An Introduction to Polymer Physics
No previous knowledge of polymers is assumed in this book which
provides a general introduction to the physics of solid polymers.
The book covers a wide range of topics within the field of polymer
physics, beginning with a brief history of the development of synthetic
polymers and an overview of the methods of polymerisation and
processing. In the following chapter, David Bower describes important
experimental techniques used in the study of polymers. The main part of
the book, however, is devoted to the structure and properties of solid
polymers, including blends, copolymers and liquid-crystal polymers.
With an approach appropriate for advanced undergraduate and
graduate students of physics, materials science and chemistry, the book
includes many worked examples and problems with solutions. It will
provide a firm foundation for the study of the physics of solid polymers.
DAVID BOWER received his D.Phil. from the University of Oxford in 1964. In
1990 he became a reader in the Department of Physics at the University of
Leeds, retiring from this position in 1995. He was a founder member of the
management committee of the IRC in Polymer Science and Technology
(Universities of Leeds, Durham and Bradford), and co-authored The
Vibrational Spectroscopy of Polymers with W. F. Maddams (CUP, 1989).
His contribution to the primary literature has included work on polymers,
solid-state physics and magnetism.
Contents
1 Introduction 1
1.1 Polymers and the scope of the book 1
1.2 A brief history of the development of synthetic polymers 2
1.3 The chemical nature of polymers 8
1.3.1 Introduction 8
1.3.2 The classification of polymers 9
1.3.3 ‘Classical’ polymerisation processes 12
1.3.4 Newer polymers and polymerisation processes 17
1.4 Properties and applications 18
1.5 Polymer processing 21
1.5.1 Introduction 21
1.5.2 Additives and composites 22
1.5.3 Processing methods 23
1.6 Further reading 25
1.6.1 Some general polymer texts 25
1.6.2 Further reading specifically for chapter 1 26
2 Some physical techniques for studying polymers 27
2.1 Introduction 27
2.2 Differential scanning calorimetry (DSC) and differential
thermal analysis (DTA) 27
2.3 Density measurement 31
2.4 Light scattering 32
2.5 X-ray scattering 33
2.5.1 Wide-angle scattering (WAXS) 33
2.5.2 Small-angle scattering (SAXS) 38
2.6 Infrared and Raman spectroscopy 38
2.6.1 The principles of infrared and Raman spectroscopy 38
2.6.2 Spectrometers for infrared and Raman spectroscopy 41
2.6.3 The infrared and Raman spectra of polymers 42
2.6.4 Quantitative infrared spectroscopy – the Lambert–Beer
law 43
2.7 Nuclear magnetic resonance spectroscopy (NMR) 44
2.7.1 Introduction 44
2.7.2 NMR spectrometers and experiments 46
2.7.3 Chemical shifts and spin–spin interactions 49
2.7.4 Magic-angle spinning, dipolar decoupling and cross
polarisation 50
2.7.5 Spin diffusion 52
2.7.6 Multi-dimensional NMR 52
2.7.7 Quadrupolar coupling and 2H spectra 54
2.8 Optical and electron microscopy 55
2.8.1 Optical microscopy 55
2.8.2 Electron microscopy 58
2.9 Further reading 62
3 Molecular sizes and shapes and ordered structures 63
3.1 Introduction 63
3.2 Distributions of molar mass and their determination 63
3.2.1 Number-average and weight-average molar masses 63
3.2.2 Determination of molar masses and distributions 65
3.3 The shapes of polymer molecules 66
3.3.1 Bonding and the shapes of molecules 66
3.3.2 Conformations and chain statistics 72
3.3.3 The single freely jointed chain 72
3.3.4 More realistic chains – the excluded-volume effect 76
3.3.5 Chain flexibility and the persistence length 80
3.4 Evidence for ordered structures in solid polymers 81
3.4.1 Wide-angle X-ray scattering – WAXS 81
3.4.2 Small-angle X-ray scattering – SAXS 82
3.4.3 Light scattering 83
3.4.4 Optical microscopy 84
3.5 Further reading 85
3.6 Problems 85
4 Regular chains and crystallinity 87
4.1 Regular and irregular chains 87
4.1.1 Introduction 87
4.1.2 Polymers with ‘automatic’ regularity 89
4.1.3 Vinyl polymers and tacticity 90
4.1.4 Polydienes 96
4.1.5 Helical molecules 96
