Membrane Materials for Gas andVapor Separation

Membrane Materials for Gas and VaporSeparation

Synthesis and Application of Silicon-Containing Polymers

Edited by

Yuri Yampolskii and Eugene FinkelshteinA.V. Topchiev Institute of Petrochemical Synthesis, RAS, Moscow, Russia

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Library of Congress Cataloging-in-Publication Data

Names: Yampolskii, Yuri, editor. | Finkelshtein, Eugene, editor.Title: Membrane materials for gas and vapor separation : synthesis andapplication of silicon-containing polymers / Yuri Yampolskii, Eugene Finkelshtein.

Description: Chichester, West Sussex, United Kingdom : John Wiley & Sons, Inc., [2017] |Includes bibliographical references and index.

Identifiers: LCCN 2016036752| ISBN 9781119112716 (cloth) | ISBN 9781119112730 (epub) |ISBN 9781119112723 (Adobe PDF)

Subjects: LCSH: Gas separation membranes–Materials. | Silicon polymers.Classification: LCC TP248.25.M46 I35 2017 | DDC 660/.28424–dc23LC record available at https://lccn.loc.gov/2016036752

Cover image: ALFRED PASIEKA/SCIENCE PHOTO LIBRARY/Gettyimages

Set in 10/12pt Warnock by SPi Global, Pondicherry, India

10 9 8 7 6 5 4 3 2 1

Contents

Contributors xiPreface xv

1 Permeability of Polymers 1Yuri Yampolskii

1.1 Introduction 11.2 Detailed mechanism of sorption and transport 31.2.1 Transition-state model 31.2.2 Free volume model 41.2.3 Sorption isotherms 51.3 Concentration dependence of permeability and diffusion coefficients 61.4 Effects of properties of gases and polymers on permeation parameters 10

Acknowledgement 13References 13

2 Organosiloxanes (Silicones), Polyorganosiloxane Block Copolymers:Synthesis, Properties, and Gas Permeation Membranes Based on Them 17Igor Raygorodsky, Victor Kopylov, and Alexander Kovyazin

2.1 Introduction 172.2 Synthesis and transformations of organosiloxanes 172.2.1 Polyorganosiloxanes with aminoalkyl groups at silicon 192.2.2 Organosilicon alcohols and phenols 212.3 Synthesis of polyorganosiloxane block copolymers 232.3.1 Polyester(ether)–polyorganosiloxane block copolymers 242.3.2 Synthesis of polyurethane–, polyurea–, polyamide–, polyimide–

organosiloxane POBCs 252.4 Properties of polyorganosiloxane block copolymers 292.4.1 Phase state of polyblock organosiloxane copolymers 292.5 Morphology of POBCs and its effects on their diffusion properties 302.5.1 Types of heterogeneous structure 302.6 Some representatives of POBC as membrane materials and their

properties 322.6.1 Polycarbonate–polysiloxanes 322.6.2 Polyurethane(urea)–polysiloxanes 39

v

2.6.3 Polyimide(amide)–polysiloxanes 422.7 Conclusions 45

References 46

3 Polysilalkylenes 53Nikolay V. Ushakov, Stepan Guselnikov, and Eugene FinkelshteinAcknowledgement 65References 65

4 Polyvinylorganosilanes: The Materials for Membrane Gas Separation 69Nikolay V. Ushakov

4.1 Introduction: Historical background 694.2 Syntheses and polymerization of vinyltriorganosilanes 714.2.1 Syntheses of vinyltriorganosilanes 714.2.2 Vinyltriorganosilane (VTOS) polymerization 734.2.2.1 VTOS homopolymerization 734.2.2.2 Statistical copolymerization of VTOS with other monomers 834.2.2.3 Block-copolymerization of VTOS with monomers of other types 854.3 Physico-chemical and membrane properties of polymeric PVTOS

materials 884.4 Concluding remarks 94

Acknowledgement 95References 95

5 Substituted Polyacetylenes 107Toshikazu Sakaguchi, Yanming Hu, and Toshio Masuda

5.1 Introduction 1075.2 Poly(1-trimethylsilyl-1-propyne) (PTMSP) and related polymers 1105.2.1 Synthesis and general properties 1105.2.2 Permeation of gases and liquids 1125.2.3 Aging effect and cross-linking 1145.2.4 Free volume 1155.2.5 Nanocomposites and hybrids 1165.3 Poly[1-phenyl-2-(p-trimethylsilylphenyl)acetylene] and related

polymers 1175.3.1 Polymer synthesis 1185.3.2 Gas separation 1215.4 Desilylated polyacetylenes 1245.4.1 Desilylation of poly[1(p-trimethylsilylphenyl)-2-phenylacetylene] 1245.4.2 PDPAs from precursor polymers with various silyl groups 1255.4.3 Soluble poly(diphenylacetylene)s obtained by desilylation 1275.4.4 Poly(diarylacetylene)s 1285.5 Polar-group-containing polyacetylenes 1305.5.1 Hydroxy group 1305.5.2 Sulfonated and nitrated poly(diphenylacetylene)s 1325.5.3 Other polar groups 134

