i
Quartz Crystal Microbalance/ Heat Conduction Calorimetry (QCM/HCC), a new
technology capable of isothermal, high sensitivity, mass and heat flow
measurements at a solid/gas interface.
A Thesis
Submitted to the Faculty
of
Drexel University
by
Hamid M. Shirazi
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
December 2000
ii
To my loving wife Eva and my daughters Jasmine and Dominique
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Acknowledgments
First and foremost the author wishes to express his gratitude to his advisor, Dr.
Allan Smith, for providing guidance and support throughout the years. I am truly grateful
for the opportunity of having worked under Dr. Smith’s supervision. I have come to
appreciate his breadth of knowledge and expertise in so many different areas. But, I am
even more impressed by Dr. Smith’s other qualities of integrity, fairness, and respect
towards his students.
Next, I wish to thank the following persons and acknowledge their contributions to
this work.
Dr. Ingemar Wadsö has been involved in the early stages of design and construction
of QCM/HCC. Dr. Lars Wadsö provided us with a Matlab program for thermal peak
integration. Jay Bhatt helped with the construction of the first isothermal bath used for the
QCM/HCC. Tom Cachaza has built a glass bubble-through container and other items used
for this project. Nikolaus Kwasnjuk and Zoltan Boldy have designed, built and modified
various items, which we have used for many of our experiments. Wolfgang Nadler and
Maryann Fitzpatrick have helped with maintenance and repair of the QCM oscillator
drivers and also built an additional set for us. Mr. Kurt Wessendorf from the Sandia
National Laboratories provided us with oscillator drivers with an additional output channel
for measurement of the QCM oscillation resistance. Dr. Neal Shinn, also from the Sandia
National Laboratories, provided us with purified samples of alkylthiols and surface treated
QCMs. Jennifer Atchison helped us to locate some of the electronic equipment used with
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the QCM/HCC. Dr. Richard Beard from the electrical and computing engineering
department allowed us to use his impedance analyzer on several occasions to obtain
admittance spectra for coated QCMs as well as for the thermal calibration of thermopiles.
We would like to thank Dr. Wei for offering the use of a spin-coating apparatus in his lab
and also Dr. Li for his help with its operation. Dr. John DiNardo and Dan Brennan from
the Physics department helped us with thickness measurements of two of our thin film
samples using an atomic force microscope. Dr. Kay Kanazawa from Stanford University
shared with us some of his great insight with a model developed to estimate a correction
factor to Sauerbrey’s equations for viscoelastic coatings. Dr. Tysoe form the University of
Wisconsin-Milwaukee presented us with some work from his laboratory through private
communications regarding the catalytic hydrogenation of ethylene over palladium. Dr. S.
Bone from the University of Wales kindly provided us with the original data from one of
his publications regarding the measurement of hydration/dehydration enthalpy of
lysozyme. Several graduate and undergraduate students have been actively involved in
different projects in our laboratory. We wish to acknowledge the contributions from David
Schneider, Anna Ayrapetova, Betty Jacob, Kirk Edwards, John Lee, and Ed Lavender
towards various aspects of the work presented here. Justine Ciraolo initiated the lysozyme
hydration studies. Sister Rose Mulligan has done a great deal of the work for data analysis of
lysozyme hydration/dehydration experiments.
Finally, I wish to thank my fellow graduate students at Drexel for making my work
at Drexel an enjoyable experience.
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Table of Contents
LIST OF TABLES .........................................................................................................viii
LIST OF FIGURES ........................................................................................................ ix
ABSTRACT ..................................................................................................................xviii
CHAPTER 1- INTRODUCTION ..................................................................................1
1.1 The invention of the QCM/HCC ....................................................................................................................... 1
1.2 QCM/HCC as a new technique .........................................................................................................................3
1.3 Thesis overview .......................................................................................................................................................6
References.......................................................................................................................................................................9
CHAPTER 2- QUARTZ CRYSTAL MICROBALANCE...........................................12
2.1 The Piezoelectric Effect ...................................................................................................................................... 12
2.2 Mass sensitivity ..................................................................................................................................................... 14 2.2.1 Historical Review .............................................................................................................................................14 2.2.2 Different models ..............................................................................................................................................20 2.2.3 The correlation of complex dynamic modulus measurements with temperature and frequency. ..........60
References.....................................................................................................................................................................67
CHAPTER 3- HEAT CONDUCTION CALORIMETRY........................................ 70
3.1 Heat flow sensor ...................................................................................................................................................70 3.1.1 Thermal calibration of the thermopile ......................................................................................................73
3.2 Nonscanning heat conduction calorimeters .................................................................................................88 3.2.1 General application areas of isothermal heat conduction calorimeters .....................................................93 3.2.3 Calibration issues and the accuracy of isothermal heat conduction calorimetry measurements.............96
References.....................................................................................................................................................................99
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CHAPTER 4- DESCRIPTION OF QUARTZ CRYSTAL MICROBALANCE/HEAT CONDUCTION CALORIMETER (QCM/HCC) AND ITS DEVELOPMENTAL STAGES.................................................................103
4.1 Description of the QCM/HCC apparatus and its advancement with time......................................... 103
4.2 Data processing and analysis .......................................................................................................................... 140
References................................................................................................................................................................... 145
CHAPTER 5- EXPERIMENT 1: SOLVENT VAPOR SORPTION INTO AN ALIPHATIC POLYETHERURETHANE (TECOFLEX™) THIN FILM...........146
5.1 Introduction ......................................................................................................................................................... 146
5.2 Experimental ....................................................................................................................................................... 154 5.2.1 Ethanol sorption/desorption in a drop-coated TecoflexTM thin film......................................................154 5.2.2 Organic vapor sorption/desorption in spin-coated TecoflexTM thin films. ............................................165
5.2 Results and conclusions ...................................................................................................................................207
References...................................................................................................................................................................229
CHAPTER 6- EXPERIMENT 2: HYDROGEN SORPTION IN THIN PALLADIUM FILMS; EXPERIMENT 3: SELF ASSEMBLED MONOLAYER FORMATION ON GOLD ..........................................................................................231
6.1 Hydrogen sorption; introduction.................................................................................................................... 231 6.1.1 The Hydrogen storage problem ...................................................................................................................231 6.1.2 Hydrogen sorption in palladium ..................................................................................................................234 6.1.3 Experimental ..................................................................................................................................................237 6.1.4 Results and conclusions.................................................................................................................................250 6.1.5 Ethylene hydrogenation over palladium hydride........................................................................................255
6.2 Self assembled monolayer formation of nonylthiol on a gold surface ..................................................264
References...................................................................................................................................................................277
CHAPTER 7- EXPERIMENT 4: HYDRATION/DEHYDRATION OF LYSOZYME..................................................................................................................281
7.1 Introduction ......................................................................................................................................................... 281
7.2 Experimental .......................................................................................................................................................284
7.3 Results and discussions.................................................................................................................................... 291
References...................................................................................................................................................................299
CHAPTER 8- SUMMARY AND SUGGESTIONS FOR FUTURE ACTIVITIES305
8.1 Summary and suggestions for future activities, chapters 1-4 ..................................................................300
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8.2 Summary and suggestions for future activities, chapters 5......................................................................304
8.3 Summary and suggestions for future activities, chapters 6......................................................................306
8.4 Summary and suggestions for future activities, chapters 7......................................................................308
8.5 Possible applications of the QCM/HCC in the pharmaceutical industry...........................................309
References ...................................................................................................................................................................314
APPENDIX A: STEPHEN MARTIN’S MODEL FOR A QCM RESONATOR WITH A VISCOELASTIC SURFACE LOAD (MATLAB PROGRAM).................315
APPENDIX B: KAY KANANZAWA’S MODEL FOR CORRECTION OF SAUERBREY’S EQUATION FOR A VISCOELASTIC SURFACE LOAD (MATLAB PROGRAM) ...............................................................................................316
APPENDIX C: VAPOR PRESSURE OF WATER AND ORGANIC SOLVENTS AT DIFFERENT TEMPERATURES................................................ 324
APPENDIX D: NOMENCLATURE AND ABBREVIATIONS USED................ 333
VITA ............................................................................................................................341
viii
List of Tables
2-1: Typical values for a 5Mhz AT cut QCM....................................................................23 3-1: Thermal conductivity of some materials present in QCM/HCC................................74 3-2: Thermal calibration of the left thermopile.................................................................80 3-3: Thermal calibration of the right thermopile...............................................................80 3-4: Correction factor obtained for the calibration coefficient of the right thermopile for the lysozyme hydration/dehydration experiments.......................................................84 3-5: Values obtained for the time constant of the heat flow sensor...................................87 3-6: Summary of commercial heat conduction calorimeters from different manufacturers ..................................................................................................................92 4-1: Defaults and specifications for 4192A sweep.vi (Hamid’s setup) .............................113 4-2: List of controls and indicators for the QCM/HCC control program.......................118 4-3: List of SubVIs used in the QC/HCC LabView control program.............................123 4-4: Measured data for calibration of the low-noise preamplifier....................................127 4-5: Calibration of MFC1 (UNIT UFC 8100) for nitrogen @20.4°C..............................134 4-6: Calibration of MFC1 (UNIT UFC 8100) for nitrogen @23.5°C..............................135 4-7: Calibration of Hasting mass flow meter (0-50sccm).................................................137 4-8: Calibration of the MFC3 (Tylan 0-400sccm)............................................................137 4-9: Conversion factors to be used for mass flow controllers calibrated with nitrogen....139 5-1: Enthalpy of sorption of ethanol in the drop-coated TecoflexTM film........................164 5-2: Enthalpy of sorption of carbontetrachloride in TecoflexTM (0.78µm) (99-07-23-1)...180
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5-3: Enthalpy of sorption of chloroform in TecoflexTM (0.78µm) (99-07-16-1) ...............181 5-4: Enthalpy of sorption of toluene in TecoflexTM (0.78µm) (99-07-18-1) .....................182 5-5: Enthalpy of sorption of ethanol in TecoflexTM (0.78µm) (99-07-15-1) .....................183 5-6: Enthalpy of sorption of acetone in TecoflexTM (0.78µm) (99-07-19-1) .....................184 5-7: Enthalpy of sorption of hexane in TecoflexTM (0.78µm) (99-07-19-2)......................185 5-8: Enthalpy of sorption of carbontetrachloride in TecoflexTM (2.09µm) (99-07-27-1)...198 5-9: Enthalpy of sorption of chloroform in TecoflexTM (2.09µm) (99-07-28-2) ...............199 5-10: Enthalpy of sorption of toluene in TecoflexTM (2.09µm) (99-07-28-3)....................200 5-11: Enthalpy of sorption of ethanol in TecoflexTM (2.09µm) (99-07-30-1)....................201 5-12: Enthalpy of sorption of acetone in TecoflexTM (2.09µm) (99-07-30-2) ...................202 5-13: Enthalpy of sorption of hexane in TecoflexTM (2.09µm) (99-08-02-1) ....................203 5-14: Diffusion coefficients of three solvent vapors in TecoflexTM .................................211 5-15: Summary of results of sorption of solvent vapor in two TecoflexTM films..............215 5-16: LSER for two TecoflexTM films .............................................................................216 6-1: Summary of the results of hydrogen sorption enthalpies in thin palladium film (141nm) (99-05-24-1) .....................................................................................................246 6-2: Summary of the results of hydrogen sorption enthalpies in thin palladium film (141nm) (99-06-09-2) .....................................................................................................249 6-3: Summary of reported and measured values of enthalpy of SAM formation and other related reactions....................................................................................................274 7-1: Enthalpy of hydration/dehydration of lysozyme as a function of water vapor activity............................................................................................................................290 C-1: Vapor pressure of water and some other organic solvents at different temperatures ..................................................................................................................324 C-2: Vapor pressure of some chlorinated solvents..........................................................330
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List of Figures
2-1: Typical quartz crystal cuts. Figures taken from http://online-product.com/crystal/quartz03.html and http://literature.agilent.com/litweb/pdf/5965-7662E.pdf...............................................13
2-2: Sauerbrey's model of an oscillating QCM, a) before addition of mass, b) after addition of mass...............................................................................................................15 2-3: Equivalent circuit of a quartz crystal microbalance...................................................22 2-4: Phasor diagram, alternating current through a resistor, phase angle=00 ....................25 2-5: Phasor diagram, alternating current for a capacitor, phase angle=-900 ......................25 2-6: Phasor diagram, alternating current through an inductor, phase angle=900...............26 2-7: Phasor diagram for a LCR circuit (not at resonance) ................................................27 2-8: Phase angle of admittance for a 5MHz AT-cut quartz crystal measured with an impedance analyzer..........................................................................................................28 2-9: Admittance magnitude for a 5MHz AT-cut quartz crystal measured with an impedance analyzer..........................................................................................................29 2-10: Susceptance and conductance of a 5MHz AT-cut quartz crystal measured with an impedance analyzer......................................................................................................30 2-11: B-G curve for a 5MHz AT-cut quartz crystal, as measured with an impedance analyzer............................................................................................................................31 2-12: Equivalent circuit of a mass loaded QCM...............................................................33 2-13: Transmission line model for a mass loaded QCM...................................................33 2-14: The magnitude of normalized impedance response to that of an ideal mass for G"/G'=0.1.......................................................................................................................39 2-15: The phase angle for the normalized impedance response for G"/G'=0.1 ...............40
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2-16: The magnitude of normalized impedance response to that of an ideal mass for G"/G'=1..........................................................................................................................41 2-17: The phase angle for the normalized impedance response for G"/G=1 ..................42 2-18: The magnitude of normalized impedance response to that of an ideal mass for G"/G'=2....................................................................................................................43 2-19: The phase angle for the magnitude of normalized impedance response for G"/G'=2..........................................................................................................................44 2-20: The magnitude of normalized impedance response to that of an ideal mass as function of frequency ratio (f/ff) and loss tangent (G"/G') ..............................................45 2-21: The phase angle for the normalized impedance response to that of an ideal mass as function of frequency ratio (f/ff) and loss tangent (G"/G')..................................46 2-22: Geometry of a composite resonator .......................................................................47 2-23: Electrical admittance for an uncoated QCM and a QCM coated with SiO2.............50 2-24: Admittance phase angle for an uncoated QCM and a QCM coated with SiO2 ........51 2-25: Electrical admittance for a QCM coated with thin films of a polymer near its transition state..................................................................................................................52 2-26: Admittance phase angle for a QCM coated with thin films of a polymer near its transition state .............................................................................................................53 2-27: Electrical admittance for a QCM coated with thin films of a polymer approaching its glassy state...............................................................................................54 2-28: Admittance phase angle for a QCM coated with thin films of a polymer approaching its glassy state...............................................................................................55 2-29: Electrical admittance for a QCM coated with thin films of a polymer approaching its rubbery state............................................................................................56 2-30: Admittance phase angle for a QCM coated with thin films of a polymer approaching its rubbery state............................................................................................57 2-31: An example of time-temperature superposition......................................................62 2-32: Correction to Sauerbrey’s relationship....................................................................65 3-1: A semiconductor thermocouple ...............................................................................71
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3-2: A semiconductor thermocouple plate.......................................................................71 3-3: A thermocouple plate made of n- and p-type semiconductors..................................72 3-4: A thermocouple plate...............................................................................................72 3-5: The setup for the thermal calibration of the thermopiles..........................................77 3-6: Thermal signal obtained for an oscillating QCM, left thermopile (98-08-19-1)..........79 3-7: Thermal signal obtained for an oscillating QCM, right thermopile (98-09-17-1) .......79 3-8: An alternative setup for thermal calibration of the thermopiles ................................81 3-9: The QCM electrical circuit representation for the setup in figure 3-17......................82 3-10: a) Time constant obtained for heating event 2 b) Time constant obtained for cooling event 2.................................................................................................................86 4-1: The sketch of the QCM/HCC ...............................................................................106 4-2: Block diagram of the complete QCM/HCC setup.................................................107 4-3: The flow subsystem for vapor introduction............................................................108 4-4: Connector panel and front panel of the HP 54510A digitizing scope (2)................110 4-5: Block diagram of the control program for the HP 54510A digitizing scope (2).......111 4-6: Connector panel and front panel of the HP 4192A sweep VI.................................114 4-7: Block Diagram of the control program for the HP 4192A sweep VI......................115 4-8: Front panel of the QCM/HCC virtual instrument..................................................117 4-9: Block diagram of the QCM/HCC LabView control program.................................121 4-10: Block diagram of the QCM/HCC control program (continued)...........................122 4-11: Circuit diagram of the QCM oscillator driver........................................................125 4-12: The linear fit of the measured voltage at (a) 10mV setting on the preamplifier and (b) 3mV...................................................................................................................128 4-13: The linear fit to the measured voltage at 1mV setting on the preamplifier............129 4-14: Calibration of (a) MFC1 and (b) MFC2 ................................................................136
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4-15: Calibration of (a) Hasting mass flow meter and (b)Tylan mass flow controller .....138 4-16: A typical data file opened in Excel Microsoft........................................................141 4-17: The data flow diagram for the QCM/HCC experiments ......................................144 5-1: The partitioning process for a thin film exposed to solvent vapors.........................151 5-2: The repeat unit of Tecoflex (SG-60D) polyetherurethane.......................................155 5-3: The mass of the drop coated Tecoflex thin film.....................................................156 5-4: (a) Ethanol vapor concentration above TecoflexTM film; (b) Mass of ethanol sorbed into the TecoflexTM film......................................................................................159 5-5: (a) Thermal power for ethanol sorption in TecoflexTM with both QCMs on (sample on right side); (b) Thermal power for ethanol sorption in TecoflexTM with the right QCM off (sample on right side) .......................................................................160 5-6: (a) Ethanol concentration over two bare gold QCM surfaces; (b) difference in thermal power dissipated on two gold surface................................................................163 5-7: Difference in mass signal between two uncoated QCMs ........................................164 5-8: Carbontetrachloride sorption in Tecoflex film (0.78µm) (99-07-23-1) (a) solvent vapor activity (b) mass trace...........................................................................................168 5-9: Carbontetrachloride sorption in Tecoflex film (0.78µm) (99-07-23-1) (a) thermal trace (b) partition coefficient..........................................................................................169 5-10: Chloroform sorption in Tecoflex film (0.78µm) (99-07-16-1) (a) solvent vapor activity (b) mass trace.....................................................................................................170 5-11: Chloroform sorption in Tecoflex film (0.78µm) (99-07-16-1) (a) thermal trace (b) partition coefficient...................................................................................................171 5-12: Toluene sorption in Tecoflex film (0.78µm) (99-07-18-1) (a) solvent vapor activity (b) mass trace.....................................................................................................172 5-13: Toluene sorption in Tecoflex film (0.78µm) (99-07-18-1) (a) thermal trace (b) partition coefficient ........................................................................................................173 5-14: Ethanol sorption in Tecoflex film (0.78µm) (99-07-15-1) (a) solvent vapor activity (b) mass trace.....................................................................................................174
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5-15: Ethanol sorption in Tecoflex film (0.78µm) (99-07-15-1) (a) thermal trace (b) partition coefficient...................................................................................................175 5-16: Acetone sorption in Tecoflex film (0.78µm) (99-07-19-2) (a) solvent vapor activity (b) mass trace.....................................................................................................176 5-17: Acetone sorption in Tecoflex film (0.78µm) (99-07-19-2) (a) thermal trace (b) partition coefficient ........................................................................................................177 5-18: Hexane sorption in Tecoflex film (0.78µm) (99-07-19-1) (a) solvent vapor activity (b) mass trace.....................................................................................................178 5-19: Hexane sorption in Tecoflex film (0.78µm) (99-07-19-1) (a) thermal trace (b) partition coefficient ........................................................................................................179 5-20: Carbontetrachloride sorption in Tecoflex film (2.09µm) (99-07-27-1) (a) solvent vapor activity (b) mass trace ...............................................................................186 5-21: Carbontetrachloride sorption in Tecoflex film (2.09µm) (99-07-27-1) (a) thermal trace (b) partition coefficient .............................................................................187 5-22: Chloroform sorption in Tecoflex film (2.09µm) (99-07-28-2) (a) solvent vapor activity (b) mass trace.....................................................................................................188 5-23: Chloroform sorption in Tecoflex film (2.09µm) (99-07-28-2) (a) thermal trace (b) partition coefficient...................................................................................................189 5-24: Toluene sorption in Tecoflex film (2.09µm) (99-07-28-3) (a) solvent vapor activity (b) mass trace.....................................................................................................190 5-25: Toluene sorption in Tecoflex film (2.09µm) (99-07-28-3) (a) thermal trace (b) partition coefficient ........................................................................................................191 5-26: Ethanol sorption in Tecoflex film (2.09µm) (99-07-30-1) (a) solvent vapor activity (b) mass trace.....................................................................................................192 5-27: Ethanol sorption in Tecoflex film (2.09µm) (99-07-30-1) (a) thermal trace (b) partition coefficient ........................................................................................................193 5-28: Acetone sorption in Tecoflex film (2.09µm) (99-07-30-2) (a) solvent vapor activity (b) mass trace.....................................................................................................194 5-29: Acetone sorption in Tecoflex film (2.09µm) (99-07-30-2) (a) thermal trace (b) partition coefficient ........................................................................................................195 5-30: Hexane sorption in Tecoflex film (2.09µm) (99-08-02-1) (a) solvent vapor activity (b) mass trace.....................................................................................................196
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5-31: Hexane sorption in Tecoflex film (2.09µm) (99-08-02-1) (a) thermal trace (b) partition coefficient ........................................................................................................197 5-32: Ethanol vapor over two bare gold surfaces (99-06-07-02) (a) ethanol vapor activity (b) mass trace.....................................................................................................204 5-33: Ethanol vapor over two bare gold surfaces (99-06-07-02) (a) ethanol vapor activity (b) mass trace.....................................................................................................205 5-34: Fit of the mass trace used to determine the diffusion coefficient for the (a) toluene in Tecoflex at low solvent content (b) toluene in Tecoflex at higher solvent content (c) carbontetrachloride in Tecoflex (d) ethanol in Tecoflex................................206 5-35: Measured partition coefficients and LSER results for (a) 0.78 µm Tecoflex film (b) 2.09 µm Tecoflex film...............................................................................................217 5-36: Partition coefficients and sorption enthalpies for several solvent vapors as the function of solvent vapor mass percent in the Tecoflex film (2.09µm) ...........................218 5-37: Atomic force microscope images of the Tecoflex film (2.09µm) near the center of the QCM ...................................................................................................................221 5-38: Atomic force microscope images of the Tecoflex film (2.09µm) closer to the edge of the QCM ...........................................................................................................222 5-39: Atomic force microscope images of the Tecoflex film (0.78µm) near the center of the QCM ...................................................................................................................223 5-40: Chloroform/acetone hydrogen bonded complex..................................................225 5-41: Thermodynamic quantities for sorption of (a) chloroform, (b) ethanol vapors in Tecoflex.....................................................................................................................227 6-1: An example of a typical hydrogen sorption isotherm for palladium........................235 6-2 Hydrogen sorption in thin palladium film (141nm) (99-05-24-1) (a) hydrogen pressure (b) mass trace (c) thermal trace.........................................................................243 6-3: Two hydrogen sorption cycles in thin palladium film (141nm) (99-05-24-1) (a) hydrogen pressure (b) mass trace (c) thermal trace .........................................................244 6-4: Hydrogen gas over two gold surfaces (99-05-25-1) (a) hydrogen pressure (b) mass trace (c) thermal trace............................................................................................245
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6-5: (a) Mass and thermal traces for two bare gold surface (b) hydrogen pressure over two gold surfaces (99-06-09-1) (c) hydrogen sorption in a thin palladium film (141 nm) (99-06-09-2) ....................................................................................................247 6-6: Two hydrogen sorption cycles in a thin palladium film (141nm) (99-06-09-2) (a) hydrogen pressure (b) mass trace (c) thermal trace .........................................................248 6-7: Schematic diagram of C2 species identified spectroscopically on nickel, platinum and palladium surfaces (circles represent surface metal atoms).......................................256 6-8: Ethylene hydrogenation over a palladium film (a) p(C2H4) (b) thermal trace (c) mass trace (00-08-16-2) ..................................................................................................260 6-9: Ethylene hydrogenation over a palladium film (a) p(C2H4) (b) thermal trace (c) mass trace (00-08-23-1) ..................................................................................................261 6-10: (a) Baseline corrected thermal power for hydrogenation of ethylene (00-08-16-2) (b) the catalytic surface activity vs. ethylene partial pressure .......................................262 6-11: Sample introduction setup for SAM formation experiment ..................................267 6-12: (a) mass trace of the self assembled monolayer formation of nonylthiol on a QCM, (b) thermal trace for self assembled monolayer formation of nonylthiol, (c) automatic baseline assignment to the thermal trace by OriginTM .....................................268 6-13: (a) thermal power with baseline fit (I) (b) thermal power, baseline fit (I) subtracted (c) integrated heat using baseline fit (I) (d) thermal power with baseline fit (II) (e) thermal power, baseline fit (II) subtracted (f) integrated heat using baseline fit (II) .................................................................................................................................269 6-14: Break down of energetics of SAM formation........................................................272 6-15: Enthalpy of (a) condensation (b) fusion for straight chain alkyl thiols (sulfur at position 1)......................................................................................................................273 7-1: lysozyme hydration/dehydration (a) water vapor activity (00-02-03-2) (b) mass trace (00-02-03-2) (c) thermal power (00-02-03-2) (d) water vapor activity (00-02-04-1) (e) mass trace (00-02-04-1) (f) thermal power (00-02-04-1)............................................................................................286 7-2: lysozyme hydration/dehydration (a) water vapor activity (00-02-06-1) (b) mass trace (00-02-06-1) (c) thermal power (00-02-06-1) (d) water vapor activity (00-02-07-1) (e) mass trace (00-02-07-1) (f) thermal power (00-02-07-1).........................................287 7-3: lysozyme hydration/dehydration (a) mass trace (00-02-09-2) (b) thermal power (00-02-09-2) (c) water vapor activity (00-02-09-2) (d) mass trace (00-02-10-1) (e) thermal power (00-02-10-1) (f) water vapor activity (00-02-10-1)....................................288
xvii
7-4: determination of the enthalpy of hydration for lysozyme (a) baseline subtracted thermal power (00-02-03-2) (b) integrated heat (00-02-03-2) (c) ratio of the integrated heat trace over the mass trace (00-02-03-2), enthalpy of hydration of lysozyme ........................................................................................................................289 7-5: D’Arcy and Watt sorption isotherm for water vapor sorption by lysozyme (1) first term of D’Arcy Watt equation, water sorption in region (I) (2) second term, weak nonpolar sorption sites, region (II) (3) sorption at multilayer binding sites, region (III) (4) combined terms (5) measurements by QCM/HCC................................292 7-6: Water vapor sorption in Tecoflex (99-10-26-2) (a) water vapor activity (b) mass trace (c) thermal power; water vapor sorption in lysozyme (99-08-10-2) (d) water vapor activity (e) mass trace (f) thermal power...............................................................294 7-7: Hydration enthalpy of lysozyme as the function of water content (a) QCM/HCC measurements (b) from temperature dependence of gravimetric measurements by Bone (ref 15) and Lüscher-Mattli (ref 16) ...........................................296 7-8: Entropy of hydration of lysozyme as a function of water content (obtained form QCM/HCC measurements) ..................................................................................297 8-1: Possible forms of pharmaceutical formulations ......................................................311 C-1: Log vapor pressure vs. inverse absolute temperature for (a) water (b) methanol…....................................................................................................................325 C-2: Log vapor pressure vs. inverse absolute temperature for (a) ethanol (b) acetone….......................................................................................................................326 C-3: Log vapor pressure vs. inverse absolute temperature for (a) hexane (b) toluene.....327 C-4: Log vapor pressure vs. inverse absolute temperature for (a) acetonitrile (b)triethylamine ..............................................................................................................328 C-5: Log vapor pressure vs. inverse absolute temperature for N,Ndimethylformamide.................................................................................................329 C-6: Log vapor pressure vs. inverse absolute temperature for (a) CCl4 (b) C2H2Cl2........331 C-7: Log vapor pressure vs. inverse absolute temperature for (a) C2HCl3 (b) CHCl3......332
xviii
Abstract Quartz Crystal Microbalance/ Heat Conduction Calorimetry (QCM/HCC), a new
technology capable of isothermal, high sensitivity, mass and heat flow measurements at a solid/gas interface. Hamid M. Shirazi
Allan Smith
A new technology called the quartz crystal microbalance/heat conduction
calorimeter (QCM/HCC) capable of simultaneous, high sensitivity mass change and heat
flow measurements under isothermal conditions, was developed. The QCM/HCC consists
of two highly sensitive sensors. A quartz crystal microbalance measures mass changes on its
surface (to±0.25ng/cm2), while a thermopile positioned between the QCM and a heat sink
measures heat flows (to ±50nW) to and from the surface of the QCM.
In the preliminary developmental stage the operation of the QCM/HCC was
examined. The QCM/HCC setup was improved by the integration of a gas flow system and
an isothermal housing. Different models describing the viscoelastic behavior of the coating
of QCMs were employed to evaluate the mass sensitivity of the QCMs. In an attempt to
minimize human supervision the operation of the QCM/HCC was fully automated by a
LabView program.
In the application phase the QCM/HCC was utilized in five separate experiments,
each investigating one important system.
The sorption/desorption enthalpies of six different organic vapors in two
polyetherurethane (Tecoflex) thin films (0.78µm and 2.09µm) were measured. A linear
xix
solvation energy relationship (LSER) was established for Tecoflex. It was shown how the
QCM/HCC could be used to determine thermodynamic parameters (∆sorptionH, K, ∆sorptionG,
and ∆sorptionS) as well as kinetic information (diffusion coefficient) for sorption processes
under isothermal conditions.
The energetics of hydrogen sorption in a thin electrodeposited palladium film was
investigated. The hydrogen sorption enthalpies were comparable to those measured by
other investigators for the β-phase of hydrogen-palladium solid solution. The surface
activity of the same palladium sample for catalytic hydrogenation of ethylene at ambient
temperature was estimated from the heat flow measurements.
The energetics of self-assembled monolayer formation (SAM) of nonylthiol on gold
was measured directly for the first time. A model proposed for the breakdown of the
enthalpy of SAM formation into three individual steps explained an observed increase in
the magnitude of the ∆SAM formationH at higher surface coverage.
Hydration/dehydration enthalpy of lysozyme was measured directly for the first
time. The measured hydration enthalpies had a large magnitude at low water vapor activity,
but approached the enthalpy of condensation of water for higher water contents.
1
Chapter 1- Introduction
1.1 The invention of the QCM/HCC
The quartz crystal microbalance/heat conduction calorimeter (QCM/HCC) is a
new technology capable of measuring mass change and heat flow at a surface
simultaneously with high precision. The QCM/HCC has two very sensitive sensors: a
5MHz "AT cut" quartz crystal microbalance (QCM)*, which measures mass changes in the
ng range; and a thermopile†, which measures heat flow in the µW range. The idea of
combining these two sensors in such fashion was originated by Professor Allan Smith as he
was on his sabbatical leave at Lund University in Sweden, and was faced with the challenge
of measuring the enthalpy of sublimation of solids with very low vapor pressures under
ambient conditions. Professor Ingemar Wadsö was also actively involved in the early stages
of developing and designing this apparatus. The first prototype of the QCM/HCC was
physically realized at the Thermochemistry division of Lund University in May of 1997. It
then arrived at Drexel University in Philadelphia in late summer of the same year.
As with any new instrumentation considerable time and effort was spent to
understand the behavior of the individual sensors in the QCM/HCC in order to bring it to
a fully operational condition. Because of the high sensitivity of the QCM/HCC good
control of its environment was essential. In order to take full advantage of the high
* Maxtek, P/N 149211-1, Model SC-501-1 † Melcor, Small, FC 0.45-66-05
2
sensitivity of this instrument, a controlled isothermal surrounding had to be employed as
the housing for the QCM/HCC. Next a series of experiments was conducted to use the
thermal power dissipated in the QCM to calibrate the heat flow sensors. A gas flow system
was also designed and built to control the composition of chemical vapors above the active
surface of the QCM/HCC.
In the application phase we tried to identify worthwhile systems to the scientific
community, where the QCM/HCC could be utilized. We planned to conduct experiments
in the following five areas:
1. Studying thin polymeric films as they are exposed to organic vapors. The
results of these experiments are of special interest to the industry of food
packaging, paints and coatings. Other polymers such as those used as
stationary phases in separation techniques and chemical sensing can also
be characterized1-12.
2. Studying the hydrogen/Pd system (and hydrogen/carbon allotropes)
could provide a better understanding of important processes such as
surface catalysis, corrosion and metal hydride chemical stability13-20.
3. Hydration/dehydration of thin protein films have been the subject of
many ongoing investigations. These studies are aimed toward gaining a
better understanding of protein conformation and its effects on the
biological functions of the protein in the hydrated state21-25.
4. Understanding the details of the formation of a self-assembled monolayer
on metallic surfaces is essential for surface engineering and lubrication
techniques of micromachinery26-39.
3
5. Finally, to complement another parallel project in our research laboratory,
we are interested in measuring enthalpies of sorption of organic vapors in
C60 fullerene films40-42.
So far we have conducted experiments in the first three of the above-mentioned areas. The
results of these experiments will be discussed in this thesis.
1.2 QCM/HCC as a new technique
Although the two sensors in the QCM/HCC have never been coupled in such a
manner before, each one of them individually has been used extensively in a number of
well-established techniques. Since the earliest applications of QCMs as thickness
monitoring devices, they have been used for detection and quantification of many gaseous
compounds, aerosols and suspended particles in air, electrogravimetric analysis and even as
GC and HPLC detectors 43-45.
Thermocouple plates as heat flow sensors have also been widely used in heat
conduction calorimetry and other techniques 46-50. Nevertheless, currently there is no
other single method that can provide the same kind of information with the same sensitivity
as the QCM/HCC. All other methods fall either under Thermal Analysis (TA): the analysis
of a change in a sample property, which is related to an imposed temperature alteration, or
Calorimetry: the measurement of heat 22. The thermoanalytical methods can be divided
into the following main subdivisions (not including those analyzing mechanical, electrical,
optical, magnetic and acoustic properties of samples):
4
1. Differential thermal analysis (DTA). This technique is based on analyzing
the difference in temperature between the sample and a reference as they
are subjected to a controlled temperature program.
2. Differential scanning calorimetry (DSC). In both heat flux DSC and
power compensating DSC the difference in the heat flow rate to the
sample and to a reference is analyzed as they are subjected to a controlled
temperature program.
3. Thermogravimetric analysis (TGA), thermogravimetry (TG). Here the
change in the sample mass is analyzed as the sample is subjected to a
controlled temperature program.
The three primary classifications for calorimetric techniques are related to:
1. The principle of measuring
a. Heat-compensating: determination of the energy (power) required for
compensating the heat to be measured.
b. Heat-accumulating: determination of temperature change resulted by the
heat to be measured.
c. Heat-exchange: determination of difference in temperature between
sample and surrounding resulted by the heat to be measured.
2. The mode of operation
a. Static: isothermal (constant temperature), isoperibol (constant
temperature surrounding with the possibility of difference in the
temperature of the measuring system) and adiabatic (no heat exchange
between the measuring system and the surroundings)
5
b. Dynamic: scanning of surrounding, isoperibol scanning (scanning of
sample in a constant temperature surrounding), adiabatic scanning.
3. The construction mode
a. Single measurement
b. Twin or differential measurement
In principle the QCM/HCC could function as either a thermal analyzer or a
calorimeter. As a thermal analyzer the change in sample mass as well as the heat flow to the
sample and reference could be analyzed as they are subjected to a controlled temperature
program. In this mode the QCM/HCC would classify as a DSC/TGA in a controlled
chemical composition environment. Although the QCM/HCC has never been used in this
mode, it is worthwhile to recognize and explore its potential capabilities in the future. In all
experiments conducted so far the QCM/HCC has been used to measure heat flow and
mass change under isothermal conditions, hence as a calorimeter. According to the above
classifications the principle of measurement of the QCM/HCC is heat-exchange, the mode
of operation is isothermal, and the construction principle falls under twin measuring
systems. We need to point out that the QCM/HCC is different from all other calorimetric
methods. It is unique because in addition to thermal data it simultaneously provides
information about mass changes in the sample as the composition of the atmosphere above
the sample is altered.
To give an example of the variety of information that can be extracted from data
obtained during a single measurement period consider the sorption of an organic vapor in a
thin polymeric film. During such a run we gather data from three different channels
simultaneously, as the vapor pressure of an organic compound above the polymer film is
changed periodically. From the oscillation frequency of the QCM we obtain the mass of the
6
dry film and the mass of organic compound sorbed into the film at different vapor
pressures. The thermopile signal is converted to thermal data and the data from the flow
system provides the concentration of the organic vapor above the polymer film. Using the
thermal data and mass of the organic compound in the polymer film we can directly arrive
at the molar enthalpy of sorption (∆sorptionH). Concentrations of the organic compound in
the film and in the gas above the film gives the partition coefficient or equilibrium constant
(K) at different vapor pressures. This information can be used to construct an isotherm for
the sorption process. The Gibbs free energy (∆sorptionG) can also be obtained from the
partition coefficient and finally the sorption entropy (∆sorptionS) can be calculated using
∆sorptionG and ∆sorptionH. Furthermore, in addition to the above thermodynamic information,
kinetic data from the mass trace can be used to determine the diffusion coefficient of the
organic compound in the polymer film as the function of vapor pressure above the film.
1.3 Thesis overview
The next two chapters of this thesis are organized with the intention to give the
reader a better understanding of the principles involved in the operation of the two sensors
of the QCM/HCC. In the next chapter the operation of the QCM as a balance is described
in detail. The mass sensitivity of the QCM is discussed along with parameters that may
affect it. A historical review of different theories describing the mass sensitivity of the QCM
is given. Different models used to predict the oscillatory behavior of a coated QCM as the
viscoelastic property of the coating may change are introduced.
7
In chapter 3 the operation of the thermopile as a heat flow sensor is discussed. The
principles involved in heat conduction calorimetry are introduced. The equivalent circuit of
the QCM was described in chapter 2. In chapter 3 it is shown how the power dissipated in
this circuit can be used for the calibration of the thermopile. A brief summary of general
application areas of heat conduction calorimetry is also presented.
Chapter 4 gives a description of the QCM/HCC apparatus and its components.
The development of the QCM and major improvements over time are described. Important
advances during this stage came about as the result of four major projects. As the final
design of the electronic circuitry of the QCM/HCC was complete, a low noise preamplifier
was calibrated at different settings. Two mass flow controllers were calibrated and used as
part of a gas flow system to be used as the sample introduction system. A LabView
program was written to fully automate the operation of the QCM/HCC. Finally, different
thin film preparation methods were explored for making thin and uniform films over the
entire QCM surface. However, the film preparation methods will be discussed as part of the
experiments where they were used in the following chapters.
Each of the experiments presented in chapters 5, 6 and 7 is the study of one or
more important systems. Finally chapter 8 summarizes the results of all of the experiments
and gives suggestions for future activities.
Chapter 5 presents measurement of sorption/desorption enthalpies of six different
organic vapors in two polyetherurethane (Tecoflex) films. A linear solvation energy
relationship (LSER) was established for Tecoflex. Diffusion coefficients of some of the
organic vapors in Tecoflex were also determined.
The results of three separate experiments are presented in chapter 6. Sorption of
hydrogen in a thin palladium film was investigated. The catalytic activity of the same
8
palladium film during ethylene hydrogenation was estimated from the observed heat flow
on the surface of the QCM. A model was proposed for the breakdown of the enthalpic
contributions from different processes during the self-assembled monolayer (SAM)
formation of nonylthiol on gold.
In chapter 7 we describe the details of an experiment, where the
hydration/dehydration enthalpy of lysozyme was measured directly for the first time.
9
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12
Chapter 2- Quartz Crystal Microbalance
2.1 The Piezoelectric Effect
"Piezo" comes from the Greek word piezin meaning "to press". Cady1 defined
Piezoelectricity as " electric polarization produced by mechanical strain in crystals belonging
to certain classes, the polarization being proportional to the strain and changing sign with
it." He believed Coulomb to be the first to hypothesize the possibility of production of
electricity by application of pressure upon certain material. But the credit of being the first
to actually observe piezoelectricity goes to the Curie brothers, Pierre and Jacques2. In 1880
they published a paper in which they reported the observation of generation of a potential
between deformed surfaces of a quartz plate under strain. This phenomenon can only be
observed in certain crystals containing positively and negatively charged ions, which are
displaced as the crystal experiences strain. Only 20 of the 32 crystal classes, which lack a
center of inversion, can exhibit piezoelectricity3. The most commonly used piezoelectric
material is crystalline α quartz (SiO2). The advantage of using quartz over other crystals is
that it is a completely oxidized material and insoluble in water. It can also resist
temperatures up to 5790C still maintaining its piezoelectricity4.
Not predicted by the Curies, the converse piezoelectric effect was later suggested by
Lippman5. According to the converse piezoelectric effect application of an electrical field
across any piezoelectric material results in its deformation. Thus when a piezoelectric crystal
13
such as a quartz wafer is placed in an alternating electric field, it will oscillate in a
mechanically resonant mode resulting in a standing acoustic wave across the quartz wafer.
The mode of oscillation of the quartz wafer will depend upon the angle at which it was cut
with respect to the principle optic axis. The optic axis is the major axis of growth of the
quartz crystal and is usually labeled as the Z-axis in an orthogonal X, Y, Z coordinate
system. As can be seen in figure 2-1 three separate Y axes perpendicular to the prism faces
can be identified along with three separate X axes bisecting the edges of the prism.
Figure 2-1: Typical quartz crystal cuts. Figures taken from http://online-product.com/crystal/quartz03.html and
http://literature.agilent.com/litweb/pdf/5965-7662E.pdf
14
When a quartz plate cut along the X-axis is compressed, a relatively large voltage is
produced. On the other hand, for a similar plate cut along the Y-axis a voltage is generated
as the result of pure shear stress. Although both of the above plates will oscillate in an
alternating electric field, their oscillation frequency is easily influenced by changes in the
temperature. An X plate quartz has a negative temperature coefficient, whereas a Y plate
exhibits a positive temperature coefficient. Most commonly used crystal oscillators are the
AT and BT crystals, cut at 35015' and 49000' angles (with respect to the optic axis)
respectively. Both cuts exhibit shear waves in the thickness direction and have temperature
coefficients of virtually zero at temperatures near 250Celcius6.
2.2 Mass sensitivity
2.2.1 Historical Review
As additional mass is bound to the surface of a thin quartz resonator, its resonance
frequency decreases. When a QCM is used for mass measurements, a quantitative
relationship between the oscillation frequency shift and the added mass must be established.
In 1959 Sauerbrey7,8 derived the first equation describing the frequency to mass
relationship. In his work Sauerbrey made the assumption that for small mass changes, the
added mass could be treated in the same manner as an additional mass of quartz resulting in
an added thickness.
15
quartz Mq
λq/2 lq
quartz Mq
λq/2 lq
∆Mq
∆lq
a)
b)
Figure 2-2: Sauerbrey's model of an oscillating QCM, a) before addition of mass, b) after addition of mass
Figure 2-2a) shows Sauerbrey's model to represent an uncoated oscillating QCM
with a mass of Mq and a thickness of lq. The resonant frequency (fq) of this QCM is then
simply:
where λq is the wavelength of the propagating acoustic wave, which is twice the
thickness of the QCM (lq). Vq is the speed of the propagating wave (Vq =λq fq).
In the case of addition of a mass on the surface of the QCM a change in the
thickness of the QCM (∆lq) will occur, which further causes a change in the oscillation
q
q
q
qq l
VVf
2==
λ(1)
16
frequency of the QCM (∆fq). An increase in thickness and mass results in a decrease in the
frequency in accordance with equations (2) and (3).
Equation (4) can be obtained from the combination of equations (1) and (3)
In equations (4) and (5) A is the area of the quartz crystal in cm2, ρq is the density of
quartz (2.648 g cm-3) and Vq is the speed of the propagating acoustic wave (3.336×105 cm s-
1).
For a quartz crystal microbalance with a resonant oscillation frequency of 5MHz the
mass sensitivity C in equation (6) is –56.6 Hz µg-1 cm2.
According to equation (6) an addition of 1µg of mass over an area of 1 cm2 of the
QCM surface results in 56.6 Hz decrease in the oscillation frequency. In other words, a shift
q
q
q
q
l
l
f
f ∆−=
∆(2)
q
q
q
q
M
M
f
f ∆−=
∆(3)
qqq
q
q
q MAV
f
f
f∆
−=
∆
ρ
2 (4)
AM
ff qqq
∆×−=∆ − 261026.2 (5)
(6) AM
f∆
=∆ C
17
(7) qq
qf
MM∆
=−
τ
ττ
of 1 Hz in the oscillation frequency corresponds to a mass change of 17.7 ng cm-2 on the
QCM surface.