4.2 The determination of crystal structures by X-ray diffraction 98
4.2.1 Introduction 98
4.2.2 Fibre patterns and the unit cell 99
4.2.3 Actual chain conformations and crystal structures 106
4.3 Information about crystal structures from other methods 109
4.4 Crystal structures of some common polymers 111
4.4.1 Polyethylene 111
4.4.2 Syndiotactic poly(vinyl chloride) (PVC) 111
4.4.3 Poly(ethylene terephthalate) (PET) 111
4.4.4 The nylons (polyamides) 113
4.5 Further reading 115
4.6 Problems 115
5Morphol ogy and motion 117
5.1 Introduction 117
5.2 The degree of crystallinity 118
5.2.1 Introduction 118
5.2.2 Experimental determination of crystallinity 119
5.3 Crystallites 120
5.3.1 The fringed-micelle model 121
5.3.2 Chain-folded crystallites 122
5.3.3 Extended-chain crystallites 127
5.4 Non-crystalline regions and polymer macro-conformations 127
5.4.1 Non-crystalline regions 127
5.4.2 Polymer macro-conformations 129
5.4.3 Lamellar stacks 129
5.5 Spherulites and other polycrystalline structures 133
5.5.1 Optical microscopy of spherulites 133
5.5.2 Light scattering by spherulites 135
5.5.3 Other methods for observing spherulites 136
5.5.4 Axialites and shish-kebabs 136
5.6 Crystallisation and melting 137
5.6.1 The melting temperature 138
5.6.2 The rate of crystallisation 139
5.6.3 Theories of chain folding and lamellar thickness 141
5.7 Molecular motion 145
5.7.1 Introduction 145
5.7.2 NMR, mechanical and electrical relaxation 146
5.7.3 The site-model theory 148
5.7.4 Three NMR studies of relaxations with widely
different values of c 150
5.7.5 Further NMR evidence for various motions in polymers 156
5.8 Further reading 160
5.9 Problems 160
6 Mechanical properties I – time-independent elasticity 162
6.1 Introduction to the mechanical properties of polymers 162
6.2 Elastic properties of isotropic polymers at small strains 164
6.2.1 The elastic constants of isotropic media at small strains 164
6.2.2 The small-strain properties of isotropic polymers 166
6.3 The phenomenology of rubber elasticity 169
6.3.1 Introduction 169
6.3.2 The transition to large-strain elasticity 170
6.3.3 Strain–energy functions 173
6.3.4 The neo-Hookeian solid 174
6.4 The statistical theory of rubber elasticity 176
6.4.1 Introduction 176
6.4.2 The fundamental mechanism of rubber elasticity 178
6.4.3 The thermodynamics of rubber elasticity 179
6.4.4 Development of the statistical theory 181
6.5 Modifications of the simple molecular and phenomenological
theories 184
6.6 Further reading 184
6.7 Problems 185
7 Mechanical properties II – linear viscoelasticity 187
7.1 Introduction and definitions 187
7.1.1 Introduction 187
7.1.2 Creep 188
7.1.3 Stress-relaxation 190
7.1.4 The Boltzmann superposition principle (BSP) 191
7.2 Mechanical models 193
7.2.1 Introduction 193
7.2.2 The Maxwell model 194
7.2.3 The Kelvin or Voigt model 195
7.2.4 The standard linear solid 196
7.2.5 Real materials – relaxation-time and retardation-time
spectra 197
7.3 Experimental methods for studying viscoelastic behaviour 198
7.3.1 Transient measurements 198
7.3.2 Dynamic measurements – the complex modulus and
compliance 199
7.3.3 Dynamic measurements; examples 201
7.4 Time–temperature equivalence and superposition 204
7.5 The glass transition in amorphous polymers 206
7.5.1 The determination of the glass-transition temperature 206
7.5.2 The temperature dependence of the shift factor: the VFT
and WLF equations 208
7.5.3 Theories of the glass transition 209
7.5.4 Factors that affect the value of Tg 211
7.6 Relaxations for amorphous and crystalline polymers 212
7.6.1 Introduction 212
7.6.2 Amorphous polymers 213
7.6.3 Crystalline polymers 213
7.6.4 Final remarks 217
7.7 Further reading 217
7.8 Problems 217
8 Yield and fracture of polymers 220
8.1 Introduction 220
8.2 Yield 223
8.2.1 Introduction 223
8.2.2 The mechanism of yielding – cold drawing and the
Conside`re construction 223
8.2.3 Yield criteria 226
8.2.4 The pressure dependence of yield 231
8.2.5 Temperature and strain-rate dependences of yield 232
8.3 Fracture 234
8.3.1 Introduction 234