Contentsvi

5.6 Concluding remarks 135References 136

6 Polynorbornenes 143Eugene Finkelshtein, Maria Gringolts, Maksim Bermeshev, Pavel Chapala,and Yulia Rogan

6.1 Introduction 1436.2 Monomer synthesis 1446.2.1 Synthesis of silicon-substituted norbornenes and norbornadienes 1456.2.1.1 [4π + 2π]-cycloaddition of Si-substituted ethylenes and acetylenes to

cyclopentadiene 1456.2.1.2 Synthesis of silyl-substituted norbornenes and norbornadienes with alkyl and

functional substituents via Si–Cl bond transformation 1506.2.1.3 Other approaches to silylnorbornene and norbornadiene preparation 1516.2.2 Synthesis of Si-containing exo-tricyclo[4.2.1.02,5]non-7-enes 1526.2.2.1 The[2σ + 2σ + 2π]-cycloaddition reaction of quadricyclane with Si-containing

alkenes or relative compounds as a simple way to highly active monomers 1536.2.2.2 Cycloaddition of Q with vinylsilanes or relative compounds 1546.2.2.3 Cycloaddition of Q with Si-containing disubstituted alkenes/acetylenes 1576.2.2.4 Cycloaddition of Q with Si-containing 1,2,3-trisubstituted alkenes 1596.3 Metathesis polynorbornenes 1636.4 Addition polymerization 1836.4.1 Addition polynorbornenes and polynorbornenes with alkyl side groups 1846.4.2 Silicon and germanium-substituted polynorbornenes 1876.4.3 Composites with addition silicon-containing polytricyclononenes 2056.5 Conclusions 209

Acknowledgement 210References 210

7 Polycondensation Materials Containing Bulky Side Groups: Synthesisand Transport Properties 223Susanta Banerjee and Debaditya Bera

7.1 Introduction 2237.2 Synthesis of the polymers 2247.2.1 Polyimides 2247.2.1.1 One-step polymerization 2247.2.1.2 Two-step polymerization 2257.2.2 Poly(arylene ether)s (PAEs) 2277.2.3 Aromatic polyamides (PAs) 2287.2.3.1 Low temperature polymerization 2287.2.3.2 High temperature polymerization 2297.3 Effect of different bulky groups on polymer gas transport properties 2297.3.1 Gas transport properties of the polyimides containing different bulky

groups 2297.3.2 Gas transport properties of polyamides containing different bulky groups 2417.3.3 Gas transport properties of poly(arylene ether)s containing different bulky

groups 248

Contents vii

7.3.4 Concluding remarks 263References 265

8 Gas and Vapor Transport Properties of Si-Containing and RelatedPolymers 271Yuri Yampolskii

8.1 Introduction 2718.2 Rubbery Si-containing polymers 2728.2.1 Polysiloxanes 2728.2.2 Siloxane-containing copolymers (block copolymers, random copolymers and

graft copolymers) 2748.2.3 Polysilmethylenes 2778.3 Glassy Si-containing polymers 2788.3.1 Polymers with Si–O–Si bonds in side chains 2788.3.2 Poly(vinyltrimethyl silane) and related vinylic polymers 2828.3.3 Metathesis norbornene polymers 2858.3.4 Additive norbornene polymers 2868.3.5 Polyacetylenes 2908.3.6 Other glassy Si-containing polymers 2938.4 Free volume in Si-containing polymers 2948.5 Concluding remarks 296

Acknowledgement 298References 298

9 Modeling of Si-Containing Polymers 307Joel R. Fried, Timothy Dubbs, and Morteza Azizi

9.1 Introduction 3079.2 Main-chain silicon-containing polymers 3099.2.1 Polysiloxanes 3099.2.2 Polysilanes and silalkylene polymers 3149.3 Side-chain silicon-containing polymers 3169.3.1 Poly(vinyltrimethylsilane) 3169.3.2 Poly[1-(trimethylsilyl)-1-propyne] 3179.3.2.1 Conformational studies 3189.3.2.2 Simulation of gas transport 3199.4 Conclusions 324

Appendices 3259.A Molecular flexibility 3259.B Simulation of diffusivity 3259.B.1 Einstein relationship 3259.B.2 VACF method 3259.C Simulation of solubility: Widom method 3259.D Molecular mechanics force fields 3269.D.1 DREIDING 3269.D.2 Polymer-consistent force field (pcff ) 3269.D.3 GROMOS 3269.D.4 COMPASS 326

References 327

Contentsviii

10 Pervaporation and Evapomeation with Si-Containing Polymers 335Tadashi Uragami

10.1 Introduction 33510.2 Structural design of Si-containing polymer membranes 33510.2.1 Chemical design of Si-containing polymer membrane materials 33610.2.2 Physical construction of Si-containing polymer membranes 33610.3 Pervaporation 33710.3.1 Principle of pervaporation 33710.3.2 Fundamentals of pervaporation 33810.3.3 Solution–diffusion model in pervaporation 33910.4 Evapomeation 34010.4.1 Principle of evapomeation 34010.4.2 Principle of temperature-difference controlled evapomeation 34110.5 Technology of pervaporation with Si-containing polymer membranes 34210.5.1 Alcohol permselective membranes 34210.5.2 Hydrocarbon permselective membranes 35310.5.2.1 Aromatic hydrocarbon removal 35310.5.2.2 Chlorinated hydrocarbon removal 35810.5.3 Organic permselective membranes 36010.5.4 Membranes for separation of organic–organic mixtures 36110.5.5 Membranes for optical resolution 36210.6 Technology of evapomeation with Si-containing polymer membranes 36310.6.1 Permeation and separation by evapomeation 36310.6.2 Concentration of ethanol by temperature-difference controlled

evapomeation 36410.7 Conclusions 365

References 365

11 Si-Containing Polymers in Membrane Gas Separation 373Adele Brunetti, Leonardo Melone, Enrico Drioli, and Giuseppe BarbieriExecutive summary 373

