTON AND J. J. ROONEYSchool of Chemistry, The Queens University of Belfast, Belfast BT9 5AG,Northern Ireland, UK

1.1 INTRODUCTION

The NMR method of studying the microstructure of macromolecules is the mosteffective available, provided that the materials can be obtained in solution. Themethod is now routinely employed to characterise and to identify the structurespresent in polymers, both those in common use and those created by the chemistwhen working with new monomers or new catalyst systems [1-6]. Derivatives ofpolymers and reactions on polymers are similarly accessible to study. The NMRparameter that is sensitive to these structural issues is the chemical shift,commonly measured in ppm from an internal reference. It senses readily informa-tion on the framework of the polymer—its connectivity—by providing informa-tion on the number and type of atoms linked to each particular nucleus, and alsosenses such factors as the relative chirality of pairs of such centres and cis/transisomerism within double bonds.

The nucleus most often employed for both man-made and natural macro-molecules is 13C, despite its being rather dilute (only 1% of the carbons). This isbecause in the spectrum the dispersion of shifts is particularly large; much detailor fine structure is generally encountered that is directly related to the polymerstructure itself, and signal intensity is rarely a problem with modern high fieldinstruments. Many other NMR-active nuclei such as 19F and 31P may be usedtoo when they are present in the macromolecule. Proton NMR spectra arecomplicated by the presence of coupling effects between the spins of the protons if,as is usual, the protons are present on directly bonded carbon atoms. In certaincases these coupling effects are of extreme value: as Bovey showed forpoly(methyl methacrylate) [2,7], the tacticity of the polymers may be identifieddirectly, and the value of vicinal coupling constants provides information on theconformational properties of the bond [5,8]. However, frequently, as for examplewith polyolefins, they conceal the shift effects associated with the microstructure

Polymer Spectroscopy. Edited by Allan H. Fawcett© 1996 John Wiley & Sons Ltd

by creating a multiplicity of splittings, a complicating factor which may berelieved only by the use of a substantial proportion of selective deuteration, as hasbeen demonstrated for polypropylene [9,10].

We may note two rather special cases of proton NMR spectra: for highlysyndiotactic polystyrene the methylene protons, being equivalent, have a simplethree line 1:2:1 pattern that derives from the coupling effect of the two flankingmethine protons [ H ] . The highly isotactic polymer has a slightly more complexbut still recognisable spectrum [12]. Features in the spectrum of the atacticpolymer are quite unrecognisable, as proton coupling effects intermingle withchirality effects, coupled with substantial chemical shift anisotropy from thephenyl ring [13]: each main chain carbon bears at least one proton, a situationthat is unfortunately more usual. We are familiar with only one case, involvingthe furfurol oligomer bis(5-furfuryl-2-furylmethane), in which the methyleneprotons are more sensitive to position than is the carbon of the same group; this isprobably because the central methylene protons sample the anisotropic shieldingcone of the furan rings in a manner different from that for the protons of theflanking methylene groups, but the carbons, being in the plane of the rings,experience a constant effect [14].

During the last 25 years the development of the NMR method, firstly in termsof the power of the magnet employed and secondly by turning to computer-basedoperating systems, has often been stimulated, if not driven, by the need tounderstand polymer microstructure. In 1971 the chemical companies Dow, ICIand Du Pont themselves commissioned new magnets that increased the magneticfield beyond 5 T in order to pursue their studies of polymers so vital to theirbusiness. This magnetic field, equivalent to more than 200 MHz in terms of theproton resonance frequency, was achieved by employing superconducting wind-ings at cryogenic temperatures [15]. The stronger the magnetic field, the greaterthe sensitivity and the dispersion of shifts (and the closer the proton spectra cometo being first order). Initially man-made polymers were the subjects of study, butmore recently biological polymers have been the targets. The last ten years hasseen field strengths in common use rise to 11.74 T (equivalent to 500MHz forprotons and 125.7 MHz for carbons) by the adoption of superconducting mag-nets, and similar technical improvements associated with versatile signal trans-mitter and receiver coil design have also come into common practice. Indeed,17.5 T instruments have recently been announced.

Just as important as these developments in magnet design has been the intro-duction of pulsed Fourier transform methods, for these permit the performance ofnew types of experiment by the computerised systems that control the produc-tion, acquisition and processing of the experimental data. New pulse sequencesincreasingly made available by instrument manufacturers within their softwaresuites permit the routine performance of these new experiments: an early exampleis the distortionless enhancement polarisation transfer, or DEPT, experiment toidentify the number of protons attached to a carbon by controlling the final

proton pulse flip angle [16]. A later example is provided by 2-D and 3-Dexperiments, the introduction of which has made the connectivity of the carbonand protons much clearer [17,18], has much reduced the problem of distinguish-ing coupling effects from shift effects by providing extra dimensions for displayingthe NMR signal, and has even provided an extra structure-discriminating route[19-22].

One development that exploits the storage of data on the computer base forsubsequent processing can be optimised for a particular purpose, such asresolution enhancement using the Lorentz-Gaussian transformation technique,in which the free induction decay data is multiplied by the product of a Lorent-zian and a Gaussian weighting function prior to the Fourier transformation [23].Similarly, the computer base has been used for some time to control measure-ments within the time domain and to provide values for such parameters as T1,the spin-lattice relaxation time, which is sensitive to the motions of the chains,such as those of polysulphones, whose dynamic response is dispersed on oppositesides of the Larmor frequency when made from 1-olefins and 2-olefins [24]. Thenuclear Overhauser enhancement (NOE effect) is also sensitive to the motions ofthe polymer chains, and good practice, when careful quantitative measurementsof 13C signals are required, is to use instrument settings that eliminate the NOE[25], so preventing it from enhancing the signals of certain carbons relative tothose of others.

1.2 BRANCHED MOLECULES: POLYETHYLENEAND A POLYESTER SYSTEM

We choose to start our discussion of the 13C chemical shift effects in macro-molecules with a mention of the substitution parameter schemes such as those ofGrant and Paul [26], which were introduced into polymer spectroscopy byBovey at an earlier conference in the series [I] . The rule that a carbon's chemicalshift increases by a fairly constant increment when a covalently attached hydro-gen atom is replaced by a methyl group, the alpha effect, has proved of value whenspectral assignments are made. Similar parameters associated with substitutionat progressively more remote sites, the beta, gamma and even delta effects, havebeen established and found to diminish in magnitude (alpha = 11 to 2.5 ppm,beta = 9 to 7ppm, gamma= —2.5ppm, delta = O to 0.5ppm). Although quiteprecise values are often given [2,3], the values of these parameters are sensitive tothe exact structure of the site of supposed structural change, and the best practiceutilises model compounds close to the target structures, as in Randal's studies onthe side chains of polyethylene [27-29]. A development of this substitutionapproach, which is appropriate to molecules containing heteroatoms, is to studythe effect on chemical shifts of replacing a —CH2— group with another atom orgroup. This has been used to predict shifts in molecules and polymers containing

Figure 1.1 100 MHz 13C NMR spectrum of a high density polyethylene sample insolution at 125 0C. The spectrum shows peaks from end groups (E) and methyl, ethyl andbutyl side chains. The sample had been irradiated at 423 K with 300 KGy of gamma rays[32] and shows minor features near 29,32 and 41 ppm from the H structures thus formed

—O—, —NH— and —SO2— groups, the electronegativity of these groupscausing in general a down-field effect. Thus, the shifts of polymers containingheteroatoms may also be predicted from first principles, for assignment purposes,if the shift of the corresponding hydrocarbon is known [30].

For the high density polyethylene spectrum of Figure 1.1, the main feature isthe intense signal at 30 ppm from the long runs of methylene units. The shifts ofthe end groups (marked E1, E2, E3 as we move inwards from the methyl signal)are the next feature, but a number of resonances from side chains are present. Themethyl group of a butyl side chain coincides with E1, but the second methylenegroup, E2, is distinguished at % 23.4 ppm. The methyl groups of a small propor-tion of ethyl side chains (Et x) and methyl side chains (Me1) are also seen at 20 and11 ppm respectively. The main chain carbons at the root of and next to thebranches are also seen, the assignments for those next to the butyl unit beingshown in the first part of Scheme 1. Methyl and ethyl side chains are probablyderived from traces of propene and but-1-ene within the ethylene feedstock. Thefeatures from these are clear, but are in very small proportions compared with theend group signals for this linear polyethylene.

- C H 2 - C H 2 - C H - C H 2 - C H 2 -

CH2-CH2-CH2-CH3

Bu3 Bu2 Buj

Butyl side chains to polyethylene

— C H 2 - C H 2 - C H - C H 2 - C H 2 - — C H 2 - C H 2 - C H - C H 2 - C H 2 -

- C H 2 - C H 2 - C H - C H 2 - C H 2 - C H 2 - C H 2 - C H 2 -

H crosslinks Y links / long branches (1)

Scheme 1 Elementary structure in polyethylenes.

Application to the field of low density polyethylenes was prompted by the needto understand the high proportion of carbons in the form of methyl groups(perhaps as much as 8%), an early result from the IR spectra. The studies led tothe recognition of an elaborate branched structure, for the production of whichthe mechanism of Roedel, backbiting by the propagating radical, was introduced.The normal process produces butyl side chains as a result of a cyclic transitionstate of five carbons-I-one hydrogen for the intramolecular hydrogen atomabstraction. Ethyl side chains (Et) may have formed by two consecutive backbit-ings. Randal has characterised low density polyethylene and related copolymersby carbon-13 NMR spectroscopy: complex dendritic structures are revealed bythe analysis [30]. Long side chains form also by intermolecular abstractions ofhydrogen atoms—chain transfer to polymer. A study of linear low densitypolymers, the side chains of which, as they derive from a 1-olefin component ofknown structure and occurrence, are well-defined, allowed the derivation ofsubstitution parameters appropriate to the polyethylene problem itself, gavemuch security to this approach [27,28], and so led to the full assignment of themethylene carbon shifts dispersed on each side of the main signal at 30.0 ppmfrom the long runs of methylene groups. More assignments subtle were alsofound, such as a distinction between the methyl groups at the end of butyl sidechains (14.21 ppm) and those at the ends of longer chains (14.01 ppm) [29].Besides the use of substitution parameters, assignments were also made usingspecial spectrometer settings: APT (attached proton test) and DEPT techniquesallow the direct recognition of quaternary carbons, of methylenes and of methylsand methines together [30]. A coherent view of the complex dendritic structure offree radically-produced low density polyethylene is now available. The usualmicrostructural features of high density polyethylene, alkyl side chains, have alsobeen observed in ultra high molecular weight polyethylene, but in much smallerproportions [31].

A related study has been the elucidation of the crosslink structures inducedwithin polyethylene by high energy radiation. The secondary carbon radicalsthus produced by C—H bond scission may diffuse by hydrogen atom abstrac-tion. They have been shown to combine in pairs to form H type junctions, and tocreate Y type junctions by reactions with the vinyl end groups of the chains andwith primary carbon radicals produced by main chain scission. In each case theshifts characteristic of the new structure were identified [32]. The shifts of theH junctions are distinct, being 41.1, 31.9 and 28.7 ppm respectively at the (CH)junction and the first and second linked carbons, as is shown in Scheme 1, but theshifts of the Y junctions coincide with those at the roots of long branches, andtheir formation is recognised only when a careful comparison has been made ofthe areas of these shifts before and after irradiation.

In a similar area, that of the characterisation of branched and networkpolyesters from difunctional acids and tri- or tetra-functional alcohols, in systemsthat were first used about 150 years ago when there was no understanding of theirpolymeric nature, our studies have found a similar sensitivity in the NMRspectrum [33] within the 55-75 ppm region, where the carbons of the alcohol andester functions are found; see Scheme 2. The shifts of the carbons of glycerol [33]or erythritol [34] during the progressive conversion of alcohol functions to estergroups by a reaction with succinic anhydride change after each step by a few ppmin a manner that is readily recognised, for the sequence in time and symmetry ofsubstitution of the molecules that form reflects the greater reactivity of theprimary alcohol sites. Thus, replacing the —O—H group of an alcohol with an

O—Hi

I CH2-CH-CH2-O-H II CH2-CH-CH2-O-H

O-SA-OH O - H O-SA-OH

O—H O—H

III CH2-CH-CH2 IV CH2-CH-CH2-O-SA-OH

O—SA-OH O—SA-OH O—SA-OH

O—SA-OH

V CH2-CH-CH2-O-SA-OH

lO—SA- OH

Scheme 2 Primary oligomers of glycerol and succinic acid

—O—succinate has at the first, second and third carbons alpha, beta and gammaeffects of respectively +2.6, —3.1 and — 0.4 ppm [33]. (These alpha, beta andgamma parameters correspond to the beta, gamma and delta parameters ofGrant and Paul [26] because of the intervening oxygen atom.) If the second site ofthe succinic acid residue subsequently forms an ester, the shifts of the previouslylinked glycerol residue appear in slightly different places. Thus, a glycerol residuelinked 1, 3 within a chain has different shifts from one linked 1, 3 at the end ofa chain and from the oligomeric 1,3-discuccinate (III). We have introduced theterm III" for such a chain-extending unit and III' for a unit at the end of a branch,the number of primes indicating how many of the second, and more remote, acidgroups have reacted. The shifts of the glyceryl residues of the oligomers of Scheme2 thus provide good guides to the shifts of glyceryl residues at branch points (V),in chain extenders (III and IV) and at chain ends (I and II) in the highly branchedor fractal polymers that may be made, thus allowing the assignments of Figure 1.2.

The trisuccinate oligomer V can be readily obtained in pure form [33], unlikethe other oligomers. It may be polymerised in a single process by heating ina vacuum, where succinic acid is first lost as the anhydride to the vapour phase,and the vacated alcohol site (in a III or IV type residue, for which evidence ispresent in Figure 1.3) then forms an ester with an acid group of another oligomer.The consequence of this development of linkages is seen in the shifts of eachcarbon of the glycerol residue, where extra fine structure develops as the moleculeevolves towards a dendritic or fractal structure. The initial molecule is a heptamer(XV of Scheme 3 [33]), but others emerge. The shifts are sensitive not only towhether the link at the remote site has formed an ester, but also (in the case of thecentral carbon) to whether that site was a primary or a secondary alcohol. Theshifts of the network node are sensitive to the structure of the immediately

Figure 1.2 13C NMR spectrum at 126 MHz of the mixture of oligomers formed by thereaction of glycerol with succinic anhydride [33]. Only the region of the glycerol residueshifts is shown. The oligomers are identified in Scheme 2; G refers to glycerol

Figure 1.3 13C NMR spectrum at 126MHz of the mixture of oligomers formed byheating oligomer V in a vacuum at 180 0C. Parts (a) and (c) for 40 min, part (b) for 20 min,part (d) for 60 min. The labels refer to Scheme 3. The region of the glycerol residue shifts isshown in (a), and for the higher resolution plots (b-d) only the signal from the centralmethine carbon. The resolution of the latter parts was obtained with zero line broadening.Reproduced with permission from [33]

adjacent nodes when the link is succinic acid, but not if glutaric acid is used, forthe extra methylene group renders the linkage too remote. In Figure 1.3 the shiftsat three early stages may be seen, as the molecules evolve towards a polymericform of III: peaks z and y3 we assign to the shifts of the primary and secondaryglycerol carbons when the primary carbon is linked to another glycerol residue;peaks yx and y2 come from a secondary carbon of a glycerol which is linkedthrough a succinic acid residue to respectively a primary and a secondary site ofa glycerol residue, as shown in Scheme 3. These distinctions in the fine structureare relatively minor, are best observed with a high field system [33], and assist inthe development of the chemistry of the formation of fractal polyesters. Novelliquid crystalline forms, for example, have been produced using such means, the

XV[V'- S A - VT

3 y3 z yi 1H—O—SA-O—CH2-CH-CH2-O—SA-O—CH-(—CH2-O-SA-OH)2

O—SA-OH3 y3 z

XVI H - O - S A - O - C H 2 - C H - C H 2 - O - S A[V-SA-V"- SA-Vl I I

HO—SA-O O

Y2 CH-CH2-O-SA-OH

zCH2

O

H-O-SA-O-CH2-CH-CH2-O-SA

HO—SA-O

xvn[V1-SA-V]

3 k c* 2 1H—O—SA-O—CH2-CH-CH2-O—SA-O—CH-(—CH2-O-SA-OH)2

O—H

Scheme 3 Some higher oligomers of glycerol and succinic acid; the numbers are those ofref. [33]

mesogenic units being present as pendent groups demonstrably in full comple-ment upon what was a poly(erythntolfractal glutarate [O—H] 2 backbone [34].

13 THE MICROSTRUCTURE OF LINEAR CHAINS

The first microstructural issue of linear homopolymer chains that we examine istacticity, which we illustrate with spectra from two systems from our own work:the poly(alkyl cyanoacrylates) [ - C H 2 - C ( C N ) C O O R - ] , which constitutea vinylidene system the spectra of which are shown in Figure 1.4, and thepolyalkene sulphides and sulphones: [—CH2—CHR—S—] and [—CH2—CHR—SO2—], spectra of which are shown in Figure 1.5. We show meso orm dyad structures of two of these polymers in Scheme 4. Note how the two chiralcentres of the first polymer appear to be equivalent, but for the second polymerthe equivalence is less immediately evident, for the residues contain three bonds

Figure 1.4 NMR spectra of poly(ethyl cyanoacrylate) samples. Part (a) has the mainchain methylene proton signals at 400 MHz of samples prepared in acetone with sparteineas initiator (A2) and in THF with cinchonidine as initiator (A5). Part (b) shows the 13Cspectrum of the side chain methylene carbons of the samples A2 and A5, with triad andpentad assignments [38]

(a)CNH CN H C H 2 - C H 3

I I I I I—C—C—C— - S O 2 - C H 2 - C - S O 2 - C H 2 - C - S O 2 -

COH CO CH 2 -CH 3 HI (b) I

OEf ; OEt

Scheme 4 Meso structures of poly(ethyl cyanoacrylate) and poly(but-l-ene sulphone).The projections have the backbones in a planar ziz-zag, and show the chain from above

and in successive residues a particular atom is in turn in the "up" and the "down"position. Triad, tetrad, pentad and longer sequences may be obtained by thesuccessive inclusion of extra residues and may be recognised by NMR. Thestereochemical structure of these longer sequences are described in terms ofthe m or r relationships of the successive pairs of chiral centres [2,3]. In the case

Figure 1.5 13C NMR spectra of the backbone methylene carbons of (a) a tactic poly(but-l-ene sulphide), (b) of the tactic poly(but-l-enesulphone) made from it by oxidation, and (c) of an atactic polysulphone. The dispersion of shifts of the sulphone polymer is greater becauseof the gamma-gfaucfie effect of the oxygens. The small peak at 6 = 49.2 ppm is from H — H sequence.

ppm ppm

of the first polymer the residues, as they have just two backbone carbons, aresensitive to influences equally from each direction along the chain, and mr and rmheterotactic sequences are identical as far as the signals from carbons at orpendent to the central chiral centre are concerned. At high resolution theinfluence of the next two chiral centres may be expressed, so we may be able todistinguish the rmrr and mmrr pentads. For the polysulphides and polysul-phones the residues have three components, so that the influence upon chemicalshifts of one residue that derives from the chiral centres of the two neighbouringresidues is diflferent, and depends upon the direction: thus, an mr sequence willnot for symmetry reasons have the same shifts as an rm sequence. (The mechan-ism that generates shift multiplicity depends upon fine differences in bondrotation populations for different chiral sequences that are coupled to thegamma-âuc/ie interactions, as Tonelli describes elsewhere [8]). As in the relatedolefin oxide and styrene oxide polymers [34,35], the residues of the polysulphidepredominantly orientate in only one direction, so that head to head junctions arealso encountered, and provide minor features in the spectrum, as we indicate inFigure 1.5. This type of enchainment has been termed positional isomerism,orienticity [3] or regioselectivity, the last term being used below for ring-openingmetathesis polymerisation (ROMP) systems. Another consequence of the pres-ence of three distinct groups in each residue of the linear backbone is thepossibility of optical activity, a property that independently permits recognitionof isotacticity [37].

We first discuss the spectra of poly(ethyl cyanoacrylate), proton spectra beingshown in Figure 1.4(a) and the corresponding 13C spectra in Figure 1.4(b) [38].We use the classical route, first used by Bovey and Tiers for poly(methyl-methacrylate) [2,7], PMMA, for determining the type of tacticity that predomi-nates. They recognised the four-line pattern of an AB quartet in the 60 MHzspectrum of a predominantly isotactic polymer in the signal from the main chainmethylene protons within a meso dyad—this was distinctly different from thesingle line from the methylene protons of a racemic dyad that was found ina polymer produced by a different mechanism (the absence of an effect from thecoupling constant deriving from the equivalence of the two protons). For ourassignment two polymers were available, poly(ethyl cyanoacrylate)s that hadbeen made in different solvents and with different chiral initiators for the anionicpolymerization process (it transpired that the solvent was the important factor).In contrast to the case with PMMA, an AB quartet was not immediatelyapparent in the proton NMR spectrum, and a pair of clear lines (a and b in Figure1.4(a)) considered for part of such a system was found to be unsuitable: thesplitting between the lines was not —14 Hz (the value of a geminal coupling) norwere there signals nearby at that splitting. Moreover, their relative intensitieschanged in a simple manner with the value of the tacticity parameter deducedfrom the 13C NMR spectrum. They were thus assigned to rrr and rrm finestructure, and these assignments were confirmed by checking their relative

intensities with values predicted with the aid of a single (Bernoullian) tacticityparameter obtained from the side chain methylene carbon spectrum. Discrepan-cies between the Bernoullian and the experimental intensities were of the order of2% within both proton and carbon spectra. The direct recognition of an ABquartet in spectra such as those of Figure 1.4(a) was prevented by partial overlapof m dyad signals dispersed by tetrad effects and a coincidence with the remainingr-centred tetrad, as a two-dimensional experiment has subsequently made clear[39]. The main components of the AB structure lie near 2.6 and 2.8 ppm. In thecarbon spectrum pentad effects were resolved within the rr-centred triad of theside chain methylene carbons (Figure 1.4(b)). The two peaks of the mr-centredtriad may be assigned as indicated in the figure to mrmm and (mrmr + rrmm)sequences, of expected relative intensities of 0.100 and 0.096 respectively of A2;the remaining sequence rrmr, of Bernoullian intensity 0.02, is apparently notresolved in the signal. This set of pentads may be more readily recognised on thebasis of more clearly different line intensities in the spectrum of A5. They and theother peaks were assigned, once the chains were recognised as being predomi-nantly isotactic, on the manner in which their intensities varied with the value ofP1-, a practice which is widely adopted when samples of different tacticities areavailable.

In the case of polyacrylonitrile [—CH2—CH(CN)—], which gives an atacticpolymer when the free radical reaction is performed in solution, enhancement ofthe tacticity to Pf values as high as 0.70-0.87 has been provided by performinga polymerisation when the monomers were constrained, or lined up, within a ureacanal complex. This allows the development within the 13C NMR spectrum ofintense peaks from certain heptads [12], the emphasis providing clear indicationof the origin of the signals from sequences of high isotactic content. The finestructure of the 13C NMR signals from the methyl groups of polypropylenedisplays pentad and partial heptad fine structure, for the assignment of whicha number of methods were adopted, depending mainly upon the availability ofpolymers of known tacticity, as their crystal structures had previously beendetermined, but also using 13C-labelled model compounds of known stereosequence content [40]. Highly isotactic polystyrene has been produced usinga titanium trichloride-derived catalyst [41]. Once such a material is available thespectra may give an insight into the manner in which the process behaves:a catalyst for isotactic polypropylene sometimes allows errors in stereochemistry,but these are immediately corrected, as the presence of mrrm but not mrmmpentads testifies [2]. Such interesting evidence on the manner in which a catalystfunctions helps us to understand the mechanism; we conclude this review with anaccount of such effects discovered in our studies of ring-opening metathesispolymerisation, or ROMP, which likewise use metal-centred catalysts.

The Bernoullian nature of the free radical or ionic propagation in a polymermay be ascertained from the relative intensities of the rr, mr -I- rm, and mmcomponents of the triad fine structure, as in our studies of the side chain

methylene group in poly(ethyl cyanoacrylate)s. Provided that each new chiralcentre forms in a manner that depends only upon the type of the previous chiralcentre, so that only one statistical parameter is involved for dyad occurrences, theweights of the triads are respectively [2,3] (1 - F1)

2,2P1(I - P1) and (P,)2. Usingin turn (from left to right) the first two areas, the second two, and then the first andthird of each part of Figure 1.4(b), we solve for P1 to obtain 0.63,0.72 and 0.68 forsample A2, values which are hardly significantly different from each other; andfor sample A5 we have correspondingly 0.52, 0.60 and 0.56, which are close. Atest for Markov behaviour is provided by the relationships involving two para-meters [2, 3]:

JV/m) = « = (nn)/(2(m)) = (mr)/(2(mm) + (mr))

and

P(m/r) = w = (rm)/(2(r)) = (mr)/(2(rr) + (mr)),

where P(r/m) is the probability that an r dyad will follow an m dyad. Markovbehaviour has u + w < 1.00. For the cyanoacrylate spectra of Figure 1.4(b) thevalues of u and w are respectively 0.28 and 0.66 for polymer A2 and 0.46 and 0.54for polymer A5, indicating that both polymerisations are close to Bernoullian.Sample A2, which deviates more from the ideal was made using as initiatorsparteine. As this compound is a dinitrogen base, it may enhance the formation ofa complex between the oppositely charged initiator and the propagating ends ofthe chain in a zwitterion. A clear case of Markov behaviour is given below. Thestatistical index P = 4IS/H2 = (4(mm)(rr)/(mr)2] has been used to characterisethe isotactic acrylonitrile polymers prepared within the canal complexes [12].Two distinct mechanisms were identified from the dependence of this index uponthe isotactic content, a much stronger dependence being found for the polymersproduced at low temperatures after irradiation than for those produced duringirradiation at a moderately low temperature, for which canal coherence mighthave been upset by the evolution of heat and the irradiation itself.

The second aspect of linear polymers from our own field may be considered asa whole, for polysulphones may be obtained by oxidation of polysulphides as wellas by the free radical copolymerisation of SO2 with an olefin. Indeed, thischemical change is beneficial to the spectroscopy, for fine structure develops asa result of oxidation, as may be seen in Figure 1.5, where the shifts, each at500 MHz, of the methylene carbons of an isotactic polysulphide and the polysul-phone prepared from it are displayed in parts (a) and (b) respectively. As discussedelsewhere [2, 5, 8], fine structure may be the consequence of gamma-grawc/ieinteractions weighted according to the occupancy of the intervening bondconformational states. In this case the fine structure undoubtedly developsa larger dispersion and becomes more sensitive to the stereochemistry because wehave introduced oxygens gamma with respect to each main chain carbon; suchoxygens may cause a shift effect as large as — 9.4 ppm, the particular value

depending upon the conformation adopted by the intervening C—S bond[30,42].

Poly(l-olefin sulphone)s have been found to be atactic when made from themonomers by the free radical reaction; when first observed the backbone carbonsshowed incipient or clear triad fine structure [41,42]. The first carbon of the sidechain displays dyad stereochemical sensitivity at low resolution, the upfield halfof the signal being assigned to an m dyad when a comparison was made with anisotactic poly(propylene sulphone) made by oxidising an isotactic polysulphide[41]. The poly(but-l-ene sulphone)s prepared by free radical means showedsimilar spectra of the main chain methine when examined at high field (Figure1.5(c)), showing clearly mm, mr + rm, and rr triads, as labelled by comparisonwith the other spectrum, that of the optically active polymer prepared froma polysulphide. The test on the Markov nature finds M = 0.51 (±0.01) andw = 0.480 (±0.005), giving u + w = 0.99 (±0.01), so the free radical polymerisa-tion process was clearly Bernoullian. For the polymer prepared by oxidation ofthe polysulphide the parameters are w = 0.25 (±0.01) and w = 0.51 (±0.01),giving M + W = 0.76 (±0.02) and indicating the Markov nature of the polymerisa-tion process the polysulphide precursor had experienced. (From the spectrum ofthe polysulphide itself we were able to obtain only one parameter, P1 = 0.66,a number very close to w/(u + w) = 0.67, as expected.) It may well be that thepolysulphide formation was not Bernoullian, for the catalyst used was anoptically active zinc-centred species that favoured the R enantiomer of thesulphide, and the monomer itself contained an excess of the S enantiomer [44].A second feature in the spectrum reflecting the polysulphide formation mechan-ism is the presence of three minor features near 49.2 ppm in Figure 1.5(b) that weassociate with head to head structures. During propagation, the sulphide anion atthe end of the chain may occasionally attack the methine carbon site as well as themethylene carbon site in the monomer, and this remains when the polysulphoneis prepared.

We note that the heterotactic triads signal of Figure 1.5(c) has more than threecomponents, consistent with the mr and the rm heterotactic sequences beingdistinguishable; as the relative intensities of the four not quite resolved lines forthe atactic polymer of Figure 1.5(c) are roughly in the proportion of 1:2:3:2, andthe four heterotactic-centred sequences mmrm, mmrr, rrmm and rrmr would beexpected to have similar proportions (as Pr = P1n) = 0.5), one of these pentadsmust be sensitive to an extra chiral centre. Our most recent work in this area hasshown that tactic main chains may be obtained in a free radical reaction if the1-olefin bears a chiral centre of a particular type (K 6r S) at the site next to theolefin group: the carbon NMR spectrum then displays from each atom within orclose to the backbone widely spaced pairs of peaks, the relative intensity withineach pair being 6:4 or 7:3. This reflects within a residue a preferred relationship ofthe two chiral centres [45], the one initially present within the olefin and thesecond created by the addition reaction.

1.4 THE PARTICIPATION OF A CHARGE-TRANSFERCOMPLEX IN A FREE RADICAL POLYMERIZATIONREACTION

A long-standing issue in the formation of alternating copolymers, such as arefound when electron-rich and electron-deficient monomers polymerise by freeradical means, has been the question of the role of the charge-transfer complex inthe polymerisation mechanism. For poly(olefin sulphone) feeds, many experi-mental techniques have demonstrated that the complex is present, but is thecomplex incidental or is it the reacting species? One possibility is that each type ofradical may react only with the other type of monomer; a second is that thecharge-transfer adduct itself is the only reacting species [46]. In Scheme 5 belowthese two possibilities are shown respectively as the vertical (c + d) and thehorizontal (a) propagation reaction paths. The rate-determining step for poly-merisation is apparently the reaction of an electron-deficient radical, presumablya sulphonyl radical, with an electron-rich monomer, presumably either an olefin(d) or the olefin part of a charge-transfer complex (a), for substitution to the olefingroup enhances the rate. AU the reactions are written as reversible in Scheme 5:there is a wealth of experimental evidence in support of this, for example, theolefins are known to isomerise at temperatures above and below the ceilingtemperature for polymer formation, and the ESR spectrum of the radicals presentindicates that this may be both C-based and S-based.

P - S O 2 - C - C *

SO2 JcSo2

P-SO/ + C=C - = - P-SO2-C-C-SO*

e dC=C

P-SO2-C-C"

Scheme 5 The free radical formation of poly(but-2-ene sulphone) through charge-transfer complex reaction (horizontal route) or successive monomer addition (descendingroute)

If the precise alternation in the chain residues is the only criterion, there is noway of distinguishing between the two mechanisms. However, the stereochemis-try of the but-2-ene sulphone residues and their relationship to the cis or transnature of the olefin does provide a guide [43,46]. Broadly speaking, two methylshifts are encountered: at high temperatures, whichever olefin is used, there isa single shift at « 9 ppm, but at low temperatures, if the trans but not the cis olefin

Figure 1.6 13C NMR spectra at 101 MHz of the methyl groups of s/B three samples of poly(but-2-ene sulphone) recorded in DMSO-J6 at70 0C. The samples SCH/7, U27 and U23 were prepared at - 95 0C, - 63 0C and - 84 0C respectively, the last from the cis olefin and thefirst two from the trans olefin. Lowering the temperature has increased the intensity of the signal at 13 ppm from the meso residues obtainedfrom the trans olefin, but the signal from the polymer made from the cis olefin at an intermediate temperature shows a much greaterproportion of the racemic residues, with their methyl shift at 9 ppm [46]

is used, there is a new peak at 13ppm; see Figure 1.6 for three examples. Theassignment of the order of the methyl carbon shifts to meso or to racemicbut-2-ene residues is not straightforward; since a gamma-gauche effect from theoxygen atom of the sulphone group (9.4 ppm) may well be larger than thegamma-gauche effect from a methyl group (6.4 ppm), the shift distinction may beassociated with the conformations of the C—S bonds, rather than with that of theC—C bond as we first assumed [42]. We now make the assignment of the mesoand racemic structures on the basis of the similarity of the order of the shifts in thepolymers to models of known structure. The molecule alpha-2,3-bis(isopropyl-sulphonyl) butane has the structure shown in Figure 1.7(a), according to X-raymeasurements, making it the centrosymmetric meso form [46]. The central unitcorresponds exactly to a residue of a poly(but-2-ene sulphone) chain that isflanked by structures corresponding to a little over half the alkane component ofthe next residue. The carbon shift of the central methyls is at 13.7 ppm, comparedwith 10.0 ppm for the corresponding shift in the racemic molecule, shift differen-ces that are found in the polymers, too. (The IR spectra show similar correspon-dences [46]). The fact that at low temperatures the trans olefin converts topolymer with partial retention of the configuration of the two prochiral centres

Figure 1.7 (a) The model bis(isopropylsulphonyl) butane in the crystal [46], showingits centrosymmetry and meso characteristic of the central portion; (b) plots of meso residuecontent against temperature of preparation for the series of poly(but-2-ene sulphone)sprepared from cis and trans olefin, curves (i) and (ii) respectively. That there are twodistinct curves indicates that the charge-transfer complex is a significant reacting species.The solid symbols record the results from the spectra of Figure 1.6

T/C

on the olefin-CT complex and that the cis olefin converts similarly suggests thatthe reaction does proceed along path a of Scheme 5 at these low temperatures,when large proportions of the charge-transfer complex are present. At the highertemperatures the polymer and the monomer structures are not related, bothyielding mainly racemic residues, consistent with alkyl radicals being presentlong enough during the polymerisation for radical inversions to eliminate thememory of the initial structure. Chain microstructure therefore indicates that thecomplex is a reacting species at low temperatures. We cannot tell whether thecomplex exclusively reacts, and the sulphonyl radical partly dissociates (path b),or whether paths a and c are alternatives, a being becoming favoured as thetemperature is lowered, to some extent reflecting the greater stability of thecharge-transfer complex. The rise in meso content when cis olefin is the precursorprobably indicates that path c is used even at low temperatures, and that then theradical intermediate favours less a mode of reaction that yields the racemic type ofproduct.

1.5 THE POLYMERISATION OF DIENES

The manner in which dienes become entrained within polymer chains dependsupon a number of factors, such as the type of mechanism (free radical, ionic orcoordination), the nature of the diene itself, and whether other monomers areinvolved. If one double bond reacts, a chiral centre is formed and the polymersmay be tactic, if 1,4-addition (or 4,1-addition) takes place the main chainincorporates a double bond whose cis or trans nature may be important indetermining properties such as the glass transition temperature, and the reactionof a second double bond can cause crosslinks. The case of polychloroprene hasbeen described by Ebdon [47], where proton shifts are sufficient to detect head totail (2.35 ppm), head to head (2.5 ppm) and tail to tail (2.2 ppm) enchainments ofthis unsymmetrical monomer [47]. For poly(butadiene)s, sequence triads involv-ing three different types of residue—cis and trans 1,4-residues within the mainchain and 1,2-residues involving pendent vinyl groups—may be distinguishedeven with a 270 MHz spectrometer in the region of the spectrum between 127 and133 ppm, where are found the resonances of the 1,4-residues (see Table 1.1 andFigure 1.8). The assignments were obtained using a number of polymers ofdistinctly different but recognisable microstructure. When the spectrum is ob-tained under conditions that avoid NOE enhancement of signal intensity, andlong delays between pulses reduce systematic errors in signal proportions, fromthis region and that of the pendent vinyl groups (at 114 and 143 ppm) composi-tions accurate to better than 1% may be claimed [25]. In this study of poly-butadiene rubbers, when three different methods were compared, it was foundthat the microstructures as determined by the Raman and 13C NMR methods

Table 1.1 Triad sequences within the main chain olefinic region of thecarbon-13 NMR spectrum of poly(butadiene)s [25]. Reproduced from[25] with kind permission from Elsevier Science Ltd., The Boulevard,

Langford Lane, Kidiington OX5 IGB, UK

Carbon Atom Peak No. Triad assignment Shift (ppm)

- C = C * - I vtv 13L82 ctv, ttv 131.43 we 130.74 ctv, ttv 130.65 ccv, tcv 130.26 ctc,ctt 130.27 vcc, vet 130.18 ttc, ttt 130.1

—*C=C— 9 ctv, ttv 129.910 ccc, tec 129.711 cct, tct 129.512 ctv, ttv 129.313 vtc 128.514 vtt 128.415 vtc 128.216 vcc 128.117 vet 127.918 vcv 127.8

*Note: v = vinyl, c =* cis, t = trans.

were in good agreement but that the IR method was much less consistent [25], aspeaks were not very distinct and extinction coefficients were too variable.

We illustrate the reactions of dienes by our studies on furans as monomers infree radical copolymerisations with acrylonitrile (AN), work undertaken todevelop the polymer chemistry of materials that may be obtained from renewableresources. We have found that a variety of structures may be entrained withina polyacrylonitrile chain; to some extent their proportions depend upon thepresence and the nature of substituents at the position alpha to the furan ring[48-50]. Only furan, the least aromatic of the heterocycles, seems to behave inthis way. The five-membered furan ring remains intact. The differentiation ofstructures of types I and II was performed on the basis of the shifts of modelcompounds obtained by reacting furan and methylfuran with the 2-cyanopropylradicals from decomposing 2,2'-azobis(isobutyronitrile), AIBN. The carbonshifts of the polymer residues were consistent with attack at the alpha or C2

position of furan and at the C5 position of methylfuran by the acrylonitrileradical. The furan radical that forms then propagates in the manner of a dieneeither through the more remote alpha position or through the adjacent betaposition. A minor proportion of I residues from methylfuran in which thepolymer AN radical had attached to the C2 were also detected from theappearance of minor shifts at 130 ppm (see Figure 1.9) from the beta carbons,

Figure 1.8 13C NMR spectrum of an anionically prepared polybutadiene at 25 0C inCDCl3 at 60 MHz. The labels correspond to the peak numbers and triad sequences ofTable 1.1. In this study [25] extreme care was taken in obtaining quantitative information:avoidance of the nuclear overhauser enhancement was achieved by decoupling onlyduring the signal acquisition; pulse angle 90°, 40000 scans, 33 s pulse delay. Reproducedfrom [25] with kind permission from Elsevier Science Ltd., The Boulevard, LangfordLane, Kidlington OX5 IGB, UK

shifts that reflect the different arrangement in this residue of the methyl andnearest nitrile groups. The appearance at this place of the olefinic shifts is readilyrationalised in terms of a beta effect of 3.7 ppm and a gamma effect from the nitrilegroup of —5.5 ppm.

Other peaks were found in both proton and 13C spectra in the region below theshifts from the acrylonitrile residues, and other possible structures were sought,

i H in iv v vi

Scheme 6 The structures of five residues derived from furan in acrylonitrile (AN)copoiymers, and the methylfuran radical

Figure 1.9 13C NMR spectra of the low field region of (a) a dimethylfuran copolymer, (b)a methylfuran copolymer, and (c) a furan copolymer. Assignments of the nitrile carbon ofthe AN residues, of the olefinic carbons of the furan residues and of the bridgehead andother carbons next to an oxygen are indicated

but a certain proof of a third type of structure was more elusive. The characteristicfeature was a proton shift at « 3.9 ppm [49], a position appropriate to a protonon an ether carbon, and olefinic protons were thought to be lacking. We presenta relevant set of reactions in Scheme 7. It was eventually recognised [49] that theaddition of an excess of the furan monomer, which promoted II-AN-furansequences, had the effect of reducing the proportion of the unknown furanresidue, presumably by preventing the participation of the II structures ina second reaction (d) to give a structure of type III. Once ~ II-AN-AN' radicalswere reduced in proportion by this means, the signals from the II structuresbecame clearly enhanced in the spectrum, as route (a) was then taken. This

Scheme 7 Possible reactions of a II structure in a second manner during the acrylonitrilecopolymerisation [49]

revealed the origin of the previously obscure third structure. A proof of theentrainment of AN-furan Diels-Alder products was made by observation of theshifts of the residues formed by a direct copolymerisation involving an endoadduct of furan and a mixture of endo and exo adducts: the carbon and the protonspectra together indicated that both adducts can become entrained within anacrylonitrile chain [48] to yield a structure of type IV, with carbon shifts at80ppm from the bridgehead sites and corresponding proton shifts at about4.7 ppm.

A careful inspection of the region near 130 ppm in the spectrum of eachpolymer (Figure 1.9) reveals that each carbon of the I residues has two shifts,a feature that we attributed to the influence of the chirality of the nearest—CHCN— chiral centre. No feature that we could associate with the cis or transjunctions to the ring were identified, although for the I residues, if not the IIresidues, the structural variation seemed possible. Inspection of the spectra ata higher field strength found a further set of peaks whose intensities increased asthe furan content rose from « 5 to 25% of the residues. This was attributed toa small sequence effect.

In an effort to clarify the sequence fine structure, both of the various furanresidues and of the acrylonitrile residue signals un-field, we added Lewis acids inthe hope of causing alternation of the residues by enhancing the electrondeficiency of the acrylonitrile radical through a coordination to the nitrile group.When the polymerisation was performed in the presence of a mild Lewis acid such

as ZnCl2, it was found instead that, although the yields were enhanced by anorder of magnitude, the furan proportion was increased only a little, but thepattern of the predominant II structures became modified considerably [50]. Forthe 2-methylfuran systems, the shift of the 5-proton was diminished relative tothe shifts of the other furan protons. The search for their new position in thespectrum, to provide structural evidence for the effect of the Lewis acid upon thereaction mode, was performed with deuterium NMR spectroscopy, the methyl-furan monomer having been deuterated at the single alpha position. In reactionsleaving a furan ring from radicals of structure V at the end of chains, thedeuteriums were found to have transferred from the furan radical to the Lewisacid-activated monomer (creating D—CH2—CHCN ~ , shift at 1.5 ppm) and toacrylonitrile radicals (creating ~CH2—CHDCN, 2.2 ppm). This latter groupwas also identified at 14.3 ppm in the 13C NMR spectrum, where it wasparticularly prominent if an independent source of hydrogen atoms, in the formof a chain-transfer agent, had been added [48]. Despite the transfer reaction andthe disproportionation promoted by the Lewis acids, processes which would beexpected to lower molecular weights, yields of the free radical reaction weregreatly enhanced and gels were produced, presumably through a crosslinkingsecond reaction of II residues, and the proton NMR signals consequently becamebroader [50].

Isotopic enhancement may be also illustrated by Bevington et al.'s explorationof the use of the* 3C-enriched free radical initiators l,l'-azobis(phenylethane) andAIBN in preparing butadiene polymers [51] and the use of dimethyl 2,2'-azobis(isobutyrate) to initiate the polymerisations of styrene, acrylonitrile,methyl methacrylate and methyl acrylate [52]. The signals from the ends are thusrendered more intense, and become observable in a standard 13C NMR spec-trum, where they display information on the manner in which the initiatorradicals have attacked the first monomer to become incorporated at the start ofthe polymer chain: one can thus compare initial and mean tacticities. In a furtheruse of isotope enrichment, Moad and Willing found that selective13C enrichmentof one monomer together with carbon-13-proton correlation NMR spectros-copy allowed the separation of tacticity and sequence effects; they used thisapproach for studying copolymers of butyl methacrylate with methyl metha-crylate [53].

1.6 RING-OPENING-METATHESISPOLYMERISATIONS

Polymers formed by the ring-opening metathesis polymerisation (ROMP) reac-tion [54] exhibit a wide variety of microstructures which may be evaluated byspecctroscopic techniques. The first ROMP polymers were analysed by IRspectroscopy [55], but that can only determine the absolute stereochemistry of

The ROMP reaction of Scheme 8 is catalysed by metallacarbenes [54] thathave been formed from a wide variety of transition metal salts, often but notexclusively in the presence of an organometallic co-catalyst in systems similar tothe industrially important Ziegler-Natta catalysts. In addition, there are nowmany examples of metathesis of both cyclic and acyclic olefins using well-definedmetal carbene complexes [56]. In the former systems, which are considered here,the metallacarbene catalyst is formed from the various catalyst components andis very active, the concentration of active sites being extremely low but each sitehaving a very high turnover number [57]. As a result, observation of the workingcatalyst by any spectroscopic or other means is not possible. We view thepolymers, with their different microstructural features, as a "tape recording" ofevents at the catalyst site which may be "read" through the medium of 13C NMRspectroscopy. For highly strained monomers these events are the primary onesup to high conversion.

One may, by careful choice of monomer, study the potential of differentcatalysts to behave in a stereoselective or regioselective manner. Thus, witha symmetrical monomer such as norbornene [58], norbornadiene [59] or their5,6 [60] or 7-substituted derivatives [61,62] we have obtained polymers witha variety of cis main chain double bond contents and distributions. In a numberof the 7-substituted examples, fine structure on certain 13C NMR resonances isobserved which is attributable to tacticity effects. Conversely, one may use theunsymmetrical monomers such as 1-substituted derivatives [63] and delineatethe propensity of the different catalysts to regioselectivity, which manifests itselfas head-tail bias in the polymer.

the double bonds in the polmer, and provides no information on the sequences inwhich such microstructural variations might occur.

This limitation is largely overcome by 13C NMR spectroscopy, where sensitiv-ity to change in substitution and stereochemistry up to six carbon atoms remotefrom the particular carbon under observation is regularly seen [54], In theremaining part of this article we deal almost exclusively with polymers formedfrom the bicyclic olefins norbornene, norbornadiene and their derivatives, butwill also discuss some work with oxygen-containing analogues, thus providinga comprehensive range of different microstructural types. These monomers havea substantial ring strain, so they are good candidates for ROMP.

P * polymer chain

Scheme 8

In the case of these substituted derivatives, the polymers formed with mostcatalyst systems exhibit fine structure in the spectra due to each of the possiblemicrostructural variations, leading to very complex spectra. We have made veryextensive use of chain transfer to acyclic olefin to obtain lower molecular weights,and consequent line narrowing in the spectra of the polymers, to optimiseresolution. Also, certain of the catalysts at our disposal may behave in a verystereospecific and regiospecific manner, allowing one to pinpoint certain lines inmore complex spectra. These techniques, combined with the excellent resolvingpower and sensitivity of modern high field NMR instruments, have allowedcomplete and unambiguous assignment of most spectra.

1.6.1 STEREOSELECTIVITYINROMP

There are two basic types of stereoselectivity observed in the ROMP of cyclicolefins, both of which may be observed in the 13C NMR spectra of the polymers.The double bonds which form part of the main chain may be either cis or trans,and in the case of the prochiral monomers norbornene, norbornadiene, theirsymmetrically substituted derivatives and their chiral unsymmetrically sub-stituted derivatives the residues may be enchained in such a way as to yieldtactic or, more commonly, atactic polymers [54]. A representation of atacticpoly(norbornene) is shown in Scheme 9, where cis and trans double bonds areassociated with r or m dyad units respectively.

Scheme 9

Thus polymers with a given cis double bond content may be prepared with anappropriate catalyst, as is shown in Table 1.2. Resonances from the variousolefinic and cyclopentane ring carbon atoms are observed and fine structure dueto the effect of two or three neighbouring double bonds is resolved, Figure 1.10.One of the earliest observations to be made from these spectra was that therelative line intensities of the various cc, ct, tt and tc (etc.) resonances indicatedthat the distribution of cis and trans double bonds was non-random, and thatthere was an increasing tendency towards a blocky cis distribution as the cisdouble bond content of the polymer increased [58]. An explanation was sugges-ted, based upon chain propagation involving different metallacarbenes whichhad been distinguished in terms of the stereochemistry of the last-formed double

Table 1.2 Fraction of cis double bonds in ring-opened polymers of norbornene, norbor-nadiene and derivatives obtained with different catalysts

Catalyst

Monomer RuCl3 MoCl5/Bu4Sn OsCl3 WCl6/Me4Sn ReCl5 Ref.

0.05 - 0.50 0.55 1.00 [54]

0.00 - 0.15 0.55 0.95 [61]

0.10 - - 0.55 0.95 [60]

0.37 0.90 0.51 0.82 [59]

0.20 0.97 0.42 - [62]

1.00 - 0.36 0.73 1.00 [66]

0.10 - 0.39 - 1.00 [66]

0.00 0.31 0.10 0.75 1.00 [63]

0.05 0.11 0.30 0.70 1.00 [65]

bonds. In essence this theory emphasised the importance of steric effects at thecatalyst site. Blocks of cis double bonds are obtained by propagation througha species Pc (see Scheme 10) where the last-formed double bond is cis and wherethe next monomer unit reacts with the metallacarbene while the previously

Figure 1.10 * 3C NMR spectrum of poly(norbornene) with %60% cis, randomly distributed, main chain bonds

Scheme 10

formed cis double bond is still in the coordination sphere of the metal. The stericconstraint thus imposed aligns the incoming monomer unit in a cis orientation,leading to the formation of another cis double bond. The kinetically distinct Pt

species is believed to be too bulky sterically to be a chain carrier at all, and itrelaxes to a species P in which the last-formed double bond has left thecoordination sphere of the metal; the monomer has then the opportunity to reactin either a cis or a trans orientation, with the trans orientation preferred on stericgrounds.

This phenomenon is also observed in the case of the stereospecific metathesis ofacyclic olefins [68], where, in the pre-equilibrium stage of the reaction, cisproducts are often formed from cis substrates and trans from trans. Inspection ofTable 1.2 shows that the cis content of polymers formed from bidentate chelatingolefins is significantly higher than that observed with the mono-olefin analogue.The highly stereospecific and rather unreactive RuCl3 catalyst exhibits extremebehaviour, as it is highly trans-directing with norbornene, and incidentally withmany other mono-olefin derivatives, but highly cis directing when using endo-dicyclopentadiene as monomer [66]. It is significant that the catalytically activeresidual solution from RuCl3/endo-dicyclopentadiene polymerisation also pro-duces high cis polymers with norbornene derivatives, and that exo-dicyclopen-tadiene gives the "normal" high trans polymer. The link between steric crowdingof the catalyst site and cis stereospecificity is therefore well established, both byourselves [66] and by others [69].

1.6.2 DISTRIBUTION OF trans DOUBLE BONDS IN HIGHcis POLY(NORBORNENE)

The NMR spectra of both the cyclopentane ring and the olefinic carbon atoms inpoly(norbornene) are sensitive to the stereochemistry of the neighbouring doublebonds and, as seen above, this leads to cc/ct; tt/tc doublets for the cyclopentanering carbon atoms. There is, however, the possibility of quartet fine structure forboth cis and trans olefinic carbon resonances, owing to the inequivalence of thecarbon atoms in a given double bond [64], as in Scheme 11.

C H = C H

mt / c uc * crtCftc/c

Scheme 11In the spectrum of a poly(norbornene) of intermediate cis content, Figure 1.10,

this fine structure is well resolved for the cis resonance, but overlapp of the etc andthe ttt components occurs in the trans resonance. In high cis polymer twodifferent types of non-random trans double bond distribution have been ob-served. Figure 1.11 shows the spectra of two polymers, one prepared using ReCl5,Figure 1.1 l(a), and the other using OsCl3, Figure 1.1 l(b) in the presence ofbenzoquinone, another chelating ligand which imposes a high as directive effect[7O]. In these high cis polymers one would expect, statistically, that trans doublebonds would almost always be flanked by cis double bonds, leading to high tc/ttratios for the cyclopentane ring carbon atoms and a strong etc signal for theolefinic trans resonance. In fact, inspection of Figure l.ll(a) shows that thereverse is the case for the ReCl5-catalysed polymer; here the various ct and tt linesare of approximately equal intensity, and the centre component of the transolefinic resonance which arises from isolated trans, etc, or blocks of trans, ttt, hasbecome only a shoulder on the ttc line. This means that trans double bonds tendto occur in pairs in these predominantly cis chains. Mechanistically, this can beseen as a chain error repair process, where the aberrant formation of the first transdouble bond is corrected by the formation of a second before resumption of cisdouble bond formation. An analogous phenomenon has been observed in thelargely isotactic polymerisation of certain alpha-olefins [2], where 13C NMRspectroscopy has shown that the small proportions of syndiotactic (r) junctionsthat occur are found in pairs, as evidenced by the relatively intense rmmr andmmrr pentad signals. Here the catalyst site, which normally selects the sameprochiral face of the monomer in each cycle, occasionally reacts at the other face,leading to an aberrant r junction. Choice of the original prochiral face in the next

catalytic cycle results in the continuous formation of isotactic polymer: thismechanism is marked by the presence of pairs of syndiotactic (r) junctions.

Alternatively the catalyst, having chosen a different prochiral face, continues todo so. The result is the formation of a polymer containing isotactic blocks joinedby single syndiotactic (r) junctions, i.e. the initial error is propagated, and is visiblein the 13C NMR spectrum as the occurrence of mrmm and mmrm pentads. Hereagain an analogous situation exists in some ROMP's of norbornene and deriva-tives, and is seen in the polymerisation of norbornene using the benzoquinone-modified OsCl3 catalyst, Figure 1.1 l(b). In this case, and in contrast to the ReCl5

polymer of Figure 1.1 l(a), the various tt lines are three to four times as intense asthe tc lines, with a concomitant increase in the intensity of what must be the tttcomponent over the ttc and ctt lines in the olefinic trans resonance. This indicatesthat the small percentage of trans double bonds occur in tn blocks (n > 2). Thesame phenomenon is observed in polymers formed from 1-methylnorbornene[63], Figure 1.12. At the cis junction in these high cis polymers, monomeraddition occurs in a head-tail manner (see below) but the small proportion oftrans junctions shows no bias. However, it may be clearly seen that in the polymerformed using the WCl6/Me4Sn catalyst, Figure 1.12(a), trans double bonds tendto occur in pairs, as evidenced by the low intensity ttt/ctc signals, whereas in thepolymers formed from the OsCl3 catalyst, Figure 1.12(b), there is a tendency toform blocks.

If there is propagation through metallacarbenes of octahedral symmetry witha vacant alternating ligand position such as described above, these species may bechiral, with the formation of tactic polymer. Furthermore, cis double bondformation will be associated with syndiotactic junctions and trans double bondswith isotactic junctions, as in Scheme 12. If, however, the catalyst site is achiral, or

Scheme 12

chiral but undergoing racemisation faster that propagation, then atactic polymerwill result, and r or m dyads may be associated with either cis or trans doublebond [67]. Initially (see below) with poly(norbornene) no fine structure wasobserved, which could be attributed to this tacticity effect, but it was realised thatpolymerisation using one enantiomeric form of a chiral norbornene derivative(Scheme 13) would translate the tacticity effect into a bias toward head-head(HH) and tail-tail (TT) addition for syndiotactic polymers, and head-tail (HT)addition for isotactic polymers [65].

fa)

ppm

Figure 1.11 13C NMR spectra of high cis poly(norbornene): (a) 90% cis prepared using ReCl5 catalyst, and (b) 93% cis prepared usinga modified OsCl3 catalyst

(b)

ppm

( a ) ( b )

Figure 1.12 Olefinic region of the 13C NMR spectrum of poly(l-methylnorboraene)formed with (a) the WCi6/Me4Sn catalyst and (b) the OsCl3 catalyst: (a) Reproduced bypermission of Huthig & Wepf Verlag from [63]

Scheme 13

ROMP

This analysis was made possible because the chemical shifts of the variousolefinic carbon double bonds in these unsymmetrically substituted norbornenederivatives are very sensitive to whether they are in an HH, TT or HT/TH unit, ascan be seen for the case of poly(l-methylnorbornene) [63] in Figure 1.12. It wastherefore possible to examine a range of metathesis catalysts for their ability toproduce tactic polymers. In fact, a range of tacticities was observed, with extremesin behaviour being represented by the ReCl5 catalyst, which produced an all-dssyndiotactic polymer [65] and the W(mesityl) (CO)3 catalyst, which produceda high trans isotactic polymer [71].

1.6.3 REGIOSELECTIVITY IN ROMP

The above method of tacticity determination depends upon there being noregioselectivity, i.e. no bias towards HT or HH/TT addition in the polymerisa-tion of the racemate, and in fact this is the case with 5-substituted norbornenederivatives.

Placement of a methyl substituent on the double bond results in completeregioselectivity [72], but much more interesting is the case where an alkyl groupis in the bridgehead position, as in poly(l-alkylnorbornene) [63, 73]. Thesemonomers exhibit a strong catalyst- and substitutent-dependent selectivity,which again may be observed in the 13C NMR spectra of the polymer, Fig-ure 1.13. For example, high trans polymer may be prepared using either RuCl3 orOsCl3 as catalyst, but whereas the RuCl3 catalyst is non-regioselective the OsCl3

catalyst exhibits a strong bias towards the HT addition of monomer (Fig-ure 1.12(a)). This effect may be explained in terms of different polarities of therespective [ M t ] - = C + C ^ pi-bonds as they engage the monomer double bond,Scheme 8, in a [2 + 2] cycloaddition reaction which is the initial step of theROMP reaction [74,75]. As expected, steric effects are also important, and the morebulky ethyl substituent induces a HT bias in the polymer formed using the RuCl3

catalyst [73] and enhances the HT bias in the OsCl3 case [70][73], Figure 1.13(b).In this context a particularly interesting and unique example of the alternating

copolymerisation of enantiomers was demonstrated in the polymerisation of 1-methylnorbornene with the ReCl5 catalyst [63,75]. The analysis relied on the factthat the hydrogenated forms of these polymers (but see more recent work, p. 52),unlike their unsaturated precursors, exhibited fine structure due to the presenceof ring dyad units of different tacticities.

This catalyst gave a poly(l-methylnorbornene) which on 13C NMR analysis,Figure 1.14, was shown to be all-cis and all HT, in contrast to the OsCl3 catalyst,which produced an all-trans and all HT polymer, Figure 1.13. Both polymerswere hydrogenated, and it was found that whereas in the OsCl3 case one lineexhibited doublet fine structure, which must be due to the m/r effects, the ReCl5

polymer gave only the down-field line, indicating that the polymer was tactic. The

Figure 1.13 Olefinic region from the 13C NMR spectrum of all-trans polymer formed from various 1-alkylnorbornenes with differentcatalyst systems, (a) Reproduced by permission of the Society of Chemical Industry, London, from Br. Polym. J., 1984,16,2; (b) Reproducedby permission of the Society of Chemical Industry, London, from [73]

Figure 1.14 Olefinic region of the 13C NMR spectrum of poly(l-methylnorbornene)formed using a ReCl5 catalyst; the polymer is all HT all-cis and syndiotactic (compareFigure 1.12 (a) andd (b)). Reproduced by permission of the Society of Chemical Industry,London, from Br. Polym. J., 1984,16, 2

fact that it was syndiotactic was shown by using the OsCl3 catalyst to polymeriseoptically resolved monomer, which must result in an isotactic all-trans polymer.The 13C NMR spectrum of the hydrogenated product gave only the up-field lineof the original m/r pair, thereby proving the syndiotactic nature of the poly(l-methylnorbornene) prepared using the ReCl5 catalyst. Such a polymer can onlyform at a catalyst site which alternates in chirality in each catalytic cycle, and thusis required to choose alternate enantiomeric forms of the monomer in successivecatalytic cycles. An alternating copolymer of enantiomers was thereby formed. Itwas therefore highly significant that, in this context, we were unable to formring-opened polymer from optically resolved monomers with the ReCl5 catalyst.

Here again we may draw parallels with Ziegler-Natta polymerisations,Scheme 14. In the syndiotactic polymerisation of propylene [76] the catalyst is

ppm

Scheme 14

selecting a different prochiral face of a monomer (which exists in only onemolecular form). In the case of the 1-methylnorbornene monomer, Scheme 15,reaction is restricted to one face (exo) of the molecule [61], but two chiral formsare available. In each case the polymer is H-T biased, and the catalyst sitealternates in chirality in each catalytic cycle.

Scheme 15

Scheme 16

13C NMR studies of the ROMP of certain 7-substituted norbornadienederivatives provided a remarkable example of a substituent-dependent re-gioselectivity, Scheme 16. 7-methylnorbornadiene [62] and 7-f-butoxynorbor-nadiene [77] were polymerised using a range of catalysts; whereas the 7-Mederivative behaved in the expected manner with almost exclusive attack at theanti face of the molecule (13C NMR spectra of the polymers are discussed below),catalyst attack occurred with almost equal facility at both syn and anti faces in the7-r-butoxy derivative.

In this reaction it is envisaged that the lone pair of electrons on the 7-oxy sub-stituent interacts with the electrons of the syn double bond, and the normal [2 + 2]cycloaddition, which occurs on anti attack, becomes a facile pseudo [3 + 2]cycloaddition, overcoming the apparent steric crowding at the syn face [62].

1.6.4 DIRECT OBSERVATION OF TACTICITY

13C NMR spectra of polymers formed when there is unsymmetric substitution inthe norbornene monomer, as shown above, have been very useful in demonstrat-ing the regioselectivity of various catalyst systems. In addition, these substituentsare responsible for a decrease in the conformational mobility of the polymerchain, and consequently fine structure which may be due to tacticity is resolved incertain cases. The situation is complicated, however, by the possibility that suchsplittings may be due to longer range HT effects when HT, HH and TT sequencesare present in the polymer chain. Positioning the substituent at C7 retains thechain stiffening effect without splittings due to a regio effect; the observed finestructure may then be attributed to tacticity effects, especially in high cis or hightrans polymers where remote c and t effects do not interfere.

These 7-substituted derivatives are also important because much of the abovemechanistic interpretation depends upon the assumption that attack on thenorbornene molecule occurs at the exo face. The result of ring-opening poly-merisation of mixtures of syn- and anft'-7-methylnorbornene [61] shows that thisassumption is valid. Thus, only poly(«nr/-7-methylnorbornene) was obtainedfrom the polymerisation of syn/anti mixtures, although a small proportion of synisomer was incorporated in some cases. With particularly active catalysts the synisomer could be homopolymerised. More recently, and in relation to the re-gioselectivity studies discussed above, 7-methylnorbornadiene was prepared andpolymerised [62].

The importance of these polymers (for NMR analysis) lies in the excellentresolution of the 13C NMR spectra which may be achieved and the fact that ringtacticity may be observed directly in addition to cis/trans ratios and distribution.For example, the spectrum of the high trans polymer of anft'-7-methylnorbornene,Figure 1.15(b), which is atactic, showing sensitivity to m/r dyads, may becompared with its tactic high cis analogue, Figure 1.15(a). The syndiotacticnature of this latter polymer is inferred from the known behaviour of the ReCl5

catalyst discussed earlier. Other catalyst systems produce a variety of microstruc-

(a)

ppm

Figure 1.15 * 3C NMR spectra of poly(anft'-7-methylnorbornene): (a) syndiotactic all-cispolymer prepared using the ReCl5 catalyst; (b) atactic all-trans polymer prepared using theRuCl5 catalyst. Reproduced by kind permission of Elsevier Science Publishers from [61]

ppm

(b)

Figure 1.16 13C NMR spectra of poly(anfi-7-methylnorbornene): (a) an intermediatecis-tactic polymer prepared using the W(mesit) (CO)3/EtAlCI2 catalyst system, and (b) anatactic polymer of similar cis content prepared using the WCl6/Bu4Sn catalyst system.Reproduced by kind permission of Elsevier Science Publishers from [61]

(a)

ppm

(b)

ppm

ture types, and it is interesting that one can subtly change the behaviour of, forexample, a W-based catalyst by changing the oxidation state and ligation. TheW(mesityl) (CO)3 complex and the WVI hexachloride catalyst both producepolymers of intermediate and similar cis double bond content, Figure 1.16(a) and(b) respectively, but in the former case cis double bonds are associated solely withr dyads and trans with m, whereas in the latter case cis or trans double bonds maybe associated with m or r dyads [61].

In keeping with the general principle that polymerisation of monomers thathave a pair of double bonds capable of chelation at the catalyst site leads to theformation of high cis polymer [66], polymers formed from 7-methylnorbor-nadiene were generally high cis. Resolution of the various microstructuralfeatures is also observed in the* 3C spectra of these polymers, but paradoxically itis in the C7, tt line, Figure 1.17 (which shows no fine structure in the 7-methylnorbornene case), which is clearly resolved here; exactly the oppositesituation holds for the C7, cc line. One can therefore estimate cis content,blockiness and tacticity of the various double bond dyads from this resonancealone, which may be checked for consistency by reference to the fine structure ofother resonances in the spectrum.

Figure 1.17 The C7 resonance in the 13C NMR spectrum of poly(7-methylnorbor-nadiene) prepared using the WCl6/Me4Sn catalyst system. Reproduced by permission ofHuthig & Wepf Verlag from [62]

ppm

(a)

Figure 1.18 125 MHz 13C NMR spectrum of (a) poly(l-methylnorbornene), all cis, all HT, atactic, prepared using a tungsten carbenecomplex, (b) the same polymer prepared using the ReCl5 catalyst

An important consequence of the foregoing discussion is that it is impossible topredict which resonance will be split by any of the possible microstructuralfeatures, and one must therefore be careful not to assume that a polymer is, forexample, tactic simply because no fine structure is resolved. Also, spectra ofpolymers taken on modern high field instruments (125 MHz for 13C) may showup fine structure not resolved on lower field instruments. A most appositeexample of this was observed recently in the * 3C NMR spectroscopy of polymersformed from 1-methylnorbornene using a tungsten alkylidene complex [78].A spectrum was taken initially at 62.5 MHz and fine structure was not observed.The polymer was high cis, all HT, assumed to be syndiotactic and thoughtinitially to be another example of the alternating copolymerisation of enan-tiomers described in detail above. However, on obtaining the spectrum at highfield (125 MHz, Figure 1.18(a), each line exhibited considerable fine structure,showing that the polymer was in fact only partially syndiotactic [79]. In contrast,it was gratifying to observe that the alternating copolymer of enantiomers formedfrom this monomer using the ReCl2 catalyst, Figure 1.14, when re-examined at125 MHz), Figure 1.18(b), had a spectrum almost devoid of fine structure, therebydemonstrating its tactic nature and allowing the assignment of some of the linesin the more complex spectrum of the atactic polymer.

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1977,10, 765.[43] R.H. Cole, P.W. Winsor, A.H. Fawcett and S. Fee, Macromolecules, 1987, 20,157.[44] N. Spasky and P. Sigwalt, Bull. Soc. Chim. Fr., 1967,4617.[45] A.H. Fawcett and R.K. Malcolm, Polym. Int., 1994,35,41.[46] S.A. Chambers, A.H. Fawcett, J.F. Malone and S. Fee, Macromolecules, 1990, 23,

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2 C O N F O R M A T I O N I T H ECONNECTION BETWEEN THENMR SPECTRA AND THEMICROSTRUCTURES OFPOLYMERSA. E. TONELLIFiber + Polymer Science Program, College of Textiles, North Carolina StateUniversity, PO Box 8301, Raleigh, NC 27695-8301, USA

2.1 INTRODUCTION

The resonance or Larmor frequency of a spin-1/2 nucleus is highly sensitive to thelocal molecular environment in which it resides. When placed in a strong, staticmagnetic field H0 of several tesla, the cloud of electrons about the nucleusproduces orbital currents resulting in the creation of small local magnetic fields,which are proportional to H0, but are opposite in direction. These local inducedmagnetic fields effectively screen or shield the nucleus from H0 and result in thenucleus experiencing a net local magnetic field Hloc = H0 (1 — a), where a is thescreening constant, a is highly sensitive to chemical structure, i.e., the numbersand types of atoms and groups of atoms attached to or near the observed nucleus.It is the dependence of a upon molecular structure that lies at the heart of NMR'sutility as a probe of molecular structure.

Any structural feature that alters the electronic environment around a nucleuswill affect its screening constant o and lead to an alteration in its resonancefrequency or chemical shift 8. Consequently, to predict the chemical shift of,say, a 13C nucleus in a particular molecular environment, the electronic wavefunction of the molecular system in the presence of the strong applied fieldH0 must be known. For this reason it has been extremely difficult to make a prioripredictions of the resonance frequencies or chemical shifts of spin-1/2 nuclei[1-4]. If, for example, we wish to calculate the relative chemical shifts of the13C nuclei in methane and methyl fluoride, we must be able to determineaccurately the electronic wave functions of both molecules in the presence ofHo;Polymer Spectroscopy. Edited by Allan H. Fawcett© 1996 John Wiley & Sons Ltd

To date it has not been possible to make accurate predictions of the chemicalshifts observed for spin-1/2 nuclei, even when applying the most sophisticated abinitio quantum mechanical methods. Instead, the empirically observed effects ofsubstituents and local conformation have been used to correlate chemical shifts(usually 13C) with the microstructures of molecules, including polymers [5].

2.2 SUBSTITUENT EFFECTS ON 13CCHEMICAL SHIFTS

Substituent effect rules useful in predicting the 13C chemical shifts observed in the13C NMR spectra of paraffinic hydrocarbons have been derived [6-9] . 13Cchemical shifts are ordered in terms of the effects produced by substituentsattached to the observed carbon at the a, /?, and y positions. Some of the data usedto establish these rules are reproduced in Tables 2.1-2.3, where it is apparent thateach carbon substituent added a and/or j? to the observed carbon C° deshields itby ^ 9 ppm. On the other hand, each carbon y-substituent results in shielding of% 2 ppm of the observed carbon. Using these substituent rules makes it possibleto assign the 13C NMR spectra of paraffinic hydrocarbons, including their highlybranched members.

Table 2.1 a-substituent effect on ^13C [10]

<Fcfrom TMS, a-effect,

ppm ppm(a) 0CH3-^H " 2 1

(b) 0CH3-I-01CH3 5.9 8.0

/ C H 30CH I

(C) *[ 16.1 10.2

/CH3

°CH-f-aCH3

(d) X a CH 3 25.2 9.1

/ C H 3

° c 4; c H 3

(e) XT01CHs 2 7 9 2 7

>CH3

Table 2.2 0-substituent effect on S* 3C [ 10]

<513Cfrom TMS,

ppm^-effect,

ppm

5.9

15.6

24.3

31.5

9.7

8.7

7.2

(a)

(b)

(C)

(d)

Table 2.3 y-substituent effect on <5*3C [10]

<513Cfrom TMS,

ppmy-effect,

ppm

15.6

13.2

11.5

8.7

25.0

22.6

20.7

18.8

-2 .4

-1 .7

-2 .8

-2 .4

-1 .9

-1 .9

(a)

(b)

(C)

(d)

(e)

(0

(g)

(h)

Figure 2.1 Possible regiosequences of monomer units in PP

Table 2.4 Value OfS13C observed in thespeatra of H - T [13] and H-H: T - T [14]PPs

<513Cvs.TMS,flppm

Carbon H-T b H -H c T-Tc

CH 28^5 37X)CH 2 46.0 - 31.3CH 3 20.5 15.0

"All S13C values are averaged over the differentstereosequences [14].''Schilling and Tonelli [ H ] .cM611eretal. [12].

We may understand why the 13C nuclei in head-to-tail (H-T) polypropylene(PP) (see Figure 2.1) resonate in the order CH2, CH, CH3 from low to high ISeId(see Table 2.4) in terms of their a-, /?-, and y-substituent effects. Methine carbonshave two additional a- (4- 18ppm) and two additional y-substituents (—4ppm)compared with methyl carbons and should resonate 18 — 4=14 ppm downfield.Methylene carbons have two additional p- ( + 18ppm), one fewer a- (-9ppm),and two fewer y-substituents (+ 4 ppm) compared with the methine carbons, andshould resonate 18-9 + 4 = 13 ppm further downfield.

Suppose that PP possesses head-to-head (H-H) and tail-to-tail (T-T) units inaddition to the predominant H-T enchainment of monomer units. As seen inFigure 2.1, the H-H methine carbons have an additional /?- ( + 9 ppm) and twofewer y-substituents (+ 4 ppm) than H-T methine carbons, and should resonate9-1-4=13 ppm downfield from their H-T counterparts. T-T methylene carbonshave one fewer y8-( — 9 ppm) and two more y-substituents (—4 ppm) than the H-Tmethylene carbons, and should move — 9—4 = —13 ppm upfield from the H-Tmethylene resonances. H-H methyls should resonance - 2 ppm upfield from theH-T methyls, because they have a single additional y-substituent. Note in

H - T

H-H:T-T

ppm vs. TMS

Figure 2.2 25MHz 13CNMR spectra of (a) isotactic, (b) atactic, and (c) syndiotacticPP [13]

Table 2.4 that all these expectations are borne out in the 13C NMR spectra ofH-T PP [11] and H-HiT-T PP [12], and are consistent with the a-, j?-, andy-substituent effects on 13C chemical shifts derived from paraffins.

However, it is clear from the 13C NMR spectra of three PP samples presentedin Figure 2.2 [13] that the multiple resonances appearing in the spectrum ofatactic-PP(b), which are well known to be produced by different stereosequences[11], cannot be explained by the usual a-, /?-, and y-substituent effects. Eachmethyl carbon in PP has one a-, two /?-, and two y-substituents, each methinecarbon has two a-, two /?-, and four y-substituents, and each methylene carbonhas two a-, four /?- and two y-substituents independent of stereosequence. Somefactor other than numbers and types of a-, /J-, and y-substituents, and whichdepends on PP stereosequence, must be responsible for the multiplicity of

SYNDIOTACTIC

ATACTIC

ISOTACTIC

resonances observed in the atactic PP spectrum. As we shall shortly see, thatother factor is the stereosequence-dependent local conformation of the PP chain[11,13,14].

23 y-GA UCHE EFFECT METHOD OF PREDICTINGNMR CHEMICAL SHIFTS

We have mentioned that y-substituents in paraffinic hydrocarbons shield carbonnuclei relative to unsubstituted carbons. In Figure 2.3 it is apparent that theobserved carbon C° and its y-substituent CY can alter their mutual arrangement(distance and orientation) via rotation about the central of the three bonds whichseparate them. Note that the distance between C° and Cy (do_y) is reduced from4 to 3 A on changing their arrangement from trans to gauche.

Grant and Cheney [15] first suggested a conformational origin for they-substituent effect on S* 3C. Polarization of the C°-H and C7-H bonds as a resultof their compression by proton-proton (o-y) repulsion was suggested as thesource of y-gauche shielding. More recently, Li and Chesnut [16] have suggestedthat the shielding y-effects correlate with attractive van der Waals forces and notrepulsive steric interactions, though they still suggest that the gauche arrange-ment of the observed carbon and its y-substituent is required for shielding.Seidman and Machiel [17] concluded, based on semiempirical and ab initoquantum mechanical calculations, that the y-substituent effect is conformational

Figure 2.3 Newman projctions of an n-alkane chain in the (a) trans (<£ = 0°) and gauche(<t> = 120°) conformations

in origin, but is not exclusively attributable to the proximity of the interacting C°and (7 groups. Most recently, Barfield and Yamamura [4] concluded thatnuclear shielding of the methyl carbons in n-butane is dominated by changes inthe paramagnetic contributions for the C1—C2 and C1—H bonds, rather thanthe steric compression of C1—H bonds produced by the crowding of terminalmethyl groups in the gauche conformation.

Though its fundamental origins remain uncertain, the y-substituent effect on(513C values has a conformational sensitivity and, as we will shortly demonstrate,is potentially useful in characterizing both the conformations and the microstruc-tures of polymers.

For a carbon nucleus to be shielded by a y-substituent we have suggested thatthey must be in a gauche arrangement (see Figure 2.3). This suggestion issupported by comparing the <513C values observed for the methyl carbons inn-alkanes. The methyl carbons in n-butane and higher n-alkanes have a singley-substituent, whereas the methyl carbons in n-propane have no y-substituents,but the same number and kinds of a- and jS-substituents as the higher n-alkanes.In their crystals the n-alkanes adopt the extended, all-trans conformation, whereboth methyl carbons are trans to their y-substituents. If the y-substituents aretrans to the methyl carbons in the higher solid n-alkanes, then we would expect(513CH3 (solid CnH2n+2, n ̂ 4) = (513CH3 (liquid n-propane). VanderHart [18]has observed the methyl carbons in the solid n-alkanes with n — 19,20,23, or 32 toresonate between 15 and 16ppm (relative to TMS), while the methyl carbon inliquid n-propane resonates at 15.6ppm. [19]

On the other hand, in the liquid state, the methyl carbons in the highern-alkanes (n ̂ 4) resonate upfield at 13.2-14.1 ppm. [19] Of course in the liquidstate the C—C bonds in n-alkanes possess a significant gauche content, and thisresults in the shielding of <513CH3 for n-butane and the higher n-alkanes com-pared to that observed for the methyl carbons in n-propane or the higher solidn-alkanes in the all-trans conformation.

If we know how much gauche character Pg is possessed by the central bondbetween C° and X y [ C ° — C ^ - C - X 7 ] , then we can estimate the shieldingproduced by Xy, yc x, when in a gauche arrangement with C°. This procedure isillustrated in Figure 2.4, where the gauche shielding effects of the y-substituents C,OH, and Cl are derived. As an example, when the shielding produced at themethyl carbon in n-butane by the other methyl group (its y-substituent), i.e.,A(513CH3= <513CH3 (n-butane)-(513CH3 (n-propane)= 1 3 . 2 - 1 5 . 6 = - 2 . 4ppm, is divided by the gauche character of the intervening bond, P9 = 0.46:yc,c = A(513CH3/P^= -2.4/0.46= -5 .2 ppm.