In his work Sauerbrey reported experimental mass measurements with a 14 MHz
AT-cut QCM to be accurate within 2% of values obtained using equation (5) for mass
loadings up to 20µg cm-2. In the subsequent years to Sauerbrey’s original work the useable
mass range for QCM was significantly expanded mostly due to improvements in the crystal
design (plano-convex crystals)9, better feedback gain control of oscillator driver circuits and
new theories describing the frequency to mass relationship. In 1971 Behrndt10 showed that
the mass change on the QCM surface is directly proportional to the oscillation period (τ,
τ=1/f).
τq and τf in equation (7) are the oscillation periods for a QCM before and after mass
loading, respectively. Comparison of the workable range mass loading for Sauerbrey’s
equation (∆M/Mq <2%) with that for Behrndt’s equation (∆M/Mq <10%) may be
confusing at first. Benes11,12 argues that an inspection of the two equations (3) and (7)
reveals the latter to make more sense mathematically, since Sauerbrey’s equation is based on
an inverse proportionality between the thickness (lq) and the oscillation frequency (fq) and
Behrndt’s on a direct proportionality, so that
(8) q
q
q
q
q
q
q
q
f
f
l
l
M
M ∆−≅
∆=
∆=
∆
τ
τ
18
The work of Miller and Bolef13,14 in 1968 constituted the first basis for the
treatment of an oscillating quartz/film as a composite resonator. They described a one-
dimensional continuous acoustic wave originating from a quartz plate and its behavior at
the quartz/film interface based on its transmission (Tqàf) and reflection (rqàf) coefficients.
They obtained the expression
for a loaded quartz crystal microbalance, where f is the composite resonant frequency,
and Zq=ρqVq and Zf=ρfVf are the characteristic acoustic impedances of quartz and of the
mass loading, respectively.
In 1972 Lu and Lewis15 adopted the above expression and by applying lengthy but
simple algebra reduced it to
(9) 0)
2sin()
2sin()1(
)]2
cos()2
cos(1)[1()]2
cos()2
[cos(2
2
2
=−+
−++−
fq
fqqf
ff
ff
r
ff
ff
rf
ff
fr
ππ
ππππ
(11) fq
fqqffq ZZ
ZZrrr
+
−=−== →→
fq
qfq ZZ
ZT
+== →
2T (12)
(13) 0tantan =+ ππf
fq
q ff
Zff
Z
(10) f
f
ff
q
q
c
lf
c
lf
ρρ 21
,21
==
19
(14) fffffqqqqq cVZcVZ ρρρρ ==== ,
)tanarctan(qf
q
q
qf
q ff
Z
Z
fZ
fZ
MM π
π−=
∆ (15)
Finally using the following elementary substitutions (10) and (14) they arrived at
equation (15).
where the cq and cf are the shear stiffness constants for quartz and the mass layer,
respectively. The usable mass range for equation (15) (∆M/Mq<70%) has experimentally
been evaluated to be superior to those of Sauerbrey’s (∆M/Mq<2%) and Behrndt’s
(∆M/Mq<10%) for rigid material. It can be shown that both Sauerbrey’s and Behrndt’s
equations are special cases of equation (15) where the ratio of the acoustic impedances
(z=Zq/Zf) is unity. The above method gave birth to the so-called Z-match technique
devices. The only shortcoming of this technique is the fact that knowledge of acoustic
impedances of different materials is required, which may not be always readily available.
20
2.2.2 Different models
In the absence of information about the ratio of acoustic impedances (z=Zq/Zf)
equation (15) becomes useless, as there are two unknowns in a single equation. However,
since equations (13) and (15) are derived from Miller’s and Bolef’s model, which is valid for
not only the fundamental resonant frequency but also for all overtone frequencies, it is
possible to solve for two unknowns, if measurements can be performed at the fundamental
as well as at an overtone oscillation frequency. This requires hardware capable of switching
from the excitation of the fundamental to that of an overtone frequency. For multiple
frequency measurements equation (15) takes the form11
where the subscript n in fn is the number of the overtone frequency and nq is an integer
number closest to fn/fq. The combination of two such equations for two different
frequencies yields the ratio of acoustic impedances, which can be entered back in equation
(15) for either of the frequencies to give the mass loading.
)]tanarctan(1
[q
n
f
nq
qf
q ff
Z
Znn
fZ
fZ
MM π
ππ−−=
∆ (16)
1)]tanarctan()(
)]tanarctan()(
222
111
1
2 =−−
−−
q
n
f
q
n
f
n
n
ff
Z
Znn
ff
Z
Znn
ff
ππ
ππ
(17)
21
There is extensive experimental data in the literature validating the useable mass
range of the above method for relatively large mass loading of rigid material such as metallic
films (Cu, Ag, Al, etc)11. For other non-rigid materials, however, the description of the
behavior of an acoustic wave penetrating a soft film is much more complex. The amplitude
of the acoustic wave is damped in a non-rigid material. When a QCM is coupled with a
“soft” material such as a polymer or even a liquid, both the amplitude and the phase of the
acoustic wave can be influenced by the density (ρf), viscosity (ηf), complex shear modulus
(Gf) and the thickness (hf) of the mass loading16. More comprehensive models considering
the above effects usually relate the acoustical impedance (Za) of the QCM/mass composite
to the electrical input impedance of the QCM/mass equivalent circuit (Ze)17. In order to
apply these models, one needs to understand the electrical equivalent circuit of the QCM as
well as the nature of interaction of acoustical energy with matter.
A quartz resonator as an electroacoustical device can be described mechanically in
terms of its mass, its ability to yield elastically (its shear modulus) and resistance. It can also
be presented as a network of lumped electrical parameters consisting of an inductor, a
capacitor and a resistor (the Butterworth-Van Dyke equivalent circuit)9.
22
In figure 2-3 the inductor L1 represents the inertial component (the oscillating
mass), the capacitance C1 represents the energy stored during oscillation due to the
elasticity, and the resistance R1 represents the energy dissipation due to internal friction and
mechanical and acoustical losses to the mount and the surroundings. C0 is the static
capacitance of the quartz and its electrodes, which is parallel with the series or the motional
branch. In the series branch a fully charged capacitor C1 will immediately begin to discharge
resulting in a current through the inductor L1. Since an inductor resists changes in the
current by self-induction, the current will continue to flow until it is all used to charge the
capacitor C1, this time with the opposite polarity. Once the current drops to zero the
capacitor will discharge again. If R=0, the repetition of this process will result in electrical
oscillation indefinitely. If R>0, the oscillation will be damped so that it decays in amplitude
until it disappears completely. In terms of the mechanical model describing the
displacement of the surface of the quartz crystal in a shear mode, when the capacitor (C1) is
R1 L1 C1
C0
Figure 2-3: Equivalent circuit of a quartz crystal microbalance
23
fully charged the potential energy and the shear displacement are at a maximum, while the
kinetic energy is zero. The potential energy is completely converted to kinetic energy when
the shear displacement of the quartz surface is zero. The displacement will again approach
its maximum value as all the kinetic energy reverts to potential energy. The relationship
between the electrical and the mechanical models is best seen in the their equations of
motion (18 and 19).18
The terms in equations 18 and 19 will be discussed later in this chapter and may be
represented by other symbols, but for the purpose of showing this relationship at this point
we define F as the force, V as the voltage and K (K=F/V) as the electromechanical
coupling coefficient, m is mass, r is a dissipation factor, cm is elasticity, x is displacement, q
is charge and V is the applied voltage. We will continue with the description of the
electromechanical model until a similar relationship is obtained containing the electrical and
acoustical impedances.
Table 2-1: Typical values for a 5MHz AT cut QCM
R1 14.80Ω
L1 0.011µH
C1 90nF
C0 0.053nF
xcdt
dxdt
xdmF
m
)1
()()(2
2
++= r (18)
qCdt
dqR
dtqd
LV )1
()()(1
12
2
1 ++= (19)
24
It is instructive to have a good understanding of the complete electrical equivalent
circuit and all its components. To this end, the behavior of the single components with an
alternating current will be reviewed.
An alternating voltage can be described by a sine or cosine function, which gives the
instantaneous magnitude of the voltage (v) as the function of time (t).
When an alternating voltage v is applied across a resistor R, the instantaneous
current (i) in R is simply:
The relationship between the current and the voltage can best be seen on a phasor
diagram. Such diagram shows the current (I) and the voltage (V) as rotating vectors, of
which the projections along the x-axis represent the instantaneous current (i) and voltage
(v).
timetfrequencyangularpotentialmaximumVpotentialousinstantanevtVv
=====
,,,)cos(
ωω
(20)
)cos( tRV
Rv
i ω==
(21)
25
Next, if the resistor is replaced by a capacitor, the instantaneous current (i) is the
rate of change of the charge (q) on the capacitor:
I V
v i
Figure 2-4: Phasor diagram, alternating current through a resistor, phase angle=00
)90cos(
)90cos()sin(
)cos(
0
0
+=
+=−==
==
tIi
tCVtCVdtdq
i
tCVCvq
ω
ωωωω
ω
(22)
I
V
v i
Figure 2-5: Phasor diagram, alternating current for a capacitor, phase angle=-900
26
Finally, for the circuit with only an inductor the instantaneous current can be
described as follows:
When all three components are connected in series, in a LCR circuit, the phasor
diagram becomes more complex. If current (I) passes through the circuit, according to
Kirchhoff's law the total instantaneous voltage (v) across all three components is the vector
sum of the phasors of the individual voltages.
v Ldidt
V t
diVL
t dt iVL
t constant if i at t then constant
i I t
= =
= = + = = =
= −
cos( )
cos( ) , sin( ) ,
cos( )
ω
ωω
ω
ω
0 0 0
900
(23)
I
V
v i
Figure 2-6: Phasor diagram, alternating current through an inductor, phase angle=900
27
In the above diagram V=IZ is the vector sum of the individual voltages, where Z
denotes the total impedance of the circuit, XL and XC are the inductive and capacitive
reactances, respectively.
At the series resonance the impedance (Z) reaches a minimum and the inductive
and capacitive reactances become equal.
I
VR=IR v i
VL=IX
VC=IXC
V=IZ
Figure 2-7: Phasor diagram for a LCR circuit (not at resonance).
Z R X X
X L XC
L C
L C
= + −
= =
2 2
1
( )
,ωω
(24)
CL XXLC
resonanceAt == ,1
0ω
(25)
28
Figures 2-8 and 2-9 show the admittance phase angle (θ) and the admittance
(Y=1/Z) measured at different frequencies for a 5MHz AT-cut QCM. On two occasions
the phase angle approaches zero. The first occurs at the series resonant frequency, also
coinciding with the maximum for the admittance magnitude. The second marks the parallel
resonant frequency, which corresponds to the minimum admittance. At low frequencies the
capacitive reactance dominates and the circuit behaves as a pure capacitor. The admittance
phase angle (θ) is close to 90o indicating that the voltage is leading the current. As the
frequency approaches the resonant region, the inductive reactance becomes more
pronounced. Exactly at resonance the contributions from the capacitive and the inductive
reactance cancel one another, so that the phase angle becomes zero (θ=0o) and the
-100
-80
-60
-40
-20
0
2 0
4 0
6 0
8 0
100
4994000 4995000 4996000 4997000 4998000 4999000 5000000 5001000 5002000
Frequency/Hz
Adm
ittan
ce p
hase
ang
le/d
egre
e
Figure 2-8: Phase angle of admittance for a 5MHz AT-cut quartz crystal measured with an impedance analyzer
29
impedance reaches a minimum. The admittance, on the other hand, is at its maximum. At
this point the circuit behaves as a pure resistor. As the frequency increases, the admittance
phase angle decreases until the circuit becomes totally inductive in nature (admittance phase
angle (θ) =-90o).
Increasing the frequency gives the circuit one more chance to resonate when the
parallel inductive and capacitive reactances cancel. At parallel resonance the admittance
phase angle passes through zero again and for higher frequencies goes back to 90o.
The admittance plot can also be broken into its imaginary (susceptance) and real
(conductance) components as is shown in figure 2-10.
1 .E-05
1 .E-04
1 .E-03
1 .E-02
1 .E-01
1 . E + 0 0
4 9 9 4 0 0 0 4995000 4 9 9 6 0 0 0 4997000 4998000 4999000 5000000 5 0 0 1 0 0 0 5002000
F r e q u e n c y / H z
Adm
ittan
ce/S
Figure 2-9: Admittance magnitude for a 5MHz AT-cut quartz crystal measured with an impedance analyzer
30
The correlation between the susceptance (B) and the conductance (G) can be
formulated as
According to equation (26) the B-G curve is anticipated to be a circle, of which the
radius equals the reciprocal of the resistance of the QCM at resonance.
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
4994500 4995000 4995500 4996000 4996500 4997000
Frequency/Hz
B-G
/S
Figure 2-10: Susceptance and conductance of a 5MHz AT-cut quartz crystal measured with an impedance analyzer
220
2 )21
()()21
(R
CBR
G =−+− ω
(26)
31
To consider the electrical or acoustical impedance of an added mass layer to the
QCM it needs to be incorporated in the equivalent circuit of the QCM. The modified
circuit is shown below twice, first as the Butterworth-Van Dyke model, and then as a
transmission line model19. Here, L2 represents the added mass, R2 represents the resistive
viscosity component and C2 represents the elasticity (shear modulus) of the added mass.
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Conductance(G)/S
Susc
epta
nce(
B)/
S
Figure 2-11: B-G curve for a 5MHz AT-cut quartz crystal, as measured with an impedance analyzer
32
Figure 2-13 is Mason's transmission line model. The transmission line from the EF plane to
the IJ plane represents an acoustic propagation across the quartz, which is coupled to the
AB electric junction through a transformer. The turns ratio 1:n of the transformer is
proportional to the electromechanical coupling factor of quartz (K).
33
C0
jX
1 : n
D C
F E
H G
Film
Quartz Resonator
Z=0
Z=0 J I
Figure 2-13: Transmission line model for a mass loaded QCM
Figure 2-12: Equivalent circuit of a mass loaded QCM
L2 Quartz Resonator Film
A B
R1 C1 L1
C0
R2
C2
34
The voltage and current in this model represent shear stress and the particle
velocity, respectively.
In the above model (figures 2-12, 2-13) the electrical input impedance is given by19
where f is the excitation frequency, and Φq is the complex acoustic wave phase shift.
Zm is the electrical impedance for the motional arm parallel to the static capacitance
C0, obtained from setting Z=(j2πfC0 +1/Zm)-1 in equation (27).
The electrical impedance Zm can be further separated into two terms, Z1 and Z2
where Z1 represents the electrical impedance of the unperturbed QCM and Z2 is the
electrical impedance due to the mass loading20.
Φ−
−Φ
Φ−=
)cot()(1
)()2
tan(2
12
1 2
0q
q
f
q
fq
q
Z
Zj
Z
Zj
KfCj
Zπ
(27)
−−
Φ
Φ
Φ−
= 1)()
2tan(2(
)cot()(1
21
20
q
fq
q
f
m
Z
Zj
K
Z
Zj
fCjZ
π(28)
21
1
02
20 )2
tan(2
)(
124
)(
1)
2tan(2
21
ZZZ
Zj
fCK
Z
Z
KfCj
Zq
q
f
q
fq
q
qm +=
Φ−
Φ
+
−Φ
Φ=
−
ππ(29)
35
First we consider the first part of equation (29) representing the electrical
impedance (Z1) for the unperturbed QCM and try to decompose it further to show the
contribution of the individual electrical components (resistance, capacitance and
inductance). Since at resonance Re(Φq)=Nπ , N being an odd integer for the resonator
harmonic number, the tangent function can be written as
The phase shift (Φq)=2πfhq(ρq/cq)1/2 is a complex quantity, where (hq) is the
thickness of quartz and (cq=cq0+j2πfηq) is the shear modulus of quartz. The real part of the
shear modulus (cq) here represents the shear stiffness (cq0) and its imaginary part (ηq) is the
phenomenological viscosity of quartz signifying losses in the quartz. Substituting these
quantities in equation (31), which itself was obtained from the first part of equation (29)
and equation (30), we arrive at equation (32).
22)(
4)
2tan(
q
N Φ−
Φ≅
Φ
π(30)
−
Φ−≅ 1
8
)(
21
2
22
01 K
N
fCjZ qπ
π(31)
−+
+
≅
02
22
2
02
02
2
02
22
1 88)(
21
82
8
)2(
CKKN
fjcCK
chfj
cCK
hfZ
q
qqq
q
qqq ππ
ρπ
ηρπ (32)
1111 2
12
fCjfLjRZ
ππ ++= (33)
36
Comparison of equations (32) and (33) clearly shows the relationship between the
electrical impedance circuit elements and the acoustical/mechanical properties of quartz. A
similar relationship can be established for a mass loading starting from the second part of
the equation (29). The surface mechanical impedance for a film with thickness h is
G (G=G'+jG") is the complex shear modulus of the film. The real part of the shear
modulus is called the storage modulus (G') representing energy storage during oscillation.
The imaginary part is the loss modulus (G") giving rise to power dissipation in the film.
From the combination of the second term in equation (29) with equation (34) and using an
approximation of the tangent function for the film similar to that for the quartz in equation
(30) the electrical input impedance contributed by a viscoelastic film is given in equation
(35).
)2tanh( hG
fjGZ f
ρπρ= (34)
( )1
20
2
20
2
20
22
2 8
'42
21
2
'422
2
"4)2(−
+
+≅
ρπ
ππ
ππ
ππ
π
π
hN
NZCKf
fjGN
hGZCKffj
GN
hGZCKfZ qqq
(36) 1
22
22 2
12
1−
++=
fLjfCj
RZ
ππ (37)
22 )2()'(
28)2tanh(
hG
N
hG
jh
Gfj
ρπ
ρπ
ρπ
+≅ (35)
37
Comparison of the lumped-element model of the resistor, capacitor and inductor
parallel combination in equation (37) with equation (36) shows the relationship between the
electrical input impedance elements and the acoustical/mechanical properties of the film.
Z2 in equation (36) represents the electrical impedance contributed by a viscoelastic
film, where the electrical impedance of an "ideal" mass loading would be Z im1=jA2πfhρ. If
these two quantities are the same, the correction to the Sauerbrey's frequency to mass
relationship is negligible. By studying the ratio of values for the electrical input impedances
of a viscoelastic film over that of an ideal mass for different film thicknesses, it is possible
to identify a threshold value for the film thickness, beyond which corrections to the mass
measurement become necessary. For resonance to occur after the mass loading, the reactive
component (imaginary part) of the impedance in equation (37) must be Zero. The resonant
frequency is given by
After substituting equation (38) in equation (36) the ratio of the electrical impedance
for a viscoelastic film over that of an ideal film can be written as
'2
'12
22 Gh
GN
CLf f
ρ
ππ == (38)
])(1[)'"
(
)(
)'(8
2
2
21
2
f
fj
GG
f
fj
NZZ
f
f
im −+−=
π(39)
38
Figure 2-14 is a plot of the magnitude of the impedance ratio (Z2/Z im1) vs. the ratio
of the excitation frequency over the resonant frequency of a low-loss film (G"/G'<<1). For
thin films (f/ff<<1) the impedance ratio remains constant (0.81). In this regime an
acoustically thin viscoelastic film behaves in the same manner as an "ideal mass" would.
Therefore, corrections to the Sauerbrey equation are negligible. For thicker films (f/ff=1)
the impedance ratio eventually will reach a maximum. Under these conditions the observed
oscillation frequency is affected, not only by addition of mass, but also by the viscoelastic
properties of the film. Without knowledge of the mechanical properties of the film a
frequency to mass relationship is impossible to obtain. Figure 2-15 shows the phase angle
of the impedance ratio (Z2/Z im1) vs. the frequency ratio (f/ff) for the same low-loss film.
Here again there is no phase shift apparent for acoustically thin films (f/ff<<1). But as the
thickness increases, the phase angle begins to lag behind that of an ideal mass until the
oscillation of the film is completely out of phase with that of an ideal mass. Analyzing these
plots one can identify a maximum film thickness, where Sauerbrey's relationship is
applicable. For thicker films corrections need to be made to Sauerbrey's equations in order
to extract the part of the oscillation frequency related only to addition of mass on the QCM
surface.
Figures 2-16, 17, 18 and 19 show that for high-loss films deviations for the film
impedance from that of an ideal mass set in much earlier. Figures 2-20 and 2-21 show plots
of the magnitude and phase of the impedance ratio (Z2/Z im1) vs the frequency ratio (f/ff)
over a range of 0.1 to 5 for the film loss tangent (G''/G').
39
10-1
100
101
0
1
2
3
4
5
6
7
8
Figure 2-14: The magnitude of normalized impedance response to that of an ideal mass
for G"/G'=0.1
Mag
nitu
de,(Z
2/Z
im)
f/ff
40
10-1
100
101
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Phas
e an
gle,
(Z2/
Zim
)Deg
rees
f/ff
Figure 2-15: The phase angle for the normalized impedance response for G"/G'=0.1
41
10-1
100
101
0
0.5
1
1.5
2
2.5
3
3.5
Mag
nitu
de,(Z
2/Z
im)
f/ff
Figure 2-16: The magnitude of normalized impedance response to that of an ideal mass
for G"/G'=1
42
10-1
100
101
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Phas
e an
gle,
(Z2/
Zim
) deg
rees
f/ff
Figure 2-17: The phase angle for the normalized impedance response for G"/G=1
43
10-1
100
101
0
0.5
1
1.5
2
2.5
3
3.5
Mag
nitu
de,(Z
2/Z
im)
f/ff
Figure 2-18: The magnitude of normalized impedance response to that of an ideal mass
for G"/G'=2
44
10-1
100
101
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Phas
e an
gle,
(Z2/
Zim
) deg
rees
f/ff
Figure 2-19: The phase angle for the magnitude of normalized impedance response for G"/G'=2
45
Figure 2-20: The magnitude of normalized impedance response to that of an ideal mass as function of frequency ratio (f/ff) and loss tangent (G"/G')
f/ff G"/G'
Mag
nitu
de o
f Z2/
Zim
1
46
f/ff G"/G'
Phas
e an
gle
of Z
2/Z
im1
Figure 2-21: The phase angle for the normalized impedance response to that of an ideal mass as function of frequency ratio (f/ff) and loss tangent (G"/G')
47
The above model was developed by Stephen Martin and his coworkers20.
Kanazawa and Reed21-23 have taken a different approach in developing their own model.
In their work they consider the mechanical interactions between a QCM and a contacting
media caused by the coupling of the mechanical displacement and electrical potential in the
piezoelectric quartz. Their proposed geometry of the composite QCM/thin film oscillator
is described in figure 2-22.
In the above geometry the interface between the quartz and the overlayer has been
taken to be the origin (y=0). The quartz is characterized by its density (ρq), its shear
modulus(cq), its piezoelectric constant(e), its relative permittivity (ε), and a
phenomenological viscosity(ηq). The sum of two shear waves in the quartz with the form
(exp i2πft) one traveling in the +y and the other in the -y direction has been used to
describe the overall shear wave. kq and k in equations (40) and (41) are the wave vectors for
the shear wave in quartz and the overlayer respectively.
ρq, cq, e, ε, ηq
Quartz
Overlayer ρ, G, η
y=lf
y=0
y=-lq
Figure 2-22: Geometry of a composite resonator
48
The peak ac potential across the quartz is Φ0, so that -Φ0/2 is applied at the upper
quartz face (where y=0) and Φ0/2 at the bottom face (y=-lq). The shear wave equation for
the oscillating quartz and the overlayer are given in equations (42) and (43) respectively.
Equation (44) can be obtained from two successive integrations of equation (e u-ε
Φ=0) over y. E and F are undetermined integration constants.
The six undetermined (A, B, C, D, E and F) constants can be solved for by applying
the following six boundary conditions.
At y=-lq the stress is zero.
ftiykByikAu qqty π2exp)][exp(exp),( −+=
(40)
ufdy
udfi
ec qqq ρπηπ
ε2)2(
2
2
−=++
(42)
ufdy
udfiG ρπηπ 2
2
2
)2()2'( −=+
(43)
FEyue
++=Φε
(44)
ftikyDikyCu ty π2exp)][exp(exp),( −+=
(41)
0)exp()2()exp()2( =+++−−++ eElikBfie
ciklikAfie
cik qqqqqqqqqq ηπε
ηπε
(45)
49
At y=-lq the potential is + Φ0/2
Across the y=0 interface the stress is continuous
Across the y=0 interface the displacements are continuous
At y=0 the potential is - Φ0/2
At y=lf the stress is zero
Evaluation of six constants will provide the information that can be used to obtain
the current density (J).
2)exp()exp( 0Φ
=+−−− FEllikBe
likAe
qqqqq εε
(46)
0)2'()2'()2()2( =++++−++−++ eEDfiGikCfiGikBfie
cikAfie
cik qqqqqq ηπηπηπε
ηπε
(47)
0=−−+ DCBA
(48)
20Φ
−=++ FBe
Ae
εε
(49)
0)exp()exp( =−− ff iklDiklC
(50)
feEiJ π2−=
(51)
50
4.97 4.98 4.99 5 5.01 5.02 5.03 5.04
x 106
10-3
10-2
10-1
100
101
102
103
Oscillation frequency/Hz
Ele
ctric
al a
dmitt
ance
/S
Figure 2-23: Electrical admittance for an uncoated QCM and a QCM coated with SiO2
51
4.97 4.98 4.99 5 5.01 5.02 5.03 5.04
x 106
-100
-80
-60
-40
-20
0
20
40
60
80
100
Oscillation frequency/Hz
Phas
e an
gle/
degr
ees
Figure 2-24: Admittance phase angle for an uncoated QCM and a QCM coated with SiO2
52
Oscillation frequency/Hz
Ele
ctric
al a
dmitt
ance
/S
Figure 2-25: Electrical admittance for a QCM coated with thin films of a polymer near its transition state
53
Oscillation frequency/Hz
Phas
e an
gle/
degr
ees
Figure 2-26: Admittance phase angle for a QCM coated with thin films of a polymer near its transition state
54
Oscillation frequency/Hz
Ele
ctric
al a
dmitt
ance
/S
Figure 2-27: Electrical admittance for a QCM coated with thin films of a polymer approaching its glassy state
55
Oscillation frequency/Hz
Phas
e an
gle/
degr
ees
Figure 2-28: Admittance phase angle for a QCM coated with thin films of a polymer approaching its glassy state
56
Oscillation frequency/Hz
Ele
ctric
al a
dmitt
ance
/S
Figure 2-29: Electrical admittance for a QCM coated with thin films of a polymer approaching its rubbery state
57
Oscillation frequency/Hz
Phas
e an
gle/
degr
ees
Figure 2-30: Admittance phase angle for a QCM coated with thin films of a polymer approaching its rubbery state
58
The current density in equation (51) can be used to reconstruct the admittance vs.
frequency plot for the oscillating QCM. Figure 2-23 shows the admittance spectra for an
uncoated QCM oscillating at 5MHz and a QCM loaded with an ideal mass (SiO2). The
admittance is the ratio of the current over the voltage vectors (Y=I/V), which is also the
inverse of the electrical impedance (Z=V/I). At the series resonance frequency (the series
motional arm) the admittance reaches its maximum value. The minimum in the admittance
spectrum signifies the parallel resonant frequency due to the static capacitor in parallel to
the motional arm. For the uncoated QCM the admittance maximum value occurs at exactly
5MHz. This spectrum will shift down in frequency as the result of addition of any surface
mass.
The admittance phase angle can be seen in figure 2-24. Far from resonance the
capacitive component of the QCM equivalent circuit dominates. The current and voltage
are out of phase by 90 degrees. The phase angle passes through the origin at the resonant
frequency, when the current and voltage are in phase with each other. Immediately after the
series resonant frequency the inductive component takes over, until the phase angle
becomes -90 degrees. It then passes through the origin once again at the parallel resonant
frequency and returns to +90 degrees for all other frequencies. Figures 2-25 through 2-30
show the electrical admittance at its phase angle for QCMs loaded with three different
polymers. We have taken three polymers with different viscoelastic properties to
demonstrate the behavior of the electrical admittance. In figure 2-25 a polymer with a
density of 1.2g/cc and a loss tangent (G"/G') of ca. 1 has been used. More specifically we
set G' = 2×107 Pa and the viscosity =0.7 N s m -2 so that G" (G"=i2πfη) is 2.2×107 Pa. This
polymer can be said to be near its transition state and its viscoelastic properties an
intermediate between a lossy polymer (rubbery state) and a rigid one (glassy state). The
59
admittance spectrum with a maximum value closest to 5MHz is for a 0.1µm thick film of
this polymer. The others following are for films with thickness of 1µm, 2µm, 3µm and 4µm.
The admittance and its phase angle for the thinnest film (0.1µm) are identical in shape with
that of an ideal mass (SiO2). However, as the film thickness increases the oscillation is more
damped by the polymer film and so is the admittance magnitude.
The next polymer used in figures 2-27 and 2-28 has properties of a more rigid
polymer in the glassy state. For this polymer G'=2×108 Pa, G"=2.2×107 Pa and G"/G' is
about 0.1. And the same values for the film thickness have been used as in the previous
example. With this more rigid material the shape of the impedance spectra resembles that
of an ideal mass, even as the film grows thicker. No significant dampening is apparent over
this thickness range.
The third polymer has been chosen to represent a polymer at the rubbery state.
G'=2×106 Pa, G"=2.2×107 Pa and G"/G' is about 10, and same thickness values were
used.
For all three polymers, even the rubbery polymer, the electrical admittance and the
phase angle spectra for the thin films resemble that of an ideal mass. Under these
conditions the oscillatory behavior of the QCM/film composite is dominated by the QCM,
If the acoustical impedance of the film is considered in establishing the frequency to mass
relationship, their contributions will be negligible and the same results will be obtained as
would be using Sauerbrey's relationship. Films with thickness values of 0.1µm, 1µm can be
declared as "acoustically thin" for these polymers. On the other hand, for more rubbery
polymers with larger values for thickness the oscillatory behavior of the QCM/film
composite is seriously influenced by the mechanical properties of the film.
60
2.2.3 The correlation of complex dynamic modulus measurements with temperature and frequency.
Physical models such as Kananzawa’s can provide threshold values for the thickness
of a given polymer, below which Sauerbrey’s relationship holds, as well as correction factors
for thicker films. These models, however, require values for the shear modulus and density
of the film. Sources for storage and loss shear moduli data of polymers are scarce. In
general there are two types of experiments for measuring the complex shear modulus, the
low and the high frequency measurements24. Low frequency measurements are mostly
conducted by scientists interested in damping applications of polymeric material. With
recent trends towards energy conservation demanding lighter weights and higher speed,
material engineers face the challenge of designing stronger and “quieter” structures25,26.
As the damping technology advances, new material such as polymer blends are produced,
which can maintain structural integrity and damping capabilities over a wide temperature
range. Understanding the basic principles involved is driven by the desire to find successful
applications for these new materials.
Absorption of mechanical vibrational waves is in many ways analogous to the
absorption of electromagnetic waves such as infrared radiation27. In both cases an
absorption peak can be found, when the frequency of the waves, light or sound, matches
the natural frequency of the chemical group or polymeric chain. Just as in an infrared
spectrum the absorption is plotted against the frequency, the absorption of an acoustic
wave (in form of G” or tan δ=G”/G’) can also be measured as the function of frequency.
More often these measurements are made as a function of temperature, simply because in
most cases programming the temperature is more convenient.
61
(52)
There is a wide range of mechanical instrumentation from different manufacturers
for measuring the complex shear modulus of polymers such as Autovibron DDVIII (Toyo
Instruments), DuPont 983 Dynamic Analyzer (DuPont/TA), System 4 Mechanical
Spectrometer (Rheometrics), Rheogoniometer (Weissenberg) and Viscoanalyzer (Metravib
Instruments). Although these instruments operate based on different principles, almost all
of them evaluate the complex shear modulus of a sample at a few fixed frequencies as the
function of temperature28. These measurements most often cover a restricted range of
frequencies. The “time-temperature superposition principles” 24 allows the extrapolation of
the viscoelastic data in the time-frequency domain. This principle states that “time and
temperature are equivalent to the extent that data at one temperature can be superimposed
upon data at another temperature by shifting the curves horizontally along the log time or
log frequency axis.” Using the time-temperature superposition principle and the WLF
(William-Landel-Ferry) equation, a master curve can be constructed representing data at
frequencies not experimentally measured.
( ))(
logloglog02
010 TTc
TTcaff T −+
−==−
Here f is frequency, aT is the temperature shift factor, T is temperature, and T0 is an
arbitrary reference temperature. When T0 is replaced by Tg (the glass transition temperature
of the polymer), c1 and c2 are assigned the values 17.44 and 51.6 respectively. These are
universal constants, which are identical for many amorphous polymers at around the glass
transition region. Based on the WLF equation one decade of frequency increase will
62
correspond to an increase of 6-7C0 in temperature, so that the Tg is actually higher at higher
frequencies.
Figure 2-31 shows an example of the time-temperature superposition procedure.
The curves at the left of the figure are those measured experimentally each for a given
temperature. The “master curve” in the right is the shifted modulus curve relative to T4
using the WLF equation.
There are a few constraints with the time-temperature superposition procedure. For
example, the shape of the neighboring curves must match exactly and the same shift factor
Log modulus
Log frequency
T1
T2
T3
T4
T5
T6
T7
T8
0 1 2 3 4 5 2 3
Figure 2-31: An example of time-temperature superposition
63
should superpose all the viscoelastic functions. Nevertheless, it is a useful empirical
technique for determination of the complex shear modulus.
The other techniques of shear modulus measurement utilize smaller sample size and
require devices capable of oscillation at high frequencies. Indeed, piezoelectric sensors such
as QCMs have been used to measure these physical properties for some materials. But most
of the work in the literature involves monitoring the change in the shear modulus and does
not report quantitative values.
Muramatsu et al. evaluated nonrigidity of poly(pyrole), Nafion and other films based
on measurements of the resonant resistance and frequency18,29,30. Johannsmann et al.
studied the viscoelastic properties of polymer thin films by measuring the electrical
impedance of a coated QCM as well as by other methods31-37. Noel and Topart monitored
resistive dampening, resonant frequency and charge during electrochemical deposition of
poly(pyrrole) to arrive at changes in surface mass and the viscoelastic
properties38,39.Oyama et al. measured the piezoelectric admittance of quartz crystal
oscillators for several electroactive polymers and for immobilized DNA40-42. Soares,
Frubose and coworkers gave detailed description of the behavior of the electrochemical
quartz microbalance in media of changing viscoelastic properties43. Ivanchenko et al.
studied polymer solutions, gels and grafted layers44. Bandey et al. conducted impedance
measurements of polyvinylferrocene film deposition45. Etchenique and coworkers
developed a simple method using a voltage divider to measure the shear storage (G’) and
loss (G”) moduli of polystyrene with 3% plasticizer at different temperatures46. Utilizing
the same method they also conducted impedance analysis of redox hydrogel mediators and
porous thin films47-49. Lucklum and coworkers were also able to extract values for the
64
complex shear modulus of polyisobutylmethacrylate and polyisobutylene in a temperature
range of –50 to 150C0 using the transmission line theory17,19. Katz and Ward have used
Kananzawa’s model to determine the complex shear modulus of polystyrene as the function
of solvent (2-chlorotoluene) composition50. Their approach is unique and unconventional
in that they have decided to probe the polymer coating at the frequency corresponding to
the minimum resonator amplitude rather than the maximum.
We have developed a method in form of a Matlab program (see appendix B) to
determine the correction to the Sauerbrey’s relationship based on Kanazawa’s model. The
complex shear modulus of polystyrene with 15% 2-chlorotoluene solvent content reported
by Katz and Ward were used for one instance of this model. The data input for the Matlab
program (kaynew.m) were:
Film density =1.063g/cc
Shear storage modulus (G’) = 1.58e8 Pa
Shear loss modulus (G”) = 1.66e9 Pa
Viscosity (η)=52.84 kg m-1 sec-1
This program computes the admittance spectrum of an oscillating QCM coated
with an ideal mass (quartz) and that of an oscillating QCM coated with a layer of a given
material to arrive at a correction factor as the function of film thickness (or added mass).
Based on figure 2-32 the correction to the Sauerbrey equation is less than 3% for the
polystyrene film up to a thickness of 15 micron.
65
0 5 10 15 20 25 30 351
1.02
1.04
1.06
1.08
1.1
Figure 2-32: Correction to Sauerbrey’s relationship
Film thickness/µm
Cor
rect
ion
fact
or
66
In closing this chapter we emphasize the fact that the problem of extracting the
viscoelastic properties for a mass loading is underdetermined, because there are four
unkowns (density, thickness, loss modulus and storage modulus) of the film, but usually
only two measured quantities, Rf and Xf. Several researchers have found it helpful to
combine other techniques such as ellipsometry, amperometry and neutron reflection with
acoustic measurements in order to find the four film parameters. Nonetheless, complex
mathematical relations and expensive experimental equipment are needed.
67
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30, 346-356.
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(20) Martin, S. J.; Bandey, H. L.; Cernosek, R. W.; Hillman, A. R.; Brown, M. J. Anal.
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(23) Reed, C. E.; Kanazawa, K. K.; Kaufman, J. H. J. Appl. Phys. 1990, 68, 1993-2001.
(24) Ferry, J. D. Viscoelastic Properties of Polymers. 3rd Ed ; Wiley: New York, 1980.
(25) Hartmann, B. In Sound and Vibration damping with polymers; Corsaro, R., D;, Sperling,
L. H., Eds.; American Chemical Society: Washington DC, 1990.
(26) Sperling, L. H. In Sound and Vibration damping with polymers; Corsaro, R., D;, Sperling,
L. H., Eds.; American Chemical Society: Washington DC, 1990.
(27) Weismann, P. T.; Chartoff, R. P. In Sound and Vibration damping with polymers;
Corsaro, R., D, Sperling, L. H., Eds.; American Chemical Society: Washington DC,
1990.
(28) Sattinger, S. S. In Sound and Vibration damping with polymers; Corsaro, R., D, Sperling,
L. H., Eds.; American Chemical Society: Washington DC, 1990.
(29) Muramatsu, H.; Kimura, K. Anal. Chem. 1992, 64, 2502-7.
(30) Muramatsu, H.; Egawa, A.; Ataka, T. J. Electroanal. Chem. 1995, 388, 89-92.
(31) Wolff, O.; Johannsmann, D. J. Appl. Phys. 2000, 87, 4182-4188.
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(33) Habicht, J.; Schmidt, M.; Ruehe, J.; Johannsmann, D. Langmuir 1999, 15, 2460-2465.
(34) Laschitsch, A.; Johannsmann, D. J. Appl. Phys. 1999, 85, 3759-3765.
(35) Petersen, C.; Heldmann, C.; Johannsmann, D. Langmuir 1999, 15, 7745-7751.
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(38) Noel, M. A. M.; Topart, P. A. Anal. Chem. 1994, 66, 484-91.
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70
Chapter 3- Heat conduction calorimetry
3.1 Heat flow sensor
In heat conduction calorimetry a large number of thermocouples connected in
series function as the thermal path between a sample and a surrounding heat sink. The
combination of these thermocouples constitutes a thermocouple plate or a thermopile
serving as a heat flow sensor. Thermopiles are commercially available as cooling units used
in electronic equipment such as computers. They operate based on the Peltier cooling
effect, a phenomenon discovered in the early 19th century. When a voltage is applied at the
junction of two dissimilar conductors, that junction will either absorb or release heat,
depending on the polarity of the voltage applied. The reverse of this process can also take
place. According to the inverse Peltier effect, if the junction of two dissimilar conductors is
cooled down or heated, a voltage will be generated at that junction. The most common
material used to make Peltier-cooling plates (thermopiles) are n- and p-doped bismuth
telluride (Bi-Te) semiconductors. Figure 3-1 shows a thermocouple made of an n-type
semiconductor cube in contact with electrically conductive material at each end. The
second dissimilar conductor in this arrangement is actually the copper connections.
Therefore, there are two junctions at the ends of the semiconductor cube, one cold and
one hot junction. The repetition of this arrangement gives a thermocouple plate that can
be used to pump heat away from a hot surface. Figure 3-2 shows such a device where the
thermocouples are connected in parallel thermally and in series electrically. The parallel
thermal combination ensures a high thermal conductivity of the unit and therefore high
efficiency of the thermoelectric device. However, the series electrical combination is not
71
very practical. A more practical design of an alternating n-type and p-type semiconductors
arrangement (figure 3-3) eliminates the need of a cumbersome zig zag wiring.
N
Hot junction
Cold junction
Heat released
Heat consumed
e- flow
+
-
Figure 3-1: A semiconductor thermocouple
Figure 3-2: A semiconductor thermocouple plate
Heat released
Heat consumed
N
+ -
N N N
72
Figure 3-3: A thermocouple plate made of n- and p-type semiconductors
Heat released
Heat consumed
N
+ -
P N P
Figure 3-4: A thermocouple plate (taken from Thermoelectric Handbook, Melcor Thermoelectrics, Trenton, New Jersey, USA, 1995)
73
When a thermopile is used as a heat flow sensor, it is positioned between the
sample and a heat sink. Heat generated in the sample passes through the thermopile and
dissipates into the heat sink. A voltage (U) proportional to the heat flux (dq/dt or P) can
be measured across the leads of the thermopile. Heat can be transferred from the sample
to the heat sink quantitatively. When a sample and a reference thermopile are coupled in
the same thermostat environment, it is possible to measure the differential heat flux. In a
temperature program mode this arrangement is a differential scanning calorimeter (DSC)1.
A DSC is usually used to measure heat capacities or heats of phase transitions for different
material. At constant temperature the above arrangement is an isothermal heat conduction
calorimeter (HCC) or a heat flow calorimeter.
3.2.1 Thermal calibration of the thermopiles
In the QCM/HCC arrangement the heat conduction sensor utilizes the Tian
equation to give the total heat (Q) associated with any process taking place at the QCM
surface.
In equation (45) Q is the total heat, U is the thermopile voltage, and the other two
parameters, the calibration coefficient (ε ), and the time constant (τ), are characteristic
properties of the thermopile/QCM assembly. Both (ε ) and (τ) must be determined after
the thermopile is incorporated into the instrument. The time constant (τ) depends on the
dtdtdU
UQ ∫ += )( τε
(45)
74
heat capacity of all components in thermal contact with the thermopile, whereas the
calibration coefficient (ε ) also depends on other variables such as the quality of the thermal
contacts between the surfaces of different components2.
For an ideal calorimeter the calibration coefficient would be ε=k/E, where k
(W/K) is thermal conductivity and E (V/K) is the Seebeck coefficient of the thermopile.
In a real calorimeter heat can be lost through heat paths other than the thermopiles and
the measured calibration coefficient is usually somewhat larger than the calculated one. In
the QCM/HCC, whenever heat is generated (or consumed) at the surface of the top gold
electrode, it passes through the quartz, through two D-shaped brass electrodes (which
provide the electrical contacts for the QCM) and finally through the thermopiles in order
to reach the heat sink.
Table 3-1 : Thermal conductivity of some materials present in QCM/HCC
Material Thermal conductivity (Wm-1K-1)
Nitrogen 0.026 (@760 torr and 300K)* Quartz(SiO2 ll to c axis) 12 (@ 273K) * Quartz(SiO2 to c axis) 6.8 (@ 273K) * Brass, leaded 120 (@ 273K) * Gold 317 (@ 300K) * Aluminum 237 (@ 300K) * Kel-F ~0.5 (@ 300K)3 Teflon 2.25 (@ 298K)* *CRC Handbook of chemistry and Physics, 77th edition
75
The thermal conductivities of some materials present in the QCM/HCC are given
in table 3-1.
Some portion of the heat may be lost to the surrounding through the mechanical
supports (Kel-F frames for the D-shaped electrodes, Teflon encapsulated O-rings for
clamping the QCM) and the gaseous atmosphere above the QCM surface. This does not
cause any systematic errors, since all measurements will be performed under conditions
identical to those during calibration.
The sensitivity (S=1/ε ) of a calorimeter is the inverse of its calibration coefficient.
The sensitivity (S) for a heat conduction calorimeter is usually obtained by generating a
known thermal power electrically while monitoring the potential output (U) of the
thermopile. A constant current is passed through a resistor with a known resistance until a
steady state signal is reached. At the steady state the calibration coefficient of the
calorimeter becomes simply the ratio of the ohmic power (Watts) over the thermopile
output potential (Volts) 4.
To do the thermal calibration, a resistor is positioned in the thermal path of the
thermopile. For example, in a heat conduction solution calorimeter it would be immersed
in the liquid inside the calorimeter vessel. The electrical equivalent circuit of the QCM has
a resistance associated with it. Thus, when an rf voltage is applied at the series resonant
frequency, the thermal power dissipated in the QCM itself can be used to calibrate the
1/,/,/
,,0
−===
==
WVsensitivtyVpotentialthermopileUWpowerthermalP
UPdtdU
statesteadyAt
ε
ε (46)
76
thermopile. This makes the electrical calibration of the QCM/HCC especially
advantageous, because of the following reasons:
• The heat is generated on the surface of the QCM, exactly where heat is released or
consumed by chemical reactions.
• No external resistor is needed.
• The calibration can be easily repeated at the beginning or the end of each run
The instantaneous power (p) is the vector product of the current (i) and voltage (v).