11.1 Introduction 37311.2 Si-containing polymer membranes used in gas separation 37511.2.1 Silicon rubber membrane materials 37511.2.2 Polyacetylene membrane materials 37611.2.3 Polynorbornene membrane materials 37811.2.4 Other Si-containing membrane materials 37811.3 Separations 37911.4 Membrane modules 38111.5 Competing technologies for separation of gases 38411.6 Applications 38511.6.1 Air separation 38511.6.2 Hydrogen separation 38611.6.3 Hydrocarbon separation 39011.6.4 VOC separation 392

References 393

Index 399

Contents ix

Contributors

Morteza AziziDepartment of Chemical EngineeringUniversity of LouisvilleKYUSA

Susanta BanerjeeMaterials Science CentreIndian Institute of TechnologyKharagpurIndia

Giuseppe BarbieriInstitute on Membrane Technology(ITM-CNR)National Research Councilc/o The University of CalabriaCubo 17CVia Pietro BucciRende CSItaly

Debaditya BeraMaterials Science CentreIndian Institute of TechnologyKharagpurIndia

Maksim BermeshevA.V. Topchiev Institute of PetrochemicalSynthesisRASMoscowRussia

Adele BrunettiInstitute on Membrane Technology(ITM-CNR)National Research Councilc/o The University of CalabriaCubo 17CVia Pietro BucciRende CSItaly

Pavel ChapalaA.V. Topchiev Institute of PetrochemicalSynthesisRASMoscowRussia

Enrico DrioliInstitute on Membrane Technology(ITM-CNR)National Research Councilc/o The University of CalabriaCubo 17CVia Pietro BucciRende CS, Italy;Dipartimento di Ingegneria perl’Ambiente e il Territorio e IngegneriaChimicaThe University of CalabriaCubo 44AVia Pietro BucciRende CS, Italy;Hanyang UniversityWCU Energy Engineering DepartmentSeongdong-gu

xi

SeoulSouth Korea

Timothy DubbsDepartment of Chemical EngineeringUniversity of LouisvilleKYUSA

Eugene FinkelshteinA.V. Topchiev Institute of PetrochemicalSynthesisRASMoscowRussia

Joel R. FriedProfessor and Chair of ChemicalEngineeringUniversity of LouisvilleKYUSA

Maria GringoltsA.V. Topchiev Institute of PetrochemicalSynthesisRASMoscowRussia

Stepan GuselnikovA.V. Topchiev Institute of PetrochemicalSynthesisRASMoscowRussia

Yanming HuKey Laboratory of Synthetic RubberChangchun Institute of Applied ChemistryChinese Academy of SciencesChangchunChina

Victor KopylovMoscow Technological InstituteRussia

Alexander KovyazinPENTA-91 LLC CoMoscowRussia

Toshio MasudaDepartment of Polymer MaterialsSchool of Materials Science andEngineeringShanghai UniversityNanchenShanghaiChina

Leonardo MeloneInstitute on Membrane Technology(ITM-CNR)National Research Councilc/o The University of CalabriaCubo 17CVia Pietro BucciRende CSItaly

Igor RaygorodskyMoscow Technological InstituteRussia

Yulia RoganThomas Swan & Co. LtdRotary WayConsettUK

Toshikazu SakaguchiDepartment of Materials Science andEngineeringGraduate School of EngineeringUniversity of FukuiFukuiJapan

Tadashi UragamiFunctional Separation MembraneResearch CenterOsakaJapan

Contributorsxii

Nikolay V. UshakovA.V. Topchiev Institute of PetrochemicalSynthesis, RASMoscowRussia

Yuri YampolskiiA.V. Topchiev Institute of PetrochemicalSynthesis, RASMoscowRussia

Contributors xiii

Preface

Organosilicon compounds possess a number of specific properties due to the presence ofSi-containing chemical bonds. In general, this makes organosilicon chemistry an effec-tive tool for a planned macromolecular design. Thus, Si–Cl bonds are substantially moreactive in hydrolysis reactions and in interaction with Grignar reagents than their carbonanalogues. Si–H bonds smoothly react with olefins, in contrast to rather chemically pas-sive C–H bonds. The silicon atom has a very weak tendency to formation of multiplebonds under normal conditions. This prevents the possibility of numerous undesirableside chemical processes, such as dehydrochlorination of chlorosilanes, dehydrogenationof hydrosilanes, and some others. At the same time, Si–C and Si–O bonds are quite sta-ble, chemically as well as thermally. These bonds are the main “building blocks” of poly-carbosilanes and polysiloxanes. Therefore, carbosilanes and siloxanes form an attractivebasis for development of various polymer materials.Simplicity of incorporation of different organic substituents on the silicon atom,

including polar and sterically hindered groups, allows fabrication of a series of desiredstructures unattainable for purely organic compounds. This is the case for lowmolecularweight compounds (monomers), as well as for high molecular weight polymers.Organosiliconmonomers allow carbochain glassy polymers possessing high glass tran-

sition temperature (Tg) to be obtained by means of polymerization on multiple bonds,according to addition and metathesis schemes. Some monomers can also be used forsynthesis of elastomeric polymers with very low Tg by ring opening polymerizationvia breaking endocyclic Si–C or Si–O bonds. Numerous examples of organosilicon poly-mers are shown below.