When this procedure is applied to n-butane, 1-propanol, and 1-chloro-propane, the following y-gauche shielding effects are derived: yc c = — 5.2 ppm,7C,OH= —7.2 ppm, and yCtC1= —6.8 ppm. We now see that the shielding ata carbon nucleus produced by a y-substituent in a gauche arrangement can becomparable in magnitude ( - 5 to - 7 ppm) to the deshielding (+ 9 ppm) caused

CH3 -CH2 -CH2 -CHj

% gauche = 46

Xc-c "î »-5.2ppm

CH3-CH2-CH2-OH7

% gauche = 74

t - o = ~-M= -?-2 ppm

CH 3 -CH 2 -CH 2 -C* 7

% gauche s 60.0

y c - a = ^ ^ - 6 . 8 ppm

Figure 2.4 Derivation of the y-gauche shielding produced by the y-substituents C, OH,and Cl (see text)

by the more proximal a and /? substituents. More important, however, is theconformational dependence of the y-substituent effect on 13CNMR chemicalshifts. Any variation in the microstructure of a molecule which affects its local con-formation can be expected to be reflected in its S13C values via the y-gauche effect.

Let us complete our discussion of the conformational connection between themicrostructures and NMR spectra of polymers, which is provided by theconformationally sensitive y-gauche effect, by considering the nonequivalentS13C values for the isopropyl methyl carbons in several branched alkanes [8,20,21] as presented in Table 2.5. Even though the isopropyl methyl carbons in eachalkane have the same a-, /?-, and y-substituents, we note in column 2 that theobserved nonequivalence progressively decreases as the number of carbonsseparating the terminal isopropyl group from the asymmetric center is increased.This behavior can be understood [22] if we focus on the source of thenonequivalent <513C values observed for the isopropyl methyl carbons in 2,4-dimethylhexane (2,4-DMH).

In Figure 2.5 we have illustrated the possible staggered conformations aboutthe C 2 -C 3 backbone bond in 2,4-DMH, since these determine whether or not theisopropyl methyl carbons Csc, Cbb are y-gauche to the asymmetric carbon C4.From the probabilities of finding bond C2-C3 in the trans (t), gauche + (g 4-), and

Table 2.5 Nonequivalent 13C NMR chemical shifts for the isopropyl methylcarbons in branched alkanes

A<5, ppm

Alkane Obsd.0 Calcd.

C CI I

C—C—C—C—C—C 1.0 (1,9,1.1,0.9)* 1.6,1.1,0.9C CI I

C CI I

C—C—C—C—C—C—C—C 0.1 0.04C CI I

c — c — c — c — c — c — c — c — c o.o o.o" Observed between ambient temperature and 48 0C. (Kroschwitz et al. [20], Lindeman and Adams [8];

Carman et al. [21].•Observed at -120, 25, and 90 0C (Tonelli et al. [22].

Figure. 2.5 (a) 2,4-DMH in the all-trans conformation; (b) Newman projections illustra-ting rotational states about the C2-C3 backbone bond of 2,4-DMH [22]

gauche — (g - ) rotational states (Pn Pg+,Pg_), we obtain Pt + P9+, P9 + + P9 _ asthe probabilities for gauche arrangements between Csc and Cbb, respectively, andtheir y-substituent C4. Bond rotation probabilities are obtained from the con-formational model developed by Mark [23] for ethylene-propylene copolymers:

Pt = 0.38, Pg+ = 0.0 and Pg_ = 0.61. Thus, C4 is y-gauche to Csc with probability0.39 and to Cbb with probability 0.62. We expect the nonequivalence between Csc

and Cbb to be AS13C = (0.39 -0.62) x y c c = - 0.23( - 5.2 ppm) =1.1 ppm, wherewe have adopted the value yCtC = — 5.2 ppm derived from n-butane.

The observed nonequivalence (1.0-1.1 ppm) is in close agreement with thevalue expected from the y-gauche conformational calculation. The temperaturedependence of the observed magnetic nonequivalence is also successfully repro-duced by the y-gauche effect calculations, leaving little doubt that its origin is theconformationally sensitive y-gauche effect.

From the Newman projections in Figure 2.5 it might be expected that the t andg — conformations would be equally populated. However, it is well known [24]that rotational state probabilities for the backbone bonds in linear chainmolecules depend on the conformations, or rotational states, of neighboringbonds. The asymmetric center at C4 generates intramolecular interactions whichdepend simultaneously on (f> and neighboring bond rotations (see Figure 2.5(a)),which render Px^ Pg_. The values of Pt and P9_ approach each other as theasymmetric center is further removed from the terminal isopropyl group, leadingto a reduction in the expected nonequivalence of the isopropyl methyl carbons.This expectation is borne out in Table 2.5, where it is both observed and predictedthat the magnetic nonequialence of isopropyl methyl carbons vanishes once theyare separated by more than four carbons from the asymmetric center.

It is apparent from this example that the microstructural sensitivity of 13CNMR chemical shifts can have a conformational origin. <513C depends on thelocal magnetic field, which is influenced by the local conformation in the vicinityof the resonating carbon nucleus. The local conformation is determined by theneighboring microstructure. Hence, the microstructural sensitivity of1 3C NMRhas its basis in the dependence of the local conformation on microstructure

microstructure -> conformation -* Hloc -+(513C

The shielding of 13C nuclei by y-substituents in a gauche arrangement (y-gauche effect) enables us to both complete and simplify the conformationalconnection between the microstructures and NMR spectra of polymers.

y-gauche effect c l 3 - ,

microstructure • <r J C

2.4. APPLICATIONSOF y - GA UCHE EFFECTANALYSIS OF POLYMER MICROSTRUCTURES

2.4.1 POLYPROPYLENE(PP)

We are now in a position to understand the stereosequence sensitivity of the 613Cvalues observed [11] for atactic PP (see Figure 2.2(b)). When the methyl carbon

ppm vs. TMS

Figure 2.6 (a) 13C NMR spectrum at 90.52 MHz of the methyl carbon region in atacticPP in 20% w/v n-heptane solution at 67 0C. (b) Simulated spectrum obtained fromcalculated chemical shifts, as represented by the line spectrum below, assuming Lorentzianpeaks <0.1 ppm in width at half height [13]

region of this spectrum is expanded [13] we see in Figure 2.6(a) that over 20resonances are observed. Because there are 10 and 36 distinct pentad and heptadstereosequences [25], the 13CNMR spectrum of atactic PP shows sensitivity toheptad stereosequences in the methyl region. An atactic PP heptad is illustratedin Figure 2.7 along with Newman projections detailing the y-gauche interactionsinvolving the methyl group. It is clear that in the t and g~ backbone conforma-tions the methyl group is gauche to its y-substituents, the backbone methinecarbons (a). To predict the 13C chemical shifts expected for the methyl carbons inatactic PP we simply have to calculate the trans/gauche probabilities for thesebackbone bonds in each of the 36 heptad stereosequences. When this is carried

Figure 2.7 (a) Conformations of a four carbon fragment of a PP chain; (b) heptad of PP;observed methyl is marked by asterisk

out with the Suter-Flory [26] RIS (rotational isomeric state) model for PP, andthe resultant probabilities of finding CH3 in a gauche arrangement with itsy-substituents Ca are multiplied by the shielding produced by this arrangement(yCH3Ca= — 5ppm), we obtain [13] the predicted methyl 13C chemical shiftspresented in the form of a stick spectrum at the bottom of Figure 2.6(b).

Because the y-gauche effect method of calculating 13C chemical shifts onlyleads to the prediction of stereosequence-dependent relative chemical shifts, weare free in the comparison with observed spectra to translate the calculated shiftsto obtain the best agreement with the observed (513Cs. This has been done inFigure 2.6, where the agreement between the observed and calculated methly<513C values has been used to make the stereosequence assignments indicatedthere. The y-gauche effect method of assigning resonances in the methyl region ofthe 13C NMR spectrum of atactic PP to heptad stereosequences has beenachieved without recourse to the study of PP model compounds or stereoregularPP's (see Figure 2.2(a) and (c)) and without assuming a particular statisticalmodel to describe the frequencies or populations of stereosequences producedduring polymerization.

By achieving agreement between the observed 13C chemical shifts andthose predicted by the y-gauche effect method, we have not only determinedthe microstructure (stereosequence) of this polymer, but in addition we have

stringently tested its conformational characteristics as embodied in the RISmodel. Clearly then, it is possible to use 13C NMR spectroscopy to test or derivethe conformational characteristics of vinyl polymers by comparison of observed13C NMR spectra with the 513Cs calculated via the y-gauche effect method. Thisapproach has been pursued with success to test the local conformational charac-teristics of several vinyl polymers [13, 27, 28] and provides the basis for thediscussion presented in the subsequent chapter of this volume.

Having established the assignment of resonances observed in the methyl regionof the 13C NMR spectrum of atactic PP to the appropriate heptad stereosequen-ces, one might ask what use can be made of this detailed configurationalinformation. Through an analysis of the intensities of the observed resonances wemay learn if any simple statistical model, such as Bernoullian or Markovianstatistics, can describe the polymerization of atactic PP. In Figure 2.6 we comparethe observed and simulated 13C NMR spectra of the methyl region of atactic PP.The simulated spectrum was obtained [13] by assuming Lorentzian peaks of< 0.1 ppm width at half height for each of the 36 heptad chemical shifts calculatedby the y-gauche effect method. The relative intensities or heights of these heptadpeaks were then adjusted to obtain the best simulation of the observed spectrum.

The comparison presented in Figure 2.6 makes it apparent that we have beenable successfully to simulate the methyl region of the 13C NMR spectrum ofatactic PP based on our ability to calculate and assign all of the heptadstereosequence resonances. Thus, from this successful simulation we know howmuch of each heptad stereosequence is present in our atactic PP sample. Whenwe compare these heptad stereosequence populations with those predicted bysimple statistical models, we are able to conclude that our atactic PP samplecannot be described by any simple statistical polymerization model, such asBernoullian or first-order Markovian.

It has been subsequently shown by Inoue et al. [29] that a two site model ofZiegler-Natta polymerization of propylene [30] adequately describes the dis-tribution of stereosequences observed in atactic PP. At one of the catalyst sitesthe monomer addition obeys Bernoullian statistics, and at the other site a pre-dominance of monomer units is added in only one of the two possible configur-ations (R, S or d, /).

As we can see, the y-gauche effect prediction of 13C NMR chemical shifts invinyl polymers permits assignment of their 13C NMR spectra, provides anopportunity to test or derive an RIS model description of their conformationalcharacteristics, and may also permit a test of their polymerization statistics.

2.4.2 PROPYLENE-VINYL CHLORIDE COPOLYMERS(P-VC)

Although propylene (P) does not homopolymerize under free-radical initiation[31], it can be incorporated to a minor degree in a copolymerization with vinyl

chloride (VC) leading to P-VC copolymers with up to 15mol% P units. Thecombination of low P content and the inability of P to homopolymerize underthese conditions results in P-VC copolymers where all P units are isolated bylong uninterrupted runs of VC units. Consequently, we may study the stereo-chemistry of the comonomer sequences containing the isolated P units, i.e.,.. V C - V C - V C - V C - V C - V C - P — V C - V C - V C - V C - V C - V C . . . ,and compare them with the stereosequences found in the two homopolymers PPand PVC.

The methyl carbon regions of the 13CNMR spectra of two PP samples arecompared with the methyl carbon region observed in the P—VC copolymer [32]in Figure 2.8. The PP sample A in (a) is a typical commercial atactic material [11],and the PP sample B in (b) is a heptane-soluble fraction of a research-gradematerial [33]. The stick spectrum in (b) was calculated as just described; they-gauche effect13C chemical shifts calculated for the methyl carbons in the P-VCcopolymer (c) were obtained by employing Mark's [34] RIS conformationalmodel of P-VC copolymers.

Comparison of the methyl resonances in P-VC and PP reveals a decreasedsensitivity to stereosequence for the P-VC copolymer. The methyl carbonresonances in P-VC are sensitive to pentad stereosequences, whereas in PPheptad sensitivity is observed. In Table 2.6 the 13C chemical shifts calculated forthe methyl carbons in several heptad stereosequences of P-VC and PP arecompared. As observed, the methyl carbon chemical shifts calculated for P-VCare sensitive to pentads, but PP methyl carbons show significant heptad sensitiv-ity. This difference in stereosequence sensitivity between the methyl carbons inP-VC and PP is directly attributable to differences in their conformationalbehavior as embodied in their RIS models. Local bond conformations reflectpentad sensitivity in P-VC and heptad dependence in PP. In addition, note thatthe overall spreads in methyl carbon chemical shifts observed in P-VC and PPare 2.7 and 2.0 ppm, respectively, with the P-VC methyl carbons resonatingabout 1 ppm upfield from those in PP. These observations are also reproduced bythe calculated chemical shifts, which employ the same y-effect (yCH3,cH = — 5 ppm)and further indicate differences in the conformational behavior between P-VCcopolymer [34] and PP homopolymer [26].

2.4.3 P O L Y ( P R O P Y L E N E OXIDE) (PPO)

r°i(CH3CHCH2)

Propylene oxide exists in both R and S optical forms owing to its asymmetricmethine carbon. If during polymerization only one of the C—O bonds in thecyclic monomer is cleaved, then it is possible to generate four different

ppm vs. (CH^)4Si

Figure 2.8 (a) Methyl carbon region of the 50 MHz 13C NMR spectrum of PP sample A;(b) methyl carbon region of the 50 MHz 13C NMR spectrum of PP sample B with stickspectrum of 13C chemical shifts calculated for the methyl carbons in atactic PP; (c)P-methyl carbon region of the 50MHz 13CNMR spectrum of P-VC copolymer withstick spectrum of 13C chemical shifts calculated for the methyl carbons in P-VC

Table 2.6 13C NMR chemical shifts calculatedfor the methyl carbons in several heptad

stereosequences of P-VC and PP*

A<5,* ppm

Heptad P-VC PPr(rmrm)r 0 0m(rmrm)r -0.01 -0.07r(rmrm)m -0.01 -0.05m(rmrm)m -0.03 -0.10r(mrrm)r 0 0m(mrrm)r -0.04 -0.07m(mrrm)m -0.07 -0.12

Tonelli and Schilling [32].*A<5 is the difference in chemical shift among the variousheptads containing the same central pentad stereo sequence.VCH? CH = - 5 ppm was used for both PP and P-VC.

ISOTACTIC, RRR OR SSS

SYNDIOTACTIC, RSR OR SRS

HETEROTACTIC-1 RRSORSSR

HETEROTACTIC-2 SRR OR RSS

stereochemical triads in the regioregular head-to-tail (H-T) PPO polymer. TheseH-T triads are presented below in planar zigzag projection.

If, however, during the ring-opening polymerization [35, 36] both C—Obonds in propylene oxide are subject to cleavage, then, in addition to the H-TPPO triads above, three additional structural triads or regiosequences arepossible for PPO. These are illustrated here for the all-/* regioisomers, whereH-T, H-H, T-T, and T-H refer to the directions of neighboring monomers, andwhere H is the methine end and T is the methylene end of the monomer unit. Each

CH3 H H H C H 3 H

/VxVV\H H H ^CH3 H3C H

(T-H: T-T)

CH3 H CH 3HH JCH3

AWV\H HH H HH

(T-T: H-H)

HH H HCH3 .H

CH3HH CH3 H H

(H-H: T-H)

of these regioirregular triads, with H-H and T-T additions, can be furthersubdivided on stereochemical grounds, as was done above for the regioregularH-T triads. Thus, when both regiosequence and stereosequence are considered,16 unique structural triads can potentially exist in PPO. It is worth mentioningthat, independent of regiosequence (H-T, H-H, T-T), an m-diad consists of RRor SS neighboring units, whereas an r-diad consists of RS or SR neighboringunits. However, the methyl groups in a H-T m-diad are on opposite sides of theplanar zigzag projection, while in H-H and T-T diads they are on the same side.The methyl groups in r-diads are on the same side of the backbone when the diadis H-T, but on opposite sides in both the H-H and T-T r-diads. This is a directconsequence of the number of bonds separating asymmetric centers in H-T(three bonds) and in H-H or T-T (two or four bonds) regiosequences.

Because the PPO repeat untit contains three protons (two methylene and onemethine) whose resonances overlap extensively, it has not been possible to use

1H NMR spectroscopy [37-42], even at 500 MHz, to determine the microstruc-ture of PPO. Deuteration at the methine carbon simplifies the 1H NMR spectraof PPO [38-41], and two-dimensional 1H NMR spectroscopy [42] also leads togreater separation of the overlapping proton resonances. However, even theapplication of these special synthetic and spectroscopic techniques has not beencompletely successful in establishing the microstructures present in PPO.

Carbon-13 NMR generally offers the potential for greater spectroscopicresolution than 1HNMR and might be expected to be better suited for theanalysis of PPO microstructure [43-47]. This expectation is realized for re-gioregular (all H-T) PPO, where CH and CH2 carbon resonances are separatedby 2 ppm, and permits the unambiguous assignment [45] of PPO stereosequen-ces. However, as we will demonstrate here, the methine and methylene carbonresonances in regioirregular (H-T, H-H, T-T) PPO do overlap [48].

The methine and methylene carbons in PPO have the same numbers and typesof a and p substituents (CH -• two a-C, one a-O one /?-C, and one /?-O; CH2 -+ onea-C, one a-O, two /J-C, and one /J-O) independent of whether or not they are partof H-T, H-H, or T-T units (see the triad representations above). Because thedeshielding of a carbon nucleus produced by a- and /?-carbon substituents is verysimilar ( « + 9 ppm), the relativex 3C chemical shifts of both CH and CH2 carbonsin PPO should depend solely on their y-gauche interactions. In regioregular PPOthe H-T methine carbons have two y-substituents (two CH) and the methylenecarbons three y-substituents (two CH2, one CH3). We therefore expect, as isobserved [45], that the methylene carbons will resonate upfield ( « — 2 ppm) fromthe methine carbons. In regioirregular PPO the H-H methine carbons have threey-substituents (two CH2 and one CH3, or one CH, one CH2, and one CH3), as dothe H-T methylene carbons, and the T-T methylene carbons have two y-substituents (two CH, or one CH and one CH2), like the H-T methine carbons.

We therefore expect the H-H methine and H-T methylene carbon resonancesand the T-T methylene and H-T methine resonances to overlap, based on theirhaving the same numbers and types of a-, /?-, and y-substituents. In earlier studiesof PPO using 13C NMR [45], confusion developed in assigning resonances tocarbons of the H-H:T-T defects that result from the catalyst occasionallycleaving the CH—O linkage instead of the CH2—O bond when opening thepropylene oxide ring. The possible mixing of overlapping methine and methylenecarbon resonances was not considered. Additionally, spectral analysis of lower-molecular-weight samples must take into account the contributions of carbonnuclei in the chain-end structures.

Our approach [48] in analyzing the 13CNMR spectra of PPO was first todefine the type of carbon represented by each resonance, i.e., methine, methylene,or methyl. Application of the DEPT and INEPT pulse editing techniques [49]permitted achievement of this objective. Second, by analysis of PPO samplesdiffering in molecular weight we were able to assign those resonances belongingto end-group carbons. The third and final step in the analysis was to assign the

H-H and T-T defect resonances using the y-gauche effect method to calculate(513C values.

The carbon nuclei in PPO are shielded by carbon and oxygen y-substituents.From 13CNMR studies of alkanes and their oxygenated derivatives [19],yc c= —4 to — 5ppm and yc,o = —6 to — 8ppm seem likely for the shieldingsproduced by C and O y-substituents when in a gauche arrangement with carbonnuclei in PPO.

The numbers of such y-gauche arrangements were determined from the bondconformation probabilities calculated for PPO with the RIS model developed byAbe etal. [5O]. This conformational description developed for regioregular(H-T) PPO was modified [48] so as to permit the calculation of bond conforma-tion probabilities in the H-H and T-T portions of PPO as well. Effects of bothregiosequence and stereosequence were explicitly considered when calculatingrelative 13C NMR chemical shifts in PPO via the y-gauche effect method. Theresults of these calculations for the carbon nuclei in the H-H and T-T defectstructures of PPO are presented in Table 2.7. Note the significant differencesbetween the <513C values predicted for the regular H-T and defect H-H and T-Tcarbons. 13CNMR spectra of PPO 4000 (M = 4000) and isotactic PPO(M = 14 500) are presented in Figure 2.9. All three carbon types display chemicalshift sensitivity to the stereochemistry of the polymer chain. The assignment ofresonances to the regioregular portions of PPO (see Table 2.8) is made bycomparison of the two spectra, and agrees with earlier work [44,45]. In contrastto13C NMR observations for most vinyl polymers, the observed sensitivity of thePPO carbon chemical shifts to stereochemistry is very small. The total spread ofS13C is only 0.12, 0.20, and 0.25 ppm for the methyl, methine, and methylenecarbons, respectively. This can be contrasted to atactic PP [11], where the rangeof chemical shifts due to stereosequences is 2.0, 0.5, and 2.0 ppm for the samecarbon types. The reduced sensitivity in PPO reflects the presence of three bondsbetween chiral centers in contrast to the two bonds in vinyl polymers. The limitedchemical shift sensitivity is predicted by the RIS model for PPO [50]. On thebasis of y-gauche shielding interactions, a spread of H-T chemical shifts of% 0.5 ppm is predicted for each of the three carbon types.

The DEPT technique [49, 51] permits spectral editing in such a manner thatspectra containing only a specific carbon type can be produced. In Figure 2.10 weshow results of DEPT measurements on atactic PPO 4000 for the methine andmethylene carbons only. At the vertical gain used in acquiring these spectra theH-T resonances are off scale, and we are observing the resonances of the defectH-H and T-T structures as well as the chain-end carbons. In (a), all CH and CH2

resonances are observed, whereas in (b) and (c) only the CH and the CH2

resonances, respectively, are observed. The most striking feature of these DEPTediting spectra is the observation that there are clearly methine carbon reson-ances in the upfield region previously thought to contain exclusively methyleneresonances, and there also are methylene resonances in the downfield portion of

Table 2.7 Calculated 13C NMR chemical shifts for poly(propylene oxide) [48] at 23 0C

1 2 3 4 5CH3 a CH3 b CH3 c CH3 d CH3

I I I I l- C H 2 - C H - O - C H 2 - C H - O - C H - C H 2 - O - C H - C H - O - C H 2 - C H - O - -

1 1 2 2 3 3 4 4

Diada

Carbon

CH3I222233445

CH2I222233445

CH 1222233445

a

mr

mrm

mmrrm

mmrmr

b

rr

mmrm

mmrrmr

mmrrmr

C

-

d

mrm

rrm

rmm

5 5

Chem. shift,PPmb

0.00+ 0.45+ 0.49+ 0.75+ 0.79+ 0.53+ 0.82+ 0.02+ 0.04

0.000.00

-0.15-0.19+ 0.20+ 0.25+ 4.40+ 4.73+ 4.75+ 4.78

0.000.00

-4.49-4.45-4.49-4.45-4.48-4.48-0.25-0.27

0.00

"The dash (-) indicates either m or r diad placement.The + and - indicate downfield and upfield shifts, respectively, relative to the position of the 1 or 5 (H-T) carbons.

the spectra previously thought to contain only methine resonances. [Theseobservations are confirmed by INEPT spectra (not shown) [48] in whichmethylene resonances can be observed with negative intensity but methinesignals appear as positive peaks.] Certain H-H: T-T and/or end-group reson-ances at % 73.5 and 75.6 ppm can only be observed in the edited spectra, as theyare completely obscured by the H-T peaks in a normal FT spectrum.The

ppm vs. TMS

Figure 2.9 50.31 MHz 13CNMR spectra of (a) atactic PPO 4000, and (b) isotactic PPO,observed [48] at 23 0C in C6D6. see Table 2.8

comparison of resonances in the three spectra of Figure 2.10 permits us to identifyeach resonance as to carbon type, methine or methylene.

To assign resonances produced by various end-groups we compare the spectraobserved for PPO 4000 (DP = 69) and PPO1000 (DP = 17) as presented in Figure2.11. Results of a DEPT measurement on PPO 1000 agree with those for PPO4000 in establishing the carbon type represented by each resonance. AU of thevisible resonances in Figure 2.11 (a), other than the labeled H-T peaks, can beattributed to the end-groups, because the number of such groups is about 3 timesthat of the H-H: T-T defects in the low-molecular-weight PPO 1000. All of the

Table 2,8 * 3C NMR chemical shifts and relaxation data [48] for head-to-tail carbons in poly(propylene oxide) at 23 0C

Chem. shift,a T1, CarbonResonance ppm s type Stereosequence

"1 75J5 078 CH mm2 75.64 0.80 CH mr + rm3 75.50 0.81 CH rr4 73.78 0.51 CH2 m5 73.54 0.50 CH2 r6 73.47 0.50 CH2 r7 17.79 1.03 CH3 rm,mr,rr8 17.71 1.03 CH3 mm,rm, mr, rr9 75.73 CH mm

10 73.77 CH2 m11 17.72 CH3 mm

-Figure 2.9.

CH2 and CH end-group resonances occur in the H-T methine region between75.0 and 76.5 ppm.

DEPT spectra of PPO 1000 (not shown) [48] indicate that no end-group CHresonances are hidden by the H-T methylene resonance at 73.5 ppm. Compari-son of DEPT spectra permits the specific assignment of end-group methine (1)and methylene (2) resonances. Note in Figure 2.1 l(a) the end-group methyleneresonances at «75.6 ppm, which add to the complexity of the H-T CH region.Comparison of the spectra in Figure 2.11 permits the identification of end-groupresonances in PPO 4000 and, by elimination, those resonances that are cross-hatched must result from carbons in the H-HrT-T structures. These H-H: T-Tpeaks are identified as to carbon type from the DEPT spectra in Figure 2.10.A summary of the methine and methylene carbon resonances and their assign-ment to H-H:T-T defects or end groups appears in Table 2.9. The methylregions of both atactic PPO samples are displayed in Figure 2.12. Resonancesattributable to methyl carbons in or adjacent to an end-group can be assigned bycomparison of (a) and (b), where it can be seen that all H-H: T-T defectresonances occur downfield from the H-T peaks. A summary of the methylcarbon data is given in Table 2.10.

In order to make the assignments of the carbon nuclei in the H-H: T-Tstructures, a comparison was made between the experimental chemical shift data(Figures 2.10 and 2.11 and Tables 2.9 and 2.10) and the relative chemical shifts foreach carbon type resulting from the y-gauche effect calculations (Table 2.7). Thecalculated data indicate a lack of sensitivity for all carbons to the nature of thestereochemistry across the T-T portion of the chain (diad c in Table 2.7). Inaddition, for the H-H methyl and methylene carbons 2 and 3, diad b stronglyaffects their chemical shifts, but diad a has a much smaller influence. The H-H

ppm vs. TMS

Figure 2.10 Methine and methylene (a), methine only (b), and methylene only (c)50.31 MHz* 3C NMR DEPT spectra of atactic PPO 4000 observed [48] at 23 0C in C6D6

methine carbons, however, are expected to show only a very minor stereochemi-cal dependence.

Using the calculated shift data of Table 2.7, it is possible to make the specificassignments given in Tables 2.9 and 2.10. The H-H methine carbons 2 and 3 arepredicted to be significantly upfield of the H-T CH resonances (at « 72.8-73.8ppm) and are observed most clearly in the DEPT editing spectrum (Figure 2.10(b)). Methine carbon 4 cannot be resolved from the H-T CH resonances.

For the CH2 carbons (Figure 2.10 (a)) the group of resonances slightly down-field of the H-T methylene resonances is assigned to carbon 2, while themethylene resonances (3, 4, 6, 7) shifted downfield into the H-T CH region areassigned to carbons 3 and 4. Despite differences in the magnitudes of calculatedand observed shifts for the H-H: T-T vs, H-T methine and methylene carbons

ppm vs. TMS

Figure 2.11 50.31 MHz 13CNMR spectra of (a) atactic PPO 1000, and (b) atactic PPO4000 observed [48] at 23 0C in C6D6 (1 indicates methine and 2 indicates methylene.) Thecrosshatched resonances result from the H-HiT-T structure

(see below), the predicted direction of relative y-gauche shielding for each carbonpermits a consistent set of assignments as given in Table 2.9.

These results illustrate the difficulties faced by early workers in assigning the13C NMR spectrum of PPO. At first glance one is tempted simply to divide the73-76 ppm region into two parts, methine and methylene. However, a carefulinterpretation of the chemical shift effects produced by the H-HiT-T structuresshows that a large number of the methine and methylene resonances shouldoverlap, and that the identity of carbon types can be ascertained only by DEPTor INEPT editing experiments [51]. In addition, the comparison of PPO samplesdiffering in molecular weight is necessary to identify the chain-end carbonresonances.

The differences in the magnitudes of the S13C values observed and calculatedfor methine and methylene carbons in the H-HiT-T and H-T PPO structuresmay stem from the slightly different /J-substituents [19] present in each of thesestructural environments. The methine and methylene carbons in both H-T andH-HiT-T structures are P to oxygen ( C H - C H 2 - O and C H 2 - C H - O ) , andthe methylene carbons are /? to methyl carbons (CH2—CH—CH3). However,

Table 2.9 13C NMR chemical shift assignments and relaxation data[48] for the methine and methylene carbons of atactic PPO 4000 at

23 0C

Chem. shift," T\,Resonance ppm Assignment* sI 76J6 — C H - E 0.93

2 76.29 — C H - E 0.803 76.26 - C H 2 - 3,4 0.804 76.21 - C H 2 - 3,4 0.775 76.10 - C H 2 - E 1.196 75.98 - C H 2 - 3,4 0.567 75.88 - C H 2 - 3,4 0.598 75.24 — C H - E 0.829 75.13 - C H - E 0.81

10 75.08 - C H - , - C H 2 - E 0.81II 75.02 - C H 2 - E 0.9012 74.96 - C H - E 1.0813 74.91 - C H - E 1.1814 74.46 - C H 2 - 2 1.0415 74.26 - C H 2 - 2 0.5016 74.02 - C H 2 - 2 0.5117 73.82 — C H - 2,318 72.97 - C H - 2,3 0.6119 72.93 - C H - 2,3 0.6420 72.87 — C H - 2,3 0.6821 72.06 - C H 2 - E 2.1622 72.03 - C H 2 - E 2.1623 73.30 - C H - 2,324 75.65 - C H 2 - E25 75.57 - C H 2 - E

•Figure 2.10.*E indicates chain end structure; 2,3,4 indicate H-H: T-T defect structure (see Table 2.7).

the H-T methine and H-HrT-T methylene carbons are /J to methylene carbons( C H - O - C H 2 and C H 2 - O - C H 2 ) , whereas H-T methylene and H-HrT-Tmethine carbons are p to methine carbons (CH2—O—CH and CH—O—CH)(See Table 2.7). On the other hand, H-HrT-T and H-T methyl carbons haveprecisely the same a- and 0-substituents. The fact that the calculated andobserved <513C values agree so closely for the methyl carbons (see below) lendssupport to the suggestion that slightly different /?-substituents for H-T andH-HrT-T methine and methylene carbons may be the source of the disparitybetween the magnitudes of their measured and calculated <513Cs.

The methyl carbon resonances of the H-HrT-T structures are assigned inTable 2.10. Both the calculated magnitudes and the directions of the methylresonances relative to H-T resonances agree with the observed results (Fig-ure 2.12(a)). The three defect resonances (peaks 4, 5, 6) are assigned to carbons

ppm vs. TMS

Figure 2.12 Methyl region of the 50.31 MHz 13CNMR spectra of (a) atactic PPO 4000,and (b) atactic PPO 1000 observed [48] at 23 0C in C6D6. See Table 2.10

2 and 3 (Table 2.7). Because of the predicted overlap resulting from stereosequen-ces, we cannot make further specific assignments in this region of the PPOspectrum.Note that in Tables 2.8-2.10 values of the spin-lattice relaxation time T1 are

presented for each resonance. These were determined by the inversion recoverymethod and were utilized to insure that quantitative spectra were obtained. Fromthe methyl carbon data (Figure 2.12(a)) we are able to estimate that PPO 4000contains 2.2% inverted, or defect, H-HrT-T units and has a number-averagemolcecular weight Mn = 5400, or DP = 93, based on the end-group resonanceintensities. This may be compared with Mv = 4000, or DP = 69, provided by themanufacturer and based on KOH hydroxyl number.

With the aid of multiple-pulse editing techniques (DEPT, INEPT) and they-gauche effect calculations of relative 13CNMR chemical shifts, we [48] have

Table 2.10 * 3C NMR chemical shift assignmentsand relaxation data [48] for the methyl carbons of

atacticPPO4000at23°C

Chem. shift,0 T19

Resonance ppm Assignment* s"1 19.27 E 1.65

2 19.24 E 1.653 18.99 E 1.804 18.74 2,3 0.995 18.51 2,3 0.966 18.38 2,3 0.927 17.29 E 1.098 19.31 E9 19.26 E

10 19.02 E11 17.31 E

•Figure 2.12.*E indicates chain end structure; 2, 3, indicate H-H.T-T defectstructure (see Table 2.9).

assigned the 13CNMR spectrum of PPO, including the determination of carbonresonances resulting from chain-end structures. Analysis of the expected differen-ces between the y-gauche interactions of the methine and methylene carbons inH-T and H-H:T-T PPO structures indicated that H-HiT-T methine reson-ances should overlap with the H-T methylene signals and the H-HiT-Tmethylene and H-T methine peaks should also overlap. It was this analysis thatprompted our reinvestigation and assignment of the 13C NMR spectrum of PPO.From these assignments it was possible to determine quantitatively the numberof H-HiT-T defects incorporated in PPO through occasional ring opening ofpropylene oxide monomer at the CH—O bond. In addition, identification ofchain-end structures permitted an estimate of the number-average molecularweight, and (though not discussed here) determination of specific terminal struc-tures also provided insight concerning the polymerization mechanism of PPO.

2.4.4 POLY(VINYLIDENE FLUORIDE) (PVF2)

With the application of a triple-resonance scheme [52], which simultaneouslybroad-band decouples both proton and fluorine nuclei while observing carbonnuclei, it was possible to obtain 1 3CNMR spectra of fluoropolymers that werefree of both 1 3 C - 1 H and 1 3 C - 1 9 F J-couplings. As an example, the tripleresonance 13C NMR spectrum of poly(vinylidene fluoride) (PVF2) was success-fully interpreted with y-gauche effects of ycc = — 2 ppm and yCF = — 2 to

—4ppm, and an estimate of 3.2% was made for the content of H-HrT-T defectstructures shown below

-CF2-^ CH2-*-CF2-^ CH2-*- CH2-CF2 J- CH2 -*-CH2 -^CF2 -*- CH2 -^CF2 -^CH2-

Having successfully analyzed [53] the 13C NMR spectrum OfPVF2 containinga small number of inverted units [3.2% of H-H: T-T monomer additions asobserved by integration of detect (H-HrT-T) and normal (H-T) resonances], wenow attempt to assign and analyze the 19FNMR spectrum of the same PVF2

sample. The 19FNMR spectrum of PVF2 measured at 84.6 MHz is presented inFigure 2.13(a). Three small resonances appear 3.2, 22.0, and 24.0 ppm upfield

<X> p p m

Figure 2.13 Observed and calculated [54] 19F NMR spectra of PVF2: (a) measured at84.6MHz; (b) measured at 188.2 MHz; (c) calculated. Vertical expansion in (a) is x 8, in(b) x 40.

from the main H-T fluorine resonance at 91.9 ppm (relative to CFCl3) andare attributed to the fluorine nuclei belonging to H-H: T-T inverted units[55,56].

We may write expressions for the relative 19FNMR chemical shifts SF of theH-T and H-H: T-T fluorines in terms of their y-gauche effects (yFF and yFC) andthe bond rotation probabilities (P) which determine the frequencies of y-gaucheinteractions:

5JT = (I+P t)yF ,c (1)SF = (1 + 0.5 Pt,d + 0.5 Pt>e)yF,c + (1.5 - 0.5 Pt,c)yF,F, (2)

S¥ = (1 + 0.5 Pue + 0.5 Puf)yFtC + (1.5 - 0.5 PJy F i F , (3)

<5£ = (l+O.5P t,h + O.5Pu)yF,c. (4)

Comparison of Equations' (1) and (4) reveals that <5F~T an 8F are most similar.

Thus, SF — SF~T = 3.2 ppm, which leads directly to <5F c = +30 ppm (shielding).By elimination, \SF — S¥\ = 2 ppm, which yields <5FF = +15 ppm. Substitution of<5FF = 15 ppm and <5FC = 3Oppm into Equations (1-4) leads to calculated SF

values shown as sticks in (c) of Figure 2.13, and which compare well with theobserved spectrum in (a) recorded at low field strength.

At 188MHz four additional defect resonances (1, 5, 6, and 7) appear in the19FNMR spectrum OfPVF2 [see (b) in Figure 2.13]. Ferguson and Brame [57]also observed these additional defect peaks and tentatively assigned them todefect structures drawn in Figure 2.13(b) based on a-, /?-, and y-substituent effectsderived from the CF2 resonances observed in various saturated, partially fluor-inated linear alkanes. In addition to SF~T, 8F, SF, and 8F, 19F chemical shifts werealso calculated for the defect fluorines 1,5,6, and 7.19F y-effects (yF,CH2; 7F,CF2^

anc*yFF) were least-squares fitted to produce the best agreement between observedand calculated <5F values [see (b) and (c) of Figure 2.13]. Best agreement wasachieved for yFfCH2 = yF,CF2

= )V,c = 25-30 ppm and yF F =15 ppm, confirmingthe assignments proposed by Ferguson and Brame [57] and the y-effects derivedfrom the more prominent defect resonances 2, 3, and 4 observed at lower fieldstrength.

Measurement of the intensities of the defect resonances and comparison withthe total intensity of all observable resonances yields an estimate of 3.4% defectH-H:T-T addition in this sample of PVF2. This compares well with the 3.2%defect estimate described earlier using the 13CNMR analysis.

The 19FNMR spectra of poly(vinyl fluoride), poly(fluoromethylene), andpoly(trifluoroethylene) were also successfully interpreted [54] with very similary-gauche effects (yF F=15ppm and yFC = 25-30 ppm), leading to a detailedaccounting of their stereo- and regiosequences.

In addition to eliminating the need for triple resonance observation [52] of13CNMR spectra, 19F NMR spectra of fluoropolymers [54] are much more sensitiveto their microstructures, because the conformationally sensitive y-gauche shield-

ings of their 19F nuclei are nearly an order of magnitude greater than theshieldings observed for their 13C nuclei. Clearly 19FNMR provides a vastlysuperior means for characterizing the microstructures of fluoropolymers com-pared with 13CNMR observations.

2.5 NMR SPECTROSCOPY AS A MEANS TO PROBEPOLYMER CONFORMATIONS

2.5.1 STYRENE-METHYLMETHACRYLATECOPOLYMERS (S-MM)

The advent of two-dimensional NMR techniques [58-61] has resulted in a re-birth of 1HNMR as a means of studying molecular structure. Extensive J-coupling of protons, which unduly complicates one-dimensional 1HNMRspectra, is used to advantage in 2D 1HNMR to map the connectivity ofmolecules. Those protons that are scalar J-coupled, and therefore interactbetween the 90°r.f. pulses, evidence cross peaks in a 2D 1H COSY (correlatedspectroscopy) spectrum. If an additional 90°r.f. pulse is inserted between the two90°r.f. pulses of the 2D 1H COSY experiment, then the correlating influence orinteraction between proton spins which results in cross peaks is their direct,through space, dipolar coupling or NOE (nuclear Overhauser effect). This 2Dtechnique is referred to as NOESY and permits a mapping of all proton spins inthe sample which are closer than « 4 A. Let us illustrate how the 2D1HNMRtechnique NOESY, i.e., NOE correlated spectroscopy, can be applied to regularlyalternating styrene-methyl methacrylate (S-MM) copolymer to learn about itsconformational characteristics.

The methylene region of the 500MHz 2D NOESY spectrum of the regularlyalternating S-MM copolymer is presented in Figure 2.14. The stippled crosspeaks correspond to the intermethylene interactions occurring in the S-centeredco-hetero S-MM triad seen below:

CO-HETERO

These intermethylene N O t cross peaks appear to fall into three categories based

ppm from TMSF 2

Figure 2.14 Expansion of the phase-sensitive proton NOESY spectrum at 500 MHz and800C, showing only the methylene region [62]. Geminal interactions are indicated bycrosshatched cross peaks, and intermethylene interactions by stippled cross peaks. Thedesignations S, M, and W refer to the strengths (cross peak volumes) of the intermethyleneproton interactions

on their intensities: one strong (S), H^-H1; two medium (M), He-H^ and Ht-Ht';and one weak (W), He-H( etc. corresponding to short, medium, and longerinterproton distances, respectively (see Heffner et al. [62] for details of the protonpeak assignments).

By combining portions of the conformational descriptions derived for styrene,methyl acrylate, and methyl methacrylate homopolymers [63-66], Koinumaet al. [67] developed an RIS model for the 1:1 alternating S-MM copolymer.When this RIS model is utilized to calculate the conformation probabilities forthe bond pair flanking the styrene methine carbon in the co-hetero S-MM triadillustrated above, it is possible to calculate [62] the average intermethylene

ppm

from

TMS

proton distances corresponding to the four cross peaks in Figure 2.14. Thisprocedure is illustrated in Figure 2.15 and Table 2.11. The only three confor-mations allowed for the co-hetero S-MM triad are drawn in Figure 2.15 alongwith the probability calculated for each. The intermethylene proton distancesrHH calculated for the same S-MM triad are listed for each conformation inTable 2.11.

When these rHH values are raised to the — 6 power and averaged over the threepossible conformers shown in Figure 2.15 according to the calculated probabili-

FRACTlON

Figure 2.15 Ball-and-stick models of the styrene-centered MM-S-MM co-hetero triad,showing the tt, tg +, and g-t conformations, with 20° deviations from exact staggering[62]

Table 2.11 Intermethylene H-H distances (rHH) calculated [62] for theco-hetero styrene-centered triad (see Figure 2.15)

rHH> A

<t>i><t>i He-Ht> He-He, Ht-Ht, He-Ht

t,t(-20°,20°) 189 H o H o 220t,g+(-20°,100°) 3.74 2.63 3.68 2.59g-,t(-100°,20°) 3.74 3.68 2.63 2.59<0lf*2> 0.0010- 0.0016' 0.0016- 0.0063fl

<<t>l9<t>2> (0.0027)" (0.0016)* (0.0020)* (0.0030)*ar~£ averaged over all three (^1, ^2) conformations.*Same as above, except 0 , , ^2 = 0, ± 120° in the ^g* states (Heffner et al. [62]).

ties also listed there, the entries in the next-to-last row of Table 2.11 are obtained.These values should be proportional to the strengths of the intermethyleneproton-proton cross peaks seen in Figure 2.14, and this is indeed the case.

The agreement between the predicted and the observed pattern of NOESYcross peaks for the co-hetero triad of 1:1 alternating S-MM copolymer confirmsthe validity of the Koinuma et al. [67] conformational model. It is particularlynoteworthy that this agreement requires the assumption of «20° displacementsfrom the perfectly staggered rotational states as predicted for the backbone bondsin polystyrene by Yoon et al. [63] (see the Newman projections below). As anexample, in the t, t conformation (see Figure 2.15), 0, # 2 = — 20°, 20° because thisproduces relief from steric interactions of the phenyl ring and the methylmethacrylate C^ as seen in the following Newman projections:

If perfectly staggered states t(0°), g ± (+120°) are assigned in the calculation ofintermethylene proton-proton distances, then the results in the bottom row ofTable 2.11 are obtained, i.e., all interactions (<**„„» are approximately the same.It is apparent from Figure 2.14 that this is not the case.

More recently Mirau et al. [68] have derived intermethylene proton-protondistances rHH directly from the NOESY spectra of 1:1 alternating S-MM.A comparison was made with the distances rHH of Table 2.11 after conformation-ally averaging according to the Koinuma et al. [67] RIS model. Reasonableagreement was obtained, as indicated by the following observed and (calculated)conformer populations: t, t = 0.58 + 0.05 (0.53), t,g + = 0.24 ± 0.05 (0.20), andg - , t = 0.18 ± 0.05 (0.27). In addition, it was found that an 11° displacement from

perfectly staggered rotational states produced rHH values in closest agreementwith those obtained from NOESY cross peak intensities, adding further supportto the Koinuma et al. [67] RIS model, which assumed 20° displacements. This IDNOESY 1HNMR study of 1:1 alternating S-MM copolymer marked the firstattempt to derive the conformational characteristics of a flexible polymer insolution through a direct measurement of conformationally averaged inter-proton distances.

2.5.2 ETHYLENE-VINYL ACETATE (E-VAc) COPOLYMERS

Recently, a conformational description (RIS model) has been developed forethylene-vinyl acetate (E-VAc) copolymers [69] by merging the RIS modeldescriptions of the constituent homopolymers [70, 71]. Unfortunately nomeasurements of microstructurally and conformationally sensitive propertieshave been reported for these copolymers. Traditional global measures of polymerconformation, such as mean-square end-to-end distances and dipole moments,are not yet available for E-VAc copolymers. However, the 13CNMR spectra ofa complete series of atactic E-VAc copolymers have been assigned [72-74].Through comparison of ^13C values calculated [28] via the y-gauche effectmethod to those previously observed and assigned in E-VAc 13C NMR spectra,we may evaluate the ability of the RIS model derived for E-VAc copolymers todescribe the microstructural sensitivity of the local copolymer conformation,thereby providing an alternate means for testing its validity.

Wu and Ovenall [72,73] assigned the low field (22.6 MHz for 13C)13C NMRspectra of E-VAc copolymers by comparison with the 13CNMR spectra re-corded for the E-VAc model compounds presented below.

Later Sung and Noggle [74], employing higher field observations (62.9 MHzfor 13C) and using paramagnetic shift reagents, corrected some of the earlierassignments made by Wu et al. [72,73]. Even so, they were not able conclusivelyto discriminate between the assignment of resonances belonging to the methinecarbons in the mrmr, rrrr, and mrrm stereosequence pentads of atactic PVAc.

We calculated [28] the S13Cs expected for the methylene and methine carbonsin the complete series of E-VAc copolymers using ycc = — 3 ppm and7c,o — — 5 ppm and the RIS model recently developed for these copolymers [69].

Figure 2.16 presents a schematic comparison of methine carbon 513C valuesobserved and calculated for E-VAc copolymers. A similar comparison of E-VAcmethylene carbon <513C values is displayed in Figure 2.17. Whereas the chemicalshifts calculated for the methine carbons in E-VAc copolymers only reflectdifferences in the numbers and kinds (ycc and yco) of magnetic shieldingsproduced by their microstructurally sensitive gauche arrangements with C andO y-substituents (see Figure 2.16), the methylene carbon chemical shifts (seeFigure 2.17) reflect in addition different numbers of P-OAc substituents. Wu et al.[72, 73] found /J-OAc = + 5 ppm from their model compound studies, and thisvalue was employed in the calculation of E-VAc methylene carbon chemicalshifts.

Note the close agreement between <513Cs observed and calculated for thebackbone carbon nuclei in E-VAc copolymers. This provides strong support forthe efficacy of the RIS model [69] recently developed for these copolymers. Inaddition, <513Cs calculated for the backbone carbon nuclei in atactic PVAc using

Figure 2.16 Comparison of observed [74] and calculated [28] 13C chemical shifts for the methine carbons in E-VAc copolymers

Calculated

Observed

Figure 2.17 Comparison of observed [74] and calculated [28] 13C chemical shifts for the methylene carbons in E-VAc copolymers

Calculated

Observed

the homopolymer RIS model [71] and the same y-gauche effects employed forE-VAc copolymers generally agree with those appearing in the observed spec-trum [74]. This agreement permitted a conclusive assignment of those methinecarbon resonances belonging to the mrmr, rrrr, and mrrm pentad stereosequen-ces which Sung and Noggle [74] had been unable to assign unambiguously.

In Chapter 3 Howarth et al. describe an extension of the approach employedabove to actually derive the conformational descriptions (RIS models) of poly-mers by comparison of 13C chemical shifts calculated via the y-gauche effectmethod with their observed 13CNMR spectra, followed by iterative adjustmentof the RIS models until they yield calculated <513Cs in agreement with observedvalues.

2.6 NMR OBSERVATION OF RIGID POLYMERCONFORMATIONS

Although we have dealt exclusively with the analysis of polymer microstructuresand conformations by comparison of chemical shifts (<513C, <519F) calculated viathe y-gauche effect method and 1H-1H distances, averaged over all conforma-tions available to them, with their observed solution spectra, high resolution,solid state NMR observations can also probe rigidly fixed polymer conforma-tions. It has been demonstrated [75,76] that the 13C chemical shifts observed inCPMAS/DD 13CNMR spectra of solid polymers are also sensitive to the localrigid conformations of their constituent chains. This has been demonstrated inseveral instances for crystalline polymers able to crystallize in two or morepolymorphs which are distinguishable for the different conformations adoptedby their polymer chains.

As an example, syndiotactic polystyrene (s-PS) [76] can be crystallized in twoconformationally distinct polymorphs, form I, with all-trans, planar zig-zagchains, and form II, where the chains adopt the helical... ttggttgg... conforma-tion, very similar to that observed [77] in syndiotactic polypropylene (s-PP)crystals. CPMAS/DD 13CNMR spectra of both s-PS polymorphs are shown inFigure 2.18. Note in the form II spectrum (b) that two methylene carbonresonances appear at 49.1 and 38.1 ppm (vs. TMS). As half the methylene carbonsin form II s-PS are trans to both of their y-substituents(CH's), while the other halfare gauche to both of theirs, it is not surprising that two methylene carbonresonances separated by » 2 x ycc (11 ppm) are observed. Identical behavior isobserved [78] for s-PP, which also crystallizes in the ...ttggttgg... helicalconformation. All the methylene carbons in the all-trans form I crystalline chainsare trans to their y-substituents, consistent with the single CH2 resonanceobserved for this polymorph at 48.4 ppm, which is virtually coincident with thathalf of the methylene carbons in form II crystals (49.1 ppm) that are also notshielded by their y-substituents.

ppm

Figure 2.18 CPM AS/DD 13C NMR spectra [76] of form I (a) and form II (b) s-PS. Theform II sample of (b) was obtained by absorption of dichloromethane into an amorphous,melt-quenched film of s-PS

This and many other examples [75, 76, 78] clearly demonstrate the utility ofhigh resolution NMR as a probe of polymer chain conformations as they occur inrigid, solid samples.

2.7 REFERENCES

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Commun., 1981,15.

3 'MODEL-FREE' RISSTATISTICAL WEIGHTPARAMETERS FROM13C NMR DATA

O. W. HOWARTH, R. N. IBBETT, L R. HERBERTand M. A. WHISKENSCentre for Nuclear Magnetic Resonance, Department of Chemistry, University ofWarwick, Coventry CV4 IAL, UK

3.1 INTRODUCTION

This chapter describes some new attempts to exploit the rich source of conforma-tional data that is potentially available from the dependence of 13C NMR shiftsupon the local tactic sequence in a substituted carbon-based polymer. The mainlink between shift and conformation is the gamma-gauc/ie effect. This is widelyused in the interpretation of 13C chemical shifts in many types of compound. Itwas initially identified from the classic work by Dalling and Grant [1], and byothers [2], on the 13C shifts of hydrocarbons, and especially of methylcyc-lohexanes, in which specific local conformations could be frozen out by eitherchemical or physical means. If a molecule contains any partial carbon chainC1-C2-C3-C4, and if Cl and C4 are mutually y-gauche, thus making theC1,2-C3,4 dihedral angle approximately ± 60°, then both C1 and C4 experiencean additional shielding, i.e. lowering of <5C, of %5ppm (see Figure 3.1). Similarshifts are observed when CA is replaced by a wide range of groups [3]. The shifteffects of different groups do not vary in any obvious way with polarity. Indeed,the shifts that arise from, e.g., hydroxyl substituents may be somewhat smallerthan average. However, they do seem to bear some relationship to the bulk of thesubstituent, and indeed they are often interpreted in terms of steric compression.

Various more serious attempts have been made to explain the y-gauche effectby MO computations. The most recent are those of Barfield and Yamamura [4],using an ab initio method with a double-C basis set. Although this level ofcomputation is a little less than that required to give the best available absoluteshieldings, it reproduces very adequately a wide range of steric shifts in hydrocar-bons (i.e. those dependent solely upon variations in stereochemistry) and also


Figure 3.1 Illustration of stereochemical relationships. In this rotational state, A andB are both y-gauche to the next-nearest non-methylene carbon, and the two A groups aresyn-axial to each other, as are the two B groups

supports the intuitive assumption that y-gauche contributions to the shift ofa given carbon from more than one source are additive. It also draws attention toseveral other potential steric contributions to carbon shifts, including those thatarise from quite modest deviations from dihedral angles of ± 60°. These will bediscussed in a later section.

Shifts that arise from the y-gauche relationship may be readily computed forpolymers, provided that the appropriate RIS (rotational isomeric state) probabil-ity parameters [5] are known from calculations of the potential energy surface ofthe macromolecule. The basic procedure is to start with an estimate, e.g. frommolecular modelling calculations, of the free energies and bond angles of thevarious energy minima found upon rotation of the two (usually) C—C bonds inboth the meso (m) and the racemic (r) dyad units of the polymer chain. Neigh-bouring dyads are then permitted to alter these free energies through the stericrestrictions, such as the 1,5 pentane effect, that must apply to the dyad joins.Although these effects extend in theory to an infinite succession of next-neigh-bours, the calculated sequence dependence of shifts is usually small beyond theheptad/hexad level, at most. Thus one obtains an estimate of the true probabili-ties for occupation of any dyad in any steric sequence. It is then simple to explorethe effects of conformation upon the observed chemical shifts, using, e.g., they-gauche shift model.

Such calculations are described in detail by Tonelli in Chapter 2. They workspectacularly well for polypropylene, with a model having five rotameric statesper chain bond. However, Tonelli has pointed out additional factors that must beincluded when other polymers are considered. One is that the methylene shifts in,

Y - gauche interaction (two of the four present)

syn - axial interaction

"P - gaucheT shifts possible at these atoms,because of the AC y - gauche interaction

e.g., monohalo vinyl polymers, unlike the methine shifts, show some dependenceupon solvent [6]. Another is that no conceivable RIS parameters can explain therather large steric shifts that distinguish isotactic from syndiotactic poly(methylmethacrylate), either in the solution state or, even more so, in the solid state [T].These can be up to lOppm in magnitude.

A further conceptual challenge arises intuitively. It is reasonable that the shiftsat a given sidechain carbon should depend not only upon the proximity ofy-gauche atoms, but also upon the identity of the atom or group which willnecessarily be syn-axial to it, i.e. its even closer neighbour, in any vinyl polymer.This relationship is illustrated in Figure 3.1.

There is also a practical consideration. RIS parameters are not at all easy tocalculate in many cases, particularly for disubstituted vinyl polymers. In vinylpolymers with main chain methine groups, a few of the dyad rotamers will oftenhave lower energies than the others, because they place both of the methineprotons approximately syn-axial to some other group or chain portion, and thusminimise steric repulsions. However, this is not possible in disubstituted poly-mers, and indeed even the gauche and trans RIS states themselves are likely tooffer poor approximations to the real bond torsional angles. There is also someconcern that the contributions of minor conformers may be underestimated if themodel assumes unrealistically rigid elements. Furthermore, some polymers haveshift patterns for every carbon that depend noticeably upon solvent. Suchvariations lie beyond the reach of conventional RIS calculations, although theymust obviously bear witness to interesting conformational changes caused by theinfluence of the solvent on the potential energy surface of the macromolecule.

The present work is an attempt to address the above challenges by turning themethodology around. Might it prove possible to obtain reasonable RIS statisticalweight parameters, of use to other modellers, by treating the carbon shifts asgiven data and the RIS parameters as variables? Complete sets of such sequence-dependent shifts have been fairly reliably assigned at the tetrad/pentad level formany mono- and disubstituted vinyl polymers, and in some cases the spin-spincoupling constants are also available as further constraints on any model. Theobvious attraction of this approach is that the RIS variables may be overdeter-mined. Suppose that one allows only three rotameric states per chain bond, andtreats any possible sidechain rotamers as having a constant average contribution.Even if the probability of each dyad rotamer is allowed to vary independently,after due regard for symmetry, there are only 10 undetermined probability ratiosin a vinyl polymer. (Note that the ratio of the m- to the r-dyad probabilities is notsignificant in the present context). To these 10 must be added a single variable,such as the g*g*/g~g~ elements of Flory's Un, matrix [8], which controls theextent by which 1,5 syn-axial chain segments are forbidden. This extent may notbe 100% after allowance for minor distortions of the intervening torsional angles,especially when the substituent groups are small, and even more so if they arecapable of favourable interactions such as hydrogen bonding. To determine these

11 variables we typically have some 16-30 different steric shifts, or even more ifthe assignment can be made at the hexad/heptad level. Thus the quality as well asthe existence of any shift fit might be used to assess the reliability of thecalculation.

3.2 METHODS

The first problem that arises with this approach is that the y-gauche contributionsfrom many groups are not known accurately. Some may be estimated from theshifts of molecules is known conformations, e.g. substituted cyclohexanes, butothers remain to be established. An underlying principle of the present study isthat all such parameters be fixed for a given group, even if it appears in severaldifferent polymers. Another principle is that all the carbon resonance patterns ofa given polymer must be fitted simultaneously. Indeed, as a further simplification,we specify that the shift effects depend only on the substituent, and not on the typeof carbon (e.g. C, CH, CH2, CH3, CO, CN) under observation. Fortunately, thenumerical value of most shift parameters does not in practice greatly affect theresulting RIS weightings, within a reasonable range. It is the shift patterns whichdominate the calculation.

The second problem is to meet the challenge of polymers such as poly(methylmethacrylate), which fit poorly to any scheme based simply on y-gauche contribu-tions to the methyl shift. Our proposal is that, for such groups, the y-gauchecontributions should be subdivided into three separate syn-axial contributionsfrom the appropriate groups S to the carbon under observation. Thus, ana-methyl group in poly(methyl methacrylate) may be y-gauche to the next-nearestunprotonated carbon, but then it must also be sjw-axial either to anothera-methyl or to a carboxymethyl group or to the chain methylene in the next dyad.These three will not necessarily cause the same shielding at the original methyl,although their average shielding effect should not very greatly from a typicalvalue of, say, 5 ppm. One should note in this context that a hydrogen atom may bean active substituent, because the shifting unit is in fact both the syn-axial H andalso the gauche C, even though we refer to the shielding parameter for brevity asbeing simply 'syn-axiaF. Indeed, one may not even assume that H necessarilyimposes a smaller 'syn-axiaF shielding than any other group. We show below thatthis model is capable of allowing surprisingly large methyl shifts.

The next problem arises from Tonelli's observation that some methylene shiftsdepend noticeably upon solvent. If these changes are not matched by correspond-ing changes in other shift patterns, then they cannot be explained by RISweightings alone. Tonelli and Schilling have suggested [6] that they may arisefrom differential solvation of m- and r-dyads, which should affect methylene shiftsmuch more that others. We accept this suggestion by creating one more adjust-able parameter, a variable, solvent-induced shift difference between m- and

r-methylenes. In most cases this turns out to be small, but even so it turns out ingeneral to give noticeably improved fits.

Finally, one must decide on the size of the RIS dyad matrices. In this respect,the present work is not altogether 'model-free'. The main problem is that eachgauche state, and perhaps also the trans state, probably exists with two variants[5], so as to ease the concomitant syw-axial repulsions. In cases where detailedcalculations have been made [9], these variants typically shift the chain dihedralangle from ± 60° to ± 50° and to ± 70°, with unequal weightings and with a verylow or non-existent intervening energy barrier. It would probably be ideal to usea generalised 6 x 6 state model in order to allow for this. However, this wouldgenerate an unacceptable number of variables. Instead, we have chosen a simple3 x 3 state model. This implies the assumption that the probabilities of eachnearby pair of rotational states may reasonably be represented by their sum, andthus that the shift contributions from each state are comparable. Barfield andYamamura [4] have indeed shown that the y-gauche effect varies monotonicallywith dihedral angle in an approximately sinusoidal manner, so that the shiftcontributions from the ±50° and from the ±70° angles should be not toodifferent. Although the resulting, simplified RIS parameters will be more artifi-cial, they should retain their usefulness for most calculations simply because oftheir derivation from experimental data.

3.3 SOMECALCULATIONDETAILS

A spreadsheet calculation (using Microsoft Excel version 3.0) was written toconvert the 3 x 3 m- and dyad probability matrices into predicted steric shifts, bythe usual methods of matrix multiplication, to find overall conformationalprobabilities. Although the final calculations were only carried out at thetetrad/pentad level, the calculations assumed further, flanking m-dyads in eachcase in order to give more realistic weightings. The linking U i r matrix wasassumed to have one freely variable component, g*g+/g~g~, with the otherelements being fixed at unity. This has the effect of permitting all dyad joinsequally, except for those which result in syw-axial chain segments. The latter aresuppressed in proportion to the variable component. In fact, none of the fittedvalues of g*g+/g~g~ exceeds the necessary bounds of zero to approximatelyunity.

As described above, a further shift variable was then introduced, to give thesame shift increment to each r-methylene resonance. These increments were neverlarge, and typically were less than ±0.4ppm. The resulting shift patterns werecompared with the experimental data, which are described in detail below, andthe squared shift differences were summed. In some cases one resonance ofa polymer shows little spread of shifts, and so cannot be reliably assigned, andhere the calculated shifts were constrained within limits set by the overall

linewidth of the data, without regard to their detailed assignment. Such data arerepresented in the appropriate figures by single, broad Lorentzian peaks.

The sums of squared differences were then minimized with respect to the abovevariables. Minimisation was carried out by the Newton-Raphson method usingMicrosoft Solver version 3.0. It was almost invariably well-behaved, and for eachpolymer it converged to give essentially the same results from a wide range ofstarting parameters. Various calculational refinements were also tested in thehope of improved fits, but, interestingly, they had little extra success. Theseincluded attempts to reduce the g~g+/g*g~ elements in Un, to values belowunity. This gave good results only with polystyrene. The calculations also permitan estimate of the reliability of individual parameters. In some cases, the dataclosely defined all the parameters. In others, a few parameters, noted below, roseto unreasonably high values in the final fits, such as y-gauche shifts > lOppm.However, these could be reduced in all cases to reasonable values without a lossof fitting accuracy greater than the experimental errors of shift measurement. TheRIS elements were not permitted to become negative. Apart from this, thecalculations were deliberately kept as simple as possible, because of the aim ofpractical usefulness to modellers.

3.4 INDIVIDUALPOLYMERS

The method was first tested on polypropylene, because the shifts for this polymerare reliably known as is its accessibility to shift calculations. Furthermore, boththe methyl and the chain methylene groups have been shown to give (and receive)y-gauche shifts of close to —5.0 ppm [9]. This usefully reduced the number ofvariables in the calculation, though in fact little change was observed even if theywere allowed to float. The resulting fits, using our simplified 3 x 3 RIS approxi-mation, were not quite as good as those obtained by Schilling and Tonelli [9],especially in that they slightly underestimated the shift contributions from themore distant chain groups. However, the fit was still very good, as is shown inTable 3.1. The syn-axial shift from H was initially permitted to float, but ina variety of calculations it always came close to —4.0 ppm, and so it was fixedthereafter at this value.

The next polymer to be tested was poly(acrylonitrile), which is readily availablewith minor known variations of tacticity within the approximately atacticrange. Full shift data for this have not been published and are therefore pre-sented in Table 3.2, using both dimethyl sulphoxide-d6 (DMSO) and water-d2/Na+[SCN] " solvents. Our assignment, based on integration rather than peakheight and using several minor variations in tacticity, reverses a previousassignment [10] for the CN mrrm and rrrr resonances. The differential effects ofdistant groups are small and so the assignments are straightforward, except forthe unresolvable methylene resonances. Each set of RIS calculations led to a CN

Table 3.1 Relative 13C shifts in polypropylene

CH^ CH^ CH

obs. calc.0 obs. calc. obs. calc.

mmmm 1.99 1.94 mmm 0.79 0.81 mmmm 0.50 0.51mmmr 1.73 1.72 mmr 1.35 1.37 mmmr 0.45 0.51rmmr 1.46 1.50 rmr 2.07 2.03 rmmr 0.40 0.51mmrm 1.10 1.10 mrm 0 0 mmrm 0.17 0.22rmrm 0.81 0.84 mrr 0.88 0.93 rmrm 0.14 0.23mmrr 1.27 1.25 rr 1.81 1.81 mrnrr 0.28 0.25rmrr 0.96 1.00 rmrr 0.23 0.26mrrm 0 0 mrrrn 0 0mrrr 0.27 0.23 mrrr 0.04 0.03rrrr 0.49 0.43 rrrr 0.08 0.05

'y-gauche/d sjw-axial parameters: CH2, CH3 - 5.0ppm, (C)H -4.0ppm.RMS error 0.039 ppm.

Table 3.2 Observed 13C shifts/ppm for poly(acrylonitrile)

CN ciiDMSO water/NaSCN DMSO water/NaSCN

mmmm 119.73 122.8 mm 26.50 29.40mmmr 119.66 122.7 mr 27.04 29.77nnmr 119.59 122.5 rr 27.47 29.85mmrm 119.36° 122.4rmrm 119.29 122.3 CH2

mmrr 119.45 122.5 «32.6 «34.3rmrr 119.36 122.4 both almost unresolvedmrrm 119.00° 122.0mrrr 119.09° 122.1rrrr 119.18 122.2

"Some further fine structure is visible.

and syn-axial S shift parameter of —2.84 ppm. The fits are fairly good, althoughthey underrepresent the fine structure in the CN region. The favoured conforma-tions are in reasonable agreement with those deduced by Ganster and Lochmann[11] for 2,4-dicyanopentane in vacuo.

Similar calculations were then performed for poly(vinyl alcohol). They areshown as sticks, below the aqueous spectrum, in Figure 3.2. Here the sample iscomplicated by incomplete removal of acetate groups. However, the removal was>90%, and so the dominant peaks in the spectrum are those of fully hydrolysedregions. The effects of distant groups were once again small. The assignments inDMSO are published [12]: those in water were assigned largely by analogy,although the methylene data were sufficiently different to require some confirma-tion via homo- and heteronuclear shift correlation experiments. The calculated

Figure 3.2 100.6MHz 13C(1H) NMR spectrum of poly(vinyl alcohol); CH and CH2regions. Calculated shifts (with atactic weightings) are shown as sticks below, in the sameorder of assignment

RIS parameters (Table 3.3) show that H-bonding, even in water, is sufficient toovercome some of the steric repulsions, including those associated with the 1,5pentane effect, between 5yw-axial chain segments.

One possible flaw in the poly(vinyl alcohol) calculations is that the shifts mightalso be directly and differentially affected by H-bonding. However, an indepen-dent study of saccharides in water and in DMSO indicates that this is probablynot so. Another interesting feature is that, when the rotamers that were calculatedto be dominant were reset to be totally dominant, then the CH shift pattern was

CH CH2

Table 3.3 Calculated RIS statistical weight parameters"

<5(CH2)/ppm*vg g+/g+g9 9tg+fg+ttg'lg'tttT

+ 0.07

+ 0.20

-0.01

+ 0.32

-0.06

-0.77

-0.22

-0.19

+ 1.12

0.22

0.41

0.40

0.78

0.75

0*

0.07

0.00

0.00

00.94

01.04

00.96

7.510.93

0.230

02.91

00

00

00.87

00

1.790.51

0.650.51

00

00

00

00

00

00

00.08

00.41

00.12

0.401.55

0.692.71

0.010

0.391.26

0.35

0.370.16

10

10

10

00

00

10

0.280.36

0.310

10

00

00

00

01

01

00

10

0.02

0.410

0

0.08

01

10.22

0.18

0

0.01

1.01

0.041

391K

373 K

300K

295 K

295 K

363 K

363 K

300K

393 K

polypropylene

m-dyadr-dyadpoly(acrylonitrile) in DMSO

m-dyadr-dyadpoly(acrylonitrile) in water

m-dyad/NaSCNr-dyadpoly(vinyl alcohol) in water

m-dyadr-dyadpoly(vinyl alcohol) in DMSO

m-dyadr-dyadpolystyrene

m-dyadr-dyadpoly(methylacrylonitrile)

m-dyadr-dyadpoly(methyl methacrylate)

m-dyadr-dyadpoly(vinyl chloride)

m-dyadr-dyadag* and g defined as in Flory [5].bg~g+/g+g~ links across the chiral carbons were also completely forbidden in this case.

essentially magnified by a factor of « 3 . It then fitted quite well with thesolid-state data of Terao et al. [13], who obtain a CH shift spread of «10 ppm.Tonelli (Chapter 2) has interpreted solid-state polypropylene shifts in a similarway, based on structures deduced by Bunn et al. [14].

Poly(acrylonrtrile) in DMSO

Poly(acrylonitrile) in water/NaSCN

Poly(vinyl alcohol) in water

Poly(vlnyl alcohol) In DMSO

Figure 3 3 {Continued)

Polypropylene

Polystyrene

Poly(methyiacrylonrtrlle)

Poly(methyl methacrylate)

Figure 3.3 (a),(b) Upper traces: 13C(1H) NMR spectra for eight different polymersolutions, calculated at the tetrad/pentad level. Lower traces: observed shifts, simplified tothe same level, and further, to broad Lorentzian peaks of representative width, if overlapsprevent assignment. The numbers are shifts in ppm

The shift parameter for OH did not converge well, however, perhaps because ofthe unusual number of accessible conformations and the presence of only twotypes of carbon atom. Values ranging from O to — 5ppm gave acceptablepredictions of the observed shifts. To resolve this problem, we instead used anindependent and strongly convergent value of — 3.5 ppm, obtained from anextensive study of hexopyranose sugars of known conformation in both waterand DMSO [15]. This value is lower than that for H, which may help to explainthe otherwise curious observations by Stothers and coworkers [16, 17] ons>w-axial shifts in sterols and related compounds.

The other monosubstituted vinyl polymer to be studied in detail was polysty-rene. Its spectrum is made complex in the methylene region by large shiftinfluences at the hexad/heptad level. These probably arise from the anisotropicbulk of the phenyl rings. Our calculations are certainly naive in ignoring thisanisotropy. The methylene region may speculatively be divided into four broadsubsections, approximate assignments of which were checked by the classicalarea method. Our assignments confirm those of Sato etal. [18]. The un-protonated phenyl carbon shifts are more easily assigned by the same method.The shift calculations were only successful if all gg links across the chiral carbonswere fully disallowed. They then gave a broadly reasonable but less than perfectfit. Although this restrictive possibility was also investigated for other polymers,it only gave useful results in this case. The phenyl shift constant converged well, to—4.58 ppm.

The next polymer, poly(methylacrylonitrile), presented a more severe test inthat there were no remaining variable shift parameters, and also one furtherresonance region to be fitted. An initial assignment was made following Inoueet al. [19], but with a spectrum taken at higher frequency, and with the methylenesub-areas rechecked. The fit is encouraging although not perfect.

Finally, it proved possible to obtain an acceptable fit for poly(methyl methac-rylate) using a carbomethoxy shift parameter of —9.50 ppm. This shift was notvery well defined by the data, although it must certainly be large. (When it waspermitted to float freely in the minimisation, it drifted upward to ^ — 14 ppm,but with only a very minor resulting improvement in the least-squares fit.) If theconformations that we calculate to have highest probability are instead set to bedominant, then the syndiotactic chain becomes all-trans, as observed in the solidstate by Speracek et al. [20], and a 4-8.14 ppm shift increment is predicted ongoing from the syndiotactic to the isotactic polymer. The experimental figure isbetween + 6.0 and + 8.45 ppm.

The fits are all presented in diagrammatic form in Figure 3.3(a) and (b).Calculated relative shifts are plotted upright, with a standard Lorentzianlineshape and with intensities that assume a strictly atactic sample. The verticallyinverted plots are idealisations of the experimental spectra. Broad Lorentzianbands are used to depict the extent of any overlapped and hence unassignedresonances. The order of assignment of the resolved peaks, calculated and

observed, is the same in every case expect for the fine structure in the COOMeand CH3 (mr) resonances of poly(methyl methacrylate). The same fits could notbe approximated for any of the polymers by any alternative and significantlydifferent set of minimised RIS parameters. Fits (not shown) have also beensuccessfully generated for poly(vinyl chloride). In this case the experimental stericshifts for both carbon types varied by % 2 ppm. The worst methylene fitting errorwas 0.11 ppm. The Cl shift parameter minimised to —4.01 ppm, and the m-methylene shift factor was unusually large, at 1.12 ppm.

3-5 THE CALCULATED RIS PARAMETERS

The complete set of calculated RIS parameters is presented in Table 3.3, andsome of the conformations that are calculated to be dominant are depicted inFigure 3.4. Those for polypropylene confirm the simple predictions that thedominant conformations are the four where no carbon is syn-axial to any othercarbon, and that the methylene groups have a very similar bulk to the methyls.However, those for poly(acrylonitrile) deviate markedly from this. Although itremains true that the CN groups, like the methyls in polypropylene, resist beingmutually syw-axial, this may be seen from simple modelling to result fromunfavourable dipolar alignment rather than from steric interactions. Also, thepossibility exists that some other mutual orientations of CN groups may besufficiently favoured, for the same reason, to override concomitant but lessfavourable steric interactions, e.g. between CN and the chain methylenes. Suchdipolar interactions are very hard to model independently because of thedifficulty of defining the local dielectric medium. It is interesting to note that, inthe unusually polar solvent D2O/Na+[SCN]", the RIS term tt(m) is decreasedyet further with respect to that in DMSO solvent. This term involves syw-axialCN groups. Evidently their polar repulsion is increased by the very polar solvent,perhaps because the cations polarise the CN groups further while being stericallyunable to interpose themselves.

The opposite behaviour is evident in poly(vinyl alcohol). The m-dyad showsa marked preference for the tt and g~g~ conformations (see Figure 3.4) over themore normal tg* and g+t. The tt and g~g" conformations both involve closenessof the OH groups, created presumably by H-bonding, and sufficient to overcomesteric repulsions in the latter case. The same pattern holds for the r-dyad. The tg ~and g~ t conformations are now the ones with syn-axial hydroxyls, and these areagain favoured along with the unexpected g~g~ conformer, possibly in a ratherdistorted form so as to permit another H-bond. The only big effect of changingthe solvent from DMSO to water is a large increase in the g+g+(m) term. Perhapswater is able to enhance the intramolecular H-bonding that is sterically possiblefrom this conformation.

Figure 3.4 Some typical dominant dyad conformations

The calculations for polystyrene are discussed above, and should be regardedwith caution. They do, however, yield sensible RIS parameters, which are likethose for polypropylene, except for larger repulsions between phenyl and H thanbetween methyl and H. In contrast, poly(vinyl chloride) is intermediate betweenpolystyrene and polypropylene, although in this case a tendency is also evidentfor neighbouring C-Cl bonds to lie approximately antiparallel, perhaps fordipolar reasons.

poly(acrylonitrile)

m-diad. gg* rotamer

poly(methyl methacrylate)

m-diad. tt rotamer

poly(acrylonitrile)

m-diad, tg* rotamer

poly(vinyl alcohol)

r-diad, tg rotamer

poly(vinyl alcohol)m-diad. tt rotamerpoly(acrylonitrile)

r-diad, tt rotamer

The parameters for poly(methylacrylonitrile) are less easy to anticipate, be-cause most conformations will involve either steric or dipolar repulsions. Themost likely conformations will be g+f(m), tg+(m), tt(r) and g+g+(r), because thesealone allow the CN groups to lie syw-axial to other groups, and not to themselves.The CN group has less steric bulk than, say, methyl. The calculations bear outthis prediction, although they do to some extent also permit one conformer,g ~g ~(m), in which neighbouring CN groups are syn-axial.

Not surprisingly, for the reasons discussed above, the fit for poly(methylmethacrylate) has the biggest error sum of the present series. Nevertheless, the fitis acceptable given the approximations, which in this case include ignoring thecarboxymethyl orientations. Once again, there is a preference for the fourconformers as above, because the carboxymethyl group also has a low steric bulkin some orientations. However, the fit also shows a marginal preference for the ttstate in the m dyad, consistently with the solid-state data noted above [20]. Thiswill no doubt be made possible by a favourable mutual orientation of thecarbonyl dipoles.

3.6 'P-GAUCHE9EFFECTS

The experimental evidence for y-gauche shifts [3] may also point to concomitantshifts of the two carbons that connect the y-gauche groups, as marked inFigure 3.1. These 'fi-gauche' shifts seem to be of the same sign as the y-gaucheones, but of approximately half the magnitude. Unfortunately, because they aresmaller, they are less easy to quantify. We have experimented with the inclusion offt-gauche shifts in our model, with values half those for the correspondingy-gauche shifts. They do not affect the qualitative conclusions above for anypolymer, and the fits are generally a little less satisfactory in each case. Thus,although such shifts probably do occur, it is not necessary to include them at thepresent level of approximation.

3.7 COUPLING CONSTANTS

In principle, it is also possible to use interpf oton coupling data in monovinylpolymers to assess the conformational equilibria. For such calculations one needsnot only the weightings for the conformations but also their torsional angles, anda reasonable estimate of the appropriate Karplus relationship [21] between theHCCH dihedral angle and the corresponding coupling. In practice, it is not easyto separate the peak splittings due to couplings from those arising from tacticity.In some cases, and for some components, the separation can be achieved by a 2D./-resolved spectrum [22]. In favourable case this procedure may also provide anassignment, because the methylene protons in an r-dyad will be at least approxi-

Figure 3.5 Partial 2D ./-resolved 1H NMR spectrum of poly(acrylonitrile) in DMSOd6. The multiplets are effectively rotated into thevertical dimension. The large peak at 3.06 ppm arises from water, and the uneven ridge marked x is partly an artefact

ppm

CH CH2

Table 3.4 Coupling constants

polypropylene 3J(obs)/Hz 7.0 and 6.5 (m) 7.0 (r)3J(calc)/Hz 7.34 and 7.25 (m) 7.13 (r)

poly(acrylonitrile) in DMSO 3J(obs)/Hz 8.4 and 6.0 (m) 7.5 (r)V(calc)/Hz 8.16 and 5.85 (m) 7.32 (r)

mately isochronic. Figure 3.5 shows an example of such data for poly(acrylonit-rile) in DMSO. The couplings are compared with calculated values in Table 3.4,along with those for polypropylene, which have been deduced from the spectra ofoligomers. However, the calculated values are not very sensitive to conformation,and their absolute values depend on what allowance one makes for librationwithin each RI state when setting the t and g couplings for individual vicinalproton pairs. The present study uses 12.0 Hz (t) and 2.0 Hz (#, polypropylene) or4.0Hz (g, poly(acrylonitrile)).