The above equation for the power dissipated in the LCR circuit holds for all
frequencies. At the resonant frequency the phase angle (θ) approaches zero, therefore
reducing the above equation to:
rmsrmsrms VIPresonanceAt =
The actual calibration of the thermopile using the QCM as a source of heat can be
accomplished at the resonant frequency of the QCM using the resistance (R) of the QCM
and the test level voltage applied across the QCM. At all other frequencies knowledge of
anglephasewhereVIP
IVptVtIp
rmsrmsrms
==
=+=
θθ
θθωω
)cos()cos(
)]cos()][cos([
(53)
(54)
77
the phase angle (θ) is also required. This information can easily be obtained by the use of
an impedance analyzer, such as an HP4192A LF, as shown in figure 3-5.
The HP 4192A operates based on the "vector-voltage-current ratio" method. In
this method, the impedance analyzer applies a test signal voltage and measures the
magnitude and the phase angle of the current with respect to the test voltage. This
information is then sent to a processor where other parameters such as impedance,
admittance, conductance, susceptance, etc can be determined.
The data presented in figures 3-15 and 3-16 were gathered by recording the output
voltage of the right and the left thermopiles of the QCM/HCC through a low noise
preamplifier, while an HP 4192A LF impedance analyzer was used both as the voltage
source for the QCM and to measure R, L, and C for the QCM. The advantage of using the
Figure 3-5: The setup for the thermal calibration of the thermopiles
QCM
HCC
QCM
HCC
Impedance analyzer HP 4192A LF
Irms, Vrms, Y, R, C, L, θ
Data acquisition Preamplifier DC
DC
DC
RF
RF
78
impedance analyzer is its capability of measuring and displaying the root mean square
voltage (Vrms) applied across, and the current (Irms) flowing through, the device under test
(DUT). Figure 3-6 shows the thermal signal obtained for the left thermopile at four
different settings on the preamplifier: 10mV, 3mV, 1mV and 0.3mV ranges. The gain of
the preamplifier for the above settings, determined in separate calibration experiments, has
been used to arrive at the actual thermal signal in volts, as well as the proper zero offset for
the correct baseline. Each one of the eight peaks in this figure represents a heating event as
the result of the ohmic power dissipated by the oscillating QCM. The first two peaks were
obtained with the preamplifier at the 10mV range setting, the next pair at 3mV, etc. For
the last pair a smaller voltage was applied by the impedance analyzer in order to ensure
that the thermal signal would not exceed the upper limit of the range for this setting.
Figure 3-7 contains the thermal signal obtained for the right thermopile of the QCM/HCC
using the same quartz crystal as for the left thermopile. As the results in table 2 indicate,
the resistance of the QCM is different in each case. This is perhaps due to differences in
position and more importantly clamping of the QCM.
79
-5.0E-05
0.0E+00
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.0E-04
3.5E-04
4.0E-04
0 2000 4000 6000 8000 10000 12000 14000
Time/sec
Left
ther
mop
ile o
utpu
t/V
Figure 3-6: Thermal signal obtained for an oscillating QCM, left thermopile
(98-08-19-1)
-4.50E-04
-4.00E-04
-3.50E-04
-3.00E-04
-2.50E-04
-2.00E-04
-1.50E-04
-1.00E-04
-5.00E-05
0.00E+00
5.00E-05
0 2000 4000 6000 8000 10000 12000 14000 16000
Time/sec
Rig
ht th
erm
opile
out
put/
V
Figure 3-7: Thermal signal obtained for an oscillating QCM, right thermopile.
(98-09-17-1)
80
Table 3-2: Thermal calibration of the left thermopile
Setting on the preamplifier Vrms/V Irms/mA R/Ω θ/degree Prms/µW
Thermopile signal/µV
Calibration coefficient (ε)/VW-1
1 10mV 0.123 8.306 14.84 0 1022 350.2 0.343 2 10mV 0.123 8.316 14.84 0 1023 350.2 0.342 3 3mV 0.124 8.324 14.84 0.78 1032 347.1 0.336 4 3mV 0.123 8.305 14.84 0.69 1021 348.1 0.341 5 1mV 0.122 8.253 14.84 0.92 1007 348.4 0.346 6 1mV 0.123 8.305 14.82 0.94 1021 351.9 0.345 7 0.3mV 0.061 4.155 14.74 0.82 253 89.9 0.355 8 0.3mV 0.061 4.143 14.77 0.68 253 89.3 0.354 average 0.345 STD 0.0062
Table 3-3: Thermal calibration of the right thermopile
Setting on the preamplifier Vrms/V Irms/mA R/Ω θ/degree Prms/µW
Thermopile signal/µV
Calibration coefficient (ε)/VW-1
1 10mV 0.135 8.044 16.77 2.09 1085 370.7 0.342 2 10mV 0.136 8.094 16.77 2.16 1100 377.4 0.343 3 3mV 0.131 7.794 16.78 2.32 1020 348.1 0.341 4 3mV 0.135 8.040 16.80 2.41 1084 370.5 0.342 5 1mV 0.135 8.017 16.79 2.39 1081 372.5 0.344 6 1mV 0.137 8.140 16.79 2.39 1114 384.1 0.345
average 0.343 STD
0.0015
81
The two values for the calibration coefficients of the right and the left thermopiles
were incorporated into a LabView data acquisition program. The details of this program
will be discussed in chapter 4. However, later we discovered that corrections to the values
for the calibration coefficient of the thermopile were necessary, whenever a new QCM was
placed inside the QCM/HCC apparatus. It is almost impossible to produce an identical
positioning, clamping and thermal contact with the thermopiles for every QCM.
Therefore, the thermal calibration of the thermopiles has to be repeated at the beginning
or end of each experiment to obtain a correction factor. In the absence of an impedance
analyzer, we developed a new method for thermal calibration of the thermopile (figure 3-
8). With this new method the thermal output of the thermopiles is recorded, as a function
generator (HP 33120A) is used to tune in the resonance frequency of the QCM at different
voltage levels. At the same time a digitizing oscilloscope (HP 54504A) measures the drop
in the applied voltage across the QCM. This information can be used to obtain the
effective resistance of the QCM.
QCM
HCC
HP 33120A Function generator
Rint=50Ω
HP 54504A Digit. oscilloscope
Rint=50Ω
Data acquisition
Figure 3-8: An alternative setup for thermal calibration of the thermopiles
Preamplifier
DC
RF
82
The HP 54504A oscilloscope in figure 3-9 measures the voltage (VQCM) at the
points c,d. The voltage (Vout) at the terminals a,b is the output voltage of the function
generator (HP 33120A) , which is controlled by the operator and also can be measured
directly by the oscilloscope, when the QCM is not part of the circuit. In the above circuit
Ic,d=Ia,b (I is current) and
22
1 111
111
RR
V
RR
R
V
QCM
QCM
QCM
out
+
=
++
(56)
a
b
c
d
R2=50Ω
R1=50Ω
RQCM
VQCM
HP 54504A oscilloscope
HP 33120A f-generator
Figure 3-9: The QCM electrical circuit representation for the setup in figure 3-17
83
During the calibration procedure the frequency of the voltage applied across the
QCM is initially set to a value close to 5000000Hz. The thermal power dissipated in the
QCM is monitored as a multiple of 10000 Hz is added to and subtracted from 5000000Hz.
At the exact resonance oscillation frequency of the QCM its resistance approaches its
minimum value. On the other hand, the current through the QCM and the thermal power
dissipated in the QCM are at a maximum. For example, if the measured thermal power
drops as the frequency of the applied voltage is increased by 10000Hz, that change has
removed us further from the oscillation frequency. Using this methodology the frequency
can be changed in multiples of 10000, 1000, …, and 1, until the output thermal power of
the QCM reaches its maximum. At that resonance frequency, 5 to 10 minute long pulses
of heat are generated by applying different voltage amplitudes, while the thermal power is
being recorded. Using equation (56) the resistance (RQCM) of the QCM can be obtained
from the voltage (Vout) output of the function generator and the voltage (VQCM) measured
by the oscilloscope. The actual thermal power (P=VQCM2/RQCM) should agree with the
thermal power measured using the previously obtained value for the calibration
coefficients of the thermopiles (0.345 VW-1and 0.343 VW-1). In some cases, however,
correction values larger than 20% may be obtained. Table 3-4 shows an example of such
case. It should be noted that these correction factors are caused by subtle changes in the
nature of the thermal contact between the QCM and the thermopiles every time a QCM is
taken out of the apparatus and put back in place. Such correction factors are also
frequently obtained for other calorimeters such as differential scanning calorimeters.
84
Table 3-4: Correction factor obtained for the calibration coefficient of the right thermopile for the lysozyme hydration/dehydration experiments
f-generator Vout
(p-p)/mV
f-generator Vout
(p-p)/mV
scope Vqcm
(p-p)/mV Vqcm(ampl)/mV Rqcm/ Ω f-genrator
Prms/(µW) Thermopile Prms/(µW)
Adjusted thermopile Prms/(µW)
correction factor
900 859.608 558.431 279.216 46.35 840.93 1013.507 707.947 1.1878 700 671.373 432.941 216.471 45.39 516.13 733.344 427.784 1.2065 500 483.137 310.588 155.294 45.00 267.96 522.825 217.265 1.2333 300 294.902 188.235 94.118 44.12 100.39 385.026 79.466 1.2633 100 93.49 59.607 29.804 43.98 10.10 313.993 8.433 1.1975 0 0 0 0 0.00 305.56 0.00 Average
1.22
85
During the above heating and cooling events the signal Ut obtained from a
thermopile can also be used to obtain the thermal time constant (τ). The signal collected
from the time when the thermal power is applied to the time when the thermopile signal
reaches a steady state can be fit into an exponential model to determine the time constant
(τ). Here τ=Cp/k where Cp (J/K) is the heat capacity of the sample and the QCM and k
(Js-1K-1) is the thermal conductivity.
signalthermaltheofbeginningUeUUUU
t
t
=−−+=
−
1
)(
010 )1)(( τ
(57)
86
a
y = -0.0188x - 0.0804R2 = 0.9995
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.00 50 100 150 200 250
Time/sec
ln((
Uf-
Ut)
/Uf)
τ=53.19sec
y = -0.019x + 3.1422R2 = 0.9996
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 50 100 150 200 250
Time/sec
ln((
Ut-
Uf)
/Uf)
τ=52.63sec
b
Figure 3-10: a) Time constant obtained for heating event 2 b) Time constant obtained for cooling event 2
87
Table 3-5: Values obtained for the time constant of the heat flow sensor
Time constant τ (sec) R2
Heating 1 51.3 0.9998
Cooling 1 52.9 0.9992
Heating 2 53.2 0.9995
Cooling 2 52.6 0.9996
Heating 6 53.2 0.9992
Average 52.6
88
3.2 Nonscanning heat conduction calorimeters
In the following section a brief historical review of the development of heat
conduction calorimetry is given along with a survey of different types of commercial units
and their applications. This survey, however, is limited strictly to the heat conduction
calorimeters used in the isothermal mode. As most of the solution calorimeters today are
of the heat conduction type, we feel it necessary to also discuss those applications and
some of the related issues. Especially, since we hope to explore the use of our QCM/HCC
as a flow calorimeter in the future.
The first heat conduction calorimeter of its kind constructed by Tian in the early
1920s was built 7m deep in the ground to provide a stable temperature with the
surrounding5. It had two thermoelectric piles, one used as a heat flow sensor and the other
as a compensating element. Tian’s microcalorimeter was a single measuring design
operated isothermally. In 1948 Calvet modified Tian’s design by using two symmetrical
measuring systems in the same thermostat6. Since then the Calvet-Tian design has evolved
to constitute a family of highly sophisticated calorimeters used by scientists from different
disciplines. Interestingly, almost all of the modern heat conduction calorimeters available
on the market today have descended from units built in research laboratories around the
world. Professor Ingemar Wadsö, one of the pioneers in this field, in a report titled: “
Neither calorimeters nor calorimetrists are what they used to be” comments on the
progress of the world of thermochemistry in the past century7. In his report he states that
as thermochemists designed and built their own calorimeters, most of the time to study a
specific reaction, they had to invest tremendous time and effort, which gave them an
excellent understanding of the operation of the equipment and the measuring principles.
89
Today, however, all calorimeters are commercial instruments. While they allow very
convenient experimental procedures, at the same time they have become “black boxes” for
many of the scientists operating them.
An interesting account of a classical case of design and development of a family of
heat conduction calorimeters is the work at the Bingham Young University under the
supervision of Lee Hansen8,9. The search for a method of predicting the lifetime of
batteries used in heart pacemakers was the motivation for this project. A shelf study of
batteries discharging in a period of approximately 10 years was out of question, as was an
accelerated study at temperatures higher than the body temperature. For such a slow
process a calorimetric technique demanded a precision of just a few tenths of a microwatt.
At the time 10µW was the lowest detection limit reported for a heat conduction
calorimeter at Lund University. The combination of the technology at Lund University
with that of the excellent water baths manufactured by Tronac (Orem, Utah, U.S.A.) made
a measuring system with a short-term noise level of only 0.1µW. Shortly after the
description of this calorimeter was published, Tronac and later Hart Scientific marketed a
line of calorimeters to study batteries of all different sizes and shapes including the lithium
batteries used in the Mars Rover10,11.
Lee Hansen and his group, appreciating the high sensitivity of the HCC technique,
realized its potential and identified it as a kinetic method capable of studying the rate of
important slow processes, where other equilibrium methods would usually fail. In the
following years they made major contributions in the areas of kinetics of degradation of
pharmaceutical products12,13, metabolic heat rates of living organisms14-24 and sorption
processes25,26.
90
One of the most influential contributors to the development of modern heat
conduction calorimeters has been Professor Ingemar Wadsö from Lund University in
Sweden. Some have identified him as the most important calorimetrist of the second half
of the 20th century27. Today he is best known for his contributions to the knowledge of
living systems by studying their heat production rate4,28,29. Over the years Professor
Wadsö has designed and built numerous user-friendly, highly sensitive “micro-watt
calorimeters”. Many of his calorimeters have been commercialized. The earliest examples
are the batch30 and flow31 type differential twin heat conduction calorimeters, which were
commercialized by LKB Produkter AB in Bromma, Sweden. In response to the enormous
success of his flow through microcalorimeters, Professor Wadsö worked with Jaak
Suurkuusk, his former student and long-term colleague, to lay down the early design of
what later became the LKB BioActivity Monitor32(BAM). Today this unit is sold as the
Thermal Activity Monitor (TAM) by Thermometric, a company formed by Wadsö and
Suurkuusk as the result of a takeover of LKB. The TAM is currently the main product line
of modern thermometric calorimeters. It is a 4-channel twin microcalorimeter with a
variety of different insertion vessels. The vessels are generally either titration/perfusion
vessels or the closed ampoule type (also see http://www.thermometric.com/).
From the older LKB model calorimeters, besides BAM, there are still a few used at
different laboratories. For example the LKB 8700, the predecessor of the Thermometric’s
precision solution calorimeter 2225, is a general purpose reaction and solution calorimeter
still supported by Thermometric for some maintenance. Another model, the LKB 10700
rotating batch, is a flow calorimeter used with different insertion vessels. Its special
advantage is the mixing mechanism. Mixing is accomplished by rotating the entire
calorimeter block one full turn and then back. This mechanism is very useful for studying
91
processes with difficult mixing problems, such as sediments, viscous liquids and gas/liquid
mixing
Calorimetry Science Corporation (CSC) is a US-based manufacturer of heat
conduction calorimeters. Just as the design of most of the Thermometric calorimeters is
based on original work at Lund University, many of the Calorimetry Science Corporation
calorimeters have descended from research conducted at Brigham Young University. The
first commercially available calorimeter designed at BYU was manufactured and marketed
by the former Tronac in 1966. In 1978 Roger Hart formed the Hart Scientific and in 1993
the Calorimetry Science Corporation was formed as a subsidiary division of Hart Scientific.
Currently CSC manufactures calorimeters measuring heat in all three modes of heat
accumulation, compensation and conduction. Excluding calorimeters for specialized
applications, CSC produces four major isothermal heat conduction models. (also see
http://www.calorimetrysciences.com/index.html)
SETARAM, a subsidiary of Groupe KEP, is a French company manufacturing
heat conduction calorimeters, which cover the widest temperature range of operation (-196
to 1000C0). The high temperature calorimeters are of particular use for surface interaction
studies between gases, liquids and solid as well as stability studies at elevated temperatures,
whereas the low temperature calorimeters are mostly used for studies of freezing,
crystallization and superconductivity. ( also see http://www.setaram.com).
92
Table 3-6 : Summary of commercial heat conduction calorimeters from different manufacturers
Manufacturer Calorimeter
Vessels Baseline noise/µW
Time constant/sec
Temp. of operation/C0
Thermometric/ TAM # -201
Ampoule 0.05 200 Amb. to 200
Thermometric/ TAM # -202
Flow through 0.05 100 12 to 150
Thermometric/ TAM # -204
Flow mix 0.05 100 12 to 90
CSC 4200 Ampoule 0.005 5-50 0 to110 CSC 4100 Ampoule/
gas flow 2 60 -40 to 80
CSC 4400 Ampoule/ titration/
0.1-1 50-300 -40 to 80 0 to 100
CSC 2000 2 drop 4 100 5 to 50 SETARAM/
MS 80 Batch/ flow 0.3 200-400 Amb. to 200
SETARAM/ C 80
Mixing 3 100 Amb. to 300
SETARAM/ BT 2.15
Batch 3 120 -196 to 200
SETARAM/ HT 10000
Batch 3 100 Amb. to 1000
SCERES/ B-400
Batch 0.5 NA -190 to 200
SCERES/ B-900
Batch/ mixing
2.5 NA -190 to 650
SCERES/ B-600
Batch/ mixing
5 NA -190 to 650
SCERES/ BLD-350
Radioactive samples
5 NA -60 to 450
SCERES/ TL-1000
Batch 100 NA -60 to 150
93
3.2.1 General application areas of isothermal heat conduction calorimeters
Common applications of Isothermal heat conduction calorimeters used at ambient
temperature and pressure usually fall under one of the six following categories33:
1. Incremental titration calorimetry
2. Dissolution/mixing calorimetry
3. Sorption calorimetry
4. Vaporization/sublimation
5. Living systems
6. Degradation and curing
There are generally two types of calorimetric titrations, chemical reactions with
very large equilibrium constants (Kc), and reactions with moderate or small Kc’s. For
reactions with very large values for Kc any amount of the titrant will be almost completely
consumed upon addition until the endpoint has been reached. A simple example of such
case would be the titration of a strong acid with a strong base. For such reactions the
equilibrium constant cannot be obtained. The molar enthalpy of these reactions can be
directly measured and often information about the stoichiometry is also obtainable. On the
other hand, if the Kc is not very large (<108), the heat released upon successive
introduction of titrant to the sample is recorded and analyzed by a method described
extensively in the literature34.
000 ln STHKTG c ∆−∆=−=∆ R
(58)
94
There has been much advancement in both hardware and software of heat
conduction microcalorimeters in the past decades4 for their application in the areas of
biophysical and pharmaceutical chemistry35 mostly to study and obtain binding constants
for processes involving biopolymers.
Calorimetry in the areas of dissolution and mixing of pure compounds
characterizes the energetics of intermolecular interactions such as solute-solvent
interactions. These calorimetric measurements have found important applications in
biophysical chemistry and pharmaceutical industry. For example, solution enthalpies of a
compound in different solvents give information about the transfer enthalpies for that
compound between the same solvents36. Such values for a biochemical model system in
representative solvents such as water and other organic solvents provide the basis for
models developed for interactions in the interior of protein molecules or in lipid
environments.
Under ideal conditions, in the absence of a chemical reaction the enthalpy of
mixing of two pure liquids should be zero. In practice, however, large excess enthalpies
can be observed37. Flow type heat conduction calorimeters are usually used to measure
excess enthalpies of mixing for systems of interest to chemical engineers and other
scientists.
Sorption calorimetry can be employed to measure the sorption enthalpy of a
compound from either gas phase or liquid phase onto the surface or into the body of a
solid sample. The measurement of sorption enthalpies is useful in characterization of the
physical surface properties, which may demonstrate strong dependence on the physical
state (crystalline, amorphous or polymorphic) of the solid material. Heat conduction
microcalorimeters have become standard analytical tools in the pharmaceutical industry for
95
this purpose38-40. In other instances sorption heat conduction calorimeters have been
used to determine the rate (kinetics) of sorption processes26 and in some cases even to
construct the sorption isotherm41.
Applications of HCC in the area of sublimation and vaporization have not been
explored fully and may remain untouched in the near future, despite the strong need of
such work in the area of bio-thermodynamic systems42.
There have been major developments in techniques that take advantage of heat
conduction calorimeters to study living systems including microorganisms, plants, human
and animal cells and tissues, small animals and even human. The first published animal
calorimetry was conducted by Lavoisier in 178043. In his experiment Lavoisier combined
an indirect calorimetric measurement based on the respiration of a guinea pig with a direct
measurement of the guinea pig’s heat production inside an ice calorimeter. Crawford had
already proposed that the oxygen consumption of an animal should roughly be
proportional to its heat production. At the time the indirect method was cheaper and
easier to perform. The use of calorimetry as a common tool for studying the metabolic rate
of living systems was never seriously considered till relatively long after the advent of
Calvet’s calorimeter.
Much of the calorimetric work in 1950s and 60s regarding living systems
concentrated on the effort to show that exponential growth was accompanied by
exponential power44. For example, Forrest described the study of the rate of microbial
fermentation45. Prat studied the heat production of germinating seeds and some small
mammals46. There were a number of very creative works during this period, which were
generally qualitative in nature. Nonetheless, they demonstrated that kinetic analysis was
96
possible. Subsequently there was an enormous increase in the number of publications
reporting studies on biological systems.
Following calorimetric work on microorganisms ranged from simple growth and
metabolic rate studies of bacteria47 and yeast48 to the investigation of the effect of
antibiotics on a host of different living cells49. A collection of recent publications by
Kemp gives a thorough description of developments of techniques specifically used to
measure the heat production by human and animal cells50-53.
Finally, isothermal heat conduction calorimeters can also be used to study slow
degradation and decomposition processes. Examples are stability studies of explosives54
and pharmaceuticals12,13.
3.2.2 Calibration issues and the accuracy of isothermal heat conduction calorimetry measurements
Virtually all processes are accompanied by heat. This fact has made calorimeters
an important analytical tool in physics, biology and chemistry. On the other hand,
calorimetry is generally a nonspecific technique and as such it is vulnerable to systematic
errors due to processes unaccounted for such as evaporation, sublimation, condensation,
adsorption, corrosion, friction, pressure variations and unidentified chemical
reactions55,56. There is no question about the remarkable sensitivity of modern
calorimeters justly advertised by their manufacturers. But the operator has the
responsibility of considering the precision of any measurement in the context of the
overall accuracy. Almost all calorimeters are equipped with resistors built in that can be
97
used for electrical calibrations. In heat conduction calorimeters some fraction of the heat is
always lost to the surroundings. The portion of the heat actually passing through the heat
flow sensor can easily be less than 80%55. This causes no problem, if experiments are
conducted under identical conditions as those used for calibration. However one has to
ensure that the heat flow patterns are the same whether the heat originates from the
resistor or from the chemical reaction. The best way to make certain of this is to run an
experiment with well-characterized energetics as a chemical test. There are a number of
standard reactions recommended for this purpose. For example the dilution of propane-1-
ol in water has been recommended to evaluate the accuracy of microcalorimeters used for
titration and dissolution measurements. A common perception among calorimeter
operators is that the Power(measured) will equal the Power(real) once an electrical calibration has
been performed. Those who realize that Power(measured) ? Power(real) do perform chemical
calibrations for every vessel. However, they intuitively assume that the correction between
Power(measured) and Power(real) follows a linear relationship (Power(measured) /Power(real) =
constant). In fact careful chemical calibrations have shown that the correction will depend
on the magnitude of the thermal power detected57. This fact should be taken into
consideration while choosing a proper type of the standard chemical reaction as well as the
proper concentrations of the reagents.
There are international agencies such as the IUPAC that have established, and are
preparing new, guidelines for chemical test and calibration procedures. However, there is
still the need for much more work in this field, as some application areas have remained
untouched. For instance, there are currently no reliable test procedures for sorption
processes. Guidelines in this area would be of particular interest to us for their application
in the QCM/HCC.
98
Variations in the heat flow pattern in the QCM/HCC for calibration runs
compared to other experiments are not as problematic as they are for a titration or flow
microcalorimeter, for example. In a titration calorimeter, even if an insertion resistor is
used, the heat will be released from a point source, whereas the heat from a chemical
reaction would be generated throughout the solution. In the QCM/HCC during
calibration electrical energy is transformed into heat throughout the oscillating region of
the quartz. We expect the heat production profile and flow to be similar to that during a
process taking place on the quartz surface. As mentioned earlier the calibration should be
performed in a thermal power range that accommodates the power of the process of
interest. In the QCM/HCC this is accomplished by controlling the amplitude of the
excitation voltage applied across the QCM during the recalibration using a frequency
generator. Since we know that the relationship between Power(measured) and Power(real) is
not linear, we should be able to identify a trend in the variations in the correction values
(values reported in table 3-4) and should not simply use their average and treat them as
randomly scattered measurements.
We will continue to search the literature for possible guidelines for reliable test
procedures for sorption processes and will apply them as they become available.
99
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102
(53) Kemp, R. B. J. Therm. Anal. Calorim. 2000, 60, 831-843.
(54) Wadsö, I. Indian J. Technol. 1992, 30, 537-44.
(55) Wadsö, I. Thermochim. Acta 2000, 347, 73-77.
(56) Wadsö, I. Thermochimica Acta 1993, 219, 1-15.
(57) Guan, Y. H.; Kemp, R. B. Thermochim. Acta 2000, 349, 163-176.
103
Chapter 4- Description of quartz crystal microbalance/heat conduction calorimeter (QCM/HCC) and its developmental stages
4.1 Description of the QCM/HCC apparatus and its advancement with time
The current prototype of the QCM/HCC has undergone modifications during
four major developmental stages:
1. The invention, design and construction of the combination of the mass
and heat flow sensor took place at Lund University in Lund, Sweden.
2. As the QCM/HCC arrived at Drexel University its operation was
initially tested to the extent that both sensors were operational and data
could be collected from both sensors. Methods were developed to
calibrate the heat flow sensors and other electronics such as a low noise
preamplifier. Later the QCM/HCC was transferred into a thermostated
housing with a very low thermal noise.
3. A gas flow subsystem for sample introduction with the necessary
adaptation to the QCM/HCC was designed, built and integrated into the
QCM/HCC. The mass flow controllers used in this flow system were
calibrated. Several thin film preparation techniques such as drop coating,
spin coating and spray coating were explored for making thin and
uniform samples.
4. A LabView control program was designed and created to fully automate
the operation of the QCM/HCC.
Figure 4.1 is a sketch of the QCM/HCC. It shows how the sample and the
reference mass and heat flow sensors and their mounts have been integrated with a gas
104
flow cell. In this arrangement the sample is usually cast in the form of a thin film on the
(larger) top gold electrode of one of the QCMs. During experiments the chemical
composition of the atmosphere above the sample is altered periodically. If either a
chemical or physical reaction takes place on the surface as the result, the associated mass
change and heat flow can be measured simultaneously1-4. Figure 4-2 is a block diagram of
the complete QCM/HCC setup. The mass sensors are 5MHz AT-cut QCM's (Maxtek,
P/N 149211-1, model SC-501-1) with dimensions: 2.45 cm in diameter and 0.33 mm in
thickness. The 160 nm thick top and bottom gold electrodes on the QCM are vacuum-
deposited onto a 15 nm chromium adhesion layer. As mentioned above, the larger top
electrode (12.9 mm in diameter) is used as the active surface. However, the region of the
quartz exposed to the rf electric field is limited to that directly beneath the smaller
electrode (6.6 mm in diameter) resulting in a mass sensitive area of approximately 0.32 cm2
5. Both sample and reference quartz resonators are driven by rf oscillator circuits as
described by Auge et al6. The oscillation frequencies of the QCM's are measured
individually with an HP 53131A frequency counter interfaced to Macintosh computer
through a GPIB interface.
Each QCM rests on two D-shaped brass electrodes, which serve both to apply rf
power to the QCM and to conduct heat generated on the QCM surface to the top of the
thermopile. The heat flow sensors are small FC 0.45-66-05 thermopiles (Melcor, Trenton
NJ). Four thermocouple plates are used in the QCM/HCC. Two are connected in series to
form one heat flow sensor on the reference side, and the same arrangement is used for the
sample side. The differential signal of the sample and reference sides is conditioned by a
105
low noise DC preamplifier* and recorded on the same Macintosh computer with an A/D
board under the control of LabView software (National Instruments, Inc.). The details of
this program will be discussed in the following section.
Kel-F inserts which screw into the top of both aluminum sample and reference
chambers contain Teflon tubes through which gaseous samples are flowed at 1.0 atm
pressure. For many of the experiments where organic solvents had to be introduced into
gas stream of the flow cells the vapor introduction system shown in figure 4.3 was used. It
consists of two 0-50 scc⋅min-1 mass flow controllers, MFC1 and MFC2 (Unit Technologies
UFC-8100) and a bubble-through container. The nitrogen gas stream through MFC2 is
directed through the bubble-through container where it is saturated with the organic
solvent at a constant temperature, usually at 25ºC. The resulting gas stream is then
combined with that of MFC1. The entire QCM/HCC is placed in a cylindrical brass
enclosure and immersed in a constant temperature bath set at 25.00°C and regulated to
±0.0001°C (Tronac 1250). Either a pure nitrogen gas stream or the gas mixture from
MFC1 and MFC2 can be directed through sample and reference QCM/HCC. Both gas
streams are temperature-conditioned by thermal equilibrium units immersed in the bath
(Figure 4.2). Since the gas stream flows from sample and reference chambers into the
ambient atmosphere through a short tube and the flow rates are small, the sample and
reference chamber pressures can be taken to be 1.0 atm.
- * Built by Sven Hägg in the Department of Thermochemistry, Lund University
106
Heat sink
Kel-F insert
Gas outlet
Gas inlet
QCM (gold electrode)
Thermopile
o-ring
Kel-F frame
Figure 4-1: The sketch of the QCM/HCC
107
Heat sink
QCM
Thermopile
QCM
Thermopile
Isothermal bath
Flow control rf oscillator driver
HP 53131A Freq. counter
Low noise preamplifier
D to A I/O board
A to D I/O board
IEEE 488 I/O board Power Mac 7100/66
Carrier gas outlet Carrier gas inlet Thermal equilibration unit
Figure 4-2: Block diagram of the complete QCM/HCC setup
108
MFC1
MFC2
N2 in
N2 in
Bubble through
Container
Isothermal
bath
f1
fout
Pi
Figure 4-3: The flow subsystem for vapor introduction
f2
109
Three LabView programs were written for automating the data acquisition and
control of the QCM/HCC and other related measuring and test devices. One was a slight
modification of a front panel virtual instrument (VI) of a 54504A HP oscilloscope. This
program facilitated troubleshooting and understanding problems related to the oscillation
behavior of the QCMs. The second was to control a 4192A HP impedance analyzer. It was
used to measure the impedance characteristics of the QCMs during frequency sweeps. The
third was a more sophisticated program consisting of five subsections. This new program
in combination with the proper National Instruments hardware (GPIB, DAQ boards, etc)
replaced the old data collection package. The function of the new control software was to
collect and save incoming data such as the oscillation frequencies of the QCM's, the
amplified differential thermopile signals in µW at the corresponding preamplifier setting,
and the gas flow through the two mass flow controllers. Another part of this program
generated the output information for the gas flow system based on controlled parameters
defining the concentration profile of the gas flow. Although this automation was only a
preliminary experimental step, we consider it to be a major accomplishment considering
the degree of convenience that it brought into conducting all the subsequent experiments.
The figures below show the details of the Lab View programs. These figures and the
following documentation can serve as a reference for future operators of the QCM/HCC
not only for possible troubleshooting but also during further improvement attempts.
110
Figure 4-4: Connector panel and front panel of the HP 54510A digitizing scope (2)
111
Figure 4-5: Block diagram of the control program for the HP 54510A digitizing scope (2)
112
This VI (HP 54510A digitizing scope 2) has mostly been used for troubleshooting
purposes. We recommend its use in the future for calibration of the thermopiles at the end
of each experiment. A LabView program can be written specifically for this purpose. Since
the computer can be in two way communication with the HP 54510A digitizing scope and
the HP 33120 function generator through the GPIB board, the current QCM/HCC VI
could be expanded to control both devices.
The logical operations of the modified VI would evaluate the recorded thermal
power dissipated in a QCM and the magnitude of the voltage measured across that same
QCM by the HP 54510A digitizing scope. As it commands the function generator to
change that frequency in small steps, it will compare the new values for the thermal power
and the measured voltage across the QCM. Functions can be built into the software so
that the frequency is tuned to a value that corresponds to a maximum value for the
thermal power and the largest voltage drop across the QCM (see section 3.2.1 in chapter
three for the details of this procedure currently performed manually). Once the oscillation
frequency has been identified, the function generator can apply different voltage
amplitudes while the thermal power is recorded. Such a program will accomplish what
currently consumes several hours in a few minutes with minimum supervision of the
operator.
113
Table 4-1: Defaults and specifications for 4192A Sweep.vi (Hamid’s setup)
HP 4192A LF IMPEDANCE ANALYZER DEFAULTS: GPIB addr: 17
Function A: Z/Y Function B: DEG Frequency: 100 Khz Circuit Mode: AUTO Trigger: INTERNAL Osc. Level: 1.0V DC Bias: OFF Bias Level: 0V
FREQUENCY: 5 MHz to 13MHz
OSC. LEVEL: 5E-3 to 1.1V FUNCTION A INPUT: 0=Z/Y
1=R/G 2=L 3=C
FUNCTION B INPUT: 0=DEG/Q 1=RAD/Q 2=R/G
CIRCUIT MODE INPUT: 0=AUTO 1=SERIES 2=PARALLEL
TRIGGER INPUT: 0=HOLD/MANUAL 1=EXTERNAL 2=INTERNAL
BIAS: Binary Switch BIAS (V): -35 to 35V
114
Figure 4-6: Connector panel and front panel of the HP 4192A sweep VI
115
Figure 4-7: Block Diagram of the control program for the HP 4192A sweep VI
116
The HP 4192A sweep VI has been used to measure impedance characteristics such
as susceptance, conductance, resistance, capacitance, inductance and the
impedance/admittance phase angle for several QCMs during frequency sweeps. Figures 2-
8, 2-9 and 2-10 in chapter two are some examples. This VI can also be incorporated into
the QCM/HCC control program, if an HP 4192A is available. The HP 4192A is more
expensive than the function generator and a digitizing scope combined. However, in
addition to eliminating the need of both for calibration experiments, it can also provide
information about the viscoelastic properties of the QCM/coating composite.
The following figures show the details of the QCM/HCC VI. Values shown in
command boxes on the front panel in figure 4-8 are the default values. These can be
changed at the beginning of each experiment and some may be further modified during
data acquisition. Once the desired values are entered, the QCM/HCC VI can be invoked
by pushing the arrow button on the top right hand side of the LabView command menu.
Immediately a dialog window will open, where the name and the location of the data file to
be saved can be assigned. The operator’s attention is required at the beginning of the
experiment to ensure that the correct preamplifier setting has been chosen. The
QCM/HCC VI will continue to execute unless either an error occurs or the stop button is
pushed by the operator.
117
Hamid's VI(9); Connector Panel
Figure 4-8: Front panel of the QCM/HCC virtual instrument
118
Table 4-2: list of controls and indicators for the QCM/HCC control program
instruction# Select from a list of measurement types
GPIB address (3) This refers to the address of the GPIB board
stop This is the control button to stop the program
Thermopile input is channel 0 channel identifies the analog input channel you want to measure.
device This refers to the address of the data acquisition board
Sensitivity W/V This is the value for the sensitivity of the thermopile
Amplifier settings This indicates the setting on the preamplifier
channel (0) out ([string]) channels: specifies the set of analog output channels for a group and task. You cannot assign a channel to more than one group. The default input is channel 0. See the description of the AI Group Config VI for a detailed description of this parameter and the valid syntax for the channel strings.
channel (1) in channel identifies the analog input channel you want to measure.
channel (2) in channel identifies the analog input channel you want to measure.
channel (1) out ([string]) channels: specifies the set of analog output channels for a group and task. You cannot assign a channel to more than one group. The default input is channel 0. See the description of the AI Group Config VI for a detailed description of this parameter and the valid syntax for the channel strings.
Room temperature C This is the value for the room temperature
Three way valve This indicates the position of the three way valve and the direction of the gas flow
flow1cc/min ([sgl]) value: a digital control that contains data expressed in the physical units of your signal.
flow2 cc/min ([sgl]) value: a digital control that contains data expressed in the physical units of your signal.
measurement (2) Selects measurement type. 0) frequency 1 1) frequency 2 2) frequency 3 3) ratio 1 to 2 4) ratio 1 to 3 5) time interval, T1 to T2 6) period 1 7) risetime 1 8) falltime 1 9) positive width 1 10) negative width 1 11) totalize 1 12) phase 1 to 2 13) duty cycle 1 14) volt peaks 1 15) volt peaks 2
119
Table 4-2: (continued) list of controls and indicators for the QCM/HCC control program
measurement (1) Selects measurement type. 0) frequency 1 1) frequency 2 2) frequency 3 3) ratio 1 to 2 4) ratio 1 to 3 5) time interval, T1 to T2 6) period 1 7) risetime 1 8) falltime 1 9) positive width 1 10) negative width 1 11) totalize 1 12) phase 1 to 2 13) duty cycle 1 14) volt peaks 1 15) volt peaks 2
PPM (start) Vapor concentration in the gas stream
PPM (step) Desired change in the Vapor concentration at the defined interval
Total flow(cc/min) Total flow through the reference and the sample side of the QCM/HCC
Vapor P(mmHg) Vapor concentration inside the bubble through container
# of steps Number of steps for change in the vapor concentration
# of executions Number of executions during a single step. Each execution will take about 2 seconds
Gas MFC2 Flow through MFC2 controlled manually when VENT is selected
Gas MFC3 Flow through MFC3 controlled manually
frequency 1 This is a measurement result without scaling and offset. If you want a measurement with scaling and offset, first configure the function from this VI,"Read a measurement", and read from "Config Scale & Offest" VI.
frequency 2 This is a measurement result without scaling and offset. If you want a measurement with scaling and offset, first configure the function from this VI,"Read a measurement", and read from "Config Scale & Offest" VI.
frequency difference/Hz This is a measurement result without scaling and offset. If you want a measurement with scaling and offset, first configure the function from this VI,"Read a measurement", and read from "Config Scale & Offest" VI.
Chart, Frequency difference Difference in the oscillation frequency between the sample and the reference QCMs
Thermopile signals (diff.) ([sgl]) sample: a one-dimensional array that contains scaled analog input data.
Thermal power/µW
Chart, Thermal power
120
Table 4-2: (continued) list of controls and indicators for the QCM/HCC control program
Amplifier setting/ microvolt
flow1 cc/min ([sgl]) sample: a one-dimensional array that contains scaled analog input data.
flow2 cc/min ([sgl]) sample: a one-dimensional array that contains scaled analog input data.
Time/sec
PPM The vapor concentration in the gas stream into QCM/HCC
Right resistance ([sgl]) sample: a one-dimensional array that contains scaled analog input data.
Left resistance ([sgl]) sample: a one-dimensional array that contains scaled analog input data.
Chart, QCM's resistance
flow3 cc/min ([sgl]) sample: a one-dimensional array that contains scaled analog input data.
121
Figure 4-9: Block diagram of the QCM/HCC LabView control program
122
Figure 4-10: Block diagram of the QCM/HCC control program (continued)
123
Table 4-3: List of SubVIs used in the QCM/HCC LabView control program
HP 5313xA Config Measurement.vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\instr.lib\hp5313xa\HP5313XA.LLB\HP 5313xA Config Measurement.vi
HP 5313xA Read a measurement.vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\instr.lib\hp5313xa\HP5313XA.LLB\HP 5313xA Read a measurement.vi
AI Sample Channel.vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\vi.lib\DAQ\1EASYIO.LLB\AI Sample Channel.vi
AO Update Channel.vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\vi.lib\DAQ\1EASYIO.LLB\AO Update Channel.vi
Open/Create/Replace File.vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\vi.lib\Utility\file.llb\Open/Create/Replace File.vi
Close File+.vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\vi.lib\Utility\file.llb\Close File+.vi
Write File+ (string).vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\vi.lib\Utility\file.llb\Write File+ (string).vi
Simple Error Handler.vi C:\PROGRAM FILES\NATIONAL INSTRUMENTS\LABVIEW\vi.lib\Utility\error.llb\Simple Error Handler.vi
History "Hamid's VI(9) History" Current Revision: 110
124
In figure 4-8 the first two charts on the front panel of the QCM/HCC VI and the
indicators/controls to the left of those charts are related to measurement of the oscillation
frequencies of the sample and reference QCMs. An oscillator driver as shown in figure 4-
11 drives each individual QCM to oscillation6. The oscillation frequency is measured (at
the output point in figure 4-11) by an HP 53131A frequency counter. The LabView
program measures the frequency at channel one (left QCM). Then it switches from
channel one to channel two (right QCM) and takes another measurement. The difference
in the oscillation frequencies between channels one and two is recorded and displayed on
the chart labeled “Frequency Difference”. This is the slowest step in the data acquisition
program and therefore the rate-determining step. In average the frequency counter
requires two seconds for executing the above-mentioned commands.
We also have an oscillator driver (Active-bridge oscillator), which has been
donated to us by Mr. Kurt Wessendorf from the Sandia National Laboratories*. This
circuit is capable of measuring the oscillation resistance. Changes in the oscillation
resistance are indicative of variations in the viscoelastic properties of the coating of the
QCM. So far we have used this circuit only for a few experiments, since it has shown some
erratic behavior especially for large mass loadings. Nonetheless the LabView program has
two analog input channels reserved for voltage input from this circuit.
- * K.O. Wessendorf, in US Patent Office 6,169,459, Kurt O. Wessendorf, U. S. A., 2001.
125
Figure 4-11: Circuit diagram of the QCM oscillator driver
1
1
200
100
360
100n
100
100n
100n
5k 220 560
56
2 x OPA 660
2 x BAT 41
1 K
1 k
10 p
100 p
½ OPA 660
½ OPA 660
½ OPA 660 ½ OPA 660
-5 V
-5 V
QCM
Output
1
2
1
2
126
The third chart and the indicators/controls to its left are related to the
measurement of the thermal power signals from the thermopiles. The difference in
potential between the sample and the reference side thermopiles is conditioned by a low
noise DC preamplifier. An equivalent unit to this amplifier is manufactured by EM
electronics in Berks, England and is sold as the DC Nanovoltmeter model N15. This
device can operate at 11 different settings, covering ranges between ±10 mV to ±100nV.
The gain of this device at various settings has been measured and incorporated into the
LabView program. The dial indicator on the front panel of the QCM/HCC VI is a
representation of the actual knob on the preamplifier. When the correct setting is chosen,
the LabView program can use the gain at that setting to determine the original voltage
before the amplification. From the value entered for the sensitivity of the thermopile the
thermal power is calculated, recorded and displayed in µW on the chart labeled thermal
power.
The calibration of the preamplifier was accomplished by applying a small voltage
within the range of a given setting and measuring the amplified output voltage. The data in
table 4-4 were fit by linear regression of the data in figures 4-12 and 4-13 and the resulting
slopes were used to determine the gain for the corresponding setting. Based on these
values the gains at the more sensitive settings of the preamplifier were inferred. The values
used in the LabView program are shown in case structures in figure 4-10.
127
Table 4-4: Measured data for calibration of the low-noise preamplifier
Setting on the preamplifier/mV Voltage input/mV Voltage output/mV
10 5.6 498 10 7.6 678 10 9.9 885 10 7.6 677 10 5.6 495 10 2.2 195 3 0.2 61 3 0.9 250 3 1.2 361 3 1.6 465 3 2.2 650 3 2.9 853 3 2.2 650 3 1.5 451 3 0.2 63 1 0.2 127 1 0.5 457 1 0.9 787
128
0
200
400
600
800
1000
0 2 4 6 8 10 12
y = -2.2051 + 89.423x R= 0.99997
Mea
sure
d ou
tput
vol
tage
/mV
Input voltage/mV
0
200
400
600
800
1000
1200
0 0.5 1 1.5 2 2.5 3 3.5
y = 0.57765 + 294.48x R= 0.99963
Mea
sure
d ou
tput
vol
tage
/mV
Input voltage/mV
Figure 4-12: The linear fit of the measured voltage at (a) 10mV setting on the preamplifier and (b)
3mV
(b)
(a)
129
0
200
400
600
800
1000
0 0.2 0.4 0.6 0.8 1 1.2
y = -42.459 + 936.49x R= 0.99662
Mea
sure
d ou
tput
vol
tage
/mV
Input voltage/mV
Figure 4-13: The linear fit to the measured voltage at 1mV setting on the preamplifier
130
The last chart on the front panel of the QCM/HCC VI and the
indicators/controls to its left are related to the control of the chemical composition and
the flow rates of the gas stream into the QCM/HCC. This section of the program was
specifically written for the flow system described in figure 4-3, where a liquid is placed
inside the bubble-through container and the gas flown into the liquid is saturated with its
vapor. Depending on the amount of additional carrier gas added upstream from the
QCM/HCC the vapor activity (p/p0) can be varied from a value of 0 up to 1. Even so we
have used this program for controlling the composition of a mixture of three different
gases with no solvent present.