Homochain polymers

SiR

R1

R3

R2

n x

CH-CH2R = ; R1, R2, R3 = Alk (Me etc) ; n = 1

C C

Me

R

n = 1 ; R1= R2 = R3 = Me, OSiMe3

R1= R2 = i-Pr; R3 = Me

R1= R2 = Me ; R3 = Ph

n = 2 ; R1= R2 = R3 = Me

n = 3 ; R1= R2 = R3 = Me

= ; R1, R2, R3 = Alk (Me etc) ; n = 1

m

R = R =

n = 1 ; R1 = R2 = R3 = Me, OSiMe3

n = 2 ; R1 = R2 = R3 = Me

m

xv

n = 1 ; R1 = R2 = R3 = Me, OSiMe3

n = 2 ; R1 = R2 = R3 = Men = 1 ; R1 = R2 = R3 = Me, OSiMe3

n = 2 ; R1 = R2 = R3 = Me

R = R =m m

Heterochain polymers

Si

Me

Me

CH22

x x

(CH2)3

Me

Me

Si

R1

R2

(R1, R2 = Alk, c-Alk, Ar)

x

(CH2)n

Me

Me

Si

Me

Me

Si SiO (n = 1–8) O

x

Therefore, special peculiarities of organosilicon chemistry, as noted above, allow incor-poration of a great variety of substituents on the silicon atom. This makes moleculardesign of desired polymer materials as well as conscious adjustment of their physico-chemical properties realistically feasible.Among various actual directions of the use of Si-containing polymer materials, mate-

rials for gas and vapor separation membranes form an important and prospective field.Thus, the key to successful development of separation membrane materials is in findingand elaborating convenient methods for synthesis of appropriate monomers and deter-mination of their optimal polymerization conditions, resulting in polymers with good gastransport and film-forming properties.Study of gas permeation parameters (permeability, diffusivity, thermodynamic sorp-

tion parameters) and important related properties such as free volume is an independentand a wide field of research. Among other tasks, one is to make an appropriate selectionof gas mixtures that can be separated by certain membranes. Membrane science andtechnology related to the problems of gas and vapor separation are in permanent evo-lution. In this regard, modification of existing polymer membrane materials, searchingfor optimal conditions of separation and development of original syntheses of novel poly-mers provide permanent challenges for researchers. Methodologies based on organosi-licon chemistry may be quite useful for the modern membrane industry.All these issues form the subject of this monograph. In it, for the first time, we tried to

consider jointly the questions of organosilicon chemistry and membrane science, givinghistorical backgrounds, outlining the trends of development and providing the contem-porary state of the art of both fields.In Chapter 1 the main parameters of membrane gas separation are defined and

explained. Since gas permeation in non-porous polymer membranes proceeds accordingto the solution–diffusion mechanism, the role of kinetic and thermodynamic factorsin mass transfer through membranes is outlined. The role of the combination of highpermeability and selectivity is stressed as a prerequisite of highly efficient membranematerials. Special attention is devoted to the effects of the nature and properties ofgas and polymers on the observed gas permeation parameters.From Chapter 2, consideration of the synthesis and properties of Si-containing poly-

mers is started. The subject of this chapter is rubbery polymers with flexible Si–O–Si

Prefacexvi

bonds: organosiloxanes and block copolymers containing flexible siloxane blocks. Themain feature of siloxanes is their extremely low Tg and, consequently, the very highmobility of their main chains. The chemistry and applications of polyorganosiloxanesand their copolymers have been intensively studied since the 1940s. They have foundnumerous applications, and one of them is their use as membrane materials. For a longperiod polydimethylsiloxane (PDMS) was considered as the most permeable polymeramong all those known. A great impact on applications of siloxane-containing polymersstarted 20–30 years later when block copolymers with rigid and flexible blocks werecreated and studied. The chapter gives a detailed description of the developed methodsof synthesis of the polymers of this class, and numerous results of the studies of theirmembrane properties.Interesting analogs of polyorganosiloxane are known; these are polymers where the

flexible Si–O bond is replaced by the structurally similar Si–C bond: polysilmethylenes,which are the subject of Chapter 3. A comparison of these two types of polymer permitsfurther elucidation of the role of the flexibility of the main chains of Si-containing poly-mers and its effects on permeability and diffusivity. Approaches to the synthesis of poly-siloxanes and polysilmethylenes have common features: in both cases it is a scission ofstrained cycles. However, there are differences between the polymers obtained: the latterhave less flexible chains and, hence, their permeability is not that high. The polymers ofboth classes are rubbers, so the problems that can be solved using the membranes basedon them are similar. This is mainly the separation of gaseous hydrocarbons; however, inmany cases their relatively high gas permeability justifies consideration of the separationof light gases such as O2/N2 or CO2/CH4.Since the 1960s a new era has started in the chemistry and physical chemistry of Si-

containing polymers as membrane materials. A big stride was made by creatingpoly(vinyltrimethyl silane) (PVTMS) and its structural analogs. A general feature of thesevinylic polymers, described in Chapter 4, is that they contain Si in side groups and areglassy materials. On the basis of PVTMS the first industrially produced gas separationmembrane was fabricated and produced from the end of the 1970s in the Soviet Union.The properties of this polymer, which seemed rather unusual when it was prepared andstudied, undoubtedly influenced further activity in the field of Si-containing membranematerials. The chapter gives a brief review of polymerization chemistry of vinylorgano-silanes and emphasizes the role of anionic polymerization. Other vinylic polymers, e.g.Si-substituted polystyrenes, are also briefly considered.The theme of glassy Si-containing polymers obtained an exceelent development in

studies of disubstituted Si-containing polyacetylenes, the subject of Chapter 5. Thesematerials show a wide range of permeability and have demonstrated diverse manifesta-tions of structure–permeability effects. As often occurs, even the first prepared polymerof this class, poly(trimethylsilyl propyne) (PTMSP), revealed record-breaking permeabil-ity. It was with PTMSP that the phenomena of solubility controlled permeation wereobserved for the first time using glassy membranes. Another interesting reaction was dis-covered with polyacetylenes – desilylation. It resulted in formation of highly permeablematerials that do not contain silicon (solid state elimination of Si-containing groups withformation of additional free volume elements within the membrane). It is likely thatthe same concept can be applicable to other classes of glassy polymers that containC(arom)–Si bonds in side groups.