3.8 CHARACTERISTICRATIOS

One may in principle check RIS calculations [5] by the measurement ofcharacteristic ratios <r2>0/n/2, particularly as a function of tacticity. However,such correlations present several problems. The published experimental data arelimited in extent and show significant scatter. Also, the calculations requirea good estimate of the chain torsion angles in each conformer. Nevertheless, somecomparisons are possible, because in vacuo modelling calculations are likely togive reasonably accurate torsion angles even when their predictions of energy aresuspect. We have used our RIS data together with published torsion angles tocalculate the characteristic ratios for polypropylene at various temperatures inthe solution state. Table 3.5 shows that they agree well with the experimental data[23]. Earlier calculations tended to fit poorly at the extremes of tacticity, perhapsbecause they underestimated the contribution of minor conformations. Thecalculations were performed using the Biosym RIS package, with a 200-unitchain and randomised tacticity.

Table 3.5 Characteristic ratios for polypropylene

Calculated ratio Observed ratio Earlier estimates

syndiotactic 7.6(320K) 6.7(318K) 11.0(413K)atactic 5.4(435K) 5.4(426K) 5.5(415K)

6.3(305K) 6.5(307K)isotactic 5.3 (420 K) 5.0(456 K) 4.2 (413 K)

5.4(400K) 5.9(398K)

syndiotactic atactic isotactic

Figure 3.6 Observed (squares) and calculated (lines) characteristic ratios for poly(methylmethacrylate) at 333 K, plotted as a function of tacticity. The lines are based on RI stateswith chain dihedral angles of (upper line) 10,20,100,115, - 1 0 0 and -115°, (central,broken line) 10,20,100,125, - 1 0 0 and -125°, (lower, hatched line) 15,20,100,110, - 1 0 0and-110°

Calculations were also performed for poly(methyl methacrylate). These weremore complex, because modelling shows each RI state to be markedly doubledbecause of syw-axial interactions. Also, the calculated torsion angles were lessreliable than above. We approached this problem by dividing each RI state intotorsionally close pairs in the calculation, and assuming equal probabilities foreach member of a pair. In particular, this permitted some twist in a chaindominated by tt states. Calculations are presented in Figure 3.6 for threereasonable choices of torsional angle sets. The comparison with experiment [24]is encouraging. However, characteristic ratios alone are not a sensitive test of RISweightings, for many combinations of weightings will give similar results.

3,9 CONCLUSIONS

Although there is no guarantee that our simple model will be capable ofpredicting the shifts observed for any given polymer, the present fits are en-couraging. They were undertaken, in part, to assess the validity of the y-gaucheshift model. It is likely that ab initio calculations will soon be able to refine thismodel. Indeed, the work of Barfield and Yamamura [4] suggests that unusualshifts may arise in rather specific conformations over a narrow range of torsionangles. These may help to explain the rather unexpected shifts sometimesobserved in the solid state, but they are less likely to be a problem in the morewidely averaged local environments of the fluid state. One may therefore

reasonably propose that the present model generates relative RIS parameters forthe fluid state that are of genuine predictive value.

3.10 ACKNOWLEDGEMENT

We thank Dr. CJ. Samuel for many helpful discussions.

3.11 REFERENCES

[1] D. Dalling and D.M. Grant, J. Am. Chem. Soc, 1967,89, 6612.[2] D.M. Grant and B.V. Cheyney, J. Am. Chem. Soc, 1967,89,5315.[3] H.-J. Schneider and V. Hoppen, J. Org. Chem., 1978,43, 3866.[4] M. Barfield and S.H. Yamamura, J. Am. Chem. Soc, 1990,112,4747.[5] PJ. Flory, Macromolecules, 1974, 7, 381.[6] A.E. Tonelli and F.C. Schilling, Ace Chem. Res., 1981,14, 235.[7] A.E. Tonelli, Macromolecules, 1991, 24, 3065.[8] PJ. Flory, P.R. Sundararajan and L.C. DeBoIt, J. Am. Chem. Soc, 1974,96, 5015.[9] F.C. Schilling and A.E. Tonelli, Macromolecules, 1980,13, 270.

[10] J. Schaefer, Macromolecules, 1971,4,105.[11] J. Ganster and J.R. Lochmann, Polymer, 1990,31,1159.[12] T.K. Wu and M.L. Sheer, Macromolecules, 1977,10, 529.[13] T. Terao, S. Maeda and A. Saika, Macromolecules, 1983,16,1535.[14] A. Bunn, E.A. Cudby, R.K. Harris, KJ. Packer and BJ. Say, J. Chem. Soc,Chem.

Commun., 1981,15.[15] P. Hobley and O.W. Howarth, to be published.[16] W.A. Ayer, L.M. Browne, S. Fung and J.B. Stothers, Can. J. Chem., 1976,54, 3272.[17] S.H. Grover, J.P. Guthrie, J.B. Stothers and CT. Tan, J. Magn. Reson., 1973,10,227.[18] H. Sato, Y. Tanaka and K. Hatada, Makromol. Chem. Rapid. Commun., 1982,3,19.[19] Y. Inoue, K. Koyama, R. Chujo and A. Nishioka, Makromol. Chem., 1974,175,277.[20] J. Spevacek, B. Schneider and J. Straka, Macromolecules, 1990, 23, 3042.[21] J. Kowalewski, Prog. NMR Spectrosc, 1977,11,1.[22] W.P. Aue, E. Bartholdi and R.R. Ernst, J. Chem. Phys., 1976,65,4226.[23] W.W. Suter and PJ. Flory, Macromolecules, 1975,8, 765.[24] P.R. Sundararajan, Macromolecules, 1986,19, 415.

4 NMRSTUDIESOFSOLIDPOLYMERS

R. K. HARRISDepartment of Chemistry and IRC in Polymer Science and Technology, Universityof Durham, South Road, Durham DHl 3LE, UK

4.1 INTRODUCTION

It is the intention in this chapter to present an overview of some major aspects ofNMR studies of solid polymers and to give some examples of applications. It willalso provide the background to the more sophisticated multi-dimensional solid-state NMR techniques discussed in Chapter 5.

NMR studies of solids can be generally grouped into three types: (a) broadlinespectra; (b) relaxation times; and (c) high-resolution spectra.

Of course, spin-spin (transverse) relaxation directly affects the observed signal(free induction decay) from pulsed NMR operation, which is Fourier transformedto yield the spectrum, so that the three areas are not totally distinct. This articlewill address all three aspects but will only relate to 1H, 19F and 13C NMR. Inparticular, there will be no discussion of 2H spectra of polymers, importantthough that topic is. In suitable circumstances other spin- \ nuclei such as 15N,29Si and 31P can be relevant, and they will behave much like 13C.

Following the discovery of the NMR phenomenon in 1945 by two groups ofphysicists [1,2] NMR was applied to a wide range of systems, both solids andsolutions. However, it rapidly became obvious that solution-state NMR wasexceptionally useful to chemists because the high resolution achieved (withlinewidths for 1H less than 1 Hz) allowed small but important effects (i.e. chemicalshifts and splittings due to coupling constants) to be observed. Solid-state NMRbecame for a while the esoteric preserve of a few hardy physicists and physicalchemists. This situation became even more apparent after the introduction of theFourier transform principle made high-quality 13C spectra obtainable.

The reason for the relative neglect of solid-state NMR in the period 1955-1975is apparent from Figure 4.1. Although it is clear that there is some usefulinformation [3] (as the stereoregularity affects the spectrum), the resonances are% 50 kHz in width, with no fine structure. AU information on chemical shifts andcoupling constants appears to be lost. The reason for such a disappointing


Figure 4.1 200MHz proton NMR spectrum of solid isotactic polypropene: A, highstereoregularity sample; B, low stereoregularity sample

situation is that all NMR interaction of importance (especially shielding, dipolarcoupling and indirect coupling) depend on the orientation of the local nuclearenvironment in the applied magnetic field B0. In mobile isotropic liquids orsolutions the effects are averaged. The average dipolar coupling is zero, so it iseliminated from solution-state spectra; each active nucleus has an intrinsicshielding constant and each nuclear pair a single coupling constant. In solids,there is usually relatively little motion. Moreover, most samples (except singlecrystals) have a complete range of molecular orientations in the magnetic field.Both these factors lead to substantial line-broadening.

4.2 THE TECHNIQUES

Fortunately, a series of techniques can be used to overcome the problems. Themost ubiquitous is magic-angle spinning (M AS) [4], which consists of rotatingthe sample rapidly about an axis making an angle of 54.7° to B0 (Figure 4.2). Inprinciple this removes all the relevant anisotropies in most circumstances,yielding spectra comparable with those of solutions. Unfortunately, it is notnormally possible to spin fast enough (up to 50OkHz would be required forextreme cases such as protons in rigid CH2 groups). Additional techniques aretherefore required. For the observation of dilute spins (such as 13C) in thepresence of abundant spins (such as 1H), high-power heteronuclear decoupling(HPHD) is necessary. Combined with MAS, this yields 13C spectra withlinewidths as low as a few Hz in favourable cases (but at least an order ofmagnitude larger for polymers). However, HPHD is not applicable to the direct

Figure 4.3 The WAHUHA pulse sequence [5] used for homonuclear decoupling insolids. AU pulse angles are 90°. The r.f. phases are indicated above them. The middle fourpulses illustrated form the repeat unit of the sequence, s marks a sampling point

observation of abundant spins. Special pulse sequences, using phase-alternated90° pulses interspersed with single-point measurements, are used instead. Fig-ure 4.3 shows the repeat unit of the simplest such sequence [5], known asWAHUHA. When a suitable sequence is combined with MAS at modest speeds(«5kHz), anisotropic effects are removed. This combination of techniques isknown as CRAMPS (combined rotation and multiple pulse spectroscopy) [6].Multiple-pulse techniques of the WAHUHA type are also of value for protonhomonuclear dipolar decoupling in experiments where other nuclei, such as 13C,are observed under either static or MAS conditions.

An additional problem, especially for dilute spin- \ nuclei, is that relaxationtimes in solids can be very long. Consequently normal pulse Fourier transformNMR, which requires delays between pulses of about five times T1, becomes veryinefficient. However, a clever double-resonance pulse regime [7] known ascross-polarisation (CP) overcomes this difficulty; see Figure 4.4. During thecontact time, magnetisation flows from protons to carbons provided that theradiofrequency powers are matched, enhancing the signal by a factor of « 4 andallowing repetition times to depend on T1 (

1H) rather than T1 (13C), the former

being generally substantially shorter than the latter. The first example of theCP/HPHD/MAS combination of techniques [8] sparked an explosion of re-search activity, and polymer chemistry has been one of the principal beneficiaries.Figure 4.5 shows the influence of the HPHD and MAS techniques in securing

Figure 4,2 The arrangement for magic-angle spinning(diagrammatic)

Figure 4.5 Cross-polarised 75 MHz 13C spectra of solid poly(methyl methacrylate): A,static, coupled; B, static, proton-decoupled; C, with MAS, coupled; D, with MAS, proton-decoupled

Figure 4.4 The cross-polarisation pulse sequence. The con-tact time (CT) is of the order of ms. DC designates decouple

Figure 4.6 22.6 MHz 13C CP/HPHD/MAS spectrum of bisphenol-A diglycidyl ether, I.The spinning sidebands of the aromatic peaks are shaded

line-narrowing and hence high resolution. The final linewidths are affected bya number of factors, but for polymers a major effect is the range of environmentsfrequently encountered for a given carbon atom when amorphous componentsare present.

Magic-angle spinning, to be fully effective, must be greater than the staticbandwidth of the spectrum—in practice for 13C under HPHD this means theshielding anisotropy. Otherwise additional peaks, known as spinning sidebands,appear in the spectra as satellites around the isotropic resonances, as shown inFigure 4.6 for the monomer I. For many purposes, these are a nuisance, but in factthey contain extra information (on the tensor nature of shielding) and they can beused to extract such data. In other circumstances, spinning sidebands can be usedto obtain dipolar coupling constants and thence internuclear distances [9].

4.3 HIGH-RESOLUTION CARBON-13 NMROF POLYMERS

The CP/HPHD/M AS suite of techniques is ideal for the observation of 13Cspectra, which can then be used in the way traditional for solution-state NMR, i.e.to determine chemical structure. However, for solids the local environment ofa chemical group is usually rigid, and this introduces further considerations thataffect isotropic chemical shifts. These matters relate to crystallography (whereappropriate) or, more generally, to molecular packing. The emphasis may be

Figure 4.8 A, 22.6 MHz *3C CP/HPHD/MAS spectrum of isotactic polypropene [H];B, projection of the crystal structure for the a form of isotactic polypropene [13]. Thecentral pair of chains have oppositely handed helices

Figure 4.7 A, 22.6MHz 13C CP/HPHD/M AS spectrum of syndiotactic polypropene[10]; B, projection of the helical chain in the crystal structure of syndiotactic polypropene[12]

either intramolecular or intermolecular. A well-attested example is polypropene.Figures 4.7 and 4.8 show 13C spectra [10,11] and structural arrangements [12,13] for the syndiotactic and isotactic forms respectively. The doubling of the CH2

signal for the former can be readily seen to be a consequence of the curious helicalnature of the chains, which leaves all the CH carbons in equivalent positions butresults in two different types of CH2 carbons—an intramolecular effect. Thespectrum for isotactic polypropene, on the other hand, shows small, apparently2:1 splittings of both CH2 and CH3 carbon signals. These can be attributed to thepairing of the polymer chains in the crystalline domains—an mtermolecular effect.

Such spectra can be used to examine the effects at the molecular level ofpolymer processing. Thus, Figure 4.9 shows part of the spectra [14] of annealedand quenched forms of a block copolymer of nylon-6 and a polyether-containingpolyesteramide (H) with n«9 . The linking unit R is phenylene, and O — Orepresents a polyether component with both ethene oxide and propene oxide

Similarly 13C NMR can be used to study polymer degradation. Figure 4.10(A)shows part of the spectrum [15] of a complex cross-linked system containingblocks of a random copolymer of styrene, methyl methacrylate and maleicanhydride, together with cross-linking blocks formed from a polyester-tippedwith a /?-hydroxyamine (IV). Figure 4.1OB is of the polymer degraded under moistconditions. Comparison of the spectra shows that there is substantial loss of all

III

IV

units. Only aliphatic nylon signals are shown in Figure 4.9, with the carbon-numbering scheme given in III. It is clear that the annealed material gives a muchsimpler spectrum than the quenched one. AU the resonances in the former can beattributed to the a-crystalline form, whereas additional peaks from both y-crystalline and amorphous forms appear in the latter.

II

Figure 4.9 Resolution-enhanced 50.3 MHz 13C CP/HPHD/MAS spectra of a nylon-6/20% (polyether/polyesteramide) (II) copolymer (CH2 nylon signals only) [14]; A,annealed sample; B, quenched sample

Figure 4.10 50.3 MHz13C CP/HPHD/MAS spectra of a cross-linked copolymer (see thetext) [15]. A, as synthesized; B, after degradation. The asterisks indicate methylene signalsof the polyester moiety

polyester CH2 signals, indicating complete excision of polyester chains (with orwithout internal break-up) and therefore showing that hydrolysis occurs at thehydroxyamine ends.

4.4 PROTON SPIN RELAXATION

For heterogeneous materials, 13C CPMAS spectra cannot be properly under-stood without a knowledge of proton relaxation times, which are also of intrinsicimportance because of their relation to mobility at the molecular level and todomain structure. Three types of relaxation that need to be considered are:

• Spin-lattice (longitudinal) relaxation This refers to magnetisation parallel toB0, is characterised by a time T1, involves spin energy, requires motion at theresonance frequency (i.e. hundreds of MHz) and is relatively easily averaged byspin diffusion.

• Spin-lattice relaxation in the rotationframe This refers to magnetisation alongthe radiofrequency magnetic field JJ1, is characterised by a time T1 p, requiresmotion at a frequency related to the strength of B1 (i.e. tens of kHz) and issomewhat more difficult to average by spin diffusion than T1.

• Spin-spin (transverse) relaxation This refers to magnetisation perpendicular toB0 (in the absence of B1), involves spin phase-coherence (entropy), requiresonly very low-frequency motion, is not averaged by spin diffusion, and isdirectly related to the NMR signal (free induction decay).

Whereas T1 and T1 p are normally exponential or multi-exponential, transverserelaxation for solids takes a more complicated mathematical form (see below), therelevant time constant usually being given the symbol T2. For relatively rigidsolid polymers, T1, T lp and T2 are normally of the order of s, ms and /isrespectively. Since relaxation times are related to mobility, temperature andphase strongly influence the observed values. The phenomenon of spin diffusionmentioned above is a crucial ingredient of relaxation phenomena in heterogen-eous systems such as polymers. It describes transfer of spin polarisation throughspace without atomic movement, and is caused by the pairwise "flip-flop" term ofthe dipolar interaction (see Figure 4.11), which itself depends on the inverse cubepower of internuclear distances. It is efficient only in homonuclear situations,when little or no energy is required, and thus is particularly important forabundant spins such as 1H. It will cause averaging of some relaxation characteris-tics between domains in solid polymers when the sizes are small. For lamellarmorphology the factor L2DTT is involved, where L = lamellar semi-thickness,D = spin diffusion coefficient and Tx is the relevant relaxation time. Averaging ofrelaxation occurs when L 2 « DTx. This occurs for domain sizes much less thana few tens of A for T1 p, or much less than a few hundreds of A for T1. Informationon spin diffusion can be obtained in principle by the Goldman-Shen pulse

Figure 4.12 The Goldman-Shen pulse sequence [16] for the study of spin diffusion: A,short mixing time; B, long mixing time. All pulse angles are 90°. The r.f. phases areindicated above the pulses. The signal after the initial 90° pulse shows both rapidlyrelaxing and slowly relaxing components. The terms prep, evol and det refer to thepreparation, evolution and detection periods respectively

sequence [16] (Figure 4.12) which prepares the magnetisation of a system of twodomains, A and B say, such that the one with a short T2 (A, say) is zeroed. Thenthe remaining magnetisation is put back into the z direction, where it canequilibrate with B by spin diffusion during an evolution (mixing) time, after whichthe system is monitored. Unfortunately, quantitative interpretation of the resultsis complicated by spin-lattice relaxation during the mixing time.

prep evol det

A

B

Figure 4.11 Spin diffusion by the flip-flop process (dia-grammatic). Letters a-d represent successive situations,with e and f indicating later cases

Figure 4.13 Experimental (300 MHz) and computer-simulated plots [17] for T1 p ofPVC. The y axis is the natural logarithm of the normalised signal height followingspin-locking for a time t. The deviation from the upper straight line is plotted at the bottomleft to give the short-time component

Frequently polymer heterogeneity can be monitored by measurement of Tlp.Figure 4.13 shows experimental and computer-fitted plots [17] of spin-latticerelaxation in the rotating frame for a sample of PVC. The decay curve can besatisfactorily fitted by two exponentials, giving 72% with T1 p = 8.8 ms and 28%with T l p = 1.5 ms. Whereas this properly indicates heterogeneity, showing thatthere are more-ordered and less-ordered domains which are greater than a fewtens of A, the effect of spin diffusion is to give the data a mixed character, meaningthat neither the proportions nor the times are necessarily the intrinsic values ofthe different domains.

In principle, free induction decays (and/or the spectra produced therefrom)should give better information on domain structure. In several ways it makesmore sense to analyse the free induction decays directly, rather than the trans-formed spectra. However, there is no universally accepted algorithm for suchanalysis, which is not surprising given the complexity of the situation forpolymeric systems. We have adopted a mix of three mathematical functions:

• Exponential (Lorentzian): S(t) = exp( — t/T2). This is well justified for highlymobile regions.

• Weibullian [18]: S(t) = exp[—(r/r2H with 1 < n ^ 2. Although this functionhas no particular justification in theory, it has the merit of varying with theexponent from pure Lorentzian (n = 1) to pure Gaussian (n = 2).

• Abragamian: S(f) = exp[ —(£/T2)2] (sin 2nbt)/2nbt. Such a function was pro-

posed by Abragam [19] as an approximation of the CaF2 19F decay. It

t/ms

InS

Figure 4.14 60 MHz free induction decays for: A, nylon-6; and B, copolymer of nylon-6and 20% polyether/polyesteramide II (see the text) [14]. The ordinate is signal intensity onan arbitrary scale

Table 4.1 Free induction decay analysis of samples of nylon-6 and its copolymer

containing 20% of the unit II

Nylon-6 Copolymer

Population/% Time/us Population/% Time/us

Exponential 5 64 22 367Abragamian 95 18° 78 18fl

a The value of b is 21000 and 20000 for the nylon-6 and copolymer respectively.

represents a rectangular distribution of Gaussians, and its value lies partly inthe fact that it can yield a small oscillation such as is to be expected when thereare relatively isolated spin pairs such as CH2 groups.

Figure 4.14 shows free induction decays [14] for nylon-6 and the copolymercontaining 20% of the unit II. A small initial oscillation is apparent in each case,and the long-time component in Figure 4.14B is obvious. Table 4.1 shows theresults of the analysis. The small amount of the exponential for pure nylon-6probably relates to additives in the commercial sample. The time constants of thetwo domains are an order of magnitude different, showing the considerabledegree of motional heterogeneity. The proportion of the copolymer which decaysslowly clearly reflects the content of II. Of course, for more complete information,other NMR experiments, both 1H and 13C, must be performed and the resultscollated. For copolymer systems deuterated in one component, the phase bound-aries can be probed by attempting to cross-polarise from the protons in thesecond component.

4.5 DISCRIMINATION IN CARBON-13 SPECTRA

Proton relaxation data allow the NMR spectroscopist both to interpret 13CCPMAS spectra and to devise discriminating experiments [20]. One such

t/ms t/ms

sign

al

sig

nal

BA

Figure 4.15. Cross-polarisation dynamics for 50.3 MHz 13C spectra of a copolymer ofnylon-6 and 40% polyether/polyesteramide (see the text) [14]; variation of peak heightS with contact time CT: A, nylon-6-carbons (diamonds indicate the C4/C5 peak, squaresare for C2, and circles are for Cl, see III); B, polyether carbons (the symbols are for thepeaks at the following chemical shifts: triangles 18.2 ppm, circles 75.8 ppm, squares73.9 ppm, diamonds 71.2 ppm). S is expressed relative to the peak height of the mostintense signal, extrapolated to zero CT. A theoretical curve is shown for Cl in A

experiment is variation of the contact time. During the contact time of the CPprocess, transfer of polarisation will reach a maximum because of the competingeffects of creating equilibrium between the 1H and 13C spin baths and the loss ofproton magnetisation to the "lattice" by spin-lattice relaxation in the rotatingframe. When there are domains differing substantially in T1^1H), the optimumcontact time for each domain will also differ. Indeed, it is possible to measure (atconsiderable cost of spectrometer time) values of T1^1H) selectively for different13C peaks by variation of the contact time, as shown [14] in Figure 4.15. In thecase illustrated, long contact times will clearly favour the polyether carbons. In

CT/ms

l°9io

S

B

CT/ms

lo9io

S

A

Figure 4.16 Discrimination by contact time for PVC plasticised by 180pph of di-2-ethylhexyl phthalate [17]. 300 MHz* 3C CP/HPHD/M AS spectra: A, contact time 200 /is;B, contact time 5 ms. The broad peaks arise from PVC and the sharp ones from theplasticiser

such circumstances quantitative measurement of relative signal intensities can beobtained only by extrapolation of the decay curves under long contact to theirintercepts at zero contact time. Figure 4.16 shows discriminating spectra fora different polymer situation: PVC plasticised by di-2-ethylhexyl phthalate [17].The PVC itself is mostly rigid, cross-polarises efficiently but has a short asso-ciated T1^(1H). Hence a short contact time reveals PVC peaks strongly. Theplasticiser, on the other hand, is mostly very mobile, cross-polarises badly but isinfluenced by a long T1^

1H). It therefore gives intense peaks only at long contacttimes.

A second discriminating pair of experiments consists of comparinga CP/HPHD/MAS spectrum with one obtained without cross-polarisation(sometimes referred to as single-pulse excitation, SPE). Whereas the formerdepends on proton relaxation, the latter is affected only by carbon relaxation. SPEspectra are likely to be strongly influenced by carbon peaks with short T1(

13C),usually in relatively mobile parts of the sample, or, if recycle delays betweenpulses are long, by all the carbons. Figure 4.17 gives an example [14] for thenylon-6 copolymer containing 20% of II. Whereas the CP spectrum showsmostly signals from crystalline nylon domains, the SPE spectrum is dominatedby peaks from the polyether moieties and from amorphous esteramide or nylonregions. SPE spectra can yield quantitative relative intensities of signals if recycledelays are long enough. However, nuclear Overhauser effects can cause compli-cations if the duty cycle of the decoupler is significant.

A B

Figure 4.17 200 MHz * 3C MAS spectra of a copolymer of nylon-6 and 20% polyether/polyester-amide II (see the text) [14]: A, SPE/HPHD mode with recycle delay 5 s; B,CP/HPHD mode with contact time 1 ms and recycle delay 2 s. The broad peaks in A arisefrom amorphous esteramide or nylon groups. The sharp peaks in A are from PEO or PPOgroups

4.6 SPECTRA OF ABUNDANT SPINS

As indicated earlier, for direct observation of 1H or 19F spectra of solids with highresolution, it is necessary to use the CRAMP pair of techniques [6]. As yet thesehave been underused in polymer NMR, partly because they are more demandingof the instrument electronics than CPMAS operation and partly because residuallinewidths, which are frequently several hundred Hz, give only moderate resol-ution for 1H, which has a relatively small chemical shift range. However,CRAMPS is excellent for detecting strong hydrogen bonding, which gives protonsignals in the S = 10-20 region where there are seldom any other peaks. More-over, the potential for CRAMPS with 19F for polymers is high, as the shift rangeis large. Figure 4.18 gives a simple example [21], showing how information onchainênds can be readily derived. The figure also illustrates the appearance ofspinning sidebands. Comparison of Figures 4.18A and B indicates the way inwhich increasing rotational speed causes sidebands to move out from thecentrebands and to weaken. This allows the centrebands to be obtained unam-biguously.

A B

Figure 4.18 188.3MHz 19F CRAMP spectra of PTFE samples [21]: A and B, short-chain polymer (^C20F42); C, long-chain polymer. The spinning speeds were A 2.6 kHz;B 5.1 kHz, and C 2.5 kHz. The arrows in B indicate signals from chain ends. The asterisksdenote spinning sidebands

47 CONCLUSION

The scope for application of NMR to solid polymers is very wide. Information onchemical microstructure, micromorphology and molecular-level dynamics isavailable. It is important to undertake studies comprehensively using both 13Cand 1H nuclei, with measurements of both spectra and relaxation times. Variousexperiments are available for the selective examination of heterogeneous systems.More sophisticated methods are also feasible, as is discussed in Chapter 5

4.8 ACKNOWLEDGEMENTS

I am grateful to colleagues whose results are mentioned in this article and whosenames are given in the references. I particularly thank S. Friebel, S-W. Tsui and

A

B

C

A.F. Johnson for the collaboration in hitherto-unpublished work, resulting inFigures 4.9,4.14,4.15 and 4.17.1 also thank the UK S.E.R.C. for financial supportunder grants GR/E 91110 and GR/H 30175 and for allocations of time on theSolid-state NMR Service sited at Durham.

4.9 REFERENCES

[1] E.M. Purcell, H.C. Torrey and R.V. Pound, Phys. Rev., 1946,69, 37.[2] F. Bloch, W.W. Hansen and M.E. Packard, Phys. Rev., 1946,69,127.[3] P.W.R. Smith, Ph.D. Thesis, University of East Anglia, 1986. See also IJ. Colquhoun

and KJ. Packer, Br. Polym. J., 1987,19,151.[4] For a review, see E.R. Andrew, Int. Rev. Phys. Chem., 1981,1,195.[5] J.S. Waugh, L.M. Huber and U. Haeberlen, Phys. Rev. Lett., 1968,20,180.[6] L.M. Ryan, R.E. Taylor, AJ. Paff and B.C. Gerstein, J. Chem. Phys., 1980, 72, 508.[7] A. Pines, M.G. Gibby and J.S. Waugh, J. Chem. Phys., 1973,59, 569.[8] J. Schaefer and E.O. Stejskal, J. Am. Chem. Soc, 1976,98,1031.[9] J. Schaefer, E.O. Stejskal, R.A. McKay and W.T. Dixon, Macromolecules, 1984,17,

1479.[10] A. Bunn, M.E.A. Cudby, R.K. Harris, KJ. Packer and BJ. Say, J. Chem. Soc, Chem.

Commun., 1981, 15.[11] A. Bunn, M.E.A. Cudby, R.K. Harris, KJ. Packer and BJ. Say, Polymer, 1982, 23,

694.[12] P. Corradini, G. Natta, P. Ganis and P.A. Temussi, / . Polym. Sci. C, 1967,16,2477.[13] G. Natta and P. Corradini, Nuovo Cim., 1960,15 (Suppl), 40.[14] S. Friebel, R.K. Harris, S.-W. Tsui and A.F. Johnson, ubpublished work.[15] A. Findlay, Ph.D. Thesis, University of Durham, 1991.[16] M. Goldman and L. Shen, Phys. Rev., 1966,144, 321.[17] M.I.B. Tavares, R.K. Harris and E.E.C. Monteiro, unpublished work.[18] S. Kaufman and DJ. Bunger, J. Magn. Reson., 1970,3, 218.[19] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, Oxford,

1961, p. 120.[20] R.S. Aujla, R.K. Harris, KJ. Packer, M. Parameswaran and BJ. Say, Polym. Bull.,

1982,8, 253.[21] R.K. Harris and P. Jackson, Chem. Rev., 1991,91,1427.

5 MULTIDIMENSIONALSOLID-STATE NMR OFPOLYMERS

H. W. SPIESSMax-Planck-Institut fur Polymerforschung, Postfach 3148, D-55021 Mainz,Germany

5.1 INTRODUCTION

One of the key goals of materials science is the establishment of structure-property relationships in order to improve known properties and to permit thedesign of new materials. This holds in particular for synthetic polymers, whoseproperties depend on both the molecular structure and the organization of themacromolecules in the solid state: their phase structure, morphology, molecularorder and their molecular dynamics [1, 2]. Both macroscopic and microscopicparameters are influenced by the processing that follows the chemical synthesis.This calls for powerful analytical tools that can probe these aspects in thematerial as it is used predominantly in the solid state. The structural aspects arestudied mostly by scattering techniques or by microscopy. Information aboutdynamic aspects is deduced mainly from scattering or relaxation experiments [3].Among these nuclear magnetic resonance (NMR) [4,5] is well established for thestructural characterization of liquids or compounds in solution, but much less sofor solids [6, 7]. Indeed, NMR offers numerous ways to study dynamic aspectsover a large range of characteristic rates. The main advantage of NMR is itsunprecedented selectivity. It is thus desirable to develop this technique forstudying the structure and dynamics of solid polymers [8]. However, owing tothe presence of angular-dependent anisotropic interactions, the spectral resol-ution of solid-state NMR spectra is orders of magnitude lower than that of highresolution NMR in liquids. Important improvements were achieved in the 1970'sby combining high-speed mechanical rotation of the sample with ingeniousmanipulations of the nuclear spins, such as multiple-pulse irradiation, high-power decoupling and cross polarization [9]. Moreover, two-dimensional (andhigher) NMR techniques have been introduced that offer fundamental advan-tages [10]. First, as in liquids, the introduction of a new frequency dimensionprovides a means of increasing the spectral resolution. Even more important,

Polymer Spectroscopy. Edited by Allan H. Fawcett© 19% John Wiley & Sons Ltd

multidimensional spectroscopy also provides routes to new information that isunavailable from one-dimensional spectra even in the limit of high resolution.Experiments can be designed which correlate different spin interactions provid-ing different structural information, or relate various states taken up by themolecular unit during different time periods by exchange, and in this way toprobe dynamic processes in real time.

Progress in multidimensional solid-state NMR has been hampered by experi-mental and conceptual difficulties, but these are now overcome [11-14]. Thischapter briefly outlines some of the main concepts and illustrates the informationavailable from multidimensional solid-state NMR spectra concerning polymerstructure and dynamics through experimental examples selected from theauthor's laboratory.

Polymer dynamics is of central interest in our studies. Of the great variety ofmolecular motions possible in polymers (e.g., translations, rotation, vibrations),rotations have the most pronounced effects of NMR lineshapes and relaxationparameters.Thus, multidimensional NMR provides essentially unique informationabout rotational motions. Their timescales may be followed in real time overmany orders of magnitude, covering in particular that regime of slow motionswhich govern the mechanical properties of polymers. Moreover, the higher-ordercorrelation functions provided by multidimensional NMR yield previouslyinaccessible model-independent information about the geometry of rotationalmotions, the orientational memory of molecular units involved in complexdynamics, and the nature of nonexponential relaxation in disordered systems.When the information has been collected for a variety of polymers, it shouldeventually lead to a better understanding of their mechanical and rheologicalbehavior, which is of interest not only for conventional but also for new advancedpolymeric materials.

Two other aspects are particularly important for establishing structure-property relationships for polymer materials, namely chain alignment in partiallyordered systems and domain sizes in heterogeneous polymer materials. Theorientation of macromolecular units is used to improve the properties of poly-mers for such diverse applications as high-tensile-strength fibres and nonlinearoptical materials for information technology. Advanced polymer materials al-most inevitably consist of more than one component, which often leads to phaseseparation. Careful design of the molar ratios as well as the size, composition andmorphology of the different phases offers a means to control the mechanical,electrical and optical properties. Small domains that extend over only a fewnanometers, and also interfacial regions between the different phases, are particu-larly difficult to characterize. Major advances have been achieved in these areasby introducing the concepts of multidimensional spectroscopy. The new solid-state NMR techniques nicely supplement well-established scattering and micro-scopic methods, as we demonstrate by various experimental examples and byexplicit comparison.

5.2 MULTIDIMENSIONALSOLID-STATENMR SPECTRA

Solid-state NMR exploits anisotropic, angular-dependent interactions of nuclearspins with their surroundings [4, 5], in particular magnetic dipole-dipolecoupling of nuclei among themselves. This leads to broad NMR lines covering«50 kHz for 1H- 1H homonuclear coupling and «25 kHz for 1H-1 3C hetero-nuclear coupling. The anisotropy of the chemical shift results in powder patternsocvering «15 kHz at a field strength of 7 T. In addition to these magneticinteractions, nuclei with spin / > 1/2 can also have electric quadrupole moments,and are subject to quadrupole coupling to the electric field gradient at the nuclearsite. For 2H ( /= 1) in C-2H bonds this leads to spectral splittings of «250 kHz.Since C-H bonds are common in polymers, 2H labeling is particularly useful.

If one of the above mentioned couplings dominates, either because of itsstrength, or because the others have been suppressed by decoupling, the angulardependence of the NMR frequency in high magnetic fields is alike for allcouplings, and is given by:

a) = coL + ±A(3cos2O- I - rjsin20cos2(t)) (1)

Here coL is the Larmor frequency, A describes the strength of the anisotropiccoupling: i.e. the anisotropic chemical shift or x 3 C - l H dipole-dipole coupling for13C and the quadrupole coupling for 2H, and rj is the asymmetry parameterdescribing the deviation of the anisotropic coupling from axial symmetry(O ̂ Y] ^ 1). The angles 0, <f> are the polar angles of the magnetic field B 0 in thethe principal axes system of the coupling tensor. This in turn is often simplyrelated to the molecular geometry; i.e. the unique axis being along a bonddirection, e.g. dipole-dipole coupling: 1 3C-1H bond, quadrupole coupling:C-2H bond, or perpendicular to an sp2 plane as for 13C chemical shift tensors inaromatic rings etc. Depending on the total spin involved, signals described byEquation (1) and their mirror images with respect to coL may be superimposed,and in powder samples the spectra for all orientations are added to yield thepowder lineshape (e.g., the Pake pattern for 2H with spin / = 1).

Details of the experiments designed to record multidimensional NMR spectraare not given here, as ample literature exists on the subject [10-13] and anextended monograph is available [14]. However, basis knowledge of solid-stateNMR, as in Chapter 4, and of the concept of two-dimensional (2D) Fourierspectroscopy, is needed to read this chapter. A 2D NMR spectrum is generated byrecording a two-dimensional data set following pulsed irradiation as a function oftwo time variables, as shown schematically in Figure 5.1, and subsequent doubleFourier transformation. The development of the nuclear spin system in theevolution period with incremented time tx at the beginning of the pulse sequenceprovides the basis for the first frequency dimension Co1. The NMR signal isdetected in the detection period with time 12 at the end of the pulse sequence,

Figure 5.1 Time scheme of two-dimensional NMR [11]

providing the basis for the second frequency dimension co2. In the exchangeexperiments described here, a variable mixing period of duration tm, during whichdynamic processes can take place, is inserted between evolution and detection.The concept of 2D spectroscopy is readily extended to three and higher dimen-sions by inserting additional evolution and mixing times.

5.3 EXAMPLES

5.3.1 INCREASE OF SPECTRAL RESOLUTION

Let us first consider experiments which increase the spectral resolution of solidstate NMR spectra in order to characterize polymer structure in terms of chemicalmoieties on the basis of isotropic chemical shifts. This represents the mostimportant feature of standard NMR techniques, and makes up one or twodimensions of many multidimensional experiments in which the chemical struc-ture is correlated with other molecular properties such as mobility or order. In thesolid state, the tensorial nature of the chemical shift makes the NMR frequencyalso depend on the orientation of the molecular unit under study with respect tothe applied magnetic field of the NMR spectrometer, cf. Equation (1). Since theorientational dependence of the NMR frequency is comparable with or evenlarger than the variation of the isotropic chemical shifts of different structuralunits, the powder patterns resulting from the anisotropic chemical shifts overlapseverely in all but the simplest polymer structures. Thus, in many cases a quanti-tative analysis is virtually impossible. The effect of the anisotropy can be removedby rapidly spinning the sample about an axis inclined at the "magic angle" of54.7° (magic angle spinning, MAS). However, this is accompanied by a loss of theinformation about the molecular orientation, which is the basis of structural anddynamic information typical of the solid state. Thus, experiments are desired thatretain this information without sacrificing spectral resolution.

For moderate spinning speeds in the range of a few kHz, the anisotropicchemical shift is not "spun out", but leads to sideband patterns, from which theanisotropies can be retrieved [15, 16]. However, in complex polymer structures

preparation evolution mixing detection

Figure 5.2 Separation of isotropic and anisotropic chemical shifts: (a) 13C MAS spec-trum of an ether sulfone oligomer showing severe overlap of sidebands; (b) 2D 13Csideband MAS spectrum of the same compound showing resolved sidebands [18]

the sideband patterns overlap heavily and hamper a quantitative analysis. Byingenious spin manipulations through multiple-pulse sequences, these sidebandpatterns can be removed from the spectrum in one dimension and retained in theother [17, 18]. As shown in Figure 5.2, the crowded sideband patterns ofamorphous polymers can be nicely resolved in a second frequency dimension andcan then be exploited to provide structural and dynamic information.

5.3.2 SEPARATED LOCAL FIELD NMR

The dipole-dipole coupling, for instance between 1H and 13C, or 1H and 15N,provides valuable structural information. As the C-H bond lengths are known,the measurements of dipolar splittings can be interpreted in terms of anglesbetween individual bonds and the applied magnetic fields. For proteins, measure-ments of N-H bond lengths are of considerable interest, as they vary due tohydrogen bonding and therefore contain important structural information. Inorder to be useful, however, the dipolar patterns have to be separated accordingto the chemically distinct sites in a molecule or monomer unit as identified bytheir 13C or 15N chemical shits. As the dipolar couplings correspond to localfields, such experiments are often named "separated local field" (SLF) experi-ments [19]. Different schemes have been developed based on sample spinning[20, 21]. If the polymer contains only carbons with a common chemical shift,static techniques can be used [10]. As an example, Figure 5.3(a) displays the 13C

Figure 53 Separated local field spectroscopy correlating heteronuclear dipole-dipole coupling with chemical shifts: (a) ID * 3Q1H spectrum of highly oriented poly(oxy-methylene) (POM) with its order axis inclined at 30° with respect to the magnetic field[22]; (b) orientation of chemical shift tensor deduced from this spectrum (principal axesmarked by <rn, <r22, <r33) relative to local POM structure

chemical ShIfV13C-1H dipolar powder pattern for oriented poly(oxymethylene)(POM) [22]. From a quantitative analysis of such patterns, bond lengths andbond angles can be determined, as well as the orientations of the principal axes ofthe chemical-shift tensor in relation to structural units such as CH2 groups,Figure 5.3(b). Such information is needed for a quantitative analysis of otherexperiments exploiting anisotropic chemical shifts.

5.3.3 WIDELINE SEPARATION EXPERIMENTS

Multidimensional NMR provides especially interesting information about poly-mer dynamics. A long-standing method for qualitative characterization of mol-ecular mobility is 1H wideline NMR spectroscopy. There, large-amplitudemotions are detected through the reduction of the dipolar line width. However,ID proton lineshapes leave many questions open, as they typically representsuperpositions of broad and narrow lines, and their relation to different struc-tural units is often not obvious. In a straightforward combination of 1H widelineNMR, cross polarization (CP) and 13C MAS spectroscopy in a 2D experiment[23], it is possible to separate the dipolar patterns for the different structural units(Wideline SEparation, WISE). This is demonstrated in Figure 5.4, where a WISE

Figure 5.4 2D WISE NMR specrating 1H wideline spectra for different structural unitsaccording to their 13C chemical shifts: (a) conventional 1H wideline spectrum of a blend ofpoly(styrene) (PS) and poly(vinylmethylether) (PVME); (b) 2D 1H 13C WISE NMRspectrum indicating different mobilities of the two components [23]

NMR spectrum of a 50:50 wt% blend of poly(styrene) (PS) and poly(vinyl-methylether) (PVME) is presented. The 1H wideline spectrum, Figure 5.4(a),consists of a rather featureless superposition of Components with different dipolarlinewidths, which are nicely separated in the second frequency dimension (Fig-ure 5.4(b)) and related to structural units according to their 13C chemical shifts.Substantial motional heterogeneities, PVME being more mobile (narrower 1Hlines) than PS, are detected despite the fact that the spectrum is recorded about60 K above the caloric glass transition of this blend, which appears homogeneousby most classical techniques. Such information about the mobility of the differentstructural units is highly valuable for many practical applications.

5.3.4 2D and 3D EXCHANGE NMR

For a thorough understanding of the chain motions in polymers, qualitativeinformation provided by 1H wideline spectra is not sufficient. In order to relatechain motions to the structure of the polymer itself or to the packing of themacromolecular chains, one requires knowledge about the geometry of themotion, for example, the angles about which a molecular unit rotates duringindividual motional steps. This information, which is hard to get otherwise, isindeed provided by 2D exchange NMR as applied to rotational motions [12-14].In simple cases this technique yields elliptical ridge patterns from which the angleabout which the molecules have rotated can be directly read off with a ruler [24].As a specific example, Figure 5.5(a) displays such a 2H 2D exchange spectrum forpoly(vinylidene fluoride) (PVF2), a polymer of considerable technological inter-est because of its electrical properties. The geometric information from 2D NMR,together with knowledge of the dipole moment change generated by the motion,allowed us to identify the conformational change tgtg«—> gtgt of a chain defect asbeing responsible for the mechanical and dielectric relaxation in the crystallineregions of this polymer [25]. In a series of papers [26], 2D exchange NMR wasapplied to study the chain motion of amorphous polymers above their glasstransition.

For complex motions, even the information accessible by 2D techniques is notsufficient for an adequate description of the motional mechanisms involved inchain dynamics. This is due to the fact that in 2D NMR the orientation ofmolecules is measured only twice, in the evolution and in the detection periods.Therefore, no information is provided about the trajectory a molecular unitfollows when rotating from one orientation to another. In order to distinguishdifferent mechanisms one has to determine the molecular orientation at leastthree times. This is achieved in 3D exchange NMR. In a 3D exchange spectrum,as displayed in Figure 5.5(b) for natural abundance 13C in semicrystallinepoly(oxymethylene) (POM), different pathways pursued by the molecule lead todifferent exchange signals, which can therefore be clearly distinguished. From

Figure 5.5 Multidimensional exchange NMR spectra elucidating slow molecularmotions: (a) 2D 2H NMR spectrum of crystalline poly(vinylidene fluoride) reflecting chainmotions through defect diffusion [25]; (b) 3D 13C exchange spectrum of orientedpoly(oxymethylene) reflecting helical jumps in the crystalline regions [14]

analysis of such 3D spectra for different semicrystalline polymers, which pack inhelical conformations, helical jump motions have been identified in which thechain units rotate to neighboring positions and translate by one repeat unit [14].This process can eventually lead to chain diffusion between crystalline andamorphous regions with pronounced effects on the long-term mechanical prop-erties [27].

5.3.5 CHAIN ALIGNMENT FROM 2D A N D 3D NMR

Structural characterization of polymers often requires the determination of thealignment of macromolecular chains. Orientation in polymers is often induced bythe production process and has strong effects on product properties. Through theangular-dependent NMR interactions, orientation is amenable to measurementin NMR experiments. In contrast to most classical techniques, the order of bothcrystalline and amorphous components can be studied. For 2H- or 13C-enrichedsamples, one-dimensional experiments are sufficient to obtain orientation dis-tributions in terms of a single angle [28]. In order to reconstruct two-dimensionalorientation distributions, or to resolve overlapping patterns in natural-abun-dance 13C spectra, multidimensional spectra are required. Two examples arepresented in Figure 5.6. Both involve 3D spectra of 13C in natural abundance.

In the case of a biaxially drawn film of poly(ethylene terephthalate) (PET), theorientational distribution was mapped out by flipping the sample betweendifferent orientations with respect to the magnetic field (Direction Exchange withCorrelation for Orientation Distribution Evaluation and Reconstruction, DE-CODER) [29]. The NMR signals of the different structural units of PET arecompletely resolved in the 3D cube and their orientation distributions are thusseparately determined [30]. The chain axes are confined to the film plane(full-width-at-half-maximum,fwhm, of 15°), whereas the in-plane distribution ismuch broader (fwhm approx. 90°). The planes containing the phenylene rings andthe carboxyl group are oriented preferentially parallel to the plane of the film(fwhm of 55°). In the case of a liquid-crystalline side-group polymer (Fig-ure 5.6(b)), the extension to a third dimension is performed in order to achieve thenecessary spectral resolution [31]. Rotor-synchronized MAS is applied to mapout the degree of molecular order along Ox. The sidebands are separated by theirorder along o2 (see Figure 5.2), and the chemical structure is probed via theisotropic chemical shift along o3. Each dot in the 3D spectrum represents a singlesideband of a carbon position in the repeat unit with resolved 13C chemical shiftin the MAS spectrum. This allows the molecular order of relatively complexpolymers to be analyzed quantitatively even for liquid-crystalline polymers,where different moieties of the repeat unit exhibit substantially different degreesof alignment [32]. The specific example studied here is a frozen smectic polyac-rylate with a phenylbenzoate mesogenic side group and a spacer of six methylene

Figure 5.6 3D NMR spectra for determining molecular order: (a) 3D 13C DECODERNMR spectrum of biaxially drawn polyethylene terephthalate) [30]; (b) 3D 13C MASspectrum of a liquid-crystalline side-group polymer [31]

units. The 3D MAS NMR spectrum not only reveals a pronounced ordergradient from the aligned mesogen to the disordered polymer chain, it also showsthat the acrylic carbonyl group exhibits a much higher order than the hydrocar-bon units of the main chain. Because of its selectivity, high resolution solid-stateNMR is able to reveal that the carbon-carbon bond which links the acryliccarbonyl to the main chain plays a crucial role in the decoupling of the orderedside groups from the polymer chain [31].

5.3.6 DOMAIN SIZES FROM SPIN DIFFUSIONEXPERIMENTS

In heterogeneous polymers, domain sizes, or structures on the scale of up to a fewhundred nanometers, can be investigated. In NMR the proximity of molecularunits is probed by spin diffusion [4,14], which is most effective among protons.Thus, NMR is particularly suited for characterizing small domains, nano-heterogeneities or concentration fluctuations on length scales of a few nm, whereother methods often fail owing to liminations in resolution or contrast. Anadvanced approach exploiting 1H spin diffusion with highly sensitive 13Cdetection has been introduced recently [33, 34].

As a particularly clear-cut case, this technique has been applied to a series ofsymmetric diblock copolymers of PS and poly(methyl methacrylate), PMMA[34]. In Figure 5.7(a) the increase of the carbon signals of the phenyl ring in thePS block after selection of the PMMA block is plotted against the spin diffusiontime for various block lengths. The equal lengths of both blocks in the symmetriccopolymers ensures a lamellar structure which makes the quantitative analysis ofthe data easy. PMMA and PS are known to be immiscible. The spin diffusiondata yield domain sizes which are consistent with the scaling law Mn

0 66, whereMn denotes the molar mass of the blocks, as predicted theoretically [35]. Forcomparison, a statistical copolymer, in which no phase separation is possible, anda blend of both homopolymers were included in the data set. The close agreementbetween experimental intensities and the time dependence calculated from thediffusion equation is apparent in Figure 5.7(b) and demonstrates that domainsizes between 0.5 and 100 nm can be determined quantitatively. This techniquehas already been applied to a number of homogeneous and heterogeneouspolymer systems, in particular to block copolymers containing both mobile andrigid components affording detection of heterogeneities on a scale as small as2 nm in systems that exhibit a single Tg in differential scanning calorimetry [36].

5.3.7 SPATIALLY RESOLVED SOLID STATE NMR

Eventually one would like to obtain the information about molecular structureand dynamics accessible by solid-state NMR not just for the sample as a whole

Figure 5.7 Spin diffusion as a tool for determining domain sizes in heterogeneouspolymers [34]: (a) 13C MAS spectra of the symmetrical diblock copolymer PS-b-PMMAas a function of the diffusion time tm after selection of proton magnetization of the methoxygroup in PMMA; (b) signal intensity of the phenyl carbons in PS as function of tm fordifferent molecular weights. The numbers indicate domain sizes obtained from the fit

sign

al i

nten

sity

PS

tm1/2[ms"*]

(PMMA)

(PMMA)

ppm

toilms]

Figure 5.8 (a) Spatially resolved 2D 13C spectrum of an injection-molded drawn tensilebar of syndiotactic poly(propylene); (b) geometry of sample [37]

but with spatial resolution. For instance, one would like to distinguish themolecular parameters in regions close to the surface from those in the bulk. Infact, by applying pulsed magnetic field gradients, the concepts of multidimen-sional NMR can also be used to generate a spatial dimension in 2D spectrathrough Fourier imaging [10]; see also Chapter 6. As a first example, a spatiallyresolved 13C NMR spectrum of a drawn poly(propylene) sample is displayed inFigure 5.8 [37]. It reflects differences of density and chain alignment between skinand core due to the processing of the material, and demonstrates that spectro-scopic solid-state NMR imaging is indeed possible. This exciting field is still in itsinfancy and considerable progress is expected in the near future, as indicated ina recent book on the subject [38] which is based on lectures at an internationalconference.

5.4 CONCLUSION

As these examples indicate, a wealth of information about polymer structure anddynamics is available through advanced multidimensional solid-state NMRtechniques. Profound correlations between macroscopic and molecular behavior

are emerging from such studies. Examples are helical jumps or defect diffusion incrystallites, specific local motions in amorphous polymers and conformationaltransitions coupled to relaxations of larger chain units in highly viscous polymermelts. Such information has already been used successfully in the design ofpolymers with improved properties. Thus, it can be anticipated that the import-ance of multidimensional solid-state NMR as an advanced tool of polymerspectroscopy will increase substantially in the future.


It is a pleasure to thank my coworkers engaged in the work described here: Drs.B. Bliimich, B. Chmelka, J. Clauss, S. Feaux de Lacroix, E. Gunther, D. Schaefer,JJ. Titmann, M. Wilhelm and, in particular, Dr. K. Schmidt-Rohr.

5.6 REFERENCES

[1] PJ. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca,1953.

[2] J.I. Kroschwitz (Ed.), Concise Encyclopedia of Polymer Science and Technology, JohnWiley & Sons, New York, 1990.

[3] N.G. McCrum, B.E. Read and G. Williams, Anelastic and Dielectric Effects inPolymeric Solids, Dover Publishing, New York, 1967.

[4] A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, Oxford,1961.

[5] CP. Slichter, Principles of Magnetic Resonance, Springer-Verlag, Berlin, 1980.[6] F.A. Bovey, Nuclear Magnetic Resonance Spectroscopy, Academic Press, San Diego,

1988.[7] CA. Fyfe, Solid State NMR for Chemists, CF.C Press, Guelph, 1983.[8] R. A. Komoroski (Ed.), High Resolution NMR Spectroscopy of Synthetic Polymers in

Bulk, VCH, Deerfield Beach, FL, 1986.[9] M. Mehring, Principles of High Resolution NMR in Solids, Springer-Verlag, Berlin,

1983.[10] R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic

Resonance in One and Two Dimensions, Clarendon Press, Oxford, 1987.[11] B. Bliimich and H.W. Spiess, Angew. Chem. Int. Ed. EngL, 1988, 27,1655.[12] K. Schmidt-Rohr, A. Hagemeyer and H.W. Spiess, Adv. Magn. Reson., 1989,13, 85.[13] H.W. Spiess, Chem. Rev., 1991,91, 1321.[14] K. Schmidt-Rohr and H.W. Spiess, Multidimensional Solid-State NMR and Poly-

mers, Academic Press, London, 1994.[15] M.M. Maricq and J.S. Waugh, J. Chem. Phys., 1979, 70, 3300.[16] J. Herzfeld and A.H. Berger, J. Chem. Phys., 1980,73, 6021.[17] A.C. Kolbert and R.G. Griffin, Chem. Phys. Lett., 1990,166, 87.[18] S. Feaux de Lacroix, JJ. Titman, A. Hagemeyer and H.W. Spiess, J. Magn. Reson.,

1992,97,435.[19] J.S. Waugh, Proc. Natl. Acad. Sci. USA, 1976, 73, 1394.[20] T. Nakai, J. Ashida and T. Terao, J. Chem. Phys., 1988,88, 6049.

[21] J.E. Roberts, G.S. Harbison, M.G. Munowitz, J. Herzfeld and RG. Griffin, J. Am.Chem. Soc, 1987,109, 4163.

[22] K. Schmidt-Rohr, M. Wilhelm, A. Johansson and W. Spiess, Magn. Reson. Chem.,1993,31, 352.

[23] K. Schmidt-Rohr, J. Clauss and H.W. Spiess, Macromolecules, 1992,25, 3273.[24] C. Schmidt, S. Wefing, B. Blumich and H.W. Spiess, Chem. Phys. Lett., 1986,130,84.[25] J. Hirschinger, D. Schaefer, H.W. Spiess and AJ. Lovinger, Macromolecules, 1991,

24, 2428.[26] S. Wefing and H.W. Spiess, J. Chem. Phys., 1988,89,1219; S. Wefing, S. Kaufmann

and H.W. Spiess, Ibid., 1988,89,1234; S. Kaufmann, S. Wefing, D. Schaefer and H.W. Spiess, Ibid., 1990, 93, 197; D. Schaefer and H.W. Spiess, Ibid., 1992,97, 7944.

[27] K. Schmidt-Rohr and H.W. Spiess, Macromolecules, 1991,24, 5288.[28] H.W. Spiess, in LM. Ward (Ed.), Developments in Oriented Polymers, 1, Applied

Science, London, 1982, p. 44.[29] K. Schmidt-Rohr, M. Hehn, D. Schaefer and H.W. Spiess, J. Chem. Phys., 1992,97,

2247.[30] B.F. Chmelka, K. Schmidt-Rohr and H.W. Spiess, Macromolecules, 1993,26, 2282.[31] JJ . Titman, S. Feaux de Lacroix and H.W. Spiess, J. Chem. Phys., 1993, 98, 3816.[32] CB. McArdle (Ed.), Side Chain Liquid Crystal Polymers, Blackie, Glasgow, 1989.[33] K. Schmidt-Rohr, J. Clauss, B. Blumich and H. W. Spiess, Magn. Reson. Chem., 1990,

28, S3.[34] J. Clauss, K. Schmidt-Rohr and H.W. Spiess, Acta Polym., 1993,44, 1.[35] E. Helfand and Z.R. Wassermann, in I. Goodman (Ed.), Developments in Block

Copolymers, 1, Applied Science, London, 1982, Chapter 4.[36] W.Z. Cai, K. Schmidt-Rohr, N. Egger, B. Gerharz and H.W. Spiess, Polymer, 1993,

34, 267.[37] E. Gunther, B. Blumich and H.W. Spiess, Macromolecules, 1992, 25, 3315.[38] B. Blumich and W. Kuhn (Eds.), Magnetic Resonance Microscopy, VCH-Verlags-

gesellschaft, Weinheim, 1992.

6 NMRIMAGINGOFPOLYMERS

J. L. KOENIGThe J. Donnell Institute Professor, Departments of Macromolecular Science andChemistry, Case Western Reserve University, University Circle, Cleveland, OH44102-7202, USA

6.1 INTRODUCTION

Nuclear magnetic resonance imaging (NMRI) is a technique for measuringspatially resolved features of inhomogeneous samples. The technique has foundparticular utility in the medical field, where it is used for diagnosis based on thefact that the mobility of water in diseased tissue is different from that in normaltissue. However, in recent years, NMRI has found its way into the field ofmaterials, particularly polymers.

NMRI has the capability of measuring inhomogeneities in finished articles bya noninvasive and nondestructive method. Defect or nonuniform areas of thepolymeric materials will be clearly shown in the NMR image. NMRI may beconsidered as a type of chemical microscope and, as such, the concept transcendsany other methodology for generating images.

6.1.1 BASIS OF NMR IMAGING

Nuclear magnetic resonance (NMR) [1] is based on the fact that many atomicnuclei oscillate like tiny gyroscopes when in a magnetic field. In NMR, a sample isplaced in a magnetic field which forces the nuclei into alignment. The sample isthen bombarded with a radio wave. As the nuclei absorb the radio wave, theytopple out of alignment with the magnetic field. As they lose the absorbed energyfrom the radio wave, they line up again. By measuring the specific radiofrequencies that are emitted by the nuclei and the rate at which the realignmentoccurs, spectroscopists can obtain detailed information about the molecularstructure and motion of the sample they are studying.

Conventional NMR spectroscopy is used to determine chemical structure, as isdescribed in Chapter 4, but cannot locate the position of the stimulated nuclei.NMRI is a method where the stimulating signal is spatially encoded so that animage can be reconstructed showing the distribution of nuclei in the sample.


Other than spatially encoding the signal, imaging works on the same principles asstandard NMR.

The NMRI technique relies on the interaction of nuclei in only a small andcontrollable region of the sample by placing the sample in a spatially in-homogeneous magnetic field whose nuclear resonance frequency is matched tothe r.f. signal in only that region. NMR imaging is involved in obtaining thespatial distribution of all parameters that NMR can detect. The NMR signalsinherently depend on nuclear relaxation time constants T1 and T2, which in turnreflect the structural environment of the emitting nucleus. NMR is capable ofproviding information about molecular structure and motion; consequently,NMR imaging can provide a variety of structural factors measured in situ.

There are several ways of spatially encoding the NMR signal [I ] . One is toapply a linear magnetic field to the original static field (Figure 6.1). The purpose ofthe nonuniform field is to label, or encode, different regions of the sample linearlywith different NMR frequencies. As the magnetic field is varied in a knownmanner at specific positions within the sample, the frequency of the NMR signalindicates the spatial position of the resonating nuclei (Figure 6.1). In onedimension (D), the position of the sample is related to a frequency by the rela-tionship

Ao2 = O)2- (O0 = y G2Z9

where the magnetic field gradient G = dBJdz. A tailored r.f. pulse with a narrowfrequency range is used to excite only those nuclei at corresponding positions inthe z dimension. The amplitude of the NMR signal received from the z axis line isa measure of the number of resonant nuclei on that line, and so the NMRspectrum represents a graph of spin density versus distance (neglecting relaxationeffects). The field gradient is described by a tensor with nine components but, forlarge B, we need only be concerned with the three components Ga = BBJBOL,

where a = x, y, z.

Figure 6.1 Diagram of NMR imaging experiment

Fie

ld

Str

engt

h

Sample Position

In three dimensions, one operates in a three-dimensional gradient field. Thefrequency spectrum (still obtained by Fourier transforming the free inductiondecay, or FID) gives the number of resonating spins along a specific directionof the field gradient. In fact, each plane perpendicular to the direction of thefield gradient has a different resonance frequency, and the signal intensity atthat frequency will be proportional to the number of nuclei contained in thatplane. In other words, the frequency spectrum is just a projection of the spindensity (neglecting relaxation effects for the moment) along the field direc-tion.

6.1.2 RELAXATION PARAMETERS IN NMR IMAGING

The spin densities and the molecular environments of the nuclei are reflected inthe time variation of the amplitude of the measured r.f. signal, and hence arereflected in the intensity of each voxel in the image. (A voxel is the smallest volumethat the imaging process recognizes and presents.) When the values of T1 and T2

are different in the voxels of a heterogeneous sample, these differences can beexploited to develop contrast in the NMR images. The pulse sequence that isusually used to measure the T2 relaxation phenomena in images is called multiplespin-echo. At a given repetition time TR, the NMR signal is measured at severaldifferent echo times TE. These echoes provide a measure of the T2 relaxation. Byrepeating the process at different TR values, the T1 relaxation can also bemeasured.

Because differences in relaxation times and spin densities determine imagecontrast, data on relaxation times are important in the selection of the optimal r.f.pulse sequence for imaging a selected sample. Relaxation times can be measuredat any point on an image. The ability accurately to quantify relaxation rates isimportant in understanding and optimizing image contrast. Spin density, T1 andT2 images can be computed from measurements using pulse sequences withpredetermined variations [2]. These fundamental images represent the inherentdata in the system, and can be recombined to reconstitute computed images fora given pulse sequence.

Contrast in NMRI depends on both material-specific and operator-selectedparameters. The material-specific parameters include the spin density and therelaxation times T1 and T2. The operator-selected parameters include the pulsesequence (inversion recovery, spin-echo, etc.) and the pulse delay and repetitiontimes (timing parameters). For a given imaging system and pulse sequence, it isthe delay and repetition times in conjunction with the intrinsic material par-ameters which dictate the appearance of the final image. If the correct pulsesequence is employed and the relaxation times of the two materials are known, itis possible to calculate the delay and/or repetition times that will produce themaximum difference in signal intensity between those materials.

Figure 6.2 The timing diagram for a spin-echo imaging pulse sequence using a selective90° pulse

The spin-echo (SE) technique is the most common pulse sequence applied inMRI today [I]. Images are constructed by acquiring a multitude of projections(typically 256 per image) each with an identical setting of a readout gradientduring which the sequence is samples. Each projection is differentiated from theothers by a phase difference, which is produced by advancing the phase encodinggradient.

As shown in Figure 6.2, the spin-echo method consists of a series of r.f. pulseswhich are repeated many times in order to achieve a sufficient signal-to-noiseratio. Each projection is produced by a 90° pulse, followed by a 180° pulse forinduction of the spin-echo. The 90° r.f. pulse tips the magnetization into thexy plane, where it begins dephasing. The 180° r.f. pulse is applied after a timet, and forces the magnetization to refocus at a time It (also known as the echotime TE) after the 90° r.f. pulse, at which time the data is collected. The frequencyencoding gradient Gx causes the spins to precess at different frequencies de-pending on their position in the static magnetic field. The phase encodinggradient Gy is orthogonal to Gx. Varying the intensity of Gy causes the spinsto dephase at different rates, providing the second dimension of a two-dimen-sional image. The slice selection gradient G2, and the Gaussian-shaped 90°r.f. pulse determine the position and thickness of the region of interest. Thedata is Fourier transformed in two dimensions to produce the image of theselected slice. The time delay between the observation pulse and the observationis called the "echo time" (TE). The time between two consecutive pulse sequencesis labelled as the "repetition time" (TR), and usually ranges from 250 to2500 ms.

Spin-echo techniques have a unique position in NMR applications. The mainproblem with NMR imaging is the long data collection time, due mainly to thespin-lattice relaxation time T1. Each measurement necessitates a time period ofthe order of T1 (which is %0.5 s for aqueous systems) for the system to return to

equilibrium magnetization. By using spin-echo repetition, a large number ofspin-echoes can be repeated within a T1 or T2 decay period.

6.1.3 R E S O L U T I O N I N N M R I M A G I N G

Spatial resolution is limited by the smallest amount of sample that can bedetected by NMR. Spatially resolving a given volume in an NMR image isequivalent to doing NMR spectroscopy on that volume. To resolve two spatiallydistinct volume elements requires the application of a magnetic field gradient ofsufficient strength, such that the elements one wishes to resolve are shifted inresonance frequency from each other by an amount greater than the naturallinewidth. For a given magnetic field gradient strength, the spatial resolution inNMR imaging is determined by the linewidth [I]:

Ax = (O112ZyGx

where col/2 is the linewidth and G, is the gradient strength. For mobile liquids thelinewidths are very narrow, and high spatial resolution can be achieved. Thehighest resolution reached so far is 1Ox 1Ox 100 \im. This corresponds to anobservable volume element (voxel) of 10~5mm3. Routine measurements onliquids in solids typically have 40 x 40 x 100 ̂ m resolution.

The attainable resolution is limited by spectroscopic and hardware factors.Spectroscopic factors are the linewidth and the spread of the chemical shift of anNMR signal, diffusion processes and susceptibility gradients, both within theobject and at its boundaries. Hardware factors may be the magnetic fieldinhomogeneity or instability, nonlinearity of the magnetic gradient field and theachievable signal-to-noise ratio.

The difficulties of solid state imaging arise because the solid state linewidth is«1000 times its solution counterpart. Increasing the gradient by three or fourorders of magnitude to maintain spatial resolution in solids imaging is a formi-dable task, and much effort has gone into finding alternatives to such a brute forceapproach [3].

6.1.4 U T I L I T Y O F N M R I

NMRI is a means of detecting and imaging previously invisible material imper-fections in fabricated articles. Its potential applications in the field of polymericmaterials are many and diverse [4]. They include the detection and imaging ofsubsurface defects, including interfacial flaws and microcracks, and the detectionand characterization of areas modified through the introduction of foreignsubstances such as additives, degradation products, and contaminants.

The potential applications are exciting, including dynamic studies of compos-ites and other materials. The NMR imaging technique is a noninvasive monitor-

ing tool, so multiple measurements can be made on the same sample underdifferent conditions. No special sample preparation is required and this makespossible in situ studies of fabricated articles including the superposition of imagesobtained before and after application of stresses and exposure to environmentalfactors, including stress, fatigue, temperature and penetrants.

6.1.5 IMAGE PROCESSING

The underlying purpose of NMR imaging is to detect the presence or absence ofinhomogeneities in situ. By using computer enhancement techniques, it is possibleto compare a perfectly fabricated article with a modified piece, and in this mannerto concentrate on just what makes each test piece different from the ideal. Defectssuch as voids and inclusions are represented by very small image discontinuities.Using a technique called edge enhancement, it is possible for the computer tomake a numerical microshift of the image that has been stored in digital memoryand then display the result. This process can convert images to data for automaticdefect recognition. By putting the computer in the loop, we can employ averag-ing, smoothing and other forms of enhancement to let the computer make thequality decision after it has eliminated superfluous information. The computercan perform gray-scale scanning to detect any areas in the article that are imagingeither too lightly or to intensely. Either effect is a sign that bonding is not properon the fibers.

6.2 ADVANCED IMAGING TECHNIQUES

6.2.1 CHEMICAL SHIFT IMAGING

NMRI usually assumes that the spins (usually that of the protons of water)precess at the same frequency but, owing to chemical shift differences arising fromdifferent chemical types of protons in substances, some of the spins experienceslightly different local fields, and hence precess at different frequencies. The localfield change is written as 0H0, where H0 is the static field and a is the chemicalshift in parts per million (ppm). In imaging, the presence of two different types ofresonating nuclei can lead to overlapping images and artifacts as shown in Figure6.3. Figure 6.3 [5] shows the results of an image of xylene. Separate images aredue to the aromatic and methyl protons and they are separated by % 4.8 ppmfrom each other. Each individual image is centered at its resonant frequency inthe absence of a magnetic field gradient, and therefore the resulting image issmeared. As the read or frequency encoding gradient spreads out resonancefrequencies according to positions along the gradient direction, the observedimage actually consists of two or more partially overlapping sets of data (one

Figure 63 A cross-sectional chemical shift image of xylene in a vial. Separate images aredue to the aromatic and the methyl protons of xylene and are separated by 4.8 ppm fromeach other

corresponding to each type is nucleus). If the resonances are due to differentspecies, two or more different images will be obtained. If all resonances arise fromthe same molecule, they will have identical spatial distributions and images.

The usual imaging schemes apply a linear gradient G to frequency encode thedata. Applying an inverse Fourier transform maps the spin density as a functionof frequency linearly to spatial location. The linear relation between frequency(o and position x is:

co = yGx

where y is the gyromagnetic ratio for hydrogen. In a gradient free environment,the precessional frequency of the proton of a molecule a decreases by:

Ao>a = y<7a£0

This leads to a shift in the image position of the molecule a with respect to that ofthe protons of water by:

Axa = AcoJyGr

Consequently, the image of molecule a would overlap water in the region ofinterest and cause an artifact in the image, which might be incorrectly interpretedas actual spatial features. By increasing Gr, the pixel shift due to chemicaldifferences is reduced. However, much valuable information is contained in the

image if the chemical shifts can be sorted out correctly. It is possible to form animage from only a selected portion of the total NMR spectrum. This process iscalled chemical shift imaging.

A particular resonance peak can be selectively excited by r.f. irradiation to theexclusion of others in the chemical shift spectrum. A long, low-power, amplitude-shaped r.f. pulse can be used to excite a narrow range of resonant frequenciesdistributed about a particular frequency. Such a "soft" pulse is more frequency-sensitive than a short, square "hard" pulse.

High resolution NMR spectra displaying chemically shifted resonances pro-vide information on the chemical species present in the system and their relativeconcentrations. The magnetic resonance response can be simultaneously ob-tained from all regions of a heterogeneous sample by using a four-dimensionalFourier transform technique, where the high resolution spectrum obtainedduring the data acquisition defines one dimension and the other three dimensionsform a Cartesian coordinate system.

The application of various spatially resolved MRI techniques for the observa-tion of high resolution spectra has been limited. This is largely due to themutually exclusive requirements of both the highly homogeneous magneticfield which is necessary for the observation of chemical shift information, andthe inhomogeneous field which is applied as a linear magnetic field gradientand is necessary to obtain spatially resolved data. Chemical shift imagingtechniques use pulsed magnetic field gradients, which in the standard configur-ation of superconducting magnets generate sufficiently large eddy currents upongradient removal to temporarily degrade the field homogeneity. This is one of thereasons why the implementation of high resolution spatial spectroscopy isdifficult.

Currently, there are several approaches to the problem of the chemical shifteffects in NMRI. First of all, one may attempt to construct an image correspond-ing to a preselected chemical shift of a sample either locally or globally. Whendifferent chemical shifts originate from different chemical species, an image takenat a specific chemical shift will provide information on the spatial distribution ofthe corresponding species while excluding the interference of other species in theimage. A local method assumes knowledge of the chemical shift and usuallyproduces an image of the chemical species under consideration. The in-phase andout-of-phase experiments can be used for this purpose [6]. In addition, chemicalshift-selective suppression of an unwanted species or selective excitation of thespecies to be imaged [7, 8] and also a method based on chemical shift-specificslice selection [9] have been proposed as local methods. A global methodproduces essentially a chemical shift spectrum for each localized region orvolume element, and thus creates a stack of chemical shift images. A globaldeconvolution calculation technique has been proposed [10] utilizing a combi-nation of the Wiener filter and an anodization function. A method of convolutionhas also been suggested in which the image is deconvoluted by the NMR

spectrum of the sample [H] . This latter method shifts the image of eachindividual resonance such that it is centered about the carrier frequency. Nototally adequate method of suppressing the chemical shift artifacts has yet beendeveloped, but all of the methods improve the quality of the images when multiplechemical shifts are present.

On the other hand, chemical shift imaging is highly desirable. Selectiveexcitation chemical shift imaging is possible only if the spectrum of the sample isresolvable for the entire imaging volume. It has been suggested that chemicalshift-sensitve NMR images can be obtained using spectral simplification bytailoring the excitation pulses [12]. Chemical shift images have been reported fortwo rubbery polymers, polybutadiene and polydimethylsiloxane [13], and alsofor polyether polyol with an isocyanate curing agent [14].

6.3 APPLICATIONSOFNMRITOPOLYMERS

6.3.1 DETECTION OF VOIDS IN COMPOSITES

The void content of pultruded composite rods have been studied using NMRI[15]. Glass fiber-reinforced nylon rods with fiber contents of 51% by volumewere first mixed with different catalyst contents following the reaction injec-tion molding (RIM) process, and then pultruded with a pulling speed of 18 inchesper minute. Approximately 4% of the catalyst mixture, containing sodiumhydride and phenyl isocyanate, was used. The diameter of the die in the pultruderwas 0.90 cm. The rods were then soaked in water at 80 0C for 25 weeks beforeimaging. The uptake in water was 3.7%, as measured by the increase in weightof the composite rods. The images were recorded on a Bruker MSL 300 spectro-meter using a spine-echo pulse sequence. The slice thickness was 1.0 mm andthe slices were taken transverse to the fiber axis. With the rods standing in1.5 cm diameter vials containing water, the two images shown in Figure 6.4are taken 0.5 cm apart through the pultruded rod. The light areas in the imagerepresent void areas filled with water. The marker in the upper left hand portionof the image is 1 mm in diameter. Comparison of the sizes of the voids in thepultruded rod intidcates that some of the voids approach the magnitude ofthe marker. A comparison of the corresponding edge-enchanced images showthat some of the voids in the images occur in the same location, which indi-cates that the voids are connected or tubular in shape. Thus, a channel-likevoid region is suggested over a length of 0.5 cm. From the computer conparisonof the two images taken 0.5 cm apart, it is possible to identify a tubular shapedvoid running from one image to the other within the nylon rod. Such a voidcould be obtained if an air bubble was trapped in the matrix during the pul-trusion process. It appears that water diffuses by following the fabers in thecomposite.

Figure 6.4 Image of water in pultruded nylon rods reinforced with glass fibers and a contour plot of image showing the presence ofa tubular void

Image of water in pultruded nylonrods reinforced with glass fibers

Contour plot of image showingpresence of tubular void

6.3.2 DETECTION OF N O N U N I F O R M DISPERSIONOF FILLER

The improvement in mechanical properties by inorganic fillers is considerablyreduced if there is a nonuniform dispersion of particles in the polymer matrix byformation of agglomerates. NMRI can produce visual pictures of the spatialvariation of the organic phase distribution. This is accomplished by observing theproton images of the elastomers as a function of proton density and spin-spin, T2,relaxation times. These NMR parameters provide a measure of the molecularmobility, which in turn is related to the spatial variation of the polymer and thefiller in the sample.

Samples of poly(dimethylsiloxane) (PDMS) which were reinforced by in situprecipitated silica were examined by NMRI [16]. The images were obtained witha spin-echo technique, with a slice thickness of 500 |im and a digital resolution of185 urn, and required a time of 25.6 min. A dark rim was observed around thesample which indicated a reduced mobility of the network chains compared withthe sample core. This difference arises from the high concentration OfSiO2 in thisregion.

6.3.3 NMRI OF PHYSICAL AGING

NMRI has been used to study the physical aging of cross-linked cautchouc(vulcanized natural rubber filled with carbon) [17]. The nondestructive characterof NMRI provides a method to monitor various changes in the materialsproperties of a single sample rather than using the usual methods which destroythe sample during the analysis. A cylinder sample (5 mm diameter) of naturalrubber filled with carbon black was used. The sample was removed after eachmeasurement and aged for a predetermined period of time in a dry box at 130 0C.The samples were imaged using a conventional multiecho pulse sequence. Thegradient strength was 250mT/m and the spatial resolution was 80 x 80 nm witha slice thickness of 1 mm. The images revealed air bubbles resulting from themolding process. When the sample was aged, inhomogerieities of varying sizewere observed as dark spots with bright shadows around them. The shadowsarose from the difference in susceptibility of the inhomogeneities in comparisonwith the surrounding rubber. A ring in the aged surface layer was observed at theinterface of the unaged material in the interior of the sample. This ring may havearisen from the presence of stabilizers such as stearin or paraffin, which diffuse tothe reaction front.

The onset of aging in the natural rubber can be observed by NMRI after onlytwo hours. The thickness of the aged layer shows the asymptotic behaviorexpected for a radial protective film. If the aging reaction is modeled (for purposesof NMRI) as

U + O 2 - A

where U is the soft rubber reacting with oxygen at elevated temperature yieldinga hardened, aged rubber, A, in NMR terms the sample has only two possibleinternal states, i.e. soft and hard. These two states have two different T2 values,which are 5.8 ms for the unaged rubber and 0.3 ms for the aged portion. As therelaxation times are different by a order of magnitude, the first echo results onlyfrom the unaged rubber U and can be used to determine the concentration. Theconcentration dependence of the unaged rubber U on the aging time ra can beexpressed as

[U](O = [U0]exp(-/aa)

and then the amplitude of the echo becomes proportional to the concentration ofU, The inverse rate constant k~l is determined to be 8 h ± 30%.