This section of the LabView program is rather complicated. The program can alter
the composition of the gas stream based on input values describing the desired change in
concentration at set time intervals. It can increase the concentration in predefined steps to
a desired maximum value and follow back the same steps to reach the lowest
concentration completing a full cycle. The concentrations are entered as parts per million
(ppm). The saturation vapor pressure of the liquid at the temperature of its thermostat is
used to determine the corresponding values for the gas flow through mass flow controller
1 (MFC1) and 2 (MFC2). One important consideration is the volume increase due to the
addition of the vapor into the gas stream. These effects can be very large for liquids with
high vapor pressures and if neglected can lead to major errors in calculating the vapor
concentration and large variation in the flow rate.
To best understand this effect one can imagine an extreme case, where the liquid
inside the bubble through container is near its boiling point. Even with a very small
incoming gas flow a large amount of gas and vapor will exit through the outlet. This effect
can be corrected for by assuming ideal gas behavior for each component. Since the
131
number of moles of the carrier gas entering (ngas in ) the bubble through container has to
equal the number of moles of the carrier gas exiting (ngas out ), the following expression can
be used7.
outgasingas nn =
Under isothermal conditions
outginin VpVp =
Where Vin and Vout are the volumetric flow rates at the inlet and outlet,
respectively. pin is the pressure of the pure gas entering and pg is the partial pressure of the
carrier gas at the outlet. ptotal is the sum of the partial pressures of all components. If the
partial pressure of the liquid inside the container is pi, then
outitotalinin VppVp )( −=
Referring back to figure 4-3 the vapor concentration in the gas stream will depend
on values of f1 and fout, whereas the mass flow controllers can control only f1 and f2. We
had to consider this when writing the LabView control program.
The vapor concentration for compound (i) inside the bubble through container in
parts per million is
66 1010 ×=×=total
i
total
ibubblerin p
pnn
ppm
(59)
(60)
(61)
(62)
132
Since the gas flows into the QCM/HCC and eventually out to the atmosphere and
there are no restrictions in the gas flow, ptotal˜ patmospheric=1atm.
The vapor concentration in the combined gas flows from MFC1 and MFC2 into
the QCM/HCC (ppmfinal) is
+
=out
outbubblerfinal ff
fppmppm
1
From equation (61) and since ptotal˜ pin˜ 1 atm,
outout
in
ff
VV 2=
iitotal
inout p
fpp
fpf
−=
−=
1)(22
For a set value of total gas flow, when f total=f1+f2, the final vapor concentration can
be expressed as
−+
−
−×=
)(1
1)10
1(
22
2
6
ffp
fp
f
atmp
ppm
totali
iifinal
The QCM/HCC VI uses the entered values for ppmfinal, total gas flow (ftotal), the
solvent vapor pressure (pi) and the above equation to arrive at the corresponding value for
f2, which is then subtracted from ftotal to give f1. The equations used for this procedure can
be seen in the case structures of figure 4-9.
(63)
(65)
(66)
(64)
133
The above gas flow rate information are then converted into control output
voltages for the MFC1 and MFC2. The equations used are also shown in the case
structures of figure 4-9 and were obtained in previous calibration experiments. The data
for the calibration of MFC1, MFC2 and MFC3 (Tylan 0-400sccm) are shown below. A
mass flow meter (Hasting 0-60sccm) was also calibrated. Although this unit is not used in
the current setup, the calibration data is shown below for the record.
A BIOSDRYCAL DC-2 flow-calibrator (NIST traceable) was used for the
calibration of the mass flow controllers. During the calibration experiment the outlet of
each mass flow controller was connected to the flow-calibrator unit with a short ¼” OD
Teflon tubing. After the flow setup was leak tested, the nitrogen pressure out of the
nitrogen tank was regulated at 40 psi. The voltage input/output of the mass flow controller
was controlled/recorded for the flow rates measured by the calibration unit.
134
Table 4-5: Calibration of MCF1 (UNIT UFC8100) for nitrogen at @ 20.40C
Voltage/V Flow rate (cc/min) Flow rate (cc/min) @20.40C @STP
0.00 0.000 0.000 0.15 1.647 1.553 0.20 2.166 2.042 0.30 3.265 3.074 0.50 5.383 5.105 0.70 7.517 7.114 1.00 10.680 10.100 1.30 13.900 13.140 1.80 19.190 18.150 2.30 24.610 23.260 2.60 27.820 26.310 2.90 30.920 29.230 3.10 33.050 31.240 3.40 36.170 34.220 3.70 39.450 37.310 3.90 41.620 39.330 4.10 43.670 41.230 4.40 46.790 44.290 4.70 49.980 47.270 5.00 53.250 50.250
135
Table 4-6: Calibration of MFC2 (UNIT UFC8100) for nitrogen @ 23.50C
Voltage/V Flow rate (cc/min) Flow rate (cc/min) @23.50C @STP
0.00 0.00 0.00
0.15 1.719 1.585 0.30 3.357 3.088 0.50 5.554 5.133 0.70 7.733 7.110 1.00 10.980 10.070 1.30 14.290 13.160 1.80 19.770 18.190 2.30 25.310 23.290 2.60 28.540 26.280 2.90 31.770 29.150 3.10 33.960 31.200 3.40 37.260 34.190 3.70 40.520 37.280 3.90 42.700 39.220 4.10 44.680 41.020 4.40 48.020 44.140 4.70 51.360 47.160 5.00 54.730 50.330
136
0
10
20
30
40
50
60
0 1 2 3 4 5
y = 0.062067 + 10.637x R= 1 y = 0.063687 + 10.053x R= 1
Flow
rat
e/cc
min
-1
Voltage/V
0
10
20
30
40
50
60
0 1 2 3 4 5
y = 0.090549 + 10.917x R= 0.99999 y = 0.094243 + 10.028x R= 0.99999
Flow
rat
e/cc
min
-1
Voltage/V
Figure 4-14: Calibration of (a) MFC1 and (b) MFC2
(a)
(b)
137
Table 4-7: Calibration of Hasting mass flow meter (0-50sccm)
Table 4-8: Calibration of the MFC3 (Tylan 0-400sccm)
Voltage/V Flow rate (cc/min) Flow rate (cc/min) @28.00C @STP
0.91 9.621 8.707 1.19 12.780 11.580 0.68 6.804 6.159 0.63 6.346 5.752 1.15 12.310 11.110 1.87 20.570 18.580 3.23 36.560 33.060 3.92 45.280 40.920 4.51 53.180 48.080 4.88 58.560 52.930
Voltage/V Flow rate (cc/min) Flow rate (cc/min) @29.00C @STP
0.5137 22.760 20.590 0.3740 10.030 9.070 0.4207 14.400 13.010 0.5114 22.890 20.720 0.6104 32.160 29.110 0.7152 41.780 37.820 0.8117 50.710 45.890 0.9142 60.210 54.480 1.0061 68.660 62.140 1.1072 77.830 70.430 1.2077 87.230 78.940 1.3058 96.280 87.150 1.4024 105.100 95.220 1.4987 113.900 103.100 1.5959 122.800 111.100 0.2740 0.645 0.583 0.3181 5.117 4.489
138
0
10
20
30
40
50
60
0 1 2 3 4 5
y = -1.6553 + 12.127x R= 0.99962 y = -1.4874 + 10.96x R= 0.99962
Flow
rat
e/cc
min
-1
Voltage/V
0
20
40
60
80
100
120
140
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
y = -24.403 + 92.366x R= 0.99999 y = -22.128 + 83.636x R= 0.99999
Flow
rat
e/cc
min
-1
Voltage/V
Figure 4-15: Calibration of (a) Hasting mass flow meter and (b)Tylan mass flow controller
(a)
(b)
139
The calibration data for mass MFC1, MFC2 and MFC3 are written as equations
into the LabView program and are shown in the case structures in figures 4-9 and 4-10.
When the mass flow controllers are used for gases other than nitrogen, correction factors
can be used for the flow equations. Currently correction factors for hydrogen and ethylene
have been written into the LabView program. If necessary, values for correction factors
for other gases can easily be added to the current list.
The measuring element inside a mass flow controller is a small tubular thermal
mass flow sensor. It consists of a heating element and two thermometers (RTD); one
positioned upstream and the other positioned downstream with respect to the heating
element. As the gas flows through the sensor the two thermometers will sense different
temperatures depending on the molar heat capacity and the number of moles of the gas
passing through per unit time. Since nitrogen is the most common gas used for calibration
of mass flow controllers, conversion factors to extrapolate calibration data from nitrogen
to other gases are readily available. In the table below there are a few conversion factors
for gases that are used for present, and may be used for future, experiments.
Table 4-9: Conversion factors to be used for mass flow controllers calibrated with nitrogen
Name Symbol Conversion factor (Cnp/CN2)
Acetylene C2H2 0.595 Air Air 1.001
Ethylene C2H4 0.597 Hydrogen H2 1.010 Oxygen O2 0.981
Water Vapor H2O 0.817
140
For experiments where organic solvents or water vapors are introduced into the
QCM/HCC, we place the mass flow controllers upstream from the bubble-through
container to avoid the necessity of extrapolation of the flow information for every solvent
used. As mentioned previously the vapor concentration inside the bubble-through
container (pi) is needed to calculate the composition of the final gas stream (ppmfinal) into
the QCM/HCC. This information has to be obtained for the temperature of interest from
the linear regression of the log of the vapor pressure of the solvent (ln(p)) vs. inverse of
absolute temperature (T-1). The figures and tables in appendix C show the vapor pressures
and their linear regressions for a few solvents commonly used for sorption experiments.
The data for the first table was taken from the CRC Handbook of Chemistry and Physics
77th edition. The data for the second set of solvents was taken from the CRC Handbook of
Chemistry and Physics 79th edition.
4.2 Data processing and analysis
The data gathered by the QCM/HCC VI is bundled and saved as an ASCII file.
The difference in the oscillation frequencies of the sample and the reference QCM is
converted into mass using the Sauerbrey equation. The oscillation frequency of the QCM
before and after the coating is used to measure the mass of the coating. The change in the
oscillation frequency thereafter is used to determine the mass change due to conditioning
of the sample inside the QCM/HCC. Figure 4-16 shows an example of a data file opened
in Microsoft Excel.
141
Figure 4-16: A typical data file opened in Excel Microsoft
142
For this particular experiment the sample was placed in the left side of the
QCM/HCC. The oscillation frequency of the reference QCM (right side) is generally
constant. It is subtracted from the oscillation frequency of the sample QCM (left side) to
account for small drifts in the baseline due to environmental changes. Usually after the
sample is placed inside the QCM/HCC and exposed to pure nitrogen, it begins to dry. For
thin films coated from a solution there may be a relatively large amount of residual solvent
present long after the coating process. At the beginning of a run the drying of the film is
observed until the oscillation frequency of the QCM reaches a steady maximum value
(minimum mass). If the sample is placed on the left side of the QCM/HCC a minimum
mass (a dry film) corresponds to a maximum value in the column “Oscillation frequency
difference” in figure 4-16. For a sample residing in the right side of the QCM/HCC
minimum mass results in a minimum value of oscillation frequency difference. This
minimum value can be subtracted from the data and then divided by Sauerbrey’s constant
(56.6/Hz µg-1 cm-2). Finally the area of the film (˜ 2 cm2) is used to determine the absolute
mass change on the surface. The mass trace is then plotted vs. time.
The thermal power is already given in µW. A positive going thermal signal
indicates an exotherm for the right side and an endotherm for the left side of the
QCM/HCC. It is important to keep a good record of the position of the sample and
reference and to pay attention to labels on the electrical leads during
disassembling/reassembling of the apparatus. To determine the total amount of heat
released or consumed during a given time interval the thermal power is integrated and the
area under the curve is obtained. We have used a program written for Matlab (Mathworks,
Natick, MA) by Dr. Lars Wadsö from Lund University in Sweden for integrating the
thermal power for some of our experiments. We have also used Origin (Microcal Software,
143
Northampton, MA) and Grams 386 (Galactic Industries Corporation, Salem, NH). In all
cases a baseline is assigned using regions before and after a thermal peak. The baseline can
be constructed from a linear, polynomial or logarithmic fit to the selected regions. Once
the baseline has been subtracted, two points in time can be selected as the start and end
point of the integration.
The columns labeled MFC1 and MFC2 contain the output voltage from the two
mass flow controllers. Using the calibration data for the mass flow controllers and the
partial pressure of the solvent vapors the values for f1 and fout (figure 4.3 and equation 63)
can be determined, which in turn are used to find the concentration of the vapor in the gas
stream through the QCM/HCC. The equations below have been written as macros for
KaleidaGraph (Synergy Software, Reading, PA) and Microsoft Excel (Microsoft,
Redmond, WA) for this purpose. Equation (67) gives the dilution factor for the
combination of f1 and fout. Equation (68) gives the final concentration of the vapor in ppm
dilution factor =(((MFC2*-10.055)/(1-(pi/760)))/(((MFC2*
-10.055)/(1-(pi/760)))+(MFC1*-10.071)))
ppmfinal=((pi/760)*106)×(((MFC2*-10.055)/(1-(pi/760)))/(((MFC2*
-10.055)/(1(pi/760)))+(MFC1*-10.071)))
This has been a brief description of data processing for a sorption experiment and
was also intended as a reference guide for future operators of the QCM/HCC. The mass,
thermal, and vapor concentration data can be used to determine related thermodynamic
and kinetic parameters as shown in the data flow diagram in figure 4-17.
(67)
(68)
144
Oscillation frequency Thermopile potential MFCs voltage
Sauerbrey’s equation Thermal calibration Flow calibration
Kinetics info. (k)
Mass information Heat information Concentration of vapor
Mass of coating Mass of sorbed material Enthalpy(∆H)
Concentration in coating Entropy (∆S)
Gibbs free energy (∆G)
Partition coefficient (K)
Figure 4-17: The data flow diagram for the QCM/HCC experiments
145
References
(1) Smith, A. L.; Shirazi, H. M. J. Therm. Anal. Calorim. 2000, 59, 171-186.
(2) Smith, A. L.; Shirazi, H.; Wadso, I. Proc. - Electrochem. Soc. 1998, 98-8, 576-585.
(3) Smith, A. L.; Wadso, I.; Shirazi, H. Book of Abstracts, 216th ACS National Meeting,
Boston, August 23-27 1998, HYS-187.
(4) Smith, A. L.; Shirazi, H. M. Book of Abstracts, 218th ACS National Meeting, New
Orleans, Aug. 22-26 1999, COLL-076.
(5) Martin, S. J.; Granstaff, V. E.; Frye, G. C. Anal. Chem. 1991, 63, 2272-81.
(6) Auge, J.; Hauptmann, P.; Hartmann, J.; Roesler, S.; Lucklum, R. Sens. Actuators, B
1995, B24, 43-8.
(7) Berling, D.; Jonsson, B.; Olofsson, G. J. Solution Chem. 1999, 28, 693-710.
146
Chapter 5- Experiment 1: Solvent vapor sorption into an aliphatic polyetherurethane (Tecoflex™) thin film
5.1 Introduction A good understanding of solubility interactions of polymer-solvent systems is of
great importance. Many essential physical and chemical properties of polymers are related
to, and can be explained based on these interactions. For instance, mass transport
processes in a polymer are crucial in designing packaging material, protective clothing and
paints and finishes1. If there are residual solvents in a packaging material that are not
removed during processing, they may be found in the product by the time they reach the
consumer. During storage a partition phenomenon between the product, the internal
atmosphere, and the packaging material takes place. In the food industry the packaging
material acts as a barrier against aroma compounds of the product escaping the food
product as well as against organic and water vapors reaching the packaged product. It is
not acceptable if the packaging material itself becomes the source of organic compounds.
Interestingly, the solvent removal rate itself can alter the properties of a polymer2. In some
cases the solvent removal rate determines the drying mechanism. Sometime skins are
formed on the surface during drying that trap the solvent. For other semicrystalline
polymers the degree of crystallinity increases during drying, which hampers the diffusion
of the solvent through these polymers.
Permeation, sorption and migration of solvents in polymers have been modeled
and studied extensively. Yet a comprehensive experimental technique for the
characterization of a polymer-solvent system is rare3. Gravimetric measurements are
147
classically used for determination of sorption isotherms4. The polymer is placed in an
environment enriched with the solvent. The weight of the polymer is measured before and
after equilibrium has been established. This, however, may require hours or even days or
weeks.
Characterization of solvent-polymer solubility interactions is not limited to
applications in the area of designing packaging material. Thin membranes of polymers are
used for separating liquid mixtures in a process called pervaporation. This process takes
advantage of differences in the sorption and diffusion properties of solvents in polymeric
films. A hydrophilic thin polymer membrane such as a 300-500nm film of polyvinylalcohol
(PVA) on a support layer has been successfully used to separate water from organic
solvents5,6. In many wastewater treatment plants the organic solvents are separated from
water by pervaporation through a hydrophobic thin membrane such as
polydimethylsiloxane (PDMS)7,8. When it can be used, pervaporation is much more
efficient than thermal separation4.
As the everyday demands for certain physical properties of polymers increase, new
polymer blends are made to satisfy most of these highly specific requirements. In general it
is easier to formulate a polymer blend for a specific property than to synthesize and
develop an entirely new polymer. However the characterization of polymer blends is even
more complex compared to their homopolymers with respect to their interaction with
different solvents 3. The solubility interactions of such polymer blends cannot be inferred
based for the properties of their homopolymers and there is usually very little data
available in the literature. There is a strong need for a comprehensive method capable of
characterization of such polymer blends on routine basis.
148
Polymeric films are also used as coating material for chemical sensors. Chemical
sensors are usually arranged in array configurations consisting of many individual
components, each having a different polymer as its sorbing medium. In such an
arrangement the individual components of an array don’t need to be perfectly selective to
a particular compound. The collective responses of the sensors can be processed by one of
several pattern recognition methods to identify a compound or even a mixture of a few
different compounds9.
In all of the application areas mentioned above a good understanding of the
polymer-solvent solubility interactions is essential. There are many techniques used for the
characterization of these interactions. As mentioned before sorption isotherms can be
obtained from gravimetric measurements. Due to the long equilibration times required this
method has been replaced by other direct and some indirect analytical techniques. A
number of thermal techniques are available. The glass transition temperature is routinely
measured with differential scanning calorimeters (DSC)10. A thermal gravimetrical
analyzer (TGA) can be used to determine the percent composition of solvated polymers10.
There are also other techniques such as NMR11, neutron scattering12 and some
mechanical methods10.
Inverse Gas Chromatography (IGC) has emerged in recent decades as a promising
technique. Here the solid stationary phase of a GC column is the polymer of interest and
volatile solvent probes are passed through the column. Smidsröd and Guillet were the first
to use IGC in 1960s13. They studied the solubility interactions of several representative
solvent vapors with a polymer that they coated on the support material of a GC column.
149
IGC has been used to determine a number of important properties for polymers
with respect to their interaction with volatile compounds. Using the retention time of
representative volatile compounds at different temperatures and knowledge about the
dimension of the column the thermodynamic property, The partition coefficient (K), can
be evaluated. When a compound is injected into a GC column along with a small amount
of a non-retained gas such as air, the velocity of both compounds can be calculated using
the length of the column (L) and the retention times (tR=retention time of the solute;
tm=retention time of a nonretained compound). The velocity of the nonretained
compound or the velocity of the mobile phase (u) is simply the length of the column
divided by the retention time of the nonretained compound (u=L/tm). The velocity of the
solute injected (v) can also be obtained in the same manner and is always smaller than (u).
If the solute exhibits strong interactions with the stationary phase, it will be mostly
dissolved in the stationary phase and therefore will have a very slow velocity through the
GC column.
=
analyteofmolesofTotalphasemobileinanalytetheofmolesof
u#
#v
+=
+=
+
=
M
smR
mm
ssmssmm
mm
mR
VVtt
VCVCtVCVC
VCtt K
LLL
1
111;
1
1
(69)
(70)
150
where Cs and Cm are the concentrations of the solute in the stationary phase and
the mobile phase respectively and Vs and Vm are the volumes of the stationary and the
mobile phase and finally
=
−
m
s
m
mR
VV
ttt
K
The volumes of the stationary phase and the mobile phase depend on the
dimensions of the GC column and their ratio (Vs/Vm) is constant for a given column. The
partition coefficient obtained from the equation described above can be used to evaluate
other thermodynamic parameters. For example if measurements are made at different
temperatures the enthalpy of adsorption can be calculated by the integration of van’t Hoff
relationship over those temperatures.
2
0ln
T
H
Tsorption
P RK ∆
=
∂∂
Some of the systematic errors associated with the IGC are caused by fluctuations
in the flow rate of the mobile phase, large pressure gradients between the outlet and the
inlet of the column and poor temperature control.
A similar partitioning process to that in IGC takes place when a quartz crystal
microbalance is coated with a thin polymer film and placed in an environment enriched
with solvent vapors14.
(71)
(72)
151
Here Cs and Cv are the concentrations of the solute in the polymer film and in the
vapor phase respectively. In contrast to classical gravimetrical method the QCM method
doesn’t require long equilibration times because of the extremely small sample size.
Typically 50-300 µg samples in the form of a film are sufficient.
We already mentioned in chapters 1 and 4 how the QCM/HCC is capable of
measuring thermodynamic and kinetic parameters directly under isothermal conditions. If
these measurements are performed for the sorption of a large set of organic solvent vapors
in a polymer film, a theoretical model called the linear solvation energy relationship
(LSER) can be used to break down the solvent-polymer solubility interactions into
individual types of intermolecular contributions15,16.
Sorption of vapor molecules into a sorbing material can be described in three
conceptual steps16. First a cavity is formed to accommodate the incoming vapor molecule.
This step requires energy since it results in a disruption of solvent/solvent interactions.
(Here the term solvent refers to the sorbing material, the polymer thin film, and the solute
is the organic vapor). Next the solute fills the cavity with reorganization of the solvent
around the cavity. In the third step energy is gained as the solute/solvent attractive forces
Cv
Cs
K=Cs/Cv
Figure 5-1: The partitioning process for a thin film exposed to solvent vapors
152
are established. The magnitude of the driving force for these processes depends on the
nature of solubility interactions between the solute and solvent, the organic vapor and the
polymer. For nonionic organic compounds the solubility interactions include
Hydrogen-bonding
Dipole/dipole (orientation)
Dipole/induced dipole (induction)
Induced dipole/induced dipole (dispersion, or London forces)
Hydrogen bonding is a well-understood concept. It involves the directional
interactions between an acidic and a basic hydrogen-bond site. It requires the presence of
an atom with high electronegativity such as oxygen, nitrogen, etc and a hydrogen atom
directly adjacent to a highly electronegative moiety. This is not to be confused with acidic
and basic proton transfer, although in some cases correlations can be made between the
H-bonding and proton transfer of chemical functional groups. The hydrogen-bonding
properties for acidic and basic sites are described by αH2 and βH
2 respectively. These
parameters are obtained from 1:1 complex formation equilibrium constants of hydrogen
bond acids and bases in tetrachloromethane17.
Dipole-dipole interactions take place between species that possess a permanent
dipole moment. The electrostatic attractions between positively and negatively charged
regions of dipolar compounds can depend strongly on the orientation of the dipoles. The
parameter πH2 describes the dipole-dipole interactions and the ability of a molecule to
stabilize a neighboring dipole or charge. It can be obtained from partition coefficients of
solutes on a polar stationary phase of a gas chromatograph and for aliphatic solutes it is
proportional to the values of their dipole moments18.
153
Polarizability refers to dipole/induced-dipole interactions, in other words the
interaction of a dipole with the polarized electron cloud of a nondipolar species. The
parameter R2 is used to describe the polarizability of a compound. It is calculated from the
difference in molar refraction between the solute and an alkane with the same
characteristic volume19.
Dispersion interactions can arise in any species with electrons. The interactions get
significantly larger as the molecular volume and the number of polarizable electrons
increases. Log L16 is the parameter for dispersion interactions, which also includes cavity
effects. It is the logarithm of the partition coefficient of a solute on a hexadecane GC
column at 250C.
The sum of the above solubility interactions is the driving force for the overall
sorption process. The LSER relationships help to understand the nature of the individual
contributions and their magnitude. The coefficients in these relationships are related to the
solubility properties of the sorbing material, the polymers. The LSER relationship uses the
partition coefficient K in a model, which is a linear combination of the solubility
parameters and their coefficients.
16222 loglog Llbasrc HHH +++++= βαπ2RK
The solubility parameters for many solutes have been characterized extensively and
are available in the literature20. The coefficients of the linear solvation energy relationship,
r, s, a, b, l, and the regression constant, c, can be obtained by a multivariate linear
regression of the partition coefficients of a probe solute set over a polymer film. In theory
five LSER equations could be used to obtain the five unknowns. In practice the set of the
(73)
154
vapors should be representative of all the solubility interactions and should have a large
population (10-40 or more) to establish a reasonable correlation for the fit. The LSER
method has been used for characterization of solubility properties of many polymers used
as GC stationary phases or as coatings for chemical sensors 9,21. What makes this method
so attractive is the fact that once the LSER has been established for a given compound, its
partition coefficient with other solutes can be estimated without any experimental
work15,22. In the next section of this chapter the LSER for a polyetherurethane thin film
will be described.
5.2 Experimental
5.2.1 Ethanol sorption/desorption in a drop-coated TecoflexTM thin film
One of the first samples we have studied in the QCM/HCC has been a number of
thin films of an aliphatic polyetherurethane prepared by different methods. This polymer
was first developed in 1983 to be used in a left ventricular cardiac assist pump. Today it is
manufactured by Thermedics, Inc and marketed with the commercial name TecoflexTM.
TecoflexTM is used in a wide range of medical applications, in particular for coating
implants, catheters and other objects in contact with bodily fluids. It can withstand
prolonged exposure to aqueous environments, body temperature and the corrosive body
fluids and blood. TecoflexTM has also been an effective chemical sensor coating material
for detection of organic vapors23. The repeat unit of the aliphatic polyetherurethane
TecoflexTM (SG-60D) that we used in our study is shown in the top part of figure 5-2. The
manufacturer reported a glass transition temperature of –20 to –400C. A density of
1.11g/cc was measured via the displacement method and was confirmed by the
155
manufacturer. We prepared several thin films of this polymer on the surface of the QCM.
The surface of each QCM was cleaned in Piranha solution (one part 30% H2O2 in three
parts 98% H2SO4 by volume), rinsed with deionized water and dried in air or dry nitrogen
flow prior to film preparation. We have explored several methods of thin film preparation
and experienced that finding a reliable method will depend on he nature of the film to be
prepared and its matrix prior to coating. At the early stages TecoflexTM thin films were
drop-coated from a chloroform solution. Later we relied on spin-coating for producing
thin and uniform films of TecoflexTM over the entire surface of the QCM. The results of
the experiments with the drop coated TecoflexTM film will be presented first.
The experiment described here was conducted at a relatively early stage, as we were
gaining more experience with the operation of the QCM/HCC. We consider it an
important experiment, because resolving some of the issues we encountered has given us a
Figure 5-2: The repeat unit of Tecoflex (SG-60D) polyetherurethane
156
deeper understanding of some important aspects of the operation of the QCM/HCC. The
results described here should be considered in conjunction with that of the following set
of experiment. We intend to communicate the details of the process of obtaining these
results rather than emphasizing the final experimental values.
The thin TecoflexTM film studied here was drop-coated from a 10 mg/ml
chloroform solution on the center of the large gold electrode of a QCM over an area of
0.159cm2. The shift in the oscillation frequency of the coated QCM indicated a mass
change of 75.5µg/cm2 and a total polymer mass of 12.7µg. A thickness of 0.7µm was
calculated based on the mass, and the density of the film. Figure 5-3 shows the mass
change on the surface of the QCM, as this film was drop-coated. Immediately after the
Drop was placed on QCM
0
2
4
6
8
10
12
14
16
18
0 500 1000 1500 2000 2500
Time(sec)
Mas
s(µg
)
Figure 5-3: The mass of the drop coated Tecoflex thin film
Oscillation frequency could be measured
157
solution was placed on the QCM surface no oscillation frequency could be measured, since
the sample was a viscous liquid. The solution dried quickly and within a few seconds most
of the solvent evaporated. During these few seconds there was a small gap in the mass
trace, where no data could be collected. The scaling of the time axis in figure 5-3 doesn’t
show this gap. The slow mass decay after the gap represents the evaporation of only a
small amount of the total solvent present in the original drop of the TecoflexTM solution.
This film was further dried in nitrogen until no mass change was observed.
During the sorption studies this film was exposed to a gas mixture of nitrogen
(research grade 5.0 BOC Gases) and ethanol vapor (dehydrated 200 proof Pharmco)
whose composition was controlled by the flow system described in chapter 4. The flow
pattern of the ethanol vapor and nitrogen gas mixture and the resulting change in mass on
the QCM surface are shown in the figures 5-4 (a) and (b). For this experiment a complete
sorption cycle consisted of five sorption and desorption steps. Starting at a low ethanol
vapor concentration (20 parts per thousand (20ppt), at the beginning of a sorption cycle in
figure 5-4 a) the vapor concentration was increased by 5ppt in 470sec time intervals up to
a maximum concentration of 45ppt. As the ethanol vapor pressure over the film was
increased during each sorption step some of it was dissolved in the TecoflexTM film
increasing its mass. After the fifth sorption step the vapor concentration was then reduced
to 20 ppt during the next five steps. When the ethanol vapor pressure over the film was
depleted the same amount of ethanol gained during the corresponding sorption step
desorbed and reverted back to the gas phase.
Figure 5-5 (a) shows the thermal power measured at the same time. For abrupt
mass changes during the individual sorption/desorption steps we expected to observe
158
pulses of heat, since the thermal power trace should be proportional to the first derivative
of the mass trace. This relationship is described in equation 74.
Here the thermal power is expressed twice, once in Tian’s equation (introduced in
chapter 3) and a second time as the molar enthalpy of sorption for the number of moles
sorbed per unit time. MM and m are the molecular weight and the mass of the sorbed
compound respectively. Comparing the mass and the thermal trace in figures 5-4 (a) and 5-
5 (b) it is obvious that they don’t follow the relationship given above. Therefore the
thermal power measured cannot be solely due to the sorption of ethanol vapor into the
TecoflexTM.
))(()]([ )()( MM
H
dt
dm
dtdU
UP sorptiontt
∆=+= τε (74)
159
0
20
40
60
1050 3050 5050 7050 9050 11050
Time/sec
Eth
anol
con
c./p
pt (a)
0.0
0.5
1.0
1.5
2.0
1050 3050 5050 7050 9050 11050
Time/sec
Mas
s of
eth
anol
/ µg (b)
Figure 5-4: (a)Ethanol vapor concentration above TecoflexTM film; (b) Mass of ethanol sorbed into the TecoflexTM film
One sorption cycle
Sorption step Desorption step
160
Exo
0
10
20
30
40
1050 3050 5050 7050 9050 11050
Time/sec
The
rmal
pow
er/µ
W (a)
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
21150 23150 25150 27150 29150
Time/sec
The
rmal
pow
er/µ
W (b)
Figure 5-5: (a) Thermal power for ethanol sorption in TecoflexTM with both QCMs on (sample on right side); (b) Thermal power for ethanol sorption in TecoflexTM with
the right QCM off (sample on right side)
Exo
161
As discussed in chapter 2 the viscoelastic characteristics of a polymer are complex
properties (Gf=G’+iG”), which can be altered as the result of change in the temperature
or solvent content and also depend on the oscillation frequency. In general, polymeric
materials exhibit larger viscoelasticity at temperatures above their glass transition and with
higher solvent contents. In other words our TecoflexTM sample gets softer, as it picks up
more ethanol vapor. For an oscillating film the oscillation resistance increases as the
oscillation gets more damped and the film gets more lossy. We believe this happens in the
oscillating TecoflexTM film as the ethanol content increases. The oscillation resistance,
voltage and current are altered, which in turn affect the thermal power dissipated in the
film due to oscillation. This seems to be a large effect completely masking the pulses of
heat due to sorption of ethanol. To test our hypothesis we decided to turn off the right
QCM with the TecoflexTM film. Figure 5-5 (b) shows the thermal power after the QCM
was turned off. The pulses of heat are due to sorption of ethanol vapor. The integrated
area of each peak is the total amount of heat produced or consumed during sorption or
desorption steps.
Since the sample QCM (right side) was not oscillating when the thermal power in
figure 5-5 (b) was measured, we had to use the mass measurements taken before the QCM
was turned off at the same ethanol vapor compositions. The flow system generated highly
reproducible ethanol vapor concentrations. This was evident from the high repeatability of
the mass trace over several sorption cycles.
After the completion of this experiment, the same flow patterns were generated
over two bare gold QCM surfaces to determine the sensitivity of the two sensors and how
well matched the sample and the reference sides of the QCM were. At the second most
sensitive setting of the preamplifier (3µV full range) and ethanol concentrations of 20-25
162
ppt (7270-8770 sec in figure 5-6 a) the drift in the baseline was 0.3µW with a standard
deviation of 50nW. At higher ethanol concentrations (30-40-45ppt) small mass and
thermal events were observed in the absence of a sample. This explained why the
integrated area of the thermal power observed for the sorption of ethanol in TecoflexTM at
higher ethanol vapor concentrations were much smaller compared to (by up to 50%) those
at lower concentration.
Initially we believed these events to be caused by slight differences in the
adsorption of ethanol by the Teflon-encapsulated o-rings holding the QCM from above.
Later we realized that the section of the flow system where mixing of the gas flows from
MFC1 and MFC2 took place was at fault. The gas flows were not sufficiently mixed before
they were split into the inlets of the sample and the reference sides of the QCM/HCC.
However, before this discovery we had developed a correction procedure, which
subtracted the spurious thermal events in the absence of a sample from the thermal data
during the sorption experiment. Table 5-1 gives a summary of the experimental results
before and after the correction.
163
0
20
40
60
3270 5270 7270 9270 11270 13270
Time/sec
Eth
anol
con
c./p
pt (a)
-1.0
-0.5
0.0
0.5
1.0
3270 5270 7270 9270 11270 13270
Time/sec
The
rmal
pow
er/ µ
W (b)
Figure 5-6: (a) Ethanol concentration over two bare gold QCM surfaces; (b) difference in thermal power dissipated on two gold surface.
164
Table 5-1: Enthalpy of sorption of ethanol in the drop-coated TecoflexTM film.
Ethanol
conc.(ppt)
Average ∆m(µg)
Tecoflex Average Heat(µJ)
∆sorptionH kJ/mole
Gold surface Average Heat(µJ)
Corrected Average Heat(µJ)
Corrected ∆sorptionH kJ/mole
45-40 -0.190 96 23 114 211 +51 40-35 -0.182 115 29 79 195 +49 35-30 -0.181 174 44 36 210 +53 30-20 -0.174 200 53 0 200 +53 25-20 -0.164 210 59 -8 201 +56 20-25 0.158 -214 -62 7 -207 -60 25-30 0.171 -200 -54 0 -200 -54 30-35 0.175 -169 -44 -29 -198 -52 35-40 0.153 -116 -35 -80 -196 -59 40-45 0.227 -89 -18 -113 -202 -41
20
22
24
26
28
30
3270 5270 7270 9270 11270 13270
Time/sec
Mas
s of
eth
anol
/ng
Figure 5-7: Difference in mass signal between two uncoated QCMs
165
5.2.2 Organic vapor sorption/desorption in spin-coated TecoflexTM thin films.
In continuing the characterization of the TecoflexTM polymer-solvent vapor
interactions, we made use of the experience gained from the previous experiment. A gas
mixing section was added to the flow system to ensure a uniform vapor concentration in
both sample and reference sides of the QCM/HCC. Different thin film preparation
techniques were explored to produce thin and uniform films over the entire surface of the
QCM. From a variety of different techniques used, drop coating, spray coating and
electrospray, spin coating gave the best result for TecoflexTM.
Spin-coating is accomplished by spreading a solution of the material to be coated
on a rotating substrate. It has been used extensively, particularly in the electronics
industry. There was no substantial work to study and analyze the fundamental processes
involved in spin-coating until the late 1970s when there was a boom in the disk-file
substrate coating applications. Many scientists, mainly from industrial institutions such as
IBM, characterized the flow of liquids on rotating substrates24. Important variables in
modeling the spin-coating process are the density and viscosity of the solution, the
evaporation rate of the solvent and the rotation speed.
Several trials were made to identify the optimum solution concentration and the
spinning rate during the spin-coating of TecoflexTM. Four films were spin-coated on
rotating QCMs. Each film was allowed to dry in a nitrogen stream until no mass change
was evident. The mass and the density of the dry film were used to determine its thickness.
Two of the four films were prepared at 3000rpm from a 20mg/ml chloroform solution
and studied within a few days. Two other films were prepared later by two of our
166
undergraduate research students, Mrs. Anna Ayrapetova and Miss Betty Jacob. Each one
of the two films was studied with one solvent system.
In choosing the appropriate solvent vapor for the sorption experiments, instead of
a random selection of solvents, the LSER theory was consulted to select solvent vapors
each representing one major type of solubility interaction. The vapor candidates (their
solubility interaction) were: toluene (polarizability), chloroform (polarity), ethanol (H-
bonding through acidic sites), acetone (H-bonding through basic sites), n-hexane
(dispersion) and carbon tetrachloride.
The first TecoflexTM film in this series to be studied had a thickness of 0.78 µm and
a mass of 170.7µg over an area of 1.979cm2. Although the entire QCM surface was coated,
only the area enclosed by the inner diameter of the o-ring (5/8” ID) holding the QCM was
exposed to the gas flow. This corresponded to a total area of 1.979 cm2. The second film
had a mass of 459.3µg over the exposed area and a thickness of 2.09µm.
After the QCM/HCC had reached thermal equilibration with the bath, stepwise
changes in the vapor concentration above the film were made in a similar procedure
described for the previous experiment. For all the experiments the order of events was the
same. First the film was dried until no more mass change was apparent. Thermal
equilibration was established prior to each run. After the control of the gas composition
was turned over to the LabView program, the thermal power for the first few sorption
events were monitored so that a preamplifier setting could be chosen as sensitive as
possible still accommodating the thermal signals. In the following several hours the film
was subjected to many sorption/desorption cycles. The following figures show the data
for two sorption cycles for each solvent.
167
There are four figures for each sorption experiment, vapor activity, mass trace,
thermal trace and the partition coefficient. The mass trace was obtained from the QCM
oscillation frequency as described in chapter 4. The thermal power is taken directly from
the LabView output file. At the time of the data analysis of for this experiment we used a
program written in Matlab by Dr. Lars Wadsö for integration of the thermal traces. This
program has a graphical interactive subroutine for assigning baselines for the thermal
powers. Regions of the baseline can be selected by the operator to be used either for a
linear or a polynomial fit. Once the baseline has been subtracted, the beginning and the
end of a peak can be assigned and the area of the peak is measured. This method was used
to integrate the area of the individual thermal peaks during sorption and desorption steps.
The areas were tabulated and shown in table 5-2. The partition coefficients were obtained
using a macro written in KaleidaGraph, which was a further modification of the smaller
macros shown in equations 67 and 68 in chapter 4. The ratio of the final concentrations in
the thin film and in the gas phase expressed in µg/L gives the partition coefficient.
The figures below show the measurements for sorption of 6 organic vapors in a
0.78µm TecoflexTM film, which are followed by their respective summary tables. Next, the
measurements for the sorption of the same six solvents in a 2.09µm Tecoflex are shown
with their respective summary tables. The results of a null experiment are shown for two
bare gold surfaces in the QCM/HCC. Finally, the mass traces for three sorption
experiments used for obtaining the diffusion coefficient of solvent vapors in Tecoflex are
shown. The discussion of details, special features and general results of the entire data
presented in this section will follow in the results section.