Preface xvii

A wealth of information is reported in Chapter 6. There, the authors deal with numer-ous Si-containing glassy polymers of norbornene and polytricyclononenes. An unusualpeculiarity of these polymers is that the same monomers can produce materials withentirely different structures, chain rigidities and other properties depending on the selec-tion of the polymerization catalyst. Metathesis polynorbornenes have relatively flexiblechains and rather modest gas permeability. Nonetheless, after preparation and investi-gation of a large number of polynorbornenes with different structures many importantobservations were made regarding the structure–permeability relationship. Addition Si-containing polynorbornenes have very rigid main chains (high Tg) and demonstratedhigh gas permeability, similar to that of polyacetylenes. For this class of polymers solu-bility-controlled permeation was also observed.The subject of Chapter 7 is the description of synthesis and investigation of polyimides

and polyamides with bulky side groups (e.g. tert-butyl or adamantyl). The idea of thischapter is a demonstration that not only Si-containing side groups but also other bulkysubstituents can result in significant increases in permeability, often not at the expense ofpermselectivity. The chapter contains much information on the details of syntheticchemistry of these polymers and the data on their gas permeation properties, usingthe O2/N2 pair as an example.General questions of membrane science are considered in Chapter 8. In it gas perme-

ability and diffusivity of diverse Si-containing classes of membrane materials are dis-cussed. The chapter starts with consideration of rubbery polymers (polysiloxanes andpolysilmethylenes) and then proceeds to discussion of properties of glassy Si-containingpolymers that have played such an important role in the development of membrane gasseparation. Structure–property relations are again at the focus of deliberation. The roleof free volume in membrane materials is also outlined.There are many examples where the structure and properties of Si-containing poly-

mers have been the subject of theoretical works and computer simulations. These ques-tions are considered in Chapter 9. The most extensive work has been performed forPDMS among rubbery polymers and for PTMSP among polymer glasses. The authorsof this chapter focus on the role of main chain stiffness, mobility of side groups andthe effects of these properties on the diffusivity, solubility and permeability coefficientsof various gases. A large appendix is included in this chapter; it contains numerous tech-nical details used in these simulations and hence may be useful for future researchers.It is known that Si-containing polymers have proved their efficiency not only in gas

separation but also in separation of liquids – pervaporation (PV). This is the subjectof Chapter 10. It demonstrates the usefulness of siloxane polymers and PTMSP in var-ious PV processes. Another method has also been developed – evapomeation, where theliquid mixture to be separated does not contact the membranes directly. Instead, vaporphases formed by evaporated components of the liquids are separated. Numerous exam-ples of different separation processes are given.This book would not be complete had it not included a chapter on practical implemen-

tation of membranes based on Si-containing polymers. This task is accomplished inChapter 11. It can be considered as a brief introduction to membrane technology. Dif-ferent types of membrane (flat sheet and hollow fiber) are described, as well as differentdesigns of membrane modules. Special attention is devoted to general advantages ofmembrane technology in comparison with other, more traditional methods of separa-tion. Actual examples are given on separation of particular gas mixtures.

Prefacexviii

The editors would like to extend their sincere gratitude to all contributors and thereviewers of this book. We were sure, and the work on this monograph confirmed, thatthe contributors of this book are world-class experts in their specific fields. Furthermore,we would like to express our thanks to the publishers of this book, John Wiley & Sons,Ltd, Chichester, UK, for their support and guidance. The editors of this book want toexpress their gratitude to Russian Science Foundation for support publishing of thisvolume and in particular Chapters 1, 3, 4, 6, 8.

Eugene FinkelshteinYuri Yampolskii

Preface xix

1

Permeability of PolymersYuri Yampolskii

A.V. Topchiev Institute of Petrochemical Synthesis, RAS, Moscow, Russia

1.1 Introduction

Virtually all the membrane processes realized for separation of gases and vaporsemploy non-porous polymeric membranes. The phenomena of permeation of gasesand vapors through plastic films were known even in the eighteenth century [1]. How-ever, the mechanism of these phenomena became clear only in the middle of the nine-teenth century due to the works by K. Mitchell and T. Graham [1, 2]1, who advancedthe so-called solution–diffusion model. According to them the presence of micro-scopic pores within the films is not a prerequisite for realization of mass transfer.Instead, the dissolution of gaseous molecules in the film and their diffusion throughit can be a basis for gas transport in membranes. The sorbed gas, as T. Graham wrote,‘comes to evaporate… and reappears as gas on the other side of the membrane. Suchevaporation is the same into vacuum and into another gas, being equally gas-diffusionin both circumstances’ [2].An empirical observation made approximately during the same period was that

the flux of gas J through a film (mol/m2 s) is directly proportional to the gas pres-sure drop across this film Δp and inversely proportional to the thickness of thefilm l, i.e.