8.3.2 Theories of fracture; toughness parameters 235
8.3.3 Experimental determination of fracture toughness 239
8.3.4 Crazing 240
8.3.5 Impact testing of polymers 243
8.4 Further reading 246
8.5 Problems 246
9 Electrical and optical properties 248
9.1 Introduction 248
9.2 Electrical polarisation 249
9.2.1 The dielectric constant and the refractive index 249
9.2.2 Molecular polarisability and the low-frequency dielectric
constant 252
9.2.3 Bond polarisabilities and group dipole moments 254
9.2.4 Dielectric relaxation 256
9.2.5 The dielectric constants and relaxations of polymers 260
9.3 Conducting polymers 267
9.3.1 Introduction 267
9.3.2 Ionic conduction 268
9.3.3 Electrical conduction in metals and semiconductors 272
9.3.4 Electronic conduction in polymers 275
9.4 Optical properties of polymers 283
9.4.1 Introduction 283
9.4.2 Transparency and colourlessness 284
9.4.3 The refractive index 285
9.5 Further reading 288
9.6 Problems 288
10 Oriented polymers I – production and characterisation 290
10.1 Introduction – the meaning and importance of orientation 290
10.2 The production of orientation in synthetic polymers 291
10.2.1 Undesirable or incidental orientation 292
10.2.2 Deliberate orientation by processing in the solid state 292
10.2.3 Deliberate orientation by processing in the fluid state 296
10.2.4 Cold drawing and the natural draw ratio 298
10.3 The mathematical description of molecular orientation 298
10.4 Experimental methods for investigating the degree of
orientation 301
10.4.1 Measurement of optical refractive indices or
birefringence 301
10.4.2 Measurement of infrared dichroism 305
10.4.3 Polarised fluorescence 310
10.4.4 Raman spectroscopy 312
10.4.5 Wide-angle X-ray scattering 312
10.5 The combination of methods for two-phase systems 314
10.6 Methods of representing types of orientation 315
10.6.1 Triangle diagrams 315
10.6.2 Pole figures 316
10.6.3 Limitations of the representations 317
10.7 Further reading 318
10.8 Problems 318
11 Oriented polymers II – models and properties 321
11.1 Introduction 321
11.2 Models for molecular orientation 321
11.2.1 The affine rubber deformation scheme 322
11.2.2 The aggregate or pseudo-affine deformation scheme 326
11.3 Comparison between theory and experiment 327
11.3.1 Introduction 327
11.3.2 The affine rubber model and ‘frozen-in’ orientation 328
11.3.3 The affine rubber model and the stress-optical coefficient 329
11.3.4 The pseudo-affine aggregate model 332
11.4 Comparison between predicted and observed elastic properties 332
11.4.1 Introduction 332
11.4.2 The elastic constants and the Ward aggregate model 333
11.5 Takayanagi composite models 335
11.6 Highly oriented polymers and ultimate moduli 338
11.6.1 Ultimate moduli 338
11.6.2 Models for highly oriented polyethylene 340
11.7 Further reading 341
11.8 Problems 341
12 Polymer blends, copolymers and liquid-crystal polymers 343
12.1 Introduction 343
12.2 Polymer blends 344
12.2.1 Introduction 344
12.2.2 Conditions for polymer–polymer miscibility 344
12.2.3 Experimental detection of miscibility 350
12.2.4 Compatibilisation and examples of polymer blends 354
12.2.5 Morphology 356
12.2.6 Properties and applications 358
12.3 Copolymers 360
12.3.1 Introduction and nomenclature 360
12.3.2 Linear copolymers: segregation and melt morphology 362
12.3.3 Copolymers combining elastomeric and rigid components 367
12.3.4 Semicrystalline block copolymers 368
12.4 Liquid-crystal polymers 370
12.4.1 Introduction 370
12.4.2 Types of mesophases for small molecules 371
12.4.3 Types of liquid-crystal polymers 373
12.4.4 The theory of liquid-crystal alignment 375
12.4.5 The processing of liquid-crystal polymers 382
12.4.6 The physical structure of solids from liquid-crystal
polymers 383
12.4.7 The properties and applications of liquid-crystal polymers 386
12.5 Further reading 391
12.6 Problems 391
Appendix:Cartesi an tensors 393
Solutions to problems 397
Index 425
Preface
There are already a fairly large number of textbooks on various aspects of
polymers and, more specifically, on polymer physics, so why another?