168
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
10500 14000 17500 21000
Carbontetrachloride sorption in Tecoflex (0.78µm)Vapor conc. in the gas stream 99-07-23-1
P/P
º
Time/sec
0
2
4
6
8
10
12
14
10500 14000 17500 21000
Carbontetrachloride sorption in Tecoflex (0.78µm)Mass trace 99-07-23-1
Mas
s/µg
Time/sec
p/p0
Figure 5-8: Carbontetrachloride sorption in Tecoflex film (0.78µm) (99-07-23-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
169
-6
-4
-2
0
2
4
6
10500 14000 17500 21000
Carbontetrachloride sorption in Tecoflex (0.78µm)Thermal trace 99-07-23-1
The
rmal
pow
er/µ
W
Time/sec
150
200
250
300
350
10500 14000 17500 21000
Carbontetrachloride sorption in Tecoflex (0.78µm)Partition coefficient 99-07-23-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-9: Carbontetrachloride sorption in Tecoflex film (0.78µm) (99-07-23-1) (a) thermal trace (b) partition coefficient
(a)
(b)
170
0
0.05
0.1
0.15
0.2
0.25
14000 16000 18000 20000 22000 24000 26000 28000
Chloroform sorption in Tecoflex (0.78µm)Vapor conc. in the gas stream 99-07-16-1
P/P
º
Time/sec
0
5
10
15
20
14000 16000 18000 20000 22000 24000 26000 28000
Chloroform sorption in Tecoflex (0.78µm)Mass trace 99-07-16-1
Mas
s/µg
Time/sec
p/p0
Figure 5-10: Chloroform sorption in Tecoflex film (0.78µm) (99-07-16-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
171
-10
-5
0
5
10
14000 16000 18000 20000 22000 24000 26000 28000
Chloroform sorption in Tecoflex (0.78µm)Thermal trace 99-07-16-1
The
rmal
pow
er/µ
W
Time/sec
0
200
400
600
800
1000
14000 16000 18000 20000 22000 24000 26000 28000
Chloroform sorption in Tecoflex (0.78µm)Partition coefficient 99-07-16-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-11: Chloroform sorption in Tecoflex film (0.78µm) (99-07-16-1) (a) thermal trace (b) partition coefficient
(a)
(b)
172
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
14000 16000 18000 20000 22000 24000 26000 28000
Toluene sorption in Tecoflex (0.78µm)Vapor conc. in the gas stream 99-07-18-1
P/P
º
Time/sec
0
5
10
15
20
25
14000 16800 19600 22400 25200 28000
Toluene sorption in Tecoflex (0.78µm)Mass trace 99-07-18-1
Mas
s/µg
Time/sec
p/p0
Figure 5-12: Toluene sorption in Tecoflex film (0.78µm) (99-07-18-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
173
-30
-20
-10
0
10
20
30
14000 16800 19600 22400 25200 28000
Toluene sorption in Tecoflex (0.78µm)Thermal trace 99-07-18-1
The
rmal
pow
er/µ
W
Time/sec
0
500
1000
1500
2000
2500
3000
14000 16800 19600 22400 25200 28000
Toluene sorption in Tecoflex (0.78µm)Partition coefficient 99-07-18-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-13: Toluene sorption in Tecoflex film (0.78µm) (99-07-18-1) (a) thermal trace (b) partition coefficient
(a)
(b)
174
0
0.1
0.2
0.3
0.4
0.5
0.6
30000 32000 34000 36000 38000 40000 42000
Ethanol sorption in Tecoflex (0.78µm)vapor conc. in the gas stream 99-07-15-1
P/P
º
Time/sec
0.5
1
1.5
2
2.5
3
3.5
4
4.5
30000 32000 34000 36000 38000 40000 42000
Ethanol sorption in Tecoflex (0.78µm)Mass trace 99-07-15-1
Mas
s/µg
Time/sec
p/p0
Figure 5-14: Ethanol sorption in Tecoflex film (0.78µm) (99-07-15-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
175
-8
-4
0
4
8
30000 32000 34000 36000 38000 40000 42000
Ethanol sorption in Tecoflex (0.78µm)Thermal trace 99-07-15-1
The
rmal
pow
er/µ
W
Time/sec
250
300
350
400
450
500
550
600
30000 32000 34000 36000 38000 40000 42000
Ethanol sorption in Tecoflex (0.78µm)Partition coefficient 99-07-15-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-15: Ethanol sorption in Tecoflex film (0.78µm) (99-07-15-1) (a) thermal trace (b) partition coefficient
(a)
(b)
176
0
0.05
0.1
0.15
0.2
2000 4000 6000 8000 10000 12000 14000 16000
Acetone sorption in Tecoflex (0.78µm)Vapor conc. in the gas stream 99-07-19-2
P/P
º
Time/sec
0
0.5
1
1.5
2
2000 4000 6000 8000 10000 12000 14000 16000
Acetone sorption in Tecoflex (0.78µm)Mass trace 99-07-19-2
Mas
s/µg
Time/sec
p/p0
Figure 5-16: Acetone sorption in Tecoflex film (0.78µm) (99-07-19-2) (a) solvent vapor activity (b) mass trace
(a)
(b)
177
-1.5
-1
-0.5
0
0.5
1
1.5
2
2000 4000 6000 8000 10000 12000 14000 16000
Acetone sorption in Tecoflex (0.78µm)Thermal trace 99-07-19-2
The
rmal
pow
er/µ
W
Time/sec
0
50
100
150
200
2000 4000 6000 8000 10000 12000 14000 16000
Acetone sorption in Tecoflex (0.78µm)Partition coefficient 99-07-19-2
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-17: Acetone sorption in Tecoflex film (0.78µm) (99-07-19-2) (a) thermal trace (b) partition coefficient
(a)
(b)
178
0
0.05
0.1
0.15
0.2
0.25
0.3
14000 16800 19600 22400 25200 28000
Hexane sorption in Tecoflex (0.78µm)Vapor conc. in the gas stream 99-07-19-1
P/P
º
Time/sec
0
0.2
0.4
0.6
0.8
1
1.2
1.4
14000 16800 19600 22400 25200 28000
Hexane sorption in Tecoflex (0.78µm)Mass trace 99-07-19-1
Mas
s/µg
Time/sec
p/p0
Figure 5-18: Hexane sorption in Tecoflex film (0.78µm) (99-07-19-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
179
-1.5
-1
-0.5
0
0.5
1
1.5
14000 16800 19600 22400 25200 28000
Hexane sorption in Tecoflex (0.78µm)Thermal trace 99-07-19-1
The
rmal
pow
er/µ
W
Time/sec
0
20
40
60
80
100
120
14000 16800 19600 22400 25200 28000
Hexane sorption in Tecoflex (0.78µm)Partition coefficient 99-07-19-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-19: Hexane sorption in Tecoflex film (0.78µm) (99-07-19-1) (a) thermal trace (b) partition coefficient
(a)
(b)
180
Table 5-2: Enthalpy of sorption of carbon tetrachloride in Tecoflex (0.78µm) (99-07-23-1)
∆sorptionH= 36.3 kJ/mol ∆vaporizationH= 32.43 kJ/mol Heat surplus= 3.9 kJ/mol
* Based on eight measurements
CCl4 99-07-23-1 ∆sorptionH |∆sorptionH| Mass/µg Heat/µJ kJ/mol kJ/mol 2.086 ± 0.029* -508 ± 31* -37.5 ± 2.0* 37.5 2.363 ± 0.008 -553 ± 14 -36.0 ± 0.9 36.0 2.522 ± 0.007 -585 ± 14 -35.7 ± 0.9 35.7 2.745 ± 0.010 -635 ± 17 -35.6 ± 0.9 35.6 2.943 ± 0.021 -674 ± 11 -35.2 ± 0.5 35.2 -2.841 ± 0.012 697 ± 7 37.7 ± 0.5 37.7 -2.722 ± 0.011 650 ± 5 36.7 ± 0.3 36.7 -2.515 ± 0.007 596 ± 4 36.4 ± 0.3 36.4 -2.363 ± 0.006 563 ± 9 36.7 ± 0.5 36.7 -2.213 ± 0.018 517 ± 13 35.9 ± 1.0 35.9
181
Table 5-3: Enthalpy of sorption of chloroform in Tecoflex (0.78µm) (99-07-16-1)
MW=119.38 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1
0.844 2.814 1026 -43.5 43.5 3.658 3.477 1108 -38.0 38.0 7.135 3.598 1130 -37.5 37.5 10.733 3.800 1234 -38.8 38.8 14.533 3.830 1253 -39.1 39.1 18.363 -3.707 1265 40.7 40.7 14.656 -3.713 1260 40.5 40.5 10.943 -3.442 1153 40.0 40.0 7.501 -3.507 1172 39.9 39.9 3.994 -3.144 1039 39.5 39.5 0.850 0.850 2.878 1053 -43.7 43.7 3.728 3.417 1113 -38.9 38.9 7.145 3.531 1132 -38.3 38.3 10.676 3.730 1212 -38.8 38.8 14.406 3.759 1239 -39.3 39.3 18.165 -3.632 1262 41.5 41.5 14.533 -3.626 1239 40.8 40.8 10.907 -3.392 1144 40.3 40.3 7.515 -3.464 1149 39.6 39.6 4.051 -3.199 1069 39.9 39.9 0.852 ∆sorptionH= 39.9 ∆vaporizationH= 31.28 Heat surplus= 8.6
182
Table 5-4: Enthalpy of sorption of toluene in Tecoflex (0.78µm) (99-07-18-1)
MW=92.14 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.238 2.655 1146 -39.8 39.8
2.893 3.120 1374 -40.6 40.6 6.013 3.698 1657 -41.3 41.3 9.711 4.743 2129 -41.4 41.4 14.454 6.534 2853 -40.2 40.2 20.988 -6.428 3079 44.1 44.1 14.560 -4.791 2099 40.4 40.4 9.769 -3.737 1634 40.3 40.3 6.032 -3.081 1338 40.0 40.0 2.951 -2.682 1149 39.5 39.5 0.269 0.269 2.565 1117 -40.1 40.1 2.834 3.049 1343 -40.6 40.6 5.883 3.671 1620 -40.7 40.7 9.554 4.702 2090 -41.0 41.0 14.256 6.458 2889 -41.2 41.2 20.714 -6.272 2830 41.6 41.6 14.442 -4.741 2075 40.3 40.3 9.701 -3.705 1635 40.7 40.7 5.996 -3.075 1350 40.5 40.5 2.921 -2.640 1119 39.1 39.1 0.281 ∆sorptionH= 40.7 ∆vaporizationH= 38.01 Heat surplus= 2.6
183
Table 5-5: Enthalpy of sorption of ethanol in Tecoflex (0.78µm) (99-07-15-1)
MW=46.07 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 1.170 0.526 499.7 -43.8 43.8
1.696 0.588 550.7 -43.1 43.1 2.284 0.645 606.6 -43.3 43.3 2.929 0.723 692.1 -44.1 44.1 3.652 0.836 806.9 -44.5 44.5 4.488 -0.834 801.7 44.3 44.3 3.654 -0.729 709.2 44.8 44.8 2.925 -0.633 613.1 44.6 44.6 2.292 -0.596 537.8 41.6 41.6 1.696 -0.533 501.4 43.3 43.3 1.163 1.163 0.524 500.3 -44.0 44.0 1.687 0.580 541.6 -43.0 43.0 2.267 0.637 603.5 -43.6 43.6 2.904 0.721 688.4 -44.0 44.0 3.625 0.828 785.2 -43.7 43.7 4.453 -0.826 801.7 44.7 44.7 3.627 -0.719 683.6 43.8 43.8 2.908 -0.636 603.1 43.7 43.7 2.272 -0.582 552.6 43.7 43.7 1.690 -0.527 497.2 43.5 43.5 1.163 ∆sorptionH= 43.8 ∆vaporizationH= 42.32 Heat surplus= 1.4
184
Table 5-6: Enthalpy of sorption of acetone in Tecoflex (0.78µm) (99-07-19-1)
MW=58.08 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.086 0.212 116.3 -31.9 31.9
0.298 0.284 131.5 -26.9 26.9 0.582 0.310 147.3 -27.6 27.6 0.892 0.338 161.1 -27.7 27.7 1.230 0.347 175.4 -29.4 29.4 1.577 -0.319 181.1 33.0 33.0 1.258 -0.307 169.3 32.0 32.0 0.951 -0.285 156.4 31.9 31.9 0.666 -0.296 152.3 29.9 29.9 0.370 -0.267 141.9 30.9 30.9 0.103 0.103 0.217 125.5 -33.6 33.6 0.320 0.280 146.9 -30.5 30.5 0.600 0.306 148.4 -28.2 28.2 0.906 0.320 164.2 -29.8 29.8 1.226 0.341 181.2 -30.9 30.9 1.567 -0.321 186.3 33.7 33.7 1.246 -0.305 161.8 30.8 30.8 0.941 -0.286 155.9 31.7 31.7 0.655 -0.297 151.8 29.7 29.7 0.358 -0.252 128.5 29.6 29.6 0.106 ∆sorptionH= 30.5 ∆vaporizationH= 30.99 Heat surplus= -0.5
185
Table 5-7: Enthalpy of sorption of hexane in Tecoflex (0.78µm) (99-07-19-1)
MW=86.18 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.048 0.291 101.0 -29.9 29.9
0.339 0.269 107.3 -34.4 34.4 0.608 0.235 103.4 -37.9 37.9 0.843 0.215 104.2 -41.8 41.8 1.058 0.229 101.2 -38.1 38.1 1.287 -0.251 90.91 31.2 31.2 1.036 -0.246 95.38 33.4 33.4 0.790 -0.239 91.85 33.1 33.1 0.551 -0.241 91.28 32.6 32.6 0.310 -0.266 94.28 30.5 30.5 0.044 0.044 0.253 85.17 -29.0 29.0 0.297 0.254 91.07 -30.9 30.9 0.551 0.230 90.89 -34.1 34.1 0.781 0.226 95.87 -36.6 36.6 1.007 0.234 95.45 -35.2 35.2 1.241 -0.246 92.22 32.3 32.3 0.995 -0.240 89.63 32.2 32.2 0.755 -0.237 91.18 33.2 33.2 0.518 -0.229 92.27 34.7 34.7 0.289 -0.243 89.69 31.8 31.8 0.046 ∆sorptionH= 33.6 ∆vaporizationH= 31.56 Heat surplus= 2.1
186
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
2000 4000 6000 8000 10000 12000 14000 16000
Carbontetrachloride sorption in Tecoflex (2.09µm)Vapor conc. in the gas stream 99-07-27-1
P/P
º
Time/sec
0
10
20
30
40
50
60
70
80
2000 4000 6000 8000 10000 12000 14000 16000
Carbontetrachloride sorption in Tecoflex (2.09µm)Mass trace 99-07-27-1
Mas
s/µg
Time/sec
p/p0
Figure 5-20: Carbon tetrachloride sorption in Tecoflex film (2.09µm)(99-07-27-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
187
-30
-20
-10
0
10
20
30
2000 4000 6000 8000 10000 12000 14000 16000
Carbontetrachloride sorption in Tecoflex (2.09µm)Thermal trace 99-07-27-1
The
rmal
pow
er/µ
W
Time/sec
0
200
400
600
800
1000
2000 4000 6000 8000 10000 12000 14000 16000
Carbontetrachloride sorption in Tecoflex (2.09µm)Partition coefficient 99-07-27-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-21: Carbon tetrachloride sorption in Tecoflex film (2.09µm) (99-07-27-1) (a) thermal trace (b) partition coefficient
(a)
(b)
188
0
0.05
0.1
0.15
0.2
0.25
3200 6400 9600 12800 16000
Chloroform sorption in Tecoflex (2.09µm)Vapor conc. in the gas stream 99-07-28-2
P/P
º
Time/sec
0
20
40
60
80
100
3200 6400 9600 12800 16000
Chloroform sorption in Tecoflex (2.09µm)Mass trace 99-07-28-2
Mas
s/µg
Time/sec
p/p0
Figure 5-22: Chloroform sorption in Tecoflex film (2.09µm) (99-07-28-2) (a) solvent vapor activity (b) mass trace
(a)
(b)
189
0
200
400
600
800
1000
14000 16000 18000 20000 22000 24000 26000 28000
Chloroform sorption in Tecoflex (0.78µm)Partition coefficient 99-07-16-1
Par
titi
on c
oeff
icie
nt
Time/sec
-10
-5
0
5
10
14000 16000 18000 20000 22000 24000 26000 28000
Chloroform sorption in Tecoflex (0.78µm)Thermal trace 99-07-16-1
The
rmal
pow
er/µ
W
Time/sec
Figure 5-23: Chloroform sorption in Tecoflex film (2.09µm) (99-07-28-2) (a) thermal trace (b) partition coefficient
(a)
(b)
190
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
9600 12800 16000 19200 22400
Toluene sorption in Tecoflex (2.09µm)Vapor conc. in the gas stream 99-07-28-3
P/P
º
Time/sec
0
20
40
60
80
100
9600 12800 16000 19200 22400
Toluene sorption in Tecoflex (2.09µm)Mass trace 99-07-28-3
Mas
s/µg
Time/sec
p/p0
Figure 5-24: Toluene sorption in Tecoflex film (2.09µm) (99-07-28-3) (a) solvent vapor activity (b) mass trace
(a)
(b)
191
-60
-40
-20
0
20
40
60
80
9600 12800 16000 19200 22400
Toluene sorption in Tecoflex (2.09µm)Thermal trace 99-07-28-3
The
rmal
pow
er/µ
W
Time/sec
500
1000
1500
2000
2500
3000
3500
4000
9600 12800 16000 19200 22400
Toluene sorption in Tecoflex (2.09µm)Partition coefficient 99-07-28-3
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-25: Toluene sorption in Tecoflex film (2.09µm) (99-07-28-3) (a) thermal trace (b) partition coefficient
(a)
(b)
192
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
8400 11200 14000 16800 19600
Ethanol sorption in Tecoflex (2.09µm)Vapor conc. in the gas stream 99-07-30-1
P/P
º
Time/sec
0
10
20
30
40
50
8400 11200 14000 16800 19600
Ethanol sorption in Tecoflex (2.09µm)Mass trace 99-07-30-1
Mas
s/µg
Time/sec
p/p0
Figure 5-26: Ethanol sorption in Tecoflex film (2.09µm) (99-07-30-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
193
-100
-50
0
50
100
8400 11200 14000 16800 19600
Ethanol sorption in Tecoflex (2.09µm)Thermal trace 99-07-30-1
The
rmal
pow
er/µ
W
Time/sec
0
500
1000
1500
8400 11200 14000 16800 19600
Ethanol sorption in Tecoflex (2.09µm)Partition coefficient 99-07-30-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-27: Ethanol sorption in Tecoflex film (2.09µm) (99-07-30-1) (a) thermal trace (b) partition coefficient
(a)
(b)
194
0
0.05
0.1
0.15
0.2
8400 11200 14000 16800 19600
Acetone sorption in Tecoflex (2.09µm)Vapor conc. in the gas stream 99-07-30-2
P/P
º
Time/sec
0
2
4
6
8
10
8400 11200 14000 16800 19600
Acetone sorption in Tecoflex (2.09µm)Mass trace 99-07-30-2
Mas
s/µg
Time/sec
p/p0
Figure 5-28: Acetone sorption in Tecoflex film (2.09µm) (99-07-30-2) (a) solvent vapor activity (b) mass trace
(a)
(b)
195
-6
-4
-2
0
2
4
6
8
10
8400 11200 14000 16800 19600
Acetone sorption in Tecoflex (2.09µm)Thermal trace 99-07-30-2
The
rmal
pow
er/µ
W
Time/sec
0
50
100
150
200
250
300
350
8400 11200 14000 16800 19600
Acetone sorption in Tecoflex (2.09µm)Partition coefficient 99-07-30-2
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-29: Acetone sorption in Tecoflex film (2.09µm) (99-07-30-2) (a) thermal trace (b) partition coefficient
(a)
(b)
196
0
0.05
0.1
0.15
0.2
0.25
0.3
8400 11200 14000 16800 19600
Hexane sorption in Tecoflex (2.09µm)Vapor conc. in the gas stream 99-08-02-1
P/P
º
Time/sec
0
1
2
3
4
5
6
7
8400 11200 14000 16800 19600
Hexane sorption in Tecoflex (2.09µm)Mass trace 99-08-02-1
Mas
s/µg
Time/sec
p/p0
Figure 5-30: Hexane sorption in Tecoflex film (2.09µm) (99-08-02-1) (a) solvent vapor activity (b) mass trace
(a)
(b)
197
-6
-4
-2
0
2
4
6
8
8400 11200 14000 16800 19600
Hexane sorption in Tecoflex (2.09µm)Thermal power 99-08-02-1
The
rmal
pow
er/µ
W
Time/sec
0
50
100
150
200
8400 11200 14000 16800 19600
Hexane sorption in Tecoflex (2.09µm)Partition coefficient 99-08-02-1
Par
titi
on c
oeff
icie
nt
Time/sec
Figure 5-31: Hexane sorption in Tecoflex film (2.09µm) (99-08-02-1) (a) thermal trace (b) partition coefficient
(a)
(b)
198
Table 5-8: Enthalpy of sorption of carbon tetrachloride in Tecoflex (2.09µm) (99-07-27-1)
MW=153.82 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.030 10.875 3051 -43.2 43.2 10.905 12.832 3242 -38.9 38.9 23.737 13.932 3530 -39.0 39.0 37.669 15.355 3891 -39.0 39.0 53.024 16.583 4192 -38.9 38.9 69.607 -16.097 4288 41.0 41.0 53.510 -15.190 3944 39.9 39.9 38.320 -13.854 3566 39.6 39.6 24.466 -12.737 3201 38.7 38.7 11.729 -11.613 2884 38.2 38.2 0.116 0.116 10.708 2988 -42.9 42.9 10.824 12.844 3242 -38.8 38.8 23.668 13.842 3519 -39.1 39.1 37.510 15.328 3866 -38.8 38.8 52.838 16.604 4158 -38.5 38.5 69.442 -16.109 4272 40.8 40.8 53.333 -15.225 3995 40.4 40.4 38.108 -13.856 3613 40.1 40.1 24.252 -12.718 3282 39.7 39.7 11.534 -11.416 2834 38.2 38.2 0.118 ∆sorptionH= 39.7 ∆vaporizationH= 32.43 Heat surplus= 7.2
199
Table 5-9: Enthalpy of sorption of chloroform in Tecoflex (2.09µm) (99-07-28-2)
MW=119.38 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1
3.703 14.294 6025 -50.3 50.3 17.997 17.794 6482 -43.5 43.5 35.791 18.329 6580 -42.9 42.9 54.120 19.635 7207 -43.8 43.8 73.755 19.761 7488 -45.2 45.2 93.516 -19.351 7291 45.0 45.0 74.165 -18.825 7343 46.6 46.6 55.340 -17.120 6743 47.0 47.0 38.220 -18.009 6831 45.3 45.3 20.211 -16.320 6115 44.7 44.7 3.891 3.891 14.930 6078 -48.6 48.6 18.821 17.834 6526 -43.7 43.7 36.655 18.442 6638 -43.0 43.0 55.097 19.271 7498 -46.4 46.4 74.368 19.103 7542 -47.1 47.1 93.471 -18.957 7286 45.9 45.9 74.514 -18.834 7332 46.5 46.5 55.680 -17.573 6783 46.1 46.1 38.107 -17.815 6823 45.7 45.7 20.292 -16.297 6279 46.0 46.0 3.995 ∆sorptionH= 45.7 ∆vaporizationH= 31.28 Heat surplus= 14.4
200
Table 5-10: Enthalpy of sorption of toluene in Tecoflex (2.09µm) (99-07-28-3)
MW=92.14 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.877 12.909 6946 -49.6 49.6
13.786 13.707 7149 -48.1 48.1 27.493 16.621 8252 -45.7 45.7 44.114 20.611 9793 -43.8 43.8 64.725 27.221 11990 -40.6 40.6 91.946 -26.190 12760 44.9 44.9 65.756 -20.554 10010 44.9 44.9 45.202 -17.011 8367 45.3 45.3 28.191 -14.287 7196 46.4 46.4 13.904 -12.997 6615 46.9 46.9 0.907 0.907 12.480 6694 -49.4 49.4 13.387 13.835 7129 -47.5 47.5 27.222 16.635 8224 -45.6 45.6 43.857 20.450 9955 -44.9 44.9 64.307 26.961 12130 -41.5 41.5 91.268 -25.974 12630 44.8 44.8 65.294 -20.471 10020 45.1 45.1 44.823 -16.867 8349 45.6 45.6 27.956 -14.254 7181 46.4 46.4 13.702 -12.746 6502 47.0 47.0 0.956 ∆sorptionH= 45.7 ∆vaporizationH= 38.01 Heat surplus= 7.7
201
Table 5-11: Enthalpy of sorption of Ethanol in Tecoflex (2.09µm) (99-07-30-1)
MW=46.07 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.301 5.174 5334 -47.5 47.5
5.475 5.491 5845 -49.0 49.0 10.966 6.666 7057 -48.8 48.8 17.632 8.666 8888 -47.3 47.3 26.298 11.705 12030 -47.3 47.3 38.003 -11.386 11790 47.7 47.7 26.617 -8.700 9046 47.9 47.9 17.917 -6.857 7204 48.4 48.4 11.060 -5.619 5924 48.6 48.6 5.441 -5.108 5325 48.0 48.0 0.333 0.333 5.259 5432 -47.6 47.6 5.592 5.753 6098 -48.8 48.8 11.345 6.971 7358 -48.6 48.6 18.316 8.974 9262 -47.5 47.5 27.290 12.177 12500 -47.3 47.3 39.467 -12.303 12420 46.5 46.5 27.164 -9.071 9232 46.9 46.9 18.093 -7.007 7178 47.2 47.2 11.086 -5.671 5849 47.5 47.5 5.415 -5.077 5314 48.2 48.2 0.338 ∆sorptionH= 47.8 ∆vaporizationH= 42.32 Heat surplus= 5.5
202
Table 5-12: Enthalpy of sorption of acetone in Tecoflex (2.09µm) (99-07-30-2)
MW=58.08 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.501 1.181 856.1 -42.1 42.1
1.682 1.530 966.1 -36.7 36.7 3.212 1.606 956.4 -34.6 34.6 4.818 1.684 1037.0 -35.8 35.8 6.502 1.757 1106.0 -36.6 36.6 8.259 -1.713 1066.0 36.1 36.1 6.546 -1.620 1011.0 36.2 36.2 4.926 -1.512 929.4 35.7 35.7 3.414 -1.563 954.1 35.5 35.5 1.851 -1.372 835.8 35.4 35.4 0.479 0.479 1.197 869.3 -42.2 42.2 1.676 1.521 934.7 -35.7 35.7 3.197 1.575 938.1 -34.6 34.6 4.772 1.676 998.8 -34.6 34.6 6.448 1.755 1080.0 -35.7 35.7 8.203 -1.683 1134.0 39.1 39.1 6.520 -1.619 1035.0 37.1 37.1 4.901 -1.500 937.8 36.3 36.3 3.401 -1.538 1001.0 37.8 37.8 1.863 -1.377 895.3 37.8 37.8 0.486 ∆sorptionH= 36.8 ∆vaporizationH= 30.99 Heat surplus= 5.8
203
Table 5-13: Enthalpy of sorption of hexane in Tecoflex (2.09µm) (99-08-02-1)
MW=86.18 Mass /µg ∆ Mass/µg Heat/µJ ∆sorptionH /kJmol-1 0.176 1.109 648.8 -50.4 50.4
1.285 1.160 632.5 -47.0 47.0 2.445 1.251 636.1 -43.8 43.8 3.696 1.229 631.1 -44.3 44.3 4.925 1.272 646.2 -43.8 43.8 6.197 -1.256 666.1 45.7 45.7 4.941 -1.237 624.0 43.5 43.5 3.704 -1.216 625.5 44.3 44.3 2.488 -1.166 597.5 44.2 44.2 1.322 -1.149 603.0 45.2 45.2 0.173 0.173 1.107 599.8 -46.7 46.7 1.280 1.147 592.0 -44.5 44.5 2.427 1.234 620.1 -43.3 43.3 3.661 1.229 617.5 -43.3 43.3 4.890 1.271 639.1 -43.3 43.3 6.161 -1.244 630.6 43.7 43.7 4.917 -1.219 615.2 43.5 43.5 3.698 -1.222 607.3 42.8 42.8 2.476 -1.163 581.4 43.1 43.1 1.313 -1.151 591.3 44.3 44.3 0.162 ∆sorptionH= 44.5 ∆vaporizationH= 30.99 Heat surplus= 13.5
204
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 3200 6400 9600 12800 16000
Ethanol vapor over gold surface Vapor conc. 99-06-07-2
P/P
º
Time/sec
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0 3200 6400 9600 12800 16000
Ethanol vapor over gold surface, Mass trace 99-06-07-2
Mas
s/µg
cm
-2
Time/sec
Figure 5-32: Ethanol vapor over two bare gold surfaces (99-06-07-02) (a) ethanol vapor activity (b) mass trace
(a)
(b)
p0 /p
205
-4
-2
0
2
4
0 3200 6400 9600 12800 16000
Ethanol vapor over gold surface Thermal trace 99-06-07-2
The
rmal
pow
er/µ
W
Time/sec
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 3200 6400 9600 12800 16000
Ethanol vapor over gold surface Vapor conc. 99-06-07-2
P/P
º
Time/sec
Figure 5-33: Ethanol vapor over two bare gold surfaces (99-06-07-02) (a) ethanol vapor activity (b) mass trace
(a)
(b)
p0 /p
206
9.510
10.511
11.512
12.513
13.5
-0.1
0
0.1
0.2
0.3
0.4
0.5
11600 11700 11800 11900 12000 12100
y = -11.088 + 0.00095338x R= 0.98958
Mas
s/µg
Time/sec
161718192021222324
-0.1
0
0.1
0.2
0.3
0.4
0.5
11360 11440 11520 11600 11680
y = -15.972 + 0.001404x R= 0.99771
Mas
s/µg
Time/sec
1.5
2
2.5
3
3.5
4
4.5
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
9000 9050 9100 9150 9200 9250 9300 9350 9400
y = -12.717 + 0.0014104x R= 0.99891
Mas
s/µg
Time/sec
-1/?2 ln ((m
8p -m
tp ) ?2/8(m
8p -m
ip )) -1/?
2 ln ((m8
p -mtp ) ?
2/8(m8
p -mip ))
2.6
2.8
3
3.2
3.4
3.6
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
20950 21000 21050 21100 21150 21200
y = -79.298 + 0.0037817x R= 0.99483
Mas
s/µg
Time/sec
-1/?2 ln ((m
8p -m
tp ) ?2/8(m
8p -m
ip )) -1/?
2 ln ((m8
p -mtp ) ?
2/8(m8
p -mip ))
Figure 5-34: Fit of the mass trace used to determine the diffusion coefficient for the (a) toluene in Tecoflex at low solvent content
(b) toluene in Tecoflex at higher solvent content. (c) carbontetrachloride in Tecoflex (d) ethanol in Tecoflex
(a)
(b)
(c)
(d)
207
5.3 Results and conclusions
One very important improvement in the gas flow subsystem of the QCM/HCC
was the addition of the gas mixing section. After the addition of this unit, we placed two
uncoated fresh QCMs in the sample and the reference sides of the QCM/HCC and passed
a gas mixture similar to one used in our sorption experiments through both sides. During
this run (figure 5-32, 5-33) the composition of ethanol vapor was changed every ca.600 sec
in 5000 ppm steps between 45000 ppm and 20000 ppm. The same gas flow was allowed to
flow through both sides between t=700 and t=6300 sec. During this time there are
virtually no detectable mass or thermal events. From t=6300 to t=10736 sec the gas was
allowed to flow only through the right side of the QCM/HCC and the left side was kept
static. Very small mass changes on the gold surface of the right QCM were observed.
Relatively larger thermal events were also detected. When the ethanol vapor pressure is
increased over the right QCM some of it appears to adsorb on the gold surface. Some
ethanol may also absorb into the o-rings holding the QCMs, which will result in a thermal
signal but no mass change detectable by the QCM. The same behavior was observed in the
left side of the QCM/HCC but in the opposite direction, since the polarity of the
thermopile voltage is reversed for the left side. The mass trace for the left QCM was also
registered in the opposite direction, since it is collected as the difference in oscillation
frequencies of the two QCMs. Both mass and thermal events exist in the absence of a thin
film sample. However, they are identical in the sample and reference sides, having the
same magnitude but in opposite directions. This run illustrated the importance of the
differential mode of operation of the QCM/HCC.
208
The data presented in the figures 5-8 to 5-31 for the sorption of different solvent
vapors in the spin-coated TecoflexTM films may appear very similar at first glance. A more
careful inspection, however, reveals tremendous information about the differences in the
magnitude, energetics and time scales of solubility interactions for each individual vapor.
First we shall describe the results for sorption of vapors in one TecoflexTM film. Then we
can compare results obtained for two different films.
In terms of the magnitude of solubility interaction and changes thereof at different
solvent contents no specific expectations can be predicted. For an organic polymer the
incoming vapor during sorption will diffuse into the free volume space in the polymer
structure. In contrast with other compounds such as proteins where many different
functional groups are present, which behave distinctly at different solvent contents, no
major change in the chemical environment is anticipated at different solvent compositions.
Usually changes in the physical properties of polymers induced during sorption play a
greater role. An increase in the solvent content may change the glass transition
temperature, viscosity, shear modulus and the diffusion rate of a solvent. These in turn
may make the polymer more susceptible to sorption. The partition coefficient for a
polymer-solvent system as the function of solvent vapor activity is indicative of such
physical changes in a polymer. The value of the partition coefficient many remain constant
over the entire range of the solvent vapor activity. In some cases it may increase sharply at
higher values of solvent content and for other systems it may even decrease.
For the first Tecoflex film (0.78µm) the mass change for the same change in the
vapor composition is slightly larger at higher solvent content in most cases. This is also
apparent in the plots of the partition coefficient vs. solvent vapor mass percent in the
Tecoflex film presented later in this section (see figure 5-35). A comparison of toluene
209
sorption and ethanol sorption shows quite different variations of partition coefficient with
solvent vapor activity (or solvent vapor mass percentage in the film), whereas for carbon
tetrachloride the effect is smaller. The partition coefficients for acetone and chloroform
seem to stay constant and independent of the solvent content. A slight decrease of the
partition coefficient may be visible for hexane at higher solvent contents.
Slight changes in the partition coefficients point out differences in the free energy
of the sorption process for different solvent contents. It is of interest to see if similar
trends exist for the enthalpy of sorption. Such trends may be present for solvents such as
toluene, which induce changes in the partition coefficient, but are difficult to identify.
Nonetheless it is important to acknowledge the presence of possible systematic trends
along with random variations of the sorption enthalpies at different solvent vapor
activities. The largest source of error in the values for the sorption enthalpies is introduced
during the integration of the thermal peaks. The assignment of the baseline, the initial and
end times for integration is an arbitrary procedure. The repetition of the integration of a
peak by the same operator rarely produces the same results. We continue to seek out a
better method for developing an accurate integration procedure.
The reported sorption enthalpies have been compared to the values of the
vaporization enthalpies of the respective solvents. Vaporization/condensation of a solvent
is similar to the desorption/sorption process in many respects. The difference in the values
for sorption and vaporization enthalpies is indicative of excess energy for the polymer-
solvent interactions. The values for the sorption enthalpies are close to the vaporization
enthalpies with the largest difference for chloroform, carbontetrachloride and toluene, and
virtually no difference for acetone. We encountered a few problems with hexane due to its
high vapor pressure. Occasionally some of the hexane vapor condensed in the tubing of
210
the gas flow system, which slowly evaporated at a later time causing an increase in the
vapor concentration in the gas stream (see figure 5-18 (b)). Hexane also caused the o-ring
of the bubble-through container to swell. As the result, a small amount of water from the
bath entered the bubble-through container and mixed with hexane. Although several runs
were disregarded for which the presence of water was detected, the larger values for
hexane sorption enthalpies for one film compared to the other indicates that a small
amount of water may have been present for one set of the hexane sorption experiments.
Diffusion coefficients of a solvent in a polymer are important properties that are
difficult to measure. Whenever a solution is used for coating a surface or preparing a thin
film the dry time will depend on the diffusion rate of the solvents through the film. The
diffusion coefficient of a solvent can be determined from the mass traces for the
sorption/desorption processes. We have used a method described by Hernandez-Munoz
et al.25 to calculate diffusion coefficients for some of the solvent vapors in this study .
The fitting equation used in this method is based on the solution to Fick’s differential
equations with the following assumptions: thickness of the polymer film, temperature and
pressure are constant26.
( )( ) t
lD
mm
mmipp
tpp
2
2
2 8ln
1=
−
−−∞
∞ π
π
Here D is diffusion coefficient, mpt is the total mass of the film and the sorbed
solvent vapor at time t, superscripts i and 8 refer to initial and final times, and l is the film
thickness.
(75)
211
Figure 5-34 shows the fit of the mass data using equation 75 for four experiments.
The highest diffusion rate is observed for the ethanol vapors. The figures 5-34 (a) and (b)
show the mass measurements used to determine the diffusion coefficients for toluene for
two different sorption steps, one at high solvent content and another for low solvent
content. There were no significant differences in the values obtained. The slowest
diffusion rate was observed for carbon tetrachloride, which is relatively bulky. Below is a
summary of the diffusion coefficients for these solvents in the 0.78µm thick TecoflexTM
film.
Table 5-14: Diffusion coefficients of three solvent vapors in Tecoflex
In comparing the sorption data for the thin film (0.78µm) with those for the
thicker TecoflexTM film (2.09µm), generally larger mass and thermal signals are measured
for the thicker film. One important feature is the shift in the baseline in the thermal trace
for the thicker film after each sorption/desorption step. The best examples are toluene
and chloroform. The shift in the baseline indicates a change in the magnitude of the
thermal power dissipated in the oscillating QCM, as its effective resonance resistance
Solvent vapor Diffusion coefficient/cm2 sec-1
Ethanol 2.3 × 10-11
Toluene 8.5 × 10-12
Carbon tetrachloride 5.8 × 10-12
212
changes. When the solvent content of the TecoflexTM film increases, it becomes softer.
The damping of the QCM/thin film composite resonator and the increase in the
oscillation resistance takes place for all the solvents and for both TecoflexTM films.
However the magnitude of the shift in the thermal baseline relative to the thermal power
from the sorption is very small and can be neglected for the thin film (0.78µm). This is
another case showing the advantage of the ability of simultaneous mass and heat flow
measurement in the QCM/HCC. The magnitude in the shift in the thermal baseline
provides valuable information about changes in the oscillatory behavior of the QCM. If
these changes become significant the oscillation frequency doesn’t follow Sauerbrey’s
relationship to mass change on the surface. Under those conditions accurate mass
measurements without knowledge of the shear modulus of the film is not possible.
Although the thermal trace clearly shows changes in the shear modulus of the TecoflexTM
film, these changes are still not large enough to cause serious deviations from Sauerbrey’s
relation. We believe this statement to be true based on the model introduced in chapter 2
and used for a similar polymer with 15% solvent content for thicknesses up to 30µm, and
also based on the small magnitude of the shift in the thermal baseline indicating a small
change in the oscillation resistance. The actual value of the change in the effective
resistance of the QCM can be calculated form the shift in the thermal base line (see figures
3-8 and 3-9)
In comparing the values for sorption enthalpies obtained for the two TecoflexTM
films, the values for the thicker film (2.09µm) are systematically larger in all cases by 10-
15%. We believe the mass measurements during the sorption/desorption cycle to be
accurate. It is conceivable that a better thermal contact was established for the QCM
coated with the 2.09µm TecoflexTM, as it was placed inside the QCM/HCC. It is
213
impossible to reproduce the exact position and clamping of a QCM, when it is placed
inside the QCM/HCC. As discussed in chapter 3 a recalibration procedure can give
correction factors as large as 20%. At the time of these experiments we had not developed
an alternative calibration method yet nor could we reproduce the original calibration, since
it required an impedance analyzer. As matter of fact the discrepancies in the values for the
sorption enthalpies from this experiment were the motivation for reevaluating our original
calibration method and developing a new procedure that could be used on a routine basis.
At this stage it is impossible to determine which set of experiments gave the more accurate
results without repeating the experiment for some of the solvents.
The values calculated for the partition coefficients for the 2.09µm TecoflexTM film
are all twice as large as those obtained for the 0.78µm TecoflexTM film. These values should
be the same for both films at a given solvent vapor activity. There are three possible
sources of error in calculating the partition coefficients, the concentration of solvent vapor
in the gas phase above the film, the mass of the film itself and the mass of the sorbed
solvent vapor. Here again we don’t believe the mass measurements during the
sorption/desorption steps to be the source of the error. There may be slight variations in
the vapor composition generated by the flow system but it is not reasonable to believe that
the concentrations would be larger or smaller by a factor of two for all the solvents, when
the sample film was replaced.
The masses of the thin TecoflexTM films were obtained from the differences in
oscillation frequencies of the QCMs before and after spin-coating. The procedure of
taking the QCM out of its mount and putting it back after it has been coated introduces
the largest errors for the mass measurement of the film. Even when the same uncoated
QCM is put back in the mount, differences in the oscillation frequency will be observed.
214
These differences may range from a few to several hundred Hz in extreme cases and are
due to slight differences in clamping and capacitive coupling of the QCM with its mount.
This observation and the results from an atomic force microscope measurement (see
figures 5-36 to 5-38 lead us to believe that the mass of the thin TecoflexTM film (0.78µm)
may in fact have been somewhat smaller than what was originally believed to be but not by
a factor of 2. There must be other factors involved that we don’t fully understand yet.
The partition coefficients for the two TecoflexTM films were used in a multivariate
linear regression to establish a linear solvation energy relationship (LSER) with respect to
their solubility interactions with solvent vapors. The two equations for the two TecoflexTM
films were obtained using the data in table 5-15 and are presented below in table 5-16. For
the same polymer material these should be the same, but the fact that all the values
obtained for one of the films is larger by a factor of two, resulted in two different
equations. The equation for the second film (2.09µm) is believed to be somewhat more
accurate because of reasons already discussed.
215
Tecoflex (0.78µm)Vapor K ∆vaporizationH ∆sorptionH ∆ sorptionG ∆sorptionS
kJ mole-1 kJ mole-1 kJ mole -1 J K-1 mole -1
Carbontetrachloride 266 32.43 -36 -14 -73Toluene 1542 38.01 -41 -18 -76
Chloroform 484 31.28 -40 -15 -82Ethanol 419 42.32 -44 -15 -97Acetone 86 30.99 -31 -11 -65
n-Hexane 46 31.56 -34 -9 -81
Tecoflex (2.09µm)Vapor K ∆vaporizationH ∆sorptionH ∆ sorptionG ∆sorptionS
kJ mole-1 kJ mole-1 kJ mole -1 J K-1 mole -1
Carbontetrachloride 532 32.43 -40 -16 -81Toluene 2357 38.01 -46 -19 -89
Chloroform 925 31.28 -46 -17 -97Ethanol 975 42.32 -48 -17 -103Acetone 168 30.99 -37 -13 -81
n-Hexane 85 31.56 -45 -11 -112
Table 5-15: Summary of results of sorption of solvent vapor in two Tecoflex films
216
LSER for selected organic vapors in Tecoflex (2.09µm)Vapor Polarizability Polarity Acidity Basicity Dispersion Log(K) K
R2 π*2 αH
2 βH2 LogL 16
observed
Carbontetrachloride 0.458 0.38 0 0 2.82 2.726 532Toluene 0.601 0.55 0 0.14 3.34 3.372 2357
Chloroform 0.425 0.58 0.20 0.02 2.48 2.966 925Ethanol 0.246 0.40 0.33 0.44 1.49 2.989 975Acetone 0.179 0.71 0.04 0.50 1.76 2.225 168
n-Hexane 0 0 0 0 2.67 1.929 85
Vapor Polarizability Polarity Acidity Basicity Dispersion Log(K)r*R2 s∗π*
2 a∗αH2 b∗βH
2 l*LogL 16calculated
Carbontetrachloride 0.833 -0.118 0.000 0.000 1.518 2.726Toluene 1.093 -0.171 0.000 0.161 1.796 3.372
Chloroform 0.773 -0.181 0.524 0.023 1.334 2.966Ethanol 0.447 -0.125 0.865 0.507 0.801 2.989Acetone 0.325 -0.221 0.105 0.576 0.947 2.225
n-Hexane 0.000 0.000 0.000 0.000 1.436 1.929
l b a s r c0.538 1.153 2.620 -0.311 1.818 0.493
LSER for selected organic vapors in Tecoflex (0.78µm)Vapor Polarizability Polarity Acidity Basicity Dispersion Log(K) K
R2 π*2 αH
2 βH2 LogL 16
observed
Carbontetrachloride 0.458 0.38 0 0 2.82 2.425 266Toluene 0.601 0.55 0 0.14 3.34 3.188 1542
Chloroform 0.425 0.58 0.20 0.02 2.48 2.685 484Ethanol 0.246 0.40 0.33 0.44 1.49 2.622 419Acetone 0.179 0.71 0.04 0.50 1.76 1.934 86
n-Hexane 0 0 0 0 2.67 1.663 46
Vapor Polarizability Polarity Acidity Basicity Dispersion Log(K)r*R2 s∗π*
2 a∗αH2 b∗βH
2 l*LogL 16observed
Carbontetrachloride 0.701 -0.053 0.000 0.000 2.094 2.425
Toluene 0.920 -0.076 0.000 0.184 2.478 3.188Chloroform 0.651 -0.081 0.566 0.026 1.840 2.685
Ethanol 0.377 -0.056 0.935 0.579 1.105 2.622Acetone 0.274 -0.099 0.113 0.658 1.306 1.934
n-Hexane 0.000 0.000 0.000 0.000 1.981 1.663
l b a s r c0.74 1.32 2.83 -0.14 1.53 -0.32
Table 5-16: LSER for two Tecoflex films
217
0
200
400
600
800
1000
1200
1400
1600
Tolu
ene
Chl
orof
orm
Eth
anol
Car
bont
etra
chlo
ride
Ace
tone
n-H
exan
e
0
500
1000
1500
2000
2500
Tolu
ene
Eth
anol
Chl
orof
orm
Car
bont
etra
chlo
ride
Ace
tone
n-H
exan
e
16222 log74.032.183.214.053.132.0log LHHH +++−+−= βαπ2RK
16222 log538.0153.1620.2311.0818.1493.0log LHHH +++−+= βαπ2RK
Figure 5-35: Measured partition coefficients and LSER results for (a) 0.78 µm Tecoflex film (b) 2.09 µm Tecoflex film
(a)
(b)
218
-50
0
50
0
2 0 0
4 0 0
6 0 0
8 0 0
-2 0 2 4 6 8 10 12 14
Carbontetrachloride sorption in Tecoflex (2.09µm)
E n t h a l p y o f s o r p t i o n / k J m o l e - 1E n t h a l p y o f d e s o r p t i o n / k J m o l - 1
Pa r t i t i on coe f f i c i en t
Ent
halp
y of
sor
ptio
n/kJ
mol
e-1
Partition coefficient
Percent mass
-60
-40
-20
0
20
40
60
0
5 0 0
1 0 0 0
1 5 0 0
2 0 0 0
0 5 10 15 20
Chloroform sorption in Tecoflex (2.09µm)
E n t h a l p y o f s o r p t i o n / k J m o l e - 1E n t h a l p y o f d e s o r p t i o n / k J m o l - 1
P a r t i t i o n c o e f f i c i e n t
Ent
halp
y of
sor
ptio
n/kJ
mol
e-1
Partition coefficient
Percent mass
-50
0
50
0
5 0 0
1 0 0 0
1 5 0 0
2 0 0 0
2 5 0 0
3 0 0 0
3 5 0 0
4 0 0 0
0 5 10 15 20
Toluene sorption in Tecoflex (2.09µm)
E n t h a l p y o f s o r p t i o n / k J m o l e - 1E n t h a l p y o f d e s o r p t i o n / k J m o l - 1 Pa r t i t i on coe f f i c i en t
Ent
halp
y of
sor
ptio
n/kJ
mol
e-1
Partition coefficient
Percent mass
-60
-40
-20
0
20
40
60
0
4 0 0
8 0 0
1 2 0 0
1 6 0 0
0 1 2 3 4 5 6 7 8
Ethanol sorption in Tecoflex (2.09µm)
E n t h a l p y o f s o r p t i o n / k J m o l e - 1E n t h a l p y o f d e s o r p t i o n / k J m o l - 1
Pa r t i t i on coe f f i c i en t
Ent
halp
y of
sor
ptio
n/kJ
mol
e-1
Partition coefficient
Percent mass
-50
0
50
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
3 0 0
3 5 0
4 0 0
0 0.5 1 1.5 2
Acetone sorption inTecoflex (2.09µm)
E n t h a l p y o f s o r p t i o n / k J m o l e - 1E n t h a l p y o f d e s o r p t i o n / k J m o l - 1
Pa r t i t i on coe f f i c i en t
Ent
halp
y of
sor
ptio
n/kJ
mol
e-1
Partition coefficient
Percent mass
-60
-40
-20
0
20
40
60
0
5 0
1 0 0
1 5 0
2 0 0
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Hexane sorption in Tecoflex (2.09µm)
E n t h a l p y o f s o r p t i o n / k J m o l e - 1E n t h a l p y o f d e s o r p t i o n / k J m o l - 1
P a r t i t i o n c o e f f i c i e n t
Ent
halp
y of
sor
ptio
n/kJ
mol
e-1
Partition coefficient
Percent mass
Figure 5-36: Partition coefficients and sorption enthalpies for several solvent vapors as the function of solvent vapor mass percent in the Tecoflex film (2.09µm)
219
Based on the coefficients of the equations obtained for the LSER of both films,
Tecoflex exhibits the strongest solubility interaction for compounds capable of hydrogen
bonding through an acidic site. Ethanol was chosen to represent this type of interaction
but as can be seen in figure 5-34 (a) and (b) it doesn’t have the largest partition coefficient,
as one would expect. In fact to make such predictions one should consider the sum of the
products of the coefficients (for the polymer) and variables (for the vapor) in the LSER.