6.3.4 NMRI STUDIES OF DIFFUSION IN POLYMERS

NMR imaging techniques has been used for the study of sorption and diffusionand of the desorption of multiple chemical substances in polymeric materials[18-28]. NMR imaging can directly provide the diffusion coefficients as a char-acteristic quantity of a liquid component in a sample, making it possible to mapmolecular migration on a microscopic scale. NMR imaging also providesadditional information on the microdynamic and structural properties of hetero-geneous systems, such as subregion diameters, exchange times, and phaseboundary resistances [29, 30].

The principal advantage of NMR imaging is the possibility of making spatiallylocalized diffusion measurements [30]. One can examine by NMR imaging theconcentration and location of a permeating liquid in a solid sample. A truediffusion parameter image is obtained, where calculated diffusion coefficients areencoded into an intensity scale.

One of the obvious advantages of NMR imaging for the study of diffusion is thevisual presentation of the data in the form of images. Such a presentation allowsone to view directly the concentration and location of the penetrant and to ignoreextraneous factors influencing the diffusion. Another advantage of NMR imagingis that it allows the study of samples of virtually any shape, and allows thedetection of initial imperfections in the sample being studied. It is generallydifficult to interpret liquid sorption measurements in solids because the samplesbeing examined are not perfect, that is, they initially contain cracks and voidswhich increase both the diffusion and the uptake of the liquid. Also, the inducedvolumetric changes, though small, can cause microcracking or void formation.

The NMR imaging technique also allows the system to be studied dynamically,as measurements can be made on the solid sample immersed in the penetrant. Themeasurements are rapid. Using the FLASH techniques [22], an image can beobtained in a few minutes. In this fashion, it is possible to study the dynamics of

the diffusion process. Of course, the sample-penetrant system can be studiedunder isothermal conditions.

Finally, a primary advantage of NMR imaging is the fact that all of the NMRparameters of the sample can be measured and used to interpret the diffusion orsorption process [30]. Images obtained utilizing different pulse sequences andinterrupt times can be used to calculate the spin-lattice T1 and spin-spin T2

relaxation times and the spin density. These additional parameters relate to thebonding and environment of the penetrant in the polymer system. These types ofmeasurements have been useful in understanding the morphological changeswhich are observed [22].

NMR imaging techniques have been used for the study of sorption, diffusionand chemical reactions as well as the desorption of chemical substances inpolymeric materials [23]. NMR imaging can directly provide the diffusioncoefficient as a characteristic quantity of the fluidity of a component in a sample,making it possible to map molecular migration on a microscopic scale.

The diffusion coefficients have been quantitatively evaluated from a series ofimages recorded with different gradient field strengths [22]. Analysis involved thesimulation of the effects of diffusion using the dynamic magnetization equationsto calculate the magnetization for each pixel, which ultimately yielded an imagewhose intensities represented the spatially resolved diffusion coefficients. Finally,a true diffusion constant image was obtained in which the calculated diffusioncoefficients were encoded into an intensity scale [22]. In this scale, high intensitiescorresponded to fast diffusion. In this manner, the spatial diffusion of a liquid intoa solid material was characterized in a quantitative fashion.

NMR imaging has been used for methanol diffusing into PMMA [22].Figure 6.5 shows the image from the PMMA in methanol after 48 h. The diffusioncoefficient can be calculated by measuring the thickness of the sorbed layer asa function of time. With data processing techniques, it is possible to simplify themeasurements by giving the images a three-level gray scale and then drawinga profile across the sample as shown in Figure 6.6. The results are shown in Figure6.7, where the thickness of the layer is plotted versus time. The linearity of thisplot with time confirms that case II diffusion is occurring. The nonzero interceptat time zero is indicative of an initial Fickian diffusion process followed by case IIdiffusion. The constant level of methanol in the penetrant front is also reflective ofcase II diffusion.

NMR relaxation parameters are useful probes of molecular motions in poly-mers. Each correlation time represents the average value of the system, with somedistribution around that average. NMR imaging permits the determination of thespatial distribution of NMR relaxation times. This distribution provides infor-mation concerning the local motions of the system. In this case, the polymer ispartially swollen with solvent, and the spatial distributions of relaxation timesreveal the interactions between the solvent and the polymer in the diffusionprocess.

Figure 6.6 The intensity profile of the image on the right side of Figure 6.5. The featuresare: (a) bulk methanol; (b) equilibrium methanol volume in PMMA; (c) sharp concentra-tion front; and (d) glassy PMMA. Reprinted with permission from John Wiley & Sons Inc.Journal of Polymer Science 1989

Acetone swells PMMA to a greater extent than methanol, and the self-diffusion coefficients of the system are about two orders of magnitude greaterthan those of the methanol/PMMA system. This is apparently due to theincreased volume available to the acetone molecules. The self-diffusion coeffi-cients decrease by 35% from equilibrium in the outer regions to the region nearthe glassy core. The decreasing motions of the polymer chains as the core is

Figure 6.5 The proton NMR image of a 30 mm PMMA sphere initially submersed inmethanol (left) and the image taken after 48 h of exposure to methanol at 30 0C. Reprintedwith permission from John Wiley & Sons Inc. Journal of Polymer Science 1989

Figure 6.7 The plot of diffusion distance measured with NMR imaging vs. exposure timefor the PMMA shere in methanol at 300C. Reprinted with permission from John Wiley& Sons Inc. Journal of Polymer Science 1989

approached reduce the solvent mobility, as reflected in the self-diffusion coeffi-cients [22].

6.3.5 DESORPTION OF LIQUIDS FROM POLYMERS

Desorption is one diffusion process that has been given little attention, primarilybecause of the lack of adequate analytical techniques. Desorption measurementsabove the glass transition temperature of an unswollen polymer are expected tofollow Fickian characteristics. Likewise, a polymer swollen so that the Tg is belowthe experimental temperature initially exhibits Fickian desorption. The solvent isthought to desorb rapidly from the surface of the polymer and raise the Tg of thesurface layer. After the surface T8 is above the experimental temperature,the desorption process slows, and the process is controlled by the diffusionthrough the glassy surface layer. NMR imaging provides the spatial distributionof solvent in the polymer and also the spatial distribution of the rate of desorption[23].

The desorption process can be related to Td, which is the inverse of the rate ofnet solvent loss for a given pixel through the equation:

M = M oexp(-exp7/7d )

A nonlinear least-squares fit of the experimental data is used to calculate a Td

image on a pixel-by-pixel basis [23].We have reported some results on the NMR imaging of the desorption process

[23]. Images of the desorption of methanol from swollen rods of PMMA wereobtained [23]. The methanol volume fraction was 0.26. The rods were thenplaced in fully deuterated cyclohexane. The first image acquisition began 6minafter initial submersion. Images were collected in Ih increments over a 104 hperiod. The signal intensity decreased with time, the maximum intensity of the

Time (hours)

Diff

usio

n di

stan

ce (

mm

)

Figure 6.8 A Td image calculated from 20 images at 5 h increments over a 100 h interval.Reprinted with permission from [22]. Copyright 1990 American Chemical Society

last image being only 50% of that of the initial image. The diameter of the roddecreases by 816 ±68 mm over the 10Oh period as measured from the images.

A Td image calculated from 20 images taken at 5 h intervals over 100 h is shownin Figure 6.8. In this image, the light portion represents the largest Td and darkrepresents the smallest T6, which corresponds to the slowest and the fastestintensity decreases, respectively. This image shows that the faster intensitydecreases are near the surface of the rod and the slower intensity decreases arenear the glassy PMMA core. The Td at the surface is 58 h and that at the glassy coreis 450 h, as determined from this image. This agrees with the Fickian characteris-tics, and indicates that imbibed solvent near the surface desorbs quickly, with thedesorption rate decreasing toward the sample core. However, for this systemthere is no evidence of a glassy skin developing on the polymer surface [23].

6.3.6 MULTICOMPONENT DIFFUSION AS STUDIEDBY NMRI

It is possible to use NMRI to study multicomponent diffusion in a number ofdifferent ways, utilizing differences in chemical shifts, relaxation times or byisotopic labeling. We have chosen the last method [26]. We studied the simulta-neous diffusion of acetone and methanol into polycarbonate by completelydeuterating one of the components and recording the images of the othercomponent in the PC. Using perdeuterated methanol (MeOH-J4) and acetone(AC), the FLASH images show the movement of the acetone diffusion frontwithin the PC rod. These images show that the 75:25 ACrMeOH-J4 mixturediffuses more rapidly than the 50:50 AC:MeOH-J4.

Perdeuterated acetone :hydroxy-deuterated methanol (AC-J6: MeOD) mix-tures of 75:25,65:35 and 50:50 volume ratios AC-J6: MeOD were also studied.From these images we can monitor the solvent front movement of acetone andmethanol into the PC rods. The movement of the solvent front of acetone into PCversus the square root of time is shown in Figure 6.9(a) for the 75:25,65:35 and50:50 AC .MeOH-J4 mixtures. The diffusion into PC increases as the acetonecontent of the mixture increases. In addition, there is a linear dependence betweenthe solvent front movement and the square root of time. This indicates that thediffusion of AC: MeOH-J4 into PC is Fickian [26]. This result was anticipated, asthe diffusion of both pure methanol' and pure acetone has previously beendetermined to be Fickian [33]. (Note, however, that the diffusion of pure acetonewas found to be Fickian after an initial period in which the diffusion was reportedto be anomalous [33]). This may seem contrary to what is usually found for thediffusion of solvent into a glassy polymer which is below its glass transitiontemperature Tr Instead, either case II or anomalous diffusion is most oftenencountered in this temperature region. This is because, below the Tg, the polymerchains are in the glassy state, and are therefore not mobile enough to accommo-date the solvent. In contrast, Fickian diffusion is prevalent above the 7̂ becausethe polymer chains are in the rubbery state and can therefore accommodate thesolvent more readily. Although the T% of dry PC is 149 0C, acetone and methanoldiffuse into PC in a Fickian manner because the 7̂ is reduced to « —9 0C by thesolvent ingress [31]. In this way, PC is able to relax and accommodate the solventalmost immediately, allowing the solvent movement not to be inhibited by therate of polymer relaxation.

The solvent front was also monitored for the AC-J6: MeOD mixtures. Forthe mixtures of 75:25,65:35 and 50:50 AC-J6: MeOD into PC, similar behaviorwas also seen in Figure 6.9(b), where the methyl resonance of methanol wasmonitored. There is an increase in the rate of the front movement as the ace-tone content increases, and also a linear dependence of the front movementwith the square root of time. This linear dependence indicates Fickian dif-fusion.

Square root time (h1/2)

Figure 6.9 Solvent front movement of (a) acetone into PC for the 75:25,65:35, and 50:50v/o AC/MeOH-^ mixtures and (b) methanol into PC for the 75:25,65:35, and 50:50 v/oAC-</6\MeOD mixtures versus the square root of time. Reprinted with permission from[26]. Copyright 1992 American Chemical Society

We were interested in determining whether the two solvent fronts move at thesame rates for a particular acetone to methanol ratio. Comparison of the rates ofthe solvent front movements of the 65:35 AC:MeOH-^4 and the 65:35 AC-d6:MeOD mixtures revealed that they were equal within experimental error.There is an overlapping of the front movement when plotted as a function ofsquare root of time. This indicates that acetone and methanol are diffusing jointlythrough the PC rod in a Fickian manner and do not appear to separate. Similar

Mill

imet

ers

Mill

imet

ers

Square root time (h1/2)

behavior is also found when comparing the 50:50 AC:MeOH-^4 and the 50:50AC-d6:MeOD mixtures.

It may be proposed that this joint diffusion through PC is the result of theformation of a weak "complex", possibly a weak hydrogen bonding interaction[22] between acetone and methanol. The 65:35 v/o AC:MeOH mixture hasapproximately a 1:1 molar ratio, and thereby all the acetone may be complexedwith methanol. This would account for the overlap of the front movement plotswithin error. In the 50:50 v/o AC:MeOH mixture, the molar ratio is « 35:65AC: MeOH. If all the acetone complexes with methanol, that leaves approximate-ly equal amounts of ACMeOH complex and free methanol which would diffusetogether. As shown by the 65:35 v/o AC:MeOH mixture diffusing at a greaterrate than the 50:50 v/o AC:MeOH mixture, the "complex" may have a greaterinteraction with PC than the free methanol would in the 50:50 v/o mixture. Thecomplex may be able to reduce the T% further than the free methanol, allowing anincreased rate of penetration of slovent.

6.3.7 ABSORPTION-DESORPTION CYCLING OF LIQUIDSIN POLYMERS

We have studied the absorption-desorption cycling of water and methanol intoand out of the PMMA rods to determine its effect on the diffusion characteristics.There is an increase in the rate of weight gain with cycling. The increase in the rateof weight gain becomes even more evident as the initial water content in PMMAincreases. This may be caused by the increased plasticization of PMMA by thewater for higher water contents followed by higher methanol contents. This mayhave created increased porosity within the PMMA as the solvent contents wereincreased.

A similar effect can be seen for the cyclic diffusion of methanol into water-soaked PMMA with water contents of 0.6 and 0.75 wt%. The percentage weightgain versus time of diffusion is linear with time except for an initial lag time, whichis anomalous. The lag time may be attributed to methanol desorbing a thin layerof water from the PMMA, which causes the layer to be in tension from theshrinkage back to the unswollen state. This descreases the mobility of thepolymer in this layer and makes the polymer less accommodating to methanoldiffusion [27].

For polymers which are in the glassy state, the removal of diluents or smallmolecules may cause an increase in sorption and mass transport properties of thepolymer [32]. It has been found that the removal of liquids from a polymer belowits Tg can increase the porosity within the polymer [32]. This would thereforeresult in an increase in the rate of diffusion of diluents such as water and MeOHinto PMMA. It should be noted that there was no reduction in dry weight witheach successive absorption-desorption cycle of water and MeOH, which would

indicate initially that unreacted monomer and other small molecules were notleaching out. This would also indicate that the initial drying was sufficient toremove unreacted monomers and other small molecules from the PMMA rods,and none were further released by the absorption-desorption of methanol andwater.

In a sense, this conditioning of the PMMA rods allows the uptake of increasedamounts of solvent with each successive cycle [33]. These increased uptakes maybe attributed to reduced packing or lack of reconsolidation when the solvent isremoved from the swollen polymer in the glassy sate [32,33]. It may be suggestedthat increases in uptake are due to an increase in free volume [33], although noincrease in dry volume was observed. It is possible that not all the methanol wasremoved in the drying process, and there may have been some loss of other lowmolecular weight materials, such as unreacted monomer, from the PMMAsample. It has been well established that it is difficult to remove solvents ormonomers from polymers [34]. The PMMA rods were kept in a vacuum at 60 0Cuntil no further weight loss was apparent.

It has been shown in previous experiments [32] that, when PMMA is exposedto solvents such as MeOH, unreacted monomer present within the material willleach out. It is expected that, after drying the polymer to remove the solvent thathas diffused into PMMA, the zero weight of the sample should decrease.However, the zero weight of the samples analyzed in this experiment remainedthe same. This indicates that not all of the methanol that diffused into the PMMAis removed during the drying periods between the absorption cycles.

In addition to using weight gain measurements to describe the effects of cyclingon the diffusion characteristics of water and methanol in PMMA, NMRI wasused to observe the solvent front movements within the PMMA rods [27]. Theproton NMR images were obtained for the diffusion of MeOD into threedifferent PMMA samples. These three samples had previously been subjected tono, one and two cycles of the absorption and desorptuon of MeOD. The FLASHimages were obtained, and show the movement of the MeOD diffusion frontwithin the PMMA rods after 5.92,18.75, 23.70 and 31.2Oh. The images showedthat the diffusion of MeOD increased with an increase in the number of cycles.This corresponded to our previous weight gain experiments. The rate of MeODdiffusion increased with cycling. A linear dependence of the solvent front move-ment with time was seen for the PMMA samples subjected to no and to one cycle.This indicated that case II diffusion occurred after an initial time period ofanomalous diffusion. However, the MeOD front movement for the second cyclewas not linear with time, but rather was linear with the square root of time. Afteran initial lag period of anomalous diffusion, the front movement for the secondcycle behaved in a Fickian manner. This indicates that the diffusion character-istics of the PMMA are altered with absorption-desorption cycling.

The solvent front velocities were determined for case II diffusion as being 12.6and 14.5 nm/s, respectively. These values are more than twice the magnitude of

those found by Thomas and Windle [35] and by Weisenberger and Koenig [22,23] for methanol diffusion in PMMA. This can be explained by the fact that thewater content and the drying treatment of the PMMA were never taken intoaccount in their experiments. The removal of water and the leaching out ofunreacted monomer were also not considered. The increases in diffusion ofMeOD may be accounted for by the plasticization by water of PMM A, which canbe demonstrated between the samples exposed to zero and one cycle. Theincreased plasticization allows for the increased rate of relaxation of the polymerchains and a greater solvent front velocity.

The translational diffusion coefficient was determined to be 4.0 x 10" Vs. Thiscompares with a value of 2.4 x 10" Vs for the diffusion of methanol into PMMAat the elevated temperature of 60 0C reported by Weisenberger and Koenig [22]for as-received PMMA rods. This shows that, even at a low concentration, thecyclic absorption-desorption of water and MeOD has a more significant effecton the characteristics of the methanol diffusion into PMMA than does thetemperature at which diffusion occurs. The value of 4.0 x 10" Vs for the diffusionof MeOD after two cycles of absorption-desorption of water and MeOD appearsto be comparable with that of MeOD diffusion in PMMA for a high watercontent (.25 wt% of polymer).


The author acknowledges the support of ALCOM (Advanced Liquid CrystallineOptical Materials) DMR 8920147 and the students whose work was responsiblefor the citations in this paper.

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1992.[30] P. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Claredon

Press, Oxford, 1991.[31] R.A. Ware, S. Tirtowidjojo and C. Cohen, J. Appl Polym. ScL, 1981, 26, 2975.[32] E.E. LaBarre and D.T. Turner, J. Polym. Sci.f Polym. Phys. Ed., 1982, 20, 557.[33] A.R. Barens and H.B. Hopfenberg, J. Polym. ScL, Polym. Phys. Ed., 1979,17, 1757.[34] L. Mandelkern and F.A. Long, J. Polym. ScL, 1951, 6, 456.[35] N.L. Thomas and A.H. Windle, Polymer, 1978,19, 255.

7 FOURIER TRANSFORMINFRARED AND RAMANSPECTROSCOPIES IN THESTUDY OF POLYMERORIENTATION

P. J. HENDRA and W. F. MADDAMSDepartment of Chemistry, University of Southampton, Highfield, Southampton,SOU IBJ, UK

7.1 INTRODUCTION

Infrared and Raman spectroscopy can be used to detect the presence of orienta-tion in polymer specimens and also to quantify it. The use of infrared methods forfilms has a long history, but more recently the technique has been extended tobulky specimens. Raman scattering can in principle provide a more detailedinsight into molecular anisotropy, but is dogged by experimental difficulties. Toreview the field in its entirety would be quite impossible, but it is feasible tointroduce the subject and through examples to explain its scope. Orientationmeasurements based on infrared or Raman methods can be applied to staticsamples or more recently, to those exposed to sinusoidally varying stress. We willconsider first the principles governing the effect that orientation has on theobserved vibrational spectra, review some of the applications and then move onto the dynamic studies, and conclude with an account of the effect of large strainon elastomers.

Any molecular property which is anisotropic, i.e., that shows a direcionaldependence, is per se capable of providing information on orientation both insolids and in appropriate melts or liquids. Such properties include opticalbirefringence, infrared polarization, anisotropic Raman scattering, broad lineNMR and X-ray diffraction, each of which has been exploited in the study ofpolymers. These various approaches yield differing amounts of information, forfundamental reasons; in order to appreciate why this is so it is necessary toconsider their theoretical basis, and also to have a convenient mathematicalframework by which to quantify degrees of orientation. These two topics will now


be considered, first in the case of infrared spectroscopy, which provides a com-paratively simple introduction, and then for Raman spectroscopy which, inprinciple, provides more detailed information at the expense of complexity ofinterpretation of the experimental measurements.

7.1.1 THE BASIS OF ORIENTATION MEASUREMENTSBY INFRARED SPECTROSCOPY

The absorption of infrared radiation occurs to a maximum degree when thedirection of the electric vector of the radiation is parallel to the direction of thedipole moment changes involved in the various vibrational modes of the absorb-ing molecule. If the direction of the electric vector lies at an angle to the directionof the dipole movement change, the component of the former resolved along thelatter direction is involved in the absorption process, which thus occurs lessstrongly. This is the directional property that makes infrared spectroscopy usefulfor orientation studies.

This directional property is not usually a pertinent factor in determining theintensities of the bands in an infrared spectrum, because the radiation is notpolarized and the direction of the electric vector is random in the plane perpen-dicular to the propagation direction. Furthermore, in solutions, and in manysolid samples, the absorbing molecules are randomly oriented.

In the situation where the incident light is plane polarized, so that the electricvector lies in a fixed direction, and the sample is partially or completelyorientated, as is often the case with polymer specimens, changes in peak intensitywill usually occur. This is readily understood by reference to Figures 7.1 (a), (b)and (c). The first shows the simple situation of a group of molecules, which areconveniently taken to be polymer chains in the present context, lying parallel toeach other. This type of orientation is known as uniaxial, and it often occurs as theresult of stretching or rolling in the direction along which the chains are lined up.Consider a molecular vibration in which the direction of the dipole movementchange lies along the chain, or the principal orientation direction. Considerfurther the situation when the electric vector is plane polarized parallel to thisdirection. In these circumstances maximum absorption will occur, and itsmagnitude will be determined by the rate at which the dipole moment changeswith changes in bond length during the vibration.

Complete uniaxial orientation seldom occurs in practice, and the typicalsituation is that of a range of orientations about the direction of completeorientation. One such chain is shown in Figure 7.1(b). The component of theelectric vector resolved along this chain, lying at an angle 9 to the completeorientation direction, is cos 6. Then, since the absorption intensity is proportionalto the square of the dipole moment change, it follows that, if the intensity ofabsorption is / along the direction of complete orientation, it will be / cos2 0 for

Figure 7.1 The relationship between the directions of incidence and the vibrator ina polymer

the chain at angle 0. It is evident that for 0 = 90°, zero intensity will be observed.The converse is that in the situation shown in Figure 7.1(a), with completeuniaxial orientation, if the direction of the electric vector is perpendicular to thechain direction, / will be zero. If these two intensities are denoted by J1 and J1,their ratio, which is known as the dichroic ratio Z), will tend to infinity. If thedipole moment change lies perpendicular to the chain direction it follows that forcomplete uniaxial orientation the dichroic ratio will be zero. In both situationsthe dichroic ratio will be unity for random orientation, so measurements on theway in which it changes during a process such as stretching or rolling, whichfrequently induce orientation, will yield useful information.

Figure l(c) shows the situation which is common in practice, a range oforientations which, in the uniaxial situation, will be symmetrical about thedirection of maximum orientation. The average value of cos20, denoted by<cos20>, will then define the overall orientation of this system. It may be shownthat <cos20> = /„//, + 2I1 and, therefore, that <cos20> = D/(D + 2). Thus,<cos20> may be determined by measuring D. The situation considered inFigures l(a)-(c) is simplistic in that, in general, the direction of dipole momentchange in the polymer molecule will not lie precisely along the chain axis, but atsome angle <j>. If </> is known it then becomes possible to determine <cos20> in thegeneral situation. In practice <t> is often hard to locate for two reasons. Althoughdetailed crystallographic studies and molecular vibrational calculations havebeen undertaken for most of the better known addition polymers, this is not thecase for some newer materials, and <j> for some vibrational modes is not known.Secondly, for amorphous polymers, and indeed for the amorphous component ofpartially crystalline polymers such as polyethylene, the chains may occur in morethan one conformational form, so that perpendicularity becomes rather indeter-minate. Nevertheless, the examination of D as a function of processing operationswill often yield very useful comparative information which is unobtainablefrom X-ray diffraction studies, which are specific for crystalline regions only. In

Direction of dipolemoment change

1a 1b 1c

particular, it is worth noting that X-ray diffraction applies only to crystallinefragments, but infrared dichroism is indicative of orientation throughout thesystem.

7.1.2 THE BASIS OF ORIENTATION MEASUREMENTSBY RAMAN SPECTROSCOPY

The information provided by the Raman spectrum of an oriented polymer differsfrom its infrared counterpart because of the fundamentally different processesinvolved in the generation of the spectra. In the infrared absorption process, asalready noted, the absorption intensity is dependent on the angle between theelectric vector and the direction of the dipole moment change. The Ramanspectrum results from inelastic photon scattering, details of which are determinedby changes in the polarizability of the chemical bonds involved. Polarizability isa tensor quantity, which results in complications but, in principle, providesadditional information. As we have seen, infrared spectroscopy involves only onebeam of polarized radiation, and the fraction of the radiation absorbed bya molecule depends only on the orientation of the molecule with respect to thepolarisation vector of the radiation. However, Raman scattering involves twobeams of radiation, those of illumination and collection, and the scatteredintensity depends on the orientation of the molecule with respect to the polarisa-tion vectors of both beams, which may, of course, be different. This necessitatesmore detailed measurements in order to obtain the relevant information.

It may be shown that the Raman measurements are capable of yieldinginformation on both < cos2 0 > and < cos4 6 >. The availability of < cos4 6 > data canbe valuable is distinguishing between the differing types of stress deformationmechanisms that have been proposed. However, an interpretation of the bandintensities in terms of <cos20> and <cos40> is possible only when the principalcomponents of the derived polarisability tensor are known. This information isoften not available and assumptions must then be made; these then render themethod non-absolute. Examples of this approach will be considered briefly below.

The interpretation of detailed orientation measurements by Raman spectro-scopy has led to the use of various abbreviated procedures. However, unlike theuse of infrared dichroic ratios for comparative purposes, simplified Ramanprocedures present pitfalls for the unwary and must be used with due care andattention.

It is useful at this juncture to note the capabilities of the other major methodsfor assessing orientation in polymers. Birefringence measurements yield valuesfor <cos20> and broad line NMR provides <cos20> and <cos40>, together with<cos60> in certain favourable circumstances. X-ray diffraction measurementsdefine orientation uniquely, and so give values for <cosn0>, where n takes on alleven values. Infrared spectroscopy and birefringence measurements yield the

least detailed information, but are by far the simplest methods from the experi-mental point of view, and this is often the decisive factor.

There is no difficulty in making infrared measurements on polymer specimenshaving some degree of biaxial orientation, but the interpretation of the resultsmay not be straightforward. It is possible in principle to express the results interms of a more generalized type of mathematical orientation function. However,the approach that has tended to be used in practice, so far as is possible, is toutilize bands arising from vibrations for which the direction of the dipole momentchange is well established, and is presumably either parallel or perpendicular tothe chain axis. The complexity of interpretation of the Raman spectra of biaxiallyoriented specimens has discouraged work in this area.

7.2

7.2.1 EXPERIMENTAL TECHNIQUES O N STATIC SAMPLES

In the infrared, plane polarized radiation is required, and is provided by passingthe radiation through a polarizer transparent in the wavelength domain ofinterest.

A variety of these devices has been used over the years, but today the use ofa fine wire grid on a KRS-5 (thallium bromoiodide) support is pre-eminent. Thedevice is usually in the form of a disc 25 mm in diameter mounted in a metalholder, but the devices are very fragile because only the slightest accidentalcontact with the face coated with the gold grid is fatal to its efficiency. It is normalto study polymers as films in transmission, having identified a reference directionin the specimen. To remove polarization effects arising from the interferometer,the polarizer should lie in a fixed orientation and the sample should be rotated,rather than the reverse. Where orientation has been introduced by processingoperations such as drawing or rolling, visual inspection of the specimen usuallyreveals the processing directions, widely known as the 'machine' directions, andcan be uniaxial or biaxial. The major experimental limitation in infrared trans-mission measurements is the requirement for films to be thin enough to obtainadequate results. In practice, this requires film thicknesses in the range 25-100/midepending on the type of polymer involved. See Figure 7.2.

Measurements have been successfully made using polarized infrared radiationin attenuated total reflectance (ATR) and specular reflectance. In the ATR experi-ment the conventional prism is replaced by a 'pent roof device and the polymer isclamped to its surfaces with the machine direction parallel to one of the sides. Theexperiment is then carried out through two adjacent faces, i.e. with the polarizedradiation passing along or normal to the machine direction. See Figure 7.3.Comparison of the two spectra is as for transmission. Specular reflection hasa much more complex theoretical background and is not considered here.

Abso

itoan

ce

Wavenumber v (cm~1)

Figure 7.2 Dichroic infrared measurements on a film of biaxially oriented polyethyleneterephthalate

Sample

AT. R. Crystal

Sample oriented

Pent roof A.T.R. prismIl PositionRotation about axis Gproduces 1 PositionBeam enters face A

Figure 7.3 ATR carried out with polarised light. The method was developed by the late

Figure 7.4 The optical arrangements typical of a FT Raman spectrometer operatinganisotropically. The laser is turned by prism P1 to the left and brought to a focus in plane S.Samples in this plane scatter light collected by lenses L2 and L3 and pass it to theinterferometer, which lies to the right

Confining our attention to FT Raman experiments and to polymers makes theexperimental arrangements involved far simpler than they might otherwise be. InFT instruments backscattering is almost invariably used. See Figure 7.4. Theradiation, which is from a laser source and almost always plane polarised,irradiates the sample. The scattered light leaving the sample in the reversedirection to the incident beam is collected with a large lens or mirror and passedto the interferometer and detector. The collected radiation is analysed with ananalyser in the optical train (frequently between the interferometer and thedetector). Several experiments can be attempted by rotating the sample asrequired and also by rotating the polarization analyser. In theory, correctionshould be made for the polarization effect of the interferometer itself, but this isusually ignored. The various experiments are too disparate to describe as || or1 and so a nomenclature originally devised by the late S.P.S. Porto is normallyinvolved. It is defined in Figure 7.5. In principle, samples of any reasonablethickness can be studied with FT Raman spectroscopy and the sampled volumecan be located from the surface back into the bulk at will. However, a high degreeof optical clarity is essential if the polarization sense is not to be scrambled.With care, convincing measurements can be made on opalescent materials,e.g., ultrahigh-modulus polyethylene, which is milky and non transparent. SeeFigure 7.4. If study in the bulk phase of an inhomogeneous specimen, e.g.a transparent moulding in, say, polymethyl methacrylate or poly-4-methyl-l-pentene is planned, a word of caution is pertinent. As the laser passes through the

Micrometer

Figure 7.5 The experimental nomenclature defined by the late Dr S.P.S. Porto

surface of the specimen and then the anisotropic bulk on its way to the volumeviewed by the spectrometer, the plane of polarization will be rotated. Thescattered light will also be affected, so the conclusions reached about theorientation within the specimen may be unreliable.

7.2.2 INFRARED SPECTROSCOPIC STUDIES ONORIENTED POLYMERS

The purpose of this section is to give readers an indication of the type ofinformation that may be obtained, not to provide a detailed literature survey. Itcovers both the use of dichroic ratio measurements, the more common approach,and the formal use of orientation functions.

The value of dichroic ratio measurements, taken in conjunction with polymerprocessing variables, is demonstrated excellently by a study on cold drawn linearpolyethylene, made a quarter of a century ago by Glenz and Peterlin [I ] . Theresults are shown in Figure 7.6. Consider first the results for the band at1894 cm " l . The dichroic ratio decreases rapidly with increasing draw ratio andasymptotically approaches zero as the draw ratio exceeds « 5 . The 1894 cm"1

band is a combination mode of the Raman active methylene rocking mode at1170 cm ~ * and the methylene rocking mode at 720 cm " *, and is characteristic forcrystalline regions of the polymer. Its dipole moment is perpendicular to the

Crystal axes

Direction of View

Direction of Illumination

Analyze

Laser Polarisation

Draw ratio

Figure 7.6 Dichroic ratio D vs. draw ratio for cold drawn linear polyethylene [1]

c axis, i.e., the long chain direction of the polymer. Hence, the early decrease in thedichroic ratio with increasing draw ratio shows conclusively that there is rapidorientation of the c axes of the crystallites parallel to the draw direction as thesample is deformed.

The peak at 1368cm"x arises from the symmetric CH2 wagging mode for theCH2—CH2 group, where the C—C band is at the centre of a gauche-trans-gauche sequence. It differs from the behaviour of the band at 1894 cm"x in twoobvious respects: namely, that the approach to the limiting value with increasingdraw ratio occurs decidedly more slowly as deformation increases, and theultimate value indicates that there is only partial orientation of this structuralunit. This was interpreted as evidence for a clear segregation of the crystalline andamorphous phases. The corresponding asymmetric wagging vibration gives riseto the band at 1303 cm"1, and the polarized intensity of this is virtuallydependent on draw ratio, showing that substantial orientation is not occurring,although a knowledge of the direction of dipole moment change is required inorder to interpret the results more fully. The peak at 1078 cm"1 comes froma gauche C—C stretching and some CH2 wagging. Its behaviour is intermediatein that it reaches its ultimate dichroic ratio of «0.7 at relatively low draw ratios,but the final value is a reasonable indication of partial orientation only, as wouldbe expected for methylene units in amorphous regions.

The value of the approach using dichroic ratios coupled with a knowledge ofthe assignments of peaks is further illustrated by measurements on plain poly-ethylene films [2]. The production process leads to a rather complex orientationpattern. The molten polymer is extruded as a thin, hollow cylinder, in what maybe termed the machine direction. It is simultaneously expanded in a planeperpendicular to the machine direction by the application of internal pressure.Additional variables are the extrusion temperature and the rate at which theblown film has been cooled. The resulting orientation behaviour is best studiedby x-ray diffraction pole figure measurements [3,4,5] but the infrared approachprovides a relatively simple means for obtaining a useful amount of information,particularly for the behaviour of chains in amorphous regions.

Dichroic ratios were measured for the bands at 1080, 1303, 1352 and1368 cm"1. The first of these is associated with tie chains between crystallinelamellae in amorphous regions, and the remaining three involve methylene groupvibrations of loose chain folds in amorphous domains. It was possible to correlatethe results with the occurrence of two types of orientation that had earlier beencharacterized by X-ray diffraction measurements. They are termed high- and low-stress orientation, whose occurrence depends on the blowing conditions and thoseduring film production. The first type of orientation is analogous to that found incold drawn polyethylene, discussed above, in having the c axis distribution of thecrystalline regions substantially along the machine direction. The low-stressorientation, which occurs the more frequently, is the result of the type of crystal-lization process described by Keller and Machin [6]. The a and c axes are inclinedat an angle to the plane of the film, with a strong tendency for the greater concen-tration of a axes to lie near to the machine direction. The three peaks at 1303,1352and 1368 cm" * show appreciable orientation in the high-stress type of films but verylittle with the low-stress materials. Conversely, the extended tie chains, characterizedthrough the 1080 cm" i band, are appreciably oriented in the low-stress films butnot so in their high-stress counterparts. These results, together with those fromX-ray diffraction measurements, proved to be of appreciable value in selecting thebest blowing conditions to manufacture films having optimum tear strengths.

The more formal approach, involving values of <cos20>, has been used byPurvis et al. [7] to study uniaxially oriented specimens of polyethylene tereph-thalate). These measurements were part of a wider study involving birefringenceand Raman studies, and the results are more conveniently considered in thefollowing section.

7.2.3 RAMAN SPECTROSCOPIC STUDIES O NORIENTED POLYMERS

The ability of Raman spectroscopic studies on oriented polymers to yield valuesfor both <cos20> and <cos40> has led to its use with polyethylene, atactic

poly(methyl methacrylate), poly(ethylene terephthalate) and poly(vinyl chloride).Some results that have been obtained will be considered briefly.

Despite the problems of Raman spectroscopic studies when working withpolyethylene specimens, Maxfield et al. [8] obtained spectra of adequate qualityby immersing thin drawn films of low density polyethylene in silicone oil tominimize surface scattering. They used the 1170cm"1 band, characteristic forchains in crystalline regions, and one at 1081 cm" \ specific for the amorphousones, to obtain values for <cos20> and <cos40>. The former agreed well withthose deduced from infrared measurements. Both sets of values are reasonably inline with theoretical estimates obtained from the Roe and Krigbaum [9] cross-linked rubber network model, and the crystalline orientation factors are asexpected on the basis of the phenomenological theory of Yoon et al. [10].

The major workers in the field have been Professor LM. Ward and hiscolleagues at the University of Leeds. The technique was first applied topoly(ethylene terephthalate) [T]9 abbreviated to PET for convenience, usinguniaxially oriented tape specimens. Measurements were confined to the benzenering mode band at 1616cm"x and only three independent intensities, in terms ofpossible orientations, were measured. Nevertheless, some interesting results wereforthcoming. Values of <cos20> were plotted as a function of birefringence, anda straight line was obtained. Extrapolation to <cos20> = 1 permitted a value forthe maximum birefringence to be obtained, and this agreed well with thatsuggested by Kashiwagiet al. [H] . Plots of <cos20> and <cos40> as a functionof draw ratio were compared with the predictions from the affine rubber elasticitymodel and the pseudo-affine aggregate deformation model. There is moderatelygood agreement with the rubber model for draw ratios less than « 3 , and someindication that for those in excess of 4.5 the pseudo-affine aggregate modelbecomes more appropriate.

Purvis and Bower [12] subsequently extended the work, using four additionalRaman peaks, all of which predominantly involve motion of the terephthalylmoiety, to a first approximation. The results suggested that there is no preferredorientation of the plane of the ester group with respect to the plane of the benzenering in the amorphous phase. They also concluded that the drawing of PEToccurs in a similar manner to the extension of a rubber-like network.

Purvis and Bower [13] also examined drawn specimens of amorphouspoly(methyl methacrylate), using four peaks in the Raman spectrum. They werenot able to distinguish between two plausible structural models, one essentiallylinear and the other helical, but they were able to show that their results areconsistent with the affine deformational model.

The success of these measurements prompted a study on drawn specimens ofplasticized PVC [14]. This poses problems because of the complexity of thespectrum, which shows overlapping peaks arising from configurational andconformational isomers. In this first study, attention was confined to peaks at 608and 638 cm"1 specific for long planar syndiotactic sequences, the type of unit

W A V E N U M B E R (C m-1)

Figure 7.7 FT Raman measurements on ultra high-modulus polyethylene. Spectrarecorded in two ways-analyzer vertical or horizontal polarised vertically.

involved in the crystalline regions of the polymer. All possible orientation andpolarization combinations were used, giving a total of eight intensity measure-ments per peak. The results, including a comparison of < cos2 6 > values with thosefrom birefringence measurements, showed that the crystalline regions are morehighly oriented than the non-crystalline ones in samples containing the largeramounts of plasticizer and drawn at the higher temperatures. In a continuation ofthis work, Bower et al. [15] used the intensity of the 616 cm" * band, specific forshort syndiotactic sequences probably present in amorphous regions. The resultssupport the earlier tentative conclusion that amorphous chains behave ina rubber-like way during orientation.

The results described above all refer to Raman measurements made prior tothe introduction of FT methods and near-infrared sources. More recent workshows that anisotropic measurements are far easier than they were, and can bemade at room temperature on heated or cooled specimens with consummateease. The measurements on highly oriented polyethylene shown in Figure 7.7 aresimple to produce both at room temperature and at — 1800C. An analysis isavailable [16].

Several very preliminary reports have appeared in the recent literature, wherea 'dichroic' measurement has been attempted, in that spectra have been recordedwith no polarization analyser and with the machine direction of the sample set

INT

EN

SIT

Y

parallel or perpendicular to the electric vector of the laser. They are, of course, ineach case the sum of several of the spectra shown in Figure 7.7. Further, thepolarization of ingoing and outgoing radiation may be rotated as described inSection 7.2.1. The results indicate the orientation and variations thereof butcannot be used to give quantitative data. We find the approach useful but it has tobe used with caution.

7.3 TIME RESOLVED MEASUREMENTS

As we have seen, the changes to a vibrational spectrum as orientation is inducedare ones of intensity. Application of stress is well known to induce frequencyshifts. However, both effects only subtly change a well developed spectrumcharacteristic of the specimen itself. One obvious way to study these subtlechanges is to apply force sinusoidally and to discriminate electronically betweenthe DC component of the signal (the invariant) and the AC (that of interest).Further, in several practical situations polymers are regularly subjected tovariable loads, and their behaviour under these situations is critical. In addition,their deformations under quasi-static stresses are very different from those underalternating ones.

Polymers behave to varying degrees as viscoelastic materials, and this hasconsiderable consequence for their response to loading at moderately highfrequencies. Their behaviour under such conditions has been studied by a varietyof methods that come under the general heading of dynamic mechanical testing.However, until comparatively recently, spectroscopic methods have not beenapplied to the problem. The work in this area will be considered and, in order toprovide the foundation for this discussion, the basic theory for the response ofa viscoelastic system to sinusoidal stress will be given first.

7.3.1 THE RESPONSE OF A VISCOELASTIC SYSTEM TOSINUSOIDAL STRESS

Consider an applied stress varying as a function of time according to the rela-tionship (T = (T0 sin co, where co is the stress frequency. If the material were whollyelastic, and obeyed Hooke's law, the strain would then vary as e = e0 sin cot.

However, for a viscoelastic material the strain lags behind the stress. Let thislag be denoted by S9 which may be called the phase angle or the phase lag, and isthe relative angular displacement of the stress and strain.

The appropriate equations then become

G = a0 sin cot

and

e = e0 sin ((Dt — S)

Hencee = e0 sin cot cos 3 — e0coscot sin S (1)

The strain can therefore be considered in terms of two components, one ofwhich, e0 sin cot cos <5, is in phase with the strain, and the other, e0 cos cot sin <5, isout of phase with the strain by n/2. It is therefore possible to define two dynamicmoduli, E1 in phase with the stress and E2, which is n/2 out of phase with thestress. E1 = (cr Je0) cos d and E2 = ((T0Ze0) sin S.

E1=(V0Ze0)COsS + E2 = {<70/e0)sin8

Substitution into (1) then gives

e = EÎ/GQ sin cot — E2e\/a0cos cot (2)

and

tan S = E2/EX (3)

tan S is frequently used as a measure of viscoelastic character. For a giventemperature, E1Ê2 and tan S are functions of the frequency of the applied stress.In general, tan 5 and E2 are usually small at very low and very high frequenciesand their values pass through maxima at some intermediate frequency. On theother hand, E1 is high at high frequencies in the case of glassy polymers and low atlow frequencies for rubbery polymers.

One of the main reasons for studying the frequency dependence of the dynamicmechanical properties is that it is often possible to relate peaks in E2 and tan S toparticular types of molecular motion in the polymer, via what may be regarded asa 'resonance' effect. For example, there are particularly strong 'resonances' at theglass transition. Peaks in E2 are also often found at the melting temperature insemi-crystalline polymers, a consequence of the greater freedom of molecularmotion that is possible when the molecules are no longer arranged into a regularcrystalline structure. Other types of molecular motion, such as those involvingthe rotation of branches, often give detectable but smaller peaks in E2 and tan <5,and these are usually referred to as secondary transitions. If a series of suchtransitions occurs over a range of temperature, the peak which occurs at thehighest temperature is termed a, and the subsequent ones are called /?, etc.

Hence, dynamic mechanical measurements are usually made over a range oftemperature and frequencies in order to cover the various types of molecularmotion that may occur. The oscillatory strain amplitudes used are very small,typically below 1.0% of the total sample dimension, to ensure a linear viscoelasticresponse.

Molecular motions in polymers, particularly those types that involve somereorganization of functional groups such as branches, should be amenable tostudy by vibrational spectroscopy. The spatial movement of functional groupsinvolves a change in the directions of dipole moment and polarizability changesduring molecular vibrations. Hence, the measurement of linear dichroism using

polarized radiation should prove useful as a complement to dynamic mechanicalmeasurements, or as a characterizational technique in its own right.

Because the oscillatory strain amplitudes involved are very small, it is easier tomeasure the difference between A1 and A19 the absorbances measured fora particular peak for light polarized in planes parallel and perpendicular toa fixed reference direction of the sample, than to measure their ratio A^fA19 as iscommonly done in making orientation measurements on appreciably deformedpolymers. A1 — A1 is termed the dichroic difference and is usually denoted by AA,or AA(t) in the case of a time dependent signal. It is then easy to show, using thetype of reasoning involved in obtaining Equation (2), that the dynamic dichroismsignal AA(t) can be separated into two orthogonal components given by theequation

AA(t) = AA' sin ot + AA" cos cot (4)

and tanS = AA11JAA1, where tan<5 is termed the dichroic dissipation factor,analogous to the mechanical dissipation factor considered above. The terms AA'and AA" are known as the in-phase spectrum and the quadrature spectrumrespectively of the dynamic infrared linear dichroism. They represent compo-nents of dynamic optical anisotropy caused by the re-orientation of electricdipole transition moments. The in-phase spectrum is a measure of the instan-taneous strain and the quadrature spectrum characterizes the component ofre-orientation proportional to the rate of strain which is n/2 out of phase with thestress. The applied oscillatory stress provides a mechanism for perturbing thesystem and stimulating individual functional groups into the specific reorienta-tional responses, which are then characterized by the resulting dichroic measure-ments.

7.3.2 EXPERIMENTAL

The equipment required to measure in-phase and quadrature linear dichroicspectra consists of two components, the transducer necessary to provide the smallamplitude oscillatory strain and a suitably modified infrared spectrometer. So faras the former is concerned, it is desirable that the transducer system is capable ofoperating over a range of frequencies, in order to provide the flexibility that maybe required in probing a change of re-orientational responses. The transducermay either form part of a dynamic mechanical analyzer, as described by Nodaet al. [17] or may be a simple unit used solely as part of an infrared spectrometersystem.

The majority of the measurements reported hitherto have been made onmodified dispersive spectrometers, and the system of Noda et al. [17] is typical.This involves three successive modulations of the infrared beam as it passesthrough the spectrometer, which is custom designed and built. The first stage of

modulation is via a mechanical light chopper, in order to eliminate backgroundradiation and sample emission. The beam is then polarization modulated usinga combination of a wire grid polarizer and a photoelastic modulator, whereby theplane of polarization of the light alternates rapidly between directions paralleland perpendicular to a fixed reference axis, conveniently the direction alongwhich the strain occurs. Two photoelastic modulators were used, having modula-tion frequencies of 37 and 84 kHz, with corresponding time resolutions of 14 and6 ̂ s. The dynamic dichroism of the sample leads to the third modulation of thebeam.

In view of this triple modulation process, a rather complicated demodulationscheme has been employed in order to extract the required information from thesignal from the detector. This involved a set of five lock-in amplifiers. A fullmathematical analysis of this system has been provided by Noda et al. [17]. Inaddition to the fine time resolution performance already noted, the sensitivity ofthe instrument is such that it will detect a signal as small as 10" 4 absorbence unitat a resolution of 4cm" *. Chase and Ikeda [18] have also described a dispersiveinstrument of this type.

More recently, and predictably, Fourier transform infrared spectrometers havebeen used to measure dynamic linear dichroic spectra. However, substantialmodifications to the conventional type of FTIR spectrometer have been necess-ary in order to overcome a basic problem. This arises from the fact that it isnecessary to separate the time dependence of the sample response from that of thespectral multiplexing, because the interferogram itself is a cosine function of time.For example, if the moving mirror has a velocity of 0.5 mm per second at3000 cm"1 the radiation is frequehcy modulated at 300Hz.

Until recently the almost universal approach to the problem has been the use ofstep-scanning FT interferometers. Such instruments avoid the problem of theseparation of two time dependent variables by creating the interferogram pointby point. At each retardation position of the interferometer mirrors, data arecollected for as long as is required to obtain the desired signal-to-noise ratio, anda single interferogram is recorded for Fourier transformation. By this means thespectral multiplexing is uncoupled from the time domain.

The essential difference between conventional FT instruments and the step-scan devices is that, for successful operation, it is necessary to control theretardation (mirror) velocity in the case of the former and the retardation (mirror)position for the latter. In both cases, the method used to control the retardationinvolves a collinear or parallel helium/neon laser interferometer. In continuousscan operations the laser interference fringes are used to generate feedback signalsto maintain constant mirror velocity, and in the step-scan mode the laserinterferogram provides the means for the control of the mirror position viaa feedback signal.

Several methods are available for setting the retardation and the stepping. Anearly approach was that of Manning et al. [19,20] for use with an IBM IR-44

spectrometer. The control signal is generated by path difference modulation or'dithering' of the moving mirror via an AC voltage applied to the drive mechan-ism. The resulting 'phase modulation' in the control laser detector signal is used ina lock-in feedback circuit to the drive mechanism system. This step-scan instru-ment has a retardation position uncertainty of +15 nm and a minimum steppingrate adjustable over the range 0-100 Hz, although data are normally collectednear to the bottom of this range.

Gregoriov et al. [21], in a subsequent development, used either completedigital control of the position and stepping or a combination of analogue anddigital control, with phase modulation available as an optional extra, in convert-ing a Nicolet System 800 into a step-scanning instrument. They were able toachieve a positional uncertainty of « ± 1 nm. This type of control has been usedby Bruker in their IFS 88 instrument and the more recent Bio-Rad Digilab FTS70A. Fuller details of step-scan instruments are given in the excellent reviewarticle by Palmer et al. [22] Marcott et al. [23] have made comparative dynamicmeasurements on a thin film of atactic polystyrene, using their dispersivespectrometer described above in comparison with a Bio-Rad FTS 60A instru-ment operating in the step-scanning mode. They concluded that, although thedispersive approach produces higher signal-to-noise ratios over small spectralregions, the multiplex advantage makes the FT approach attractive whenbroader spectral coverages are required.

Block Diagram of Dynamic Infrared SystemBased on Rapid Scanning FTIR Spectrometer

toADC

ADCtrigger

90'PhaseShifter

S/H

Control

Osc25Hz Reference

S/H S/H

SYS2000FTIR

AmpLowPassFilter

S/H Multiplex

Polariseir SampleStretcher

MCTDetector S/H

Infrared beam

Sample & Hold

Figure 7.8 Block diagram of the Perkin-Elmer 2000 system for studying time resolvedphenomena.

WAVENUMBER/cm1

Figure 7.9 Bennett's experiment on heated polystyrene. He applies a modulation to thelaser source at 540 Hz. This shifts the Fourier transformed spectrum by ± 5260 cm "!. Theshifted spectrum labelled 'upper side-band' is that of the polymer, the unshifted one, theDC spectrum, that of polystyrene over the black body emission

Turner and Hoult [24] have demonstrated recently that very satisfactoryresults may be obtained from a conventional scanning FTIR system, usingsynchronous lock-in detection. Their system has a photoelastic polarizationmodulator operating at 74 kHz. A reference signal is taken from this modulatorand fed to the lock-in amplifier and sampled at the same time as the infraredsignal at the detector. There are, therefore, two associated data points for eachoptical path difference of the interferometer, namely the modulated interfero-gram signal and the photoelastic modulation signal. The data are demodulatedand then accumulated with an appropriate software routine. See Figure 7.8. Thisapproach has also been successfully exploited by Bennett [25] for the removal ofthermal backgrounds from Raman spectra using a modulated laser source inconjunction with a conventional scanning FT Raman spectrometer; see Fig-ure 7.9. There are therefore now proven methods for obtaining dynamic lineardichroic infrared spectra. This has already prompted a range of studies and morewill doubtless follow.

In the early studies the in-phase and quadrature spectra were examined byconventional interpretational techniques, and useful information was forthcom-ing. However, the value of correlation analysis quickly became evident, as theresult of the pioneering activities of Noda [26, 27], and this had led to the use of

AR

B.

UN

ITS

RAYLEIGH LINE

ALIAS OF 2ND HARMONICRAMAN SPECTRUM

MODULATIONFREQUENCY

WATER

ARTEFACTS

D.C. SPECTRUMUPPER SIDE-BAND

SHIFTED BY 5260 CM-1

so-called two dimensional infrared (2D IR) spectroscopy to display graphicallythe results of correlation analysis.

As noted above, the in-phase and quadrature spectra represent components ofdynamic optical anisotropy caused by the re-orientational behaviour character-istic of the type and local environment of each group. Reorientation processestend to synchronize if there is a specific chemical interaction or connectivitybetween them, and herein lies the value of correlation analysis, in that it providesa valuable method for studying the time dependent variation of infrared dichro-ism signals.

If dichroic differences are measured at two wavenumbers V1 and v2, twoorthogonal correlation spectra may be defined as follows:

0(V1, v2) = IAAXv1)AAXv2) + A^l"(v1)A^'/(v1)A^//(v2)]/2 (5)

*(vi, v2) = IAA-(V1)AAXv2) - AAXv1)AAXv1)AA-(V2W (6)

They are respectively referred to as the synchronous and asynchronous 2Dinfrared spectra. The synchronous spectrum characterizes the degree of coher-ence between the dynamic fluctuations of signals measured at two wavenumbers,and the correlation intensity becomes significant only if the reorientation rates ofdipole transition moments are similar to each other. The asynchronous spectrum,however, characterizes the independent, uncoordinated out-of-phase fluctu-ations of the signals. Hence the asynchronous correlation intensity becomesnon-vanishing only if the signals vary at different rates.

Peaks along the diagonal position of a synchronous 2D spectrum are referredto as autopeaks. They indirectly represent the local mobility of chemical groupscontributing to the molecular vibrations at that wavenumber. Peaks located atoff-diagonal positions of a 2D spectrum are known as cross peaks. They appearwhen the dynamic vibration of infrared dichroism at two different wavenumbersare correlated with each other because the two signals are fluctuating more or lessin phase with each other. As long as the normal modes of vibrations correspondto reasonably pure group frequencies, the cross peaks in a synchronous 2Dspectrum may be used to map out the degree of intra- and inter-molecularinteraction of various functional groups.

Cross peaks in an asynchronous 2D spectrum provide complementary infor-mation. They appear if the signals are out of phase with each other. Even if thecharacteristic band frequencies are similar and absorption peaks in the conven-tional infrared spectrum overlap an asynchronous 2D spectrum can differentiatethem, because their time dependent intensity fluctuations differ slightly. Spatialand temporal information about the re-orientation processes of transition mo-ments and their associated chemical groups can be obtained from the sign of crosspeaks. If the sign of a synchronous cross peak is positive, the corresponding pairof dipole transition moments reorients in the same relative direction. If the sign isnegative the re-orientation directions are perpendicular to each other. A positive

Wavenumber, V1

Figure 7.10 A schematic representation of synchronous 2D correlations. For details seetext. Diagram due to Noda et al. [44]

peak in an asynchronous spectrum indicates that the transition moment withvibrational frequency V1 re-orients before v2.

This may be appreciated more readily by reference to Figure 7.10, which showsschematic synchronous 2D correlations for two pairs of peaks A and C, and B andD. The shaded areas represent negative intensity correlations. A cross peak isnegative if the changes are in opposite directions, as in the case with bands A andC. To summarize, 2D spectra are capable of revealing rather detailed informa-tion, as will emerge clearly below when typical examples are considered.

7.3.3 SOME EXAMPLES OF DYNAMIC LINEARDICHROIC INFRARED STUDIES

A detailed review of the published work is not possible in the available space.Selected examples will therefore be used to illustrate the information that may beobtained from the inspection of in-phase and quadrature spectra, and from theuse of correlation analysis. Studies on polystyrene provide a very convenientintroduction.

Noda et al. [17] have measured the in-phase and quadrature spectra of thinfilms of polystyrene supported on a Teflon film, concentrating on the spectralregions 1425-1525 cm~* and 2800-3200cm"1. The former contains two peaks ofparticular interest, at «1450 and 1490 cm"1. The first of these is made up ofoverlapping bands from two uncoupled vibrations: a CH2 scissoring motion in

Wav

enu

mb

er, V

2

the polymer backbone and an aromatic ring stretching vibration that is locallypolarized along the bond between the phenyl group and the polymer backbone.The 1490 cm" l band is assigned to the coupling of an aromatic CH deformationwith another aromatic ring stretching mode, locally polarized in the plane of thering, perpendicular to the bond between the phenyl group and the backbonealiphatic chain. The 1490 cm"1 band has a significant signal in the quadrativecomponent, which is shifted to higher wavenumbers, whereas the 1450 cm"1

peak is closer to being in phase with the applied stress. This difference suggeststhat there may be some fraction of the aromatic side chains which is respondingto the applied stress at a rate different from that of the polymer backbone.

Unlike the situation at 1450 cm "x, where there is clear separation between thearomatic and aliphatic C-H stretching bands, the specific band assignments inthe aromatic C-H stretching region are not wholly certain. There are two clear,positive peaks at 3028 and 3058 cm"1 in the in-phase spectrum, and this couldindicate that the relevant transition moments are locally polarized in the plane ofthe phenyl ring, perpendicular to the band between the phenyl group and thebackbone aliphatic chain. However, this does not prove that this is universallythe case; in a non-crystalline polymer such as atactic polystyrene, individualfunctional groups can be oriented in a variety of directions relative to thereference strain axis. The aliphatic CH2 symmetric stretching mode giving theband at 2854 cm"1 is also interesting. This band is quite strongly negative in

Wav

enum

ber,

v2

Wavenumber, V1

Figure 7.11 The infrared spectrum of polystyrene shown in a 2D presentation. Fordetails see text. Diagram due to Noda et al. [17]

Asymmetric Symmetric

AutopeakCross peak

CH2-stretchtng

the in-phase spectrum and is consistent with the polymer chains tending to alignin the direction of the applied stress.

Noda et al. [28] have interpreted measurements on atactic polystyrene usingthe correlation technique, and the two groups of C-H stretching bands are againof interest. Figure 7.11 shows the synchronous 2D correlation spectrum over thealiphatic C-H stretching region. The large autopeak on the diagonal representsthe re-orientational motions of dipole transition moments assignable to thesymmetric and antisymmetric methylene CH2 stretching vibrations. The appear-ance of synchronous cross peaks at the corresponding spectral coordinatesindicates that the dipole transition moments for these two bands re-orient ata similar rate, as might be expected. The sign of the synchronous cross peaks ispositive, suggesting that the transition moments of the two vibrations are bothrealigning in the same direction, namely perpendicular to the direction of appliedstress. As both dipole transition moments are known to lie perpendicular to thepolymer backbone, it is reasonable to conclude that the chain of polystyrene mustbe aligning in the direction of applied stress, even in the glassy state.

The re-orientation dynamics of the side group phenyl rings is more complex.Figure 7.12 shows the asynchronous spectrum involving the phenyl side groupsand the backbone methylene groups, and strong cross peaks are present. Thissuggests that the re-orientational motion of the phenyl groups under strain isquite different from that of the backbone. This, in turn, requires that there must be

Wav

enum

ber,

v2

Bac

kbon

e m

ethy

lene

Side-group phenyl

Wavenumber, V1

Figure 7.12 The infrared spectrum of polystyrene shown in an asynchronous form.Diagram due to Noda et al. [17]

substantial freedom for the side groups to realign independently of the mainpolymer chain. Consequently, it is impossible to characterize the main chaindynamics of polystyrene simply by studying the re-orientation of phenyl groups.However, 2D correlation spectra in the ring stretching modes region are moreproductive, because the dipole transition moment directions are well established.Such spectra show that, in the glassy state, side group phenyls tend to re-orientalong the direction of the main chain backbone. This is somewhat unexpected, assuch re-orientational motions require highly distorted local conformations ofchain segments. As the temperature is raised well above the glass-to-rubbertransition point, the asynchronous relationship between side groups and themain chain of polystyrene decreases considerably. It is therefore reasonable toconclude that the anomalous re-orientation behaviour of phenyl groups of glassypolystyrene results from highly localized and constrained motions of functionalgroups in a molecular environment with limited free volume at temperaturesbelow Tr

Polymer blends have proved another fruitful field for study, with considerabletechnological implications. Particularly simple, but commercially important, isthe behaviour of a blend of low density polyethylene (LDPE) and high densitypolyethylene (HPDE); a 50:50 blend of these two materials is semi-crystalline. In

Wav

enum

ber

Wavenumber

Figure 7.13 The asynchronous correlation map for low and high density polyethylenes.Diagram due to Gregoriou Noda et al. [29]

view of the spectral similarity of these two materials, Gregoriou et al. [29] useda blend of perdeuterated HDPE and conventional LDPE. A portion of theasynchronous correlation map is shown in Figure 7.13. There are clearly twocomponents within the 1088 cm"1 band, at 1085 and 1091cm"1, as is evidentfrom the appearance of the corresponding cross peak. Additionally, a negativecross peak exists between the transition dipole moments at 730 and 1091 cm" \suggesting that the crystalline component of rf-HDPE of the blend re-orientsfaster than the crystalline LDPE portion under a positive cross peak between thedipoles at 721 and 1085 cm ~ l and also that, in the corresponding synchronousplot, the corresponding peak is also positive.

It has been suggested [30] that, when a melted blend of HDPE and LDPEcools, HDPE crystallizes first because of its higher melting temperature, resultingin a volume-filling superstructure of HDPE crystals forming a skeletal network.When the LDPE begins to crystallize it forms disjointed crystallites filling theinterstitial space of the HDPE network. If such a system is deformed, the initialobservable response will result from the deformation of the HDPE crystallinenetwork. The stress will then transfer to the interstitial spaces, and there will bea secondary orientation of LDPE crystallites. The interpretation of the 2Dspectra of the polyethylene blend is in good agreement with this model.

The miscibility of some polymer blends is of considerable technologicalimportance although, fundamentally, the reasons for the miscibility are notcompletely understood. Polystyrene (PS) and poly(2,6-dimethyl-l,4-phenyleneoxide) (PPO) is one such system. 2D correlation studies have been made ona blend of 80% of the former and 20% of the latter by Palmer et al. [31]. Theresults suggest a different dynamic behaviour for the PS and PPO portions of theblend, depsite their compatibility, with the PS chains responding to the pertur-bing force faster than those of PPO. Some asynchronous cross peaks developbetween the constituents, indicating the possible existence of submolecular levelmicroheterogeneity.

Atactic polystyrene and poly(vinyl methyl ether) provide another case ofmiscibility of two very different polymers, the latter being water soluble. Al-though the conventional infrared spectrum shows a single peak for the C-Hstretching mode of the methoxyl group, the asynchronous 2D spectrum of theblend reveals two separate peaks assignable to this mode. Strong synchronouscross peaks exist between one of these two methoxyl peaks and some phenylgroup modes of the polystyrene, indicating the possible existence of a specificintermolecular interaction between the phenyl and methoxyl groups.

The tri-block polymer styrene-butadiene-styrene, with a weight ratio of 78/28in favour of butadiene, has also been studied [32]. The in-phase and quadraturespectra over the region 2700-3100Cm"1 show that, at room temperature, thestyrene portion of the copolymer displays negligible dynamic response whenbutadiene forms the continuous matrix. This is not unexpected, as PS is in theglassy form whereas PB is a rubbery phase. The interesting feature of the two

spectra is the appearance of incipient fine structure centred at « 2920 cm l. The2D correlation spectra prove revealing. The synchronous map indicates theexistence of peaks at 2933 and 2915Cm -Mn the asynchronous correlation mapthere are several peaks in the vicinity of the asymmetric C-H stretch at2920cm"1. There are a positive cross peak between 2936 and 1915cm"1,a positive cross peak between 2936 and 2930 cm " \ a negative one between 2930and 2922 cm"1 and a positive cross peak between 2922 and 2915 cm" *. Interest-ingly, Fourier self-deconvolution failed to resolve these features under the broadasymmetric C-H stretching peak.

This ability to enhance spectral resolution has also been demonstrated in thecase of atactic poly(methyl methacrylate). This has three very overlapped peaks inthe C-H stretching region, whose presence has been revealed by studies onpolymers with varying degrees of deuteration [33], a useful but not particularlyconvenient approach. The three peaks are specific for the ester methyl groups, thea-methyl groups and the backbone methylene groups. The 2D correlationapproach yields equally specific information without resort to deuterated poly-mers. Strong synchronous cross peaks occur at spectral coordinates specific forester methyl groups, and the a-methyl group is clearly differentiated from theester methyl group on the basis of cross peaks appearing in the asynchronousspectrum. Furthermore, analysis based on the signs of cross peaks providesdetailed information on submolecular reorientation mechanisms that occur withsmall strains.

The technique has also been used to study the dynamic behaviour of a poly-mer-dispersed liquid crystal subjected to an electric field [18]. The liquid polymerused was the commercially available nematic liquid crystal mixture E7, whichcontains four nitrile and ethyl substituted bi- and tri-phenyls. It was blended witha polymer precursor consisting of a mixture of an acrylate monomer, an acrylateoligomer and a UV curing agent. The 2D correlation analysis showed that therigid core of the liquid crystal molecules re-orients as a unit, and suggests that thepolymer side chains existing in the interface between the polymer and the liquidcrystals may re-orient in phase with the liquid crystal re-orientation by interac-tion with the liquid crystal molecules.

The work discussed hitherto has been concerned solely with polymers subjec-ted to sinusoidally varying stress. The use of stress with this simple wave form isnot a necessary condition for the production and use of 2D infrared correlationspectroscopy. Noda [35] has shown that signals fluctuating as an arbitraryfunction of time may be dealt with and, in some circumstances, offer advantagesover sinusoidal signals. He has provided the necessary mathematical frameworkfor this more general approach, and the method has been used to study thephotopolymerization of acrylic and epoxy monomers [36]. By this approach,features associated with spectral intensity changes and peak shifts arising fromthe polymerization reactions were clearly observed. It is reasonable to predictthat the method will find further applications in this field.

7.4 ELASTOMERS UNDER STRESS

Unlike thermoplastics, elastomers are capable of supporting massive reversiblestrains and yet recovering their original dimensions, i.e., they behave as 'classic'springs recovering their dimensions elastically and reversibly after deforming tothree and even six times their original length. Examination of the stress: straincurve shows, however, that many rubbers do not obey Hooke's law, theirmodulus rising with strain. This comes about because they partially crystallize athigher strains, the micelles of crystalline order lying parallel to the stressdirection. Since crystalline polymers show molecular vibrational characteristicsdifferent from the non-crystalline materials (because the vibrations are sensitiveto the rotational isomerism of the backbone and the intermodular interactions),the spectrum of the highly strained polymer will differ from that of the relaxedstate. In addition, of course, the spectrum will reflect the onset of orientation inthe otherwise random matrix and in the crystallites as they form. To demonstratethese points, we offer in Figure 7.14 spectra of vulcanized natural rubber, bothstressed and relaxed [37].

The vibrational changes that occur on orientation and crystallization havebeen used to research the origin of the residual orientation frequently found inblown or extruded film. These materials frequently show quite well developedorientation, and hence are useful as shrink wrapping. As the flowing melts fromwhich they are formed are optically dichroic, it seems reasonable to proposea model involving flow-orientation-crystallization and solidfication in anoriented manner. It has been shown, however, that the orientation of a flowingpolyethylene melt (as measured by infrared, Raman diffraction and X-raydiffraction) is very small [38].

This can only mean that the few longer chains present are oriented under flow,and these nucleate oriented crystallization. The thesis has been confirmed byexamining the virbational spectra of polyethylene rubber [39] (linear polyethy-lene cross-linked and kept above its melting point). The material shows hardlyany orientation when highly extended, but cooling the film without relaxationproduces highly oriented and crystalline material.

Although most of the investigation of the effect of strain on the vibrationalspectrum of elastomers has been confined to the infrared spectrum of naturalrubber films, more recently FT Raman results have appeared. Again see Fig-ure 7.14. An analysis of the bands which alter under strain is in hand [40].Similarly, work on butyl rubber (polyisobutylene) containing a small concentra-tion of a diene and cross-lined shows that the spectrum changes dramatically asthe rubber is strained. See Figure 7.15. There is, however, a persistent experimen-tal problem in this type of investigation. FT Raman study is far more convenientand relevant than infrared because the sample does not have to be restricted toa thin film, and any stretching rig can simply and easily be mounted in the samplearea of the instrument. Unfortunately, however, the near-infrared laser radiation

Stretched

Relaxed

inte

nsity

/arb

itrar

y un

its

Frequency /wavenumber

Stretched

Relaxed

Inte

nsi

ty/a

rbitr

ary

uni

ts

Frequency /Wavenumber

Figure 7.14 The FT Raman measurements on crosslinked natural rubber stretched andrelaxed and recorded in two ways as illustrated. Laser polarised vertically.

Raman shift / wavenumbers

Figure 7.15 Raman spectra of butyl rubber

focused into the specimen causes heating and hence atypical stress: strainpatterns around the sampled point. The problem is simply illustrated in thatchanges to the spectrum induced by strain may be apparent only if low laserpowers are used. Although experimentally most restricting, one excellent methodof avoiding the problem is to stretch and then cool in a cold cell. Clearly, novelcold cell/stretching facilities need developing, but fortunately pioneering work inthis field was completed many years ago by Downes [42], who recordedconventional Raman spectra on elastomers strained near their Tg. The pro-ceedures used have been refined and are reported in Ref. 40.

7.5 CONCLUSION

Quite clearly, the advent of Fourier transform infrared and Raman methods andthe extension to dynamic or time resolved processes have already produceda whole raft of new results and will certainly continue to do so. The measurementof orientation and the structural changes that occur to specimens when stressedin a variety of ways are bound to be studied in detail, if for no other reason thanthat both FTIR and Raman spectroscopies are versatile, simple to apply andrapid.

(ii) Butyl Rubber, stretched

(i) Butyl Rubber, unstretched

Inte

nsity

At a conference held recently, Everall [43] described a newly developed Ramansystem involving fibre optical coupling between the optical system and thespectrometer, and showed how it could be used to monitor and control on-linethe commercial production of polyethylene terephthalate film. Thus, the exten-sion of these methods into commercial control is upon us.

7.6 REFERENCES

[1] W. Glenz and A. Peterlin, J. MacromoL ScL, Phys., 1970, B4,473.[2] M.A. McRae and W.F. Maddams, J. Appl. Polym. ScL, 1978, 22, 2761.[3] W.F. Maddams and J.E. Preedy, J. Appl. Polym. ScL, 1978, 22, 2721.[4] W.F. Maddams and J.E. Preedy, J. Appl Polym. ScL, 1978,22, 2739.[5] W.F. Maddams and J.E. Preedy, J. Appl. Polym. ScL91978, 22, 2751.[6] A. Keller and MJ. Machin, J. MacromoL ScL Phys., 1967, Bl, 41.[7] J. Purvis, D.I. Bower and LM. Ward, Polymer, 1973,14, 398.[8] J. Maxfield, R.S. Stein and M.C. Chen, J. Polym. ScL, Polym. Phys. Ed., 1978,16,37.[9] RJ. Roe and W.R. Krigbaum, J. Appl. Phys., 1964,35, 2215.

[10] D.Y. Yoon, C. Chang and R.S. Stein, J. Polym. ScL, Polym. Phys. Ed., 1974,12,209.[11] M. Kashiwagi, A. Cunningham, AJ. Manuel and LM. Ward, Polymer, 1973,14,111.[12] J. Purvis and D.I. Bower, J. Poly. ScL, Polym. Phys. Ed., 1976,14, 1461.[13] J. Purvis and D.I. Bower, Polymer, 1974,15, 645.[14] M.E.R. Robinson, D.I. Bower and W.F. Maddams, J. Polym. ScL, Polym. Phys. Ed.,

1978,16,2115.[15] D.I. Bower, J. King and W.F. Maddams, J. MacromoL ScL Phys., 1981, B20, 305.[16] PJ. Hendra and P. Bentley, Spectrochim. Ada, Part A, 1995, in press.[17] I. Noda, A.E. Dowrey and C. Marcott, Appl. Spectrosc, 1988, 42, 203.[18] B. Chase and R. Ikeda, Appl. Spectrosc, 1993, 47, 1350.[19] MJ. Smith, CJ. Manning, R.A. Palmer and J.L. Chao, Appl. Spectrosc, 1988,42,546.[20] CJ. Manning, R.A. Palmer and J.L. Chao, Rev. ScL Instrum., 1991,62,1219.[21] V.G. Gregoriou, M. Dawn, M.W. Schauer, J.L. Chao and R.A. Palmer, Appl.

Spectrosc, 1993,47,1311.[22] R.A. Palmer, J.L. Chao, R.M. Dittmar, V.G. Gregoriov and S.E. Plunkett, Appl.

Spectrosc, 1993,47,1297.[23] C. Marcott, E.A. Dowrey and I. Noda, Appl. Spectrosc, 1993, 47,1324.[24] AJ. Turner and R.A. Hoult, Poster presented at the 9th International Conference on

Fourier Transform Spectroscopy, Calgary, August 1993.[25] R. Bennett, Spectrochim. Ada, Part A, 1994,5OA, 1813.[26] I. Noda, J. Am. Chem. Soc, 1989, 111, 8116.[27] I. Noda, Appl. Spectrosc, 1990, 44, 550.[28] I. Noda, A.E. Dowrey and C. Marcott, Makromol. Chem., Makromol. Symp., 1993,

72,121.[29] V.G. Gregoriou, I. Noda, A.E. Dowrey, C. Marcott, J.L. Chao an R.A. Palmer, J.

Polym. ScL, 1993, B31.[30] H.H. Song, D.Q.Wu, B. Chu, M. Satkouski, M. Ree, R.S. Stein, and J.C. Phillips,

Macromolecules, 1990,23, 2380.[31] R.A. Palmer, V.G. Gregoriou and J.L. Chao, Polym. Prepr., 1992, 33(1), 1222.[32] K. Saijo, S. Suehiro, T. Hashimoto and I. Noda, Polym. Prepr. Jpn., 1989,38,4212.[33] S.K. Dirtikov and J.L. Koenig, Appl. Spectrosc, 1979, 33, 555.

[34] R. Hasegawa, M. Sakamoto and H. Sasorki, Appl. Spectrosc, 1993, 47,1386.[35] I. Noda, Appl Spectrosc, 1993,47,1329.[36] T. Nakano, S. Shimada, R. Saitoh and I. Noda, Appl Spectrosc, 1993,47,1337.[37] C. Jones, Spectrochim. Ada, Part A, 1991, 47A, 1313.[38] PJ. Hendra, M.A. Taylor and H.A. Willis, J. Polym. ScL, 1986, 24, 83.[39] PJ. Hendra, T.H. Stevenson, W.F. Maddams, V. Zichy and M.E.A. Cudby, Plast.

Rubber, Process. Appl, 1990,14, 7.[40] A.M. Healey, PJ. Hendra and Y.D. West, Spectrochim Ada, 1995, 51A in press[41] PJ. Hendra and P. Bentley, Spectrochim. Acta, in press.[42] J.B. Downes, MPhil Thesis, University of Southampton 1972.[43] N. Everall, ICI Wilton Research Centre, Personal communication; J. Andrews,

Spectrosc Eur., 1995,7(8), 8.[44] I. Noda, A.E. Dowrey and C. Marcott, Appl Spectrosc 1993,47, 1317.

8 DEFORMATIONSTUDIESOFPOLYMERS USING RAMANSPECTROSCOPY

R. J. YOUNGManchester Materials Science Centre, UMIST/University of Manchester,Manchester Ml 7HS, UK

8-1 INTRODUCTION

Developments in the area of the application of Raman spectroscopy of polymershave been covered elsewhere in this book [1] and this chapter is concerned witha specific application, the use of Raman spectroscopy for the characterization ofthe deformation of a wide range of both polymers and polymer-based compos-ites. It is found that the wavenumbers Av of the bands in the Raman spectra ofsome of these materials change under the action of stress a or strain e. This changein the band position is characterized by either dAv/d(T or dAv/de, which can berelated directly to the deformation of the individual bonds in the materials.

There are several reasons for the upsurge of interest in the use of Ramanspectroscopy for deformation studies. There have recently been significantimprovements in the hardware available for Raman spectroscopy. The introduc-tion of array detectors has enabled a particular region of a spectrum to beacquired simultaneously rather than stepping through single points. This reducesdrastically the time required to obtain a spectrum. A significant development inthis area has been the introduction of highly sensitive charge coupled device(CCD) cameras [2], Using a typical Raman microprobe system incorporatinga CCD detector, the spectrum of a Kevlar fibre consisting of a single band in theregion of 1580-1640Cm"1 can be obtained from areas of the order of 2jim indiameter in a few seconds using a low-power 10 mW He-Ne laser [3]. A typicalfull spectrum for a fibre of Kevlar 49, made up by joining several such single-bandspectra, is shown in Figure 8.1.

More recently there have been reports [1,4, 5] of the development of FourierTransform (FT) Raman systems which have certain advantages over conven-tional dispersive systems. FT Raman systems have been described in Chapter 7,and are potentially highly efficient, with a high calibration accuracy. Oneparticular advantage for polymers is that the use of IR excitation wavelengths


Wavenumber / cm"1

Figure 8.1 Raman spectrum for a single filament of Kevlar 49 in the region 1100-1700cm"* obtained using a low-power He-Ne laser (after [38])

greatly reduces the problems of fluorescence. Unfortunately, however, the inten-sity of the Raman scattering is reduced by an order of magnitude by the use of IRradiation rather than excitation in the visible region because the scatteringintensity depends on the fourth power of the excitation frequency, vjj. The choicebetween the use of a dispersive or a FT system depends upon the scatteringcharacteristics of the material under investigation and the type of informationbeing sought. Another significant advance is the development of the Ramanmicroprobe into a true Raman microscope, reported recently by Batchelder andcoworkers [6,7], whereby images of the Raman scattered light may be obtainedand spectra may be recorded under confocal conditions. There is clearly plenty ofscope for the use of these new systems in the analysis of polymers, and there is nodoubt that there will be many such reports in the years to come.

8.1.1 POLYDIACETYLENE SINGLE CRYSTALS

The first reported and one of the best examples of the use of Raman spectroscopyto follow deformation in polymers is the case of substituted polydiacetylene singlecrystals [8-12]. The macroscopic polymer crystals are produced by the solid-state polymerization of substituted diacetylene single crystal monomers. Thereaction is a topochemical solid-state polymerization [13], and the crystalsproduced have a high degree of perfection [14].