J =P Δp l 1 1

The proportionality coefficient in this equation, P, was defined as the permeability orpermeability coefficient. However, this empirical equation does not reveal the molecularbasis of permeation and the complicated nature of this quantity.In order to understand the ‘solution–diffusion model’ let us consider a steady-state

isothermal flux through a homogeneous polymer film with thickness l that separates

1 Reproduced in Böddeker KW. Special issue: Early history of membrane science. J Membr Sci 1995; 100: 1–68.

1

Membrane Materials for Gas and Vapor Separation: Synthesis and Application of Silicon-ContainingPolymers, First Edition. Edited by Yuri Yampolskii and Eugene Finkelshtein.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

two gas phases containing a single gas with pressure p2 > p1.2 The transport within the

film can be described by Fick’s first law:

J = −D dC dx 1 2

where C is concentration, x is the coordinate across the film, and the diffusion coefficientD in the first approximation does not depend onC or x. It can easily be integrated, but theboundary conditions are usually unknown. On the other hand, pressure p1 and p2 caneasily be measured and established in the experiment. Therefore, one must considerthe relationship between C and the pressure or sorption isotherm. As will be discussedlater on in this chapter, the form of sorption isotherms in polymers can be complicated,but now it is sufficient to consider the simplest case, that is, the Henry’s law isotherm:

C = Sp 1 3

where S is the solubility coefficient. It is commonly expressed as cm3(STP) cm−3 atm−1.Here the term cm3(STP) characterizes the volume of gas in the standard conditions(273.15 K and 1 atm or 101.3 kPa) and the term cm−3 characterizes the unit volumewithin the film. By replacing C by p in Eq. (1.2) one obtains

J =DS p2−p1 l =DSΔp l 1 4

so it is obvious that

P =DS 1 5

This is a key equation in membrane science. It indicates that the empirical parameter Pincludes two components: the diffusion coefficientD, which characterizes the mobility ofdissolved gas molecules, and the solubility coefficient S, which characterizes the affinitybetween the polymer material and the diffusing gas. It is evident that S is a thermody-namic property of the gas–polymer system.In the SI system, permeability coefficients are expressed in the following units:

molm−1 s−1Pa−1

However, a more widely used and accepted unit for P is the Barrer:

1Barrer = 10−10 cm3 STP cmcm−2 s−1 cmHg −1

All the gas–polymer systems are characterized by permeability or permeability coeffi-cients in the range 10−4–104 Barrer.Equations (1.1) and (1.4) include the thickness of a polymer film l. In membranes this

parameter is unknown, or different parts of the membrane have different thicknesses.Therefore, in the important case of membranes, pressure normalized steady-state fluxor permeance (Q or P/l) is used to characterize the gas transport rate. The accepted unitsfor P/l are mol m−2 s−1 Pa−1 or m3(STP) m−2 h−1 atm−1. Permeance is often expressedusing the gas permeation unit (GPU), where 1GPU= 10−6cm3 STP cm−2 s−1 cmHg −1.

2 In the literature, sometimes different terms are used indiscriminately: polymer films (sometimes called densefilms or uniform films) and membranes. The former term should be applied to a layer with uniformcomposition and a certain thickness. Films are used for the determination of the transport properties ofpolymer–gas systems. On the other hand, a membrane is a device that can consist of several layers (two ormore) of different natures. They are used in the actual gas separation process. More details can be found inReferences 3 and 4.

Membrane Materials for Gas and Vapor Separation2

Since membranes are used for separation, another key characteristic of gas separationmembranes is their selectivity. The ideal selectivity is defined as follows:

αAB = PA PB 1 6

where PA and PB are the permeability coefficients of gases A and B, respectively, meas-ured in runs with permeation of individual gases. Commonly, the more permeable gas istaken as A, so that αAB > 1. In the literature different terms (synonyms) are used for αAB:selectivity, permselectivity, ideal separation factor. They will be used throughout thechapters of this book. Ideal separation factors vary in much narrower ranges than per-meability coefficients and in strong dependence on the gas pair: thus α(O2/N2) changesin the range from 2 to very seldom 20, while α(He/N2) in the much wider range of 2–104

[5]. Bearing in mind Eq. (1.5), the ideal selectivity can be partitioned into diffusivity andsolubility selectivities as follows:

αAB = DA DB SA SB = αDABα

SAB 1 7

so it is possible to speak of the selectivity of diffusion and sorption. The analysis ofαDAB and αSAB is very helpful in understanding the mechanism of gas permeation in poly-

mers. Ideal separation factors can also be considered for membranes as the ratiosαAB =QA QB.Equations (1.6) and (1.7) hold when interactions between diffusing molecules in mixed

gas permeation can be neglected, and also when they do not noticeably affect the proper-ties of the polymeric matrix. In such situations the ideal selectivity measured in experi-ments with pure gases only approximately characterizes the actual selectivity of amembrane. The separation factor α∗AB determined from the ability of a membrane to sep-arate a binary feed gas mixture is defined as follows [6]:

α∗AB = yA yB xA xB 1 8

where yA and yB are the mole fractions of the components produced in the permeate, andxA and xB are their corresponding mole fractions in the feed. In mixture separations withlarge stage-cuts (or when the fraction of the permeate stream is comparable with that ofthe feed stream) sometimes xA and xB are taken as the mole fractions of these compo-nents in the retentate.

1.2 Detailed mechanism of sorption and transport

The solution–diffusion mechanism provides an overall principle of the mass transferthrough non-porous polymer membranes. However, in depth understanding of themechanism of gas transport is impossible without more detailed, desirably atomisticmodels of what occurs when gas molecules are dissolved in polymers and diffuse throughpolymer films or membranes. Two approaches can serve for this aim.