Toluene has the highest partition coefficient with largest contributions from its
polarizablity and dispersion characteristics. A negative coefficient for dipolarity indicates
the least favorable type of interactions. Chloroform has a large permanent dipole moment.
However, the lack of solubility interactions through dipole/dipole interactions for
Tecoflex/chloroform is made up for, mostly by dispersion, polarizabiliy, and somewhat by
hydrogen bonding through its only hydrogen, so that the overall solubility interaction is
still very strong relative to other solvent vapors such as acetone and hexane.
As mentioned earlier the difference in the two LSER equations obtained for the
two Tecoflex films was caused by the fact that the values for the partition coefficients were
twice as large for the thicker film (2.09µm). To correct for this discrepancy we analyzed
our results in an attempt to identify possible sources of error. The values for the partition
coefficients were obtained by taking the ratio of the concentration of the solvent vapor in
the Tecoflex film (µg/L) over the vapor concentration in the gas phase (µg/L) (see figure
5-1). The vapor concentration in the gas phase is computed from the vapor pressure of the
vapor in the bubble-though container and the dilution factor for the gas flows of MFC1
and MFC2 (see equations 65-68). The same procedure for calculating these values was
used for both films. If there were any mistakes involved, they would be the same in both
cases and would affect the values for the partition coefficients to the same extent. The
220
ratio of the values for the partition coefficients would be the same. In other words, even if
we assume that the values for the vapor concentration in the gas phase were twice as large
or small as those used in the calculations, since the same values were used for both films
they could have no effect on the relative values of the partition coefficients with respect to
each other.
The concentration of the solvent vapor in the Tecoflex film is obtained from direct
mass measurements for the sorbed compound and the film itself. Again considering an
extreme case, we could assume deviations from Sauerbrey’s equation as the result of
change in the shear modulus of the film for high solvent contents. Here again it is not
reasonable to assume that this deviation would be twice as large for six different solvents
and for almost all solvent compositions.
At this point the only other values in question were those for the mass of the
Tecoflex films. We decided to seek an independent method for measuring the thickness of
the Tecoflex films. The results of an independent thickness measurement would validate
the accuracy of our mass measurements with the QCM, which were also used to determine
the thickness of the films. Dr. John DiNardo from the Physics department at Drexel
University kindly agreed to help us with these measurements using their atomic force
microscope. Mr. Daniel Brennan operated the AFM and helped with analyzing the results.
The figures below show the results of the AFM measurements. The results of these
experiments were very significant to us, not only for examining the behavior of the QCM
as a balance, but also to evaluate the performance of our film preparation method for
producing a uniform film thickness over the entire QCM surface.
221
Figure 5-37: Atomic force microscope images of the Tecoflex film (2.09µm) near the center of the QCM
Tecoflex
Gold
Tecoflex Gold
Top view
Side view
222
Figure 5-38: Atomic force microscope images of the Tecoflex film (2.09µm) closer to the edge of the QCM
223
Figure 5-39: Atomic force microscope images of the Tecoflex film(0.78µm) near the center of the QCM
224
To obtain the atomic force microscope (AFM) images the QCMs were cut with a
diamond into small squares (ca. 4mm by 4mm). Some portion of the Tecoflex film was
then shaved off with a sharp blade. The tip of the AFM probe was placed at the edge of
the Tecoflex film and an area of 100 by 100µm for the first image and 120 by 120µm for
the next two images were scanned. The thickness of the film was measured at two
different points for each scan (see vertical distance on figures 5-36, 37 and 38). Figure 5-36
is the image of the 2.09 µm Tecoflex film near the center of the QCM. The values for the
vertical distance at the edge of the Tecoflex film, 2.092µm and 2.082, are in good
agreement with those calculated from the mass measurements (2.09µm). The measured
values for film thickness near the edge of the QCM, 2.034 µm and 2.063µm, are shown in
figure 5-37. These values are slightly smaller, but still very close, and indicate good
uniformity of the film thickness over a long distance.
The values for the thickness of the second Tecoflex film (0.78µm) are shown in
figure 5-38. For this film getting a clean edge for the Tecoflex was more difficult. Several
attempts were made, but in all cases the Tecoflex film curled up after it was cut and
created a large bump right at the edge. During the thickness measurement when the AFM
probe scans over such a large object (see section analysis in figure 5-38) the uncertainty in
the exact location of the probe on either side of the object increases. The values for the
thickness of the Tecoflex at two different locations were 692.6nm and 700.3nm.
In order to gain a better understanding of the significance and validity of the
thermodynamic quantities we have measured for the sorption of the organic vapors in
Tecoflex, we searched the literature for other work similar to our own. Unfortunately, the
sorption enthalpies of organic vapors in Tecoflex had never been reported before.
225
The sorption process can be broken into two conceptualized steps: first, the
condensation of the vapor and then the mixing of a small amount of liquid with the
polymer27,28. The energetics of these processes have been measured and are well
understood for many organic solvents, their binary solutions, and mixtures with some
polymers. The values for the enthalpies of vaporization of many solvents are available in
the CRC handbook of physics and chemistry. Surprisingly, sources for the values of
entropy of vaporization of organic solvents are not as abundant.
For those organic solvents, which form ideal solutions, the enthalpy of mixing is
zero. The entropy is always positive and the only driving force of the mixing process
(∆mixingG =-T∆mixingS for ideal solutions). There are two kinds of nonideal solutions whose
vapor pressure doesn’t follow Raoult’s law. Solutions of compounds that have weak acidic
and basic functional groups exhibit a negative deviation from Raoult’s law. Classical
examples are acetone and chloroform, which form a complex through H-bonding. Mixing
enthalpies for such compounds are exothermic. The entropy, on the other hand, is less
positive than for an ideal solution.
H
Cl
Cl
Cl
CH3
CH3
O
Figure 5-40: Chloroform/acetone hydrogen bonded complex
226
The formation of the other type of nonideal solutions (regular solutions) results in
weaker intermolecular interactions compared to the pure solvents before mixing. Such
solutions exhibit, larger vapor pressures than predicted by Raoult’s law, endothermic
enthalpies of mixing, and generally slightly less positive values for the entropy of mixing
than ideal solutions. Other investigators have measured mixing enthalpies of organic
solvents in polymer thin films using a quartz crystal microabalance and van’t Hoff
equation and compared their results to calorimetric measurement27. The polymer thin
films used in these experiments were polysiloxane chains modified with 8% to 10% of
certain functional groups. Our polymer thin film sample, Tecoflex, has many different
types of functional groups (ether, ketone, amine and cyclohexyl group), which makes the
predication and interpretation of their collective behavior very difficult. For example, the
ketone functional group of Tecoflex can form a complex with chloroform as shown in
figure 5-39. But the mixing of chloroform with Tecoflex with respect to the other
functional groups may exhibit the properties of a “regular solution”. Figure 5-40 shows the
thermodynamic quantities for sorption of chloroform and ethanol in Tecoflex. The free
energy, ∆sorptionG, is shown as the sum of the enthalpic and entropic contributions. In each
case the measured values for sorption enthalpy and entropy have been divided into two
parts, condensation and mixing. The enthalpies of mixing for both solvent vapors are
exothermic. The entropic contribution to the free energy (-T ∆mixingS) is positive for
chloroform and negative for ethanol. This can be an indication of the complexation of
chloroform with the ketone functional group of Tecoflex.
227
-60-40-20
02040
1 2 3
∆sorptionG
−Τ∆sorptionS
∆sorptionH
condensation
mixing
condensation mixing
kJ/m
ol
-60-40-20
02040
1 2 3
kJ/m
ol
∆sorptionG −Τ∆sorptionS
∆sorptionH
(a)
(b)
Figure 5-41: Thermodynamic quantities for sorption of (a) chloroform, (b) ethanol vapors in Tecoflex
228
We have shown the capability of the QCM/HCC to measure directly important
thermodynamic and kinetic properties under isothermal conditions. We don’t intend to
report any final quantitative results for the thermodynamic quantities for mixing of organic
vapors in this polymer system. The QCM/HCC apparatus was still undergoing
improvements and modifications during these experiments. The results of the above
experiments need to be further examined with films of the same polymer but with
different thickness. If the variations in the values for the partition coefficients for different
films persist, they may be attributed to the film thickness, processing or other preparation
related issues. The accuracy of the values of the sorption enthalpies can be improved with
application of the present thermal recalibration methods and perhaps with devising other
simple and reliable procedures. The random deviations in the ∆sorptionH values will be
reduced, if better peak integration software can be applied. A paper to the Analytical
Chemistry journal reporting the results of a third set of experiments with this polymer film
would complement the work of other investigators in the area of thin film characterization
for applications in chemical sensors and separation sciences.
229
References
(1) Gavara, R.; Catala, R.; Aucejo, S.; Cabedo, D.; Hernandez, R. J. Polym. Sci., Part B:
Polym. Phys. 1996, 34, 1907-1915.
(2) Ngui, M. O.; Mallapragada, S. K. J. Appl. Polym. Sci. 1999, 72, 1913-1920.
(3) Al-Saigh; Y., Z. Polym. News 1994, 19, 269-79.
(4) Hernandez, R. J.; Gavara, R. J. Polym. Sci., Part B: Polym. Phys. 1994, 32, 2367-74.
(5) Rautenbach, R.; Albrecht, R. J. Membr. Sci. 1984, 19, 1-22.
(6) Rautenbach, R.; Herion, C.; Franke, M.; Asfour, A. F. A.; Bemquerer-Costa, A.;
Bo, E. J. Membr. Sci. 1988, 36, 445-62.
(7) Boeddeker, K. W.; Bengtson, G.; Bode, E. J. Membr. Sci. 1990, 53, 143-58.
(8) Bengtson, G.; Boeddeker, K. W. Chem.-Ing.-Tech. 1990, 62, 937-9.
(9) Grate, J. W.; Wise, B. M.; Abraham, M. H. Anal. Chem. 1999, 71, 4544-4553.
(10) Brown, M. E.; Editor Handbook of Thermal Analysis and Calorimetry, Volume 1:
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(11) Kwei, T. K.; Nishi, T.; Roberts, R. F. Macromolecules 1974, 7, 667-74.
(12) Hadziioannou, G.; Stein, R. S. Macromolecules 1984, 17, 567-73.
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(14) Grate, J. W. Chem. Rev. (Washington, D. C.) 2000, 100, 2627-2647.
(15) Grate, J. W.; Martin, S. J.; White, R. M. Anal. Chem. 1993, 65, 940A.
(16) Grate, J. W.; Abraham, M. H. Sens. Actuators, B 1991, B3, 85-111.
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J. Chem. Soc., Perkin Trans. 2 1989, 699-711.
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(18) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. J. Chromatogr. 1991,
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(19) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. J. Chem. Soc., Perkin
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231
Chapter 6- Experiment 2: Hydrogen sorption in thin palladium films; experiment 3: Self assembled monolayer formation on gold
6.1 Hydrogen sorption; introduction
6.1.1 The Hydrogen storage problem
There has been extensive work to investigate the interaction of molecular
dihydrogen with candidate chemical systems for hydrogen storage. Hydrogen is an
exceptional fuel, which burns extremely cleanly. However, despite all advances in modern
hydrogen fueled internal combustion engines with thermal efficiencies as high as 56% and
zero NOX emission1, the exploitation of hydrogen as a fuel on a massive scale is still being
hampered by the lack of a practically sound method of hydrogen storage. A new affordable
and safe method of hydrogen containment would not only revolutionize the fuel industry
but also improve the quality of all life in the future.
The energy density of hydrogen gas is too low. Liquid hydrogen, on the other
hand, has an acceptable energy density but inconvenient cryogenic temperatures. Certain
transition metals and metal alloys can absorb large quantities of hydrogen to form metal
hydrides. The basis for potential use of metal hydrides as H2 storage units is twofold. In
addition to their rapid exchange rate of hydrogen, some have shown proton densities 50%
higher than that of liquid hydrogen under relatively mild conditions (250C and 2
atmospheres)2,3.
There already has been extensive research on metal hydrides, not only because of
their possible application in the area of hydrogen containment, but also because of their
232
close relation to other areas such as heterogeneous catalysis and surface corrosion.
However, there is still some disagreement in the experimental thermodynamic and kinetic
data, mainly because of the changing nature of the metal hydride formation reaction over
time. For example, the rate of the overall reaction depends on factors such as the rate of
heat conduction in the metal and the metal particle size4.
Thermodynamic information such as ∆sorptionH have been obtained either from
isotherms at several different temperatures5, or from calorimetric experiments such as
differential scanning calorimetry6 and isothermal heat conduction calorimetry5.
Differential scanning calorimetry experiments are especially valuable for determination of
hydrogen induced amorphization (HIA) enthalpies. However the ∆sorptionH cannot be
measured isothermally and are reported as kJ/mol of the metal host6. Heat conduction
calorimetry generally measures ∆sorptionH for bulk samples isothermally, making the
assumption that the number of surface metal atoms are much smaller compared to the
number of the bulk metal atoms5. There still exist ample difficulties in gathering
reproducible and reliable thermodynamic data, although traditionally this has been blamed
on poor quality material or presence of contaminants4.
The presently accepted model for hydride formation consists of four elementary
steps. This model is not universal for all metal hydrides, but is usually a good starting point
for conceptualizing the individual steps.
H2(gas)àH2(adsorbed)à2H(adsorbed)à2H(absorbed)à2H(diffused)
233
Many different systems have been studied for their hydrogen solubility properties.
Examples are pure transition metals such as Pd7, Pt8, Ni9and Ti8 or their metal alloys.
Among the alloys the Lanthanum/nickel alloy (LaNi5) is the best-known metal hydride
capable of storing hydrogen under moderate conditions10. There are other systems such as
representative members of RCo3, R2Co7 and R3Co5 (where R is a rare earth metal)
intermetallic alloys, which have been of special interest because they possess two isotherm
"plateau regions". These alloys can undergo hydrogen absorption-desorption cycles at two
completely different H2 partial pressures3.
The search for possible hydrogen storage units is not limited to metal hydrides. In
the recent years, storage of hydrogen in carbon has received increased attention due to the
presence of new and novel carbon nanomaterials such as fullerenes, nanotubes and
nanofibers11,12. The graphite nanofibers are the newest form of carbon allotropes. These
are prepared from decomposition of carbon-containing gases at temperatures between
450-7500C over selected metal and metal alloy surfaces. They consist of very small graphite
platelets stacked on top of each other to form a structure 30-500Å in cross section and 10
to 100 microns in length. The graphite platelets can be arranged parallel, perpendicular or
at an angle with respect to the axis of the fiber. In all cases the graphite platelets are
stacked at a minimum distance of 3.35Å. This distance makes the edges of the nanofiber a
suitable entering site for H2 with a kinetic diameter of just 2.89Å. This partially explains
the enormous hydrogen uptake of this material. Excess adsorption of up to 2kg H2/1kg of
carbon has been reported at 112 atm. and 298K11.
234
6.1.2 Hydrogen sorption in palladium
The palladium/hydrogen system has been studied extensively as early as the 1860s.
There are numerous publications regarding the thermodynamics of hydrogen sorption in
palladium, although there are some discrepancies because of reasons explained earlier.
Deville and Troost made the first observations of the permeability of hydrogen in iron and
palladium in 186313. Shortly thereafter Thomas Graham realized that a hot palladium
septum used in a hydrogen permeation experiment retained a relatively large amount of
hydrogen after it was cooled to room temperature14.
Palladium has a peculiar position among the group VIII (referred to as the
platinum family) metals. It has the highest hydrogen solubility and can absorb and desorb
hydrogen under mild conditions very rapidly7. Figure 6-1 is an example of a typical
hydrogen sorption isotherm for palladium. It shows the formation of a nonstoichiometric
hydride, PdHn. Two different phases of the hydride can form depending on the hydrogen
composition: α phase for small H/Pd atomic ratios (n in PdHn <0.015 5 or 0.01 15 at
298K) and the β phase (n in PdHn >0.58 5 or 0.61 15 at 298K). The plateau region of the
sorption isotherm indicates the region, where both α and β phase of the solid solution can
coexist (0.015<n<0.58 at 298K). The critical temperature for the sorption isotherm is
~300C0.
235
Historically hydrogen sorption isotherms for palladium have been determined by
one of the three common methods. The pressure-composition-temperature (p-c-T)
relationship has been studied from direct measurements of the partial (total) pressure of
hydrogen above a palladium sample as a known volume (amount) of the hydrogen gas is
admitted into the sample container15. Hydrogen can also be introduced into palladium by
electrolysis. The cell potential of an electrochemical cell has been used to determine the
hydrogen content of a palladium electrode16. The current through two electrochemical
cells separated by a palladium bielectrode membrane has been used to determine the
H/Pd atomic ratio
Log
p H2/
atm
0
0.8
α phase β phase
α+β phase 0
2
Figure 6-1: An example of a typical hydrogen sorption isotherm for palladium
236
diffusion coefficient of hydrogen in palladium17. The hydrogen content can also be
determined by measuring the electrical resistance of the palladium hydride. The electrical
resistance of a palladium hydride increases linearly from R0 to 1.8R0, as the H/Pd ratio (n)
increases from zero to ca. 0.72 18. This relationship provides for a very convenient way of
measuring the hydrogen content in palladium.
The enthalpy of hydrogen sorption in palladium has been measured either directly
by calorimetric methods or indirectly from p-c-T relationships (through the Clausius
Clapeyron equation) and electrochemical experiments. Since hydrogen tends to absorb at
very low pressures, distinguishing between the energetics of the α phase formation and the
adsorption of hydrogen on the surface is not straightforward. Most of the measurements
performed before the 1970’s were in the α-β phase region. With improvements of the
ultrahigh vacuum technology, the data for the α phase have increased over the past
decades. The enthalpy for hydrogen sorption at 298K in the α phase starts with a value of
approx.-19 kJ/mol (PdHn, n<0.01) and decreases to -23 kJ/mol for n= 0.0119. For the β
phase (n=0.6) the sorption enthalpy reaches a minimum of -46 kJ/mol and increases to -
27kJ/mol with increasing hydrogen content (n=0.69).
237
6.1.3 Experimental
The hydrogen sorption experiments discussed below were performed in three
separate stages. First, two thin palladium films were electrodeposited on the gold
electrodes of two QCMs. In stage two hydrogen sorption enthalpies in the thin films were
measured. And in phase three one of the palladium films was used as a room temperature
catalyst for hydrogenation of ethylene gas. The experimental work described here was the
result of the efforts of three people: Mr. David Schneider (stages I and II), Mr. Ed
Lavender (stage III) and Hamid Shirazi (stage I-III).
Two QCMs were cleaned in piranha solution. Both sides of the QCMs, with the
exception of their larger gold electrodes (area =1.307cm2), were masked with nail polish
prior to electroplating. An aqueous solution/dispersion of Pd(NO3)2 in nitric acid at pH
~1 was prepared and used as the electroplating bath. The bath was gently stirred and its
temperature regulated at 50C0 throughout the plating process. Two QCMs were plated for
1 and 2.5 hours at a plating current of 14mA with thicknesses 54nm and 141nm
respectively. The nail polish was removed with acetone. The QCMs were cleaned in a cold
piranha solution for 3 minutes, rinsed with deionized water and dried in a nitrogen stream
before they were placed in the QCM/HCC. Because of the extremely low plating
efficiency the current recorded during the electrodeposition could not be used to calculate
the mass of the palladium films. Instead, the shift in the oscillation frequency (QCMI ∆f=
3668 Hz, QCMII ∆f=9589 Hz) before and after the electroplating was used to determine
the mass (QCMI ∆m=221.4µg, QCMII ∆m=84.7µg) of the palladium films. The thickness
was estimated from the density (12.0g/cc) of palladium20.
238
During the sorption experiments a nitrogen/hydrogen gas mixture was passed over
the palladium film whose hydrogen composition was changed periodically. The figures
below (6-2 to 6-6) show two sets of experiments. In the first set the palladium film
(141nm) was subjected to 13 sorption cycles. Each cycle consisted of three
sorption/desorption steps. A small mass change was observed when the hydrogen gas was
introduced for the first time. This is due to the adsorbed oxygen on the palladium surface,
which reacts with hydrogen to form water21. The slow downward drift in the mass trace in
figure 6-2 (b) has been observed by other researchers and is attributed to remanent elastic
stresses in the palladium film22. It is known that palladium undergoes a volume expansion
of 11% during hydrogen sorption23. The palladium film is firmly bound to the
gold/quartz layer. The volume expansion results in a large strain on the QCM surface.
This effect has also been studied for erbium films. In contrast to palladium, erbium
experiences elastic compressions upon the formation of a hydride, which lead to tension in
the quartz. These effects can have substantial effects on the oscillation frequency of the
QCM24,25. In such cases the shift in the oscillation frequency has two components: a
gravimetrical frequency shift following Sauerbrey’s relation and a frequency shift due to
the surface stress. The exact magnitude of the stress related frequency shift can be
determined, if two quartz plate resonators cut from a single crystal at different angles are
used in the so-called double resonator technique. The double resonator technique is based
on the superposition of the shift in oscillation frequency due to mass change and the shift
in the oscillation frequency from stress effects. If an AT-cut and BT-cut (see chapter 2)
resonator pair is used, the total frequency shift for each QCM is given in the equation
below 24,25
239
BTq
BT
BTq
BTBTBT
ATq
AT
ATq
ATATAT
MSKff
MSKff
τρτ
τρτ
∆−
∆=
∆
∆−
∆=
∆
0
0
where f0AT and f0
BT are the original resonant frequencies of the AT-cut and BT-cut
QCMs, ∆f is the shift in the resonant frequency, ∆M is change in the mass loading, ∆S is
the change in the lateral stress, K is the stress related proportionality constant, and ρ and τ
are the mass density and the quartz plate thickness respectively. The constants KAT and
KBT have almost the same magnitude but the opposite sign, KAT=2.75e10-12 cm2/dyn and
KBT =-2.65e10-12 cm2/dyn. For an AT-cut QCM the hydride formation induced stress
results in a decrease in the oscillation frequency as does an added mass loading, whereas
for a BT-cut QCM the oscillation frequency will increase. Cheek a nd O’Grady have shown
that the shift in the resonant frequency of an AT-cut QCM overestimates the mass by a
factor of ~2 (∆factual mass=-185Hz, ∆fAT=-351Hz), where the same H loading in a palladium
film with a BT-cut QCM will result in no significant frequency shift (∆factual mass=-185Hz,
∆fBT=-20Hz)23,26. Using an electrochemical quartz crystal microbalance Liu et al.
calculated the mass of sorbed hydrogen from the electrochemical current and were able to
account for the shift in the oscillation frequency of a 10MHz AT-cut QCM due to surface
stress27. A frequency shift of -423Hz was separated into the gravimetrical (-210 Hz for
181 ng of hydrogen) and the surface stress components (-213 Hz for a surface stress of
1071MPa). Since the double resonator technique was not used in our work, we used the
(76) (77)
240
relationships given in the references above to estimate the actual hydrogen mass in the
palladium film.
In figure 6-2 (b) the magnitude of the mass change due to hydrogen sorption
during the sorption/desorption steps seem to be increasing for the first 6 sorption cycles.
Due to the nonlinearity of the baseline for the mass trace this effect may be more visible in
the increase in the height of the thermal peaks in figure 6-2(c), although it is more
appropriate to compare the integrated areas of the thermal peaks. During hydrogen
sorption cycling palladium undergoes slow changes in its crystal morphology as well as its
surface cleanliness. Utilizing optical microscopes, these accounts report gradual
development of families of parallel lines representing the intersection of (111) planes with
the (100) face on the surface of large palladium crystals7. On the (111) face itself
formation of interesting triangular patterns has been reported. Hydrogen cycling induced
annealing of a single large palladium crystal decreases the hydrogen loading capacity as the
number of defects in the lattice structure decrease. For powder samples that break into
smaller pieces during hydrogen sorption the hydrogen uptake capacity increases as the
result of the increase of sample surface area. The hydrogen uptake can also increase as the
result of surface cleaning during repetitive sorption cycles.
For a closer look at the mass and thermal events during individual sorption steps
two sorption cycles are shown in figure 6-3. The enthalpy of sorption for each sorption
step was obtained from the integrated area of the thermal peak and the mass change. As
described in chapter 5 corrections to the values for the integrated heat were necessary. For
experiments performed before the addition of the gas mixing section in the flow system
(before June of 1999) correction values were obtained from runs with two gold surfaces
for sample and reference with identical flow patterns used for the sorption experiment.
241
One such run is shown in figure 6-4. The same flow pattern used in the (00-05-24-1) run
for a palladium film was produced over two gold surfaces for the first ~12000 sec of the
run (figure 6-4). There is virtually no mass change detectable on the gold surface during
this period. The small thermal peaks indicate that the hydrogen concentration is somewhat
higher in the left side of the QCM/HCC because of insufficient mixing of the gas flows of
MFC1 and MFC2. The flow to the right side of the QCM/HCC was stopped from
t=12000sec to t=17000sec. There are small mass changes on the gold surface due to
adsorption of hydrogen. The large thermal peaks are mostly due to hydrogen sorption in
the o-rings holding the QCM. Similar peaks in opposite direction are observed, when the
flow of the hydrogen/nitrogen gas mixture through the right side of the QCM/HCC is
resumed and the left side remains static. The integrated areas of the thermal peaks during
t=0sec to t=12000sec (run 99-05-25-1) were subtracted from those for the hydrogen
sorption in palladium (99-05-24-1) at the same H2 gas compositions to arrive at the values
for the corrected ∆sorptionH in table 6-1. Further correction was made to account for the
stress related effect on the QCM response. Based on the work in refs 23-26for a 5MHz
AT-cut QCM the measured mass is overestimated by a factor of ~2.
A second set of experiments was conducted with the same palladium film (141nm)
after the addition of the gas-mixing unit in the flow set up. The mass and thermal
responses of two clean gold surfaces were measured for the same flow pattern used in the
subsequent sorption experiment. The mass and thermal trace in figure 6-5 (a) show
marked improvements. Although, there are still small thermal peaks in the absence of the
palladium sample, their areas are much smaller relative to those measured during the
sorption experiment (see figure 6-6 (c)). A correction procedure in this case would have
negligible effects and, therefore, was not performed.
242
Figure 6-6 shows two of the eight sorption cycles for the (99-06-09-2) run. Each
sorption cycle consisted of 6 sorption/desorption steps. The sorption enthalpies were
calculated for the individual steps from the integrated heats and mass changes. The values
for the sorption enthalpies had to be corrected only for stress related effects. Table 6-2
gives a summary of the results for the hydrogen sorption enthalpies during the two
sorption cycles shown in figure 6-6.
243
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10000 20000 30000 40000 50000
Mas
s/µg
Time/sec
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10000 20000 30000 40000 50000
Hyd
roge
n pr
essu
re/a
tm
Time/sec
-20
-10
0
10
20
30
0 10000 20000 30000 40000 50000
The
rmal
pow
er/µ
W
Time/sec
Figure 6-2 Hydrogen sorption in thin palladium film (141nm) (99-05-24-1) (a) hydrogen pressure (b) mass trace
(c) thermal trace
(a)
(b)
(c)
244
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
38400 40000 41600 43200 44800
Mas
s/µg
Time/sec
-30
-20
-10
0
10
20
30
40
38400 40000 41600 43200 44800
The
rmal
pow
er/µ
W
Time/sec
0
0.1
0.2
0.3
0.4
0.5
0.6
38400 40000 41600 43200 44800
Hyd
roge
n pr
essu
re/a
tm
Time/sec
Figure 6-3: Two hydrogen sorption cycles in thin palladium film (141nm) (99-05-24-1) (a) hydrogen pressure
(b) mass trace (c) thermal trace
(a)
(b)
(c) Exo
245
-0.05
0
0.05
0.1
0.15
0.2
0 5000 10000 15000 20000 25000
Mas
s/µg
Time/sec
-40
-30
-20
-10
0
10
20
30
40
0 5000 10000 15000 20000 25000
The
rmal
pow
er/µ
W
Time/sec
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5000 10000 15000 20000 25000
Hyd
roge
n pr
essu
re/a
tm
Time/sec
Figure 6-4: Hydrogen gas over two gold surfaces (99-05-25-1) (a) hydrogen pressure (b) mass trace (c) thermal trace
(a)
(b)
(c)
246
Table 6-1: Summary of the results for hydrogen sorption enthalpies in thin palladium film (141nm) (99-05-24-1)
99-05-24-1 corrected ∆ sorptionH /kJmol-1 Mass/µg ∆Mass/µg Heat/µJ corrected Average
0.100 0.330 -2319.7 -14.1 -14.0 0.430 0.154 -1021.9 -13.3 -13.2 0.584 0.103 -641.4 -12.5 -12.4 0.687 0.678 -0.117 650.4 11.1 11.2 0.561 -0.167 1030.2 12.3 12.4 0.394 -0.323 2353.3 14.6 14.7 0.071 0.068 0.332 -2329.8 -14.0 0.400 0.155 -1011.4 -13.1 0.555 0.104 -644.7 -12.4 0.659 0.652 -0.116 645.1 11.1 0.536 -0.166 1031.3 12.4 0.370 -0.323 2360.3 14.6 0.047 0.044 0.333 -2336.7 -14.0 0.377 0.158 -1040.2 -13.2 0.535 0.103 -643.4 -12.5 0.638 0.631 -0.116 651.3 11.2 0.515 -0.168 1041.8 12.4 0.347 -0.320 2381.3 14.9 0.027
Corrected for stress
-28 -26 -25
22 25 29
Sorp
tion
cycl
e 1
Sorp
tion
cycl
e 2
Sorp
tion
cycl
e 3
247
-10
-5
0
5
10
0
0.02
0.04
0.06
0.08
0.1
0 2600 5200 7800 10400 13000
The
rmal
pow
er/µ
W
Mass/µg
Time/sec
0
0.05
0.1
0.15
0.2
0 2600 5200 7800 10400 13000
Hyd
roge
n pr
essu
re/a
tm
Time/sec
-30
-25
-20
-15
-10
-5
0
5
10
-0.2
0
0.2
0.4
0.6
0.8
1
0 15000 30000 45000 60000
The
rmal
pow
er/µ
W
Mass/µg
Time/sec
Figure 6-5: (a) Mass and thermal traces for two bare gold surface (b) hydrogen pressure over two gold surfaces (99-06-09-1)
(c) hydrogen sorption in a thin palladium film (141 nm)(99-06-09-2)
(a)
(b)
(c)
248
0
0.1
0.2
0.3
0.4
0.5
32000 36000 40000 44000 48000
Mas
s/se
c
Time/sec
-10
-5
0
5
10
32000 36000 40000 44000 48000
The
rmal
pow
er/µ
W
Time/sec
0
0.05
0.1
0.15
0.2
32000 36000 40000 44000 48000
Hyd
roge
n pr
essu
re/a
tm
Time/sec
Figure 6-6: Two hydrogen sorption cycles in a thin palladium film (141nm) (99-06-09-2)
(a) hydrogen pressure (b) mass trace (c) thermal trace
(a)
(b)
(c)
Endo
249
Table 6-2: Summary of the results for hydrogen sorption enthalpies in a thin palladium film (141nm) (99-06-09-2)
99-06-09-2 ∆ sorptionH /kJmol-1 Mass/µg ∆Mass/µg Heat/µJ Average
0.114 0.102 -641.3 -12.6 -12.5 0.216 0.057 -342.3 -12.0 -11.8 0.273 0.043 -264.8 -12.3 -11.9 0.316 0.039 -204.6 -10.5 -10.9 0.355 0.036 -202.6 -11.3 -11.4 0.391 0.032 -187.7 -11.7 -11.4 0.423 -0.045 181.4 8.1 8.0 0.378 -0.046 204.8 8.9 8.9 0.332 -0.047 222.2 9.5 9.4 0.285 -0.053 263.3 9.9 9.9 0.232 -0.066 344.9 10.5 10.5 0.166 -0.106 630.0 11.9 11.8 0.060 0.105 -650.6 -12.4 0.165 0.058 -335.7 -11.6 0.223 0.045 -257.7 -11.5 0.268 0.038 -213.0 -11.2 0.306 0.036 -207.4 -11.5 0.342 0.034 -189.2 -11.1 0.376 -0.044 176.7 8.0 0.332 -0.044 195.1 8.9 0.288 -0.046 215.6 9.4 0.242 -0.053 259.9 9.8 0.189 -0.064 335.0 10.5 0.125 -0.109 635.5 11.7 0.016
Corrected for stress
-25 -24 -24 -22 -23 -23 16 18 19 20 21 24
Sorp
tion
cycl
e 1
Sorp
tion
cycl
e 2
250
6.1.4 Results and conclusions
The slow drift in the baseline of the mass trace was observed for both sets of
experiments, (99-05-24-1) and (99-06-09-2). In both cases the drift in the baseline seemed
to be approaching a steady value with increasing number of the sorption cycles. The
palladium film had already been subjected to many sorption/desorption cycles before the
second set of the experiments (99-06-09-2). The reoccurrence of the stress related shift in
the mass trace baseline indicates that the palladium lattice reverts to its original state in the
absence of hydrogen sorption cycling. It should be emphasized that the hydrogen sorption
induced changes alter only the dimension of the lattice structure but not its geometry.
Palladium maintains its face centered cubic (f.c.c.) lattice structure in its pure state as well
as α and β hydride phase. With increasing hydrogen pressure the edge (a) of the f.c.c.
palladium unit cell enlarges upon hydride formation. For α phase at 303K f.c.c. a
=0.389nm and for the β phase f.c.c. a =0.402nm28.
The variations in the values for enthalpies of hydrogen sorption for the two
different experiments are caused by two reasons. As discussed earlier the value of sorption
enthalpy depends on the hydrogen content of palladium. Secondly, at the time these
experiments were conducted the procedure for recalibration of the thermopiles had not
been developed yet (see chapters 3 and 4). This would cause the results of one set of the
experiments to be systematically larger that the other. Despite the multitude of correction
procedures for the mass and the thermal data, we still believe our results to be within
reasonable agreement with those in the literature, as will be further discussed below.
In order to compare our measured values of enthalpies of hydrogen sorption with
the literature values, the hydrogen content of the palladium has to be known. To
251
determine the original amount of the pure palladium all hydrogen has to be removed. This
is usually done by heating the palladium sample to a temperature above its critical
temperature (Tc˜ 300C0) in vacuum. It is known that an electroplated palladium film can
contain moderate amounts of hydrogen, which form a chemically stable hydride at room
temperature16,21,29. Without thermal treatment of the sample and in the absence of a
vacuum system in the gas flow cell of the QCM/HCC, it was impossible to remove all of
the sorbed hydrogen. Therefore, the exact hydrogen content of the palladium film was not
known. We could only estimate the range of the region of H/Pd ratio on the sorption
isotherm based on, the hydrogen partial pressure during the sorption/desorption cycles,
the magnitude of the measured sorption enthalpies, and the trend in the change of their
magnitude.
Sorption enthalpies in the α phase range between 19 to 23kJ/mol. The magnitude
of the ∆sorptionH increases with increasing H/Pd ratio. We don’t believe to have made
measurements in this region, because of the chemical stability of the α phase at room
temperature as well as the fact that the magnitude of the measured ∆sorptionH for our
experiment decreases for higher hydrogen partial pressures. The magnitude of the ∆sorptionH
at the plateau region of the sorption isotherms (α + β phase coexistence region) stays
constant for H/Pd ratio range of 0.01<n<0.55 at ~37kJ/mol and reaches a maximum
(46kJ/mol at n=0.6). It then decreases sharply for n>0.61. Based on the magnitude of the
∆sorptionH, the decrease in its magnitude for increasing hydrogen pressure, and the range of
the hydrogen pressure over the palladium film (range for log(pH2/Pascal) =
0…3.4,…4.2,…4.7), the hydrogen sorption enthalpies must be for the β phase hydride
formation at n>0.61).
252
It should be noted that there are numerous publications describing various aspects
of hydrogen solubility in palladium dating back to the late 1800s. However not all of the
reported data are in perfect agreement. Observation of variations in the energetics and
hydrogen uptake capacity of palladium has been attributed mainly to three factors
- The degree of surface cleanliness, and presence of impurities in the
palladium sample or hydrogen gas
- Sample pretreatment, annealing, crystallinity and the number of defects in
its lattice structure
- The nature of the palladium sample with respect to its size a nd surface to
volume ratio
In comparing our work with that from other laboratories in relation to the above
mentioned issues we should point out the major differences.
The hydrogen gas used for our experiments was technical grade (99.9% and better
in purity). Some have used a palladium silver alloy membrane for purification of hydrogen
to avoid poisoning of the surface by carbonmonoxide and other impurities. Surface
poisoning slows down the kinetics of hydrogen sorption30. Since hydrogen dissociation is
fast for clean surfaces and the diffusion is the rate-determining step, Fick’s law can be used
to obtain the diffusion coefficient of hydrogen in palladium 17. The magnitude of the
increase in the apparent measured diffusion coefficient of hydrogen in palladium is usually
a good measure of the degree of surface poisoning 19. Diffusion coefficients for hydrogen
in palladium for α phase (Dα phase=1.3-3.1 *10-7 cm2/s at 250C) are an order of magnitude
smaller than for β phase (Dβ phase~10-6 cm2/s at 250C)17. In order to accurately measure the
diffusion coefficient for such a fast process the thickness of the palladium film should be
253
at least 5 to 10µm. For the thin palladium sample (141nm) used here a fit of the mass trace
similar to those shown in chapter 5 for diffusion of organic vapors in Tecoflex won’t be
possible. The apparent curvature of the mass trace during each hydrogen sorption step is
due more to the time constant of the gas flow cell for adjusting to the new hydrogen
composition than to hydrogen sorption in palladium.
Annealing of the palladium sample increases the reproducibility of the measured
quantities for hydrogen sorption experiments. But, in general it also reduces the hydrogen
uptake capacity of palladium, since a relatively large quantity of hydrogen can reside in the
defects in the lattice structure. A palladium film electrodeposited on the gold electrode of a
QCM would form a palladium/gold alloy upon annealing 31. Although our palladium
sample was not annealed, we need to acknowledge the possibility of the presence of some
gold impurity, especially near the gold/palladium interface. It has been shown that
depending on the magnitude of the electrodeposition potential palladium can form an alloy
with gold 32. At 900mV vs. SHE the diffusion coefficient of gold in palladium can be as
high as 1.4*10-15 cm2/sec 16. When palladium is alloyed with gold the lattice parameter
slightly increases and the sorption enthalpy becomes somewhat more exothermic 33.
One of the largest sources of scatter in the experimental results of hydrogen
sorption is variation of the surface to volume ratio of palladium samples used17,28,29,34-
36. Three different types of sites exist where hydrogen sorption can take place: sites at the
surface of palladium, sites within the lattice structure of bulk palladium and sites within
defects in the lattice structure. Each type of these sites exhibits different energetics for
hydrogen sorption. The enthalpy of adsorption of hydrogen on the surface of palladium
releases the largest amount of heat (H2 +2Pd à 2PdH, ∆adsorptionH ˜ -100kJ/mol-1)37. For
254
a palladium film the number of palladium surface adsorption sites is much smaller
compared to the absorption sites in the bulk. However as the particle size of the palladium
sample decreases, the surface adsorption related effects are no longer negligible compared
to hydrogen sorption in the bulk. The hydrogen uptake capacity of the palladium sample,
as well as the magnitude of the enthalpy of sorption, gets larger with increasing surface to
volume ratio (decreasing particle size), until the particles get too small (1nm or smaller) to
be able to have an appreciable amount of hydrogen sorption in the bulk28. When
comparing experimental results for hydrogen sorption if one does not consider the nature
of the palladium sample, the results may appear to be highly irreproducible.
The entropy of sorption of hydrogen in palladium can be obtained using the
enthalpy and the partial pressure of hydrogen gas, if the sorption reaction can be written
as:
½ H2 (g) +PdHa/(b-a) ßà PdHb/(b-a)
STHpG sorptionsorptionHsorption ∆−∆=−=∆ )ln(21
2R
where a and b are the initial and final hydride compositions, respectively. The
hydrogen sorption isotherm exhibits strong to moderate hysteresis over its plateau region
(α-β phase coexistence region) depending on the nature of the palladium sample 38. Over
this region the pH2 is usually taken as (pH2 sorption* pH2 desorption)0.5. For other points along the
sorption isotherm pH2 has a single value39. Reported values for hydrogen sorption
entropies are -80 J mol-1K-1 (α-phase) and -92 J mol-1K-1 (plateau region). ∆sorptionS
approaches a maximum value of ~-120 J mol-1K-1 (for β-phase at H/Pd~6.2) but increases
(78) (79)
255
for H/Pd>6.2 until it becomes positive 39. The fact that the mass trace from our sorption
experiments doesn’t exhibit any noticeable hysteresis and small positive values for sorption
entropies are further indications of hydrogen sorption/desorption in the β-phase region
during our experiments. The significance of a positive ∆sorptionS is not fully understood, but
it may indicate a breakdown of the tendency for some ordering of hydrogen atoms above
certain H/Pd ratios 40.
Before closing this section we will briefly show the results of an experiment
subsequent to hydrogen sorption in palladium. In this experiment after the hydrogen was
sorbed into the palladium, it was used in a room-temperature-catalyst for hydrogenation of
ethylene gas.
6.1.5 Ethylene hydrogenation over palladium hydride
Palladium catalysts are widely used for hydrogenation of dienes, alkynes and mono-
olefins. In this experiment the observed rate of the hydrogenation of ethylene gas over
palladiumhydride was compared to other reported values in order to determine the
catalytic surface activity of the Pd sample. No comprehensive details about the mechanism
of the reaction will be given. However, we will introduce a different mode of operation of
the QCM/HCC, where the net kinetic rate of a very complex reaction has been
investigated.
During ethylene hydrogenation, and at steady state, chemisorption of hydrogen
proceeds concurrent with chemiadsorption of ethylene gas on the palladium surface. As
the ethylene gas adsorbs on the palladium, the nature of the resulting surface species will
depend on the temperature and the surface structure. Figure 6-7 shows some C2 species,
256
which have been spectroscopically identified on nickel, platinum and palladium surfaces8.
Ni and Pt surfaces favor the formation of di-σ-species, whereas palladium has a strong
preference for π-adsorbed complexes especially at lower temperatures.
HH
H H
H
H H
H
H
H H
H
vinylidene π-bonded ethylene di-σ/π-bonded ethylene
HH
H
H
H
H
HH
H
H
HH
HH
H
HH
H
HH
H
HH
H
tetra-σ-bonded ethylene di-σ-bonded ethylene ethylidyne ethylylidyne
Figure 6-7: Schematic diagram of C2 species identified spectroscopically on nickel, platinum and palladium surfaces (circles represent surface metal atoms)
Studies on single crystals of palladium have shown the formation of, π-adsorbed
and di-σ-adsorbed ethylene on the Pd(100) at 80K, π-adsorbed ethylene on the Pd(110) at
90K and on Pd(111) at 150K, and at room temperature ethylidyne species form on the
Pd(111) surface but they don’t form on the Pd(100) even after heating to 500K41.
257
Although the details of the individual steps involved in this reaction can become
very complex, the net energetics for ethylene hydrogenation can easily be determined from
indirect methods such as calorimetric measurements of the heat of combustion of the
reactants and products.
C2H4(g) +H2(g)à C2H6(g) , ∆reactionH=-136.4 kJ/mol
Using the above information and a rate expression for the catalytic hydrogenation
of ethylene gas over palladium previously derived by other investigators the heat flow rate
on the palladium surface at different hydrogen and ethylene gas partial pressures could be
estimated and compared to measured values obtained in our QCM/HCC, and finally used
to determine the catalytic activity of the palladium film sample. Three sources for the rate
expression of ethylene hydrogenation on a palladium surface could be found in the
literature. All other expressions found were derived for ethylene/acetylene mixtures.
)2008300
exp()()(105.8 01.022.042
02.002.12
4
THCpHpRate
R±−
×= ±−±
)2009200
exp()()(1047.1 08.016.042
08.0485.02
7
THCpHpRate
R±−
×= ±±
)2009000
exp()()(1014.4 042
5.02
6
THCpHpRate
R±−
×=
The first expression shown in equation (81) was obtained from private
communications with Dr. Tysoe from the University of Wisconsin, Milwaukee42. The
expression in equation (82) was the result of modeling the kinetics with first-principle-
(80)
(81)
(82)
(83)
258
based molecular simulation43. Equation (83) is an extrapolation of experimental
measurements at 193K 44. In all three equations the pre-exponential factor is in rxn.sec-
1.site-1, the pressure (p) is given in torr, and the universal gas law constant (R) in the units
of calories. mol-1. K-1. The rate is given in rxn.sec-1.site-1.