Cottle et al. [15] reported in 1978 that the imposition of hydrostatic pressurecaused an increase in frequency of the four Raman-active vibrational modes in

Inte

nsity

(Arb

itrar

y Un

its)

poly(2,4-hexadiyne-l,6-bis(p-toluenesulphonate) (polyTSHD) [14]. They relatedthese shifts to the decrease in the separation between the carbon atoms on thepolymer backbone. A perhaps more significant discovery had been reporteda year earlier by Mitra et al. [8], who found that there was an approximatelylinear decrease in two vibrational frequencies of single crystal fibres ofpoly(bisphenylurethane-2,4-hexadiyne-l,6-diol) (polyPUHD) [14] subjected toa tensile stress. They showed that this decrease could be explained in terms of theanharmonicity of the bonds between the carbon atoms on the chain. This studyhas been followed by a series of measurements of the dependence of the vibrationfrequencies upon stress and strain for several different substituted polydiacety-lenes [9-12]. Batchelder and Bloor [9] performed an elegant series of experi-ments upon cleaved single crystal fibres of polyTSHD fixed to the aluminiumjaws of a small micrometer-driven straining rig by an epoxy resin adhesive. Theyshowed that care had to be taken to obtain an accurate estimate of the strain inrelatively short fibres during deformation, and suggested that the exact values ofstrain reported by Mitra et al. [8] may be in error.

The dependence upon strain of the wavenumbers for the Raman modes ofseveral different substituted polydiacetylene single crystal fibres has been meas-ured by various groups of workers [10,12,14]. Most attention has been paid tothe behaviour of the V1 mode which is essentially the symmetrical stretching modeof the C = C triple bond, as this is the most sensitive to applied strain. Thedependence of the wavenumber of this band upon applied strain for a polyTSHDsingle crystal [11] is shown in Figure 8.2, and the dependence of the position ofthis Raman band upon strain for four polydiacetylenes [14] with different

Strain (%)

Figure 8.2 Dependence of the wavenumber of the C = C Raman band upon strain fora polyTSHD single crystal (after [H])

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/cm

*1

Table 8.1 Values of the strain-induced Raman bandshifts for the C = C stretching band of different sub-

stituted polydiacetylene single crystals

Polymer [14] dAv/de(cm" 7%) Reference

polyPUHD ^20 [8]polyTSHD -20.3 ±0.5 [9]polyDCHD -19.7±0.4 [18]polyEUHD -18.8 ±0.4fl [10]

-19.0 ±0.3»

"Phase 1fcPhase 2.

side-groups is summarized in Table 8.1. It is important to note that the rate ofchange of the wavenumber of the band with applied strain, dAv/de, for the C=Cstretching V1 mode is « — 20 cm " 7 % and is virtually identical for all poly-diacetylene single crystals, even though they may have different modulus values[14]. This is because the structure of the backbone is very similar in each case andthe shift of the Raman band wavenumber with applied strain is a function only ofthe backbone structure, whereas the Young's modulus depends upon both theproperties of the backbone and the size of the side-groups [12,16, 17].

8.1.2 EXTENSIONOFTHETECHNIQUETOOTHER MATERIALS

Over the 15 years since the original Raman deformation studies upon poly-diacetylene single crystals, the technique has been developed and refined toinvolve the study of a wide range of different high-performance polymers andother materials. These have included rigid-rod polymer fibres [19-21], carbonfibres [22-24] and ceramic fibres [25-27]. This present chapter will concentrateupon recent research concerning the use of Raman spectroscopy to follow thedeformation of aramid fibres and gel-spun polyethylene fibres and the possibilityof the extension of the technique to isotropic polymers, and also the importantand developing application of the method to the study of the deformation offibres within composites.

8.2 HIGH-PERFORMANCEPOLYMER FIBRES

8.2.1 AROMATICPOLYAMIDEFIBRES

Aromatic polyamide (aramid) fibres are produced by spinning from liquidcrystalline solutions using solvents such as sulphuric acid [28,29]. The properties

of the fibres can be improved by a brief heat treatment under tension at elevatedtemperatures [29]. Fibres of aramids with high levels of stiffness and strengthhave been available commercially for several years and they are now used, undertrade names such as Kevlar (Du Pont) and Twaron (Akzo), in a variety ofapplications, particularly in the areas of fibre-reinforced composites, protectiveclothing, tyre cord and ropes [30]. Original materials such as Kevlar 49 wereproduced with values of filament modulus of the order of 120 GPa, but recentdevelopments have led to fibres with higher degrees of crystallinity such as Kevlar149, which has a modulus of 170GPa [29].

The first report of the Raman spectrum of an aramid fibre was made in 1979 byPenn and Milanovich [31], and a typical spectrum for a single filament of Kevlar49 was given in Figure 8.1. Aramid fibres generally give strong Raman scatteringwith little fluorescence, and well-defined spectra can be obtained from singlefilaments using low-power laser beams [32-38]. The structure of the most widelyused aramid, poly(p-phenylene terephthalamide) is shown below.

It has been pointed out [30] that the C-N bond has considerable double bondcharacter which, along with the para-substituted phenyl group, leads to a reson-ance conjugated system giving restricted rotation about the bond. These factorshelp to give rise to liquid crystalline solutions, which allows the formation ofhighly oriented fibres. They also lead to the characteristic yellow coloration ofaramid fibres and probably increase the intensity of the Raman scattering due toresonance enhancement [H] . Penn and Milanovich [31] were able to assignsome of the Raman bands to vibrations of structural groups in the poly(p-phenylene terephthalamide) molecule by comparison with model compounds,and the strong band at «1610cm"1 has been assigned to stretching of thep-phenylene ring.

Penn and Milanovich [31] looked at the effect of deformation upon the Ramanspectrum of Kevlar 49 and, although they found that stress caused a change in therelative band intensities and depolarization ratios, they did not find any measur-able shift in the band wavenumbers with stress [31]. This finding is completely atodds with the findings of Young and coworkers [32, 33], who have shown thatsignificant and measurable frequency shifts of several Raman bands in Kevlartake place on the application of stress or strain.

It is found that the position of the Kevlar 1610cm"1 Raman band shifts tolower frequency under the application of a tensile stress, as shown in Figure 8.3.The peak position of the band is plotted as a function of strain in Figure 8.4 for

Wavenumber / cm*1

Figure 8 3 Shift in the position of the 1610 cm ~~ * Raman band for Kevlar 49 at differentlevels of tensile strain (indicated) (after [38])

Inte

nsi

ty (

Arb

itra

ry U

nits

)

Fibre Strain, e / %

Figure 8.4 Variation of the peak position of the 1610cm"1 Raman band with tensilefibre strain for the five different aramid fibres (after [38])

two different commercial fibres and three experimental fibres [38], and it can beseen that there is an approximately linear shift in peak position Av with strain e upto failure at « 3 % strain. The slope of the line is given by dAv/de, and it isnormally found [33, 37, 38] that for different aramid fibres the slope is propor-

Peak

Pos

ition,

Av

/ cnv

1

Figure &5 Dependence of the rate of shift per unit strain for the 1610cm * Raman bandupon fibre modulus for the five different aramid fibres shown in Figure 8.4. The symbolshave the same meaning as in Figure 8.4 (after [38])

tional to the fibre Young's modulus £f, i.e.

dAv/deocEf (1)

Figure 8.5 give a plot of dAv/de versus fibre modulus £ f, and it can be seen thatthere is an approximately linear relationship consistent with Equation (1). This isan indication that the Raman technique is probing molecular stretching directly[37] and is consistent with the theoretical work of Northolt and coworkers[39-41]. They suggested that, for the deformation of aramid fibres such asKevlar, the total strain is the sum of the strains due to two deformation processes,stretching and rotation, such that

t̂otal = ^stretch + r̂otation w

It has been shown [37] that the Raman technique follows only the crystal andmolecular stretching and, moreover, that the change in the peak position dAv isa measure of the molecular stress rather than the molecular strain [37]. The rateof shift per unit strain in the higher modulus fibres is a reflection of the higherlevels of molecular stress in such fibres.

Penn and Milanovich [31] expressed surprise that they did not find anyfrequency shifts during the deformation of aramid fibres, bearing in mind theearlier polymer deformation studies using infrared [42] and Raman spectroscopy[8] and wide-angle X-ray scattering (WAXS) studies of deformed aramid fibres[39]. The situation was confused further by the publication by Edwards andHadiki [34], who reported that no Raman band shifts were found when Kevlar

Fibre Modulus, E1/Gpa

Rat

e of

Ban

d S

hift,

dA

v / d

e cm

1 / %

fibres were deformed. They claimed that their work supported the findings ofPenn and Milanovich [31] and disputed the findings of Young and coworkers[32, 33]. The situation was eventually sorted out by a careful study by Youngetal. [35], who repeated the experiments of both groups. One significantdifference was that Penn and Milanovich [31] and Edwards and Hadiki [34] hadboth used a relatively high-power argon ion laser, whereas Young and coworkers[32,33] had used a low-power He-Ne laser. It was demonstrated that the 488 nmline of argon ion lasers caused significant radiation damage to Kevlar fibres andled to the fibres fracturing at very low stresses and strains [35]. Hence the groupsusing argon ion lasers [31,34] had damaged their fibres, and careful inspection oftheir data showed that they had not been able to apply very high strains, at leastnot large enough to cause significant Raman band shifts. In contrast it was shownthat the 632 nm line of the He-Ne laser produced virtually no radiation damage,and so high strains could be applied and significant band shifts obtained [35].Hence the dispute was resolved.

8.2.2 POLYETHYLENE FIBRES

There has been considerable interest recently in preparing highly oriented fibresof polyethylene with very high values of stiffness and strength [43-45]. Thetechniques employed to achieve this end include ultra-drawing [43], solid-stateextrusion [44] and gel drawing or spinning [45]. It has been possible by gelprocessing of ultra-high molar mass polyethylene to produce fibres with Young'smodulus values of up to 200 GPa and strengths in the range 2-5 GPa, and suchmaterials are now available commercially under the trade names of Spectra fromAllied Signal in the USA and as Dyneema from DSM in the Netherlands. Thesevalues of stiffness and strength are close to the theoretical limits for polyethylene,which are about 300GPa for the modulus [46] and 20-30GPa for the strength[47]. Although real materials rarely have mechanical properties so close to theirtheoretical limits, it is of considerable interest to know how structural featurescontrol the mechanical properties of these high-modulus fibres and what factorslead to this shortfall in properties. For example, it is found that fibres producedunder different conditions may have the same levels of orientation and degrees ofcrystallinity but very different levels of stiffness and strength [45]. There mustclearly be structural differences in the fibres which lead to a difference in themolecular deformation processes in the fibres.

It has been relatively difficult to devise experiments to follow the deformationof these high modulus fibres on the molecular level. Wide-angle X-ray scatteringexperiments upon fibres subjected to stress have been used extensively to monitorstrains in the crystalline regions of high-modulus polyethylene fibres [48, 49].Such experiments can be relatively tedious, requiring long data-collection times(unless synchrotron radiation sources are employed [50,51]), and the interpreta-

tion of the data often requires assumptions to be made about the state of stress inthe materials. It has been known for many years that the vibrational modes ofpolyolefin molecules are affected by the application of stress, particularly in theoriented state [42,52,53], and considerable effort has been put into studying theeffect of stress upon the infrared spectra of such materials. In general it has beenfound that some infrared bands shift to lower frequency and increase in width,often also accompanied by the development of an asymmetric tail. However,difficulties are often encountered in obtaining infrared spectra from fibres, and ithas been recognized recently that the measurement of Raman spectra during thestressing of highly oriented polyethylene fibres offers a unique opportunity tofollow the deformation of these materials on the molecular level [50-60].

It is found that well-defined Raman spectra can be obtained from highlyoriented polyethylene fibres when the polarization direction of the laser beam isparallel to the fibre axis. Figure 8.6 shows a Raman spectrum in the region of1080-1150 cm ~ l for a high-modulus gel-spun polyethylene fibre before and afterdeformation [59]. It can be seen that there is a change in the position and shape ofthe 1128 cm ~ * Raman band, which has been assigned to the symmetric stretchingof C-C single bonds [55]. It can be seen that, following deformation, the banddevelops a low-frequency tail, and it is possible to fit the band to two Gaussiancurves. In fact, it has also been found that even before deformation the asymmetryof the band can be fitted to two peaks [59,60]. The variation in the position of thetwo peaks with strain is shown in Figure 8.7, and it can be seen that they bothmove to lower frequency, although the smaller peak moves most rapidly. Thistype of behaviour for polyethylene has been interpreted as being due to thepresence of two populations of molecules in the microstructure of the gel-spunmaterial. During deformation they experience different levels of stress. It is found[59, 60] that the size of the rapidly moving peak and the rate of shift per unitstrain scale with the Young's modulus of the fibre, and hence it appears that thechanges in the Raman spectra are related to the presence of microstructuralfeatures which give rise to the impressive mechanical properties of the fibres.

There has been some controversy in the literature concerning the exact form ofthe stress-induced Raman shifts in polyethylene fibres. Some workers reportednon-linear peak shifts with significant broadening of the bands and the develop-ment of a low-frequency tail [53, 55], whereas others apparently found linearpeak shifts with little broadening [54, 56]. There is no doubt that, in someinstances, the differences stem from differences in fibre structure due to variationsin manufacturing route and testing conditions. Band splitting is certainly moreapparent in the gel-spun polymer deformed rapidly and obtaining spectra usinga CCD camera. However, it appears that there is also a difference in the methodsof data interpretation. If the Raman band is fitted to a single function (e.g.Gauss-Lorentz sum function [55]) then it is difficult to deal with any bandasymmetry. For example, Prasad and Grubb [55] reported that, although theshift of the band peak fitted to a symmetrical function is not linear with applied

Wavenumber/cnr1

Figure 8.6 Raman spectrum in the region 1080-1150Cm"1 for an experimental high-modulus gel-spun polyethylene fibre (after [59]). The Raman band has been fitted to twoGaussian curves, (a) Fibre undeformed; (b) at a strain of 4.06%

stress, the shift of the centre of gravity of the full band is linear. Such problems areovercome if the shifting Raman band is fitted to more than one function, i.e. if it isassumed that the band splits into several components as in Figure 8.6. Thisclearly implies that either the fibres must have a two-phase structure or theremust be different stresses on certain molecules in the structure. Prasad and Grubb[55] interpreted the low-frequency tail of the 1063 cm"1 C-C asymmetricstretching band of their spectra as non-crystalline overstressed tie molecules, asthey did not observe the development of any tail in their WAXS peaks. However,recent WAXS studies [57] has indicated that the Bragg peaks in gel-spun

Wavenumber/cm1

Inte

nsity

(A

rbitr

ary

Uni

ts)

Inte

nsity

(A

rbitr

ary

Uni

ts)

Strain %

Figure 8.7 Variation in the position of the two peaks in the Raman spectra of thehigh-modulus gel-spun polyethylene fibre in Figure 8.6 with strain (after [59])

polyethylene may also split into two during deformation. Clearly more work isrequired to ascertain the relationship between Raman band movement and thebehaviour of WAXS peaks under stress, since this may enable a better insight tobe obtained concerning the relationship between crystalline and moleculardeformation processes.

Several models have been proposed to explain the mechanical properties ofhigh-modulus polymer fibres [54, 61-63], and they all assume that the fibrescontain some highly stressed molecules or crystals contributing to the high levelof modulus, with other molecules or crystals taking lower levels of stress. Wongand Young [61] have shown that there is a bimodal distribution of stress in thecrystalline regions of gel-spun polyethylene fibres due to their two-phase micro-structure, and have demonstrated that the molecular deformation behaviour canbe interpreted quantitatively using a parallel-series Takayanagi model. Theyhave shown that the Young's modulus of the crystalline regions increases with thedegree of chain extension, and that for the highest-modulus fibres may be close tothe theoretical modulus of polyethylene crystals. It appears that for the first timeRaman spectroscopy allows the deformation of the different components in thestructure to be determined directly [60, 61].

NARROW PEAK

BROAD PEAK

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8.3 ISOTROPIC POLYMERS

Fina et al. [64] found that significant shifts in the wavenumbers of the Ramanbands in poly(ethylene terephthalate) with moderate degrees of orientation couldbe obtained, and so the question arises as to whether or not measurable shifts inRaman bands could be obtained using isotropic polymers which contain little orno molecular orientation. In a little-quoted letter published in 1976, Evans andHallam [65] reported measurable shifts to lower frequency in the wavenumbersof the bands in the Raman spectra of polymers such as polypropylene, polycar-bonate, polystyrene and nylon 66 from samples which were presumably un-oriented (although they did not give any details of specimen preparation). Shiftsof the order of 1 cm" * were obtained for specimens deformed up to the point ofspecimen necking, but the exact values of shift were found to depend upon theband in question [65]. They did not give any values of stress but, assuming a yieldstress of their polypropylene of % 30 MPa, then the shifts they measuredapproach — 30 cm ~ VGPa, which is quite significant. However, the relatively lowyield stress of the material means that the magnitudes of the shifts will always berelatively small. Their data for polypropylene showed that between the point ofyield and eventual specimen fracture the behaviour of the Raman bands isrelatively complex, and that the wavenumber increases, decreases or stays thesame for different bands. Unfortunately, they did not give sufficient detail of theirmeasurements to explain this effect. Evans and Hallam [65] pointed out thesignificant advantages of the Raman technique over similar infrared measure-ments; although a full publication of their work was promised, no record of itspublication has been found.

Over recent years a completely different approach has been adopted by Hu,Day, Stanford and Young [66-69], who have shown that, through the syn-thesis of specially designed copolymers, it is possible to prepare isotropicpolymers for which the deformation can be followed using Raman spectroscopy.They have demonstrated that such materials can be used for the study of polymersurface and interface deformation [68,69] and their work in this area is reviewedbelow.

8.3.1 URETHANE-DIACETYLENE COPOLYMERS

The approach that was adopted [66-69] was to prepare a series of urethane-diacetylene copolymers in which polydiacetylene units are incorporated intosegmented copolyurethanes. It was shown in Section 8.1.1 that large strain-induced Raman band shifts can be obtained during the deformation of poly-diacetylene single crystal fibers [8-12]. In fact, it is found that the largest shiftmeasured so far ( — 20 cm"7% strain) is for the C = C triple bond stretchingband of polydiacetylenes (Table 8.1).

Polyurethanes constitute a versatile class of materials ranging from softelastomers to glassy resins, and are readily produced by a variety of processes inmany different forms. Fibres, films, bulk sheets and surface coatings can all beformed either from solution or in bulk. Segmented copolyurethanes, because oftheir phase-separated structures, are particularly attractive, as they enable thecombination of disparate polymer properties to be obtained within a singlematerial. Polydiacetylene single crystals are formed by the rapid solid-statepolymerization [13, 14] of substituted diacetylene monomer crystals on theapplication of heat or radiation. It is possible to induce similar solid-statereactions known as "cross-polymerization" in the diacetylene groups of repeatunits in certain copolyurethanes and copolyesters [70-72]. Cross-polymerizationwithin the crystalline diacetylene regions produces a network structure in whichthe chains connecting the polydiacetylenes are analogous to the substituentside-groups in the polydiacetylene single crystals[13,14]. In this way, linearcopolyurethanes containing phase-separated, diacetylene-containing domainscan be crosslinked in situ and transformed into insoluble and infusible materials[73-75]. These previous studies were concerned only with elastomeric materialsformed via a two-stage solution process [73-75] at only one composition. Themore recent studies [66-69] have been concerned with the development of morerigid copolymers formed by a relatively simple one-shot bulk polymerizationroute.

The reactants used to prepare the copolyurethanes were 4,4'-methylene-diphenylene diisocyanate (MDI), 2,4-hexadiyne-l,6-diol (HDD) and a poly-propylene glycol (PPG400). It is possible to vary the structure and consequentproperties of the materials by varying the relative proportions of HDD andPPG400. The exact details of the reaction conditions are give elsewhere [67],and linear polymers can be produced with molar masses of the order of10000 gmol"1. These linear segmented urethane copolymers are soluble ina variety of solvents, and can therefore be processed into a variety of forms such assurface coatings [68].

The structure of the material consists of diacetylene-urethane hard segmentsA and polyether-urethane segments B. The development of this alternatingsegmented structure results in phase separation owing to the incompatibility ofthe chemically distinct segments A and B. Thermodynamic incompatibilitydepends primarily on the interaction parameter between the diacetylene- andpolyether-based segments (determined by their intrinsic solubility parameters)and their sequence lengths (degrees of polymerization). The development ofhydrogen bonding and potential crystallinity of the hard segments furtherenhances the driving force for phase separation. The linear copolyurethanes thusform as essentially a two-phase morphology consisting of rigid, highly hydrogen-bonded hard segment domains (with a distribution of sizes) dispersed in a ductilepolyether-urethane phase. The formation of linear diacetylene-containingcopolyurethanes provides the distinct advantage, in subsequent applications, of

enabling the copolymers to be processed from solution. During or after removalof solvent, the phase-separated copolymers can be rapidly crosslinked in situusing heat or radiation, either of which causes cross-polymerization of diacety-lene units within the hard segment domains.

In practice, however, the solid-state topochemical reaction involves manychains packed within the hard segment domains, and the resulting cross-polymerization occurs three-dimensionally as depicted in Figure 8.8. The dia-cetylene-urethane hard segments are assumed to be crystalline and have fullyextended conformations in which the HDD unit is alUtrans, and the chains are

Figure 8.8 Schematic representation of the solid-state topochemical polymerization ofthe diacetylene-urethane hard segments: (a) linear segmented block copolymer; (b) cross-polymerized material (after [67])

staggered so that adjacent chains are linked by straight C = C • • • H—N hydrogenbonds in both directions perpendicular to the urethane chain axes. It is found[68] that these hard segment domains are organized in the form of spheruliticentities, which are seen to be of the order of 1 ̂ m in diameter using transmissionelectron microscopy.

The idealized structure in Figure 8.8, however, is unlikely to be totallyrepresentative of the overall structure actually obtained for the hard segmentdomains, although regions of such three-dimensional order must exist withindomains dispersed throughout the copolyurethanes in order to achieve overallcross-polymerization. The formation of fully conjugated polydiacetylene (PDA)chains within the phase-separated copolyurethanes produces dramatic colourchanges (white -• red -* deep purple) and transforms the copolymers into com-pletely insoluble and infusible materials. The extent of cross-polymerization thatis achieved depends upon a number of factors such as the time and temperature ofheating, the concentration of hard segment domains and the degree of orderwithin the domains [67].

The relationship between chemical composition, structure and properties forthe copolymers has been described in detail elsewhere [68, 69]. In general it isfound that the glass transition temperature Tg and the Young's modulus E in-crease with hard segment content and heat treatment temperature. It was foundthat the material with the optimum composition and properties had a value of T%

of %80°C and a Young's modulus (isotropic) of « 1.7GPa, both of which aretypical of a conventional glassy polymer.

8.3.2 DEFORMATION STUDIES

A Raman spectrum for a sample of the cross-polymerized copolyurethane isshown in Figure 8.9 and it can be seen that it has four main scattering bands [67,68]. The spectrum is remarkably similar to that obtained from a polydiacetylenesingle crystal fibre [H] . For the fibres, a strong spectrum is obtained only whenthe fibre axis is parallel to the direction of polarization of the laser beam, whereasit is found that the spectrum from the copolymer is identical for all orientations ofthe sample [67,68]. This shows clearly the isotropic nature of the copolymer. Itwas found [67,68] that the intensities of the bands in the Raman spectrum variedwith both the hard segment content and the heat treatment temperature and,moreover, it was demonstrated that this variation could be used to follow thecross-polymerization reaction. In particular, the C = C triple bond stretchingband at « 2090 cm ~ l is not present before cross-polymerization and is indicativeof the formation of the polydiacetylene chains in the structure.

Figure 8.10(a) shows the position of the C = C stretching Raman band for oneof the copolymers in the undeformed and deformed states [68]. Upon deforma-tion there is a pronounced shift to lower frequency and a slight broadening of the

Wavenumber

Figure 8.9 Full Raman spectrum for the cross-polymerized diacetylene-urethanecopolymer (after [67,68])

Raman band. This shift is a clear indication of stress transfer from the polyether-urethane matrix to the diacetylene-urethane hard segments, and shows that thisstress is translated into direct deformation of the polydiacetylene chains.Broadening of the bands suggests that a distribution of stresses is developedwithin the non-uniform hard segment domains during deformation.

The dependence of the band position upon tensile strain is shown in Figure8.10(b). It can be seen that it is approximately linear up to %1% strain witha slope dAv/de of the order of - 5 c m " 7% strain, and is also completelyreversible on both unloading and reloading. The slope of the line in Figure 8.10(b)is significantly lower than that for polydiacetylene single crystal fibres (Table 8.1)but is comparable with that of high-performance fibres such as those based uponaromatic polyamides [37, 38] or rigid-rod polymers [19-21].

It has been found that the relationship shown in Figure 8.10(b) can be used tomeasure strain in a wide variety of situations. It is known that polydiacetylenesabsorb visible light very strongly, and so for the bulk copolyurethane thespectrum is obtained only from material in the surface regions. Hence any strainmeasurements will be only for surface material. Moreover, since it is possible tofocus the laser beam in the spectrometer to a spot of the order of 2 jim in diameter,it is possible to obtain considerable spatial resolution.

Various examples of using these materials for surface strain mapping have beenpresented in a recent publication [69]. The determination of stress concentra-tions around defects such as holes or notches in a deformed plate of thecopolyurethane is shown in Figure 8.11. A circular hole and a notch of pre-determined dimensions were accurately machined into a 3 mm thick specimen ofthe copolymer. The specimen was deformed in tension in the Raman spec-

lnte

nsit

y

Strain %

Figure 8.10 (a) Shift of the 2090 cm "1 Raman band with strain for the cross-polymerizedurethane-diacetylene copolymer (after [68]); (b) dependence of the peak position of the2090 cm"1 Raman band upon strain; •,first loading; • ; unloading, O, reloading (after[68])

trometer and the change in position of the C = C stretching band at 2090 cm" l

with copolymer strain (measured remotely with a resistance strain gauge) wasdetermined at different positions around the defects, as shown schematically(inset) in Figure 8.11. The slope (dAv/de) of each line, relative to that for theremote applied deformation data (open O) is proportional to the stress concentra-tion at each position. For the hole, the stress concentration, as expected, is highestat the equator (solid • ) and is essentially zero at the pole (solid • ) . For the notch,

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Overall strain/%

Figure 8.11 The effects of stress concentrations on the peak position of the C=C Ramanband for a 3 mm thick cross-polymerized diacetylene-urethane plate deformed in tension.The data were obtained from spectra obtained at the different positions indicated (after[69])

the stress concentration (open O) increases sharply depending on the notch tipradius and the distance from the tip. The results obtained for the various defectgeometries [69] show the stress concentration values measured by Ramanspectroscopy to be very similar to those determined from conventional stressanalyses [76].

The good solubility and adhesive characteristics of the diacetylene-containingcopolyurethanes make them attractive materials for use as surface coatings thatcan be applied with controlled thickness to a variety of substrates. Subsequentcross-polymerization, in situ, would then convert the coatings into crosslinkedmaterials with strain-sensitive properties that can be determined quantitatively,in conjunction with the substrate, using Raman spectroscopy. To illustrate thisuse [68], a solution of the copolyurethane was applied as a 0.05 mm coating to thefollowing substrates: (a) a sheet of highly crosslinked (non-diacetylene- contain-ing) polyurethane resin, (b) an inorganic glass filament (% 25 ^m diameter) and (c)a sheet of aluminium. The solvent was removed by evaporation and the coatingswere thermally treated at 1000C for 4Oh. The coated substrate specimens weredeformed in tension in a Raman spectrometer and the shift in the position (Av) ofthe C=C triple bond stretching band was monitored as a function of the overallspecimen strain e. Excellent linearity between Av and e was obtained in each case.The strain sensitivities of the three coated substrates determined from the slopesof the plots are given in Table 8.2; the values near — 5 cm " 7% strain for dAv/de

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Table 8.2 Strain sensitivities of the Ramanfrequencies of the C = C triple bond stretch-ing band for the diacetylene-urethanecopolymer and for the copolymer coated on

different substrates (after [68])

Substrate dAv/de (cm " 7%)

Pure copolymer 5.3 ± 0.4Polyurethane 5.5 ± 0.4Glass fibre 5.7 ±0.4Aluminium 5.5 ± 0.4

are almost identical to that of the bulk sheet material. Clearly, these resultsdemonstrate that the copolymers can be used as coatings to monitor accuratelythe deformation of a substrate, which is particularly useful if the substrate is ofcomplex geometrical shape or is not readily accessible for direct measurements.As such, the polydiacetylene- containing copolyurethanes are shown to behave asoptical strain gauges.

8.4 COMPOSITES

The shifts in the peak position of the 1610cm" * aramid Raman band, shown inFigure 8.4, can be used as calibration curves to monitor the deformation of fibresin a composite under any state of stress or strain. Previous studies have shown[77-81] that it is possible to map out the distribution of stress or strain alonga single short, discontinuous fibre in a low-modulus epoxy resin. This is describedin detail next.

8.4.1 SINGLE-FIBRECOMPOSITES

Figure 8.12 shows the distribution of strain along a single Kevlar 149 fibre ina model single-fibre epoxy composite [38] calculated from the point-to-pointvariation of the shift of the 1610cm" * aramid Raman band. Measurements weretaken at 20 \im intervals along the fibre for different levels of matrix strain em

ranging from 0% to 2.0% in intervals of 0.4%, and the curves drawn are best fitsto the experimental data. It can be seen that in the unstrained case (em = 0%)there is no strain in the fibre. As em increases the strain in the fibre increases fromthe fibre end up to a plateau value along the middle of the fibre. It is shown thatthe strain in the central region of the fibre is approximately equal to the matrixstrain em for matrix strain levels up to 1.6%. This behaviour is qualitativelyidentical to the distribution of fibre stress and strain predicted by classicalshear-lag theory [82,83], where it is found that, following the shear-lag analysis

Distance Along Fibre, x / pm

Figure 8.12 Derived variation of fibre strain with distance along the Kevlar 149 fibre ina single-fibre composite tensile specimen at different indicated levels of matrix strain em

(after [38])

of Cox [83] , the variation of tensile stress a in the fibre with distance along thefibre x is given by

_ T cosh fli/2-x)1

' - 1 ^ - L cosh/?//2 Jwhere

where E1 is the Young's modulus of the fibre, em is the matrix strain, Gm is theshear modulus of the matrix, A1 is the cross-sectional area of the fibre, r0 is thefibre radius and R is the radius of the cylinder of resin around the fibre.

This behaviour is shown more clearly in Figure 8.13, in which the data pointsfrom Figure 8.12 are fitted to theoretical curves calculated from Equation (3) atmatrix strain levels of 0.4%, 0.8% and 1.2%. The value of R was assumed to bethe half-width of the matrix resin bar, and the matrix shear modulus Gm wascalculated from the matrix tensile modulus and Poisson's ratio at the relevant

Fibr

e St

rain

, ef/

%

Distance Along Fibre, x / fim

Figure 8.13 Derived variation of fibre strain with distance along the Kevlar 149 fibre ina single-fibre composite tensile specimen at different indicated levels of matrix strain em.The curves are fitted using Equation (3) (after [38])

matrix strains. It can be seen that, while the data points are a good fit to thetheoretical curves in the central region of the fibre, there is a slight deviation at thefibre ends. This is due in part to the geometry of the cut fibre ends [84] and the factthat some of the assumptions of the Cox analysis [83], such that the strain at theend of the fibres is equal to zero, are not appropriate.

It can be seen from Figure 8.12 that at 2.0% matrix strain, when the failurestrain of the fibre is exceeded, fibre fracture occurs, with the fibre breaking intothree fragments. The strain increases from the fibre ends in each of the fragmentsto a value equal to or less than the failure strain of the fibre, at which point thefibre strain decreases. The distance from the fibre end to the point of maximumstrain defines the region IJl where the maximum length of a fibre fragment isgiven by [85]:

where xy is the shear yield stress of the fibre-matrix interface, o> is the failure stressof the fibre, /c is the critical length of the fibre, and d is the fibre diameter (2r0).

Fib

re S

trai

n,

e f /

%

The fibre fragments initially over a large distance of between 200 and 500 ̂ m,with the crack running at an angle to the fibre axis [86]. In this region thedistribution of strain is mapped along a fibrillar section of the fibre which is stillbonded to the matrix. The points of minimum strain along the fibre are recordedwhere the laser is focused on the propagating crack at the surface of the fibre. Theuse of Raman spectroscopy to study the fragmentation of aramid fibres in a resinmatrix has the advantage that the strain can be mapped at intervals of 20 jim orless in order to define the fragmented regions. This may be compared withconventional polarized light experiments [87], which do not clearly define thefibrillar fractured regions associated with aramid fibres [86].

8.4.2 INTERFACIAL MICROMECHANICS

It will be shown finally that Raman spectroscopy may be used to compare theinterfacial properties of Kevlar fibres with different surface treatments [38].Figures 8.14(a) and 8.14(b) show the variation of fibre strain with distance x alongthe left-hand end of a sized and de-sized Kevlar 49 fibre respectively for matrixstrains ranging from 0% to 2.4%. The solid lines are a fit of the experimental datausing either asymmetric or logistic sigmoid functions with correlation coefficientsgreater than 98%. The distribution of fibre strain, at matrix strain levels up to1.2%, is similar to that shown in Figure 8.12 for the Kevlar 149 fibre, and is inqualitative agreement with that predicted by classical shear-lag theory [83]. Atmatrix strain levels greater than 1.6%, the fibre strain increases from the fibre endat a slower rate than at lower matrix strains. This effect is clearly morepronounced in Figure 8.14(b) for the de-sized fibre, where it is seen that thetransfer of stress from the matrix to the fibre is greatly reduced at the fibre end,when em = 2.4%, compared with the strain in the sized fibre at the same level ofapplied matrix strain.

It is possible to derive the variation of interfacial shear stress T with distancex along the fibre from the data in Figures 8.14(a) and 8.14(b) using the relationship[88]:

where T is the interfacial shear stress and (de/dx) is the differential of the variationof fibre strain with position along the fibre. Figures 8.14(a) and 8.15(b) show thederived variation of interfacial shear stress with distance x along the sized andde-sized Kevlar 49 fibres respectively. At matrix strains up to 1.2% the interfacialshear stress is a maximum at the fibre end (x = 0), decreasing to zero at a distancex along the fibre equal to IJl. At matrix srains greater than 1.6%, the epoxy resinexhibits plastic deformation, which leads to a reduction in the transfer of stressfrom the matrix to the fibre. This is clearly shown in Figure 8.15(b), where the

Distance Along Fibre, x / urn

Figure 8.14 Derived variation of fibre strain with distance along the left-hand end ofa Kevlar 49 fibre in a single-fibre composite tensile specimen at different indicated levels ofmatrix strain em: (a) sized fibre; (b) de-sized fibre (after [38])

Fibr

e S

trai

n, e

f / %

Fibr

e S

trai

n, e

f / %

Distance Along Fibre, x / urn

Distance Along Fibre, x / |im

Figure 8.15 Derived variation of the interfacial shear stress (ISS) T with distance alongthe left-hand end of a Kevlar 49 fibre in a single-fibre composite tensile specimen atdifferent indicated levels of matrix strain em using the data from Figure 8.14: (a) sized fibre;(b) de-sized fibre (after [38])

ISS

, x

/ M

Pa

ISS 1

T/M

Pa

Distance Along Fibre, x / ^m

Matrix Strain, em/%

Figure 8.16 Dependence of the maximum interfacial shear stress upon matrix strain forthe sized and de-sized Kevlar 49 fibres in an epoxy resin matrix (data taken from Figure8.15). The horizontal dashed line represents the shear yield stress of the epoxy resin, alongwith the scatter band of the measurements (after [38])

iterfacial shear stress at the fibre end is only of the order of 3-4MPa for anapplied matrix strain of 2.4%, compared with « 4 3 MPa for an applied matrixstrain of 1.2%.

The maximum interfacial shear stress values for the sized and de-sized Kevlar49 fibres are shown in Figure 8.16 as a function of applied matrix strain. It isclearly shown that the values of maximum interfacial shear stress rmax for thede-sized fibres are less than those for the sized fibres at all levels of applied matrixstrain. It is shown that the interfacial shear stress for the de-sized fibres reachesa maximum value of 43 MPa, which is close to the shear yield stress of the epoxyresin matrix [77] indicated by the dashed line in Figure 8.16.

8.5 CONCLUSIONS

It has been demonstrated that Raman spectroscopy is not only a very powerfultechnique for following the deformation of high-performance fibres and compos-ites but is also of use in the study of the deformation of isotropic polymers. It hasbeen shown that the shifts in the Raman bands is related directly to deformationof the bonds in the polymers, and so the technique offers a unique method offollowing molecular deformation in polymers. The relationship between the shift

Max

imum

IS

S 9 r

mtx

/MP

a

in a particular Raman band and stress or strain can be used to map deformationin a wide variety of systems. For example, the point-to-point variation of strain inhigh-performance fibres in a composite can be determined with a spatial resol-ution of the order of 2 ̂ m, which enables the micromechanics of compositedeformation to be studied with a resolution and precision which were hithertounobtainable. Smart polymer coatings have been developed which allow strainmapping in the substrates with a similar level of resolution. It is clear that the useof Raman spectroscopy to follow deformation is in its infancy, and over years tocome there will be significant developments in instrumentation and in itsapplication to different materials which will allow further significant advances tobe made.

8-6 ACKNOWLEDGEMENTS

The author is grateful to a large number of colleagues and research workers inManchester who have helped with his work on the development of Ramanspectroscopy for the study of mechanical properties in materials. He is alsograteful to the Royal Society for support in the form of the Wolfson ResearchProfessorship in Materials Science.

8.7 REFERENCES

[1] P. Hendra and W.F. Maddams, Chapter 7, in "Polymer Spectroscopy", Edited byA.H. Fawcett, John Wiley & Sons, Ltd., Chichester, 199.

[2] D.N. Batchelder, Eur. Spectrosc. News, 1988, 80, 28.[3] RJ. Young, Chapter 6 in WJ. Feast, H.S. Monro and R.W. Richards (Eds.), Polymer

Surfaces and Interfaces II, John Wiley & Sons, Chichester, 1993.[4] CH. Zimba, V.M. Hallmark, J.D. Swalen and J.F. Radbolt, AppL Spectrosc, 1987,

41,721.[5] FJ. Purcell, Spectrosc. Int., 1990,1, 33; Spectroscopy, 1989,4, 24.[6] D.N. Batchelder, C. Cheng and G.D. Pitt, Adv. Mater. 1991,3, 566.[7] R.V. Sudiwala, C. Cheng, E.G. Wilson and D.N. Batchelder, Thin Solid Films, 1992,

210/211,452.[8] V.K. Mitra, W.M. Risen, Jr., and R.H. Baughman, J. Chem. Phys., 1977,66, 2731.[9] D.N. Batchelder and D. Bloor, J. Polym. ScL, Polym. Phys. Ed., 1979,17, 569.

[10] C. Galiotis, RJ. Young and D.N. Batchelder, J. Polym. ScL, Polym. Phys. Ed., 1983,21, 2483.

[11] D.N. Batchelder and D. Bloor, Resonance Raman spectroscopy of conjugatedmacromolecules, in R.J.H. Clark and R.E. Hester (Eds.), Advances in Infrared andRaman Spectroscopy, Vol. 11, Wiley-Heyden, Chichester, 1984.

[12] G. Wu, K. Tashiro and M. Kobayashi, Macromolecules, 1989, 22, 188.[13] G. Wegner, Pure AppL Chem., 1977,49, 443.[14] RJ. Young, Polymer single crystal fibres, in LM. Ward (Ed.), Developments in

Oriented Polymers—2, Applied Science, London, 1987.

[15] A.C. Cottle, W.F. Lewis and D.N. Batchelder, J. Phys. C, 1978,11,605.[16] C. Galiotis and RJ. Young, Polymer, 1983,24,1023.[17] C. Galiotis, R.T. Read, P.H.J. Yeung, RJ. Young, LF. Chalmers and D. Bloor, J.

Polym. ScL, Polym. Phys. Ed., 1984, 22,1589.[18] C. Galiotis, RJ. Young, P.HJ. Yeung and D.N. Batchelder, J. Mater. ScL, 1984,19,

1640.[19] RJ. Day, LM. Robinson, M. Zakikhani and RJ. Young, Polymer, 1987, 28, 1833.[20] RJ. Young, RJ. Day and M. Zakikhani, J. Mater. ScL, 1990, 25,127.[21] RJ. Young and P.P. Ang, Polymer, 1992,33, 975.[22] LM. Ribinson, M. Zakikhani, RJ. Day, RJ. Young and C. Galiotis, J. Mater. ScL

Lett., 1987, 6, 1212.[23] C. Galiotis and D.N. Batchelder, J. Mater. ScL Lett., 1988,7, 545.[24] Y. Huang and RJ. Young, J. Mater. ScL, 1994,29,4027.[25] RJ. Day, V. Piddock, R. Taylor, RJ. young and M. Zakikhani, J. Mater. ScL, 1989,

24, 2998.[26] X. Yang, X. Hu, RJ. Day and RJ. Young, J. Mater. ScL, 1992, 27,1409.[27] X. Yang and RJ. Young, J. Mater. ScL, 1993, 28, 536.[28] J.R. Schaefgen, Chapter 8, A.E. Zachariades and R.S. Porter (Eds.), The Strength and

Stiffness of Polymers, Marcel Dekker, New York, 1983.[29] S.L. Kwolek, W. Memeger and J.E. Van Trump, in M. Lewin (Ed.), Polymers for

Advanced Technologies, VCH Publishers, New York, 1988, p. 421.[30] D. Tanner, J.A. Fitzgerald, P.G. Riewald and W.F. Knoff, in M. Lewin and J. Preston

(Eds.), High Technology Fibers—Part B, Marcel Dekker, New York, 1989.[31] L. Penn and F. Milanovich, Polymer, 1979,20, 31.[32] C. Galiotis, LM. Ribonson, RJ. Young, B.E J. Smith and D.N. Batchelder, Polym.

Commun., 1985, 26, 354.[33] S. Van der Zwaag, M.G. Northolt, RJ. Young, LM. Robinson, C. Galiotis and D.N.

Batchelder, Polym. Commun, 1987,28, 276.[34] H.G.M. Edwards and S. Hadiki, Br. Polym. J., 1989,21, 505.[35] RJ. Young, D. Lu and RJ. Day, Polym. Int., 1991,24, 71.[36] RJ. Day, LM. Robinson, M. Zakikhani and RJ. Young, in PJ. Lemstra and L.A.

Klientjens (Eds.), Integration of Fundamental Polymer Science and Technology—2,Elsevier Applied Science, London 1988, p. 571.

[37] RJ. Young, RJ. Day, L. Dong and W. Knoff, J. Mater. ScL, 1992,27, 5431.[38] M.C. Andrews and RJ. Young, J. Raman. Spectrosc, 1993,24, 539.[39] M.G. Northolt and JJ. Van Aartsen, J. Polym. ScL, Polym. Symp., 1978,58, 283.[40] M.G. Northolt, Polymer, 1980,21,1199.[41] M.G. Northolt and R. Van der Hout, Polymer, 1985, 26, 310.[42] D.K. Roylance and K.L. Devries, J. Polym. ScL, Polym. Lett, 1971,9, 443.[43] G. Capaccio, A.G. Gibson and LM. Ward, in A. Ciferri and LM. Ward (Ed.),

Ultra-High Modulus Polymers, Applied Science, London, 1979.[44] A.E. Zachariades, WT. Mead and R.S. Porter, A. Ciferri and LM. Ward (Eds.),

Ultra-High Modulus Polymers, Ed. Applied Science, London, 1979.[45] P. Smith and PJ. Lemstra, J. Mater. ScL, 1981,15, 505.[46] L. Holliday and J. W. White, Pure Appl. Chem., 1971, 26, 545.[47] AJ. Kinloch and RJ. Young, Fracture Behaviour of Polymers, Applied Science,

London, 1983.[48] J. Clements, R. Jakeways and LM. Ward, Polymer, 1978,19, 639.[49] K. Nakamae, T. Nishino and H. Ohkubo, J. Macromol. ScL, Phys., 1991 B30,1.[50] DT. Grubb and JJ.-H. Liu, J. Appl. Phys., 1985,58, 2822.[51] K. Prasad and DT. Grubb, J. Polym. ScL: Part B: Polym. Phys., 1990, 28, 2199.

[52] R.P. Wool and W.O. Station, J. Polym. ScL, Polym. Phys. Ed., 1974,12,1575.[53] R.P. Wool, R.S. Bretzlaff, B.Y. Li, CH. Wang and R.H. Boyd, J. Polym. ScL, Polym.

Phys. Ed., 1986, 24,1039.[54] K. Tashiro, G. Wu and M. Kobayashi, Polymer, 1988, 29,1768.[55] K. Prasad and D.T. Grubb, J. Polym. ScL, Polym. Phys. Ed., 1989,27, 381.[56] BJ. Kip, M.C.P. Van Eijk and RJ. Meier, J. Polym. ScL: Part B: Polym. Phys., 1991,

B29,99.[57] J.A.H.M. Moonen, W.A.C. Roovers, RJ. Meier and BJ. Kip, J. Polym. ScL, Polym.

Phys. 1992,30,361.[58] D.T. Grubb and Z. Li, Polymer., 1992,30, 2587.[59] W.F. Wong, Ph.D. Thesis, Victoria University of Manchester, 1992.[60] W.F. Wong and RJ. Young, J. Mater. ScL, 1994, 29, 510.[61] W.F. Wong and RJ. Young, J. Mater. ScL, 1994, 29, 520.[62] PJ. Barham and R.G.C. Arridge, J. Polym. ScL, Polym. Phys. Ed., 1977,15, 1177.[63] A.G. Gibson, G.R. Davies and LM. Ward, Polymer, 1978,19, 683.[64] LJ. Fina, D.I. Bower, and LM. Ward, Polymer, 1988, 29, 2146.[65] R.A. Evans and H.E. Hallam, Polymer, 1976,17, 838.[66] J.L. Stanford, RJ. Young and RJ. Day, Polymer, 1991,32,1713.[67] X. Hu, J.L. Stanford, RJ. Day and RJ. Young, Macromolecules, 1992, 672.[68] X. Hu, J.L. Stanford, RJ. Day and RJ. Young, Macromolecules, 1992, 684.[69] X. Hu, RJ. Day, J.L. Stanford and RJ. Young, J. Mater. ScL, 1992, 27, 5958.[70] G. Wegner, Makromol. Chem., 1970,134, 219.[71] D. Day and J.B. Lando, J. Polym. ScL, Polym. Lett. Ed., 1981,19, 227.[72] A.O. Patil, D.D. Deshpande, S.S. Talwar and A.B. Biswas, J. Polym. ScL, Polym.

Chem. Ed., 1981,19, 1155.[73] M.F. Rubner, Macromolecules, 1986,19, 2114.[74] R.S. Liang and AJ. Reiser, J. Polym. ScL, Polym. Chem. Ed., 1987, 25, 451.[75] R.A. Nallicheri and M.F. Rubner, Macromolecules, 1991, 24, 517.[76] J.G. Williams, Stress Analysis of Polymers, Longman, London, 1973.[77] M.C. Andrews, RJ. Day and RJ. Young, Comp. ScL and Tech., 1993,48, 255.[78] RJ. Young, C. Galiotis, LM. Robinson and D.N. Batchelder, J. Mater. ScL, 1987,22,

3642.[79] RJ. Young and P.P. Ang, in I. Verpoest and F.R. Jones (Eds.) lnterfacial Phenomena

in Composite Materials '91, Butterworth-Heinemann, Oxford, 1991, pp. 45-52.[80] H. Jahankhani and C. Galiotis, J. Compos. Mater., 1991, 25,609.[81] M.C. Andrews, RJ. Day, X. Hu and RJ. Young, J. Mater. ScL Lett., 1992,11,1344.[82] M.E. Cates and S.F. Edwards, Proc. R. Soc. Lond. A, 1984,395, 89.[83] H.L. Cox, Br. J. Appl. Phys., 1952,3, 72.[84] CF. Fan and S.L. Hsu, Macromolecules, 1989,22, 1474.[85] A. Kelly, Strong Solids, Clarendon Press, Oxford, 1966, p. 130.[86] A.N. Netravali, Z.-F. Li, W. Sachse and H.F. Wu, J. Mater. ScL, 1991,28,6631.[87] L.T. Drzal, MJ. Rich and P.F. Lloyd, J. Adhes., 1982,16,1.[88] A. Kelly and N.H. Macmillan, Strong Solids, 3rd edn., Clarendon Press, Oxford,

1986.

9 SPIN-LABELSTUDIESOFHETEROGENEOUSPOLYMER SYSTEMS

G. G. CAMERON and L G. DAVIDSONDepartment of Chemistry, University of Aberdeen, Old Aberdeen AB9 2UE, Scot-land, UK

9.1 INTRODUCTION

The spin-label and spin-probe techniques have been used to study a wide varietyof polymers, both in bulk and in solution, and several reviews of the subject havebeen published [1-3]. The object of this article is to provide a brief outline of thetheoretical background, with particular, reference to spin-labelling, before dis-cussing some recent applications of the technique to polymers in heterogeneoussystems.

The shape and width of the electron spin resonance (ESR) spectrum of a spinlabel or probe is sensitive to the mode and rate of rotation of the radical. Thus,examination of the ESR spectrum of the labelled or probed polymer can yieldinformation on the dynamics and relaxations of the polymer and is thereforecomplementary to such techniques as mechanical, NMR and dielectric relaxationmeasurements.

In the spin-probe experiment the free radical is simply dispersed in the polymermatrix. However, as any interaction with the polymer is only by secondaryvalence forces, the motion of the probe may not directly reflect the motion of thepolymer. Spin-labelling, where the radical is covalently attached to the polymerchain, does give information on the dynamics of that part of the polymer to whichit is joined. It is possible to label polymers specifically at either inner or terminalsegments, and thus, provided that the label does not rotate independently orperturb the motion of the polymer, specific information about the dynamics ofthese particular sites can be obtained. An advantage of the ESR technique is itshigh sensitivity, so that, in favourable circumstances, spin concentrations as lowas 10" 6 M may be used. In practical terms, this relates to approximately one spinlabel per polymer chain.


9.1.1 SYNTHESIS OF SPIN LABELS

Spin labels are almost invariably di-t-alkyl-substituted nitroxide (nitroxyl oraminoxyl) free radicals. These are used because they are quite stable to heat andlight, and nitroxides with a wide variety of structures and functional groups canbe readily synthesised, so facilitating the labelling of a range of polymers [4].Many labels are functionalised piperidine and pyrroline derivatives (Table 9.1),although other types are also sometimes used.

The simplest method of spin labelling is to utilise a functional group on thepolymer to attach the label, usually via a condensation reaction (Scheme 1).Labels can also be introduced by less direct methods. For example, the Keanasynthesis [6] (Scheme 2) has been used to label polyethylene that had beencopolymerised with a small amount of carbon monoxide [7]. Polystyrene hasbeen labelled by reacting the lightly lithiated polymer with either 2-methyl-2-nitrosopropane or nitrosobenzene (Scheme 3) [8].

Direct ionic or radical copolymerisation of vinyl-substituted nitroxides is notusually feasible, as either the initiators or the growing polymers can react with thenitroxide. However, if the spin label is converted into the amine or hydroxylaminesuch a polymerisation is possible, the nitroxide being subsequently generated byoxidation. In most spin-label experiments, the label is attached as a pendentgroup. It is possible to place a spin label directly into the polymer backbone usingeither radicals [9] or ionic [10] polymerisation (Scheme 4). Such labels have norotational freedom independent of the polymer, and so their motion directlyreflects that of the polymer segments.

Table 9.1 Some nitroxides used for spin-labelling

Scheme 1

Scheme 2

Scheme 3

AU of these methods produce randomly labelled polymers with the labels onin-chain segments. End-labelled polymers are generally prepared by anionicpolymerisations. The living chain end is terminated with a suitably functionalisedspin label, usually an acid chloride [11]. A different method was used to prepareend labelled poly(w-butyl isocyanate) [12]. Here the spin label 2,2,5,5- tet-ramethyl-l-pyrrolidinyloxy-3-carboxamide was used as an initiator in competi-tion with cyanide ion (Scheme 5). This produced a spin concentration of one labelper three polymer chains.

9.2 THEORETICAL BACKGROUND

The ESR spectrum of a nitroxide free radical consists of three lines arising fromthe interaction of the unpaired electron with the 14N nucleus (nuclear spinquantum number / = 1). The spectra are anisotropic, as the position of the centreof the spectrum—g tensor—and the splitting of the lines—hyperfine couplingtensor A—depend on the orientation of the nitroxide with respect to the appliedmagnetic field (Figure 9.1). In bulk polymers, or at low temperatures, where themotion of the label is restricted, a powder average or slow-motion spectrum isobserved (Figure 9. l(d)). When the nitroxide is rotating freely, e.g. in dilutesolution or at high temperatures, the anisotropies are averaged out, givinga motionally narrowed or fast-motion spectrum (Figure 9.1(e)) whose centre isdefined by

0iso = l(0xx + 9yy + 0zz)

and which has a splitting given by

<*N = îso = i(^xx + ^yy + Azz)

where gxx, gyr gzz and Axxi Ayr Azz are the principal values of the g and hyperfinecoupling tensors respectively.

9.2.1 CORRELATIONTIMES

The ESR spectra of nitroxides can be characterised by the rotational correlationtime TC, which is inversely proportional to the rate or frequency of rotation of theradical. The correlation times for nitroxides can be divided into three distinctregions, designated fast (10"1MO"9 s), slow (10"9-10" 7 s) and very slow (10"7-10" 3s). The limits to these regions are determined by the anisotropies of themagnetic interactions of the radicals, and different methods of calculating TC arerequired for each region.

Scheme 4

Scheme 5

Figure 9.1 Idealised ESR spectra of nitroxide radicals: (a), (b) and (c) single crystalspectra with the applied magnetic field along the x, y and z principal axes; (d) slow-motionspectrum; (e) fast-motion spectrum

9.2.1.1 Fast Motion

The line widths (W) of a motionally narrowed or fast-motion spectrum dependboth on the correlation time and on m7, the component of the nuclear spin alongthe direction of the applied magnetic field. For 14N, m7 = 1,0, — 1, correspondingto the low, middle and high field lines in the ESR spectrum. In general thedependence of W upon m7 is given by [13]

W(Yn1) = A + Bm j + Cm]

where A% B and C are coefficients which depend on the correlation time and theprincipal values of the g and hyperfine coupling tensors. The A term includesfactors arising from homogeneous broadening independent of mj, bu t as W{0) = Athe equat ion can be rearranged to

W(mj) _ Bm1 Cm]

For nitroxide spin labels, assuming isotropic rotat ional diffusion and near axialsymmetry of the coupling tensor, i.e. A x x % Ayy9 B and C are given by

B = ^bAyHoic

where

* = y [ ^ - 0.5(Axx + Ayy)] and Ay = J [g22 - 0.5(gxx + gyy)]

H 0 is the applied magnetic field and ft is the Bohr magneton. Two values of thecorrelation time can then be calculated:

4>W \5Wt . ( D - - ^ C * + r - -2)andrc(2) = ^ ( r + - r _ ) (1)

It is usual to obtain accurate values for r± from peak to peak intensities Y of therelevant lines, thus:

_ ^(±1) = r(Q) {1\

1 (̂O) L J (± i )J

If the two TC values are not in close agreement, then the assumption that therotation of the spin label is isotropic must be suspect. A more rigorous approachbased on the assumption of axially symmetric rotation of the spin label must thenbe used [14].

It should be noted that the lines of the ESR spectrum of a spin-labelled polymerare broadened by unresolved hydrogen couplings. This inhomogeneousbroadening is not accounted for in the above equations, but there are severalmethods of overcoming this problem [I].

9.2.1.2 Slow Motion

As the motion of the spin label is slowed, the lines gradually broaden. When thecorrelation time is « 3 x 10" 9 s the spectrum suddenly changes from a motionallynarrowed to a slow-motion one. The spectrum then remains essentially the sameexcept that the distance between the low and high field extrema increases withincreasing correlation time until the rigid limit is reached.

The most rigorous method of determining TC in this region is by computersimulation [15,16]. The variable input parameters of correlation time and linewidth are varied until a good match between the computed and the observedspectra is obtained. Anisotropic rotation and various rotational diffusion modelscan be accommodated by this method. In many cases, however, simpler methodsbased on analysis of the outer extrema, either their inward shift from the rigidlimit or their line width, are adequate. Such methods have been extensivelyreviewed elsewhere [1,15, 17,18].

It is important for all of these methods to choose an appropriate diffusionmodel for the system. It has been shown that the ratio of the shifts of the high andlow field extrema (AHJAH1) with change in AH1 is sensitive to the mode ofreorientation of the nitroxide, and so can be used in the choice of diffusion model[19].

For correlation times longer than «10 7S, the technique of saturation transfer(ST) ESR spectroscopy must be used [20]. In this technique, either the firstharmonic of the dispersion or the second harmonic of the absorption signal, asopposed to the usual first derivative ESR espectrum, is observed. The shapes ofthese spectra are sensitive to changes in the correlation time in the range10" 7-10~ 3 s. As for the slow-motion spectra, correlation times are calculated bycomputer simulation of the STESR spectra.

9.2.2 THE GLASS TRANSITION AND T50G

As was noted above (Section 9.2.1.2), as a spin-probed or labelled polymer iscooled, the fast-motion spectrum of width « 30 G reaches a point where it rapidlychanges into a slow-motion spectrum of width 65-70 G (Figure 9.1(d),(e)). Thetemperature at which this transition occurs is taken as the temperature at whichthe spectrum is 50G wide, the 750G [21] (Figure 9.2).This change occurs overa narrow temperature range (i.e. it is a guasz-discontinuity) and is usuallyassociated with the glass transition temperature Tg of the polymer. However,T5QG is generally higher than Tg because the frequency of rotation of the nitroxideat 750G is ^107Hz, whereas Tg is measured at ^ IHz. Thus, T50G is oftenconsidered as a high frequency T r although it must be noted that it is possible fora probe to exhibit a T50G with the polymer still in its glassy state.

The T50G for a particular polymer increases with the molecular volume of theprobe, as the mobility of the probe is associated with the free volume of the

Figure 9.2 Plot of extrema separation versus temperature showing T50G

polymer [22]. This increase has a limiting value where the volume of the probe iscomparable with the volume of the polymer segment undergoing relaxation.Thus, spin labels can be regarded as large probes, and reflect the relaxationvolume of the segment to which they are attached [I ] .

It has been shown that the correlation time of a spin probe is related to thetemperature T of the system by [23]

- [1303C 1 1 C 2 1 IlnT' = lnT" + 4 r - r g ; c ; J (3)

where T00 is the high temperature limit of TC, C l g and C2g are constants for a givenpolymer, as defined by Williams et al. [24], and / is the ratio of the activationvolume of the probe to the activation volume of the polymer segment. Thus,a plot of In tc against 2.303 Cl%C2J{T — T1 + C2g) is linear, with a slope of / andintercept T00. A simpler but less exact method of evaluating / assumes thatT00 = 1.1 x 10~12s and, at T500, TC = 10" 8S, giving on rearrangement of Equa-tion (3) [I]:

T T-C P ° 3 C i » / j l (4)

It must be noted that there is no general correlation between / and probe volume.This is because no account is taken of any differences in probe flexibility or any

Temperature

Extre

ma

sepa

ratio

n /G

polymer-probe interactions which will depend on the chemical structure of bothpolymer and probe [23].

9.3 HETEROGENEOUSSYSTEMS

The above discussion has considered the spin-label or spin-probe to be ina homogeneous system with a single correlation time. In some cases, however, theobserved ESR spectrum is of neither the fast- nor the slow-motion type but isa mixture of the two (Figure 9.3). Such composite spectra arise when thespin-labels or probes simultaneously occupy two motionally distinct environ-ments, one of which is significantly more restricting than the other. Thisbehaviour may occur in situations such as adsorption of a polymer onto a solid[9], phase separations of polymers or polymer blends [25], polymer networks[26] or any other system where more than one phase is present.

Analysis of composite spectra can be achieved by computer simulation of thefast and slow components, yielding the relative proportions of the label or probein the different environments. It must be noted that a few percent of fast motion inan otherwise slow-motion spectrum is readily detected, whereas this is not true ofthe reverse situation. This is because the peak-to-peak intensity of an ESR line isproportional to the inverse of the square of the linewidth (see Equation (2)) andfast-motion lines are much narrower than slow-motion lines.

Among the first heterogeneous systems involving polymers to be studied by thespin-label technique were solids suspended in polymer solutions [5, 9, 27-29].The aim of these studies was to obtain new and complementary information onthe nature and mechanism of polymer molecule adsorption at the solid-solutioninterface. In most of these studies the labelled polymer adsorbed from solution onthe surface of adsorbents, such as silica, yielded composite ESR spectra compris-

Figure 93 Composite ESR spectrum

ing a slow- and a fast-motion component. These spectra were interpreted asshowing that the polymer molecules in the adsorbed state, but still in contact withsolvent, had some regions of their chains in a hindered state, probably fiat on orvery close to the surface ('trains'), and other regions in a relatively unhinderedstate more distant from the surface ('loops' and 'tails'). The former gave theslow-motion and the latter the fast-motion component in the ESR spectra. Bydeconvolution or spectral simulation, it is possible to calculate the relativeproportions of hindered and mobile nitroxides, and hence the proportions of theadsorbed polymer chains in the 'train' mode and the 'loop'/'taiF mode. Theproportions of the hindered and free segments are dependent on the nature of thesurface and the thermodynamic quality of the solvent for the polymer. Theadsorption isotherm may be obtained by measuring the intensity of the ESRspectrum before and after shaking the solution with the solid adsorbent [9].

A good example of this application concerns poly(vinyl acetate) (PVA), whichwas labelled both in the in-chain position (Scheme 4) [9] and with a pendentnitroxide (Scheme 1) [5]. The ESR spectra of these labelled polymers both insolution and in the adsorbed state reflect the greater motional freedom of thependent label. Thus, the correlation times TC for the in-chain and pendentnitroxide groups were 0.6 and 0.04 ns respectively in chloroform solution and 0.8and 0.06 ns respectively in toluene solution [9].

With silica as adsorbent, it was observed that the adsorption capacity dimin-ished with decreasing surface silanol content. Furthermore, the adsorptioncapacity was greatest when toluene, a thermodynamically poor solvent, wasemployed, and least with the good solvent ethyl acetate [9].

The ESR spectra of in-chain labelled PVA adsorbed on a silica sample ofrelatively high silanol content (Microsil GP) from toluene, chloroform and ethylacetate solution are shown in Figure 9.4. The spectra of the polymer adsorbedfrom toluene and chloroform solutions (Figure 9.4(a) and (b)) are almost identicaland are of the slow-motion type, with only a hint at most of fast motion. Thissuggests rathet-strong adsorption and a relatively flat polymer conformation onthe surface. The ESR spectrum of the labelled polymer adsorbed from the goodsolvent ethyl acetate (Figure 9.4(c)) is clearly a composite one with a well-definedfast-motion component. In this case, some of the segments at the surface aremotionally quite free, probably in the form of loops or tails.

The above observations are physically quite reasonable. One would expectrelatively stronger adsorption from solution when polymer-solvent interactionsare energetically rather unfavourable. Interestingly, when most of the surfacesilanol groups are trimethylsilylated, adsorption still occurs and the ESR spec-trum (Figure 9.4(d)) again shows a fairly strong polymer-surface interaction.However, the ESR spectrum of the polymer on the modified silica surface is quitedistinct from its spectrum on the unmodified substrate. There appears to bea change in the type of motion, as opposed to facility of motion, when the surfaceis altered. The change is probably associated with a change in the anisotropy of

Figure 9.4 ESR spectra of PVA adsorbed on Microsil GP: (a) from toluene solution,equilibrium cone. 0.077 gdl" *; (b) from chloroform solution, equilibrium cone.O.llOgdl"1; (c) from ethyl acetate solution, equilibrium cone. 0.076gdl"1; (d) ontrimethylsilylated Microsil GP from toluene solution, equilibrium cone. 0.084 g dl"i

probe tumbling which could, in turn, indicate a change in the mode of adsorptionat the surface [9]. This is a subtlety which requires a more detailed spectralanalysis for clarification.

In experiments of this type it is important to establish that there is no strong orpreferred affinity between the nitroxide label and the surface. This can usually beascertained by checking a small-molecule analogue of the label. In the studydescribed above, experiments with the free label 3-carbamoyl-2,2,5,5-tetra-methylpyrrolidine-1-oxyl established that only with toluene as solvent was thenitroxide group adsorbed on the silica surface in detectable quantities. Thus, thePVA segments in general have a stronger affinity for the surface than thenitroxide label.

The principles applied in studying polymers adsorbing on to solid surfacesfrom solution can be applied to other types of interactions involving polymersolutions and solid surfaces. A recent example of such an application concernspolymers containing suitable sequences of methylene units which interfere withthe crystallisation of a straight-chain hydrocarbon from solution. In the presenceof ppm quantities of such polymers, the crystallisation temperature is depressed

The problem was approached by preparing the spin-labelled fumarate-VAcopolymer shown above. To a solution comprising 2% dotriacontane indodecane was added 0.1% w/w of this polymer [31]. Above the cloud point ofthis homogeneous mixture, the ESR spectrum of the polymer is of the fast-motiontype, with three rather broad but clearly defined lines typical of a spin-labelledpolymer in solution (Figure 9.5(a)). As the temperature of the solution is lowered,crytallisation of the dotriacontane commences at the cloud point (20 0C), which iswell above the temperature (6 0C) at which the polymer itself precipitates fromdodecane solution. Just below this temperature (Figure 9.5(b)) the ESR spectrumof the polymer shows the beginnings of a broad-line slow-motion spectrum whichcan be ascribed to polymer interacting with the solid crystalline dotriacontane.As the temperature is lowered further, the slow-motion spectrum increases inintensity at the expense of the fast-motion spectrum (Figure 9.5(c)) as increasingquantities of polymer are incorporated with the progressively crystallizingn-alkane, and by 10 0C very little fast-motion character remains. Simulation ofthe spectra allows the proportion of fast- and slow-motion spectra shown inFigure 9.5 to be calculated. However, infrared spectral examination of theprecipitated dotriacontane shows that the proportion of incorporated polymer isgreater than the proportion of slow-motion in the composite spectrum. In otherwords, some of the polymer associated with the crystalline dotriacontane showsa fast-motion spectrum, rather in the manner of labelled PVA adsorbed on silica[9]. Clearly, a proportion of the polymer is not 'locked up' or cocrystallised andmust reside on the surface of the growing crystals. It seems probable that furthergrowth is inhibited at the crystal face where the polymer molecule is located.

9.4 POLYMER BLENDSApplications of the spin-label technique to polymer blends have been relativelyrecent. Shimada et al. have studied blends of end-labelled polyethylene oxide)-

and the n-alkane crystals which eventually form are much smaller and usuallyneedle-shaped rather than plate-like [30]. Much remains to be learned about theprecise mode of interaction of the polymer with the w-alkane crystals.

Figure 9.5 ESR spectrum of 0.1% (w/w) fumarate-vinyl acetate copolymer, 2% dot-riacontane in dodecane: (a) 23 0C, above the cloud point; (b) 19 0C, just below the cloudpoint; (c) 15 0C

(PEO) with isotactic poly(methyl methacrylate) (PMMA) [25, 32] and labelled(both random and chain-end) PMMA with poly(vinylidene fluoride) (PVDF) [33,34]. These are complex systems because they show partial miscibility and becausein each case one of the components is capable of crystallising. Nevertheless, theseauthors obtained fundamental information on the morphology of the blend andphase separation. In the PEO-PMMA blends, the spectra were of the compositetype, and they ascribed the fast- and slow-motion spectra to nitroxides located inPEO-rich regions and PMMA-rich regions respectively.

In our own work [11, 35] we have studied blends of polystyrene (PS) andris-l,4-polyisoprene (PIP), the former labelled either at random in the m-site ofthe benzene ring, as in Scheme 3, or at chain ends, as in Scheme 5. This pair ofpolymers was chosen because they are immiscible, amorphous and have widelydifferent Tg values. Thus, any significant interaction of the two should lead to

Figure 9.6 ESR spectra of in-chain labelled PS and its 1:1 (w/w) blend with cis- 1,4-PIP:(a)-(d) temperature increased progressively from 292 to 453 K. Reproduced from [35] bypermission of the publishers, Butterworth-Heinemann Ltd.

plasticisation of the PS, which could then influence the ESR spectrum of thelabel.

Figure 9.6 shows the temperature dependence of the ESR spectrum of thein-chain labelled PS both in the pure (bulk) state and in a 1:1 w/w blend with PIP[35]. The spectra of the pure and the blended PS are identical and remainessentially of the slow-motion type up to « 450 K, above which decomposition ofthe nitroxide group is fairly rapid. In both systems the slight spectral changesobserved on heating are completely reversed on cooling. There is no evidence ofeven limited miscibility in these spectra.

However, the behaviour of the end-labelled PS is quite different (Figure 9.7).The spectrum of the blend shows a motionally narrowed component at «420 K(Figure 9.7(c)) where the spectrum of the pure PS is still of the slow-motion type.At 433 K the differences between the spectra of the two samples are very marked,the 1:1 blend showing an intense narrow-line component in its compositespectrum and the pure PS a gradual shift to line-narrowing. On cooling from433 K to room temperature, the spectra of the pure PS are identical to thoserecorded during heating, i.e. there is complete reversibility. In the blend, bycontrast, the changes in the ESR spectrum on heating are not exactly reversed oncooling. Thus, the motionally narrowed component persists and is clearly visibleat temperatures well below the temperature at which it was first detectable duringthe heat-up procedure. On cooling to room temperature after heating to 433 K,the spectrum of the blend closely resembles the spectrum at 423 K in Figure 9.7(c).

Bulk PS1:1 (w/ w) Blend with cis -1,4 PIP

Figure 9.7 ESR spectra of end-labelled PS and its 1:1 (w/w) blend with cis- 1,4-PIP:(a)-(d) temperature increased progressively from 292 to 433 K; (e) samples heated to 433 K,cooled to room temperature then reheated to 343 K. Reproduced from [35] by permissionof the Publishers, Butterworth-Heinemann Ltd.

The fifth pair of spectra (Figure 9.7(e)) was obtained by reheating to 343 K, andunderlines the contrasting behaviour of the pure labelled PS and its blend withPIP: the spectrum of the pure PS maintains the slow-motion shape but that of theblend contains a sharp fast-motion component. After storing the heat-treatedblend at room temperature under vacuum for one week, the motionally narrowedcomponent reappears on heating again to 343 K, though at a somewhat reducedintensity.

It is clear from these observations that, on heating to «430 K, the blend,originally prepared by freeze-drying a co-solution in benzene, is reorganised insuch a manner that more nitroxide chain ends reside in a region relatively rich inPIP. We have concluded that these groups are in fact located in the interphasebetween the PS and PIP domains, where they experience increased motionalfreedom because of the plasticising influence of PIP in the interphase [35] andpossibly also because of a concentration of free volume in this region.

Similar results were obtained with a blend of chain-end labelled PMMA(prepared by group transfer polymerisation) and an immiscible partner, poly(2-ethylhexyl methacrylate), of low Tg (263 K) [36].

These observations are in accord with Helfand's general theory that atthermodynamic equilibrium the interphase in a blend of immiscible polymers

PS2 1:1 (w/ w) Blend with cis -1,4 - PIP

contains more than the statistical concentration of chain ends [37-39]. Indeed,spectral simulations have indicated that composite spectra of the type inFigure 9.6(c) comprise «25% nitroxide groups in the fast-motion regime [40].These spin-label experiments on polymer blends appear to be the first experimen-tal verification of Helfand's theory.

With heterogeneous polymer blends such as those under discussion here, it isstrictly speaking not possible to obtain an accurate value of the parameter T500.However, if the temperature is noted at which the motionally narrowed spectrum(with an extrema separation of « 30 G) becomes just visible, a value of T50G maybe estimated [ H ] . The extrema separations for pure labelled PS and PS-PIPblends are plotted in Figure 9.8, from which estimated values of T50G for the threesystems were calculated to be 425, 405 and 400K for blends comprising a PSweight fraction of 1.0,0.5 and 0.025 respectively. These figures re-emphasise the

EX

TR

EM

A S

EP

AR

AT

ION

/ G

TEMPERATURE/K

Figure 9.8 Extrema separation vs. temperature for pure PS, O; 1:1 blend of PS and PIP,D; 1:39 blend of PS and PIP, A. Reproduced from [11] with permission of PergamonPress Ltd., Headington Hill Hall, Oxford 0X3 OBW, UK

W1

Figure 9.9 T50G vs. composition for PS and blends with PIP. W1 = wt fraction of PS.Reproduced from [11] with permission of Pergamon Press Ltd., Headington Hill Hall,Oxford 0X3 OBW, UK

plasticising influence of the PIP on the labelled PS chain ends, and the T50G

values may be regarded as pertaining to the labels with the least hindered motionin each of the three systems.

If it is assumed that these T50G values refer to labels in a homogeneousenvironment—the interphase—the composition of this environment may becalculated from the relationship [41]

VT500 = WJT5001+ W2ZT5001

= W1(T5 0Q2 — ^5OG|)/^5OG, ^SOG2 + 1/T5 0Q2 (5)

where W refers to a weight fraction and the subscripts 1 and 2 to the components.Setting PS as component 1, at W1 = 1, T50G is 425 K, and at W1 = O, T50G2 is veryclose to 400 K (see Figure 9.9). With T50G = 405 K for the 1:1 blend, Equation (5)yields W1 =0.21. Thus, in the 1:1 blend the labelled PS chain ends which firstshow evidence of being plasticised appear to be in a PIP-rich environment, i.e.79% by weight of PIP. Notwithstanding the approximations and assumptions inthis calculation, it does show that a proportion of the PS chain-end labels is ina region well removed from the pure PS phase [ H ] .

In the above calculation the labelled PS is being treated as a macromolecularspin probe—in pure PS when W1 = I and in pure PIP when W1 = 0. Bysubstituting the values of T50G (425 and 400 K for W1 = 1 and W1=O respective-ly) and those of the other parameters T^C1% and C2g into Equation (4), the valueof the parameter / may be calculated.

For pure, bulk PS / = 0.62; this approximates to the ratio of the volume of thelabelled PS chain end to the effective volume of an inner segment. For thespin-probed PIP / = 1.01, which approximates to the ratio of the volume of the

labelled PS chain end to that of an inner PIP segment. Thus, an in-chain PSsegment is about 1.6 times bulkier than an in-chain PIP segment. These figuresare qualitatively reasonable, and are consistent with the generalisation that, ina series of polymers, the effective volumes of segments involved in the glass-to-rubber transition increases with increasing Tg [42].

The results of these experiments show that the spin-label technique is capableof providing detailed information at a molecular level on the structure andcomposition of polymer blends.

9.5 REFERENCES

[1] G.G. Cameron, in C. Booth and C. Price (Eds.), Comprehensive Polymer Science,Vol. 1, Pergamon Press, Oxford, 1989, p. 517.

[2] LJ. Berliner (Ed.), Spin Labelling Theory and Applications, Academic Press, NewYork, 1976.

[3] LJ. Berliner and J. Reuben (Eds.), Biological Magnetic Resonance 8: Spin LabellingTheory and Applications, Plenum Press, New York, 1989.

[4] E.G. Rosantsev, Free Nitroxyl Radicals, Plenum Press, New York, 1970.[5] T.M. Liang, P.M. Dickenson and W.G. Miller, Am. Chem. Soc. Symp. Ser., 1980,

142,1.[6] J.F.W. Keana, S.B. Keana and D. Beetham, J. Am. Chem. Soc, 1967,89, 3055.[7] AT. Bullock, GG. Cameron and P.M. Smith, Eur. Polym. J., 1975,11,617.[8] AT. Bullock, G.G. Cameron and P.M. Smith, J. Phys. Chem., 1973, 77, 1635;

Polymer, 1973,14, 525.[9] AT. Bullock, G.G. Cameron, I. More and LD. Robb, Eur. Polym. J., 1984,20, 951.

[10] C. Friedrich, C. Noel, R. Ramasseul and A. Rassat, Polymer, 1980,21, 232.[11] G.G. Cameron, M.Y. Qureshi, E. Ross, LS. Miles and J. Richardson, Eur. Polym. J.,

1991,27,1181.[12] R. Olayo, M.A. Patron and W.G. Miller, Macromolecules, 1990,23,1680.[13] A. Hudson and G.R. Luckhurst, Chem. Rev., 1969,69,191.[14] S.A. Goldman, G.V. Bruno, CF. Polnaszek and J. H. Freed, J. Chem. Phys., 1972,56,

716.[15] J.H. Freed, in LJ. Berliner (Ed.), Spin Labelling Theory and Applications, Academic

Press, New York, 1976.[16] DJ. Schneider and J.H. Freed, in LJ. Berliner and J. Reuben (Eds.), Biological

Magnetic Resonance 8: Spin Labelling Theory and Applications, Plenum Press, NewYork, 1989, p. 1.

[17] G.G. Cameron, in R.F. Boyer and S.E. Keineth (Eds.), Molecular Motions inPolymers by E.S.R., MMI Press, Symposium Series Vol. 1, Harwood, Chur, 1980.

[18] T.N. Khazanovich, A.D. Kolbanovsky, A.I. Kokorin, T.V. Medvedeva and A.M.Wasserman, Polymer, 1992, 33, 5208.

[19] A.N. Kuznetsov and B. Ebert, Chem. Phys. Lett., 1974, 25, 342.[20] M.A. Hemminga and P.A. de Jager, in LJ. Berliner and J. Reuban (Eds.), Biological

Magnetic Resonance 8: Spin Labelling Theory and Applications, Plenum Press, NewYork, 1989, p. 131.

[21] G.P. Rabold, J. Polym. ScL, Part A-I, 1967,7, 1203.[22] N. Kusumoto, in R.F. Boyer and S.E. Keineth (Eds.), Molecular Motions in Polymers

by E.S.R., MMI Press, Symposium Series Vol. 1, Harwood, Chur, 1980, p. 223.