1.2.1 Transition-state model

It is well known that diffusion in condensed media is an activated process. When a mol-ecule of dissolved gas (penetrant) permeates through the membrane it performs numer-ous elementary acts: ‘jumps’ from one equilibrium position in the polymer matrix intoanother (neighboring) one. The passage between these ‘microcavities’ or ‘cells’ implies

1 Permeability of Polymers 3

overcoming forces of attraction between more or less aligned chains of macromolecules.This means that the diffusing dissolved gas molecule must overcome an energy barrier[7]. This barrier can be considered as an activation energy of diffusion ED, so for the dif-fusion coefficient the following Arrhenius equation holds:

lnD= lnD0−ED RT 1 9

By combining this equation with Van’t Hoff’s formula for the solubility coefficients

ln S = lnS0−ΔHs RT 1 10

one obtains the Arrhenius equation for permeability coefficients:

ln P = lnP0 –EP RT 1 11

The parameters of these equations are related by a simple formula: EP = ED +ΔHs.The most important application of this approach is that it logically explains the temper-

ature dependence of the diffusion and permeability coefficients of gases in polymers. Thevalues of ED are always positive, so the diffusion coefficients always increase when temper-ature increases. However, the sign of EP depends on the relativemagnitudes of EP andΔHs.For light gases typically ED > ΔHs , so the resulting values EP > 0 and permeabilityincreases when temperature increases. However, there are rather frequent situationswhen EP < 0 and enhanced temperature causes decreases in the permeability coefficients.This occurs in vapor permeation, when ΔHs have large absolute values, or in polymerswith rigid main chains and unusually low energy barriers for diffusion (small ED values)such as Si-containing disubstituted polyacetylenes [8] or addition polynorbornenes [9].The above interpretation of the mechanism of diffusion of small molecules in

amorphous polymers suggests a description of diffusion as a sequence of successive,infrequent jump events, with the rate constant for each jump being estimable fromthe transition-state theory. The theory well accepted for description of elementary chem-ical reactions [10] is also applicable for dissolved gas transport in membranes [7, 11].The parameters ED, EP, and ΔHs are strong functions of molecular size of penetrants.

A simple interpretation of this phenomenon was given by Meares’ equation [12]:

ED = 0 25N0πd2λCED 1 12

whereN0 is the Avogadro number, d is the kinetic cross-section of a diffusant, CED is thecohesion energy density in a polymer, and λ (adjustable parameter) is a diffusion jumplength. This equation explains not only the dependence of ED on Vc or d2 but alsodecreases of diffusivity for gases with larger sizes d or critical volume. Relatively recentlyit was shown [13] that analysis of Meares’ equation in conjunction with the data of pos-itron annihilation on the size and concentration of free volume elements in polymers canlead to a conclusion that the diffusion jump length λ is close to the average distancebetween adjacent free volume elements in glassy polymers: that is, this quantity acquiredspecific physical meaning.

1.2.2 Free volume model

Another alternative model for description of gas transport in polymeric membrane isthe free volume model. The notion of free volume is of paramount importance for

Membrane Materials for Gas and Vapor Separation4

physics of the condensed state. Originally it was formulated for liquids [14]; it was latertransferred to amorphous polymers either above or below the glass transition state [15,16]. It determines numerous physical properties of polymers, among them the rate ofdiffusion in them of low molecular mass compounds (gas and vapors). The thermalmovement of molecules in the liquid phase is impossible without random fluctuationof the local density. Molecules in liquids perform irregular oscillations around theirequilibrium positions. The same concept holds for rubbery polymers; however, herekinetic segments play the role of individual molecules in low molecular mass liquidcompounds. In glassy polymers free volume is formed due to inefficient packing ofmore or less rigid chains.The simplest assumption that can be made regarding free volume Vf is based on its

representation as the difference between the total or specific volumes of polymers(Vsp), which can be defined as the reciprocal density Vsp = 1 ρ , and occupied volume:Vf =Vsp−Vocc. Of course, it is necessary to find a way to estimate Vocc. An approach tofind the occupied volume of polymers was proposed by Bondi [17], who suggested usingthe formula Vocc = 1 3Vw, where Vw is the van der Waals volume of the repeat units andcan be found via tabulated increments of atoms and small groups. Found in this way, Vf

or another parameter, fractional free volume (FFV), defined as the ratio Vf/Vsp, serves asan approximate but useful measure of free volume in polymers (predominantly glassy).Abundant correlations of the type logD versus 1/FFV or log P versus 1/FFV can be foundin the literature (see e.g. Reference 18 or Figure 8.2 in this book regarding properties ofSi-containing polymers). In the equations

D=Aexp −B FFV 1 13

P =A exp −B FFV 1 14

the parameters B and B correlate with the molecular size of the penetrants [19].Several experimental methods (so-called probe methods) are now available for the

estimation of the size of free volume elements and their concentration in glassy polymers[20–22]. The data obtained using different probe methods are in satisfactory agreementwith each other. It is even more important that they are in agreement with the results ofatomistic computer simulations of the nano-structure of polymers [7] (see also Chapter 9of this book).It seems to be logical to combine the two approaches described in this section using the

formula

D=Aexp −ED RT exp −V∗ Vf 1 15

Lin and Freeman proposed an equation that related the activation energy of diffusion andfractional free volume [19].