There has been some speculation about the number of reaction sites that should be
used for different palladium samples. Temperature programmed desorption (TPD) spectra
reveal a saturation surface coverage of 0.3543 to 0.37 ML45 at 270-300K for ethylene on a
well-characterized clean palladium surface, whereas the surface coverage of hydrogen in
presence of ethylene can be 0.19 to 0.4ML. As shown in figure 6-7 different forms of
adsorbed ethylene have been identified on a palladium surface. However, there is evidence,
based on TPD spectra and simulation techniques, that most of these intermediates are
merely spectators. Based on changes in the intensity of the C-H stretching frequencies of
ethylidyne, di-σ and π−adsobed ethylene, hydrogenation is believed to proceed primarily
though the weak π bound species, which occupies only a small portion of the surface, 1.5-
4.5% for palladium and 4% for platinum 46. This indicates a relatively low catalytic activity
for palladium at ambient temperature.
We attempted to examine the number of reaction sites and the catalytic activity of
our palladium film by comparing the measured thermal power with expected heat flow
from the rate expressions shown above. The rate expression in equation (83) was not
applied, as the magnitude of the thermal trace (the rate) was dependant upon the ethylene
concentration and an order of zero for ethylene could not be confirmed. The rate
expression in equation (81) predicted a negative order for the reaction with respect to
ethylene. This would result in a decrease in the rate of the reaction for higher ethylene
259
concentrations, where our results indicated an increase of the rate. Furthermore, the ratio
of the measured thermal response over the calculated values from equation (81) gave a
surface activity of ~2%. For an electrodeposited palladium film, in the absence of a
vacuum system, without a surface cleaning pretreatment procedure, and in the presence of
nitrogen gas and other possible impurities (H2 gas was 99.9% pure, ethylene gas was 99.8%
pure), we expected the surface activity to be much smaller than 2%. Using the rate
expression in equation (82) a maximum of 0.2 % surface activity was calculated, as will be
further discussed below.
The figures below show two sets of runs at different partial pressures for hydrogen
and ethylene. The ethylene was 99.8% pure (Scott Specialty). The flows of hydrogen,
nitrogen and ethylene were regulated with three mass flow controllers (MFC1: ethylene,
MFC2: nitrogen, MFC3: hydrogen)47. The hydrogen flow was kept constant at 20 cc.min-1
for the first run (00-08-16-2) and at 25 cc.min-1 for the second (00-08-23-1). The combined
flow of the gas mixture into the QCM/HCC was 60cc.min-1 for both runs. The flow rates
of nitrogen and ethylene gas were changed periodically to obtain the ethylene partial
pressures shown in figures 6-8(a) and 6-9(a).
The palladium electroplated QCM (141nm Pd thickness) was placed in the left side
of the QCM. Another QCM with a gold surface was placed in the reference side. For both
runs there was a slight increase in the surface mass as the partial pressure of ethylene was
increased (see mass trace in figure 6-9(c)). This is probably due to an increase of surface
concentration of C2 species on the palladium surface. The increase in the magnitude of the
exothermic thermal power for higher ethylene concentrations is directly related to an
increase in the rate of ethylene hydrogenation on the palladium surface. Based on the net
enthalpy of this reaction ethylene was hydrogenated at a rate of ~10-11 mol/sec over an
260
area of 1.307cm2 at the highest ethylene concentration in the gas phase with a turn over
frequency of ca. 2 rxn.sec-1.site-1.
0.3
0.35
0.4
0.45
0.5
10000 20000 30000 40000 50000 60000 70000
Mas
s/µg
Time/sec
0
0.1
0.2
0.3
0.4
0.5
10000 20000 30000 40000 50000 60000 70000
p(C
2H4)/
atm
Time/sec
0
1
2
3
4
5
10000 20000 30000 40000 50000 60000 70000
Ther
mal
pow
er/µ
W
Time/sec
EXO
(c)
(b)
(a)
Figure 6-8: Ethylene hydrogenation over a palladium film (a) p(C2H4) (b) thermal trace (c) mass trace (00-08-16-2)
261
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 5000 10000 15000 20000 25000 30000 35000 40000
Mas
s/µg
Time/sec
00.10.20.30.40.50.60.7
0 5000 10000 15000 20000 25000 30000 35000 40000
p (C
2H4)/
atm
Time/sec
-1.5-1
-0.50
0.51
1.52
0 5000 10000 15000 20000 25000 30000 35000 40000
Ther
mal
pow
er/µ
W
Time/sec
Figure 6-9: Ethylene hydrogenation over a palladium film (a) p(C2H4) (b) thermal trace (c) mass trace (00-08-23-1)
(a)
(b)
(c)
EXO
262
0.0 0.2 0.4
0.0
0.4
Cal
atyl
ic su
rfac
e ac
tivity
/per
cent
are
a
p(C2H4)/atm
Figure 6-10: (a) Baseline corrected thermal power for hydrogenation of ethylene (00-08-16-2) (b) the catalytic surface activity vs. ethylene partial pressure
-1.2-1
-0.8-0.6-0.4-0.2
00.20.4
0 10000 20000 30000 40000 50000 60000 70000
Ther
ml p
ower
/µW
Time/sec
(b)
(a)
263
Based on the lattice parameter of palladium the Pd atom surface population over
an area of 1.307cm2 was estimated to be ~1.72*1015. The values for p(H2) and p(C2H4)
were computed in the rate expression in equation (82) to obtain the reaction rate. Using
the calculated rate of the reaction, the enthalpy of the reaction, and the Pd atom
population, a value for the thermal power was obtained, as if each of the Pd atoms could
be taken as a reaction site. The ratio of the measured thermal power over the calculated
thermal power was then used to obtain the percent Pd atoms at the actual reaction sites.
Figure 6-10(a) shows the baseline corrected thermal power used for this calculation. The
catalytic surface activity as the function of ethylene concentration in figure 6-10(b) exhibits
a slight increase. This must be due to an increase in the surface concentration of π-
adsorbed ethylene.
The catalytic hydrogenation of ethylene over palladium is a complex reaction
involving multiple steps, which can be affected by the nature of the palladium surface.
There is very little data regarding the mechanism and the rate expression for this reaction.
Here we have shown the capability of the QCM/HCC for determining information
regarding the kinetics of this and possibly other catalytic reactions. However, in order to
obtain reproducible results it is crucial that the surface of the palladium film has a uniform
morphology and is clean at an atomic level.
264
6.2 Self assembled monolayer formation of nonylthiol on a gold surface
The term “self assembled monolayer” (SAM) refers to ordered molecular
assemblies formed by the adsorption of an active surfactant on a solid surface48. In 1946
Zisman et al. published the first account of the formation of a self-assembly monolayer of
a surfactant onto a clean metallic surface49. With recent trends in modern chemistry and
the movement towards more interdisciplinary areas of chemistry with biology, physics and
engineering sciences, the science of preparation and manipulation of molecular assemblies
has gained tremendous interest. There has been enormous growth in research in the area
of synthesis and construction of well-defined organic surfaces and interfaces50,51.
Potential applications of self assembled monolayers (SAM)s have been explored in the
areas of corrosion prevention, wear protection in micro machinery, chemical and biological
sensing, and electro-optic devices48,52.
In most cases self-assembly of a monolayer on a surface is the result of strong
interactions of one or more functional groups (head groups) of long chain molecules.
Examples of self-assembled monolayer include:
- adsorption of long chain n-alkanoic acids on metallic surfaces
- polysiloxane formation of organosilicon compounds on silicon oxide,
aluminum oxide, and gold
- alkyl monolayers on silicon
- multilayers of diphosphates
- organosulfur compounds on metallic and semiconductor surfaces
265
Sulfur compounds exhibit strong affinity to surfaces of transition metals such as
palladium, platinum, silver and gold. The most extensively studied SAMs are those of
alkanethiols on gold. Kinetics measurements for adsorption of alkylthiol from gas phase as
well as from dilute solution have been used to determine the reaction rate and
mechanism50,53-56. Karpovich et al. and others have been able to evaluate the
thermodynamic parameters of the adsorption reaction (reaction in equation 84) for SAM
formation from kinetics data 57.
.)(221
)()(.)( solvs
k
kssolv HAuRSAuHRS
a
d
+−↔+−
For low concentrations of sulfur compounds, the kinetics of the adsorption
reaction follows the Langmuir adsorption isotherm and can be described by the equations
below
θθθ
da kCkdtd
−−= )1(
)]exp(1[')])(exp(1[)( tkKtkCk
kk
C
Cobsda
a
dt −−=+−−
+=θ
eqa
d
KC
C
kk
C
C1)(
+=
+=∞θ
Here ? is the fraction of the monolayer formed. By fitting the experimental data to
the right hand side of equation (86) the values of observed rate constant (kobs.) can be
(84)
(85)
(86)
(87)
266
determined and plotted vs. C (concentration of thiol) for a series of thiol concentrations.
This plot gives a straight line whose slope and intercept will be the rate constants for the
adsorption and desorption reactions (ka and kd), respectively. And finally, the ratio of the
rate constants (ka/kd) of the two elementary adsorption and desorption reactions, gives the
equilibrium constant for the adsorption reaction of self-assembled monolayer formation57.
Using this procedure one can determine the thermodynamic quantities ∆adsorptionG,
∆adsorptionH, and ∆adsorptionS for the adsorption reaction from kinetic data. In the following
section we will present the results of one such experiment and compare those to our own
results.
Dr. Neal Shinn from the Sandia National Laboratories kindly provided us with a
purified nonylmercapten (C9H21SH) sample and treated three of our AT-cut 5 MHz
QCMs, through a common procedure in their laboratory, in order to reduce their surface
roughness to <10Å rms. During this procedure the thin gold electrodes are removed and
redeposited slowly in vacuum so that the resulting gold electrode can have a small surface
roughness relative to the dimensions of the SAM to be formed52.
The gas flow setup of the QCM/HCC had to be redesigned for this experiment.
The usual bubble-through container could not be used, since only a trace amount of
nonylthiol vapor was needed. Even if a very small gas flow was to be passed through the
bubble through container, the gas flow controllers in the flow setup could not function as
shutoff valves when the flow was set to zero. Very small quantities of the gas could leak
into the gas stream prematurely and initiate the SAM formation. Several attempts were
made to design a method for sample introduction without perturbation of the overall gas
flow. In the first experiment a 3 liter gas cylinder was filled with nitrogen along with 2 ml
of liquid nonylthiol sample. This cylinder was connected to the flow system through a T-
267
adaptor. The valve of the cylinder was opened so that some of the thiol vapor could leak
into the gas stream. The thermal events due to fluctuations in the gas pressure inside the
QCM/HCC as the valve was opened were larger then the expected heat signal from SAM
formation.
Next a small GC vial with a Teflon septum was used. The gas flow of the sample
side (right side) of the QCM/HCC was redirected through the GC vial as shown in figure
6-11. A few microliters of the liquid thiol was injected into the GC vial. The liquid was
kept at the tip of the syringe needle and was monitored as it slowly vaporized and
eventually disappeared. In the (00-07-05-1) run two drops were injected at t=17116sec and
t=18205sec. The mass and thermal traces are shown in figure 6-12 (a) and (b). Since two
separate injections were made the SAM formation proceeded in two steps. This allowed us
to compare the energetics of the process at two different points along the reaction
coordinate. The energetics of the SAM appeared to get larger as the reaction proceeded.
Possible implications of this observation will be discussed below.
To QCM/HCC N2
Figure 6-11: Sample introduction setup for SAM formation experiment
Nonylthiol droplet
268
0
0.05
0.1
0.15
0.2
16000 17000 18000 19000 20000 21000 22000 23000
Mas
s/µg
Time/sec
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
16000 17000 18000 19000 20000 21000 22000 23000
Ther
mal
pow
er/µ
W
Time/sec
(a)
(b)
20000
-0.4
0.0
0.4
Ther
mal
pow
er/µ
W
Time/sec
(c)
Figure 6-12: (a) mass trace of the self assembled monolayer formation of nonylthiol on a QCM, (b) thermal trace for self assembled monolayer formation
of nonylthiol, (c) automatic baseline assignment to the thermal trace by OriginTM
EXO
?=0.89
?=0.54
269
20000
-0.5
0.0
0.5
Ther
mal
pow
er/µ
W
Time/sec
15000 20000 25000
0.0
0.5
Ther
mal
pow
er/µ
W
Time/sec
15000 16000 17000 18000 19000 20000 21000 22000 23000
0
50
100
150
200
250
300
Inte
grat
ed h
eat/
µJ
Time/sec
20000
-0.5
0.0
Ther
mal
pow
er/µ
W
Time/sec
20000
0.0
Ther
mal
pow
er/µ
WTime/sec
15000 16000 17000 18000 19000 20000 21000 22000 23000-20
0
20
40
60
80
100
120
140
160
180
Inte
grat
ed H
eat/
µJ
Time/sec
(a)
(b)
(c)
(d)
(e)
(f)
5µJ
125µJ
288µJ
-2µJ
69µJ
162µJ
Figure 6-13: (a) thermal power with baseline fit (I) (b) thermal power, baseline fit (I) subtracted
(c) integrated heat using baseline fit (I) (d) thermal power with baseline fit (II)
(e) thermal power, baseline fit (II) subtracted (f) integrated heat using baseline fit (II)
270
The mass increase on the QCM surface for this run was obtained from Suerbrey’s
equation in the usual manner. The thermal peaks shown in figure 6-12 (b) have been the
smallest thermal events we have ever attempted to quantify. For such small thermal events
the baseline assignment is crucial. Two fits for the baseline and resulting values for the
integrated heat are shown in figures 6-13 (b) (c) (e) and (f). For baseline fit(I) the baselines
before and after the thermal peak have been connected by a straight line. Baseline fit(II) is
an extension of the baseline after the peak back to baseline before the peak. We believe the
integrated heats obtained using the baseline fit(II) to be closer to the true values. The
resulting values for the enthalpy of self-assembled monolayer formation are 135kJ.mol-1
and 244kJ.mol-1 for the first and second portion of SAM formation, respectively.
No direct measurements of the ∆SAM formationH have been reported in the literature.
To examine the validity of our measurements we consider the energetics of the steps
involved in order to establish a basis for comparison. Figure 6-14 shows the breakdown of
the individual steps. The fate of the hydrogen atom on the gold surface will be discussed
later in this section. At this point for the sake of simplicity we will ignore the contributions
of hydrogen to the energetics of the SAM formation. At the beginning of the process and
for low surface coverage by nonylthiol the observed heat is the sum of the heats of
condensation of alkylthiol and its adsorption through the sulfur head group on gold.
Towards the end of SAM formation process and for a higher surface coverage the
formation of a densely packed assembly is analogous to crystallization of the alkylthiol.
The energy involved to disrupt the packing of this assembly (leaving the S-Au bond intact)
should require the same energy as the heat of fusion. No enthalpies of either condensation
or fusion for nonylthiol could be found in the literature. Figures 6-15 (a) and (b) are the
enthalpies of condensation and fusion of other straight chain alkylthiols (with sulfur at
271
position 1), which were used to extrapolate the ∆condensationH and ∆fusionH for nonylthiol.
Alkylthiol compounds lose the hydrogen atom bonded to sulfur upon adsorption on gold.
Since sulfur doesn’t exhibit any appreciable H-bonding, the values for enthalpies of
condensation and fusion of the parent alkythiol before adsorption can still be applied.
Karpovich et al. using kinetics data and the methodology described earlier have
reported the enthalpy of adsorption of alkylthiol compounds from a solution onto a gold
surface to be –84 kJ.mol-1. This value is claimed to be for the initial adsorption of the thiol
moiety and independent of the nature of the alkyl tail group57. Estimating a dissolution
enthalpy of +33 kJ.mol-1 for their alkylthiol sample in hexane they propose the magnitude
of the actual ∆adsorptionH to be larger and report a value of –117 kJ.mol-1 for the ∆adsorptionH
from gas phase based on their own findings and results from the work of Nuzzo et al.
published elsewhere. The reference used to arrive at this figure actually cites the activation
energy of desorption of dimethyldisulfide, which should not have been compared to
results for an alkythiol. This must have been an oversight. In the same reference Nuzzo
also reported the activation energy for desorption of methylthiol at low surface coverage
into vacuum to be –58kJ.mol-1 and relates this value to the ∆SAM formationH of methylthiol on
gold56. Table 6-3 gives a summary of the heat of individual steps involved in SAM
formation.
The extent of surface coverage by alkylthiol on gold was calculated from the mass
signal and the area occupied by the head groups during SAM formation (at ?~1, S-S
spacing is 4.97 Å with an area of 21.4Å2/alkylthiol molecule)48 over the entire area of the
QCM gold electrode (1.31cm2).
272
H
Gas phase
Adsorbed SAM ∆adsorption(S-Au)H ∆condensationH
∆crystallizationH
∆adsorption(S-Au)H ∆condensationH ∆crystallizationH ∆SAMformation H
Gold Substrate
H
H H
H
Figure 6-14: Break down of energetics of SAM formation
273
0
5
10
15
20
25
30
35
40
2 4 6 8 10 12 14
alkanesalkylthiolsE
ntha
lpy
of f
usio
n/kJ
mol
-1
Number of carbon atoms
-70
-60
-50
-40
-30
-20
0 2 4 6 8 10 12
y = -17.547 - 4.7835x R2= 0.99989
Ent
halp
y of
con
dens
atio
n/kJ
mol
-1
Number of carbon atoms
(b)
(a)
Figure 6-15: Enthalpy of (a) condensation (b) fusion for straight chain alkyl thiols (sulfur at position 1)
274
Table 6-3: Summary of reported and measured values of enthalpy of SAM formation and other
related reactions
(1)∆bond formationG (RS-Au)/kJ.mol-1 -23 ref 48
(2)∆condensationH (C9H19SH)/kJ.mol-1 -61 Figure 6-15
(3)∆condensationH (CH3SH)/kJ.mol-1 -22 Figure 6-15
(4)∆crystallizationH (C9H19SH)/kJ.mol-1 -40 Figure 6-15
(5)∆adsorptionH (RS-Au from solution)/kJ.mol-1 -84 ref 57
(6)∆adsorptionH (CH3S-Au from gas phase)/kJ.mol-1 -58 ref 56
(7)∆sorptionH (H in Au)/kJ.molH-1 -9 ref 59
(8)∆SAM formationH (C9H19SH at low surface coverage)/kJ.mol-1 -154 (2)+(5)+(7) based on ref57
(9)∆SAM formationH (C9H19SH at high surface coverage)/kJ.mol-1 -194 (8)+(4) based on ref57
(10)∆SAM formationH (C9H19SH at low surface coverage)/kJ.mol-1 -106 (2)+(6)+(7)-(3) based on ref56
(11)∆SAM formationH (C9H19SH at high surface coverage)/kJ.mol-1 -146 (10)+(4) based on ref56
(12)∆SAM formationH (C9H19SH at low surface coverage)/kJ.mol-1 -135 measured by QCM/HCC
(13)∆SAM formationH (C9H19SH at high surface coverage)/kJ.mol-1 -244 measured by QCM/HCC
275
The enthalpy of sorption of hydrogen into gold has been listed in table 6-3,
because there has been some evidence that the atomic hydrogen resulting from the
adsorption of alkythiol could be absorbed into the gold substrate rather than to recombine
forming H2 gas 58,59. Although hydrogen has a low sticking probability on gold at room
temperature, if atomic hydrogen can be generated on a gold surface it will absorb into the
bulk. Azofeifa et al. have shown the same behavior for sorption of hydrogen in
aluminum60. The sticking probability of hydrogen gas on aluminum at room temperature
is less than 10-4. But when a thin palladium film was deposited on an aluminum coated
QCM the hydrogen could be delivered to the aluminum surface in a state in which it could
be absorbed to give concentrations as high as 0.9% by mass.
The measured values of the ∆SAM formationH are within the same order of magnitude
as those obtained by other indirect methods. The fact that the magnitude of the ∆SAM
formationH increases for higher surface coverage is an indication of the validity of the model
proposed for breaking down the individual steps involved in SAM formation (see figure 6-
14). In order to further examine the accuracy of this model we recommend a set of
experiments with a homologous series of straight chain alkylthiols. For such series the
same heat will be detected for the adsorption of the thiol moiety on gold but the enthalpies
of condensation and fusion will increase for increasing number of carbon atoms.
In closing we remind the readers once again of the difficulties encountered during
baseline assignment and sample introduction for this experiment. Some of the heat
detected during the SAM formation could be due to other processes such as fluctuations in
the pressure inside the QCM/HCC. Furthermore, since in this experiment the alkylthiol
sample was introduced only through one side of the QCM/HCC, we can’t claim a true
differential setting (pure nitrogen was flown through the reference side). Adsorption of the
276
alkylthiol on surfaces other than the QCM may have caused small extraneous thermal
events.
A detailed review of the literature for the catalytic ethylene hydrogenation and
SAM formation was not provided. However, we have shown the application of the
QCM/HCC in important areas of surface catalysis and molecular self-assembly, where no
direct measurements of the energetics of the reactions have been reported before. The
experiment for the SAM formation of nonylthiol on gold is a good example of the high
sensitivity of the two sensors of the QCM/HCC. Using the experience and knowledge
gained during these experiments we hope to be able to repeat our measurements and
report our results to other investigators.
277
References
(1) Van Blarigan, P.; Keller, J. O. Int. J. Hydrogen Energy 1998, 23, 603-609.
(2) Goudy, A. J. , University of Pittsburgh, 1976.
(3) Goudy, A.; Wallace, W. E.; Craig, R. S.; Takeshita, T. Adv. Chem. Ser. 1978, 167,
312-26.
(4) Dantzer, P. Top. Appl. Phys. 1997, 73, 279-340.
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298.
281
Chapter 7- Experiment 4: Hydration/dehydration of lysozyme
7.1 Introduction
Lysozyme is a globular protein of mass 14.6 kDa (Hen egg white (HEW)
lysozyme), which was first discovered by Alexander Fleming. It is an enzyme that destroys
bacterial cell walls1. It has been detected in many tissues and secretions of body including
tears, saliva, skin, and fingernails, where it helps to dispose of bacteria after they have been
killed by other means. Lysozyme has 129 amino acid residues cross-linked by four disulfide
bonds. Its X-ray structure reveals an ellipsoidal shape with dimensions 30×30×45Å1. Most
of its nonpolar side chains reside in the interior of the molecule. Lysozyme has been
studied extensively, in particular with respect to its hydration/dehydration behavior at
different water contents2.
In general, protein-water interactions may alter the three-dimensional structure of
proteins and therefore their overall stability as well as some of their functions such as their
catalytic activity. There have been a number of reviews summarizing studies of protein-
water interactions2-8. Studies in this area can be categorized into two groups. Some have
employed protein solutions, where the water activity has been controlled by manipulating
the percent composition of water-cosolvent mixtures. Others have studied hydrated
protein powders, films, or glasses. The most interesting properties of proteins are those
observed at low water content in the absence of bulk water. In most cases the intercellular
environment in which proteins function in vivo resembles hydration states for hydrated
powders and films more than dilute solutions2. For these low water content states,
282
variation in the amount of internal and surface water for a protein can have pronounced
effects.
Water vapor sorption isotherms show three possible regions where incoming water
may reside8:
- region(I), binding sites at charged and highly polar groups (monolayer
coverage)
- region(II), binding sites on the polypeptide backbone and less polar groups
(onset of transition from monolayer to multilayer).
- region(III), condensation of H2O at very weak binding sites and further
growth of water multilayers.
Studying the nature of a protein for a given degree of hydration helps in
understanding the chemical stability, conformational stability and the activity of the
protein. Residual moisture content beyond a monolayer increases the conformational
flexibility and the ability of less bound water to mobilize reactants, thereby accelerating
decomposition of the protein. On the other hand, overdrying exposes the surface of the
protein and may result in unwanted reactions such as aggregation and ultimately
denaturation. The amount of absorbed water can also determine the mechanical properties
of a protein. Water acts as a plasticizer2. Its addition increases the free volume and
suppresses the glass transition temperature (Tg).
Lysozyme is rather robust with regard to decomposition. Its denaturation
temperature remains constant for water contents down to 0.4 g water/g Lysozyme (h), but
it increases sharply for drier samples (at h>0.4, Td=343K and ∆denaturationH=300kJ.mol-1)9.
A wide variety of spectroscopic, calorimetric (mostly DSC) and other techniques
have been used for characterization of changes in the properties of lysozyme during
283
hydration/dehydration experiments. In all cases there is evidence of changes in the
conformation of lysozyme. These changes do not correspond to folding/unfolding of the
protein but are rather slow processes best described as expansion and compression10.
Solid state NMR studies of some proteins have shown the existence of a population of
possible conformations, whose distribution increases during dehydration11. Traditionally
infrared spectra have been used to monitor the removal of water. It has been suggested
that spectral perturbations can be due more to conformational changes rather than water
removal12.
Heat capacity measurements at different hydration states of lysozyme have
revealed several distinct regions along the plot of heat capacity vs. the extent of hydration
(h)13. The heat capacity is constant for dilute solutions down to 0.38 h (g water/g protein).
In the range 0.38>h>0.27 the heat capacity increases slightly. The water is believed to be
bound to weakly interacting nonpolar sites in this region. For 0.27>h>0.07 the heat
capacity of lysozyme decreases. In this range the water is bound to main chain carbonyl
groups and other polar surface regions. For lower values of h the heat capacity increases
slightly. The remaining water in this region is believed to be in strong interaction with
ionizable groups. The changes in the heat capacity measurement can be correlated to the
individual regions of the sorption isotherm, (vide infra).
Measurements of the amount of nonfreezing water in lysozyme have also been
used to determine the critical water content for a monolayer coverage of lysozyme.
Nonfreezing H2O is the amount of water incapable of forming ice because of interactions
with protein. To determine the amount of nonfreezing water the hydrated protein is
cooled down to –400C where the intensity of NMR peaks for ice and free water are
284
compared14. NMR measurements give 0.34 g H2O/g protein (h) as the amount of
nonfreezing water in lysozyme. This is in good agreement with heat capacity
measurements, which show that below h=0.38 the water is at least weakly bound to the
protein.
7.2 Experimental
The work presented here has been the result of efforts of three persons. Miss
Justine Ciraolo was involved in the initial evaluation of the proper thin film preparation
methods from lysozyme solution and some of the earlier measurements, which are not
shown here. Sister Rose Mulligan and Hamid Shirazi have worked closely during the thin
film preparation and the hydration/dehydration experiments. Sister Rose Mulligan was
also responsible for conducting an independent mass measurement of the lysozyme film
using a UV spectrophotometer. Her efforts during the data analysis should also be
acknowledged.
Hen egg white (HEW) lysozyme from Sigma (L-6876, Lot 65H7025) was used
without further purification to prepare an unbuffered, dilute solution in dionized water.
The QCM was cleaned in a Piranha solution in the usual manner. A thin film of lysozyme
was deposited on the larger gold electrode of the QCM using an air brush (Badger, Model
200). The lysozyme solution was sprayed using nitrogen at 15 psi (research grade 5.0 BOC)
as carrier gas. To ensure uniformity of the lysozyme film the airbrush was constantly
moved from the top to bottom and left to right at a distance of 20cm above the surface of
the QCM at an approximate rate of twice per second. After two to three applications of
the lysozyme solution four/five strokes of only nitrogen were sprayed to allow for some
drying of the film. This process was continued until a thin film became visible. The coated
285
QCM was placed in the right side of the QCM/HCC. A QCM with a clean gold surface
was used in the reference side.
During the hydration/dehydration experiments the water vapor activity was
changed periodically between 0.89 (or 28000ppm) to 0 (0ppm) at 250C in six separate runs.
Each one of the first five hydration runs consisted of 5 successive hydration/dehydration
steps. Each step was about 4000sec long and corresponded to 1000ppm (~3% RH)
increase/decrease in the water vapor concentration above the lysozyme film. The sixth run
consisted of only three hydration/dehydration steps, each corresponding to a 1000ppm
change in the water vapor concentration. At the beginning of each run the lysozyme thin
film was conditioned for six hours at the highest water vapor activity for that run followed
by five decreasing steps in the aH2O. Figures below show the gas flow pattern for each run
and the resulting mass change and heat flow in the lysozyme sample. The mass at the
lowest water activity was taken as the mass of the dry lysozyme film. The task of assigning
the proper baseline for the thermal trace has been very difficult, since there was a shift in
the baseline for most of the hydration/dehydration steps. After the assigned baseline was
subtracted, the thermal trace was integrated over time. The plot of the ratio of the
integrated thermal trace over the mass trace (converted to moles of water) was used to
determine the enthalpy of hydration for lysozyme (∆hydrationH). One such treatment of the
data for the (00-02-03-2) run is shown in figure 7-3. The sharp transient peaks in figure 7-
3(a) are due to the difference in the time constants of the mass and heat flow sensors. For
the last desorption step as the value for the mass approaches zero, the ratio of integrated
heat over mass becomes too large resulting the large peak at the end of the curve. This
graph illustrates that the enthalpy of hydration can be measured under non-equilibrium
286
conditions. The values for ∆hydrationH at different water vapor activities have been tabulated
below (see table 7-1).
42
44
46
48
50
52
54
56
10000 20000 30000 40000 50000 60000 70000
Mas
s/µg
Time/sec
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-10
0
10
20
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40
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The
rmal
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W
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0.7
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p/p0
Time/sec
32
33
34
35
36
37
38
39
10000 20000 30000 40000 50000 60000 70000
Mas
s/µg
Time/sec
0.55
0.6
0.65
0.7
0.75
10000 20000 30000 40000 50000 60000 70000
p/p0
Time/sec
-20
-10
0
10
20
30
40
10000 20000 30000 40000 50000 60000 70000
The
rmal
pow
er/µ
W
Time/sec
Figure 7-1: lysozyme hydration/dehydration (a) water vapor activity (00-02-03-2) (b) mass trace (00-02-03-2) (c) thermal power (00-02-03-2) (d) water vapor activity (00-02-04-1) (e) mass trace (00-02-04-1) (f) thermal power (00-02-04-1)
(f)
(a)
(b)
(c)
(d)
(e)
EXO
287
0.4
0.45
0.5
0.55
0.6
10000 20000 30000 40000 50000 60000 70000
p/p
0
Time/sec
24
25
26
27
28
29
10000 20000 30000 40000 50000 60000 70000
Mas
s/µg
Time/sec
-10
-5
0
5
10
15
20
25
30
10000 20000 30000 40000 50000 60000 70000
The
rmal
pow
er/µ
W
Time/sec
0.2
0.25
0.3
0.35
0.4
0.45
10000 20000 30000 40000 50000 60000 70000
p/p0
Time/sec
17
18
19
20
21
22
23
10000 20000 30000 40000 50000 60000 70000
Mas
s/µg
Time/sec
-20
-10
0
10
20
30
10000 20000 30000 40000 50000 60000 70000
The
rmal
pow
er/µ
W
Time/sec
Figure 7-2: lysozyme hydration/dehydration (a) water vapor activity (00-02-06-1) (b) mass trace (00-02-06-1) (c) thermal power (00-02-06-1) (d) water vapor activity (00-02-07-1) (e) mass trace (00-02-07-1) (f) thermal power (00-02-07-1)
(b)
(c)
(a) (d)
(e)
(f)
288
0.05
0.1
0.15
0.2
0.25
0.3
10000 20000 30000 40000 50000 60000 70000
p/p
0
Time/sec
7
8
9
10
11
12
13
14
10000 20000 30000 40000 50000 60000 70000
Mas
s/µg
Time/sec
-20
-10
0
10
20
30
40
10000 20000 30000 40000 50000 60000 70000
The
rmal
pow
er/µ
W
Time/sec
0
0.02
0.04
0.06
0.08
0.1
0.12
10000 20000 30000 40000 50000 60000 70000
p/p
o
Time/sec
0
1
2
3
4
5
6
7
8
10000 20000 30000 40000 50000 60000 70000
Mas
s/µg
Time/sec
-40
-20
0
20
40
60
10000 20000 30000 40000 50000 60000 70000
The
rmal
pow
er/µ
W
Time/sec
Figure 7-3: lysozyme hydration/dehydration (a) mass trace (00-02-09-2) (b) thermal power (00-02-09-2) (c) water vapor activity (00-02-09-2) (d) mass trace (00-02-10-1) (e) thermal power (00-02-10-1) (f) water vapor activity (00-02-10-1)
(c)
(b)
(a) (d)
(e)
(f)
289
10000 20000 30000 40000 50000 60000
0
5000
10000
15000
20000
25000
30000
Inte
grat
ed h
eat /
µJ
Time / sec
10000 20000 30000 40000 50000 60000-30
-20
-10
0
10
20
Ther
mal
Pow
er/µ
WTime/sec
0
20
40
60
80
100
120
10000 20000 30000 40000 50000 60000 70000
Time/sec
Hyd
ratio
n en
thal
py/k
J.mol
-1
Figure 7-4: determination of the enthalpy of hydration for lysozyme (a) baseline subtracted thermal power (00-02-03-2)
(b) integrated heat (00-02-03-2) (c) ratio of the integrated heat trace over the mass trace (00-02-03-2), enthalpy of
hydration of lysozyme
(c)
(b)
(a)
290
Table 7-1: Enthalpy of hydration/dehyration of lysozyme as a function of water vapor activity
∆hydrationH ∆hydrationS ∆dehydrationH
a H2O mass% (kJ/mol) (J/mol.K) a H2O mass% (kJ/mol)
0.03 0.3 -71 -203 0.03 0.5 71 0.06 1.6 -65 -173 0.06 1.8 62 0.10 2.4 -62 -163 0.10 2.4 62 0.13 3.4 -62 -162 0.13 3.7 50 0.16 3.9 -57 -147 0.16 4.1 49 0.19 4.3 -55 -142 0.19 4.4 50 0.22 4.5 -55 -141 0.22 4.6 52 0.26 4.8 -54 -138 0.26 4.8 54 0.29 6.8 -51 -127 0.29 6.9 58 0.32 7.1 -54 -139 0.32 7.2 52 0.35 7.4 -54 -139 0.35 7.5 50 0.38 7.7 -53 -134 0.38 7.8 50 0.42 8.0 -51 -128 0.42 8.0 51 0.45 9.1 -44 -105 0.45 9.2 34 0.48 9.4 -43 -103 0.48 9.5 37 0.51 9.7 -46 -113 0.51 9.8 41 0.54 10.0 -46 -113 0.54 10.0 44 0.58 10.2 -46 -111 0.58 10.2 46 0.61 11.6 -46 -111 0.61 11.7 50 0.64 11.9 -48 -118 0.64 12.1 44 0.67 12.3 -48 -119 0.67 12.5 42 0.70 12.6 -46 -111 0.70 12.8 42 0.74 13.1 -44 -105 0.74 13.1 44 0.77 14.8 -48 -119 0.77 15.1 57 0.80 15.2 -47 -115 0.80 15.7 46 0.83 15.8 -45 -109 0.83 16.4 43 0.86 16.6 -42 -98 0.86 17.0 42 0.90 17.7 -44 -104 0.90 17.7 44
291
7-3 Results and discussions
We are not aware of any direct calorimetric measurements of the enthalpy of
hydration of lysozyme. However, the ∆hydrationH has been determined indirectly by
gravimetric techniques4,5, dielectric spectroscopy15 and other measurements conducted at
a series of different temperatures and employing the van’t Hoff expression. Lüscher-Mattli
et al. have reviewed hydration enthalpy determinations for ten proteins including lysozyme,
which have been computed from gravimetric measurements yielding hydration isotherms
at various temperatures16. The lysozyme hydration isotherm has the typical sigmoidal
shape of BET isotherms. D’Arcy and Watt have added an additional term to the usual
BET type isotherm of proteins to account for water sorption at the weak binding sites17.
04
4302
01
01
11
'
ppK
KKp
pK
ppK
ppKh
hp
−++
+=
p/p0 is the water vapor activity. h is the degree of hydration (g H2O/g lysozyme).
h’p (0.036 for lysozyme) and K1 (30.91 for lysozyme) are constants proportional to the
number and activity of the ionizable and highly polar groups (region I). K2 (0.1336 for
lysozyme) is proportional to the number of weak binding sites (the peptide backbone,
regionII). K3 (0.0215 for lysozyme) and K4 (0.9392 for lysozyme) correspond to the
number and affinity of water at the multilayer binding sites. Using the total mass of
lysozyme and the sorbed water at different water vapor activities, we have computed the
(88)
292
water vapor sorption isotherm for lysozyme from our data and compared it to that
reported by others5.
Figure 7-5 shows the breakdown of the contributions of the individual terms in the
D’Arcy and Watt equation. As can be seen in this figure our measured values used for
constructing the sorption isotherm are in good agreement with those reported by other
investigators. Contrary to the sorption isotherm for hydrogen sorption in palladium and
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1
h (g
H2O
/g ly
sozy
me)
p/p0
1
2
3
4
5
Figure 7-5: D’Arcy and Watt sorption isotherm for water vapor sorption by lysozyme (1) first term of D’Arcy Watt equation, water sorption in region(I) (2) second term, weak nonpolar sorption sites, region (II) (3) sorption at multilayer binding sites, region (III) (4) combined terms
(5) measurements by QCM/HCC
293
inert gases (Helium and Argon) in lysozyme, water vapor sorption in lysozyme is
independent of the surface to volume ratio of the sample2. We believe that our measured
sorption isotherm is lower than that of Lüscher-Mattli’s5, because we were not able to
remove all water form lysozyme at the lowest humidity. In other words, some of the mass
attributed to the dry lysozyme sample (250.9µg) was due to a small amount of buried
water, which is very difficult to remove. For determining the mass of dry proteins, others
have stored their sample at the lowest hydration level in vacuum over phosphorous
pentoxide for several days, or at an elevated temperature (1050C) for 24 hours16. At room
temperature the lowest hydration level obtainable in vacuum for pressures above 10-6 torr
has been estimated to be 0.01h or 8 moles of water/mole protein2. Correcting for the
residual amount of water at the lowest water vapor activity will raise the sorption isotherm
slightly and improve its agreement with prior experimental results.
The discontinuity in the sorption isotherm for different runs is due to hysteresis in
the absorption/desorption cycle in lysozyme. This phenomenon has been observed for
many protein-water systems. Figure 7-6 (a) and (b) illustrates how lysozyme differs from
Tecoflex (discussed in chapter 5) with respect to the amount of water sorbed for the same
water vapor activity, the time scale for the process, and hysteresis. For the lysozyme
sample different water contents are obtained depending on the path of the hydration
process (within the time scale of this experiment). This is attributed to gradual
conformational changes during the hydration/dehydration process. The amount of interior
water in the lysozyme determines its structural conformation and the extent of exposure of
the interior water binding sites, which in turn can cause gradual changes in the amount of
the interior water itself.
294
0
0.5
1
1.5
2
2.5
3
1600 3200 4800 6400 8000
Mas
s/µg
Time/sec
0
5
10
15
20
27200 28800 30400 32000 33600
Mas
s/µg
Time/sec
-150
-100
-50
0
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100
150
200
250
27200 28800 30400 32000 33600
The
rmal
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W
Time/sec
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
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1600 3200 4800 6400 8000
The
rmal
pow
er/µ
W
Time/sec
0
0.2
0.4
0.6
0.8
1
1600 3200 4800 6400 8000
p/p
0
Time/sec
0
0.2
0.4
0.6
0.8
1
27200 28800 30400 32000 33600
p/p
0
Time/sec
(c)
(b)
(a) (d)
(e)
(f)
Figure 7-6: Water vapor sorption in Tecoflex (99-10-26-2) (a) water vapor activity (b) mass trace (c) thermal power;
water vapor sorption in lysozyme (99-08-10-2) (d) water vapor activity (e) mass trace (f) thermal power
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Dr. S. Bone of the University of Wales, UK, kindly provided us with the original
data from one of his publications, in which the enthalpy of hydration of lysozyme was
determined from hydration isotherm measurements as a function of temperature15.
Figure 7-7 shows the results of the measurements by QCM/HCC (figure a) and those by
Bone et al. (figure b). Our measured values are somewhat lower but follow the same
trends. Interestingly there is a discontinuity at mass%~10 in both cases (see arrows in
figure 7-7). Bone et al. have related this phenomenon to the possibility of a re-ordering of
the lysozyme-bound water from a more disordered (dispersed) to an ordered (clustered)
structure. Figure 7-8 (b) shows reported values of hydration enthalpy by Lüscher-Mattli
obtained form hydration isotherms16. These results are closer to our measured values at
high water vapor activities. However, a decrease in the magnitude of the hydration
enthalpy at mass% <5 could not be confirmed by our measurements.
The baseline assignment for the thermal traces of this experiment has been very
difficult. Small variations in the position or curvature of the baseline for a peak integrated
over 4000sec or longer resulted in very large effects in the final value for the hydration
enthalpy. Although a recalibration procedure of the thermopiles was conducted, we take
the coincidence of the enthalpy of hydration at the highest water vapor activity with the
enthalpy of condensation of water (-44kJ/mole) as the validation of the measured values
for lysozyme hydration enthalpies at lower water vapor concentrations.
Figure 7-8 (a) shows the calculated values for the entropy of hydration of
lysozyme. These also show a break at mass%~10 and approach the entropy of
condensation of water for higher water vapor activities (-118.8 J.mol-1.K-1).
296
Figure 7-7: Hydration enthalpy of lysozyme as the function of water content (a) QCM/HCC measurements (b) from temperature dependence of gravimetric
measurements by Bone (ref 15) and Lüscher-Mattli (ref 16)
-65
-60
-55
-50
-45
0 5 10 15 20
BoneLuscher-Mattli
Ent
halp
y of
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rati
on/k
J.m
ol-1
Mass%
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-60
-55
-50
-45
-40
0 5 10 15 20
Ent
halp
y of
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ratio
n/kJ
.mol
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Mass%
(a)
(b)
297
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-160
-140
-120
-100
-80
0 5 10 15 20
Ent
ropy
of
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atio
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mol
-1K
-1
Mass%
Figure 7-8: Entropy of hydration of lysozyme as a function of water content (obtained form QCM/HCC measurements)
298
We are pleased with the outcome of this experiment. We realize the strong need
for direct calorimetric measurements of the energetics of protein-water interactions.
Results of such measurements can provide a better understanding of important processes
such as protein folding, unfolding, misfolding and enzymatic activity. We hope to develop
a more accurate and efficient thermal peak integration method for the next set of
experiments. For future experiments we also recommend the measurement of the mass of
the dry protein sample at elevated temperatures after the completion of the experiment to
improve the accuracy of the sorption isotherm. Furthermore, measurements of the
diffusion coefficient of water in the protein sample at different points in time for several
hydration/dehydration steps may provide information regarding the time scale of changes
in the conformation of proteins at different degrees of hydration.
299
References
(1) Voet, D.; Voet, J.; Pratt, C. Fundamentals of biochemistry; John Wiley & Sons. Inc:
New York, 1999.
(2) Gregory, R. B. In Protein-Solvent Interact.; Marcel Dekker, Inc.: New York, 1995.
(3) Kuntz, I. D., Jr.; Kauzmann, W. Advan. Protein Chem. 1974, 28, 239-345.
(4) Luescher-Mattli, M.; Ruegg, M. Biopolymers 1982, 21, 419-29.
(5) Luescher-Mattli, M.; Ruegg, M. Biopolymers 1982, 21, 403-18.
(6) Rupley, J. A.; Gratton, E.; Careri, G. Trends Biochem. Sci. (Pers. Ed.) 1983, 8, 18-22.
(7) Rupley, J. A.; Careri, G. Adv. Protein Chem. 1991, 41, 37-172.
(8) Towns, J. K. J. Chromatogr., A 1995, 705, 115-27.
(9) Fujita, Y.; Noda, Y. Bull. Chem. Soc. Jpn. 1978, 51, 1567-8.
(10) Morozov, V. N.; Morozova, T. Y.; Kachalova, G. S.; Myachin, E. T. Int. J. Biol.
Macromol. 1988, 10, 329-36.
(11) Gregory, R. B.; Gangoda, M.; Gilpin, R. K.; Su, W. Biopolymers 1993, 33, 1871-6.
(12) Prestrelski, S.; Tedeschi, N.; Arakawa, T.; Carpenter, J. F. Biophys. J. 1993, 65, 661-
71.
(13) Yang, P.-H.; Rupley, J. A. Biochemistry 1979, 18, 2654-61.
(14) Kuntz, I. D., Jr. J. Amer. Chem. Soc. 1971, 93, 516-18.
(15) Bone, S. Phys. Med. Biol. 1996, 41, 1265-1275.
(16) Luescher-Mattli, M. In Thermodynamic data for biotechnology; Hinz, H.-J., Ed.; Springer-
Verlag: Berlin, 1986.
(17) D'Arcy, R. L.; Watt, I. C. Trans. Faraday Soc. 1970, 66, 1236-45.
300
Chapter 8- Summary and suggestions for future activities
8.1 Summary and suggestions for future activities, chapters 1-4
In the previous chapters, reviews of applications and operation of the mass and
heat flow sensors of the QCM/HCC were given. In the description of the QCM/HCC we
have shown how these two sensors have been coupled in such manner for the first time.