[23] AT. Bullock, G.G. Cameron and LS. Miles, Polymer, 1982, 23,1536.[24] M.L. Williams, R.F. Landel and J.D. Ferry, J. Am. Chem. Soc, 1955,77, 3701.[25] S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1990, 23, 3769.[26] R. Harvey and S. Schlick, Polymer, 1989,30,11.[27] K.K. Fox, LD. Robb and R. Smith, J. Chem. Soc, Faraday Trans. 1,1974,70,1186.[28] LD. Robb and R. Smith, Polymer, 1977,18, 500.[29] LD. Robb and M. Sharpies, J. Colloid Interface ScL, 1982,89, 301.[30] K. Lewtas, R.D. Tack, D.H.M. Beiny and J.W. Mullin, in J. Garside, R. Davey and

A. Jones (Eds.), Advances in Industrial Crystallisation, Butterworth-Heinemann,Oxford, 1991, p. 166.

[31] LG. Davidson and G.G. Cameron, Polymer International, 1994, 34, 443 and 449.[32] S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1992,25, 2771.[33] S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1988, 21, 2107.[34] S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1988, 21, 3454.[35] G.G. Cameron, M.Y. Qureshi, E. Ross, LS. Miles and J. Richardson, Polymer, 1993,

34, 25.[36] G.G. Cameron, D. Stewart, R. Buscall and J. Nemcek, Polymer, 1994,35, 3384.[37] E. Helfand and Y. Tagami, J. Chem. Phys., 1972,56, 3592.[38] T.H. Weber and E. Helfand, J. Chem. Phys., 1980,72,4017.[39] E. Helfand, in K. Sole (Ed.), Polymer Compatibility and Incompatibility, Harwood,

Chur, 1982.[40] E. Ross, Ph.D. Thesis, University of Aberdeen, 1990.[41] G.G. Cameron, LS. Miles and AT. Bullock, Br. Polym. J., 1987,19,129.[42] AT. Bullock, G.G. Cameron and LS. Miles, Polymer, 1982,23,1536.

10 THE USE OF ESRSPECTROSCOPY FORSTUDYINGPOLYMERIZATION ANDPOLYMER DEGRADATIONREACTIONS

T. G. CARSWELL, R. W. GARRETT, D. J. T. HILL,J. H. O'DONNELL, P. J. POMERY and C. L. WINZORPolymer Materials and Radiation Group, Department of Chemistry, University ofQueensland, Brisbane, QLD 4072, Australia

10.1 INTRODUCTION

Electron spin resonance spectroscopy offers a unique technique to study the roleof radical species as intermediates in both polymerization and polymer degrada-tion processes. The technique has been developed significantly since its introduc-tion to chemical applications in the 1950s [1], with major advances in thestability of the magnetic field, in the sensitivity to low radical concentrations—and hence the limit of detection and measurement—and in data collection andmanipulation. ESR spectrometry enables both the identification of radicalsand the measurement of their concentration. It is a non-destructive technique andspectra can be recorded both during polymerization, and, in suitable circumstan-ces, during degradation of polymers [2].

New quantitative studies of free radical polymerization kinetics are currentlybeing undertaken by a number of researchers using pulse laser techniques [3,4].However, the pulsed laser methods cannot be used for crosslinking systems.There has also been development of a number of new theoretical models forpolymerization [5-7]. The experimental information available comprises mono-mer concentration and polymer molecular weight. ESR spectroscopy offers thepossibility of an additional piece of information—the radical concentrationduring polymerization. There is increasing interest in polymerization to highconversion, which is of great practical importance, and ESR spectra can be


obtained readily under these conditions when other methods can be difficult toapply [8].

Degradation of polymers is often understood from a practical viewpoint asa deterioration in the properties of polymer materials leading to failure in service.Changes in the molecular structure, and particularly the molecular weight, of thepolymer is the fundamental degradation process. High-energy radiation, e.g.gamma-rays and electron beams, is an important cause of controlled polymerdegradation [9]. The degradation reactions usually involve free radical inter-mediates, and therefore ESR spectroscopy is a valuable technique for investigat-ing the chemical mechanism of degradation.

We have studied the degradation by high-energy radiation of a number offamilies of polymers by using a variety of techniques, including ESR spectroscopy[10, H]. In this paper we show the similarities and differences in the role of freeradicals in the radiolysis of poly(methyl methacrylate), polystyrene, and randomcopolymers of methyl methacrylate and styrene.

10.2 EXPERIMENTAL

The ESR spectra were recorded using a Bruker ER200D spectrometer fitted witha liquid nitrogen dewar for measurements at 77 K, and with a variable tempera-ture cavity having a heated supply of cold nitrogen for temperature control from100 to 400K.

Methyl methacrylate (MMA) was distilled under a reduced pressure of nitro-gen; ethylene glycol dimethacrylate (EGDMA) was purified by passage throughan alumina column. Polymerization mixtures containing azobisiso- butyronitrile(AIBN) as initiator were sealed in 3 mm i.d. quartz tubes under vacuum. Somemeasurements were also made in 1 mm i.e. tubes in order to minimize increases inthe temperature of the polymerization which could result from the exothermicheat of polymerization during the Norrish-Trommsdorff region. The conversionof monomer (C=C concentration) was measured by near-infrared Fouriertransform spectroscopy using the C=CH vibration at 6152cm"l.

CH3 CH3 CH3

I I ICH 2 =C CH 2 =C C=CH2

COOCH3 CO COI I

0 - C H 2 - C H 2 - OMMA EGDMA

Poly(methyl methacrylate), polystyrene and their random copolymers wereprepared by free radical polymerization in vacuum using AIBN as initiator.

Samples of the polymers were evacuated with heating and sealed in high-purityquartz tubes. Cobalt-60 gamma-irradiation was carried out in liquid nitrogen(77 K) and at ambient temperature (300 K) at a dose rate of « 1 kGy/h.

10.3 RESULTS AND DISCUSSION

10.3.1 FREE RADICAL POLYMERIZATION

10.3.1.1 Identification of the Radicals in the ESR Spectrum

The ESR spectrum is recorded in the first-derivative form as shown in Fig-ure 10.1. A number of characteristics of the spectrum of a radical can be predictedfrom its structure and used to identify the presence of the radical in an ESRspectrum. These characteristics are illustrated in Figure 10.1, which is the ESRspectrum of the methyl radical at 77 K. They include:

(1) g value—the centre of the spectrum—corresponding to the proportionalitybetween the magnetic field H and the microwave frequency, expressed in therelationship fcv = gfiH;

(2) the number of lines in the spectrum—resulting from interactions betweenthe unpaired electron spin on the radical and the nuclear spins of adjacent atoms,particularly hydrogen;

Figure 10.1 ESR spectrum of the methyl radical (CH3') showing the characteristicfeatures of g value, number of lines, relative intensities of the lines, hyperfine splitting (hfs),line width, and line shape

Linewidth

Intensity

Lines

(3) the relative intensities of the component lines of the spectrum of theradical—frequently described by a binomial distribution of intensities;

(4) the hyperfine splitting, hfs, between the lines—this separation of the linesdepends on the electron spin on the radical site, the magnitude of interactingnuclear spins and the conformation of the radical;

(5) the line widths—usually measured between the positive and negative peaksof the derivative spectrum, or the width at half height of the absorption spectrum.

(6) the line shape—usually represented by a Gaussian or Lorentzian express-ion, or a combination, depending on the curvature of the wings of the absorptionspectrum, reflecting the environment of the radical.

10.3.1.2 Measurement of Radical Concentration

ESR spectra are obtained as first-derivative spectra of signal intensity versusmagnetic field because of the method of observation of the absorption ofmicrowave power. Integration of the experimental spectrum gives the corre-sponding absorption spectrum and a second integration gives the area of thespectrum, which is proportional to the radical concentration provided thatmicrowave power saturation is avoided.

Saturation of the upper energy level of the unpaired spins can occur at highmicrowave powers, the actual power depending on the relaxation time and henceon the nature of the radical. Therefore for quantitative measurements of radicalconcentrations the power dependence of the spectrum must be examined. Devi-ation from linearity in a plot of spectrum area versus the square root of themicrowave power indicates the onset of microwave power saturation and theupper limit for quantitative measurements of radical concentrations. Microwavepower saturation measurements for methacrylate propagation radicals duringpolymerization is shown in Figure 10.2.

The area of the absorption spectrum does not yield an absolute value forradical concentration. This must be obtained by calibration with a samplecontaining a known concentration of radicals using standardized conditions ofmeasurement. A sample of pitch/KCl provided by Varian was used in the presentstudy, and this sample was calibrated with a measured concentration of recrystal-lized diphenylpicrylhydrazine (DPPH) in benzene.

10.3.1.3 Monomer Concentration during Polymerization

We have utilized a variety of techniques for determination of the conversion ofmonomer to polymer, by measurement of the concentration of C = C bonds atdifferent times during the polymerization of vinyl and allyl monomers. The 1HNMR spectra of samples quenched and dissolved in deuterated solvent showedresonances due to the different H atoms of the monomer and polymer, and 1HNMR was a very good method for determination of conversion. However,

1/2

(Microwave power)Figure 10.2 Microwave power saturation plot of the area of the ESR spectrum versus thesquare root of the microwave power: (•) (experimental values; ( ) linear relationshipassuming no saturation, S is the maximum power level that can be used without saturationoccurring

Fourier transform near-infrared spectroscopy, using the C = C H band at6152 cm"1 for methacrylates, enabled the conversion to be followed in a singlesample throughout the polymerization to high conversion. Parallel experimentswere performed for near-infrared spectroscopic determination of monomer con-centrations and for ESR measurements of radical concentrations. A further advan-tage of the near-IR method is its applicability to insoluble crosslinked systems.

A typical conversion curve for the polymerization of methyl methacrylate isshown in Figure 10.3. The three regions in the conversion curve correspond to (1)the pre-gel region, (2) the Norrish-Trommsdorff region between the gel point andthe glass point, and (3) the glass region. The steep rise in the polymerization rateabove the gel point is attributed to a marked decrease in the termination rateparameter, kv and the decrease in polymerization rate to near zero above theglass point is attributed to a decrease of several orders of magnitude in theapparent propagation rate parameter, kp.

10.3.1.4 Radical Concentration during Polymerization

Typical plots of radical concentration versus time during the polymerization ofmethyl methacrylate are shown in Figure 10.4. The lower limit of sensitivity of

Are

a o

f E

SR

sp

ec

tru

m

Time / min

Figure 103 Typical conversion curve for polymerization of methyl methacrylate show-ing the gel and glass points and the (1) pre-gel, (2) Norrish-Trommsdorff, and (3) glassregions. Polymerization temperature 45 0C; [AIBN] = 0.1 M

current ESR spectrometers is «10" 7 M, which is not sufficient to enable measure-ment of the concentration of propagating radicals during the polymerization ofmost monomers below the gel point. An ESR spectrum of propagating radicalscan be obtained below the gel point by quenching the polymerization systemin liquid nitrogen and accumulating spectra at 77 K, which also utilizes thefavourable Boltzmann distribution at this temperature. Radical concentra-tions obtained below the gel point by the quenching technique are also shownin Figure 10.4.

In favourable circumstances, the radical concentration below the gel point maybe obtained by accumulation of spectra in situ. However, the limited timeavailable for accumulation and the changing nature of the spectrum withconversion militate against this procedure. Radical concentrations obtainedabove the gel point by the quenching and in situ methods (without accumulation)were in good agreement.

Comparison of the monomer concentration (Figure 10.3) and the radicalconcentration (Figure 10.4) during the polymerization shows that, whereas therate of conversion decreases very suddenly at the glass point, the radicalconcentration continues to increase, but at a steadily decreasing rate. At longpolymerization times the radical concentration reaches a maximum and thendecreases due to the depletion of initiator, indicating that termination reactionscontinue above the glass point, although more slowly.

% C

on

vers

ion

glass point

gel point

Time/ min

Figure 10.4 The variation of the radical concentration [R#] with time during thepolymerization of methyl methacrylate at 45 0C for different concentrations of AIBNinitiator: (A) 0.2 M; (o) 0.1 Af; (•) 0.05 Af, spectra obtained in situ during polymerization inthe ESR spectrometer. (•) 0.05 M AIBN, spectra obtained by quenching to 77 K, enablingaccumulation of scans

103.1.5 Correction for Changing Sensitivity of the Spectrometer

The dielectric constant of the polymerizing system decreases during the polymer-ization owing to changes in the molecular mobility of the polar ester groups andthe conjugation between C=C and C = O . This effect will be greatest in theNorrish-Trommsdorff region, between the gel and the glass point. The changesin the dielectric constant cause changes in (1) the frequency of resonance, and (2)the sensitivity, or Q value, of the spectrometer, i.e. in the area of the spectrumwhich would be obtained from a constant radical concentration.

A procedure which can be used to measure the change in sensitivity of thespectrometer during polymerization is to record the spectrum of a referenceunpaired spin species with an ESR spectrum which does not overlap the spectrumof the methacrylate propagating radical. We have found that the Mn2+ species(conveniently found in MgO) provides a suitable spectrum [12]. The Mn2+ (inMgO) was coated on the outside of the ESR tube as an external standard by

[FT)

/ mol

dm

3

Time / min

Figure 10.5 Simultaneous measurement of the ESR spectra of Mn2 + and methacrylatepropagating radicals during the polymerization of methyl methacrylate: Mn area, sensitiv-ity of the spectrometer; Mn field, conversion: [R*], corrected concentration of MMAradicals

exposing the tube to the flame from burning magnesium metal. The variation insensitivity is shown in Figure 10.5 as the area of one peak in the spectrum ofMn2 + . The increase in sensitivity occurs mainly in the Norrish-Trommsdorffregion and corresponds to a factor of % 3 in the area. The measured area of thespectrum of the methacrylate propagating radical can then be corrected accord-ing to the change in area of the Mn2 + peak.

An additional aspect of using Mn2 + to measure the changing sensitivity of thespectrometer during the polymerization of methyl methacrylate was found to bethat the field position of the Mn2+ peak also varied, and this variation could becorrelated with the C = C conversion. The position of the propagating radicalshowed an identical variation in resonance frequency. Thus, the concentrationsof both R* and C = C can be obtained throughout the polymerization from theESR spectra. Typical data obtained for the polymerization of MMA at 60 0C withAIBN initiator are shown in Figure 10.5.

10.3.1.6 Kinetic Analysis

The mechanism of polymerization of methyl methacrylate initiated by AIBNinvolves the three kinetic steps:

Initiation

I—>2Y

Propagation

P;+M^P;+1

Termination

The instantaneous rate of polymerization and the net rate of formation ofradicals are given by the following equations

-d[M]/df = fcp[F][M]

d[P]/dr = 2fcd/[I]-2fcf[P-]2

where [M], [P'] and [I] are the concentrations of monomer, propagatingradicals and initiator, respectively, / is the initiator efficiency and kd is the rate ofdecomposition of the initiator.

The values of fcp and kt can be obtained directly from these equations usingthe experimentally determined values for [M] and [P-], provided that /remains constant. We have shown that a suitable manipulation of the secondequation enables the values of / and kt to be derived for incremental increasesin conversion. Good agreement is obtained with current theories of freeradical polymerization for the polymerization of methyl methacrylate at 60 0C[13].

10.3.1.7 Crosslinking Methacrylate Monomers

A major objective of the current research programme is to extend the treatment ofpolymerization kinetics based on direct measurements of monomer and radicalconcentrations to crosslinking systems. Conventional methods for measurementof monomer concentrations are not suitable, as they require soluble polymer. Wehave been able to apply our procedure for utilizing the near-infrared spectrum ofthe C = C bond in methyl methacrylate to systems containing ethylene glycoldimethacrylate (EGDMA) [14].

Figure 10.6 shows the variation of the concentration of C = C bonds during thepolymerization of a MMA-EGDMA mixture containing 36% of EGDMA. Theinitial rate of polymerization is much higher than for MMA, and this can beattributed to the absence of a pre-gel region. However, the plateau region of theconversion is lower. This results from the crosslinking reaction, with the radicalsand C = C bonds immobilized in the network.

Figure 10.7 Dependence of radical concentration [R#] on polymerization time for (a)MMA and (b) a MMA-EGDMA mixture (36% EGDMA): polymerization temperature600C; initiator 0.05 M AIBN. Note that the concentration scales differ by a factor of 40

The radical concentration in MMA-EGDMA mixtures might be expected tobe higher than in MMA owing to the retardation of the termination reaction bythe network. In Figure 10.7 the absence of a pre-gel region is indicated by theincrease in radical concentration from the beginning of the polymerization. The

Time / min

[R*]

x1

0-6

/mo

ldn

rr3

Time / min

Figure 10.6 Dependence of C = C concentration on polymerization time for (a) MMAand (b) a MMA-EGDMA mixture (36% EGDMA): polymerization temperature 60 0C;initiator 0.05 M AIBN

% C

onve

rsio

n

most significant difference between the MMA-EGDMA mixture and MMA isthe radical concentration in the plateau region. It is approximately 40 timesgreater in the mixture, and is almost millimolar.

Kinetic analysis of the propagation and termination rate constants in thepolymerization of MMA-EGDMA mixtures is more difficult than for MMA. Anunderstanding of the polymerization depends on knowledge of the individualconcentrations of C = C bonds that are (1) in monomer molecules and (2)attached to polymer molecules. This information may be obtainable for NMRspectra utilizing differences in the relaxation times of the two types of C=Cenvironments. However, it is likely that the polymerization is heterogeneous witha non-spatially random distribution of crosslinks.

10.3.2 POLYMER DEGRADATION BYHIGH-ENERGY RADIATION

The effects of high-energy radiation, principally y-rays and electron beams, onpolymers have been studied extensively for many years. The main interest hasbeen in the changes in material properties, such as strength and elongation. Thesechanges in properties have been related to changes in molecular weight of thepolymer molecules, either by main-chain scission or by chain crosslinking,frequently with the formation of an insoluble gel fraction. The applications ofradiation effects on polymers have been two-fold: (1) the use of polymer materialsin radiation environments, such as nuclear reactors, and more recently in space,(2) modification of the properties of polymer materials by reduction in molecularweight or crosslinking, especially in the microelectronics industry as electronbeam resists, and perhaps in the future as X-ray resists.

Fundamental understanding of the mechanism of degradation of polymers byhigh-energy radiation has been based mainly on structural changes observed inthe polymers, and to a much smaller extent on measurements of small moleculeproducts. ESR has been used since 1960 to observe radicals produced inirradiated polymers, and hence to provide evidence for intermediate species in theradiolysis. However, recent improvements in the stability and sensitivity of ESRspectrometers and in computer manipulation of the spectra have enhanced theuse of this technique.

The capabilities of the ESR technique for providing fundamental informationabout the mechanism of radiation degradation of polymers are shown inobservations on gamma-irradiated poly(methyl methacrylate), polystyrene andtheir random copolymers.

10.3.2.1 Poly(methyl methacrylate)

The ESR spectrum of poly(methyl methacrylate) at 300K, shown in Fig-ure 10.8(a), is well known. This characteristic 13 line (9 + 5) alternating spectrum

Figure 10.8 ESR spectra of poly(methyl methacrylate) after y-irradiation in vacuum:radiation dose 1 kGy; radiation temperature (a) 300 K, (b) 77 K

has been the subject of much debate, but it is now generally accepted to be due tothe methacrylate propagating radical with two conformations.

The ESR spectrum after irradiation at 77 K, shown in Figure 10.8(b), is quitedifferent from the spectrum after irradiation at 300K. It is evidently due toa number of radicals; the propagating radical is not a significant component atthis temperature, and must be formed by subsequent reactions of the radicalsproduced at 77 K.

Analysis of spectra

A variety of techniques can be used to analyse for the component radicals in anESR spectrum. They include:

(1) dose saturation—spectra are obtained after irradiation to a series ofradiation doses. The yield of trapped radicals does not increase linearly with doseabove certain doses which are characteristic of particular radicals. In particular,radical ions show 'dose-saturation' at low doses;

(2) microwave power saturation—the observation of an ESR spectrum de-pends on the relaxation of the radicals (which are excited into the higher energylevel by the microwave radiation) back to the lower energy level in accordancewith the requirements of the Boltzmann distribution. Some radicals, and particu-larly radical ions, have a slow relaxation and hence they will not be observed athigh microwave powers;

(3) Photobleaching—radical ions can be distinguished from neutral radicalsby irradiation with visible light above a critical wavelength, which is usually«500nm. The radical ions are bleached and disappear, whereas the neutralradicals are unaffected. The efficiency of this technique does depend on theinteraction of the light with the radicals and hence requires a transparent or finelypowdered sample;

(4) Fourier transform masking—the ESR spectrum can be converted to itsFourier transform in the frequency domain. Lines in the original spectrum withdifferent line-widths can be separated by masking of different parts of thespectrum and then conversion back into the original domain;

(5) accumulation of spectra—the signal to noise ratio must be high to enableseparation of different radicals in a spectrum, especially if some of the radicals arepresent in small proportion of the total spectrum. Accumulation of the spectra,possible with high stability of the magnetic field, enables the signal to noise ratioto be enhanced. The effect of spectral accumulation is illustrated in Figure 10.9for poly(a-methylstyrene);

Figure 10.9 ESR spectrum of poly(a-methylstyrene) after y-irradiation in vacuum at300 K (dose 6 kGy): (a) one scan of 200 s; (b) 150 scans

(6) thermal annealing—when a number of different types of radicals aretrapped in a polymer during irradiation at a particular temperature, they willreact in different ways at different temperatures on subsequent heating. Theprocess of radical disappearance is known as thermal annealing, and can be usedto distinguish different radicals present at a lower temperature. The greatestnumber of radicals will be produced by irradiation at the lowest possibletemperature. Usually, liquid nitrogen is used to enable irradiation at 77 K for thisreason, and the procedure is known as cryogenic trapping;

(7) subtraction techniques—recording of ESR spectra by computer enablesa variety of computational procedures to be used to identify and quantify thecomponent radicals and their reactions. In particular, subtraction of spectraobtained after progressive stages of warming (thermal annealing after cryogenictrapping) will frequently show a triplet or other spectrum characteristic ofa particular radical which has disappeared. The effectiveness of this procedure isenhanced if the sample is cooled back to the same reference temperature to recordthe spectrum after each warming step;

(8) simulation—confirmation of the presence of different types of radicals andestimates of their proportions, and hence of their concentrations, can be obtainedby simulation of the ESR spectrum. This procedure requires values for theparameters of the spectrum, Le. g value, number of lines, relative intensities of thelines, hyperfine splittings, line-widths, line shape (Gaussian or Lorentzian ora mixture). Simulated spectra can be computed for a wide variety of values for thedifferent parameters, the simulated ESR spectrum being matched to the experi-mentally observed spectrum.

We have utilized all of these techniques to analyse the ESR spectrum ofpoly(methyl methacrylate) at 77 K after y-irradiation. The progressive disappear-ance of different types of radicals, and the formation of the chain scission radical(which is the same radical as the propagating radical), eventually as the onlyspecies, during thermal annealing after cryogenic trapping, are shown in Figure10.10.

We have identified seven different radical species A-G, including the polymerradical anion G, in the ESR spectrum of poly(methyl methacrylate) at 77 K aftery-irradiation in vacuum (the spectrum shown in Figure 10.8(b)), as follows:

C H 3 I I C H 3

I 1 . 1 ICH3- -CHO -COOCH3 - C H 2 - C - - C — C H - C — C H 2 - C -

COOCH^ I ' COOCH2

A B C D E F

The progressive disappearance of these radicals, based on the spectra shown inFigure 10.10, is shown in Figure 10.11. The five regions shown in Figure 10.11correspond to the disappearance of different radicals as follows: stage (1) A, B and

C; stage (2) C and D; stage (3) E; stage (4) propagating radical (F) is the onlyspecies present and is stable; (5) F.

The mechanism of the degradation of poly(methyl methacrylate) by y-radi-ation can be deduced on the basis of the disappearance of radicals shown inFigure 10.11. This mechanism (Scheme 1) is consistent with the formation ofmolecular products, as previously reported.

CH3 CH3 OI I Il

^ C H 2 - C ^ - - C H 2 C - C H 2 - + -C-O—CH 3 + OTHERSC = O # C H 3

O -CHO

(LjJ3 - C O - O - C H 2

CH3 CH3 CH3

I I I- C H 2 C - C H 2 - SCISSION • - C H 2 - C - + C H 2 = C - C H 2 -

C = O

OICH3

- C O - O - C H 3 CO + CO2 + CH4 + CH3OH

Scheme 1 Mechanism of degradation of poly(methyl methacrylate) by y-radiation de-duced from ESR studies of radical intermediates

10.3.2.2 Polystyrene

The ESR spectrum of polystyrene after y-irradiation in vacuum at 77 K is shownin Figure 10.12(a). The spectrum is quite different from that of poly(methylmethacrylate). It can be assigned to three species: (1) the oc-carbon radical, (2) thecyclohexadienyl radical, and (3) a radical anion. The proportions of cyclo-

a-carbon cyclohexadienyl

Figure 10.10 ESR spectra of poly(methyl methacrylate) after y-irradiation at 77 K andprogressive wanning to 300 K. All spectra (except that at 77 K) were recorded on coolingback to 140K after 10 min at the specified temperature

hexadienyl radicals and of radical anions are strongly dose-dependent, whichprovides a method for their assignment.

The two neutral radicals are consistent with crosslinking being the major effectof radiation on polystyrene, in contrast to main-chain scission in poly(methylmethacrylate).

The ESR spectrum after irradiation at 300K, shown in Figure 10.12(b), issimilar to the spectrum at 77 K except that the centre line is reduced, owing to theabsence of the radical anion, and the large outer peaks of the 'triplet' show greaterresolution into subsidiary peaks.

10.3.2.3 Random Copolymers of Methyl Methacrylate and Styrene

The effect of high-energy radiation on random copolymers of styrene and methylmethacrylate provides an excellent system for testing hypotheses for intra-

T / K

Figure 10.11 Decrease in radical concentration in poly(methyl methacrylate) after 1 kGyof y-irradiation at 77 K on progressive warming to 360K. The numbers refer to stages ofradical reactions during wanning

molecular and inter-molecular interactions of energy transfer and radical reac-tions.

The ESR spectra of a series of copolymers of styrene and methyl methacrylateacross the composition range between the two homopolymers are shown inFigure 10.13 after irradiation at 300K. The spectra show a progressive changebetween the spectra of the homopolymers, but it is apparent, e.g., considering thecopolymers containing 20% and 50% of styrene, that the proportions of'styrene'radicals in the spectra are greater than the proportions in the compositions of thecopolymers. Thus, there is a preference for the formation of styrene radicals. Thiseffect has one component occurring during irradiation at 77 K (attributed toenergy transfer) and another component occurring during warming to 300 K (oroccurring during irradiation at 300K), which we have attributed to radicaltransfer reactions.

This preference for the formation of styrene radicals is a manifestation ofa protective effect by styrene units on the degradation of methacrylate units in thecopolymer. The protective effect is also shown by the variation in the yield ofradicals, G(R"), with the composition of the copolymer. Figure 10.14 shows howthe value of G(R*) in the copolymers is always much less than the value whichwould be obtained from the additivity of the electron densities of the twomonomer units. The protective effect is even greater at 300 K than at 77 K, whichis consistent with the additional mechanism of protection which occurs above77 K.

10.3.2.4 ESR and the Mechanism of Radiolysis

The number of different types of radicals observed in the ESR spectra ofirradiated polymers is always greater after irradiation at 77 K than at 300 K. The

Btf

rel

Scheme 2 ESR procedure of cryogenic trapping and thermal annealing to provide anunderstanding of reactions which occur rapidly during the irradiation of polymers at

Figure 10.12 ESR spectra of polystyrene after y-irradiation in vacuum. Radiation dose10OkGy; radiation temperature: (a) 77 K, (b) 300K

Figure 10.13 ESR spectra of random copolymers of styrene and methyl methacrylateafter y-irradiation in vacuum at 300K. Radiation dose 3kGy. The compositions of thecopolymers are specified in mol% styrene

100% STY

20% STY 50% STY

8% STY0%STY

% STYRENE

Figure 10.14 Protective effect against degradation by y-radiation provided by styreneunits in random copolymers of styrene and methyl methacrylate, shown by the radicalyields G(R#) derived from the ESR spectra, (a) Experimental values for y-irradiation at77 K; (b) experimental values for y-irradiation at 300 K. The lines correspond to the G(R*)values for the copolymers calculated from the G(R') values for poly(methyl methacrylate)and polystyrene based on the additivity of electron densities

G(R

-)G

(R)

ESR spectra are usually similar after irradiation at 300K or irradiation at 77 Kand warming to 300 K, although the concentrations of radicals may be different.A model for the mechanism of the radiolysis can then be deduced from theradicals which are observed at 77 K and the reactions which they undergo onwarming. The procedure is outlined in Scheme 2.

10.4 CONCLUSIONS

ESR provides a powerful technique for developing a fundamental understandingof the mechanism and kinetics of free radical polymerization and of the mechan-ism of degradation of polymers by high-energy radiation. The assignment of ESRspectra to component radicals and the measurement of the concentrations ofthese radicals require a variety of experimental and computational procedures,which have been greatly enhanced by improvements in spectrometer perform-ance and computer capabilities.


The authors are grateful to the Australian Research Council and the AustralianInstitute of Nuclear Science and Engineering for supporting this research, and tothe Australian Nuclear Science and Technology Organization for the provisionof irradiation facilities.

10.6 REFERENCES

[1] P.B. Ayscough, Electron Spin Resonance in Chemistry, Methuen, London, 1967.[2] D.J.T. Hill, J.H. O'Donnell and PJ. Pomery, in Electron Spin Resonance, Royal

Society of Chemistry Specialist Periodical Reports, Vol. i3A, Cambridge, 1992,p. 202.

[3] O.F. Olaj, I. Bitai and F. Hinkelman, Makromol. Chem., 1987,188,1689.[4] T.P. Davis, K.F. O'Driscoll, M.C. Piton and M.A. Winnik, Macromolecules, 1989,

22, 2785.[5] S.K. Soh and D.C. Sundberg, J. Polym. ScL, Polym. Chem. Ed., 1982,20,1345.[6] MJ. Ballard, R.G. Gilbert, D.H. Napper, PJ. Pomery, P.W. O'Sullivan and J.H.

O'Donnell, Macromolecules, 1986,19,1303.[7] G.T. Russell, D.H. Napper and R.G. Gilbert, Macromolecules, 1988, 21, 2141.[8] R.W. Garrett, DJ.T. Hill, J.H. O'Donnell, PJ. Pomery and CL. Winzor, Polym.

Bull, 1989,22,611.[9] M. Dole (Ed.), The Radiation Chemistry of Macromolecules, Academic Press, New

York, 1972.[10] R.W. Garrett, DJ.T. Hill, TT. Le, J.H. O'Donnell and PJ. Pomery, Radiat. Phys.

Chem., 1992,39,215.

[11] DJ.T. Hill, S.Y. Ho, J.H. O'Donnell and PJ. Pomery, Radiat. Phys. Chem., 1990,36,467.

[12] T.G. Carswell, DJ.T. Hill, D.S. Hunter, PJ. Pomery, J.H. O'Donnell and CL.Winzor, Eur. Polym. J., 1990, 26, 541.

[13] T.G. Carswell, DJ.T. Hill, D.I. Londero, J.H. O'Donnell, PJ. Pomery and CL.Winzor, Polymer, 1992,33,137.

[14] T.G. Carswell, DJ.T. Hill, R. Kellman, D.I. Londero, J.H. O'Donnell, PJ. Pomeryand CL. Winzor, Makromol. Chem., Macromol. Symp., 1991,51,183.

11 DYNAMICS OF BULKPOLYMERS ANDPOLYMERIZING SYSTEMS ASSTUDIED USING DIELECTRICRELAXATIONSPECTROSCOPY

G. WILLIAMS, C. DUCH, J. FOURNIERand J. R. HAYDENDepartment of Chemistry, University College of Swansea, Singleton Park,Swansea SA2 SPP, UK

11.1 INTRODUCTION

Dielectric relaxation spectroscopy (DRS), with its wide frequency range 10~6 to1011 Hz, has been used for over fifty years as a leading method for studying thereorientational motions of molecules in the liquid, amorphous solid, crystallineand liquid-crystalline states [1-6]. Most of these studies involved point-by-pointmeasurements of permittivity ef(co) and loss factor e"(a>) at chosen frequenciesusing different apparatus for each frequency range, e.g. transient current re-corders, LCR impedance meters, microwave transmission lines and cavity res-onators. Such difficult and tedious procedures hindered the progress of DRS incomparison with that made by other methods such as NMR, ESR, dynamicquasi-elastic light scattering in the time and frequency domains, quasi-elastic neutron scattering and time-resolved fluorescence depolarization (foraccounts of such techniques applied to polymer science see ref. [7]). However,during the past eight years or so modern DRS equipment has appeared in theform of automatic-measuring LCR meters, transient equipment and time-do-main reflectometry for microwave frequencies, which together with computercontrol and modern data-processing methods now provide techniques for thefast, accurate determination of permittivity and loss over the range 10 " 6 -1010Hz. In addition to allowing conventional DRS studies of polymers to bemade more conveniently, the new techniques allow studies to be undertaken that


were not practical hitherto, e.g. (i) for reasons of experimental time and (ii) forsystems that change with time where manual point-by-point measurements areinappropriate. As a result, broad-band DRS now provides a powerful method forstudying new problems in polymer science and takes its place alongside the othermethods for studying polymer dynamics mentioned above [3, 8-10].

The present account summarizes briefly selected aspects of earlier DRS studiesof polymers and of recent development, especially those concerning short- andlong-range motions of chains and systems undergoing polymerization.

11.2 AMORPHOUS POLYMERS: PHENOMENOLOGICALAND MOLECULAR ASPECTS

The phenomenological theory of the dielectric relaxation behaviour of linearsystems is well-established [1-5]. The fundamental relationship joining thefrequency-dependent complex permittivity e(a>) measured at frequency / = o)/2nand the transient step-response function <j>(t) is the Fourier transform relation-ship

where e((o) = e'(co) — ie"{a>), e0 and S00 are the limiting low and high frequencypermittivities and 3 indicates a one-sided Fourier transform; i = -y/—1. Thusmeasurements of e(a)) give information on <t>(t) and vice versa through theinversion relationships [11] that follow from Equation (1). For a polymermaterial exhibiting multiple relaxation regions, multiple peaks will be observedin e"((o) and corresponding multiple decays will occur for (f>(t).

For amorphous solid polymers, multiple relaxations have been observed andanalysed in great detail [3, 12-17]. For T< Tr where Tg is the apparent glasstransition temperature, a single broad /? process is observed. For T>Tg theOL process emerges from low frequencies, so that in a limited range both a and/? relaxations are observed in plots of e" vs. log/. As temperature is furtherincreased, the a and fi processes tend to coalesce to form at high temperaturesa single <xfi process, which is a continuation of the a process to higher frequencies,only now all of the relaxation strength is contained within the single process. Thisis the pattern of behaviour exhibited by all amorphous polymers, including theacrylates, methacrylates, halogen polymers, oxide polymers and polyesters, as wehave described and discussed [12-17], including the effects of temperature andapplied pressure [18-20]. Such behaviour is well-represented by the relaxationfunction [16-17]

№ = <t>a(t)LAa + Afi<l>0(tn (2)where Aa + Afi=l and <j>a(t) and < (̂f) are normalized decay functions for the

a and /J processes respectively. For T< Tg, <t>a(t) is approximately constant in thetime-scale of interest, so only a part, A0Ae9 of the total relaxation strength Ae isrelaxed through the /? process. For T ^ Tg, two relaxation regions occur ofrelative strengths Aa:Afi. At still higher temperature <f>a(t) begins to decay fasterthan <t>p(t\ and is this continues to the range where <t>a(t) decays much faster than(f)p(t) the a and P process coalesce so that all the relaxation strength Aa is relaxedthrough <t>a(t), which corresponds to the a/? process. In the range where a andP coexist and are observed as two processes in the time or frequency domains, thisphenomenological description requires that the conservation rule [ 12,13,15-17]holds

A£ = A£a + Ae, (3)

Thus, if an increase in pressure decreases the strength of the P process, then therewill be a consequent increase in the strength of the a process in order to conserveAE, as we and others have observed [12,17, 20].

A further feature of dielectric relaxations in amorphous polymers is that thea (or a/?) relaxations are well-described by the 'stretched-exponentiaF or 'Kohl-rausch-Williams-Watts' function [21-23]

0(t) = e x p [ - ( t / t o n (4)

0 < / ? ^ 1 and T0 = T0(T5P) is the effective correlation time. For the dielectrica-relaxation in such polymers as poly(vinyl acetate), poly(methyl acrylate),polypropylene oxide and polyethylene terephthalate the loss curves are well-fitted by the KWW function, with p values being in the range 0.4-0.6. Thecalculated curves for the KWW function with different values of P have beendescribed [21-23] and tables of ef and e" values are available [24].

The a process observed in the time or frequency domains for amorphouspolymers using dynamic-mechanical, NMR, ESR, light-scattering and fluor-escence depolarization methods is also well-fitted using the KWW function withsimilar /lvalues. In addition, glass formation is small molecule liquids (molecularand ionic) gives relaxation phenomena that are entirely similar to those found foramorphous polymer [6, 25]. This observation, that the KWW function isubiquitous in relaxation phenomena in all glass-forming materials, has beena focus of attention in condensed matter physics and chemical physics in recentyears, and many models have been proposed to rationalize behaviour [6,12,25,26]. Notable among recent developments are those due to Ngai [27] and byGoetze [28,29] and Mazenko [30]. In the works of Ngai [27,31-33], the startingpoint for applications of theory to diverse relaxation phenomena is the firsttime-derivative of the KWW equation (4) in which T0 is given, through a secondrelationship, a dependence on a primitive relaxation time and the P parameter. Inthe works of Goetze and Mazenko, a 'mode-mode coupling theory' is proposedwhich is formally equivalent to Mori-Zwanzig continued fraction representationof a relaxation function in which the frequency-dependent relaxation function

<j>((o) is related to a higher-order memory function K(a>), thus closing the problemand allowing both <f>(co) and K((o) to be determined. The results of̂ such a theorydepend entirely on the assumed form of interrelationship between K(o) and <t>(co).One difficulty with these approaches is that they do not specify the particularmolecular property whose relaxation behaviour is being considered. Thus <f>(t) issimply a relaxation function from any of the relaxation experiments. However,the molecular origins of such relaxation phenomena have been well-establishedfor dielectric, NMR, quasi-elastic light and neutron scattering experiments andfor fluorescence depolarization through the time-correlation function representa-tion for molecular reorientations and translations and theories (linear-responsetheory, field-perturbation theories) that connect the observable (a vectorial ortensorial quantity) to such time-correlation functions. For the special case ofdielectric relaxation of an amorphous material composed of dipolar polymermolecules, linear-response theory gives the following result [34-36] for e(co)

r^^T^J^l-icoSWr)] (5)L £o-£oo J

where p(co) is an internal field factor, and O(f) is a time-correlation function for thefluctuations in the macroscopic dipole moment M(t) of a spherical volume V inthe dielectric.

<M(0)-M(t)>1 1 ^ M ( O ) - M ( O ) ) ( 6 )

For flexible polymer chains having no persistent dipole moment along the chaincontour, we may show that [34-36, 8]

XZM(QY »j(t)> 7

^ ' 1,-ZM(O) /*,-(0)> l 'where /x,(0 is the dipole moment of group i along the chain at time t. The terms(/X1(O)^(O)) express the equilibrium angular correlations between dipoles i andj along a chain, and the magnitude of such terms decreases rapidly in magnitudefor \i—j\ increasing [12, 34]. The terms </Xi(O)/x,(r)> are autocorrelation func-tions for the motions of dipole i, and </x,(O)-/X;(O> are cross-correlation termsbetween dipoles i and j . For a bulk polymer or for a polymer in solution, it isnormally assumed that the contributions to O(f) are dominated by intra-chainterms and that inter-molecular contributions are negligible. We may rewriteEquation (7) for the case of chains containing equivalent dipole groups as

W-W+frW (8)where atJ = </i,(0)-/i/0)>/</if > and

, „, <tt(0)7*.(0>. , M <ft(0)-tt(*)> ,Qa wXii{t)= <»?> ' Xi+t)=WO)-^m (9a'b)

Equations (8) and (9) give a clear physical insight into the molecular quantitiesthat determine the dielectric properties of flexible chains in solution and in thebulk amorphous state. The autocorrelation functions XH(t) are equal for all i anddominate <t>(t). The cross-correlation terms make a contribution weighted bythe equilibrium factors a^ that are determined by average chain conformation.It has been reasoned [34, 37] that X{j(t)« A11-(O for amorphous polymers, so inthis approximation <b(t)« Aif(t). This, together with the observation that entirelyequivalent a,/? and a/? dielectric relaxations are observed for small-moleculeglass-forming liquids [6, 38], suggest that the mechanisms for these processesdo not depend upon the presence of cross-correlation terms or on chain con-nectivity but may be deduced from a general model for the motions of anyreference group i along a chain. We proposed such a model [39, 12] that leadsto Equation (2), with all its consequences for the pattern of behaviour for a, Pand aj8 processes. It was shown [13, 39] that partial relaxation of the dipolemoment vector Ji1 (by local motions, to be prescribed, in a variety of temporarylocal environments) gave the P process and that subsequent microbrownianmotions of the environment around the dipole gave the a process, leading to theresult

A. = [<*>]2/<ft2>; A, = {<fif > - [<(iI>]2}/</i?> (IQa, b)

Thus the mean moment </if> that is not relaxed by local motions (p process) isrelaxed by the a process, which is an alternative statement of the conservationrule. Quite recently, Smith and Boyd [40] used a theory to describe the p process(in vinyl acetate copolymers) that is formally equivalent to that described above.The single dipole theory that leads to Equation (10) has been extended byWilliams [12] to include cross-correlation terms in the general expression for O(t)in Equation (8).

Thus, the experimental facts regarding multiple dielectric relaxation processesin amorphous polymers are well-established, and phenomenological theory isable to rationalize their occurrence and their dependence upon temperature andapplied pressure. The actual forms of </>a(t) and <j>fl) still await adequate descrip-tions using molecular theory, and this is a continuing challenge not only for theDRS of polymers but also for related relaxation and scattering phenomena insuch systems. It may transpire that analytical models will not be successful, andthat progress in understanding will come from simulations using moleculardynamics or Monte Carlo methods. In an attempt to deduce the form of dielectrica and P relaxations in amorphous polymers, Rosato and Williams [41] evaluateda multi-site barrier model which developed the early models of Bueche to thedynamical situation. Their theory gave (i) a cluster of 'fast' modes for the P pro-cess and (ii) a single mode at low frequencies for the a process. Although tworelaxation regions are predicted, the low frequency process is not in accord withthe experimental result, which gives a broad asymmetrical process of KWWtype with j8«0.5. Jernigan [42] considered the model of conformational tran-

sitions for a flexible polymer chain involving a master equation in time of theform

^ = T p W (11)

where p(f) is a generalized probability of obtaining the different conformationsat time t(f(t) is a vector of elementary probabilities) and T is a transition matrixthat expresses the transition probabilities between conformational states.T involves the local energy barriers and energy differences between conforma-tional states. The dielectric properties were calculated as <P(0)P(0 >, where P(t) isthe dipole moment of a whole chain at time t. Jernigan deduced the dielectricproperties of oc,co dibromide chains and found that <P(0)P(t)> was given bya weighted sum of exponential decay terms plus a constant value. The latterquantity has a value that is dependent on the choice of reference coordinates, andthis is a basic problem with this theory. Jernigan [42] multiplied <P(0)P(f)> bya correlation function <t>ov(t) for motions of the chosen reference coordinates, thusgiving a decay to zero for the total correlation function, but this is artificial.Beevers and Williams [43] showed how <P(0)P(t)> changed when the referencecoordinates were changed, demonstrating the inadequacy of this approach. Theorigin of the problem is clear: Equation (11) is a scalar equation but measuredproperties such as dielectric permittivity, Kerr constant, nuclear magnetizationand fluorescence emission are related to time-correlation functions for themotions of molecular axes—which are vectorial or tensorial quantities. Al-though the Jernigan approach is inapplicable to the motions of chains in the bulkamorphous state or in solution, it would be applicable where the referencecoordinates are well-defined, e.g. for a chain tethered to a surface.

11.3 CRYSTALLINEPOLYMERS

Numerous account of the dielectric properties of partially crystalline polymersare available [3,12,14,17,44,45]. Two classes of partially crystalline polymersare important, those of high crystallinity, such as polyethylene, i-polypropyleneand polyoxymethylene, and those having only a medium degree of crystallinity,such as the nylons and polyethylene terephthalate (up to « 50% crystallinity).Multiple relaxations are observed, e.g. lightly oxidized and lightly chlorinatedpolyethylenes have, in descending order of temperature, ac, /?a and yc relaxations.These have been documented by Ashcraft and Boyd [46] and others [3,4,5]. The<xc process in polyethylenes was first explained by Frohlich [47] using a chain-twist-assisted rotational model in an alkane crystal. Subsequently Hoffman et al.[44] and Williams et al. [48] extended the theoretical model and applied itsuccessfully to polyethylenes and alkanes of different chain lengths. Furtherdevelopment of the chain-twist-assisted rotation and model was made by Mans-

field and Boyd [49], who carried out a computer simulation for a realisticmodel of a chain moving in the crystal. In all cases it is predicted that the ave-rage relaxation time for the ac process increases linearly with chain length forshort chains, and that a plateau level is reached for long chains when chain-twisting becomes an essential part of the chain rotation mechanism. The /?a

absorption in polyethylenes is generally accepted as being due to large-scalemotions in the disordered phase [44,45,46], while the yc process is thought to bedue to local motions in the amorphous phase [46] or to local motions in bothamorphous and crystalline phases [44]. While many dielectric studies have beenmade of oxidized and chlorinated polyethylenes, we note that pure polyethylenewould not give any dipole relaxation owing the low polarity of the methylenegroup.

For polymers of medium degree of crystallinity, again motions in bothamorphous and crystalline phases are observed [3,12,14,17, 23]. Polyethyleneterephthalate (PET) is an interesting case, as samples can be obtained in theamorphous state by quenching from the melt or in the partially crystallinestate by melt crystallization or quench annealing. Since partially crystallinesamples are entirely composed of spherulites, it follows that the amorphousregions (up to 50% of polymer) are contained within the spherulites. Thus thisis an 'abnormal amorphous phase', whose relaxation behaviour would beexpected to be qualitatively different from that for a wholly amorphous polymer.This has been demonstrated to be the case from the dielectric measurementsof Ishida (see [3,45] and subsequently of Tidy and Williams (see data reportedin [12]). The amorphous PET exhibits a well-defined a dielectric relaxation,but the partially crystalline sample exhibits a broad a' relaxation whose fre-quency location is removed to lower frequencies when compared with that forthe oc relaxation. Tidy and Williams followed the evolution of the a and a'relaxations in time as an amorphous material was annealed, leading to crystalli-zation, above its T%. As the normal a process disappeared the a' process emerged,and grew as crystallization proceeded. This demonstrates that the 'amorphous'regions within the spherulites suffer a range of constraints imposed by thecrystalline regions, giving a slower, broader a process than that for a normalamorphous phase. Thus real time dielectric studies are able to give informa-tion on the dynamics of the amorphous regions within spherulites that can-not be readily obtained through NMR and dynamic mechanical relaxationstudies.

For accounts of DRS studies of other crystalline polymers, including poly-oxymethylene, polyvinylidene difluoride, polyvinyl fluoride and the nylons, thereader is referred to the text by McCrum et al. [3], the reviews [12-14,17,23,44,45] and references therein. In all cases multiple dielectric relaxations are ob-served, arising from motions within crystals, on crystal surfaces and in theconstrained amorphous regions within crystals. These processes are also ob-served in NMR and mechanical relaxation studies of such polymers.

11.4 LIQUID CRYSTALLINE (LC) POLYMERS

Liquid-crystal-forming (mesogenic) groups may be incorporated into mainchain, side chain or main chain and side chain, giving MCLC, SCLC andMCSCLC polymers respectively [50]. MCLC polymers show promise as highmodulus, high melting thermoplastics, whereas SCLC polymers show promise aselectroactive and electrooptical materials for optical data storage and non-linearoptics [51]. For MCLC polymer the long stiff chains have only slight reorienta-tional freedom in the LC or 'glassy' LC states, as has been shown from DRSstudies [52,53]. Araki et al. [53] studied the following MCLC polymer where m is2 or 3. For m = 3 a well-defined dielectric a process was observed having anapparent activation energy of 290 kJ mol ~ *. This material could not be aligned indirecting electric fields [53].

Dielectric studies of SCLC polymers are more numerous (see [14], [54-60]and references therein). The dielectric behaviour of unaligned SCLC polymersgives little information on the underlying motions since the observed loss curvescorrespond to a superposition of several components. Alignment may beachieved using directing electric (E) or magnetic (B) fields or by surface forces.Thealignment process in directing E fields is a dielectric phenomenon [58] anddepends on the dielectric anisotropy Ae{a)) at the frequency / = a>/2n at which theE field is applied. Homeotropic (n\\Z) and planar (n iZ) alignments may beobtained by choice of the frequency of the directing E field. Here n is the LCdirector axis and Z is the laboratory axis defined as the normal to the parallelplates that confine the LC material. The two-frequency-addressing principle thatleads to homeotropic (H) and planar (P) alignments for LC polymers has beenreviewed [58]. Studies have been made of LCSC polymers of the followinggeneric structures

where m denotes a spacer group; m typically lies in the range 2 < m < 12. R1 isH (for acrylates) or CH3 (for methacrylates) and R2 is typically an alkyl-cyanobiphenyl group or an aromatic ester group, as follows

For such materials, which may be smectic or nematic liquid crystals, thedielectric properties of the LC phase are anisotropic. For a uniaxial LC phase, thedielectric tensor is diagonal such that

e((o) = d iag [E1(O)), E1(G)), E1(O))]

where, for a material for which Ae(co) is positive at low frequencies, we find thatS11(O)) and E1(O)) are measured for H-aligned and P-aligned samples respectively[58].

The permittivity E'(CO) and loss factor E"(O)) change markedly when a SCLCpolymer is aligned in directing E fields or B fields [54-60]. As one example,Figure 11.1 shows plots of our recent results [61] for a carbon chain polymerhaving m = 2 and an alkyl cyanobiphenyl mesogenic head group in the side chain.The plot shows dielectric loss G/co = E"C0, where G is the equivalent parallelconductance of the sample and C0 is its geometrical electrode capacitance, asa function of log(//Hz) and temperature for an unaligned sample (Figure 1 l.l(a))and for the same sample that was aligned homeotropically using a low frequencyE field (30Hz, 50 V across a 70 urn thick sample) (Figure ll.l(b)). For theunaligned sample one broad loss peak is observed, which moves rapidly to higherfreqencies with increasing temperature. Only a slight change in property isobserved when the material transforms from the LC state to the isotropic liquidat 89 0C. Figure 1 l.l(b) shows data for the H-aligned sample. The loss peak in theLC state is nearly twice the height of that for the unaligned sample and muchnarrower, being only slightly broader than that for a single relaxation timeprocess. As the clearing temperature Tc = 89 0C is approached in the LC statethere is a marked fall in the peak height to the level of that for the isotropic liquid.A part of the fall is due to the decrease in local order parameter S(T) as Tc is ap-proached, and the remainder is due to the onset of the biphasic region, which in thiscase is restricted to « 2 0C. These data serve to illustrate the anisotropic nature ofmolecular motions in LCSC and show (compare Figures 11. l(a) and (b)) that it isnecessary to align samples macroscopically in order to reveal this property.

DRS provides a particularly useful means of monitoring the nature and extentof macroscopic alignment in SCLC samples that have been subjected to E fields,B fields, surface forces or are aligning/disaligning after electrical and/or thermaltreatments. As we have shown [56], the complex permittivity of a uniaxial sampleof intermediate alignment is given, to a good approximation, by the linear-addition relationship

E{O)) = (1 4- 2Sd)£|)M/3 + 2(1 - S6)E1(O))P (12)

Here, S6 is a macroscopic director order parameter

Sd = O c O S 2 ^ 2 - l > / 2 (13)

where 6nZ is the angle between a local director n and the laboratory Z axis (Z is

Figure 11.1 Plots of G/co = e"C0 as a function of log frequency/Hz and temperature for(a) unaligned and (b) homeotropically aligned SCLC polymer. Note the marked change inloss on melting the H-aligned material (Tc« 89 0C) and the lack of change on melting theunaligned material [61]

UNSUBTRACTED DATA FOR HOMEOTROPIC LCP95

UNSUBTRACTED DATA FOR UNALIGNED LCP95

(GZo

))ZpF

(GZ(

O)/p

F

normal to the plane of the parallel electrodes, as described above). Thus Sd = 1,0,-0 .5 for H-aligned, unaligned and planarly aligned samples respectively.Application of Equation (12) using both its real part e'(ca) and/or its imaginarypart s"(co) allows Sd to be determined for a sample of intermediate alignmentif e\(co), s'^G)), e'±((o)9 and e'[(a>) are known. Two crossover frequencies occur,at / ' , say, when s[((o) = ei(co), and at /", say when ej[(co) = el(cw). (Insertion ofthese conditions in Equation (12) show that e'((o) is independent of Sd fors'^co) = e'L(a>) and s"(co) is independent of Sd for ej,'(co) = £ (̂co)). The accuracy ofthe method for determining Sd can be checked via the consistency of Sd valuesdetermined at different frequencies through the spectral range, and this has beenshown to be very successful in practice for siloxane polymers [54, 56, 57, 62].Thus DRS provides a direct unambiguous means of determining the extentof macroscopic order, through Sd, in SCLC samples. We note that opticalmicroscopy and infrared and Raman spectroscopy may not be used easily tomonitor alignment in SCLC samples owing to the scattering of light by LCmaterials, but NMR provides a further method. Furthermore, DRS may beused to monitor the kinetics of alignment of SCLC polymers, as we have desc-ribed [62, 63]. In our studies of a chiral nematic LC polymer, the changes ofloss spectra with time as a sample realigned from P to H alignment in the pre-sence of a steady d.c. E field were monitored, and were fitted using a continuumtheory first described by Martins et al. [64] and further developed by Esnaultet al. [65]. An important consequence of this theory is that it predicts thatSd reaches a plateau determined by the balance between dielectric forces (in-volving Ae £2) and elastic forces (involving elastic constants of the LCphase).

It has been shown [58] that the ease of alignment in SCLC polymers is stronglydependent on chemical structure and the thermal/electrical treatments given tosamples. In most cases it is difficult to align SCLC polymers in the LC stateusing directing E fields [56-58,66], so cooling from the melt with an a.c. E fieldof chosen frequency and amplitude may provide an alternative route—although dielectric breakdown is then a problem because E fields of 100 V/50 ^mare required, typically, in order to achieve full H of P alignment. An 'elec-trical cleaning' method may be used to reduce the extrinsic conduction ofmelt samples and hence to allow the sample to sustain higher aligning E fieldsin the melt before breakdown occurs (see [58] and references therein for areview).

In addition to providing a method for determining the alignment of SCLCsamples, DRS data also give information on the anisotropic reorientationaldynamics of the dipolar mesogenic groups in a LC polymer. As we have shown[57,67], the generalization of the earlier theories [68,69] of dielectric relaxationof low molar mass liquid crystals can be achieved in the following way.

The field-free orientation distribution function /°(Q0) af ld the field-perturbedorientation distribution function fE(Cl0) of mesogenic groups may be written as

expansions involving the Wigner rotation matrix elements DQ 0 as follows

QO / 9 J - L i X -

AQ0) = A Z - J V pJooDoo("o) (14)j=0\ ™ /

AOo) = *(l+^+-)AQo) (15)

where A and B are normalization constants, D 0 0 are order parameters andD00(Q0) describes the orientations of mesogenic dipolar groups (each of dipolemoment fi) in Euler space with respect to the laboratory frame.

When the dipolar units reorientate in the LC potential, the conditionalprobability of finding the dipole group in the orientation around Q at time t giventhat it was around the orientation Q0 at t = O is given formally by the furtherexpansion

f(0,t/Qo,0) = S I Z DUO0)DL(O)GLW <16)J m n

where the G n̂(O are time-correlation functions of the motion of the group, andare defined by the relationship

< „ ( ' ) = [ f/(Q,t/Q0,0)D^n(Q0)DU")dQodQ (17)

The dipole moment in the laboratory frame (X, Y, Z) following the step with-drawal of the measuring electric field is then determined from the relationship[57]

W W ) = f f /E(Qo)/(ar/Qo,0)^P)dQodQ (18)JnoJn

where P = O, ± 1 and relates to the laboratory axes. Insertion of Equations(14)—(16) into Equation (18) and using standard relations for integrals of tripleproducts of the rotation matrix elements leads to expressions for (fifab(t)} and<ji£b(f) > (= <^£b(f) >) in terms of weighted sums of Clebsch-Gordan coefficients.Relating these quantities to dipole polarization and hence to permittivities sfah(t)and s^h(t), then Fourier transformation into the frequency domain, gives theimportant result that [57]

e,(co) = S0011 + ^ [ ( 1 + 2S)tiF{(co) + (1 - S)Ai12FJ(CO)] (19a)

« » = Sooi + 3^r [(I + S)^1(W) + (1 + SWrfFô)-] (19b)

where G is a constant involving internal field factors, S0011 and S001 are limiting highfrequency permittivities, S is the local order parameter in the LC and /z, and /*t are

the longitudinal and transverse components of the dipole moment of the me-sogenic group. The different F)(O)) are given by F)(Co)- 1 — io>3[£j(r)] where3 indicates a one-sided Fourier transform and the Cj(O are (real) time-correlationfunctions which correspond to certain linear combinations of the different Oîn(0as follows

^W = Oj0W; CJ(O = Oj1(O + 0^ 1 (OCiW = OL10W + *io(0 (20a-d)CiW = ol . x _ ,w + ol. x x(t) + 0 ^ 1 W + Oi1W

Thus, four active dielectric relaxation 'modes' are predicted, corresponding to thereorientational motions of /i( = (/^,/if)) with respect to the reference framedefined by the LC potential, giving two modes for eô) and two for E1(O)). Thestrengths of these modes are governed by \i{j\iK and the magnitude of the localorder parameter S (and hence depend on sample temperature).

When a SCLC polymer is aligned macroscopically, then e^co) and e±(o)) areunchanged, as these are quantities that relate to local regions in the LC materialand are defined in terms of molecular properties (see Equation (19)). However, themacroscopic dielectric properties change with macroscopic alignment as Sd ischanged, as we have discussed above in connection with Equation (12) and Figure11.1. For H alignment (Sd = 1), E,,(CO) is measured, and is usually dominated byF^1(O)), which is the S process (or W mode), and this is the case in Figure 11.1. Thecorrelation function for this process is given by

OJ0(O = <D£0(O)D>0(O)>

= <cos0(O)cos0(O> (21)

where O is the polar angle between the molecular z axis and the laboratory Z axis.In many cases samples initially in an unaligned state may be aligned homeo-

tropically but not planarly, owing to experimental difficulties of two kinds: (i) thatthe frequency required to prepare P alignment is too high for practical generatorsin the temperature range where P alignment is possible, and (ii) that Ae is toosmall to allow realignment to the P state to occur in practical time-scales forapplied fields below breakdown levels. In these cases, if data for unaligned (U) andH-aligned samples have been obtained, then 1̂(a>) may be calculated as follows.For the unaligned sample Sd = O, so Equation (12) gives

£ u M = [IS1(Oi) + 2 e » ] / 3 (22)thus

£xM = [3%M-e(l(a>)]/2 (23)

Thus, the permittivity and loss spectra for P-aligned material may be cal-culated from the permittivity and loss spectra of U- and H-aligned material.

We note that the above treatments consider only the anisotropic dielectricproperties arising from the anisotropic motions of dipolar mesogenic groups in

the LC phase. However, it has been emphasized by Haase that isotropic motions,e.g. of a dipole unit in the main chain removed from the dipolar mesogenic headgroup will give an additional term in each of Equations (19) which is independentof S, the local order parameter. This is important for acrylate and methacrylatepolymers with mildy polar mesogenic groups but of lesser importance forsiloxane polymers with strongly polar mesogenic groups of the kind we haveinvestigated [54-58].

11.5 REAL-TIMESTUDIESOFCHEMICALAND PHYSICAL CHANGES

The speed of operation of modern measuring equipment now allows measure-ments of e(co) to be made in real time as a system undergoes chemical or physicaltransformations such as polymerization or crystallization, respectively. Thiscapability greatly extends the applications of DRS in polymer science and posesnew challenges for theoretical interpretations of the observed dielectric phenom-ena, as we shall mention below. One subject presently receiving much attention isthat of the bulk step polymerization of epoxides with amines. Dielectric spectros-copy of such systems has been studied for many years, notably by Lane andSeferis [70], and has been reviewed by Senturia and Sheppard [71,72]. In a seriesof recent papers, Mangion and Johari [73-78] have given extensive data forpermittivity e'(co,t,TK) and loss factor e"(a),t, TR) for the diglycidyl ether ofbisphenol-A (DGEBA) reacting with diaminodiphenylmethane (DDM) and/ordiaminodiphenylsulphone (DDS) as a function of reaction time t for fixedmeasuring frequencies ( / = l/27ico) and fixed reaction temperatures TR. Samplesof different compositions of DGEBA/DDM and DGEBA/DDS andDGEBA/DDM/DDS were investigated in real time; also, post-cured materialswere studied over a wide range of temperature, including the glassy state at lowtemperatures, in order to detect changes in sub-Tg processes resulting from cureand post-cure. It was found that, as a reacting mixture transformed from a liquidto a (thermoset) glass, e'((o, t> TK) showed dispersion and s"((o, f, TR) showed anabsorption peak. Thus, the DRS method detects 'vitrification' of the thermoset-ting material, but this is a relaxation phenomenon whose interpretation relates tothe measuring frequencies used. As one example of the dielctric behaviour ofa thermosetting system Figure 11.2 shows real-time e\ a" data obtained recentlyby us [79] for a 1:2 molar mixture of DGEBA with an alicyclic diaminediaminodicyclohexylmethane (DDCM)

In Figure 11.2(a), s'(co,t, TR) is plotted against time for different measuring

time / s

Figure 11.2 Plots of e' and e" against reaction time at different measuring frequencies fora 1:2 molar mixture of DGEBA with DDCM at 60 0C [79]

frequencies, and dielectric dispersion is seen to occur and move to longer times asthe frequency is lowered. Figure 11.2(b) shows the complementary data forfi"(co, U 7R)> and a well-defined loss peak is seen to occur that moves to longer timesas / is lowered. Such data were obtained by continual measurements of e\e" atchosen frequencies and recording the time of each measurement. Post-processing

note: the frequency step betweenthe curves is 0.4 in Iog(f/Hz)

Log(F)=3Log(F)=5

(a) Variation of e' as a function of timefor the thermoset (DGEBA/DDCM) at Tcure= 60 0C

time / s

(b) Variation of e" as a function of timefor the thermoset (DGEBA/DDCM) at 1=60 0C

Log(f)=5

Log(f)=3

e"e1

of these data allows values of s\ e" to be calculated for chosen times, thus enablingplots of e\e" to be made as a function of frequency, as shown Figure 11.3, wheredispersion and absorption are now seen in a familiar representation. An instruc-tive representation of these data is provided by the 3D plots of permittivity andloss as a function of both log / and t, as shown in Figure 11.4. These data showthat an a process, far broader than the 'normal' a process described above forconventional amorphous polymers, is observed, which moves rapidly to lowerfrequencies as reaction time increases. Evidently, when the frequency of maxi-mum loss e'n occurs below, say, 10"2Hz, we would regard the material to bea glass operationally; extrapolation of such dielectric data to lower frequenciesthus provides a method of dielectrically monitoring the 'effective cure-time' ofa given reaction mixture, and this is useful for practical thermosetting systems.

Mangion and Johari [73-78] have made quantitative analyses of their data.For example, they found that plots of logrcure vs 1/TR for a fixed measuringfrequency were linear. Here, fcure is defined as the time at which s" = e^ for thegiven measurement frequency and given reaction temperature. They derived anapparent activation energy which was 47 kJ mol"1 and 44.51CmOl"1 for theirDGEBA/DDM and DGEBA/DDS mixtures, respectively. With regard to thetime-temperature variation of e' and s", they write

^cure) = £oo(^cure)+[^cure)~£ao(tc«re)]( eXP - k J ^ ~ d * (24)

where rcurc is the reaction time, £(*curc) = S(Q)9 tcurc). A difficulty with this equationis that a Fourier transform relationship between the frequency-dependent per-mittivity e((o) and a relaxation function 4>(t) is valid only for a stationary system:i.e. one whose thermodynamic properties are independent of time. <f>(t) necessarilyhas the meaning of the relaxation function [3] for the decay of polarizationfollowing a step withdrawal of a steady applied d.c. E field. For a non-stationarysystem, and that includes a thermosetting polymer, this experiment cannot beperformed, as the chemical and physical properties evolve in time. It is said [73]that <l>tmn(t) is the dielectric decay function at the instant of tcure, but this confusestwo time variables fcure and t and therefore has no physical significance. It is alsoclear that the Fourier integral in Equation (24) cannot be performed in practice.Therefore there are basic difficulties with Equation (24) that cannot be overcome.Alternative descriptions that relate the measured e\co) and e"(co) to time-depend-ent polarization processes are required. Mangion and Johari show that theArgand diagrams ('Cole-Cole plot') of e"{a), t, TR) against ef(co, t, TR) for fixedco and TK is asymmetric and may be fitted with a KWW function with parameterj8 in the range 0.2 < ft < 0.4. However, care should be taken in assuming that suchplots actually correspond to the KWW form, whose origins lie in stationarysystems where t and co are Fourier-paired variables. It appears that, as cureproceeds, the a process moves rapidly to low frequencies (see Figure 11.2(b)) withapproximately constant shape and that at each reaction time t the plots of s" vs. sf

Logf/Hz

Figure 113 Plots of ef and e" against log frequency/Hz for different reaction times fora 1:2 molar mixture of DGEBA with DDCM at 60 0C [79]. Curves 1-10 correspond to25 min to 225 min in increments of 6 min

(a) Variation of e' with the frequency of measurementfor the thermoset (DGEBA/DDCM) at 7 = 60° Cmeasurements every 6 mins, 4 ^ 0 , « 25 min

Logf/Hz

(b) Variation of e" with the frequency of measurementfor the thermoset (DGEBA/DDCM) at 7 = 60° C

e1eM

Figure 11.4 3Dplotsofe' ande" against reaction time for a 1:2 molar mixture of DGEB Awith DDCM at 60 0C [79]

are fitted approximately by the KWW function. Thus, fixing the frequencyf=co/2n and constructing the Argand diagram for e' and e" variations ast changes would lead to a skewed arc of KWW type. However, the variations ofthe KWW parameter with reaction time need to be investigated.

(b)Evdlution of the loss factorT=60°C

(a) Evolution of the permittivity7=60 0C

e"e'

In many studies of polymerizing systems, low frequency conductivity-relatedprocesses are large and may obscure the dipole relaxation process. Some evidenceof these processes is seen in Figures 11.2-11.4 at low reaction times and lowfrequencies, but in other systems they may dominate the overall behaviour, e.g. asin the case of phase-separating elastomer-epoxy resins described by Pethrick andcoworkers [80, 81] and by Maistros et al. [82]. In such cases the apparentlydominating conductivity processes may be represented alternatively by themodulus representation [73] M = [1/e], which gives

M' = ^ ; A*" = ^ (25a,b)

Such a duality of representations is well-known in dynamic mechanicalrelaxation [3] for compliance and modulus. The apparent correlation timesCompliance a n d Modulus a r e related through the ratios (E0/EJ = [JJJ0), wheresubscripts 0, oo refer to limiting low and high frequencies respectively and E and Jare modulus and compliance respectively. In the view of the author, the permittiv-ity representation should be used for the dipolar relaxations in cure-monitoringdata. The M representation may be useful where it is known that conductivityprocesses are involved, but in this numerical representation space-charge andelectrode processes appear to have less importance than their true contributions.

Finally, we note that present applications of DRS to polymerizing systems haveemphasized epoxy-amine thermosetting mixtures. Clearly much informationcould be obtained for photosetting and thermosetting addition polymerizations.We have conducted such studies recently using dimethacrylate monomers, whichare photopolymerized using blue light (480 nm) and a camphoroquinone-amineinitiator [83]. The dielectric data obtained during photoreaction are qualitative-ly different from those shown in Figures 11.2-11.4 for a thermosetting system.Analysis of our data show that the a process in the unreacted liquid monomertransforms into two processes as reaction proceeds, and that a /? process remainsat low frequencies when polymerization is essentially completed.

It is anticipated that DRS will be applied to real-time studies of phase-separating polymer-polymer mixtures and to crystallizing polymers (see the dataof Tidy and Williams in [12] for early results for isothermal crystallization ofamorphous polyethylene terephthalate). Although such measurements are en-tirely feasible in the usual low frequency region 10-107Hz, it would be highlydesirable to develop experimental dielectric cells and fast measuring methods forthe high frequency range 108-1010 Hz, thus providing the wide frequency rangenecessary to document and define the multiple dielectric relaxations that arisefrom dipole motions in the different phases.

11.6 CONCLUSIONS AND FUTURE PROSPECTSIt is apparent that DRS provides an important method for studying the reorien-tational dynamics of polymer chains in bulk amorphous, crystalline and liquid-

crystalline polymers and in polymerizing, phase-separating and crystallizingsystems. The merits of DRS include small sample size (typically 1 cm2 x 50 jim),wide frequency range (typically 10" 3 to 107 Hz) and its sound theoretical basisboth in phenomenological and molecular terms. Difficulties with DRS include (i)low frequency conductivity-related processes, which may obscure the dipolerelaxation processes, and (ii) the present limited access to high frequency (108-1010Hz) techniques. It is anticipated that DRS studies of polymers will beextended to more complicated systems, e.g. where two phases may be present andelectrical-field-induced processes occur. One example is polymer-dispersed liquidcrystals (PDLC), which may be formed in several ways, in which liquid-crystaldroplets are dispersed in a polymer matrix. Such PDLC materials as films50-500 ^m in thickness may be switched optically using moderate E fields, andthe required voltage depends both on the response of the liquid crystal and thedielectric properties of the host polymer. In such cases a knowledge and control ofthe dielectric properties of guest and host materials will enable the opticalswitching properties to be optimized, especially in regard to the lowering of theE field required for switching. A further example where DRS properties are usefulis non-linear-optical (NLO) films, which show promise for second- and third-harmonic generation of laser light [84]. It is generally observed that the non-linear susceptibility for second-harmonic generation of E-poled films decays withtime, and this may be due partly to the intrinsic motions of the electroactivemolecules in the glassy amorphous or glassy LC state of the poled material. Suchmotions can be characterized using DRS, and this provides direct information onsuch electro-optical phenomena which may not be readily obtained by othermethods such as NMR and quasi-elastic light scattering.


The author acknowledges the support of the SERC and AFOSR and the Erasmusscheme for studies of the dielectric properties of polymers, and thanks Prof. CIi veBucknall for information regarding the 'Axum' programs used for the 3D plotsshown in this paper.

11.8 REFERENCES

[1] CP. Smyth, Dielectric Behaviour and Structure, McGraw-Hill, New York, 1955.[2] N.E. Hill, W.E. Vaughan, A.H. Price and M. Davies, Dielectric Properties and

Molecular Behaviour, Van Nostrand, London, 1969.[3] N.G. McCrum, B.E. Read and G. Williams, Anelastic and Dielectric Effects in

Polymeric Solids, Wiley, London, 1967, Dover, New York, 1991.[4] C.J.F. Bottcher and P. Bordewijk, Theory of Electric Polarization, Vol. 2, Elsevier,

Amsterdam, 1978.

[5] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London,1983.

[6] J. Wong and CA. Angell, Glass; Structure by Spectroscopy, Marcel Dekker, Basel,1976.

[7] G. Allen and J.C. Bevington (Eds.), Comprehensive Polymer Science, Vol. 1, PolymerCharacterization, Pergamon Press, Oxford, 1989.

[8] E. Riande and E. Saiz, Dipole Moments and Birefringence of Polymers, Prentice Hall,New Jersey, 1992.

[9] F.I. Mopsik, Rev. ScL Instrum., 1984,55, 79.[10] J.M. Pochan, JJ. Fitzgerald and G. Williams, in B.W. Rossiter and R.C. Baetzold

(Eds.), Determination of Electronic and Optical Properties, Physical Methods ofChemistry Series, 2nd edn., Vol. VIII, Wiley, New York, 1993, Ch. 6, p. 392.

[11] G. Williams, Chem. Rev., 1972,72, 55.[12] G. Williams, Adv. Polym. ScL, 1979,33,60.[13] G. Williams and D.C. Watts, in NMR Basic Principles and Progress, Vol. 4, NMR of

Polymers, Springer Verlag, Heidelberg, 1971, p. 271.[14] G. Williams, in G. Allen and J.C. Bevington (Eds.), Comprehensive Polymer Sciences,

Vol. 2, Polymer Properties, Pergamon Press, Oxford, 1989, p. 601.[15] M. Cook, D.C. Watts and G. Williams, Trans. Faraday Soc, 1970,66, 2503.[16] G. Williams, M. Cook and PJ. Hains, J. Chem. Soc, Faraday Trans, 2,1972,69,1045.[17] G. Williams, in R. Pethrick and R.W. Richards (Eds.), Dynamic Properties of Solid

Polymers, NATO ASI, Reidel, Dordrecht, 1982.[18] G. Williams and D.A. Edwards, Trans. Faraday Soc, 1966,62,1329.[19] G. Williams, Trans. Faraday Soc, 1964,60,1548,1556.[20] G. Williams, Trans. Faraday Soc, 1966,62, 2091.[21] G. Williams, D.C. Watts, Trans. Faraday Soc, 1970, 66, 80.[22] G. Williams, D.C. Watts, S.B. Dev and A.M. North, Trans. Faraday Soc, 1971,67,

1323.[23] G. Williams, IEEE Trans. Electr. Insul., 1982, El-17, 469.[24] N. Koizumi and Y. Kita, Bull Inst. Chem. Res. Kyoto Univ., 1978,56, 300.[25] G. Williams in M. Davies (Ed.), Dielectric and Related Molecular Processes, Vol. 2,

Chemical Society, 1975, p. 151.[26] G. Williams, IEEE Trans. Electr. Insul., 1985, El-20, 843.[27] K.L. Ngai, in T.V. Ramakrishnan and M. Raj Lakshmi (Eds.), Non-Debye Relax-

ation in Condensed Matter, World Scientific, Singapore, 1987, p. 1.[28] W. Goetze, Rep. Progr. Phys., 1992,55, 241.[29] W. Goetze, Ferroelectrics, 1992,128, 307.[30] G.F. Mazenko, J. Non-Cryst. Solids, 1991,131-133,120.[31] A.K. Rajagopal, K.L. Ngai, and S. Teitler, J. Non-Cryst. Solids, 1991,131-133,282.[32] K.L. Ngai, Commun. Solid. State Phys., 1979,9,127, 141.[33] K.L. Ngai, A.K. Rajagopal and S. Teitler, J. Chem. Phys., 1988,88, 5086.[34] G. Williams and M. Cook Trans. Faraday Soc, 1971,67,990.[35] R.H. Cole, J. Chem. Phys., 1965, 42, 637.[36] U.M. Tituiaer and J.M. Deutch, J. Chem. Phys., 1974,60,1502.[37] G. Williams in E. Wyn-Jones (Ed.), Chemical and Biological Applications of Relax-

ation Spectroscopy, Reidel, Dordrecht, 1975, p. 515.[38] G. Williams and D.C. Watts, in Dielectric Properties of Polymers, Plenum Press,

1971, p. 17.[39] G. Williams and D.C. Watts, Trans. Faraday Soc, 1971, 67, 2793.[40] G.D. Smith and R.H. Boyd, Macromolecules, 1991, 24, 2725, 2731.[41] V. Rosato and G. Williams, Adv. MoL Relax. Processes, 1981, 20, 233.

[42] R.L. Jernigan, in Dielectric Properties of Polymers, Plenum Press, 1971, p. 99.[43] M.S. Beevers and G. Williams, Adv. MoL Relax. Processes, 1975, 7, 237.[44] J.D. Hoffman, G. Williams and E. Passaglia, J. Polym. ScU Part C, 1966,173.[45] Y. Ishida, J. Polym. ScU 1969,7,1835.[46] CR. Ashcraft and R.H. Boyd, J. Polym. ScU Polym. Phys. Ed., 1976,14, 2153.[47] H. Frohlich, Proc. Phys. Soc. (London), 1942,54,422.[48] G. Williams, J.D. Hoffman and J.I. Lauritzen, J. Appl. Phys., 1967,38,2503.[49] M. Mansfield and R.H. Boyd, J. Polym. ScU Polym. Phys. Ed., 1978,16,1227.[50] Adv. Polym. ScL, 1984,60/61.[51] CB. McArdle, (Ed.), Side Chain Liquid Crystal Polymers, Blackie, Glasgow, 1989.[52] F. Laupretre, C Noel, W.N. Jenkins and G. Williams, J. Chem. Soc, Faraday

Discuss, 1985, 79,191.[53] K. Araki, M. Aoshima, N. Namiki, S. Ujiie, N. Koide, K. Imamura and G. Williams,

Makromol. Chem. Rapid Commun., 1989,10, 265.[54] G.S. Attard, K. Araki, JJ. Moura-Ramos and G. Williams, Liq. Cryst., 1988,3,861.[55] A. Kozak, JJ. Moura-Ramos, G.P. Simon and G. Williams, Makromol. Chem., 1989,

190, 2463.[56] G.S. Attard, K. Araki and G. Williams, Br. Polym. J., 1987,19,119.[57] K. Araki, G.S. Attard, A. Kozak, G. Williams, G.W. Gray, D. Lacey and G. Nestor, J.