1.2.3 Sorption isotherms

Gas sorption is the driving force of transport in non-porous polymer membranes, sothermodynamics of gas sorption in polymers is very important issue. Sorption isotherms,i.e. the concentration of dissolved gas expressed as C (cm3(STP)/cm3 polymer orcm3(STP)/g polymer) as a function of pressure can have different shapes depending

1 Permeability of Polymers 5

on the natures of the gas and polymer and on the temperature. At sufficiently lowpressure all the sorption isotherms can be approximated by Henry’ law:

C = Sp 1 16

For light gases having relatively low solubility (e.g. He or H2), Henry’s law isothermscan be observed up to high pressure. In rubbers, a sorption isotherm convex to thepressure axis is observed [23]. It is described by the Flory–Huggins isotherm [24]. In par-ticular, such an isotherm was reported for gas sorption in polydimethylsiloxane (PDMS).Most membrane materials are glassy polymers, so sorption isotherms in them (i.e.

below Tg) are concave to the pressure axis. The so-called dual mode sorption isotherm(1.17) well describes [25] gas dissolution below Tg:

C = kDp+CHbp

1 + bp1 17

where kD is the Henry’s law parameter characterizing sorption into the densified equi-librium matrix of the glassy polymer, CH is the Langmuir sorption capacity, which char-acterizes sorption into the non-equilibrium excess volume associated with the glassystate, and b is the Langmuir affinity parameter. Obviously, extrapolation to zero pressuregives the Henry’s law part of the isotherm with the following initial slope or solubilitycoefficients:

S = kD +CHb 1 18

where in highly permeable polymers such as poly(trimethylsilyl propyne) the secondterm prevails. Such an inequality CHb kD is especially true for the polymers with highTg [25]. The Langmuir sorption capacity parameter CH in many aspects behaves asapproximate measure of free volume. For example, it correlates with the permeabilitycoefficients Pi in the same manner as Pi correlates with FFV [26].Although the dual mode sorption model gives a very good description of gas sorption

in glassy polymers, one must remember that it is a completely empiric one. In addition, itlacks any prediction ability. Therefore, more sophisticated models are needed for thedescription and prediction of solubility of gases in glassy polymers. Several contemporarymodels can play such a role. One of the most efficient among them is the so-called non-equilibrium lattice fluid (NELF) model developed by G.C. Sarti and his school [27]. It isbased on real properties of polymers (equation of state), includes only one adjustableparameter, and very efficiently predicts the solubility coefficients and the shape of thesorption isotherm up to high pressure.

1.3 Concentration dependence of permeability anddiffusion coefficients

When the concentration of dissolved penetrants in a polymer is low, they only weaklyinfluence the properties of the polymer matrix. Moreover, the diffusing molecules atlow concentrations do not affect each other. Therefore, in such conditions the D valuesdo not depend on penetrant concentration C (Figure 1.1a).

Membrane Materials for Gas and Vapor Separation6

However, at greater concentrations the diffusion coefficients become concentrationdependent. This phenomenon is observed for example in transport of hydrocarbonsin silicon containing poly(tricyclononene), as Figure 1.1b shows.The same behavior is typical for sorption and transport of vapors of organic solvents in

polymers.The model of dual mode sorption was extended to description of gas transport in

glassy polymers [25]. On this basis it was shown that the concentration dependencesof the diffusion coefficients have S-shaped form, as Figure 1.1c indicates.Some penetrants tend to cluster, i.e. form dimers or trimers in the process of diffusion.

This is especially true for water vapor or the vapor of lower alcohols. At greater concen-trations the tendency of clustering increases, so the average size of the diffusing speciesbecomes larger. This results in decreases in the diffusion coefficients. Figure 1.1d serves

01

10

2 4

1

2

6 8 10c, cm3(STP)/cm3

D·1

08 , c

m2 /

s

Figure 1.1a Diffusion coefficients D at 75 C and different concentrations of CO2 inpolybenzylmethacrylate. 1, sorption; 2, desorption. Adapted from Reference 28.

00

10

20

30

40

50

20 40 60 80 100 140

c, cm3(STP)/cm3

D·1

08 , c

m2 /

s

120

1

2

Figure 1.1b Concentration dependences of diffusion coefficients D of hydrocarbons in poly(3,4-[bis(trimethylsiloxy)silyl]tricyclononene-7). 1, propane; 2, ethane. Adapted from Reference 29.

1 Permeability of Polymers 7

as an illustration of such behavior for the cases of diffusion of methanol and ethanol inglassy amorphous Teflon AF2400.Equation (1.5) in its simple form holds only whenD = const. and S = const., i.e. Henry’s

law is obeyed. This is true, for example, for the permeability of methane in PDMS(Figure 1.2a). In the more general caseD values are functions of penetrant concentrationor pressure and S is not constant, that is, non-linear isotherms are observed. Therefore,the permeability coefficient becomes pressure dependent.The model of the dual mode sorption and permeation in glassy polymers predicts

monotonic non-linear decreases in the P values when pressure increases (Figure 1.2b).In reality, gas sorption and permeation in glassy polymers are often exacerbated by

plasticization phenomena at higher concentrations of solutes. This can cause increases

00

1

2

3

4

5

6

10 20 40

c, cm3(STP)/cm3

D·1

08 , c

m2 /

s

30

Figure 1.1c Concentration dependence of the diffusion coefficients D according to the dual modesorption model. The system is CO2 in polycarbonate at 35 C. Adapted from Reference 30.

00

2

4

6

8

10

16

10 20 30

c, cm3(STP)/cm3

D·1

08 , c

m2 /

s

5

12

14

15 25

1

2

Figure 1.1d Concentration dependence of the diffusion coefficients D of methanol (1) and ethanol(2) in amorphous Teflon AF2400 at 25 C. Adapted from Reference 31.

Membrane Materials for Gas and Vapor Separation8