The description of the complete QCM/HCC setup including its LabView control program
in chapter 4 was intended as a reference document for future users of the QCM/HCC.
Below are a few considerations for possible improvements of the future designs of the
QCM/HCC.
1) Minimizing the time constant (t) for heat flow measurements.
2) Introducing a three-way valve (controlled by the LabView program) to the gas
flow system.
3) Eliminating the housing of the QCM/HCC.
4) Developing new convenient procedures for routine calibration of thermopiles.
5) Developing an accurate and time efficient peak integration procedure.
6) Further development of the LabView control program to make it user-
friendlier.
1) Minimizing the time constant (t) for heat flow measurements: The present time
constant for the thermal trace (~53sec) can be reduced, if the mass of the material in the
thermal path between the surface of the QCM and the thermopile can be minimized.
301
Currently there are two D-shaped brass electrodes in a Kel-F frame providing the electrical
contacts for the oscillating QCM, which are positioned between the QCM and two
thermopiles connected in series. For future designs we have considered positioning the
QCM directly on a thermopile with a hole in the center. In this configuration the
oscillating region of the QCM does not make contact with the thermopile and the
electrical contact to the QCM can be made through two thin gold films evaporated on the
top face of the thermopile.
2) Introducing a three-way valve (controllable by the LabView program) to the gas
flow setup: When the input voltage to the mass flow controllers in the gas flow setup is set
to zero a very small flow of the carrier gas (<0.1 cc/min) may still be detected.
Furthermore, the MFC2 has been positioned upstream from the bubble-through container
to eliminate the need of recalibration of the MFC for each solvent vapor used (see figure
4.3). Even with no flow through the MFC2, small doses of the solvent vapor can leak into
the gas stream. A three-way valve downstream from the bubbler was originally intended
for blocking the gas flow to the QCM/HCC at zero flow through the MFC2. However,
the entire gas flow system including the three-way valve is placed inside the isothermal
bath and is not easily accessible. We propose the addition of an electronic actuator to the
three-way valve, which will allow it to be controlled by the LabView program.
3) Elimination of the housing of the QCM/HCC: Immersing the QCM/HCC
directly in the isothermal bath eliminates the need of a housing and reduces possible
thermal pathways for heat leak. The housing prevents direct contact of the water of the
bath with the QCM/HCC. In order to eliminate the need for a housing an o-ring seal is
necessary between the two aluminum blocks of the QCM/HCC (the aluminum heat sink
and the calorimeter head). Ultra-torr connectors are currently used to interface the Teflon
302
tubings of the gas flow system with the QCM/HCC housing. These Ultra-torr connectors
can be directly screwed to the calorimeter head. There are also four wires carrying the
electrical signals of the sample and reference QCMs and thermopiles. The area near the
outlet point of these wires can be sealed using a silicon paste.
4) Developing new convenient procedures for routine calibration of thermopiles:
Reexamining the quality of thermal contact between the sample and the heat-sensing
device of a calorimeter, (as well as recalibrating the sensitivity) is common practice. The
details of one such procedure for the QCM/HCC were described in chapter 3 (3.2.1).
However, this procedure is currently time consuming. The automation of this procedure
(also explained in chapter 3) can minimize human supervision, but we have recently
learned about a more accurate and time efficient possibility. This alternate procedure uses
a commercially available oscillator driver (Maxtek, PLO-10), which is capable of
simultaneous measurement of the QCM’s oscillation frequency and resistance. Using the
resistance of the QCM and the voltage applied the thermal power can be calculated and
compared against the measured values.
In addition to the routine calibration procedures, we also recommend chemical
calibrations such as evaporation of liquids from dilute solutions in thin films (see chapter
7, hydration enthalpy of lysozyme at high water content), or sublimation of organic solids
with moderate vapor pressures such as naphthalene (∆sublimationH=73kJ/mole; vapor
pressure at 24.10C=10 Pa)
5) Developing an accurate and time efficient peak integration procedure: The need
for developing an accurate integration procedure has the highest priority on this list.
Currently, the baseline assignment for the thermal trace is highly arbitrary and the largest
source of error in the data analysis step. The scatter in the reported values for the
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measured enthalpies does not represent the true precision of QCM/HCC. For
measurements where a standard deviation of less than ±0.1 kJ/mole would be expected
based on the standard deviations in the mass and thermal measurements with an “ideal”
baseline, variations as large as 4-5kJ/mole may be observed in the actual results for the
enthalpy to our great disappointment. This problem becomes more pronounced for
increasing integration times and shift in the baseline. The use of several software packages
has been examined but no satisfactory baseline assignment method has been identified yet.
6) Further development of the LabView control program to make it user-friendlier:
The LabView control program has brought great convenience to the operation of the
QCM/HCC. However, it can still be made simpler and user-friendlier. An optimum front
panel VI would require the operator to enter only three variables for typical sorption
experiments: the desired concentration range of the analyte, the number of
(sorption/desorption) steps, and the duration of each step. Equations describing the vapor
pressure of several organic solvents as a function of temperature such as those in appendix
C can easily be incorporated into the LabView program and selected from a list.
Another major improvement would be the communication of the setting on the
preamplifier to the LabView program. This is currently accomplished manually. A mistake
in entering the correct setting would render the thermal trace useless.
Finally, we propose developing macros or modifying the LabView program to do
parts of the calculations involved in the data analysis step. Obtaining the values for the
mass of the analyte at the beginning or end of a sorption/desorption step, or the
equilibrium constant (K) is currently very time consuming. The proper macro written in
Excel or other software such as Matlab or Origin could produce all the results in just a few
seconds.
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8.2 Summary and suggestions for future activities, chapter 5
The sorption of six organic solvent vapors in thin films of Tecoflex was studied.
The energetics of the overall sorption process was broken into two parts: the condensation
and mixing of the organic solvent with the polymer film. The balance of the enthalpic and
entropic contributions to the energetics of the two conceptualized steps of the sorption
process was discussed. Recommendations for future activities for this experiment are
outlined below.
1) Repeat this experiment and use 20 to 30 different probes to improve the
correlation of the LSER relationship for Tecoflex.
2) Study the sorption of organic vapors in other polymeric material, which have
been studied by other investigators.
3) Evaluation of the storage and loss shear moduli for viscoelastic film samples.
4) For this and other experiments use other in/ex-situ techniques, such as optical
microscopy, ellipsometry, profilometry or other surface techniques.
1) Repeat this experiment and use 20 to 30 different solvents to improve the
correlation of the LSER relationship for Tecoflex: The sorption enthalpies of organic
solvent vapors in Tecoflex had never been measured before. To obtain a comprehensive
picture of energetics and kinetics of the sorption process and to establish an LSER
relationship with a good correlation for Tecoflex, the above experiment should be
repeated for 20 to 30 more solvent vapors.
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2) Study the sorption of organic vapors in other polymeric material, which have
been studied by other investigators: There are only a few polymer systems for which
sorption enthalpies have been reported. Organic vapor sorption studies of one or some of
these polymers would allow the comparison of the measured values from the QCM/HCC
with those obtained from the van’t Hoff relationship.
3) Evaluation of the storage and loss shear moduli for viscoelastic film samples:
Shifts in the oscillation frequency of QCMs coated with viscoelastic films due to changes
in the shear modulus are usually very small for acoustically thin films. However, sometimes
the nature of the experiment may require a certain film thickness. Ideally, the viscoelastic
properties of the film should be determined for each data point and compiled along with
the thermal trace and frequency data. The determination of the shear modulus requires the
use of an impedance analyzer or other complex procedures such as multiple simultaneous
measurements of the oscillation frequency and resistance using the Maxtek oscillator driver
(Maxtek, PLO-10) for several films with different thicknesses under identical conditions.
Nonetheless, for acoustically thick films an accurate mass measurement will not be
possible without knowledge of shear moduli.
4) For this and other experiments use other in/ex-situ techniques, such as optical
microscopy, ellipsometry, profilometry or other surface techniques: Coupling the
QCM/HCC with other surface characterization techniques can provide additional valuable
information. For example, currently the film thickness is determined using the density and
the mass the film. But the density of film cannot be known after the sorption of chemical
vapors. Ellipsometry or profilometry can be used to determine the thickness (thickness
àvolume, volume and massàdensity) of the film and the sorbed material.
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8.3 Summary and suggestions for future activities, chapter 6
Enthalpy of hydrogen sorption in an electrodeposited film was measured.
Corrections to the mass measurements were necessary to account for surface stress
induced shift in the oscillation frequency of the QCM. The corrected values for the
enthalpy of hydrogen sorption in palladium were in reasonable agreement with those
previously reported for the βphase region of the hydrogen sorption isotherm.
The surface activity of the same palladium film was estimated for the catalytic
hydrogenation of ethylene at ambient temperature in presence of a hydrogen/ nitrogen gas
mixture.
A model was proposed for the break down of the enthalpy of self assembled
monolayer formation by nonylthiol on a gold surface. This model explains the basis for an
increase in the measured enthalpy for high surface coverage. Further work is required in
this area to examine the accuracy of the proposed model. Below are suggestions for future
work.
1) Preparation of a vacuum evaporated palladium film on Cr instead of gold to
avoid formation of gold/palladium alloy.
2) Measurements in the α-phase and α−β phase region of the sorption isotherm.
3) Study the rate of hydrogenation of acetylene or acetylene/ethylene mixture on
a palladium surface
4) Devising a new method for sample introduction with good control of the
alkylthiol vapor in the gas phase for SAM formation experiment.
5) A systematic study of the energetics of SAM formation by a homologous series
of alkylthiols.
307
1) Preparation of a vacuum evaporated palladium film on Cr instead of gold to
avoid formation of gold/palladium alloy: Palladium alloys with gold upon annealing. A
thin film of Chromium is usually used in a QCM as an adhesion layer between the gold
and quartz. Palladium deposited directly on quartz peels off during hydrogen sorption. For
the next set of experiments the gold electrode of the QCM should be removed so that
palladium can be deposited on the thin Cr layer of the QCM. We also propose the
preparation of palladium films on an AT as well as a BT-cut QCM so that the surface
stress related effects could be measured accurately.
2) Measurements in the α-phase and α−β phase region of the sorption isotherm:
In order to conduct measurements in the α-phase region a vacuum system has to be
employed so that all the previously sorbed hydrogen in palladium can be removed. The
vacuum system will also improve the cleanliness of the palladium surface. To ensure the
absence of possible contaminants the hydrogen gas can be purified as it is passed through
a palladium/silver alloy filter.
3) Study the rate of hydrogenation of acetylene or acetylene/ethylene mixture on a
palladium surface. Because of the industrial importance of ethylene the hydrogenation of
acetylene in presence of ethylene for acetylene/ethylene mixtures over palladium surfaces
has been studied more extensively. The existing references for this reaction allow
comparison of the results obtained from the QCM/HCC with other reported values.
4) Devising a new method for sample introduction with good control of the
alkylthiol vapor in the gas phase for SAM formation experiment: The results of this
experiment are very preliminary. However, they can be of great importance for
understanding the details of individual steps involved in SAM formation process. If a
reliable method of introducing known amounts of alkylthiol vapors into the existing flow
308
cell cannot be devised, a vacuum system may have to be employed. A small container
equipped with a leak valve into the vacuum line may produce satisfactory results.
5) A systematic study of the energetics of SAM formation by a homologous series
of alkylthiols: This experiment will allow separating the enthalpic contributions to the
SAM formation by the tail group from those by the Au-S bond formation. A study of
SAM formation by alkydisulfides may help to determine the fade of H atom resulting from
the adsorption of alkythiols on gold.
8.4 Summary and suggestions for future activities, chapter 7
Hydration/dehyration enthalpy of lysozyme was measured directly for the first
time. The results are in good agreement with those obtained from indirect measurements.
The enthalpy of hydration has a large magnitude for low water contents but approaches
the enthalpy of condensation of water at higher values of water vapor activity.
1) Study of enzyme-substrate interactions as a function of water vapor activity.
If a thin film can be prepared containing both an enzyme and a substrate, the
energetics of enzyme-substrate interactions can be investigated at different water contents.
The hydration state of an enzyme determines its conformation and therefore its enzymatic
activity. Starting with a dry film, a critical water content corresponding to the maximum
enzymatic activity of the protein sample can be identified as the aH2O over the sample is
gradually increased.
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In addition to producing the typical step changes in the chemical composition of
the gas stream above a sample film during sorption/desorption steps, we have developed a
different mode of operation for QCM/HCC, where the composition of the gas stream can
be scanned within a set range. This mode of operation was originally used during the water
vapor sorption studies for thin film formulations used by Merck. The application of this
mode of operation of the QCM/HCC is particularly useful for samples that are known to
form stoichiometic solvates/hydrates. An excellent candidate to be used in this mode of
operation is C60 fullerene. Solubility measurements as well as DSC experiments have
shown that C60 can form solvates at certain temperatures. We propose the use of
QCM/HCC to study the sorption/desorption of organic vapors in C60 thin films.
8-5 Possible applications of the QCM/HCC in the pharmaceutical industry
Although most of the general application areas of isothermal heat conduction
calorimetry have been discussed in chapter 3, here we will expand upon two of those areas,
namely sorption and degradation applications, with respect to pharmaceutical products.
The motivation to dedicate this section of this thesis to pharmaceutical products is a recent
project in our lab supported by a grant from Merck. No detailed information regarding this
project will be discussed here. But a short overview of introduction to pharmaceutical
applications of gravimetric/calorimetric measurements will be given.
Calorimetric measurements are performed throughout the pharmaceutical industry
starting at stages as early as drug discovery and synthesis to the scale up and storage of the
final product1. The many successive stages during manufacturing any pharmaceutical
product can be separated into two major categories: Manufacturing the active ingredient,
310
and the formulation in a deliverable form to the patient. The nature of formulation
determines the delivery speed and site of the active ingredient. An important, integral part
of the formulation is the excipients. These are pharmacologically inert substances that act
as auxiliary compounds to bind the contents of the formulation. The control of drug
substance and its excipients ensures that the formulation maintains its integrity and
effectiveness of its action throughout its shelf life. Thermal analysis and calorimetric
techniques have been used extensively to monitor these properties of the drug formulation
products during processing and storage.
Since most drug formulations exhibit polymorphism2,3, it is important to
understand this phenomenon and its effect on the stability and action of the drug
formulation. Polymorphism refers to the ability of a solid to exist in different crystalline
states. Different forms of the same solid are called polymorphs or crystalline
modifications. Polymorphs are chemically and physically equivalent in the liquid and
gaseous phase. But they may behave very differently in the solid state. The same solid may
also become amorphous, in a non-ordered structure similar to the liquid state. Hydrates or
solvates of a solid can form ordered structures, which are called pseudo-polymorphs.
Polymorphism and pseudo-polymorphism of pharmaceuticals can cause different
behaviors with respect to their activity, toxicity, solubility and stability. Under certain
conditions one polymorph may transfer into another through a phase transition. If the
phase transition is reversible, the polymorphs are called enantiotrops. But if the phase
transition is not reversible, the two polymorphs can exist as either a stable or metastable
homotrop. Sometimes metastable homotrops can exist outside of their phase diagram
because of kinetic reasons. Such metastable forms may exist for years (e.g. diamond with
graphite as the stable homotrop). It is, therefore, very important to consider both
311
thermodynamic and kinetic aspects in order to understand failures and unforeseen
phenomena. Nonetheless, gaining a good understanding of such issues can be very
complex, especially since in some cases different solid forms may coexist. Amorphous
solids are generally more hygroscopic, more soluble and exhibit better bioavalibility.
Efforts are usually made to promote their formation during processing steps. These efforts
include precipitation, fast crystallization, drying and freeze-drying. Amorphous solids are
chemically less stable. Depending on temperature and humidity some partial transition of
the amorphous form to some other polymorph may take place. A final formulation
product may contain less than 5% of the original amorphous form depending on the
duration of storage3.
Solid pharmaceuticals
Amorphous Crystalline
Polymorphs Pseudo-polymorphs
Enantiotrops Homotrops Solvates Hydrates
Enantiotrops Homotrops
Figure 8-1: Possible forms of pharmaceutical formulations
312
Differential scanning calorimeters are routinely used to measure temperature and
enthalpies of transition of one polymorph form into another. However changes of
crystalline modification are not always only temperature related. Water is a component of
the atmosphere. Water vapor sorption/desorption can also result in phase transitions. For
many compounds a critical relative humidity can be observed at a given temperature, at
which water sorption initiates. Medetromidine is such a compound. At ambient
temperature it remains anhydrous up to a relative humidity of 30%. In such cases sub-
ambient DSC measurements have been performed to calculate the amount of bound
water4,5. But these measurements are not as informative and other isothermal techniques
should be applied.
All pharmaceuticals are required to be assigned expiration dates, beyond which
their potency is compromised. Equilibrium studies may require months or even several
years and are not feasible6. Accelerated testing at elevated temperatures can be misleading,
since almost always decomposition follows mechanisms different from those at room
temperature7. Currently there are no other analytical methods capable of direct
measurements under controlled ambient conditions with sufficient sensitivity. There are
numerous instances in the literature where isothermal heat conduction calorimetry has
proven to operate at the required sensitivity level 8-10. Yet in some cases relating the heat
rate to chemistry is not as straight forward. We believe the additional mass information
provided by the QCM makes the QCM/HCC a promising tool to evaluate drug
formulation stability.
A large portion of this thesis was written with the intention to familiarize the
reader with the details of the operation of the QCM/HCC. Since only a few people have
worked closely with this instrument, the detailed description was necessary to ensure the
313
continuity of expertise for future operators. The experiments described here have initiated
investigations of several important systems. Each one of these areas deserves an in depth
exploration and can become the subject of a single research project. We hope to witness
the commercialization of the QCM/HCC in the near future and experience its full
potential as other investigators may utilize it in innovative ways that we may not have
imagined possible.
“All knowledge is known by all people, but all people are not born yet”
314
References
(1) Thompson, K. C. Thermochim. Acta 2000, 355, 83-87.
(2) Giron, D. Thermochim. Acta 1995, 248, 1-59.
(3) Giron, D. J. Therm. Anal. Calorim. 1999, 56, 1285-1304.
(4) Giron, D.; Goldbronn, C. J. Therm. Anal. 1997, 49, 907-912.
(5) Giron, D.; Golbronn, C. J. Therm. Anal. Calorim. 1998, 51, 727.
(6) Hancock, B. C.; Dalton, C. R. Pharm. Dev. Technol. 1999, 4, 125-131.
(7) Beezer, A. E.; Gaisford, S.; Hills, A. K.; Mitchell, J. C. Int. J. Pharm. 1999, 179, 159-
165.
(8) Hansen, L. D.; Eatough, D. J.; Lewis, E. A.; Bergstrom, R. G.; Degraft-Johnson,
D.; Cassidy-Thompson, K. Can. J. Chem. 1990, 68, 2111-14.
(9) Hansen, L. D.; Lewis, E. A.; Eatough, D. J.; Bergstrom, R. G.; DeGraft-Johnson,
D. Pharm. Res. 1989, 6, 20-7.
(10) Hansen, L. D.; Pyne, M. T.; Wood, R. W. Int. J. Pharm. 1996, 137, 1-9.
APPENDIX A
STEPHEN MARTIN’S MODEL FOR A QCM
RESONATOR WITH A VISCOELASTIC SURFACE LOAD (MATLAB PROGRAM)
315
APPENDIX A
STEPHEN MARTIN’S MODEL FOR A QCM RESONATOR WITH A VISCOELASTIC SURFACE
LOAD (MATLAB PROGRAM)
This appendix contains a program written for MATLAB. This program is based on
Martins model for a composite QCM resonator as described in the following
publication:
Martin, Stephen J.; Bandey, Helen L.; Cernosek, Richard W.; Hillman, A. Robert;
Brown, Mark J. Equivalent-Circuit Model for the Thickness-Shear Mode
Resonator with a Viscoelastic Film Near Film Resonance. Anal. Chem.
(2000), 72(1), 141-149.
%Zr=Z2/Zim1, Zratio %fr=omegaf/omega, angular frequency ratio %Gr=G"/G', ratio of the imaginary part of shear modulus over the real part. for I=1:100, fr(I)=((I)*0.1)+0.1; N=1; for J=1:100, Gr(J)=((J)*0.05)+0.1; i=(-1)^.5; Zr(I,J)=(-8*i*fr(I)^2)/(((N*pi)^2)*(Gr(J)+(i*(1-fr(I)^2)))); Fratio(I)=1/fr(I); Z(I,J)=((real(Zr(I,J))^2)+(imag(Zr(I,J))^2))^0.5; Znew=Z'; a(I,J)=180/pi*angle(Zr(I,J)); anew=a'; end end figure(1) mesh(Fratio,Gr,Znew) figure(2) mesh(Fratio,Gr,anew)
APPENDIX B
KAY KANANZAWA’S MODEL FOR
CORRECTION OF SAUERBREY’S EQUATION FOR A VISCOELASTIC SURFACE LOAD
(MATLAB PROGRAM)
316
APPENDIX B
KAY KANANZAWA’S MODEL FOR CORRECTION OF SAUERBREY’S EQUATION FOR A
VISCOELASTIC SURFACE LOAD (MATLAB PROGRAM)
eQ=9.53e-2;%piezoelectric constant for quartz(s.m^-2) i=(-1)^.5; epQ=3.982e-11;%dielectric constant for quartz(s^4.kg^-1.m^-3) I=1:1:20000; f=((I-1)*10)+4.8e06; w=2*pi.*f;%angular frequency(s^-1) %roQ=2.649e3; roQ=2.649e3;%density of quartz(kg.m^-3) %cq=29.24e9; cq=2.947e10;%shear modulus of quartz(N/m^2,Pa) nQ=9.2475e-3;%viscosity of quartz(kg.m^-1.s^-1) cQ=cq+(eQ/epQ)+i.*w.*nQ; kQ=w.*sqrt(roQ./cQ); lQ=0.3458e-3;%thickness of quartz(m) M1=200e-6;%mass1(g/cm2) M2=500e-6;%mass2(g/cm2) M3=1000e-6;%mass3(g/cm2) M4=2000e-6;%mass4(g/cm2) M5=3500e-6;%mass5(g/cm2) ro2=1.063e3;%density of overlayer(kg/m^3) U2=158489319;%shear (storage, G')modulus of the overlayer(N/m^2,Pa) n2=52.839;%viscosity (loss, G"/omega)of the overlayer(kg.m^-1.s^-1) ro1=2.649e3;%density of overlayer(quartz)(kg/m^3) U1=2.947e10;%shear modulus of the overlayer(quartz)(N/m^2,Pa) n1=nQ;%viscosity of the overlayer(quartz)(kg.m^-1.s^-1) ep1=0.01*M1/(ro1*0.001)%thickness of ideal mass(quartz)(m) ep2=0.01*M1/(ro2*0.001)%thickness of real mass(m) ep3=0.01*M2/(ro1*0.001)%thickness of ideal mass(quartz)(m) ep4=0.01*M2/(ro2*0.001)%thickness of real mass(m) ep5=0.01*M3/(ro1*0.001)%thickness of ideal mass(quartz)(m) ep6=0.01*M3/(ro2*0.001)%thickness of real mass(m) ep7=0.01*M4/(ro1*0.001)%thickness of ideal mass(quartz)(m)
317
ep8=0.01*M4/(ro2*0.001)%thickness of real mass(m) ep9=0.01*M5/(ro1*0.001)%thickness of ideal mass(quartz)(m) ep10=0.01*M5/(ro2*0.001)%thickness of real mass(m) %1,1 for ep=ep1;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro1;%density of overlayer U=U1;%shear modulus of the overlayer %cq=2.947e10 n=n1;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z1=abs(admit); Y1=180/pi.*angle(admit);%phase angle in degrees end %2,2 for ep=ep2;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro2;%density of overlayer U=U2;%shear modulus of the overlayer %cq=2.947e10 n=n2;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep));
318
D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z2=abs(admit); Y2=180/pi.*angle(admit);%phase angle in degrees end %3,1 for ep=ep3;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro1;%density of overlayer U=U1;%shear modulus of the overlayer %cq=2.947e10 n=n1;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z3=abs(admit); Y3=180/pi.*angle(admit);%phase angle in degrees end %4,2 for ep=ep4;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro2;%density of overlayer U=U2;%shear modulus of the overlayer %cq=2.947e10 n=n2;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage
319
A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z4=abs(admit); Y4=180/pi.*angle(admit);%phase angle in degrees end %5,1 for ep=ep5;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro1;%density of overlayer U=U1;%shear modulus of the overlayer %cq=2.947e10 n=n1;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z5=abs(admit); Y5=180/pi.*angle(admit);%phase angle in degrees end %6,2 for ep=ep6;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro2;%density of overlayer U=U2;%shear modulus of the overlayer %cq=2.947e10 n=n2;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep))));
320
d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z6=abs(admit); Y6=180/pi.*angle(admit);%phase angle in degrees end %7,1 for ep=ep7;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro1;%density of overlayer U=U1;%shear modulus of the overlayer %cq=2.947e10 n=n1;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z7=abs(admit); Y7=180/pi.*angle(admit);%phase angle in degrees end %8,2 for ep=ep8;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro2;%density of overlayer U=U2;%shear modulus of the overlayer %cq=2.947e10 n=n2;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u);
321
b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z8=abs(admit); Y8=180/pi.*angle(admit);%phase angle in degrees end %9,1 for ep=ep9;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro1;%density of overlayer U=U1;%shear modulus of the overlayer %cq=2.947e10 n=n1;%viscosity of the overlayer %nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z9=abs(admit); Y9=180/pi.*angle(admit);%phase angle in degrees end %10,2 for ep=ep10;%thickness of the overlayer a=((eQ/epQ).*(1-exp(-i.*kQ.*lQ)))-((i.*kQ.*cQ.*lQ/eQ).*exp(-i.*kQ.*lQ)); ro=ro2;%density of overlayer U=U2;%shear modulus of the overlayer %cq=2.947e10 n=n2;%viscosity of the overlayer
322
%nQ=9.2475e-3 u=U+i.*w.*n; k=w.*sqrt(ro./u); b=(kQ.*cQ.*(1-exp(-i.*kQ.*lQ))-(k.*u.*((1-exp(i*2.*k.*ep)))./(1+exp(i*2.*k.*ep))))./(kQ.*cQ.*(1-exp(i.*kQ.*lQ))+k.*u.*((1-exp(i*2.*k.*ep))./(1+exp(i*2.*k.*ep)))); d=(eQ/epQ).*(1-exp(i.*kQ.*lQ))+(i.*kQ.*cQ.*lQ/eQ).*exp(i.*kQ.*lQ); fi=1;%excitation rf voltage A=-fi.*(1./(a+b.*d)); B=b.*A; C=(A-B)./(1+exp(i*2.*k.*ep)); D=C.*exp(i*2.*k.*ep); E=-((i.*kQ.*cQ)./eQ).*(A.*exp(-i.*kQ.*lQ)-B.*exp(i.*kQ.*lQ)); F=-(fi/2)-(eQ/epQ).*(A+B); %J(I)=-i*w(I)*eQ*E(I); J=-i.*w.*epQ.*E;%current density admit=J./(2*(fi));%addmittance Z10=abs(admit); Y10=180/pi.*angle(admit);%phase angle in degrees end figure(1) plot(real(admit),imag(admit),'o')%susceptance vs. conductance plot figure(2) plot(f,Y1,'k-',f,Y2,'ro:',f,Y3,'k-',f,Y4,'ro:',f,Y5,'k-',f,Y6,'ro:',f,Y7,'k-',f,Y8,'ro:',f,Y9,'k-',f,Y10,'ro:')%plot of phase angle figure(3) semilogy(f,Z1,'k-',f,Z2,'ro:',f,Z3,'k-',f,Z4,'ro:',f,Z5,'k-',f,Z6,'ro:',f,Z7,'k-',f,Z8,'ro:',f,Z9,'k-',f,Z10,'ro:')%plot of addmittance [K1,p]=max(Z1); f1=((p-1)*10)+4.8e06 [K2,p]=max(Z2); f2=((p-1)*10)+4.8e06 corr1=(5000000-f2)/(5000000-f1) [K3,p]=max(Z3); f3=((p-1)*10)+4.8e06 [K4,p]=max(Z4); f4=((p-1)*10)+4.8e06 corr2=(5000000-f4)/(5000000-f3) [K5,p]=max(Z5); f5=((p-1)*10)+4.8e06 [K6,p]=max(Z6); f6=((p-1)*10)+4.8e06 corr3=(5000000-f6)/(5000000-f5) [K7,p]=max(Z7); f7=((p-1)*10)+4.8e06 [K8,p]=max(Z8); f8=((p-1)*10)+4.8e06 corr4=(5000000-f8)/(5000000-f7) [K9,p]=max(Z9);
323
f9=((p-1)*10)+4.8e06 [K10,p]=max(Z10); f10=((p-1)*10)+4.8e06 corr5=(5000000-f10)/(5000000-f9) figure(4) plot(ep2*1e6,corr1,'o:',ep4*1e6,corr2,'o:',ep6*1e6,corr3,'o:',ep8*1e6,corr4,'o:',ep10*1e6,corr5,'o:')
APPENDIX C
VAPOR PRESSURE OF WATER AND ORGANIC SOLVENTS AT DIFFERENT TEMPERATURES
324
APPENDIX C
VAPOR PRESSURE OF WATER AND ORGANIC SOLVENTS AT DIFFERENT TEMPERATURES
The values for the vapor pressures for the following solvents were obtained from the
CRC Handbook of Chemistry and Physics, 71th and 77th editions.
Table C-1 vapor pressure of water and some other organic solvent at different temperatures
wat
er
met
hano
l
etha
nol
acet
one
hexa
ne
tolu
ene
acet
onitr
ile
trie
thyl
amin
e
N-N
dim
ethy
lform
amid
e
Temp/K p/mmHg p/mmHg p/mmHg p/mmHg p/mmHg p/mmHg p/mmHg p/mmHg p/mmHg
248.15 16.43 10.05 273.15 4.50 30.23 11.25 70.13 45.38 298.15 126.77 59.03 231.03 151.52 28.43 89.26 57.76 323.15 92.26 416.31 221.28 615.08 405.8 254.28 193.53 348.15 1132.65 666.69 1395.19 922.62 615.83 493.57 373.15 759.85 2647.85 1680.22 2790.37 1845.25 559.57 22.80 398.15 5513.24 3713.00 5070.68 3345.45 1117.65 67.06 423.15 3570.48 10433.9 7320.98 8521.14 5618.25 2055.27 169.52
325
0
2
4
6
8
10
0.002 0.0025 0.003 0.0035 0.004
y = 20.399 - 5146.8x R= 0.99982
ln(p
)/ln
(mm
Hg)
T -1/K -1
0
2
4
6
8
10
12
0.002 0.0025 0.003 0.0035 0.004
y = 19.924 - 4497.6x R= 0.99989
ln(p
)/ln
(mm
Hg)
T -1/K -1
Figure C-1 log vapor pressure vs. inverse absolute temperature for (a) water (b) methanol
(a)
(b)
326
0
2
4
6
8
10
0.002 0.0025 0.003 0.0035 0.004
y = 20.741 - 4976.3x R= 0.99961
ln(p
)/ln
(mm
Hg)
T -1/K -1
23456789
10
0.002 0.0025 0.003 0.0035 0.004 0.0045
y = 17.965 - 3745.3x R= 0.99978
ln(p
)/ln
(mm
Hg)
T -1/K -1
Figure C-2 log vapor pressure vs. inverse absolute temperature for (a) ethanol (b) acetone
(a)
(b)
327
2
3
4
5
6
7
8
9
0.002 0.0025 0.003 0.0035 0.004 0.0045
y = 17.65 - 3782x R= 0.99962
ln(p
)/ln
(mm
Hg)
T -1/K -1
2
3
4
5
6
7
8
9
0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034 0.0036
y = 17.906 - 4334.3x R= 0.99987
ln(p
)/ln
(mm
Hg)
T -1/K -1
Figure C-3 log vapor pressure vs. inverse absolute temperature for (a) hexane (b) toluene
(a)
(b)
328
3.5
4
4.5
5
5.5
6
6.5
7
0.0028 0.0029 0.003 0.0031 0.0032 0.0033 0.0034 0.0035
y = 17.938 - 4006.6x R= 0.99999
ln(p
)/ln
(mm
Hg)
T -1/K -1
33.5
44.5
55.5
66.5
7
0.0028 0.0029 0.003 0.0031 0.0032 0.0033 0.0034 0.0035
y = 19.024 - 4455.4x R= 0.99959
ln(p
)/ln
(mm
Hg)
T -1/K -1
Figure C-4 log vapor pressure vs. inverse absolute temperature for (a) acetonitrile (b) triethylamine
(b)
(a)
329
2.5
3
3.5
4
4.5
5
5.5
0.0023 0.0024 0.0025 0.0026 0.0027 0.0028
y = 20.107 - 6332x R= 0.99997
ln(p
)/ln
(mm
Hg)
T -1/K -1
Figure C-5 log vapor pressure vs. inverse absolute temperature for N,N-dimethylformamide
330
Table C-2 Vapor pressure of some chlorinated solvents
Vap
or p
ress
ure
CC
l 4
cis
(C2H
2Cl 2)
C2H
Cl 3
CH
Cl 3
p/mmHg Temp./C0 Temp./C0 Temp./C0 Temp./C0 1 -50.0 -58.4 -43.8 -58.0
10 -19.6 -29.9 -12.4 -29.7 40 4.3 -7.9 11.9 -7.1 100 23.0 9.5 31.4 10.4 400 57.8 41.0 67.0 42.7 760 76.7 59.0 86.7 61.3
331
-2
0
2
4
6
8
0.0025 0.003 0.0035 0.004 0.0045 0.005
y = 18.333 - 4076.6x R= 0.99978
ln(p
)/ln
(mm
Hg)
T -1/K -1
-2
0
2
4
6
8
0.0025 0.003 0.0035 0.004 0.0045 0.005
y = 18.822 - 4028.5x R= 0.99977
ln(p
)/ln
(mm
Hg)
T -1/K -1
Figure C-6 log vapor pressure vs. inverse absolute temperature for (a) CCl4 (b) cis C2H2Cl2
(a)
(b)
332
-2
0
2
4
6
8
0.0025 0.003 0.0035 0.004 0.0045
y = 18.321 - 4187.5x R= 0.99978
ln(p
)/ln
(mm
Hg)
T -1/K -1
-2
0
2
4
6
8
0.0025 0.003 0.0035 0.004 0.0045 0.005
y = 18.65 - 3995x R= 0.99966
ln(p
)/ln
(mm
Hg)
T -1/K -1
Figure C-7 log vapor pressure vs. inverse absolute temperature for (a) C2HCl3 (b) CHCl3
(b)
(a)
APPENDIX D
NOMENCLATURE AND ABBREVIATIONS USED
333
APPENDIX D
NOMENCLATURE AND ABBREVIATIONS USED
A Area Å Angstrom ac Alternating current AFM Atomic force microscope a H2O Water vapor activity AT-cut A quartz wafer cut at an angle of 350 15’ with respect to the optic axis B Susceptance BAM BioActivity Monitor BT-cut A quartz wafer cut at an angle of 490 00’ with respect to the optic axis C Sensitivity constant for a 5 MHz QCM C Capacitance cf Complex shear modulus of thin film cm Elasticity Cm Concentration of analyte in the mobile phase Cnp/CN2 Conversion factor for mass flow controller calibrated with nitrogen Cp Heat capacity cq Complex shear modulus of quartz cq0 Storage shear modulus of quartz Cs Concentration of analyte in the stationary phase, thin film Cv Concentration of analyte in the vapor phase C0 Capacitance of the gold electrodes of the QCM, wires and clamping
334
C1 Capacitance of the resonating QCM c1 Universal constant for the WLF equation C2 Capacitance of the added mass to the QCM c2 Universal constant for the WLF equation D Diffusion coefficient DAQ Data acquisition board dc Direct current dq/dt Heat flux DSC Differential scanning calorimetry DTA Differential thermal analysis DUT Device under test e Piezoelectric constant of quartz E Seebeck coefficient Endo Endothermic Exo Exothermic f Oscillation frequency f Gas flow rate F Force fAT Resonant frequency of an AT-cut QCM fBT Resonant frequency of a BT-cut QCM f.c.c. Face centered cubic ff Resonant frequency of thin film on QCM fn Over tone frequency fout Gas flow rate out of the bubble-through container fq Resonant frequency of quartz
∆ fq Change in the resonant frequency of quartz ftotal Total gas flow f1 Gas flow rate through MFC1 f2 Gas flow rate through MFC2 G Conductance G' Storage shear modulus G" Loss shear modulus
∆ G Gibbs free energy
335
∆mixing G Free energy of mixing
∆sorption G Free energy of sorption GC Gas chromatography Gf Complex shear modulus of the thin film GPIB General purpose interphase board Gq Complex shear modulus of quartz h g H2O/ g lysozyme
∆ H Enthalpy
∆adsorption H Enthalpy of adsorption
∆condensation H Enthalpy of condensation
∆crystallization H Enthalpy of crystallization
∆dehydration H Enthalpy of dehydration
∆denaturation H Enthalpy of denaturation
∆fusion H Enthalpy of fusion
∆hydration H Enthalpy of hydration
∆mixing H Enthalpy of mixing
∆reaction H Enthalpy of reaction
∆SAM formation H Enthalpy of self assembled monolayer formation
∆sorption H Enthalpy of sorption
∆vaporization H Enthalpy of vaporization HCC Heat conduction calorimeter HEW Hen egg white hf Thickness of the thin film ΗΙΑ Hydrogen induced amorphization h'p Constant in the D'Arcy Watt sorption isotherm HPLC High performance liquid chromatography i Square root of -1 i Instantaneous current I Current amplitude ID Internal diameter
336
IGC Inverse gas chromatography Irms Root mean square current j Square root of -1 J Current density across the quartz of the QCM k Reaction rate k Wave vector of shear wave in thin film k Thermal conductivity K Electromechanical coupling coefficient K Partition coefficient/ equilibrium constant ka Rate constant for adsorption KAT Stress related proportionality constant for an AT-cut QCM KBT Stress related proportionality constant for a BT-cut QCM Kc Equilibrium constant kd Rate constant for desorption Keq Equilibrium constant kobs Observed rate constant kq Wave vector for shear wave in quartz K1 Constant in the D'Arcy Watt sorption isotherm K3 Constant in the D'Arcy Watt sorption isotherm K4 Constant in the D'Arcy Watt sorption isotherm l Thickness of the thin film L Inductance L Length of column lf Thickness of the thin film LF Low frequency Log L16 Dispersion constant (LSER) lq Thickness of resonating quartz
∆ lq Change in the thickness of the resonating quartz LSER Linear solvation energy relationship L1 Inductance of the resonating QCM L2 Inductance of the added mass to QCM m Mass
∆ M Change in the mass
337
MFC Mass flow controller ML Monolayer MM Molecular mass mp
¼ Mass of the film and the sorbed solvent vapor at infinite time
mpi Initial mass of the film and the sorbed solvent vapor
mpt Mass of the film and the sorbed solvent vapor at time t
Mq Mass of resonating quartz ∆ Mq Change in the mass of resonating quartz
n Number of the overtone frequency N Odd integer for the resonator harmonic number n gas in Number of moles of carrier gas entering n gas out Number of moles of carrier gas exiting NMR Nuclear magnetic resonance nq The ratio of the overtone frequency over the quartz resonant frequency OD Outer diameter p Pressure p Instantaneous power P Heat flux, thermal power p/p0 Vapor activity patmospheric Atmospheric pressure p0 Saturation vapor pressure PDMS Polydimethylsiloxane pg Pressure of the carrier gas pi Partial pressure PLO Phase lock oscillator ppm Parts per million ppt Parts per thousand Prms Root mean square power PVA Polyvinylalcohol q Charge Q Heat
338
QCM Quartz crystal microbalance r Acoustic wave reflectance coefficient r Dissipation factor R Resistance R Ideal gas law constant RF Radio frequency Rfàq Acoustic wave reflectance coefficient at the film/quartz interface rpm Rotations per minutes Rqàf Acoustic wave reflectance coefficient at the quartz/film interface RQCM Oscillation resistance of the QCM R0 Resistance of pure palladium R1 Resistance of the resonating QCM R2 Resistance of the added mass to the QCM R2 Polarizability constant (LSER theory) S Sensitivity constant of a thermopile
∆ S Entropy
∆mixing S Entropy of mixing
∆sorption S Entropy of sorption
∆vaporization S Entropy of vaporization SAM Self assembled monolayer
∆ SAT Change in the lateral stress on an AT-cut QCM ∆ SBT Change in the lateral stress on a BT-cut QCM
SHE Standard hydrogen electrode t Time T Acoustic wave transmission coefficient T Temperature TA Thermal analysis TAM Thermal Activity Monitor Tc Critical temperature Td Temperature of denaturation Tg Glass transition temperature TG Thermogravimetry TGA Thermogravimetric analysis
339
tm Retention time of nonretained compound in GC column TPD Temperature programmed desorption Tq àf Acoustic wave transmission coefficient at the quartz/film interface tR Retention time of the solute in GC column u Velocity of the mobile phase U Potential of a thermopile v Velocity of the solute in the GC column v Instantaneous voltage V Voltage/ voltage amplitude Vf Speed of the propagating acoustic wave in thin film VI Virtual instrument Vm Volume of the mobile phase Vq Speed of the propagating acoustic wave in QCM VQCM Voltage across the QCM Vrms Root mean square voltage Vs Volume of the stationary phase WLF William-Landel-Ferry x Displacement XC Capacitive reactance Xf Reactance of the thin film XL Inductive reactance Y Admittance z Ratio of acoustic impedance in quartz over that in the thin film Za Acoustical impedance of the QCM/mass composite Ze Electrical input impedance of the QCM/ mass composite Zf Acoustic impedance of thin film Zimp1 Electrical impedance of an ideal mass loading Zm Electrical impedance of the mass loaded QCM Zq Acoustic impedance of quartz Z1 Electrical impedance of unperturbed QCM Z2 Electrical impedance due to the mass loading
340
αH
2 Constant for hydrogen bonding through an acidic site (LSER theory) αT Temperature shift factor for WLF equation βH
2 Constant for hydrogen bonding through an basic site (LSER theory) ε Permittivity of quartz ε Calibration coefficient of the thermopile φ Phase angle of admittance Φ0 Peak potential across the quartz of the QCM Φ Potential across the quartz of the QCM Φq Complex acoustic wave phase shift η Viscosity ηf Viscosity of the thin film ηq Viscosity of quartz λq Wavelength of the propagating acoustic wave in QCM πH
2 Dipolarity constant (LSER theory) θ Fraction of monolayer ρf Density of thin film ρq Density of quartz τ Time constant in Tian equation τAT Thickness of the quartz plate of an AT-cut QCM τBT Thickness of the quartz plate of a BT-cut QCM τf Period of a resonating QCM with a mass loading τq Period of a resonating QCM with no mass loading
∆ τq Change in the period of a resonating QCM ω Angular frequency
341
VITA
Hamid M. Shirazi
PLACE AND DATE OF BIRTH Sep. 20th, 1968 Tehran, Iran
Citizenship Austrian
EDUCATION
1996 - 2000 Drexel University Philadelphia. PA Ph.D. in Chemistry
1995 - 1996 Drexel University Philadelphia. PA M.S. in Chemistry
1994 - 1995 West Chester University West Chester. PA Graduate research
1990 - 1994 St. Joseph's University Philadelphia. PA B.S. in Chemistry
PUBLICATIONS AND PRESENTATIONS
PUBLICATIONS Wadsö, L.; Muligan, R. I.H.M.; Shirazi, H.; Smith, A.; Hofelich, T.. A simple isothermal heat conduction calorimeter for studying processes in physics, chemistry, and biology, Journal of Chemical Education, in press (2000) Smith, Allan L.; Shirazi, Hamid M.. Quartz Microbalance Microcalorimetry: A New Method for Studying Polymer-Solvent Thermodynamics, Journal of Thermal Analysis and Calorimetry, vol. 59 (2000), 171-186 Smith, A. L.; Shirazi, H.; Wadsö, I. The QCM/HCC: simultaneous, isothermal, high sensitivity measurements of mass change and heat flow in polymer and fullerene films. Proc. Electrochemical. Soc. (1998), 98-8 (Recent advances in the physics and chemistry of fullerenes and related materials), 576-585.
Smith, A. L.; Strawhecker, K.; Shirazi, H.; Oloffson, G.; Wadsö, I.; Qvarnstrom, E. Solvated fullerene crystals: their growth and enthalpies of solution. Proc. Electrochemical. Soc. (1997), 97-14 (Recent advances in the physics and chemistry of fullerenes and related materials), 599-610.
PRESENTATION Smith, Allan L.; Shirazi, Hamid M.; Mulligan S. R.; Ciraola J. M.; Ayrapetova A.; Jacob B.; Schneider D. Few applications of the quartz crystal microbalance/heat conduction calorimeter, a novel thermogravimetrical tool. Book of Abstracts, 220th ACS National Meeting, Washington DC, Aug. 20-24 (2000)