Chem. Soc, Faraday Trans. 2,1988,84, 1067.[58] A. Nazemi, G. Williams, G.S. Attard and F.E. Karasz, Polym. Adv. TechnoL, 1992,3,

157.[59] W. Haase, H. Pranoto and FJ. Bormuth, Macromolecules, 1985,18,960.[60] FJ. Bormuth and W. Haase, MoL Cryst. Liq. Cryst., 1987,148,1.[61] G. Williams and J. Hayden, manuscript in preparation.[62] A. Kozak, G.P. Simon and G. Williams, Polym. Commun., 1989, 30,102.[63] A. Kozak, G.P. Simon, J.K. Moscicki and G. Williams, MoL Cryst. Liq. Cryst., 1990,

193,155.[64] A.F. Martins, P. Esnault and F. Volino, Phys. Rev. Lett., 1986, 57,1745.[65] P. Esnault, J.P. Casquilho, F. Volino, A.F. Martins and A. Blumstein, Liq. Cryst.,

1990,7,607.[66] G.S. Attard, G. Williams and A.H. Fawcett, Polymer, 1990,31, 928.[67] G.S. Attard, MoL Phys., 1986,58,1087.[68] W. Maier and G. Meier, Z. Naturforsch., 1961,162,1961.[69] P.L. Nordio, G. Rigatti and U. Segre, MoL Phys., 1973,25,129.[70] J.W. Lane and J.C Seferis, J. Appl. Polym. ScL, 1986,31,1155.[71] S.D. Senturia and N.F. Sheppard Jr., Adv. Polym. ScL, 1986,80,1.[72] N.F. Sheppard, Jr. and S.D. Senturia, Polym. Eng. ScL, 1986, 26, 354.[73] M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1990,28, 71.[74] M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1990, 28,1621.[75] M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1991, 29,1117.[76] M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1991,29, 1127.[77] M.B.M. Mangion and G.P. Johari, Polymer, 1991, 32, 2747.[78] M.B.M. Mangion and G.P. Johari, Macromolecules, 1990,23, 3867.[79] C Duch, J. Fournier and G. Williams, manuscript in preparation.[80] AJ. MacKinnon and R.A. Pethrick, Macromolecules, 1992,25, 3492.[81] D. Lairez and R.A. Pethrick, Macromolecules, 1992, 25, 7208.[82] G. Maistros, H. Block, CB. Bucknall and LK. Partridge, Polymer, 1992, 33,4470.[83] G. Williams and J. Fournier, manuscript in preparation.[84] D.S. Chemla and J. Zyss (Eds.), Nonlinear Optical Properties of Organic Molecules

and Crystals, VoIs. 1 and 2, Academic Press, Orlando, 1987.

12 LIGHTSCATTERINGFROM POLYMER SYSTEMSR, W. RICHARDSDepartment of Chemistry, University of Durham, Durham DHl 3LE, UK

12.1 INTRODUCTION

Light scattering from dilute polymer solutions has long been used by polymerscientists to determine the molecular weights, the radii of gyration and the secondvirial coefficients of polymers [1,2]. Such information has been instrumental inthe development of two-parameter theories [3] of polymer solutions, andclassical intensity light scattering has been exhaustively discussed. In addition totwo of the parameters mentioned (mean molecular weight and second virialcoefficient), classical intensity light scattering has also been used to obtaininformation on the compositional dispersity in copolymers, and depolarised lightscattering can provide information on molecular anisotropy in rod-like poly-merss such as the main chain liquid crystal polymers [4,5]. Both of theseapplications have attendant difficulties. For copolymers, light scatteringmeasurements have to be made in at least three solvents with different refractiveindices to obtain compositional heterogeneity, although the judicious choice ofsolvents can considerably simplify the calculation process [6]. Depolarised lightscattering intensity is often low and the signal-to-noise ratio can also be low.These aspects of light scattering have been plentifully discussed and will not bereviewed here.

A more recent development has been quasi-elastic light scattering [7,8], whichis often used to obtain diffusion coefficients of polymers in dilute solution.Quasi-elastic light scattering has been applied to solvent-swollen cross-linkednetworks and to semi-dilute solutions of polymers in an effort to investigatescaling theories and reptation theories. Additionally, the possibility of obtainingthe viscoelastic properties of spread films of polymers at the air-water interfaceby quasi-elastic light scattering has also been discussed. Both of these aspects willbe reviewed here.

Light scattering from solid polymer films and melts was first reported some 40years ago [9]. The experimental difficulties have been considerably simplified bynewer technology, and the increased power of computing has eased the process of


data analysis. Much simpler experiments than implied in the original theory arecapable of producing information on the kinetics of phase-separating blends andthe thermodynamics of the systems. An overview of small angle light scatteringapplied to semi-crystalline polymers and phase-separating blends will also begiven here.

All of these different types of experiment are united by a common source for thelight scattering observed, that is, the existence of fluctuations in polarisability,and hence refractive index, at microscopic length scales in the material uponwhich the light is incident. The cause of these fluctuations may differ markedlyfrom thermal fluctuations (surface quasi-elastic light scattering), concentrationgradients (quasi-elastic light scattering), density variations due to packing (cry-stallinity) etc., but such fluctuations scatter light efficiently, so that light scatteringprovides a convenient non-perturbative probe of the structure and dynamics ofpolymer systems.

112 SMALL ANGLE LIGHT SCATTERING (SALS)

12.2.1 SEMI-CRYSTALLINEPOLYMERS

The pioneering work in SALS was done by Stein and his collaborators [10] some30-40 years ago, and it is a relatively simple technique for investigating spherulitegrowth and size in nearly transparent polymers. The original equations derivedby Stein and Rhodes [10] sought to explain the 'four leaf clover' pattern ofscattered light intensity observed in the Hv scattering experimental set-up shownschematically in Figure 12.1. (Hv implies vertically polarised incident light,horizontally polarised scattered light.) Spherulites are optically anisotropic, andoriginally Stein and Rhodes explained the disposition of the scattered light aslobes along the azimuthal angle of n/4 as being due to the orientation of dipoles inthe spherulite with respect to the plane of polarisation of the incident light. Muchinteresting work has been analysed on the basis of the original equations (e.g.influence of deformation [12], size distribution of spherulites [13], influence ofchain branching [14]). However, this explanation has been shown to be funda-mentally incorrect by Meeten and co-workers [15-17], although the extractionof parameters such as spherulite size etc. from SALS data using the originalequations is not altered. Meeten and Navard [16] used Mie theory, Rayleigh-Gans-Debye theory and anomalous diffraction theory on isotropic spheresand the latter two theories on anisotropic spherical scatterers. For all theories,both types of particles produced 'four leaf clover' scattering patterns for Hv

scattering. The dependence of scattered intensity on azimuthal angle (f> andscattering angle 0 can be calculated from the dimensionless angular gaing (whichis approximately the ratio of the intensity of the scattered light to the incident

Figure 12.1 Schematic of small angle light scattering experiment: scattering angle = 0;the azimuthal angle <j> is measured from the plane of polarisation of the incident light

light intensity).

G^ = ( I A V ) I S 1 - S 2 I 2 sin220

GVv = (4AV)IS1Sm2 <t> + S2COs2 <f> \2

and

k = 2nlk

(Vv, vertically polarised incident light, vertically polarised scattered light).The Rayleigh-Gans-Debye approximations are the most easily handled expres-sions for S1 and S2.

Isotropic sphere

2/fcV5 1 = — — Ox— l)(sinu —MCOSM)

5 2 = S1COsO

V = wm/ns

with nm and ns being the refractive index of the matrix and the sphere respectively.

Laser Potariser

Sample

Analyser

Detector Plane

Anisotropic sphere

2ik3r3

51 = 3 {3(/x— l)(sinw —MCOSW) + A / * [ u c o s K - 4 s i n u + 3Si(u)]}

2ifc3r3

52 =-^~3-{3(/I- I)(sinu-Mcosw)cos0- A^(I + cos2(0/2))(wcosw-4sinwSi(u))}

where jx = (nr + 2nt)/3nm, Afi = (nr — nt)/nm, nT is the radial refractive index, nt thetangential refractive index, and Si(u) is the sine integral of u. For both cases r is theradius of the sphere and u = An/X r sin(Q/2), with A being the wavelength of lightin the scattering polymer film. Figure 12.2 shows the form of the scatteringfor both isotropic and anisotropic spheres and Hv scattering. Note that bothshow a maximum scattering disposed in lobes at azimuthal angles of n/4.Figure 12.3 shows the intensity variation with u along one such lobe; again bothhave the same qualitative features, i.e. a maximum at a defined value of u. For

Figure 12.2 (Continued)

Figure 12.2 Contour plots of Hv scattered light intensity from (a) optically anisotropicspheres (b) optically isotropic spheres; x = r sin <£, y = r cos <£, where r is the radius of thesphere

anisotropic spheres wmax = 4.09, for isotropic spheres wmax = 2.74 for the firstorder maximum.

Over the years the method of detecting the scattered light has improved;originally photographic methods were used, followed by high speed cameras,vidicons and optical multichannel analysers. Nowadays CCD cameras are ableto record scattering patterns digitally, and fast shutter speeds mean that the datacan be recorded in real time. A typical apparatus as constructed at Durham [18]is shown in Figure 12.4; a description of similar equipment has recently appeared[19]. Typically, the fastest shutter speed may be «20/xs and the time needed torefresh the detector area and store 4K pixels each with 18 bit dynamic range is« 2 s. One system on which this apparatus has been used is the crystallisation

Figure 12.3 Variation of Hv scattered light intensity at <j> = 45° for (a) optically anisot-ropic spheres, (b) optically isotropic spheres; in each case u = (4nnr/Ao)sin(0/2). (a)Reprinted with permission from Macromolecules, 1982, 15, 1004; (b) reprinted withpermission from [53]. Copyright 1982 and 1993 American Chemical Society

kinetics of linear diblock copolymer of methyl methacrylate and ethylene oxide[20]. A copolymer with 76 mol % of ethylene oxide was quenched to a tempera-ture of 308 K from 400 K and the Hv SALS pattern was recorded as a function oftime; the variation of intensity obtained is shown in Figure 12.5. From themaxima in such curves, the radius of the spherulite was obtained, and was used inan Avrami analysis of the crystallisation kinetics [21]. This provides a parameterproportional to the rate of crystallisation and the Avrami exponent. From thelatter parameter it is sometimes possible to infer something about the growthmechanism and geometry (Table 12.1). For this block copolymer the Avrami

104 I

nte

nsi

ty

Inte

nsi

ty

Figure 12.4 Block diagram of a small angle light scattering instrument

exponent obtained was 1.8; the equivalent homopolymer blend had an Avramiexponent of 1.5. A word of caution is appropriate here. Meeten's analysis showsthat the value OfU1114x depends on the anisotropy of the spherulite; thus in the earlystages the observed growth rate may appear to be smaller than the actual growthrate.

beamexpander

NDfilters

polariser

hot stage+sample

analysor

Marata plate

CCDCamera

Fibre optic link

Polar scattering angle

Figure 123 Variation of Hv scattered light intensity at <j> = 45° for a linear diblockcopolymer of methyl methacrylate and ethylene oxide. The copolymer was quenched from100 0C to a crystallisation temperature of 35 0C and the time lapse between each curve is2.1s

Table 12.1 Avrami exponents predicted for a variety of growth geometries and growthcontrol mechanisms

Exponent Nucleation" Growth geometry Growth control*

0.5 Instantaneous Rod Diffusion1 Instantaneous Rod Interface1 Instantaneous Disc Diffusion1.5 Instantaneous Sphere Diffusion1.5 Homogeneous Rod Diffusion2 Homogeneous Disc Interface2 Homogeneous Disc Diffusion2 Homogeneous Rod Interface2.5 Homogeneous Sphere Diffusion3 Instantaneous Sphere Interface3 Homogeneous Disc Interface4 Homogeneous Sphere Interface

'Instantaneous: nuclcation on existing heterogeneities. Nuclei form simultaneously at beginning.Homogeneous: sporadic formation of nuclei. Nucleation continuous in the untransformed material.^Diffusion controlled: kinetics are controlled by the rate of diffusion of molecules to the nuclei.Interface controlled: kinetics controlled by rate of attachment of molecules to the nuclei.

Inte

nsity

PEO-b-PMMA (76% w/w PEO) Block Copolymer, 7C=35 0C

12.2.2 PHASE-SEPARATING POLYMER MIXTURES

Generally, compatible polymer mixtures display a lower critical consolute (orcoexistence curve), and the variation of the Gibbs free energy change on mixingwith composition shows a pair of inflection points above a particular tempera-ture defined by the thermodynamics of the system and the mixture composition.At these inflection points (d2AGJd<j>2)TtP = 0, and they define the locus ofthe spinodal curve. This curve is the limit of stability of the mixture, i.e. withinthe curve the mixture is unstable to any fluctuation and demixing (spino-dal decomposition) takes place spontaneously. Between the coexistence curveand the spinodal curve there is a metastable region wherein large fluctuationsare necessary to initiate demixing, usually via a nucleation and growth pro-cess (Figure 12.6). Both curves meet at the critical temperature where(d2AG/d<t>2)Tp = (d3AG/d<t>3)Tp = 0. If a compatible blend is quenched into thespinodal region, phase separation takes place and the kinetics of the demixing aredescribable by the linearised Cahn-Hilliard theory of spinodal decomposition,which gives the time dependence of the composition variation as [22]

(d<t>/dt)TtP = M(d2Ald<t>2)T%pV24> - 2 M X V 4 0

where M is the mobility of the polymer and KV2<j> is the free energy density

Figure 12.6 Schematic phase diagram for polymer-polymer mixtures

Tem

pera

ture

(K

)

binodalspinodal

gradient due to composition gradients. The solution to this equation is a Fourierseries describing the compositional fluctuations in the system, i.e. the localcompositional deviations from the average value, and these fluctuations are thesource of the scattered light intensity. Since light scattering is described in Fourierspace terms, the solution to the Cahn-Hilliard equation is also needed in Fourierspace, Le. in terms of a wave vector, where the wave vector is (In/X) and X is theconcentration fluctuation wavelength. The intensity of light scattered from thephase-separating mixture is proportional to the square of the fluctuation ampli-tudes and is given by:

/ ( a 0 = /(Q^ = 0)exp[2R(Q)r]

where Q is the scattering vector = Ann sin(0)/Ao, with n the refractive index of thesample, 20 the scattering angle and X0 the wavelength of light in vacuo. The termR(Q) is known as the amplification factor and

R(Q) = - M(d2A/d<t>2)TtPQ2 - 2MKQ*

In the phase-separating system, there will be a most probable composition

Figure 12.7 Scattered light intensity (Vv conditions) as a function of angle for differenttimes for a phase-separating mixture of polystyrene and polyvinyl methyl ether. Timesafter start of phase separation (seconds)A 2 + 2 0 D 4 0 O 6 0V 10 x 30 O 50 • 70

10-3Q(Cm-1)

Time (S)

Figure 12.8 Exponential dependence of scattered light intensity for a phase separatingmixture of polystyrene and poly vinyl methyl ether at Qmmx

fluctuation wavelength which will grow preferentially as phase separation pro-ceeds. This leads to a maximum in the observed scattered intensity at a finitevalue of Q. The position of this intensity maximum does not alter as in the earlystages of phase separation but increases in intensity as phase separation proceeds.At late stages in the phase separation, there is a coalescence of particles viaOstwald ripening and the maximum will shift to lower Q values.

During the early stages, at a fixed value of Q, the scattered light intensity froma spinodally decomposing system should increase exponentially with time, andfrom this relationship the amplification factor can be obtained. A set of lightscattering data for a demixing polystyrene/polyvinyl methyl ether (PVME)mixture collected at discrete time intervals is shown in Figure 12.7 [23]; thedependence of the scattered intensity on time at the Q value (Qmax) where themaximum intensity is seen is shown in Figure 12.8. From values of R(Qn^x)the effective diffusion coefficient De, can be obtained, as Dt = 2R(QmAX)/Qliax. Atthe spinodal curve Dt = 0, and thus if Dc is obtained for a series of compositionand over a range of temperatures, the spinodal curve can be obtained. Figure 12.9shows values of Dc as a function of temperature obtained for the mixture ofpolystyrene and PVME referred to earlier, and the spinodal curve predicted fromthese data is given in Figure 12.10. Light scattering investigations of otherdemixing polymers have been reported elsewhere [24, 25] and recently a verysophisticated instrument for such studies has been described [26].

10ln

(I(Q

ma

x)

1O

10C

-D9)C

m2S

'1

Temperature (K)

Figure 12,9 Effective diffusion coefficient as a function of temperature

TEM

PE

RA

TUR

E (

K)

WEIGHT FRACTION PS

Figure 12.10 Spinodal curve (•) predicted from temperature dependence of Dc forpolystyrene/polyvinyl methyl ether mixtures

B PS(2)/PVME

cloud point curve

PS(2)/PVME

123 QUASI-ELASTIC LIGHT SCATTERING (QELS)

12.3.1 DILUTE POLYMER SOLUTIONS

Light scattering by polymers in solution is not a perfectly elastic process, smallamounts of energy being transferred between molecules and photons. This energytransfer leads to a broadening of the frequency of the scattered light relative to theincident light, and the intensity variation of the scattered light over a frequencyrange from — oo to + oo is the spectral density or power spectrum, which is givenby

I((o) = 1/2« I °° < E*{t)E{t + T) > exp iojTdt

where <£*(r)£(t+T)> is the electric field autocorrelation function gt(t). Inquasi-elastic light scattering (QELS) what is actually obtained as the output fromthe photomultiplier tube is the unnormalised intensity autocorrelation functionG2(t\ and

G2(t) = A + [Bg1(O]2 (homodyne)

where A is a constant background intensity to which the correlation functiondecays after a suitably long delay time f, and B is a constant close to unity. If wehave a single species in the solution, e.g. a monodisperse polymer, and there areonly concentration gradient relaxation processes, then

^1(O = exp(-Ff)and F l is the relaxation time of the diffusive process of the polymer down theconcentration gradients; F = DQ2 with Q = (4nn/Xo)sin(0/2) and D is the transla-tional diffusion coefficient. For polymer solutions, D is concentration dependent

D = D0(l + fcDc)

where D0 is the infinite dilution value of D and c is the concentration of polymer.The term kD is composed of thermodynamic and factional parameters for thepolymer in the particular solvent conditions investigated.

Polymers are not often monodisperse, and each different relaxation time willmake a contribution to the observed average F. A popular method of obtainingthe diffusion coefficient is to use the cumulants approach outlined by Koppel[27] and the algorithm of Pusey et al. [28]

In Q1(Z) = - T11 + (F2/2!)r2 - (F3/3!)r3 + • • •

Generally only the first two cumulants can be extracted from the correlationfunctions with any confidence, and TJQ2 = D29 the z-average diffusion coeffi-cient. About 12 years ago, Burchard et al. [29] showed that

r JQ2 = D(I+ CR2Q2)

Cj2XiO-10^kC(Cm2)

Figure 12.11 Dynamic Zimm plot for polystyrene in toluene. Reproduced with per-mission of the American Chemical Society from ref. [29]

where R9 is the radius of gyration of the polymer molecule and C is a parameterrelated to the molecular architecture and the thermodynamic environment.Incorporating the concentration dependence of D,

TJQ2 = D0(I + kDc)(l + CRlQ2)

Thus, as c->0 and Q->0, TJQ2 = D0 and D0, kD and C can be obtained froma 'dynamic' Zimm plot (Figure 12.11). The slope of the line dependent on Q2 aloneis CR2, whereas the slope of the line dependent on c only is DokD. Thus methodhas not been widely used; however, it has been applied to naturally occurringpolymers to extract C and thus to enable something to be said about theirstructure.

We noted earlier that each relaxation time will contribute to T and henceinfluence the shape of the correlation function. Consequently, all the informationon polymer polydispersity is contained within the intensity correlation functionbecause D is proportional to (molecular weight)"0. The extraction of the molecu-lar weight distribution from the correlation function is an 'ill posed problem', asthere are an infinite number of solutions to the Laplace inversion of the data thatis required to obtain the distribution. Several attempts have been made atdeveloping suitable computational methods to derive a distribution from a corre-lation function. Perhaps the most widely known and used is the constrainedregularisation programme CONTIN [30,31]. In many cases the programme workswell, but care has to be taken in choosing the right range of D to explore fora solution, and the original data must be of high quality, as 'noisy' data can lead toartefacts in the analysis. A comparison of CONTIN with maximum entropymethods has recently been published [32].

Hq

2X

iO8 (

Cm

2S1)

Diffusion Coefficient (cm2 s'x) x 1 °

Figure 12.12 Distribution in diffusion coefficients for an aromatic terpolyester in a mixedsolvent of trifluoroacetic acid and dichloromethane obtained by CONTIN analysis ofquasi-elastic light scattering data

Obtaining molecular weight distributions by this means has two benefits.Firstly, with a high power laser light source on the correlator and with fast datalinks to a work station, a full molecular weight distribution can be obtained in«2min. The second benefit is when only ferocious solvents are available, oneswhich would destroy size-exclusion chromatography (SEC) column packings;quasi-elastic light scattering then becomes a highly suitable method to obtaina molecular weight distribution. An example of this is the aromatic terpolyesterprepared from hydroxybenzoic acid, isophthalic acid and hydroquinone [33],which is soluble in a mixture of trifluoroacetic acid and methylene chloride. Thelow refractive index of the solvents and the high refractive index of the polymermake the solutions extremely strong scatterers of light and ideal for CONTIN

analysis, even with only a modest laser. An example of the distribution indiffusion coefficients (and hence molecular weight) is shown in Figure 12.12.

12.3.2 GELS

A cross-linked polymer swollen by a solvent constitutes a gel, and if swollensufficiently the concentration of polymer in the gel is that of a semi-dilute

Rel

ativ

e C

ontri

butio

n

solution, i.e. it is between c* and c** as defined by de Gennes. The gel hascontinual local fluctuations in the degree of swelling (equivalent to polymerconcentration) which lead to variations in the local osmotic pressure. Theanalysis of the intensity correlation function obtained from the scattering of lightby these fluctuations produces a co-operative diffusion coefficient. The firstQELS experiments on gels and the theoretical analysis of the data were reportedover 20 years ago by Tanaka et al. [34]. They showed that at a delay time of zero(i.e. extrapolating the correlation functiion to t = 0), the scattered light intensityabove the background was equal to the osmotic moldulus Mos (= Kos + 4Gos/3where Kos is the bulk osmotic modulus and Gos is the shear osmotic modulus),also known as the longitudinal modulus. The co-operative diffusion coefficient isgiven by

DC = (KOS + 4GOS/3)(1 -<t>p)/f

where cf)p is the volume fraction of polymer in the gel and / is the total friction ofthe polymer against the solvent per unit volume

/ = CeNAc/m

where c is the polymer concentration in gml"1, m is the monomer molecularweight, and £c is the monomeric friction coefficient at concentration c.

Since the first report there have been many papers published on light scatteringfrom polymer gels, the work of Geissler and Hecht on polyacrylamide gels[35-39] being noteworthy.

Measurements [40, 41] obtained on radiation cross-linked polystyrene gelssubsequently swollen in cyclohexane at different temperatures exemplify the typeof results obtained. A typical correlation function is shown (Figure 12.13) inwhich the ordinate axis was calibrated directly in terms of osmotic modulus usingdata obtained by Scholte [42] from ultracentrifugation analysis of polystyrenesolutions. Scaling relationships can be used to interpret the dependence of Mos

and Dc on <t>p.The dependence of Dc on the volume fraction of the polymer in the gel varied

markedly with the temperature (Figure 12.14), whereas the osmotic modulus forthese same gels could be fitted by the same scaling relationship

Mos = 4.7 x 1 0 6 ^ 6 N m - 2

Scaling laws predict that the exponent of 0 p for Mos should vary from 2.25 in goodsolvents to 3 in theta solvent conditions; for the concentration dependence ofdiffusion coefficients the same exponents are 0.75 and 1 respectively. At 308 K anexponent of 1.17 was observed, which within the experimental error agreed withpredictions. However, at 333 K, the exponent was 0.46, much lower than theorypredicts. This observation and the high exponent observed for Mos were at-tributed to the presence of dangling chains in the network, since the correlationfunctions were observed to become more non-exponential as the temperature

Time (jus)Figure 12.13 Intensity autocorrelation function obtained for a randomly cross-linkednetwork of polystyrene swollen in cyclohexane at 308 K

was increased. Increased non-exponential behaviour has been identified with theoverlapping of molecules and appears to be possible only when there are manyloose dangling chains.

12.3.3 SEMI-DILUTE SOLUTIONS A N D TRAPPED CHAINS

The broad outlines of reptation theory are well known, and the detailed theory isavailable elsewhere [43,44]. Essentially, a polymer molecule in a melt is confinedto a tube which is defined by the surrounding molecules, and can only move alongthe tube axis. The time dependence of the various dynamic modes of the moleculein the tube has been discussed by Doi and Edwards [45]. Additionally, de Gennes[46] has set out equations which relate the translational diffusion coefficient ofa probe polymer to its molecular weight (Mp), the entanglement molecular weightof the matrix (MJ and the molecular weight between cross-links (AfJ. Threeregimes are predicted:

1. Free draining (A/p < Af c, Af p > AfJ, D = D0M; K

Inte

nsi

ty

(a.u

.)

T = 308KSolvent C6H12

Baseline

Figure 12.14 Co-operative diffusion coefficient as a function of volume fraction ofpolymer in cyclohexane swollen polystyrene networks; (o) 308 K, (o) 318 K, (•) 333 K

2. Simple reptation (Mp > Me, Mc > Mc), D = D0M tM; 2.3. 'Strangulation' regime (Me > Mc, Mp > Mc), Dt = D0M0M; 2.

Attempts have been made at observing these regimes using semi-dilute sol-utions of a matrix polymer with a chemically identical probe of a differentmolecular weight incorporated in the solution. The conclusion of these experi-ments was that the reptation theory was inappropriate for such semi-dilutesolutions [47,48]. A possible explanation for the failure of reptation theory maybe in the recent analysis of Wang [49-51]. He shows that the quasi-elastic lightscattering from a semi-dilute solution has contributions from both concentrationfluctuations and density (pressure) fluctuations, and consequently the long timeviscoelastic relaxation spectrum, usually observed by dynamic mechanicalmeans, will also contribute to the autocorrelation function. The extent to whichboth contributions are seen depends on the frequency distribution of the stressrelaxation modulus and a coupling parameter j8 (proportional to the partial

DJm

2S'1)

log M

Figure 12.15 Diffusion coefficient of polystyrene tracer in polyvinyl methyl ether gels asa function of tracer molecular weight. Diffusion coefficients normalised by ratio ofmolecular weight between crosslinks of gels. Reprinted with permission from [52].Copyright 1992 American Chemical Society

specific volume of the polymer minus the partial specific volume of the solvent).Very recently, QELS investigation of reptation predictions has been made usingrandomly cross-linked networks containing chemically distinct trapped chains.Rotstein and Lodge [52] prepared polyvinyl methyl ether gels containingtrapped polystyrene chains, and obtain tracer diffusion coefficients for thetoluene-swollen gels. Values of Mc were calculated from swelling data, and4 x 103 ^ Mc ^ 14 x 103. Figure 12.15 shows the diffusion coefficient data nor-malised by the ratio of the Mc values for the three networks involved. Thereappears to be little or no influence of Mc even when Mp » Me; furthermore, theprobe molecular weight dependence of D (DocM~2S) is much stronger thanpredicted by reptation theory. Pajevik et al. [53] prepared randomly cross-linkedpolymethyl meth'acrylate gels containing polystyrene probe molecules. Theirresults are shown in Figure 12.16. When Mp < Mc («80000) then D scales asMp ° 6; above this molecular weight the influence of Mp is marked and D scales asM~ l'*±°-2

9 i.e. almost exactly in agreement with reptation theories, CONTIN or anequivalent program was used in both investigations, and the isorefractivity oftoluene with polyvinyl methyl ether and polymethyl methacrylate aids the

log

[Dt<

Mx>

/Mx]

Figure 12.16 Ratio of polystyrene tracer diffusion coefficient (D1) in toluene swollenPMMA gel to diffusion coefficient of polystyrene in dilute toluene solution (•); (A) valuesfor PS tracer in PMMA solutions. Reproduced with permission from the AmericanChemical Society from Ref. [53]

process of extracting the probe diffusion coefficient. However, about 14 years[54] ago it was noted that, when polystyrene was dissolved in a semi-dilutebenzene solution of polymethyl methacrylate, the value of D decreased as thepolymethyl methacrylate concentration increased, i.e. rather similar to themolecular weight dependence seen by Pajevik et al, and this may be due topolymer-polymer interactions.

To overcome these possible complications, polystyrene networks with trappedpolystyrene molecules have been prepared [55] and are currently being inves-tigated.

12.3.4 SURFACE QUASI-ELASTIC LIGHT SCATTERING(SQELS)

A liquid surface is continually roughened by thermal excitations, which give riseto the hydrodynamic modes known as capillary waves. The r.m.s. amplitudes ofthe waves are small ( « 2A) but they are efficient light scatterers. The displacementof the liquid surface from its equilibrium position by a wave propagating in thex direction is:

C(x,r) = C0exp(/ex-ho)0

where Q is the surface wavenumber or the scattering vector parallel to the liquidsurface. The wave frequency o is a complex quantity given by a>0 + iT, where co0

is the capillary wave frequency and F is the decay rate of the waves. A dispersionequation relates co and Q, and for pure liquids the controlling factors (for fixed Q)

D*/

D0

Mp

are the kinematic viscosity and the surface tension [56]. For most instruments theaccessible range of Q is 100-2000Cm"1 and hence the wavelengths probed are« 600-30 /mi. If a polymer film is spread on the surface of the liquid, additionalhydrodynamic modes modify the dispersion equation. Only the transverse modes(capillary waves) scatter light, but there is coupling with the longitudinal ordilational modes, and hence in principle some information is obtainable on bothmodes from the power spectrum of the scattered light. The parameters obtainableare the surface tension y and the dilational modulus e; both of these areviscoelastic properties, as energy dissipation takes place in the relaxation pro-cesses, and thus

y = y0 + icoy'

e = 60 + icoe'

where y0 and £0 are the static surface tension and dilational modulus I — I,\ A a A J

y' is the transverse shear viscosity and e' is the in-plane dilational viscosity.Although direct measurement of the frequency broadening of the scattered

light by the capillary waves has been used, the frequency shifts are rather small,and a more direct means of observing the frequency of the capillary waves is touse heterodyne quasi-elastic light scattering [57,58]. The experimental arrange-ment to collect such data is shown in Figure 12.17; the diffracted beams produced

Laser

PM Tube

rough

Figure 12.17 Schematic diagram of surface quasi-elastic light scattering apparatus. Ll,L2 = lenses, T = transmission grating, F = neutral density filter, Ml, M2, M3, M4 =mirrors

Time (us)

Figure 12.18 Heterodyne correlation function for syndiotactic polymethyl methacrylatespread on water at a surface concentration of 1.7mgm~2

by the transmission grating act as the reference beam of zero frequency shift, andthis beats with the scattered light at the photocathode to produce the typicalcorrelation function shown in Figure 12.18. From these data the capillary wavefrequency co and the decay constant F can be obtained. By assuming that y and e!are zero, y0 and e0 can be obtained from these values by solving the dispersionequation. Extracting the viscous moduli requires a non-linear least squares fit ofthe Fourier transform of the power spectrum equation to the data. A computa-tional method for this process has been developed by Earnshaw et al. [59] andexhaustively justified [60]. Wider aspects of light scattering from liquid surfacesare discussed in the book edited by Langevin [61].

To date much of the work published on SQELS from spread polymers hasemanated from Yu and colleagues [62-65], but assumed that the viscous moduliare zero.

We have reported [66] a limited study of spread polymethyl methacrylates andpolyethylene oxide. Figure 12.19 shows the variation in surface tension, shearviscosity and dilational modulus obtained from SQELS data as a function ofsurface concentration. The viscoelastic moduli both show maximum values atfinite values of the surface concentration. As the capillary waves generateoscillatory stress and strain, these are related via the complex dynamic modulusof the surface

a* =y*[G'(co) +iG"(co)]

Nor

mal

ised

cor

rela

tion

func

tion

Sur

face

tens

ion

(m

N n

rr1)

Surface concentration (mg nrr2)

She

ar v

isco

sity

(m

N s

rrr

1)

Surface concentration (mg m*2)

Figure 12.19 (Continued)

Surface concentration (mg nrr2)

Figure 12.19 Derived parameters from surface quasi-elastic light scattering as a functionof concentration of polymethyl methacrylate spread on water: (a) surface tension; (b)surface shear viscosity; (c) dilational modulus

where <x* is stress, y* is strain, G'(co) is the storage modulus (surface tension) andG"(a>) is the loss modulus (a>yf). Using volume fraction composition data obtainedfrom neutron reflectometry on the spread polymer films, it is evident that thesurface film loss modulus is linearly dependent on the volume fraction of polymerin the film. If we presume that the relaxation process in the surface film isdescribed by a Maxwell model, then

G'(co) = Ge + GCO2T2/(1 + CO2T2)

where Ge is the elastic modulus at co = O, i.e. the static surface tension. Further, ifthere is only one relaxation process in the spread film, then

T = A7c/co2y'

where An is the difference in the surface tensions measured by SQELS and fromstatic (Wilhelmy) plate methods. The dependence of relaxation time on thevolume fraction of the polymer shows an exponential increase, Figure 12.20. Toobtain further insight into the relaxation mechanism requires the frequencydependence (i.e. different Q values) of the transverse shear viscosity to be known.

Dila

tiona

l mod

ulus

(mN

nrr1)

VoI fraction of polymer

Figure 12.20 Relaxation time for spread polymethyl methacrylate as a function ofvolume fraction of polymer in the spread film

12.4 CONCLUSIONS

An overview of some of the areas where light scattering has made contributions topolymer science has been given. The emphasis has been on dynamics, either byusing light to follow a process (crystallisation or phase separation) or usingdynamic light scattering per se. A broad range of polymer types and situations hasbeen covered and the discussion has by no means been exhaustive. Evidently,despite its maturity as a laboratory technique, light scattering is still capable ofproviding much information on polymer systems. Furthermore, the developmentof newer applications such as surface quasi-elastic light scattering will enableinvestigations of surface gelation and surface ordering in polymer solutions, areaswhich have yet to be investigated.

12.5 REFERENCES

[1] M.B. Huglin (Ed.), Light Scattering from Dilute Polymer Solutions, Academic Press,London, 1972.

[2] P. Kratochvil, Classical Light Scattering from Polymer Solutions, Elsevier, Amster-dam, 1987.

SYN PMMA SQELS DATAR

elax

atio

n t

ime

(s)

[3] H. Yamakawa, Modern Theory of Polymer Solutions, Harper, New York, 1971.[4] GC. Berry, J. Polym. ScL, Polym. Symp., 1978,65,143.[5] W.R. Krigbaum and G. Brelsford, Macromolecules, 1988, 21, 2502.[6] Z. Tuzar, P. Kratochvil and D. Strakova, Eur. Polym. J., 1970,6,1113.[7] BJ. Berne and R. Pecora, Dynamic Light Scattering, Wiley, New York, 1976.[8] K.S. Schmitz, An Introduction to Dynamic Light Scattering by Macromolecules,

Academic Press, San Diego, 1990.[9] R.S. Stein and JJ. Keane, J. Polym. ScL, 1955,17, 21.

[10] R.S. Stein and M.B. Rhodes, J. Appl. Phys., 1960, 31,1873.[11] R.S. Stein, P. Erhardt, JJ. van Aartsen, S. Clough and M. Rhodes, J. Polym. Sci. C,

1965,13,1.[12] RJ. Samuels, J. Polym. Sci. C, 1965,13, 37.[13] G.E. Wissler and B. Crist, J. Polym. Sci., Polym. Phys. Ed., 1985, 23, 2395.[14] M. Ree, T. Kyu and R.S. Stein, J. Polym. ScL, Polym. Phys., 1987, 25,105.[15] J.V.Champion,A.KilleyandG.H.Meeten,J.Polym.ScL,Polym.Phys.Ed., 1985,23,

1467.[16] G.H. Meeten and P. Navard, J. Polym. ScL, Polym. Phys., 1989, 27, 2023.[17] M. Desbordes, G.H. Meeten and P. Navard, J. Polym. ScL, Polym. Phys., 1989, 27,

2037.[18] P.H. Richardson and R.W. Richards, unpublished work.[19] WT. Culberson and M.R. Tant, J. Appl. Polym. ScL, 1993,47, 395.[20] P.H. Richardson, ubpublished results.[21] J.C. Schultz, Polymer Materials Science, Prentice-Hall, New Jersey, 1974.[22] J.W. Cahn and J.E. Hilliard, J. Chem. Phys., 1958,28, 258.[23] J.G. Connell, Ph.D. Thesis, University of Strathclyde, 1989.[24] H.L. Snyder and P. Meakin, Macromolecules, 1983,16, 757.[25] T. Hashimoto, M. Itakura and N. Shimidzu, J. Chem. Phys., 1986,85,6773.[26] A. Cumming, P. Wiltzius, F.S. Bates and J.H. Rosedale, Phys. Rev. A, 1992, 45,

885.[27] D.E. Koppel, J. Chem. Phys., 1972,57,4814.[28] P.N. Pusey, D.E. Koppel, D.W. Schaefer, R.D. Camerini Otero and S.H. Koenig,

Biochemistry, 1974,13, 952.[29] W. Burchard, M. Schmidt and W.H. Stockmayer, Macromolecules, 1980,13,1265.[30] S.W. Provencher, Comput. Phys. Commun., 1982,27, 213.[31] S.W. Provencher, in E.O. Schulz-DuBois (Ed.), Photon Correlation Techniques in

Fluid Mechanics, Springer, Berlin, 1983.[32] S.W. Provencher, in S.E. Harding, D.B. Sattele and V.A. Bloomfield (Eds.), Laser

Light Scattering in Biochemistry, Royal Society of Chemistry, Cambridge, 1992.[33] A.D.W. McLenaghan, Ph.D. Thesis, University of Strathclyde, 1990.[34] T. Tanaka, L.O. Hocker and G.B. Benedek, J. Chem. Phys., 1973,59, 5151.[35] E. Gleissler and A.M. Hecht, J. Phys. (Paris) Lett., 1979,40, L173.[36] A.M. Hecht and E. Geissler, J. Phys. (Paris), 1978, 39, 631.[37] A.M. Hecht, E. Geissler and A. Chosson, Polymer, 1981,22, 877.[38] E. Geissler and A.M. Hecht, J. Chem. Phys., 1982, 77,1548.[39] EJ. Amis, P.A. Janney, J.D. Fery and H. Yu, Macromolecules, 1983,16,441.[40] N.S. Davidson, Ph.D. Thesis, University of Strathclyde, 1984.[41] N.S. Davidson, R.W. Richards and E. Geissler, Polymer, 1985, 26,1643.[42] T.G. Scholte, J. Polym. ScL A2, 1970,8, 841.[43] W.W. Merrill and M. Tirrell, in G.R. Freeman (Ed.), Kinetics of Nonhomogeneous

Processes, Wiley, New York, 1987.[44] T.P. Lodge, N.A. Rotstein and S. Prager, Adv. Chem. Phys., 1990,79,1.

[45] M. Doi and S.F. Edwards, The Theory of Polymer Dynamics, Oxford UniversityPress, Oxford, 1986.

[46] P.G. de Gennes, Macromolecules, 1986,19,1245.[47] W. Brown and P. Zhou, Macromolecules, 1989, 22, 3508.[48] T. Nicolai, W. Brown, S. Hvidt and K. Heller, Macromolecules, 1990,23, 5088.[49] CH. Wang, J. Chem. Phys., 1991,95, 3788.[50] CH. Wang, Macromolecules, 1992, 25, 1524.[51] CH. Wang and X.Q. Zhang, Macromolecules, 1993,26, 707.[52] N.A. Rotstein and T.P. Lodge, Macromolecules, 1992, 25,1316.[53] S. Pajevic, R. Bansil and C Konak, Macromolecules, 1993, 26, 305.[54] AJ. Hyde, J. Hadgraft and R.W. Richards, J. Chem. Soc. Faraday Trans II, 1979,75,

1495.[55] D.A. Davison, University of Durham, work in progress.[56] J.C Earnshaw and R.C McGivera, J. Phys. D, 1987,20, 82.[57] S. Hard and R.D. Neuman, J. Colloid Interface ScL, 1981,83, 315.[58] J.C. Earnshaw, in CA. Croxton (Ed.), Fluid Interfacial Phenomena, Wiley, New

York, 1986.[59] J.C Earnshaw, R.C McGivern, A.C McLaughlin and P. J. Winch, Langmuir, 1990,

649.[60] J.C. Earnshaw and R.C. McGivern, J. Colloid Interface ScL, 1988,123, 36.[61] D. Langevin (Ed.), Light Scattering by Liquid Surfaces and Complementary Tech-

niques, Dekker, Basel, 1992.[62] M. Kawaguchi, M. Sano, Y.-L. Chen, G. Zografi and H. Yu, Macromolecules, 1986,

19, 2606.[63] M. Kawaguchi, B.B. Sauer and H. Yu, Macromolecules, 1989, 22,1735.[64] B.B. Sauer, M. Kawaguchi and H. Yu, Macromolecules, 1987, 20, 2732.[65] K.-H. Yoo and H. Yu, Macromolecules, 1989, 22,1989.[66] J.A. Henderson, R.W. Richards, J. Penfold and R.K. Thomas, Macromolecules, 1993,

26,65.

13 NEUTRONSCATTERINGFROM POLYMERSA. R. RENNIEPolymers and Colloids Group, Cavendish Laboratory, University of Cambridge,Madingley Road, Cambridge, CB3 OHE, UK

13.1 INTRODUCTION

In the space of a few pages it would be impossible to provide a full description ofthe different investigations of polymers that can be made, or even have alreadybeen made, using neutron techniques. The intention is rather to provide anintroduction to the methods. Those readers who may wish to exploit the specialadvantages of neutrons will be able to assess the feasibility of experiments andfind some guide to the recent literature. The description of published work willnecessarily be selective and will try to reflect some of the wide range of studies thatare now in progress.

There are several reviews of both the technique of neutron scattering and itsapplication to the study of polymers. Although both provide little informationabout work on polymers, readers interested in a thorough description of thetheory of neutron scattering should refer to the books by Lovesey [1] and Squires[2]. Reviews and books concerning neutron studies of polymers can be dividedinto those that are concerned with the technique [e.g. 3-5] and those thatdescribe results, often in particular areas of the topic such as copolymers [6],networks [7], polymer motion [8-11], semi-crystalline polymers [12], polymercolloids [13] and biopolymers [14].

13.2 THE PRINCIPLES OF NEUTRON SCATTERING

The scattering of neutrons can be treated formally as an inversion problem: thescattered intensity from a plane incident beam of wavelength A into a solid angledQ, in the energy range d£, at a scattering angle 6 can be expressed as the Fouriertransform in space and time of the pair correlation function of scattering lengthdensity. In this respect the theory of neutron scattering is identical to that of weakscattering of any other form of radiation. The advantages of neutron scattering


arise from the magnitudes of the quantities mentioned above and their inter-relationships. For example, the large mass of the neutron when compared withelectrons or photons is important in providing good coupling between molecularmotion and the energy of the scattered beam. In the next few paragraphs some ofthe formalism associated with the description of scattering will be presented.Further details of the principles of scattering and the properties of neutrons willbe found in books on atomic physics such as that by Born [15]. Many people willnot be concerned with such fundamentals of the theory, and the interpretation ofmany experimental results can be adequately performed using the simple rela-tionships that derive from appropriate integrations of the wave equations. Someof these are described in the next section.

It is first useful to recall that the neutrons can be considered as either particlesor waves; the connection between the two descriptions is provided by the deBroglie relationships:

E = hv (1)p = hk/2n (2)

where E is the energy, p is the momentum (product of mass and velocity v), v is thefrequency and k is the wave vector of the neutron. The magnitude of the wavevector is given by |k| = 2n/h where X is the wavelength. A schematic diagram ofa general scattering experiment is shown in Figure 13.1. We can distinguish twogeneral cases. First, the situation in which the energy and wavelength of thescattered neutron are equal to those of the incident beam. This is known as elasticscattering, and gives the simple result that the momentum transfer | Ql is(An/X) sin (0/2). More generally, there will be some energy transfer between theneutron and the sample. The experiment is then said to involve inelasticscattering or, if the energy transfer is small and corresponds only to a broadeningof the incident wavelength distribution, quasi-elastic scattering. Advantages ofneutrons over other types of radiation for studies of polymers arise both from therelationship of energy to wavelength and from the mechanism of scattering bynuclei.

The calculation of scattering patterns is based on the summation of amplitudesor intensities scattered from all components. The intensity I of a wave described inthe usual notation of complex variables is given by

I = AA* (3)

where A is the amplitude and the star represents a complex conjugate. Theaddition of wave amplitudes from different scattering centres must take accountof the phase of each wave if the incident beam is a coherent wave front. Coherencein the context of neutrons will be discussed further below. The amplitudeA scattered by a single nucleus at a position r from an incident plane wave ofamplitude A0 is given by:

A = Aobc-^/\r\ (4)

Figure 13.1 (a) Schematic diagram of a scattering experiment; (b) the wave vectors thatdescribe the scattering process. Q is the difference between the incident and scattered wavevectors

This is known as the Born approximation for scattering from weak potentials. Itis seen that the scattered wave is spherically symmetric and decreases in intensityas l/|r|2, which is the usual inverse square law. For a distribution of scatteringlengths described by a density p(r) the resulting amplitude is

A = A0^tp(r)e-^/\rndr3 (5)

and thus the scattered intensity / is

/ = AA* = Al f [p(r)e-fQrp(r')e^7|r|2]d(r - r')3 (6)

The quantity p{r)p{r') is the spatial correlation function of the scattering lengthdensity, and the integral with e" lQ(r"r) is equivalent to a Fourier transform. Itwould be out of place to develop this formalism at great length. The results forelastic scattering are well described by Hukins [16].

Sample

Detector

Sample

It is possible to include the angular frequency co or energy E of the neutrons andthe time variation of the scattering length density in Equation (4) to device relatedresults for inelastic or quasi-elastic scattering. A more formal treatment wouldfirst treat this general case and then simplify the results for elastic scattering.These will not be derived but it is sufficient to quote the result:

dL/dodQ = I/Al

= I Mr,t)e-i(Qr+cor)p(^tV(Qr'+<ol)/M2]d(r - r'fdt (7)

Details of the theory of inelastic scattering can be found in the books of Lovesey[1] and Squires [2]. The intensity or the differential scattering cross-sectiondZ/dcodfi can be calculated for various models of structure and dynamicbehaviour using Equation (7). The models of particular importance to the studyof polymers are similar to those relevant to quasi-elastic light scattering [17,18].In practice, the calculation of such integrals is often simplified by recognising thatthey are Fourier transforms and that several theorems are available to de-scribe their properties, and are included in textbooks on mathematical methods[20,21].

Very few polymers are completely crystalline, and so the present descriptiondiffers from that of most scattering experiments, which are concerned withdiffraction or inelastic scattering from a regular lattice. The problems of predic-ting scattering patterns can generally be reduced to integrals, results for many ofwhich can be derived readily or calculated numerically. For the case of structuralstudies by elastic scattering, many of these results are available in the literature[22-24], even for amorphous or random structures. Most were originally derivedfor X-ray or light scattering.

An important feature of neutron scattering is the neutron scattering length,designated b9 which describes the probability of scattering. Unlike photons orelectrons the neutron is scattered by the atomic nucleus. Some values for elementscommonly found in synthetic polymers are listed in Table 13.1. The scatteringlengths are not correlated with atomic number and can change between isotopesof a single element. This allows isotopic labelling of individual molecules or partsof molecules without perturbing the chemistry, and has proved of particularvalue in the study of polymers, which often consist largely of atoms such ascarbon, hydrogen, oxygen and nitrogen with low electron densities and thus poorcontrast for other radiation. Of particular significance is the ability to labelindividual molecules among other chemically identical polymers to determinetheir size or investigate their mobility in the bulk.

Most readers will be familiar with the idea that structural studies of materialscarried out by light scattering can be performed only within the limits ofcoherence of the source. This is usually explained in terms of the finite time overwhich a wave is emitted from a source. Similar considerations apply to neutrons;

Table 13.1 Neutron scattering cross-sections [19]

Coherent scattering Incoherent scatteringElement lengh/fm cross-section/10"28 m2

Hydrogen 1H -3.74 79̂ 9Deuterium 2H 6.67 2.04Carbon 6.65 0.0014Nitrogen 9.21 0.49Oxygen 5.9 0.015

there is, however, a further constraint on the condition for coherent addition ofamplitudes. A neutron possesses the property known as spin, and must retain thesame spin state for coherent scattering. The nuclei of atoms can also have spin,and will in general have two separate probabilities of scattering associated withthe preservation and loss of spin coherence. It is usual to quote the coherentscattering length (often written as b) in units of length and the incoherentscattering as a cross-section <rinc, which has dimensions of area. This conventionarises from the requirement to add wave amplitudes which are proportional tob in studies with coherent scattering. The incoherent intensity does not give directstructural information, as it derives simply from the addition of intensities fromall nuclei with random phases. It can be used to investigate the dynamics ofa simple via the time dependent self-correlation function. In elastic scatteringexperiments any incoherent scattering is present only as an isotropic (uniform)background, which must be subtracted prior to analysis of the remainingcoherent signal.

13.3 NEUTRON EXPERIMENTS

There are many classes of experiment that can be made with neutrons; they covera wide range of angles, wavelengths and energy transfer and it is not possible togive a full description of them all here. Some experiments are frequently used withpolymers, and these will be outlined briefly in three categories after a few generalremarks on neutron instrumentation.

The description of scattering theory given above has indicated that theimportant variable is the momentum transfer Q rather than the wavelength orangle of scattering. It is possible to measure over the necessary range of Q valuesin two distinct ways. The first is to use a fixed wavelength and scan the angle. Thesecond is to use a fixed angle and a range of wavelengths. This second techniquecan be exploited with advantage at pulsed neutron sources: the source providesa pulse consisting of many wavelengths which can be analysed using measure-ments of the time-of-flight of neutrons from the source to the detector. This

Table 13.2 Benefits of neutron scattering

Advantages Disadvantages

Contrast with isotopes Low fluxContrast variation Large, expensive sourceMeasurements in bulkEasy control of sample environmentMeasurements of molecular motionCan be surface specific

approach can exploit a wide range of wavelengths available in a pulse, as it avoidsthe need to provide a monochromatic beam. On continuous sources it is usual touse a monochromator, either crystals used for Bragg diffraction or mechanicalvelocity selection, and measurement is made at a range of angles. These twotechniques are sometimes associated with spallation sources, which are oftenpulsed, and reactors, which are usually run as continuous sources. Exceptions toboth these rules occur, in that pulsed reactors have been built and, even moresimply, the continuous beam from a reactor can be pulsed using a rotatingchopper. Continuous spallation sources can also be built. The details of design ofboth neutron sources and the diffractometers and spectrometers associated withthem are to be found in the specialist literature [25-27].

A property common to all neutron sources is that of low flux or brightness.Even the best design of nuclear reactors cannot provide a flux of thermal neutronsin the moderator close to the core larger than a few times 1015 n cm ~ 2 s ~ *. Afterselection of wavelength (monochromation) and collimation to define the incidentbeam, the flux available at the sample on a diffractometer or spectrometer isunlikely to be more than 108n Cm-2S"1 and is often much less. This is lowerthan the flux of photons available from typical laboratory sources of light orX-rays. A consequence of this low flux is the need to use large samples (cross-sectional areas of % 1 cm2) and detectors of high efficiency covering a large solidangle around the sample. The combination of large samples and the need toobtain reasonable angular resolution on the detectors will usually lead tophysically large instruments. An extreme example is the overall length of 80 m forone small angle scattering instrument known as Dl 1, which has been built at theInstitut Laue-Langevin in Grenoble, France [28]. Characteristics of neutronscattering for comparison with other radiation are shown in Table 13.2.

13.3.1 STUDIES OF POLYMER DIMENSIONS:SMALL ANGLE SCATTERING

The most frequently encountered use of neutrons in the study of polymers is themeasurement of small angle scattering (SANS). Use of neutrons with wavelengthsin the range 0.5-2 nm and scattering angles between 0.1° and 10° readily allows

investigation of structures in the size range l-200nm. This class of study can beused to give information about the size and conformation of individual polymermolecules. These may be either in solution or in the bulk. The technique is alsoused for the study of phase separation in polymer blends or copolymers and in thestudy of structures of composite materials. The theory of small angle scatteringhas several simplifications over the more general ideas outlined above. It isconcerned only with elastic scattering, although in practice the total intensitymeasured includes both elastic and inelastic scattering [29, 30], which can giverise to some additional complications to measurements made with time-of-flightinstruments.

In the most straightforward case, the scattering from isolated objects ismeasured to determine their size and shape. The integral in Equation (6) is thusperformed over a single object such as a polymer molecule in solution. There is nocorrelation between the positions of nuclei in different objects, and so the totalintensity from a solution is found by adding the intensity from each object.Several simple results can be derived for the scattering at small Q. It is useful towrite down the result of integrating Equation (6) in the following simplified manner

/(Q) = CP(Q) (8)where P(Q) is a function describing the shape of the scattering normalised tounity at Q = 0. The constant C depends on the contrast (square of scatteringlength density difference), the number density of particles and the incident flux.A general result due to Guinier [23] states that for any object with sphericalsymmetry, in the limit of small Q9 P(Q) will be approximated by

/>(G) = exp(-e2Rg2/3) (9)

where Rg is the radius of gyration of the object. This is clearly of considerablevalue in determining the dimensions of polymer molecules, even in the absence ofdetailed models of the structure. It is trivial to show by way of series expansionsthat in this condition of QRg < 1 the result can also be written as

1/P(Q)=I-Q2 R2g/3 (10)

which is the result of Zimm [31] frequently encountered in light scattering. It is ofcourse possible to extend the analysis to include virial interactions betweenmolecules in the manner described in light scattering texts [32, 33].

In many circumstances it is possible to extend the range of measurements withneutrons to cover more than this low Q limit, and then more detailed models ofthe structure must be evaluated. Debye [22] has derived a result for the scatteringfrom a Gaussian distribution of polymer segments appropriate to a randompolymer coil which is of the form:

P(Q) = (2/Q2Rl)lexp(-Q2R2g)-(l-Q

2R2K (11)and can be used to fit data over a much wider range of momentum transfer untilthe Gaussian approximation for molecular structure fails at short distances.

The constant C describing the absolute intensity is of importance as it permitsdetermination of the molecular weight of polymers. By rearrangement of theconstants in Equation (S), it can be expressed as:

I/C = ( N A / c M w ) p > p - p s ) 2 (12)

where NA is Avogadro's number, c is the concentration, Mw is the molecularmass, pm is the mass density of the polymer, and pp and ps are the scattering lengthdensities of the polymer and solvent respectively [14, 34]. Measurements of theabsolute intensity of scattering at low Q, which can be extrapolated to Q = 0 orfitted using one of the equations above, can thus give information about theweight average molecular mass.

The real value of small angle neutron scattering lies in the realisation that thesimple theory above, which is essentially identical to that of light scattering, canbe extended in two ways. The possibility of isotopic substitution and contrastbetween chemically identical molecules can lead to measurements of moleculardimensions in the bulk rather than in solution. Some of the early work with SANSor polymers was concerned with the verification of the idea that screening ofmolecular interactions in the melt gave rise to molecular dimensions that wereidentical to those found in theta solvents [35-37]. This work has now beenextended to a wide range of investigations of molecular conformation in bulkpolymers, which can include amorphous glasses [38], melts [39], gels [40-42],elastomers [43-46] and semi-crystalline polymers [47-51].

A major boost to the application of SANS to polymers in the bulk came fromthe recognition that the screening of molecular interactions in bulk homo-polymers could be used to extend the range of concentrations over whichmeasurements can be made. This idea, which is known as the random phaseapproximation or RPA [52, 53], states that if there are no interactions, i.e. thesecond virial coefficient is zero, then measurements of molecular dimensions canbe made at any concentration. In order to optimise count rates this may often beclose to 50% blends of deuterated and protonated polymers. Several experimentshave been performed to test this theory [54, 55], which is now widely applied.

It should be remembered that there are many cases where the measurement ofinteractions is of importance. SANS has been widely used for the study ofpolymer blends. A simple extension of the theory gives the following expressionfor the scattering from a blend of two miscible polymers with a Flory-Hugginsinteraction parameter x'.

1/7(0 -1 /P 1 (Q)+ 1/P2(Q) -2X (13)

where P1 and P2 are the Debye expressions for separate polymers as given byEquation (11). Other extensions of theory can be made to describe the scatteringfrom copolymers [56,57], branched and star-like polymers [58] and also varietyof geometrical shapes that may be appropriate to describe liquid crystalline andsemi-crystalline structures [23, 24]. Local structure in polymers such as that

arising from chain rigidity has also been described [59]. It should also bementioned that the scattering from polymers bound to the interface of colloidalparticles has been the subject of several investigations with SANS.

13.3.2 POLYMERS AT SURFACE-REFLECTION

Neutrons can be reflected from planar surfaces according to the usual laws ofspecular optics. The refractive index n for neutrons is given by:

n=l-(p№t) (14)

This equation indicates that for most materials the refractive index will be veryclose to, but generally slightly less than, unity. The condition in optics known astotal internal reflection will thus be replaced by total external reflection [60]. Thiswill occur at low angles, typically about one degree for thermal neutrons. Atangles larger than the critical angle, the reflectivity is reduced, and it is thisvariation that provides information about the structure of the interface.

The intensity of a neutron beam reflected from a surface can be calculatedexactly using the optical matrix approach of approximating the interface to aseries of thin layers and calculating the reflection at each boundary in the mannerdescribed by Born and Wolf [61], Heavens [62] or Abeles [63]. It is perhaps moreinstructive to consider an alternative procedure based on the kinematic theory ofscattering [64] which gives the following approximate expression for the reflec-tivity R(Q) as a function of Q the momentum transfer normal to the interface:

R(Q)= I6n2\ H(Q)2 \Q2 (15)where H(Q) is the Fourier transform of the scattering length density distributionnormal to the interface p(z). This result is not valid close to critical reflection,butcan now be extended [65] to provide analytical forms over the entire range of Q.The experimental arrangements for such measurements are shown schematicallyin Figure 13.2(a).

This technique has emerged only recently but is rapidly growing. Reviews ofthe experimental technique [66] and the application to polymers [67] havealready appeared. The application of neutrons to the study of polymer surfaces orinterfaces can be divided into two categories. First, the study of polymersadsorbed or spread at liquid interfaces; secondly, the study of polymers in thinfilms. This second category provides interesting models for measurements onpolymer compatibility and inter-diffusion. Reports of ordering of copolymers atsurfaces [68], phase separation [69] and the width of polymer/polymer interfacesduring diffusion [70] have been made.

The results on adsorbed polymers using neutron reflection provide a usefulcomplement to studies Qf adsorption by small angle scattering and other classicaltechniques. Measurements of the excess polymer at both solution/vapour [71-73] and solution/solid [74-76] interfaces have been described. Other studies

Figure 13.2 (a) Neutron reflection experiment; the geometry is arranged so that onlyspecular reflection (angle of incidence is equal to angle of reflection) is observed; (b)observations can be made either at the interface of a sample with vapour (i) or ata solution/solid interface (ii) provided that a material of adequate transparency toneutrons such as silicon or quartz is used to form the bulk of the solid

have been made of the structure of polymer monolayers spread at the air/waterinterface on Langmuir troughs [77-79] .

13.3.3 POLYMER DYNAMICS—QUASI-ELASTICSCATTERING

The advantage of neutron scattering for studies of polymer dynamics is the directinformation that is provided about the molecular correlation functions in timeand space by the technique. Other spectroscopic probes such as NMR anddielectric or mechanical response can provide information about the time orfrequency of relaxations, but do not directly provide information about thelength scale on which the dynamic processes occur. Once again there is ananalogy to dynamic light scattering, and most of the theory is similar. Thederivation of the scattering laws describing the differential scattering cross-

Solution

Solid

Sample

Neutrons Detector

Figure 133 A schematic diagram of a neutron spin-echo spectrometer. The difference invelocities of the polarised neutron before and after the scattering process can be observedby measuring the precession in the regions of uniform magnetic field H. The difference inthe precession is easily determined from the polarisation of the beam reaching the detectorD if the fields before and after the sample S are symmetrical and the polarization is invertedwith the flipper coil marked as U/2. The coils marked n/4 are used to provide magneticfields that define the initial and final states of polarisation

section for various models of polymeric motion, such as reptation of moleculesthrough entanglements or the hydrodynamic screening described by Zimm, iscomplex. The main results can be found in the book by Doi and Edwards [80].

For our purposes it is sufficient to recognise that a diffusive process gives rise toa scattering law of the form:

/(Q, Q) = DQ2/{Q2 + D2Q2) (16)

where D is the diffusion coefficient and Q and Q refer to the momentum and theenergy transfer in the scattering process. If measurements are made directly in thetime domain, then the scattering law will ocrrespond to the Fourier transform ofthis Lorentzian, which is simply an exponential decay

I{Q,t) = exp(-DQ2t) (17)Measurements of the diffusion of polymers in the melt and in solution have beenmade using neutrons. It is of particular interest that the distance scale over whichdiffusion is measured depends inversely on Q9 and so it is possible to probe boththe regions of internal modes and overall intermolecular diffusion.

The technique that has attracted most recent attention is that of neutronspin-echo (NSE) spectrometry. This method of measuring small energy transfers,which was proposed by Mezei [81, 82], cleverly avoids the need to monochro-mate the beam precisely and thus provides gains in the incident flux. Theexperiment (see Figure 13.3) measures the energy change of each neutron byobservation of the precession of the spin in uniform magnetic fields.

Experiments using the NSE technique have been used to verify the microscopicaspects of Rouse and Zimm models of the motion in polymer solutions [83]. Theyhave also shown that the reptation process [84] of self-diffusion along a tube

precession

can be well described by Rouse modes within the tube. The effects of entangle-ments (topological constraints) can be observed in the long distance (small Q)modes in melts and networks [85-88]. More recently, experiments have lookedat the motion of copolymers [89] and of polymers close to the glass transition[90-92].

13.4 SOME EXAMPLES OF RECENT PROGRESS

Here a few examples of recent work will be mentioned. The selection naturallyreflects the author's interests, but is intended to illustrate those areas of neutronscattering that have particular prominence at present or are growing rapidly.Many of the early experiments with neutrons were concerned with the propertiesof homopolymers; indeed, physicists were often seeking the simplest systems thatcould be considered as uniform, flexible macromolecules to test fundamentalmodels of polymer conformation and dynamics. Recent work has been character-ised by an increasing complexity in the systems that are investigated to includecopolymers, blends and composite materials. In some cases the neutron studiesare a minor part of more widespread investigations of the properties of novelpolymers, their synthesis or processing. The examples below are intended toprovide some insight into the range of studies that can be made and the precisionof data that can be obtained.

13.4.1 STUDIES O F COPOLYMERS

The study of copolymers with scattering techniques is greatly aided by isotopiccontrast variation. Studies of phase separated and homogeneous states have beenmade on several systems [6]. A description of the static scattering obtained froma diblock copolymer in the homogeneous melt has been given by Leibler [56]. Itis characterised by a peak in the small angle scattering arising from the so-called'correlation-hole'. A volume around a segment of a given type is depleted in thatmonomer by the constraints of the relative monomer density imposed by themolecular block structure. This is shown in Figure 13.4. Small angle scattering onsuch materials proves to be an excellent way of measuring the interaction, as thewidth of the peak seen in the scattering pattern is very sensitive to the interactionparameter x-

Recently the neutron spin-echo technique has been used in conjunction withisotopic labelling to test theories of copolymer dynamics. The theory has beenreviewed in the context of light scattering [93]. Data for a diblock isoprene-styrene copolymer have been presented [89] that are in good agreement with theRPA theories. The findings demonstrate a general feature that is perhaps worthyof comment. The mobility of the more mobile isoprene segment can be character-ised by a relaxation time r or characteristic frequency Q. The ratio Q/Q2 is not

Q/nrrr1

Figure 13.4 Scattering from a diblock copolymer in the homogeneous melt showing thevariation with temperature. This data taken from the study of styrene-isoprene diblockpolymers described in ref. [89] is measured with X-rays, although the principles are thesame as for SANS measurements. If there is sufficient X-ray contrast (electron densitydifference) it is usually more economic to use X-rays. The width of the peak is a goodmeasure of the interaction between the two components

Inte

nsi

ty/a

.u.

Q? / nnr2

Figure 13.5 Motion of the polyisoprene block in blends of 50:50 polyisoprene/polysty-rene diblock copolymer dissolved in polyisoprene at the different temperatures indicated.The data is displayed as the characteristic frequency O divided by Q2. The relaxation timeis seen to tend to infinity at a finite Q vector that corresponds to the peak in the staticstructure seen in Figure 13.4. Full details of the interpretation of these data are to be foundin ref. [89]

constant, as might be expected for a normal diffusion process, but varies with Q.This is normal for the 'Rouse' or 'Zimm' relaxation modes of a polymer chain.The significant feature of the data for the copolymer shown in Figure 13.5 is thatthe ratio Q/Q2 tends to zero at a finite value of Q. This corresponds roughly topeak in the static structure, and demonstrates clearly that a static correlationbetween monomers of a given type at a given distance or Q-vector must bereflected in hindered diffusion in the same range.

Q/nnrr1

Figure 13.6 Reflectivity curves for deuterated polystyrene (390000 Mw) adsorbed at anamorphous quartz surface from a 0.1% w/w cyclohexane solution [94]. The scatteringlength density of the solvent was adjusted (HfD ratio) to match the quartz so that the onlysignal arises from the adsorbed polymer. The curves for 15 (•) and 35 0C (+) are shown; theadsorption between these limits was reversible. The continuous lines show approximatefits indicating an exponential polymer segment distribution with a characteristic lengthincreasing from 95 to « 800 A

13.4.2 ADSORPTIONATSURFACES

The use of neutrons to study interfaces is still relatively new, but several studieshave already been made which demonstrate the scope of the technique. By way ofexample, some data for polystyrene adsorbing to amorphous silica [94] areshown in Figure 13.6. The curves show a large difference between 15 and 35 0C,which is associated with a rapid increase in adsorption as the temperature isdecreased to 210C, which is the cloud point for the solution of deuteratedpolystyrene (molecular weight «390000) in a mixture of deuterated and proto-nated cyclohexane.

The large increase in adsorption is substantially reversible in that, on heating,most of the polystyrene will be desorbed. This contradicts the frequently heldview that physical adsorption of polymers is usually irreversible. However, itmust be remembered that in this case the adsorbed layer really corresponds toa large thickness of concentrated solution. The layer is rather thicker than that ofsingle polymer molecules, and many of the molecules may have no directinteraction with the silica surface. It must not be assumed that this type of

IgR

Q2/nm-2

Figure 13.7 (a) Schematic diagram of chain fragment diffusion in polymer glasses andmelts; after the initial fragmentation, which can occur rapidly, the polymer segmentsdiffuse apart and at long times will appear as separate smaller polymer molecules; (b)example data [101] for a deuterated poly car bonate/tetramethyl polycarbonate blendcontaining some tetraethylethane groups that can split readily under moderate heating(three or four per molecule). The data shows the diffusion at 186 0C during which thepolymer is observed

behaviour is typical of polymers in general, as rather few systems have beensubject to detailed study, although reports in the literature do refer to polyethy-lene oxide adsorbing from aqueous solution [74] and to some copolymers [75].

A further point that emerges in such studies on polymers is that isotopiclabelling can sometimes significantly alter the behaviour of a polymer solutionor blend. Detailed studies of the system polystyrene/cyclohexane have been

published [95], showing a variation of several degrees in the cloud point. Otherwork on deuterated polystyrene/protonated polystyrene has also shown interac-tions that can be significant in high molecular weight polymers [96,97].

13.4.3 KINETICS A N D POLYMER MOTION

In recent years it has been possible to extend the use of small angle neutronscattering to study many processes that concern polymers in a variety of complexsample environments. These have included deformation and yield of elastomersand glassy polymers in conditions close to those occurring in processing andservice. Other aspects of time dependent behaviour have included the study ofpolymerisation and observing the growth of polymer molecules during thescattering experiment. An example of the use of time dependent small anglescattering can be found in the chain fragment diffusion experiments described byHellmann and co-workers [98-101]. Polycarbonate molecules with links thatcan be thermally degraded were included in a matrix of other polymers. As thechain fragments diffuse apart after the degradation, the change in apparent radiusof gyration and molecular weight can be observed by SANS. This process isshown schematically in Figure 13.7(a), and some data showing the resulting datafor a sample held at 186 0C are given in Figure 13.7(b). The times shown on the

Figure 13.8 Results of diffusion measurements over a range of temperatures for thesystem shown in Figure 13.7. The comparison with the standard WLF equation [102](dashed line) and the glass transition temperature Tg is indicated

graph of normalised inverse intensity against Q2 indicate that the time scale of thediffusion process over a distance of about a molecular radius is several minutes.At a modern high flux reactor with good instrumentation it is possible to recorddata at approximately every minute. This has permitted measurements ofdiffusion coefficients in the range 10" 1 4 -10~ 1 8 cm2 s"1 such as those shown inFigure 13.8.

13.5 FINAL REMARKS

Neutrons provide a powerful investigative tool to study the structure andmolecular motion in materials. Although available in only a few specialistlaboratories, they have been widely exploited, and both sample preparation anddata analysis are relatively straightforward. It is to be expected that neutronscattering will increasingly become a standard technique available to polymerscientists for characterisation of samples, and also for measurement of thestructure of materials to correlate with physical properties. The possibilities ofbuilding realistic sample environments permit the study of polymers and theirsurfaces in conditions that are close to those in service or in polymerisationreactors.

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[72] L.T. Lee, O. Guiselin, B. Farnoux and A. Lapp, Macromolecules, 1991,24, 2518.[73] O. Guiselin, L.T. Lee, B. Farnoux and A. Lapp, J. Chem. Phys., 1991,95,4632.[74] E.M. Lee, R.K. Thomas and A.R. Rennie, Europhys. Lett., 1990,13,135.[75] S.K. Satija, CF. Majkrzak, T.P. Russell, S.K. Sinha, E.B. Sirota and GJ. Hughes,

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14 OPTICAL ACTIVITY ANDTHE STRUCTURE OFMACROMOLECULES

F. CIARDELLIDepartment of Chemistry and Industrial Chemistry, University of Pisa, Italy andCNR, Center for Stereordered and Optically Active Macromolecules, Pisa, Italy

O. PIERONIDepartment of Chemistry and Industrial Chemistry, University of Pisa, Italy andCNR, Institute of Biophysics, Pisa, Italy

and

A. FISSICNR, Institute of Biophysics, Pisa, Italy

14.1 INTRODUCTION

14.1.1 ORIGIN OF OPTICAL ACTIVITY INMACROMOLECULES

As in low molecular weight compounds, optical activity can be observed only inchiral macromolecules, that is, macromolecules for which all allowed conforma-tions lack reflection symmetry elements.

The identification of chiral macromolecules differs from that of low molecularweight molecules because of the substantially linear structure along the chainbackbone. Accordingly, analysis of the symmetry properties has been carried outon the basis of three different models: (i) the infinite length chain; (ii) the finitelength chain with equal end groups; and (iii) the finite length chain with differentend groups. Point symmetry valid for molecules having definite and 'discrete'dimensions in all directions can be used only for the last two models, whereaslinear symmetry must be used for the first model, which implies an infinitedimension [I]. In linear symmetry, in contrast to point symmetry, the newsymmetry operation 'translation' and the new symmetry element 'translationaxis' are introduced. The analysis for a flexible macromolecule, which can assumean extremely large number of conformations, is conveniently carried out on themost symmetric of these conformations, which is usually the 'planar zigzag'. The

Polymer Spectroscopy. Edited by Allan H. Fawcctt© 19% John Wiley & Sons Ltd

analysis of the derived Fischer projection of an infinite chain indicates that this ischiral when a symmetry plane containing the chain, those perpendicular to thechain and that with translation containing the chain are all lacking [I] . For finitelength chains, chirality is guaranteed by lack of symmetry in the plane containingthe chain and the plane perpendicular to the chain at its central point [I] .

Thus, in vinyl polymers, only atactic macromolecules can be chiral in the firstmodel with infinite length chain. The atactic and the syndiotactic macro-molecules with an even number of monomer residues are chiral in the finite chainmodel with identical end groups, whereas all isotactic, syndiotactic and atacticchains have a chiral structure for the last model with different end groups [1,2].

Even in vinyl polymers consisting of chiral macromolecules, extremely low orvanishing optical rotation can be predicted when the molecular weight is high,even if a complete separation of the enantiomeric pair were to be possible. Indeed,in vinyl polymers every stereogenic carbon atom is flanked by two CH2 groups,and its chirality arises only from the different lengths of the two chain sectionsattached to it. Thus an appreciable contribution to chiroptical properties isconceivable only for asymmetric centers close to the chain ends, the concentra-tion of which decreases with increasing molecular weight. The same holds forconformational optical activity referred to the presence of secondary structures,involving the macromolecule as whole or a substantial fraction of it, witha predominant handedness. This last is not attributable simply to stereogeniccenters (asymmetric centers) with a single absolute configuration in each repeat-ing unit.

Indeed, the existence of purely conformational optical activity is not a uniquemacromolecular requisite, being Well known in low molecular weight atro-pisomerism. However, in polymers it assumes a very specific characteristicconnected with the occurrence of cooperative effects which allow transmittanceof molecular asymmetry along the chain to very long distances [3].

Most isotactic vinyl polymers assume helical conformations in the crystallinestate [4], but owing to the substantial achirality of the macromolecules bothscrew senses are found in the lattice cells in equal amounts. This is even more truein a melt or in solution, where left-handed and right-handed helical sectionsalternate even within the same macromolecular chain. Certainly, an appreciableoptical rotation would be observed in the crystalline state provided that crystalli-zation occurred under a chiral field inducing a single screw sense helicity in allchains. Such an optical rotation would promptly be lost on melting or dissolution,as an immediate equilibration between the two opposite helical senses would occur.

Isotactic macromolecules derived from achiral monomers have no preferencefor right- or left-handed screw senses, and the two are perfectly balanced at inter-and intramolecular level. However, distribution of left- and right-handed helicalsecondary structures affects markedly the free energy of the system, alternation ofthe two senses in the same chain being favored for entropic reasons [4,5]. If thislast situation takes place, conformational optical activity cannot be obtained

because of intramolecular conformational compensation, which hinders anyisolation of chains with a predominant handedness.

The above considerations are described in fuller detail in previous papers [6,7]and indicate that macromolecules assuming a single chirality conformation canshow chiroptical properties characteristic of the conformation itself. Moreover, ifchromophores are present in the side chains specific chiroptical properties canarise from dipole-dipole electronic interactions among these chromophoresdisposed along the chirally arranged backbone. This situation is clearly shown inpoly-a-amino acids, in which specific and typical chiroptical properties areassociated with specific and typical conformations (a-helix, /?-structures, randomcoil) [8].

In order to make one screw sense largely predominant in a single macro-molecule, the intramolecular equilibration must be hindered by building veryrigid chains. In the limiting case the chains will form rods having helical structurewith either left- or right-handed helicity. Even if hindering of equilibration can beconsidered as a kinetic effect, it cannot be excluded that thermodynamic contri-butions are involved, particularly when rigidity is due to bulk side chains andconformational reversals have a very high internal energy [5,9]. In other words,bulky side chains in a vinyl type structure, for instance, can favor the formation oflonger helical chain sections, as the lower entropy is balanced by the gain ininternal energy due to minimization of the number of conformational reversals.Indeed these last have, in the case of macromolecules with bulky and branchedside chains, larger internal energy per structural unit than the same unit in thehelical conformation [10]. Which mechanism is actually operating cannot beestablished from primary structure as a general rule, an increase in temperature inboth cases favoring the equilibration of the two screw senses within eachmacromolecular chain.

Chiroptical properties (molar rotatory power [$ ] and molar ellipticity [0])result from a weighted average of the contributions from different conformers, asshown in the following equations:

where N1 indicates the molar fraction and [O]1 (or [G]1) indicates the molarrotatory power (or molar ellipticity) of the i-th conformer. In macromolecules themolar entities refer to one residue; thus the chiroptical properties are independentof molecular weight, at least when this is very high.

It has been demonstrated that in isotactic polymers of optically active a-olefinsthe molar optical rotation per monomeric residue can be interpreted in terms ofthe prevalence of few conformations with very high optical rotation of the samesign, corresponding to those allowed to the structural unit inserted in an onescrew sense helix [11].

Moreover, in coisotactic copolymers of optically active a-olefins with viny-laromatic monomers, it was shown that the aromatic groups in the side chainsgive rise to dichroic bands in the spectral region of the n->n* electronictransitions. In several cases exciton splitting was also observed, correspon-ding to the strong allowed n-m* electronic transition [12]. This circular-dichroism (CD) couplet was confirmed to be connected to the dipole-dipoleelectronic interaction of transition moments of aromatic moieties disposedin a mutual chiral geometry with a predominant handedness, such as that ofa one screw sense helix [13,14]. This clear demonstration that the extrinsicCD bands of side chains are related to main chain conformation indicatestheir usefulness as 'conformational probes'. A typical case comprises poly-peptides with aromatic side chains masking the peptide absorption bands[15].

14.1.2 OBJECTIVE

With reference to the concepts summarized in the previous section, opticalactivity measurements can be particularly effective in providing structuralinformation on polypeptides with side chains absorbing at a wavelength clearlydistinct from that of the peptide group. In some favorable cases, moreover,CD spectra can allow the detection of very specific structural features, inclu-ding non-bonding interactions. On the other hand, the same data can be usedfor monitoring even subtle structural changes induced by external factors.Accordingly, the evaluation of chiroptical properties allows one to followcrucial conformational changes accompanying such biological phenomenaas substrate binding, macromolecule-macromolecule interactions, and soon.

In order to substantiate these last considerations, the present paper is devotedto the description of studies, using mainly CD spectra, concerning poly (L-glutamic acid)- and poly(L-lysine)-bearing photochromic side chains. Lightirradiation of these polypeptides gives rise to reversible isomerization of thephotoresponsive chromophores attached to the macromolecule's backbone,which itself can then undergo reversible conformational changes. These may beaccompanied by reversible variations of the polymer's properties, such as viscos-ity, solubility and so on.

The main objective of this paper is to show that the examination of thechiroptical properties during the above mentioned phenomena can allow thecorrelatation of changes in conformation and properties with the photoresponseof the chromophores. On the same basis, an interpretation at the molecular levelcan be put forward of the reversible variation of viscosity and the solubility. It isalso hoped that these indications may be useful for developing photorecordingdevices which can be read using their chiroptical properties.

14.2 CHIROPTICALPROPERTIESOFPHOTOCHROMIC POLYPEPTIDES

14.2.1 POLYPEPTIDES PHOTORESPONSIVE TO UV LIGHT

14.2.1.1 Azobenzene-containing Polypeptides

Polypeptides sensitive to irradiation with near UV light can be prepared byintroducing photochromic azobenzene units into the side chains of high molecu-lar weight (Mv = 100000-250000) poly(a-amino acid)s, such as poly(L-glutamicacid) or poly(L-lysine). Macromolecules having the structures represented inFigure 14.1, and containing various percentages of azo groups, can be obtainedunder various reaction conditions [16,17].

The photoisomerization of azobenzene moieties (Figure 14.2) is the eventresponsible for the photochromic behavior of these macromolecules. At roomtemperature in the dark all azo groups are in the trans configuration, which isplanar and then fully conjugated. Irradiation produces isomerization to the cisconfiguration which, by contrast, is not planar for steric reasons. At the photo-stationary state, the relative composition of the two isomers depends only on theincident light. The maximum photoconversion to the cis isomer (85 %) is achievedby irradiating at 350-370 nm, whereas the maximum yield of the back reactionfrom the cis to the trans isomer (80%) is achieved by irradiating at 450 nm. Witha lamp having a power of 100 W, irradiation for 1 or 2 min is enough to achievethe photostationary state.

By dark adaptation, the metastable cis chromophores decay again to the transform. The thermal decay at room temperature in the dark is rather slow forazo-modified poly(L-glutamic acid) and takes more than 20Oh to restore theall-trans isomeric composition; for azo-modified poly(L-lysine) the decay in the

Figure 14.1 Chemical structures of poly(L-glutamic acid) and poly(L-lysine) containingazobenzene units in the side chains

Figure 14.2 Photochromic behavior of azobenzene-containing poly(L-glutamic acid).Reproduced by permission of Elsevier Science S.A. from J. Photochem. Photobiol. B: Bioi,1992,12,125-140

dark takes place so slowly that it cannot be observed under normal experimentalconditions. The photochromic cycles are completely reversible and can berepeated at will, without any apparent fatigue.

As a consequence of the different electronic situations, the two isomers havemarkedly different absorption, and the photo-isomerization is accompanied bystrong variations in the spectra (Figure 14.2). In particular, the trans-to-cisisomerization is revealed by a strong decrease of the intense band at « 350 nmassociated with a n-n* transition and a contemporaneous increase of the band at450 nm associated with the n-n* transition of the azo-chromophore.

14.2.1.2 Light-induced Conformational Changes

Poly(L-glutamate)s having azobenzene units in the side chains, in organic sol-vents such as trimethyl phosphate (TMP), show the typical CD curve of thea-helix structure, with two minima at 208 and 222 nm. Above 250 nm, thedark-adapted samples exhibit also a couplet of bands centered at 350 nm,corresponding to the n-n* transition of the azo chromophore in trans configur-ation. The trans-to-cis photoisomerization completely cancels the side chain CDbands in the region of 35Onm, but does not modify at all the CD spectra in thepeptide region. This indicates that, in these solvents, light causes the isomeriz-ation of the azo side chains, but the isomerization does not induce any variationof the polypeptide main chain.

Figure 143 CD spectra of poly(L-glutamic acid) bearing 36 mol% azobenzene units,before ( ) and after ( ) irradiation, in aqueous solution at various pH values: A,pH 4.8; B, pH 6.5; C,pH 8.0

The secondary structure in water depends on the molar content of azobenzeneunits and also on the degree of ionization of the unmodified COOH side chains.Below pH 5, a sample of poly(Glu) bearing 35 mol% of azobenzene units assumesa /^-structure. Irradiation does not induce any variation of the polypeptideconformation. At pH values above 7, the polypeptide adopts a random coilconformation which is again not affected by the photoisomerization of the azoside chains. However, at pH values of 5-7, irradiation produces a remarkabledecrease of the ordered structure (Figure 14.3). In this range of pH the trans-to-cisisomerization produces a higher degree of ionization of the unmodified COOHside chains, thus amplifying the first light effect and causing unfolding of thepolypeptide.

Cationic surfactants are known to affect the conformation of poly(L-glutamicacid). This suggested to us that it might be possible to combine the isomerizationof the photochromic side chains with the surfactant effect to obtain an amplifica-tion of the photoresponse. The expectation was realized by irradiating azo-modified poly(L-glutamic acid) in the presence of dodecylammonium chloride(DAC) at the critical micelle concentration (c.m.c) [18]. Figure 14.4 shows the CDspectra of a 20% azo-modified poly(Glu) both in the absence and in the presenceof DAC. In the absence of detergent at pH 7, the polymer is completely in randomcoil conformation and not affected at all by irradiation. In the presence ofdetergent at the c.m.c, irradiation at 35Onm (trans-to-cis isomerization) induces

Figure 14.4 CD spectra of poly(L-glutamic acid) bearing 20 mol% azobenzene units, atpH 7.6, before ( ) and after ( ) irradiation: A, in the absence of dodecylammoniumchloride (DAC); B, in the presence of DAC, below the c.m.c; C, in the presence of DAC, atthe c.m.c. Reproduced by permission of Elsevier Science S.A. from J. Photochem. Photo-bioi B: BioL, 1992,12,125-140

an evident coil-to-helix transition. The variation is completely reversible whenthe sample is dark-adapted or irradiated at 450 nm (cis-to-trans isomerization).Thus, in the presence of DAC micelles, the polypeptide conformation can bephotomodulated by exposure alternately to light or dark, or by irradiating at twodifferent appropriate wavelengths.

The key factor responsible for the photoinduced variations of conformation isthe affinity of the azo-polymer for the micelles. Such an affinity, in fact, is likely tobe different when the azo side chains are in trans or in cis configuration. Whenazo-units are in the planar, apolar, trans form, they dissolve within the hydropho-bic core of the micelles, forcing the polypeptide chains to assume a coil conforma-tion. Isomerization of the azo units to the skewed, polar, cis form inhibitshydrophobic interactions and causes the azo-units to leave the micelles, thusallowing the polypeptide chains to adopt the a-helix structure (which is favored inthe absence of micelles). In other words, the primary photochemical event is thetrans ̂ cis isomerization of the azobenzene units, but the driving force of thephotoresponse should be the different location of the macromolecules relative tothe micelles.

Dark-adapted (all trans azo groups) poly(L-lysine) bearing 43 mol% of azoben-zene groups, in a medium of hexafluoroisopropanol/water/sodium dodecylsulfate, shows a CD spectrum which can be attributed to the presence of a /?-form.Irradiation at 340 nm causes the disruption of the /!-structure and promotes theformation of an a-helix (helix content % 50%), as revealed by the appearance ofthe typical CD pattern. Upon irradiation at 450 nm, the spectrum reverses again

to the original one. The photoinduced /J;=± helix conformational change iscompletely reversible and the two conformations can be obtained by irradiatingalternately at the two different wavelengths.

This photoinduced fi^± helix change can readily be explained on the basis ofthe different geometry and hydrophobicity of the trans and cis azobenzene units.The /J-form is stabilized by hydrophobic interactions among the side chains andis favored when the azobenzene units have the planar geometry and the highhydrophobicity of the trans configuration. The interactions are inhibited whenthe azo units are isomerized to the skewed cis configuration, and thus the/^-structure is destabilized and destroyed. The polypeptide chains then adopt thea-helix form in the helix-supporting solvent hexafluoroisopropanol.

The photochromic behaviour of azobenzene-containing poly(L-lysine) has alsobeen reported in the monolayer state [19]. When the polypeptide monolayer iskept at constant area, alternate irradiation with visible and ultraviolet lightproduces reversible changes (% 25%) of the surface pressure of the monolayer.

14.2.13 Photostimulated 'Aggregation-Dissaggregation' Effects

CD data provided evidence that azo-modified poly(Glu) containing azobenzeneunits can undergo reversible aggregation-disaggregation processes upon expo-sure to light or dark conditions [20]. Samples stored in the dark or irradiated at450 nm (azo groups in the trans configuration) show variations of their CDspectra on aging in a TMP/water solution (Figure 14.5). The time dependence ischaracterized by the gradual appearance of an intense side chain CD couplettogether with a progressive distortion of the a-helix pattern, typical of the effectsproduced by aggregates of polypeptide chains [21,22].

Irradiation at 361 nm (tran to cis isomerization) produces the full restoration ofthe initial CD spectra, indicating dissociation of the aggregates. The spectrarevert again to the distorted ones on irradiating at 450 nm or by dark adaptation,thus confirming the reversibility of the light-induced effect.

Investigation of azo-modified poly(Glu) containing 85 mol% azobenzene unitsin the side chains has provided confirmation of the occurrence of aggregation-disaggregation processes induced by light, together with the possibility ofphotoregulating polymer solubility [23]. This polypeptide, when stored in thedark, assumes the a-helix structure in hexafluoroisopropanol (HFP). Addition ofa small amount of water (15 vol%) to the HFP solution causes the formation ofaggregates, followed by precipitation of the polymer as a yellow material. Theprecipitation is total and quantitative, as can be seen by recording the absorptionspectrum of the filtered colorless liquid.

Complete dissolution of the polymer was obtained by irradiation of thesuspension for a few seconds at 350 nm; irradiation at 450 nm or dark adaptationof the solution caused the polymer to precipitate. In a HFP/water = 85/15solvent mixture, therefore, the 'precipitation-dissolution' cycles can be reversibly

Figure 14.5 Poly(L-glutamic acid) bearing 20mol% azobenzene units. CD spectra intrimethyl phosphate/water = 50/50, recorded at various aging times: (1) freshly preparedsolution; (2) aged 1 day; (3) aged 2 days; (4) aged 3 days. ( ) Dark-adapted samples;( ) irradiated at 360 nm, at any aging time. Reprinted with permission from [23].Copyright 1989 American Chemical Society

repeated by irradiation and dark adaptation, or by irradiating at two differentwavelengths.

The dependence of the polymer solubility on the cis/trans composition of theazobenzene side chains was investigated by performing irradiation experimentsat various wavelengths of the incident light. The considerable amount of photo-dissolved polymer allowed its determination by evaporating the solutions ob-tained upon irradiation and weighing the dry residue. The solubility of thepolymer, as a function of the cis/trans ratio of azobenzene side chains, is describedby a sharp sigmoidal curve. The polymer is fully insoluble when more than 60%of the azo groups is in a trans configuration. By contrast, the maximum amount of

photosolubilization is achieved when 60% of azo groups are in the cis configur-ation; the solubility then remains unaffected at higher values of cis content [23].

The described photoresponse effects can be well interpreted on the basis ofassociation among macromolecules through hydrophobic interactions andstacking of azobenzene side chains. The planar, apolar, trans configuration givesaggregation and precipitation; when the azo moieties are photoisomerized to theskewed, polar, cis configuration, interactions and stacking between azo-groupsare inhibited, so that disaggregation of the macromolecules takes place andpolymer dissolution occurs.

14.2.2 PHOTOMODULATION OF POLYPEPTIDECONFORMATION BY SUNLIGHT

14.2.2.1 Spiropyran-containing Polypeptides

Azo-modified polypeptides could be considered as models for photoregulatedprocesses occurring in nature, but the generation of cis and trans photoisomers,and hence photoregulation, requires artificial sources of ultraviolet light. Ideally,one would like to have a model system responding to the presence or absence ofsunlight, such as polypeptides bearing spiropyran groups attached to poly(L-glutamic acid) [24] or poly(L-lysine) [25] (Figure 14.6).

Spiropyran-modified poly(L-glutamate)s in hexafluoroisopropanol (HFP)exhibit 'reverse photochromism', that is, a photochromic behavior which is

S p i r o g r o u p

Spiro Spiro

Figure 14.6 Chemical structure of poly(L-glutamic acid) and poly(L-lysine) bearingspirobenzopyran units in the side chains

Figure 14.7 Structure and reverse photochromic reactions in HFP of poly(L-glutamicacid) containing spiropyran units in the side chains

opposite to that usually observed in most common organic solvents. Thus, HFPsolutions kept in the dark at room temperature show a yellow-orange colorwhich is completely bleached upon exposure to visible light and is reversiblyrestored in the dark.

NMR data confirm that the photochromism in HFP involves the well-knowninterconversion between the colorless closed spiro structure / and the coloredring-opened merocyanine structure II (Figure 14.7). Accordingly, in the 13CNMR spectra of the colorless solution the resonances of the geminal methylgroups appear as two separate peakes, 27.0 and 21.0 ppm, as a consequence of thepresence of the chiral spiro carbon atom. In the colored solution, by contrast, thetwo methyl group resonances merge to a single signal at 28.7 ppm, analogously tothat observed for the proton resonances. The spectra of the colored species keptin the dark do not show nuclear resonances associated with the spiro form,indicating that in HFP the spiropyran ;=± merocyanine equilibrium is fully shiftedto the right.

The very polar solvent HFP is probably responsible for the reverse photo-chromism by stabilizing the charged merocyanine species II more than the apolarspiropyran species I. A protonated open structure III might also be formedbetween the zwitterionic species II and HFP, with the solvent functioning as anacid, as will be described in the following section.

The dark-adapted sample shows a spectrum which displays two absorptionmaxima, at 500 and 370 nm, of about the same intensity (Figure 14.8). Irradiationwith visible light (500-550 nm) or exposure to sunlight for a few secondscompletely dispels the absorption in the visible region and gives rise to thespectrum of the colorless spiro form, characterized by absorption maxima at 355and 272 nm. In the dark, the original spectrum is progressively restored.

In the colorless indolinospiropyran species, the two halves of the moleculeare topologically independent, so the absorption spectrum consists mainly of

dark

light

Figure 14.8 Variation of the absorption spectra as a function of irradiation and dark-adaptation time for poly(L-glutamic acid) bearing 85mol% spiropyran units in HFP(c = 5.01 x 10"2 g/1; / = 1 cm); 1, dark-adapted solution; 2, irradiated solution

localized transitions belonging to a particular half of the molecule, rather thandelocalized transitions belonging to the molecule as a whole [26]. The electronictransition at longer wavelength, which in HFP occurs at 355 nm, has beenassigned to the benzopyran, and the second transition, which in HFP is seen at272 nm, has been assigned to the indoline portion of the molecule [26]. In thecolored species, the absorption band at 500 nm can be assigned to a n-n*electronic transition of the extended and conjugated merocyanine chromophore,and the 370 nm band can be attributed to a charge-transfer transition from theoxygen atom of the benzopyran ring to the electron-accepting nitro substituent[27,28].

lig

ht

da

rk

A

Figure 14.9 Reverse photochromic reactions of spiropyran salts (see Fig. 14.7)

Considering the acidity of HFP, the band at longer wavelengths should beassigned to the zwitterionic ring-opened form II (Figure 14.9), whereas the bandat shorter wavelengths might be assigned to the presence of the ring-openedspecies III formed between the zwitterionic species and HFP, with this last actingas an acid (pKa = 9.30) [29] (shown in Figure 14.9). In the polymers, protonationof the open form by unmodified COOH side chains may also occur [27], eventhough this effect cannot play a relevant role in the 85 mol% modified polymershown in the figure. The presence of a well-defined isosbestic point shouldindicate only two interconverting species. However, the salt of the spiropyranwith trifluoroacetic acid exibits exactly the same isosbestic point (see the follow-ing section), so that one cannot exclude the presence of both the zwitterionic andthe protonated merocyanine forms.

14.2.2.2 Photomodulation of Conformation

The CD spectra of the dark-adapted samples of poly(Gluj bearing 85 mol%photochromic units are those of random coil polypeptides. CD bands of smallintensity are also present in the near UV-visible region, in correspondence withthe merocyanine electronic transitions. The solutions bleached after exposure tovisible light display the typical pattern of the a-helix, with the two minima at 222and 208 nm, thus indicating that the isomerization of the side chains producesspiralization of the main chain. The back reaction in the dark is accompanied bya progressive decrease of the helix content and restoration of the originaldisordered conformation (Figure 14.10).

The photoinduced helix content can be only approximately estimated on thebasis of the CD spectra. In fact, several polypeptides, all having a-helical

dark

light

Figure 14.10 Effect of irradiation and dark adaptation on CD spectra of poly(L-glutamicacid) bearing 85 mol% spiropyran units in HFP at 25 0C: 1, kept in the dark; 2, exposed tosunlight; dotted lines are CD spectra recorded during decay in the dark over 8h. Below250 nm, CD data are expressed in terms of molar ellipticity based on the mean residuemolecular weight; above 250 nm, the molar ellipticity is referred to one spiropyran-glutamyl residue

conformation, were reported [30] to show significant variations of the maximumellipticities when CD spectra were measured in HFP. On the basis of theliterature values [30] of [ G ] 2 2 2 ( - 3 0 0 0 0 — 40000) for 100% a-helix in HFP,the photoinduced helix content can be evaluated as 90-70%.

The photochromic reaction involves the reversible conversion of the zwit-terionic merocyanine (sample kept in the dark) to the uncharged spiro form(sample exposed to light); the isomerization is thus accompanied by largevariations of the electrostatic interactions among the side chains of the polypept-ides. Intrachain interactions should produce loops in the macromolecules,whereas intermolecular stacking should produce aggregation phenomena. As

lig

ht

da

rk

a result, the macromolecules are forced to adopt a disordered structure. When thesample is exposed to light and merocyanines are converted to the neutral spiroform, electrostatic interactions are removed and the polypeptide can adopt thea-helix structure.

When spiropyrans are treated with acids they are converted into 'spiropyransalts', which exhibit photochromic behavior differing from that of the parentspiropyran compounds. The gross mechanism proposed is illustrated in Fig-ure 14.9. In the dark at room temperature, the compounds give colored solutionsdue to the presence of the O-protonated merocyanine species III. The open formis converted by irradiation with visible light to the iV-protonated spiro form IV.As spiropyrans are fairly strong bases in the open form but very weak bases in theclosed spiro form, the charged species IV can lose a proton and the neutral speciesI can be actually formed.

Comparison of Figure 14.9 with Figure 14.7 shows that different photo-isomers are involved in acidic or non-acidic solution. Therefore we may expectspiropyran-containing polypeptides to be affected by light in a different waydepending on whether they are irradiated in the absence or in the presence of acid.Poly(spiropyran-L-glutamate) in HFP solution in the presence of TFA does notgive light-induced conformational changes. Actually, the solutions show thetypical CD spectra of random coil polypeptides both when they are kept in thedark and when they are exposed to light.

The addition of methanol as a cosolvent induces the coil -> helix conforma-tional transition, as for other polypeptides having salified side chains [31]. Themost remarkable aspect of this system is that two distinct curves are observed forthe dark-adapted sample and for the irradiated one (Figure 14.11). In particular,for the polymer containing 85mol% photochromic units, the concentration ofmethanol needed to induce the conformational transition is « 10-40% for thesample kept in the dark and « 5-10% for the sample exposed to light. Therefore,at any solvent composition in the range between the two curves, exposure to lightproduces reversible variations of the helix content (Figure 14.12).

The photochromic reactions schematized in Figure 14.9 and the above dis-cussed absorption spectra allow us to explain the conformational behavior. InHFP, in the presence of TFA, the photochromic side chains are protonated by theacid either when the sample is kept in the dark (photochromic units present asopen species III) or when the sample is exposed to light (photochromic unitspresent as closed species IV). In both cases the polypeptide is essentially a polyca-tion, so the repulsive forces among the side chains make the macromoleculesadopt an extended coil conformation, and no photoresponse is observed.

In the presence of methanol (> 10%) the equilibrium between the two colorlessspecies IV and I (Figure 14.9) is shifted toward the neutral spiro structure I. Inthese conditions the 'folding-unfolding' of the macromolecules is photocontrol-led by the isomerization of the photochromic units. In the dark, they are presentas charged species, so the macromolecules adopt a disordered conformation.

Figure 14.12 Effect of irradiation on CD spectra for poly(Glu) containing 85 mol%spiropyran units at 25 0C in various HFP/MeOH/TFA solvent mixtures (c = 2.59 x10" 2 g/1; TFA = 1 x 10" 3 ml in 2 ml of mixed solvent); MeOH % (v/v): (a) 0-5%; (b) 10%;(c) 20%; (d) 40%. ( ), dark-adapted; ( ) irradiated samples

dark

ligh

t

Figure 14.11 Variation of ellipticity at 222 nm as a function of methanol concentration(v/v) for poly(Glu) bearing 85mol% spiropyran units in HFP/MeOH/TFA solventsystem, at 25 0C: ( ) dark-adapted sample; ( ), irradiated sample

MeOH,%

m e r o c y a n i n e f o r m , %

Figure 14.13 PoIy(GIu) bearing 85 mol% spiropyran units. a-Helix relative variation asa function of spiropyran/merocyanine isomeric composition of the side chains, in pureHFP ( ) and HFP/MeOH/TFA = 90/10/5 x 10 "2 ( ). The a-helix variation in% was estimated as {[@]V[©]°} x 100, where [0]° and [ 0 ] ' are the ellipticity valuesmeasured at 222 nm at the beginning and at the time t during decay, at 25 0C

Exposure to light and the consequent photoconversion of the side chains to theapolar spiro form make the macromolecules adopt the a-helix conformation.

In order to investigate the dependence of the secondary structure on theisomeric composition of the photochromic side chains, the rate of the helix-to-coil conversion and the rate of appearance of absorbance at the longerwavelength in the dark were measured simultaneously. The helix content wasthen plotted as a function of the photochromic units present in the merocyanineform (Figure 14.13). In pure HFP (Figure 14.13, dotted line), the helical structurestarts to break up rapidly as soon as the merocyanine species begin to be formed,and the helix -* coil conformational change takes place almost entirely followingconversion of % 30% of spiropyran to merocyanine groups. A rather differentbehavior is observed in HFP/MeOH/TFA (Figure 14.13, full line): the helixcontent decreases slowly with increasing merocyanine percentage, but the helicalstructure does not collapse until « 50% of the spiro groups are isomerized to themerocyanine form.

The different dependence of the helix structure on the percentage of photo-chromic groups present in the merocyanine form is a confirmation that denatura-tion of the macromolecules in the dark occurs through different mechanisms innon-acidic and acidic media. In the former case denaturation should be caused by

a-h

elix

v

ari

ati

on

, %

stacking and aggregation between zwitterionic merocyanine species II. In thelatter case, denaturation should be caused by repulsive forces among the cationicside chains III. In both cases, exposure to light removes the electrostaticinteractions between side chains, allowing the formation by the polypeptidechains.

Also poly(Lys)-containing spirobenzopyran side chains, as well as low molecu-lar weight model compounds, exhibit intense 'negative' photochromism in HFP[25]. In the dark the solutions are orange, with two absorption maxima at«470nm (£mol = 31700) and 370 nm (emol = 32 000). Exposure to sunlight isaccompanied by prompt bleaching, with a shift of the absorption maxima to353 nm (emol = 11200) and 270-272 nm (emol = 16 200). The original spectrum isreversibly restored when the illumination is stopped. Decay in the dark at 25 0Cfollows first order kinetics for the model compounds, with a rate constant of5.7 x 10"3min"1 and a half-life of «122min. For the polymer, the kineticsdeviate slightly from monoexponential and biexponential decay; the time necess-ary to restore half of the original absorbance is « 80 min.

The analogy of these reversible processes with those observed in spiropyran-modified poly(Glu) suggests the occurrence of similar photochromic reactions.Accordingly, HFP stabilizes the colored ionic merocyanine structure, whileirradiation gives the colorless spiro structure.

In pure HFP, the CD spectra are consistent with those of random coilpolypeptide chains, and the photoisomerization reaction does not affect thepolymer conformation at all. Addition of triethylamine to the HFP solutioninduces the coil-•helix transition, but the amount of base necessary to inducethe transition is different for the dark-adapted sample (15% v/v) than forthe irradiated one (30% v/v). Thus, at any composition in the range 3-15%v/v of NEt3, exposure to sunlight produces reversible variations of the helixcontent. Combination of the effects due to the photochromic behavior withappropriate amounts of NEt3 allows modulation of the extent of the photo-response.

It appears that in pure HFP the conformation for poly(Lys)-containingspiropyran is determined by the unmodified Lys side chains protonated by theacid solvent; as a consequence, the polypeptide assumes a coil conformationwhich is not affected by the isomerization of the photochromic groups. Additionof a moderate amount (3-15%) OfNEt3 removes protons from Lys side chains,whose basicity depends on isomeric composition of the photochromic moieties.In the range between the transition curves of the dark-adapted and the irradiatedsample, the chain folding ;=± unfolding is then controlled by the isomerization ofthe photochromic side chains: when these are in the charged merocyanine form,the polypeptide chains are in the random coil arrangement, but photoconversionto the apolar spiropyran form causes the macromolecules to assume a helicalconformation. At NEt3 contents above 15%, the high concentration ofa NEt3 • HFP saline complex can probably exert a shielding effect on the charged

side chains, allowing the polypeptide to stay in the helical conformation at anyphotoisomeric composition.

The system described provides a well defined example of the combined actionof light and environment on the secondary structure of polypeptides. It can thusbe considered as a macromolecular model resembling the behavior of naturallyoccurring photoreceptors [32].

14.2.2.3 Photoinduced Variations of Viscosity

The colored solutions of poly(L-glutamic acid) and poly(L-lysine) containingspiropyran, when kept in the dark, are characterized by very high values ofviscosity, typical of those displayed by polyelectrolytes. The viscosity decreasesdramatically upon exposure to sunlight and returns to the original value alongwith the reappearance of the absorption in the visible region.

In order to correlate viscosity changes with conformational changes, samplesof photochromic polypeptides were exposed to light, then the viscosity and theCD spectra were measured over time in the dark. Viscosity progressivelyincreases with the gradual decrease of the helix content for both spiropyran-containing poly(L-glutamic acid) (Figure 14.14) and poly(L-lysine) (Figure 14.15).The high viscosity of the solutions in the dark is essentially due to the side chains,which are charged when macromolecules are in disordered conformation. Inthese conditions the polypeptides are able to coordinate many solvent moleculesto give highly solvated an extended macromolecules with a large hydrodynamic

a-h

eli

x v

ari

ati

on

,%

t i m e , m i n

Figure 14.14 PoIy(GIu) bearing 85mol% spiropyran units. a-Helix content ( ) andviscosity ( ) variation during decay in the dark at 25 0C. HFP solutions were irradiated,then dark adapted and monitored over time. The percentage of a-helix variation isestimated as indicated in Figure 14.13

t i m e , m i n

Figure 14.15 Helix content ( ) and viscosity ( ) variation during decay in the darkfor poly(Lys) bearing 46 mol% spiropyran units, in HFP/NEt3 = 94/6

volume, thus exhibiting high values of viscosity. Aggregation phenomena,through interactions between merocyanine side chains, can also contribute toviscosity increases. From the figures it appears that viscosity keeps on increasingeven when the a-helix is completely destroyed. In fact, the helix is fully destroyedby conversions of the spiro to the merocyanine form of « 60%, (Figure 14.13), butthe macromolecules go on expanding until conversion to the merocyanine formreaches 100%.

14.3 REFERENCES

[1] (a) M. Farina, Chim. Ind. (Milan), 1986, 68, 62; (b) M. Farina, Top. Stereochem.,1987,17,1.

[2] P. Pino, Adv. Polym. ScL, 1965,4, 393.[3] F. Ciardelli, M. Aglietto and G. Ruggeri, in M. Fontanille and A. Guyot (Eds.),

Recent Advances in Mechanistic and Synthetic Aspects of Polymerization, Reidel,Dordrecht, 1987, p. 409.

[4] G. Natta, Makromol. Chem., 1960,35,94.[5] P. Pino, F. Ciardelli and G.P. Lorenzi, J. Polym. ScI, Part C, 1963, 4,21.[6] P. Pino, F. Ciardelli and M. Zandomeneghi, Annu. Rev. Phys. Chem., 1970, 21,

561.[7] F. Ciardelli and P. Salvadori, Pure Appl. Chem., 1985,57,931.[8] E.R. Blout, in F. Ciardelli and P. Salvadori (Eds.), Fundamental Aspects and Recent

Developments in ORD and CD, Heyden, London, 1973, Chs. 4 and 5.

a-h

elix

va

riat

ion

,%

[9] P.L. Luisi and F. Ciardelli, in A.D. Jenkins and A. Ledwith (Eds.), Reactivity,Mechanism and Structure in Polymer Chemistry, John Wiley & Sons, New York,1974, p. 471.

[10] P.L. Luisi and P. Pino, J. Phys. Chem., 1968,72,2400.[11] P. Pino, F. Ciardelli, G.P. Lorenzi and G. Montagnoli, Makromol. Chem., 1963,61,

207.[12] F. Ciardelli, P. Salvadori, C. Carlini and E. Chiellini, J. Am. Chem. Soc, 1972, 94,

6536.[13] W. Hug, F. Ciardelli and I. Tinoco, Jr, J. Am. Chem. Soc, 1974,96, 3407.[14] F. Ciardelli, C. Righini, M. Zandomeneghi and W. Hug, J. Phys. Chem., 1977, 81,

1948.[15] F. Ciardelli and O. Pieroni, Chimia, 1980, 34, 301.[16] F. Ciardelli, O. Pieroni, A. Fissi and J.L. Houben, Biopolymers, 1984,23, 1423.[17] A. Fissi, O. Pieroni and F. Ciardelli, Biopolymers, 1987, 26,1993.[18] O. Pieroni, D. Fabbri, A. Fissi and F. Ciardelli, Makromol. Chem., Rapid. Commun.,

1988,9,637.[19] B.R. Malcolm and O. Pieroni, Biopolymers, 1990, 29,1121.[20] O. Pieroni, A. Fissi, J.L. Houben and F. Ciardelli, J. Am. Chem. Soc, 1985,107,2990.[21] M.M. Long and D.W. Ury, in E. Grell (Ed.), Membrane Spectroscopy, Springer-

Verlag, Berlin, 1981, pp. 143-171.[22] P. Bayley, in S.B. Brown (Ed.), An Introduction to Spectroscopy for Biochemists,

Academic Press, London, 1980, pp. 148-234.[23] A. Fissi and O. Pieroni, Macromolecules, 1989,22,1115.[24] F. Ciardelli, D. Fabbri, O. Pieroni and A. Fissi, J. Am. Chem. Soc, 1989, 111, 3470.[25] O. Pieroni, A. Fissi, A. Viegi, D. Fabbri and F. Ciardelli, J. Am. Chem. Soc, 1992,114,

2734.[26] N.W. Tyer, Jr, and R.S. Becker, J. Am. Chem. Soc, 1970,92,1289.[27] T.M. Cooper, K.A. Obermeyer, L.V. Natarajan and R.L. Crane, Photochem. Photo-

biol., 1992,55,1.[28] A.S. Kholmanskii and K.M. Dyumaev, Russ. Chem. Rev. (Engl. TransL), 1987, 56,

136.[29] WJ. Middleton and R.V. Lindsey, Jr., J. Am. Chem. Soc, 1964,86,4948.[30] (a) J.R. Parrish, Jr., and E.R. Blout, Biopolymers, 1971,10,1491; (b) R.W. Woody, J.

Polym. ScL, Macromol. Rev., 1977,12,181.[31] (a) M. Satoh, Y. Fujii, F. Kato and J. Komiyama, Biopolymers, 1991,31, l;(b) R.F.

Epand and H. Scheraga, Biopolymers, 1968, 6,1383.[32] B.F. Erlanger, Annu. Rev. Biochem., 1976,45,267.

15 POLYMER LUMINESCENCEAND PHOTOPHYSICSD. PHILLIPS and M. CAREYDepartment of Chemistry, Imperial College, London SW7 2AY1 UK

15-1 INTRODUCTION

Ultra-violet and visible light-absorbing chromophores in synthetic polymersmay be present due to adventitious impurities such as oxidation products,termination residues or initiator fragments (type A), or be present in the repeatunit and thus be in high concentration (type B). Many simple synthetic polymerssuch as poly(ethylene) and poly(propylene) in a pure state will exhibit only o-a*absorptions in the high-energy UV region, where most organic molecules absorb.Such excitations in general lead to photochemical reactions rather than lumines-cence, and excited states will thus be very short-lived. Here we focus attentionarbitrarily on species that absorb in the spectral region from 250 nm to longerwavelengths, where luminescence may be an additional fate of photoexcitedspecies, which are depicted in Figure 15.1, for a typical organic chromophore.

The many studies carried out on luminescence in synthetic polymers have beenmotivated by a wide range of scientific and technological aims. Some of the moreobvious are categorized below [1,2].

(a) F undamental interests: these include studies on the nature of photoemis-sion from polymers of type B, in which interchromophoric interactions are ofspecial interest.

(b) Luminescence of probe molecules: these studies permit the evaluation ofpolymer properties. In particular, measurement of the relative intensities offluorescence of a probe molecule polarized parallel to and perpendicular to theplane of linearly polarized exciting radiation as a function of the orientation ofa solid sample yields information concerning the ordering of polymer chains. Insoultion, similar polarization studies yield information on the rotational relax-ation of chains and the viscosity of the microenvironment of the probe molecule.The study of luminescence intensity of probe molecules as a function of tempera-ture has been used as a method of studying transition temperatures and sub-group motion in polymers.

(c) Luminescent species in polymer photooxidation: the problems associatedwith establishing a mechanism for the photooxidation and weathering of syn-Polymer Spectroscopy. Edited by Allan H. Fawcett© 19% John Wiley & Sons Ltd

Figure 15.1 Jablonskii state diagram depicting the fates of photoexcited polyatomicmolecules

thetic polymers are great, and any method that provides additional informationis useful. In addition to traditional methods such as product analysis, infraredspectroscopy (both conventional and ATR) and U V-visible absorption spectros-copy, luminescence methods have been employed.

(d) Identification of polymers: luminescence spectroscopy can provide a con-venient method for rapid identification of some synthetic polymers.

We will cite here a few classic examples of studies in the various categories,using steady-state measurements.

15.2 PROBES OF ORDER IN POLYMERS

Physical properties of polymers are often altered significantly by preferentialorientation of structural units by drawing or some other means. The degree ofanisotropy thus introduced requires measurement if correlation between struc-ture and physical properties is to be established. There are a number of methodsavailable for the measurement of such anisotropy, including wide-line NMR,optical birefringence, X-ray scattering, light scattering, Raman spectroscopy,

Vibrationalrelaxation

lntersystemcrossing


Internalconversion

lntersystemcrossing


Internalconversion

lntersystemcrossing

S-S

ab

sorp

tion

Ab

sorp

tion

T-T

ab

sorp

tion

Ph

osp

ho

resc

ence

Flu

ore

scen

ce

infrared dichroism and fluorescence polarization. The methods are not allequivalent in the type of information they provide, but when used simultaneouslyon the same sample they can yield complementary data. Thus, for example,birefringence is sensitive to the orientation of both the amorphous and thecrystalline units, whereas X-ray scattering reveals the orientation of crystallitesonly. Raman methods can probe much more local order than X-ray techniques.In principle it is desirable to have knowledge of the complete distributionfunction in a sample, but X-ray diffraction is currently the only method that canbe used for this purpose. However, the majority of physical properties dependonly upon the second moment of the orientation distribution, although mechan-ical properties such as Young's modulus depend also upon the fourth moment.The latter information is available from both wide-line NMR and fluorescencepolarization measurements. Experimentally the fluorescence polarization

Figure 15.2 Intensity of parallel component of fluorescence, I, as function of orientationof sample in uniaxially stretched poly(vinyl alcohol) film at draw ratios of (1) 1, (2) 1.08, (3)1.3, (4) 1.6, (5) 2.0, and (6) 5.0 (after figure in J. Polym. ScI, Polym. Symp., 1970,31, 353

measurements are simple, in that a rigid polymer sample in which fluorescentmolecules are dispersed or chemically attached is excited in a spectrofluorimeterwith (usually) vertically plane-polarized light. Measurements of the fluorescenceintensity of the probe with the analysing polarizer parallel (J1) and crossed (J1)with the excitation polarizer are taken as a function of the orientation of thesample with respect to the vartically polarized excitation radiation; that is, plotsare made of the components J11 and J1 as a function of physical ratation ofa sample through 360°. The intrinsic probe, which must be a long molecule, isassumed to align with the fibres in a material.

A typical plot is shown in Figure 15.2, in which the anisotropy introduced bydrawing is clearly illustrated. [3] The method can be used to distinguishorientations which correspond to different arrays which nevertheless have ident-ical orientation functions.

15.3 PROBES OF SUB-GROUP MOTIONS

Phosphorescence may be used as a probe of sub-group motion in syntheticpolymers, particularly be studying the temperature dependence of the emission ofan intrinsic probe. Using probe naphthalenes (or ketones), a wide variety ofpolymer films have been studied in which, over the temperature range 3OO-77K,the intensity of phosphorescence from the probe was found to vary by up to fourorders of magnitude [4]. This is illustrated in Figure 15.3; for a series of styrenepolymers with emitting comonomers, the temperature dependence showed dis-tinct linear regions with at least one common discontinuity (for each polymertype) in the slope within a narrow temperature region. These discontinuitiescoincided well with the known y-transition temperatures and secondary transi-tion temperatures for each of the polymer types investigated. The conclusion ofthis study was that the phosphorescence decrease with increasing temperaturewas not due to temperature dependent intramolecular decay or 'intermoleculardeactivation' but could be best explained in terms of the increasing accessibility ofthe excited chromophore to molecular oxygen. The observed temperatures ofdiscontinuity were explained in terms of the several possible structural relax-ations, and in general the observed temperatures were in good agreement withresults from other relaxation measuring techniques.

15.4 PHOTOCHEMISTRY IN POLYMERS

The vast literature on photopolymerization and cross-linking makes this subjectimpossible to attempt within the scope of this brief review. Photochemical effectsof formed polymers are dominated by photooxidation processes summarized in

Figure 153 Plots of In /p (J? = phosphorescence intensity) against inverse temperaturefor styrene polymers. Transitions corresponding to Ty and other sub-group motions arevisible (after figure in Macromolecules, W)% 7, 233).

Figure 15.4, which also depicts the means available to protect polymers againstthe effect of light. These are the use of UV absorbers, A; quenchers of excitedstates, B; radical scavengers, C; singlet oxygen scavengers, D; or destroyers ofhydroperoxide, E.

Figure 15.4 Mechanism of photo-oxidation and stabilisation of commercial polymers

15.5 EXCIMER-FORMING POLYMERS [5]

In type B polymers, the structural constraints of the polymer chain tend toconfine the chromophores in spatial positions such that they can be expected toexhibit strong mutual interactions. These may depend strongly upon the relativeorientation of the interacting chromophores, and the orientations themselves willusually be dependent upon the conformation of the polymer chain. Interactionbetween the excited state chromophore and a neighbouring ground state can giverise to excimer (excited dimer) formation, which proves to be a powerfuldiagnostic of interacting molecules.

The salient features of excimer formation are represented in Figure 15.5.Aromatic molecules at large separations, that is at separations much greater than4 A, may be considered as isolated entities. Consequently, if the aromaticmolecules are in an excited state, the fluorescence is unaffected by the presence ofother molecules. For small separations, less than 4 A, repulsive potentials R(r)and R'(r) will exist between molecules in their ground state and between mol-ecules in the ground and the excited state. In general, the existence of theserepulsive potentials prevents the formation of complexes. However, for theinteraction between ground and excited state molecules, an attractive potentialV(r) may be obtained, owing to configurational interaction between resonanceand exciton-resonance states. The combination of repulsive and attractivepotentials may form the excimer state shown by the potential well in Figure 15.5.The fluorescence from the 'excimer' state will thus be unstructured (since a corre-

MOLECULARDISSOCIATION

QUENCHERMETALDEACTIVATORPEROXIDEDECOMPOSER

UV-ABSORBER

QUENCHER RADICAL SCAVENGER

ROOH

* •

ROO,RO #

«'•

Figure 15.5 Energy diagram for excimer formation

sponding ground state complex does not exist) and at a lower energy than thecorresponding monomer emission. In general, excimer formation can occurwhenever aromatic chromophores adopt a face-to-face coplanar arrangementwith a separation of 0.3-0.35 nm, as shown for naphthalene in Figure 15.6.

Static measurements of intensities of monomeric fluorescence (here defined asthat from an uncomplexed chromophore attached to the polymer chain) relativeto that from the excimer can be used to yield information relating to energytransfer and migration, rotational relaxation and segmental motion, and to theheterogeneity of synthetic polymers and copolymers in solution and solid forms.Results of technological importance are available. Thus, in blends of polymers,such measurements have been used to investigate compatibility [6, 7].

fluor

esce

nce

inte

nsity

ener

gy

15.6 DYNAMICS OF LUMINESCENCE

The processes of depletion of excited-state population in Figure 15.1 lead fofluorescence decay times which may be 10 " 8-10 " *2 s or less. Molecules may thusprovide a 'clock' over this range with which to time other processes which are

Figure 15.6 Excimer formation in a naphthalene-containingmolecule

Spontaneous radiative transitions

lntersystem crossing (S1-T1)

Internal conversion (Sn - SnJ

Vibrational redistributionand isomerization

Field-induced transitions

Coherent exciton

Exchange transfer

Resonance (Forster) transfer

Rotational diffusion (1 cp)

Diff usional encounter (1 cp)

Vibrational relaxation

Geminate recombination

Chemical reaction

Typical Q-switched laser,excimer, N2 pulse duration

Typical picosecondlaser pulse duration

Shortest laser pulseyet produced

Limit of photon-countingstreak camera detection

Figure 15.7 Some physical and chemical processes which occur on the 10~6-10~l5stime scale

Figure 15.8 Time-correlated single-photon counting spectrometer based on CW mode-locked Nd: Y AG laser

subject to environmental influence, such as diffusion, energy transfer and migra-tion, etc., as shown in Figure 15.7 [8,9].

For fluorescence measurements, by far the most versatile and widely usedtime-resolved emission technique involves time-correlated single-photon count-ing [8] in conjunction with mode-locked lasers, a typical modern apparatusbeing shown in Figure 15.8. The instrument response time of such an apparatuswith microchannel plate detectors is of the order of 70 ps, giving an ultimatecapability of measurement of decay times in the region of « 7 ps. However, it isthe phenomenal sensitivity and accuracy which are the main attractive features ofthe technique, which is widely used for time-resolved fluorescence decay, time-resolved emission spectra, and time-resolved anisotropy measurements. Beloware described three applications of such time-resolved measurements on syntheticpolymers, derived from recent work by the author's group.

15.7 FLUORESCENCE DECAY IN VINYL AROMATICPOLYMERS

Fluorescence in such polymers is dominated by excimer formation, the simplestkinetics for which were described by Birks and co-workers [10,11] (Scheme 1). In

Multichannelanalyser

PC/ATcomputer TAC/SCA

Time-to-amplitudeconverter/singlechannel analyser

X100 Amplifier

CFTD

CFTD

MicroChannelplate

Constant fractiontiming discriminator

rfout

FilterTiming filteramplifier

sync out

out

Cavity dumperdriver

Mode-lockerdriver

syncrfout

KTPCavitydumper

Fast photodipde

SampleKDP

Harmonicseparator

Secondharmonic generator

Harmonicseparator

Secondharmonic generator

Scheme 1 Birks kinetic scheme

this treatment the influences of diffusion or energy migration are neglected, andonly the two chromophores directly involved in the excimer formation processare considered. In Scheme 1, M refers to the ground state monomer species, 1M*to the monomer in its first excited singlet state and 1D* represents the excimer; kM

is the molecular decay rate, which is the rate of depopulation of * M* by radiativeor non-radiative decay in the absence of other chromophores or intra-molecularchemistry; kD is the rate of radiative and non-radiative decay of the excimer; fcDM isthe rate of formation of excimer from monomer, and kMD is the rate of dissociationof the excimer to recreate the excited monomer.

Equations for the monomer and excimer population are then as follows:

[1M*] = -̂ ^ [ (A 2 -J0exp( -A , t ) + (X-A1)exp(-A2t)] (D

[»D*] = kD^ll.^*\cxp(- A l t)exp(- A2t)] (2)[A2 ~ ^V

where X9 A1 and A2 are functions of the rate parameters fcM, fcD, fcMD and /cDM, viz:

X = kM + /cDM[M] (3)

A1 = 1/2(Z + kD + kM - {(kD + fcM - X)1 + 4fcMD/cDM[M]}1/2) (4)

A2 = 1/2(Z + kD 4- /cM + {(kD + fcM - X)2 +4fcMD/cDM[M]}1/2) (5)

It can be seen from Equations (1) and (2) that the monomer and excimer decaysare both the sum of exactly two exponential decay terms, with the same lifetimesA1 and A2 appearing in both monomer and excimer decays. In addition, the twopre-exponential factors in the excimer decay are of equal magnitude but oppositesign. However, except to a first approximation, neither of these characteristics isusually seen experimentally in polymers [12-14] where, typically, the monomerand excimer decays will give different values OfA1 and A2 and the excimer decaywill not have pre-exponential factors of equal magnitude. As real polymer decaysdo not follow the Birks kinetic scheme, the scheme evidently does not takeaccount of all the photophysical processes which occur in polymers, and efforts toimprove the models have been made in two main directions. The first approach

has been to parameterize the deviations from Birks kinetics using a thirdexponential decay term in both the monomer and excimer decays. The third termcan then be interpreted in a number of ways, such as the existence of a thirdspecies. In fact, if all the photophysical processes occurring in the polymer aretime independent, i.e. can be expressed by a simple rate constant in a kineticscheme, then the existence of a third species is the only conclusion that can bedrawn from a third decay term. Some of the models proposed, and which havebeen successful in explaining polymer fluorescence decays, are as follows:

(1) two monomer species, the first one able to form the second, but only thesecond one able to form excimers [15,16];

(2) two monomer species, one of which can be formed only by dissociation ofexcimers, and cannot reform excimers [15,16];

(3) three excimer species, two of which are in equilibrium, the third beingformed only from the monomer [17-19].

The multi-exponential approach has been criticized on the grounds that thekinetic schemes are not unique: data which are consistent with two excimers mayalso be consistent with a second type of monomer [20]. Also, there is rarelysupporting spectroscopic evidence for the presence of a third species, whichwould be expected to have a different emission spectrum. However, except in thecase of poly(vinylcarbazoles) [21-24], no such evidence has been found.

15.7.1 DIFFUSIONAL MODELS

The second approach to the study of excimer kinetics has been more theoretical.In experiments on dilute solutions of unlinked chromophores, there has beensome success in considering the process of excimer formation as a diffusiveprocess [25]. Nemzek and Ware [26] used an extension of the Smoluchowskiequation [27] devised by Collins and Kimball [28], which gives for Jt(̂ DM

k(t) = 4TIDABR'N( 1 + R ) (6)

The Birks kinetic scheme can then be adjusted to include k(t)DM. Because of thecomplexity involved, the rate constant /cMD is usually neglected at this stage. Thepopulation of the monomer excited state then has the time dependence ofEquation (7):

[1M*] = [1M^]0 exp[ -(fcM + 4nDABR'Nt)- *' t1'2] (7)

Consider now the diffusion of excitation through an array of monomers. Theexcited state moves along the polymer chain from one monomer to another,probably by the Forster dipole-dipole mechanism, but other energy transfer

mechanisms such as the Dexter electron exchange mechanism may also playa part, especially in solid polymers, where the chromophores are very closetogether. The excitation may be trapped at any chromophore by formation of anexcimer. A number of different models have been used to consider the timeevolution of an excited state which may migrate to a trap site, and often severaldifferent approaches are used to approximate the observable parameters for eachmodel.

A review of these complex mathematical models is beyong the scope of thispaper, but they can be summarized as follows.

15.7.1.1 Random Walk Migration, Evenly Spaced Chromophores

This model has been investigated ]by a number of groups and solved approxi-mately using several different methods. Huber [29] solved the rate equations forthe donor (monomer) decay using the t-matrix approximation, resulting inEquation (8) for the one dimensional case.

[M*] = A exp(4n2qWt)erfc(2nqW1/2tl/2) (8)

In the asymptotic limit, i.e. for long times, the decay can be approximated byEquation (9); however, when the number of trap sites is sufficiently small, thedecay reduces to an exp — (at + btlf2) dependence similar to Equation (7)

[ M * ] = ( W W * (9)

In addition to the Mnatrix approximation, however, a various methods havebeen used to solve the deep trapping problem which has been solved exactly in theone dimensional case [30]. Movaghar et al. compared the coherent potentialapproximation (CPA) [31] and the first passage time approach (FPT) [32]results with the exact solution while stating that the Mnatrix approximation usedby Huber is less accurate than the CPA under all conditions. Movaghar et al.[30] [31] found that the FPT approach is superior to the CPA at all trapconcentrations except for very high concentrations approaching 1, where allchromophores are traps. At long times the FPT approach gives a solution whichasymptotes to exp — (ati/2)9 similar to the low trap concentration Mnatrixderived result. By contrast, the exact result asymptotes to exp — (at1/3).

15.7.1.2 Random Walk, Random Distribution Chromophores

A second, more complex model which can approximate energy migration kineticsinvolves the relaxation of the condition that there must be an even distributionof chromophores. Such a relaxation can involve, say, a random distribution ofchromophores in three dimensions interspersed by a random distribution oftraps. The GAF [34] and LAF [35] models are of this type and, in addition,

a model has been derived for polymers (FAF) [36] which relates fluorescencedecay parameters to the radius of gyration of the polymer.

15.7.1.3 Multiple Trap Energies

A further complication is to consider the disorder of the energies of the monomerexcited states as well as positional disorder. In a polymer, the chromophoresare in a range of environments, each of which will have different energies. Thisproblem has been treated theoretically [37] and in a Monte-Carlo simulation[38], both giving an approximate relationship of the form of Equation (10):

mv* = b + cf-1 (10)

More recently, the problem of energetic disorder has been considered byStein et al. [39], who treated the combination of energy migration and trappingas part way between donor-donor transfer and direct trapping of the excitation.The theory agreed well with some of their experimental polymer anisotropydecays.

15.7.1.4 Reversible Excimer Formation

In the Birks kinetic scheme, back-transfer is considered simply by the rateconstant fcMD. Weixelbaumer et al. [40] used an approximate method to ap-proach this, whereas Sienicki and Winnick [41] derived an exact result, andposed the question, what happens if monomers formed by back dissociationbehave differently from those excited directly? The question was answered byBerberan-Santos and Martinho [42], who showed that k(t)DM does not necessar-ily decrease monotonically but can sometimes increase with time.

15.7.1.5 Diffusion of Energy and Chromophore

Baumann and Fayer [43] considered a two-body problem in which diffusion andenergy transfer occurred simultaneously. Frederickson and Frank developeda simpler one dimensional array model [44].

The equation for the rate of monomer fluorescence in the FF model is given byEquation (11):

W ) = 4FMM1 " q)2 expl(4n2q2W-kM - *rot)fj crfc(2nqW1^2) (11)

In Equation (11), iM(r) is the intensity for fluorescence from the monomer,which is related to the monomer concentration by the monomer quantum yield offluorescence q^ arid the rate of decay of the monomer fluorescence in isolationfcM; q is the pre-formed trap fraction, which is the fraction of dyads which are trapsites at equilibrium; W is the rate of energy transfer between nearest neighbours

on the polymer, which is of course highly dependent on the distance between thechromophores.

Tao and Frank [45] found that 2-vinylnaphthalene homopolymer fluores-cence decays fit the FF model under conditions of relatively low temperature.However, they noted that at higher temperatures the model breaks down,probably because of the breakdown of one of the assumptions below:

(1) that the polymer may be considered as a one-dimensional string of equallyspaced chromophores;

(2) that the primary excimer forming step is energy migration, and not internalrotation. This requires that there are a number of 'pre-formed trap sites' in theground state, which just means that there must be a number of sites wherechromophores are in high-energy configurations which are very close to theexcimer configuration, or else there must be a low-energy conformation veryclose to the excimer conformation;

(3) that the number of these 'pre-formed trap sites' is low. For this concentra-tion of trap sites, the r-matrix approximation becomes poor;

(4) that the excimer formation step is irreversible.We have extended the FF model to high trap concentrations using the FPT

approximation. In this, the expression for the monomer fluorescence intensity isgiven by Equation (12), and that for excimer fluorescence by Equation (13):

'M(0 = <ZFMM1 -<?)2exp(— -q ['2WU 0(2W T)+ I1VWT)] exp(-2WT) <1T)\ T Jo /

(12)

*E(0 = <?FMkEexp(-fcEt) - ^ F E M 1 - <?)2

x expU^-g I 2Wexp(-2WT)[I0(2WT)]+ I1(HVT)IdT)

-qFEkE(kM-kE)(l-q)2[texp(-u(kE-T-1)- — -q[t "2WJo V T Jo

x exp(-2WT)lI0(2WT) +I^WTftdTjdu (13)

We have tested some of the above models using data from careful time-resolved fluorescence measurements on 1-vinylnaphthalene homopolymer, andcopolymers with methyl methacrylate, in the following way. The FF modelappears to have five variables, the amplitude, the isolated decay rate fcM, the rateof rotation fcrot, the rate of intramolecular energy transfer W, and the number oftrap sites q. However, some of the variables cannot be treated independently andthe FF function may actually by rewritten using only three variables. This is doneby substituting, say, r = l/(feM + krot) and Q = q W1/2 into Equation (11) to giveEquation (14), and fitting the data by varying only the amplitude, t and W. In fact,

if an attempt is made to fit the function while varying all of fcM, krov q andW simultaneously, all solutions with the same t and Q will fit the data equallywell. So the FF model actually has only three variable parameters, which is onefewer than the sum of two exponential decay terms.

iM(0 = A exp[(4jT2<22 - t)r] erfc(27rQt1/2) (14)

The efficacy of the FF model was investigated over the range of naphthalenemole fractions. At 290 K, fluorescence from the 25% 1-vinylnaphthalene polymerfits the FF model, whereas neither the 50% 1-vinylnaphthalene polymer nor thehomopolymer does so. Obviously the model fits only for low naphthaleneconcentrations and low temperatures. The breakdown of the FF model at hightemperatures and high naphthalene concentrations could be explained by thebreakdown of any one of the assumptions outlined above.

Tao and Frank also found that the FF model does not adequately fit2-vinylnaphthalene fluorescence decay profiles at high temperatures [45]. TheFPT model should be appropriate for high trap concentrations, but in Figure15.9 the FPT model produces very similar results to the FF model and was unableto fit any of our data which did not fit the FF model.

In the interpretation of fluorescence data, models as complex as the FF modelare seldom employed. Commercially available programs for fitting time-resolvedfluorescence data generally cover exponential decay, the exponential of a t*function, or sums of these functions, but rarely anything more complex. It wouldbe useful to know when simpler approximations, for which fitting routines are

Temperature /K

Figure 15.9 Comparison of fitting parameters from the FF model and the FPT model(see text)

homopolymer

copolymer

available, are adequate to fit data actually obeying a more complex theory, sothat information about a complex model can be inferred from the fit of theexperimental data to a simple function. It would consequently be useful to knowwhen the FF model can be successfully approximated by a simpler function.

If q2 W stays within certain limits, then fcDM in the FF model can be accuratelyapproximated by a constant term plus a term dependent on t1/2. On integration ofthe rate equations, the fluorescence decay will then follow Equation (15), which iscommonly available in fluorescence decay fitting software.

[ AQ /Wt~~\-(kM + krJt—^-J (15)

Table 15.1 shows reduced x2 test, fcM + ferot and qW112 values obtained from fitsof some of the experimental data presented earlier to the FF model and toEquation (15). The last two columns of Table 15.1 consists of values of4(1 — 2/n)q2W and feM + krov The chi-squared values are equally good for bothfunctions, but the kM + krot and qW1/2 parameters do show some deviationswhich may be not be explained by experimental error. The FF model consistentlyfinds a slightly less 'exponential decay', indicating that small inaccuracies in theapproximation have shown up.

Tao and Frank [45] presented data consistent with the FF model without anyreference to fitting the exp — (at + bt1/2) approximation. We tested this bysimulation; thus, Tao and Frank's data were simulated with the same amplitudeas shown in their paper, from their published parameters, and with Gaussiannoise added. When our simulated curves were analysed with our FF fittingprogram, they gave chi-squared values of 1.00 ± 0.05. They were subsequentlyfitted to Equation (15). The x2 values from the FF fit were then subtracted fromthe x2 values from the t1'2 fit to give a measure of the difference in the quality ofthe fit. These results are presented in Table 15.2, along with parameters extractedfrom the paper.

At low temperatures, Equation (15) is well satisfied, and #2(*1/2) —X2(FT) isalso very low. As the temperature rises, however, qW1/2 increases faster than

Table 15.1 Quality of fit and some fitting parameters for 27% l-vinylnaphthalene/72%methyl methacrylate copolymer

Tw T w kM + kTOt 4(1-2/7T)- /cM + /crotTemp (FF)/ (r1/2)/ (r1/2)/ q2W/ (FF)/(K) *2(FF) x

2(t112) 107S"1 107S-1 (xlO"4) 107S"1 107S"1

290 U 5 1.11 O20 019 115 O30 236270 1.11 1.05 0.12 0.12 116 0.18 130250 1.09 1.09 0.049 0.047 114 0.07 118230 0.99 1.06 0.041 0.038 1.95 0.06 1.99210 1.26 1.30 0.053 0.046 1.71 0.08 1.76

Table 15.2 Fitting parameters for actual and synthesized data of Tao and Frank;2-vinylnaphthalene homopolymer

Temperature/K *2(FF) *2('1/2)-X2(FF) 4(1-2/Tr)^2WyIO7S-1 ikM +Jkn^lO7S"1

293 L29 017 15 11273 1.18 0.11 1.9 3.1253 1.10 0.05 1.0 2.8233 1.10 0.03 0.62 2.4213 1.08 0.02 0.44 1.9193 1.05 0.01 0.24 1.6173 1.06 <0.01 0.09 1.5153 1.05 <0.01 0.08 1.5133 1.02 <0.01 0.02 1.4113 1.03 <0.01 0.02 1.4

fcM + kTOV until the condition that 4(1 — 2/^)9 W < WkM + fcrot is no longer satis-fied above 193 K. At the same time, x2(f1/2) - X2(ff) increases until, at « 293 K,the two models should easily be differentiated. However, by 293 K, the experi-mental x2(FF) value has also increased to a stage where the data no longer fit theFF model. So at 293 K the exp - (at + bt1/2) function may possibly fit the databetter than the FF model. In fact, nothing so far has contradicted the premise thatTao and Frank's data can fit Equation (15) as well as the FF model. This meansthat the polymer could actually be undergoing any set of processes which approxi-mates sufficiently well to an exp — (at + bt1/2) function.

15.7.1.6 Fluorescence Anisotropy Measurements

The fluorescence decay times of excited states are such that the fluorescencedepolarization technique may only be used to examine relatively high frequencyrelaxation processes of polymers. Consequently fluorescence depolarization hasbeen primarily limited to the study of relaxation processes of polymers insolution. The anisotropy of a system, r(t\ is derived from measurements of thefluorescence decays with polarizations parallel and perpendicular to the polariz-ation of excitation:

Ht) = [Z1W - IAt)WiIt) + 2Z1(O] = D(t)/S(t)

Time-resolved fluorescence anisotropy measurements [47] can provide de-tailed information on the reorientation dynamics of molecules in solution. Untilrecently, however, this information has been limited to single rotational correla-tion times, which are only strictly appropriate for the diffusion of sphericallysymmetric molecules. Improvements in instrumentation and data analysis tech-niques during the last decade have led to increasingly accurate measurements offluorescence lifetimes, with parallel improvements in determinations of fluores-cence anisotropies.

The advances in time-resolved techniques have fostered a reexamination oftheories of the rotational motions of molecules in liquids. Models consideredinclude the anisotropic motion of unsymmetrical fluorophores; the internalmotions of probes relative to the overall movement with respect to theirsurroundings, the restricted motion of molecules within membranes (e.g., wobbl-ing within a cone), and the segmental motion of synthetic macromolecules [8].Analyses of these models point to experimental situations in which the anisot-ropy can show both multi-exponential and none-exponential decay. Currentexperimental techniques are capable in principle of distinguishing between thesedifferent models. It should be emphasized, however, that to extract a singleaverage rotational correlation time demands the same precision of data andanalysis as fluorescence decay experiments which exhibit dual exponentialdecays. Multiple or non-exponential anisotropy experiments are thus near thelimits of present capabilities, and generally demand favourable combinations offluorescence and rotational diffusion times [48].

An example is cited below of study on the copolymers (a) methyl methacrylate/acenaphthylene (PMMA/ACE), (b) methyl methacrylate/1-vinylnaphthalene(PMMA/1-VN), (c) methyl acrylate/acenaphthylene (PM A/ACE), and (d) methylaery late/1-vinylnaphthalene (PMA/l-VN). The results are summarized inTable 15.3.

Averaging all the determinations for the initial anisotropy for each polymersample leads to the following values for excitation at 300 nm: PMMA/ACE,

Table 153 Fluorescence anisotropy parameters for labelled acrylic polymers

T/K Tf/ns To T R

298 ±2 17.4 ±0.2 0.10 ±0.01 0.8 ±0.3PMA/ACE 260±2 17.4±0.3 0.10±0.01 1.3±0.2

245±2 17.4±0.3 0.11 ±0.01 1.8±0.3230±2 17.5±0.3 0.12±0.02 2.5±0.3289±2 15.1 ±0.1 0.13±0.01 0.5±0.1

PMA/VN 275±2 14.9±0.1 0.13±0.01 0.8±0.1260±2 14.8±0.1 0.14±0.01 1.0±0.2245±2 14.9±0.1 0.14±0.01 1.3±0.3230±2 14.9±0.1 0.15±0.01 1.7±0.3298±2 15.5±O.l 0.13±0.01 1.3±0.1

PMMA/ACE 275±2 15.7±O.l 0.13±0.01 2.2±0.2260±2 15.4±0.2 0.13 ±0.01 3.2 ±0.5245±2 15.5±0.2 0.13±0.01 4.5±0.723O±2 15.6±0.1 0.11 ±0.02 5.6±0.7298±2 15.9±0.02 0.15±0.01 1.3±0.2

PMMA/VN 275±2 15.6±0.2 0.16±0.01 2.2±0.5260±2 15.5±O.l 0.14±0.01 2.7±0.3245±2 15.4±0.1 0.15±0.01 3.6±0.523O±2 15.4±0.1 0.16±0.01 4.9±0.7

Figure 15.10 Alignment of the transition dipoles and the direction of the independentmotion of the 1-vinylnaphthalene chromophore relative to a polymer backbone

r0 = 0.13 ±0.01; PMA/ACE, r0 = 0.11 ±0.01; PMMA/1-VN, r0 = 0.15 ±0.01;PMA/l-VN, r0 = 0.14 ±0.02. These results are in excellent agreement withvalues obtained for polymers with similar compositions. Initial anisotropies areexpected to have the value of 0.4. However, the first and second excited states ofnaphthalene and its derivatives are, in the Platt notation, designated 1L1, and 1L3

respectively. The transition dipole moments for absorption into these bands aredirected along the long (1L1,) and short (1LJ axes of the aromatic rings. Irradi-ation at 300 nm produces excitation of both absorption bands, and so naphtha-lene, when excited at this wavelength, can be considered to have a planar ratherthan a linear absorption oscillator.

The 1-vinylnaphthalene chromophore, unlike the acenaphthylene chromo-phore, would appear to be capable of motion independent of the polymer back-bone by rotation about the single bond [Fig. 15.10]. However, such rotationcannot lead to depolarization. Consequently for the 1-vinylnaphthalene labelledpolymers, as with the acenaphthylene labelled polymers, it is only segmentalmotions which lead to depolarization.

For the poly(methacrylates) and poly(acrylates), the a and /? relaxations areassociated with segmental motions of the polymer and independent motions ofthe ester substituents respectively. The merging of these transitions at highfrequencies or temperatures corresponds, at the molecular level, to the incidenceof co-operative motion between the substituent and the polymer backbone.Consequently, it is to be expected that, in solution, the high frequency motions ofboth polymer chain and fluorescent label will assume a co-operative formcharacterized by a single relaxation process/time.

The activation energies derived from the results at different temperatures(Table 15.3) show that in poly(methyl methacrylate) and poly(methyl acrylate)the segmental motions are largely controlled by solvent flow.

15.8 CONCLUSIONTime-resolved luminescence measurements have still unrealized potential for thestudy of energy migration, rotational motion and surface effects in polymers insolution and in the solid state.

Polymer

backbone backbone

Direction ofindependent motion


This paper has drawn upon the work of AJ. Roberts, G. Rumbles, R.C. Drake,C.F.C. Porter and R.L. Christensen, of Imperial College, London, and ofProfessor Ian Soutar and his group at the University of Lancaster. All arethanked for their contributions. Financial support from SERC and The RoyalSociety is gratefully acknowledged.

15.10 REFERENCES

[1] D. Philips (Ed.), Polymer Photophysics: Luminescence, Energy Migration and Mol-ecular Motion in Synthetic Polymers, Chapman Hall, London, 1985.

[2] S.W. Beavan, J.S. Hargreaves and D. Phillips, Adv. Photochem. 1979,11, 207.[3] Y. Nishijima, J. Polym. ScL Polym. Symp., 1970, 31, 353.[4] A.C. Somersall, E. Dan and J.E. Guillet, Macromolecules, 1974,7, 233.[5] D. Phillips, Br. Polym. J., 1987,19,135.[6] W.C. Tao and CW. Frank, in J.-P. Fouassier and J.F. Rabek (Eds.), Lasers in

Polymer Science and Technology: Applications, Vol. 1, CRC Press, Boca Raton, 1990,p. 161.

[7] M.A. Winnick, in J.-P. Fouassier and J.F. Rabek (Eds.), Lasers in Polymer Scienceand Technology: Applications, Vol. 1, CRC Press, Boca Raton, 1990, p. 197.

[8] G. Rumbles and D. Phillips, in J.-P. Fouassier and J.F. Rabek (Eds.), Lasers inPolymer Science and Technology: Applications, Vol. 1, CRC Press, Boca Raton, 1990,p. 91.

[9] D. Phillips, in CE. Hoyle and J.M. Torkelsen (Eds.), Photophysics of Polymers, ACSSymp. Ser., 1987, (358), 308.

[10] J.B. Birks, Photophysics of Aromatic Molecules, Wiley-Interscience, London, 1970,pp. 322-335.

[11] J.B. Birks, DJ. Dyson and T.A. King, Proc. R. Soc. London, Ser. A, 1964, 277, 270.[12] AJ. Roberts, D.V. O'Connor and D. Phillips, Ann. N.Y. Acad. ScL, 1981,366,109.[13] D. Phillips, AJ. Roberts and I. Soutar, Polymer, 1981, 22, 293.[14] D. Phillips, AJ. Roberts and I. Soutar, J. Polym. ScL, Polym. Phys. Ed., 1982,20,411.[15] D. Phillips, AJ. Roberts and I. Soutar, Polymer, 1981, 22,427.[16] D. Phillips, AJ. Roberts and I. Soutar, J. Polym. ScL, Polym. Phys. Ed., 1980, 18,

2401.[17] D.A. Holden, P.Y.K. Wang and J.E. Guillet, Macromolecules, 1981,14,405.[18] F.C. DeSchryver, K. Demayer, M. Van der Anweraer and E. Quanten, Ann. N.Y.

Acad. ScL, 1981, 109.[19] AJ. Roberts, D. Phillips, F. Aboul-Rasoul and A. Ledwith, J. Chem. Soc, Faraday

Trans. 7,1981,77,2725.[20] K. Sienicki and G. Durocher, Macromolecules, 1991, 24,1102.[21] C. David, M. Piens and G. Geuskens, Eur. Polym. J., 1972,8,1019.[22] C David, M. Piens and G. Geuskens, Eur. Polym. J., 1972,8, 1291.[23] CE. Hoyle, T.L. Nemzek, A. Mar and J.E. Guillet, Macromolecules, 1978,11, 429.[24] G.E. Johnson, J. Chem. Phys., 1975,62,4697.[25] J.C. Andre, F. Baros and M.A. Winnick, J. Phys. Chem., 1990, 94, 2942.[26] T.C. Nemzek and W.R. Ware, J. Chem. Phys., 1975, 62,477.[27] M.V. Smoluchowski, Z. Phys. Chem., 1917,92, 129.

[28] F.C. Collins and GE. Kimball, J. Colloid ScL, 1949,4,425.[29] D.L. Huber, Phys. Rev. B, 1979, 20, 2307.[30] B. Movaghar, G.W. Sauer and D. Wurtz, J. Slat. Phys., 1982, 27, 473.[31] B. Movaghar, J. Phys. C (Solid State), 1980,13,4915.[32] E.W. Montroll, J. Math. Phys., 1969,10, 753.[33] J. Klafter and R. Silbey, J. Chem. Phys., 1981,74, 3510.[34] CR. Gochanour, H.C. Andersen and M.D. Fayer, J. Chem. Phys., 1970,70,4254.[35] R.F. Loring, H.C. Andersen and M.D. Fayer, J. Chem. Phys., 1982,76, 2015.[36] G.H. Fredrickson and H.C. Andersen, Macromolecules, 1984,17, 54.[37] M. Griinewald, B. Pohlmann, B. Movaghar and D. Wurtz, Philos. Mag. B, 1984,49,

341.[38] R. Richert, B. Ries and H. Bassler, Philos. Mag. B, 1984, 49, L25.[39] A.D. Stein, K.A. Petersen and M.D. Fayer, J. Chem. Phys., 1990,92, 5622.[40] W. Weixelbaumer, J. Burbaumer and H.F. Kaufmann, J. Chem. Phys., 1985,83,1980.[41] K. Sienicki and M.A. Winnick, J. Chem. Phys., 1987,87, 2766.[42] M.N. Berberan-Santos and J.M.G. Martinho, J. Chem. Phys., 1991,95,1817.[43] J. Baumann and M.D. Fayer, J. Chem. Phys., 1986,85,4087.[44] G.H. Frederickson and CW. Frank, Macromolecules, 1983,16, 572.[45] W.C Tao and CW. Frank, J. Phys. Chem., 1989,93, 776.[46] R. Gelles and CW. Frank, Macromolecules, 1982,15, 747.[47] D. V. O'Connor and D. Phillips, Time-Correlated Single Photon Counting, Academic

Press, London, 1984.[48] R.L. Christensen, R.C Drake and D. Phillips, J. Phys. Chem., 1986,90, 5960.[49] R.C Drake, Ph.D. Thesis, University of London, 1986.

391 This page has been reformatted by Knovel to provide easier navigation.

Index

Index terms Links

A AB quartet 18

acrylonitrile-furan copolymers 27

adsorbtion 242 339

afine deformation 183

aggregation 355

alignment (Homeotropic, planar) 282

alkylcyanobiphenyl 282

alpha (shift) effect 9 56

alpha (greek) process 277

alpha helix 355

amorphous polymers 276 332

anisotropies 173 235

APT (attached proton test) 11

autocorrelation function 278

azobenzene groups 351

B Bernoullian statistics 21

beta (shift) effect 9 57

beta (greek) process 277

biaxial orientation 176

blends 245 340

392 Index terms Links


C catalysts 33

C– –C(triple) stretch 214 221

CD Circular dichroism 350

chain transfer 32

charge-transfer complex participation 22

chiral macromolecules 347

chemical shift 2

chemical shift image 157 159

cis double bonds 36

Cobalt-60 gamma irradiation 263

Cole-Cole plot 290

composites 159 221

conformation 55

conformational data 97

conformational transitions 352

correlation times 235

COSY 84

coupling constant 7 111

cross polarization Robin 135

crosslinked systems 12 261

Cryogenic trapping 270

crystalline polymers 280

D deformation 203

degradation 253 263

DEPT Assignment technique 11 73



desorption 165

diacetylene monomers 204

dichroic difference 187

dichroic ratio 180

dielectric constant/permittivity 258 287

dielectric relaxation modes 279

Dielectric Relaxation Spectroscopy (DRS) 275

dienes as monomers 25

diffusion 162 167 315

diglycidyl ether of bisphenol-A (DGEBA) 121 288

domain size 125 146

double bond dyada, triads 38

dynamic dichroic 192

E elastomers 197

electroactive 282

electron spin resonance (esr) 231 253

electrooptical 282

enantiomer copolymerization 41

ethylene glycol dimethacrylate 254

ethylene-vinyl acetate copolymers 88

excimer 374

F Fourier transform (NMR) 8

Fourier transform vibration spectroscopy 173 257

fractal 15

free radical 231 255



fumarate-vinyl acetate copolymer 245

furan-acrylonitrile copolymers 27

G g value (esr) 235 255

gamma gauche effect 57 64 97

gamma rays 263

gamma relaxation 280

gels 259 311 332

glass transition temperature 142 165 240

Goldman-Shen pulse sequence 126

H helix content 354 367

I imaging (NMR) 151

INEPT assignment technique 72

inhomogeneities 151

interfacial 224

interferometer 177

IR 173 257

isotope enrichment (D) 30

K Karplus 111

Kerr Constant 280

Kevlar 204 207

Kohlrausch-Williams-Watts 277



L lamellar morphology 125

Lewis acid effect 29

light scattering 297

linear response theory 278

liquid crystalline polymers 145 282

loss (dielectric) 275 283

luminescence 369

M Magic-angle Spinning (MAS) NMR 92 119 138

144

Markov statistics 21

merocyanine 359

meso dyads 18

metallacarbenes 35 41

methacrylate radical 260

methylmethacrylate 254

microstructure 8 18 32 55 97

molecular anisotropy 173

molecular size 331

morphology 136

Motion (of polymer) 231

Motionally-narrowed 239

multidimensional NMR 135

N natural rubber 161 198



near lR 257

neutron scattering 325

nitroxide 232

NMR 7 117 135 151

NOESY NMR assignment 87

Norris-Tromsdorf region 257

nylon 128 160 281

O optical activity 347

orientation 173

P permittivity(dielectric) 275

phase separating mixtures 305

photophysics 369

pixel 165

poly(acrylonitrile) 19 27 103

poly(alpha amino acids) 351

poly(alpha methyl styrene) 265

poly(bisphenylurethane-2,4-hexadiyne-1,6-diol) 205

poly(butadiene) 27

poly(but-l-ene sulphone) 16 21

poly(isobutylene) 199

polycarbonate 167

poly(diacetylene) single crystal fibre 205

poly(dimethyl siloxane) 161

poly(2,6-dimethyl-l,4-phenylene oxide) 196



polyester(branched) 9 12

poly(ethyl cyanoacrylate) 15

poly(2-ethylhexyl methacrylate) 248

polyethylene 9 181 184 210 212 281

polyethylene terephthalate) 145 182 189 277 281

poly(L-glutamic acid) 352

poly(2,4-hexadiyne-1,6-bis (p-toluenesulphonate)) 205

poly(isoprene) 246

poly(L-lysine) 351

polymer dynamics 136 275 338

polymerization 253

poly(methacrylonitrile) 107

poly(methyl acrylate) 277

poly(methylmethacrylate) 7 10 107 165 246 254 259 260 268

poly(n-butyl isocyanate) 235

poly(norbornene) 35 43

poly(oxymethylene) 140 143 281

polypropylene 10 58 66 103 122

poly(propylene oxide) 68 277

polystyrene 190 193 246 267 315 373

polystyrene(syndiotactic) 10 92

poly(styrene block butadiene block styrene) 196

polysulphide 15



poly(vinyl acetate) 243 277

poly(vinyl alochol) 104 371

poly(vinyl chloride) 105 130 183

poly(vinyl fluoride) 83 281

poly(vinylidene fluoride) 81 142 246

281

poly(vinyl methyl ether) 141

powder pattern spiess 137

prochiral face 35

Q quasi elastic scattering 297 309 334

R radical 231 255

Raman Spectroscopy 173 203

regio selectivity 18 38 40

resolution enhancement 12

Ring Opening Metathesis Polymerization (ROMP) 30

RIS (rotational isomeric state) 62 98 109

Rotor-synchronized MAS NMR 144

Rouse modes 338

S SALS (small angle light scattering) 298

SANS (small angle neutron scattering) 330

semicrystalline polymers 298

semidilute 313

silica absorbent 242



silicone polymer 282

simulation (esr spectrum) 266

solid polymer NMR 117 135

solution NMR 7

specular reflectance 177

spin density 157

spin label 231

spin probe 231

spin relaxation (proton) 125

spirobenzopyran 357

steroselectivity 35

stereospecific polymerization 32

strain 185 203

stress 185 203

styrene-MMA copolymers 84

substituent effects 56

surfaces 316 333

T T1 119 125 153

T1rho(ρ) 125

T2 125 153

tacticity 15

Tactic sequence 98

tensile stress 222

thermoset (epoxy amine) 288

time-resolved measurements 184

two-dimensional IR 192 two-frequency-addressing 282



U uniaxial orientation 174

urethane-diacetylene copolymers 219

UV light 351

V vinyl acetate copolymer 279

vinyl chloride copolymers 67

voxel 155

W WAAS 209

Wigner rotation matrix 286

WISE NMR 141

WLF (Williams Landel Ferry) 241

Y Young's modulus 206

Z Zeigler-Natta polymerization 31

Date post:	08-Dec-2016
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