While presenting a short series of undergraduate lectures on polymer
physics at the University of Leeds over a number of years I found it
difficult to recommend a suitable textbook. There were books that had
chapters appropriate to some of the topics being covered, but it was
difficult to find suitable material at the right level for others. In fact
most of the textbooks available both then and now seem to me more
suitable for postgraduate students than for undergraduates. This book is
definitely for undergraduates, though some students will still find parts of it
quite demanding.
In writing any book it is, of course, necessary to be selective. The
criteria for inclusion of material in an undergraduate text are, I believe,
its importance within the overall field covered, its generally noncontroversial
nature and, as already indicated, its difficulty. All of these
are somewhat subjective, because assessing the importance of material
tends to be tainted by the author’s own interests and opinions. I have
simply tried to cover the field of solid polymers widely in a book of
reasonable length, but some topics that others would have included are
inevitably omitted. As for material being non-controversial, I have given
only rather brief mentions of ideas and theoretical models that have not
gained general acceptance or regarding which there is still much debate.
Students must, of course, understand that all of science involves
uncertainties and judgements, but such matters are better left mainly for
discussion in seminars or to be set as short research tasks or essays;
inclusion of too much doubt in a textbook only confuses.
Difficulty is particularly subjective, so one must judge partly from
one’s own experiences with students and partly from comments of
colleagues who read the text. There is, however, no place in the modern
undergraduate text for long, very complicated, particularly mathematically
complicated, discussions of difficult topics. Nevertheless, these topics
cannot be avoided altogether if they are important either practically or
for the general development of the subject, so an appropriate simplified
difficult’ to ‘too easy’ for various parts of the text as it now stands, with a
treatment must be given. Comments from readers have ranged from ‘too
large part ‘about right’. This seems to me a good mix, offering both
comfort and challenge, and I have not, therefore, aimed at greater
homogeneity.
It is my experience that students are put off by unfamiliar symbols or
symbols with a large number of superscripts or subscripts, so I have
attempted where possible to use standard symbols for all quantities. This
means that, because the book covers a wide range of areas of physics, the
same symbols sometimes have different meanings in different places. I have
therefore, for instance, used to stand for a wide range of different angles
in different parts of the book and only used subscripts on it where
absolutely necessary for clarity. Within a given chapter I have, however,
tried to avoid using the same symbol to mean different things, but where
this was unavoidable without excess complication I have drawn attention
to the fact.
It is sometimes said that an author has simply compiled his book by
taking the best bits out of a number of other books. I have certainly used
what I consider to be some of the best or most relevant bits from many
more specialised books, in the sense that these books have often provided
me with general guidance as to what is important in a particular area in
which my experience is limited and have also provided many specific
examples of properties or behaviour; it is clearly not sensible to use poor
examples because somebody else has used the best ones! I hope, however,
that my choice of material, the way that I have reworked it and added
explanatory material, and the way that I have cross-referenced different
areas of the text has allowed me to construct a coherent whole, spanning a
wider range of topics at a simpler level than that of many of the books that
I have consulted and made use of. I therefore hope that this book will
provide a useful introduction to them.
Chapters 7 and 8 and parts of chapter 11, in particular, have been
influenced strongly by the two more-advanced textbooks on the
mechanical properties of solid polymers by Professor I. M. Ward, and
the section of chapter 12 on liquid-crystal polymers has drawn heavily
on the more-advanced textbook by Professors A. Donald and A. H.
Windle. These books are referred to in the sections on further reading in
those chapters and I wish to acknowledge my debt to them, as to all the
books referred to there and in the corresponding sections of other chapters.
In addition, I should like to thank the following for reading various
sections of the book and providing critical comments in writing and
sometimes also in discussion: Professors D. Bloor, G. R. Davies, W. J.
Feast, T. C. B. McLeish and I. M. Ward and Drs P. Barham, R. A.
P. Unwin read the whole book between them and checked the solutions to
Duckett, P. G. Klein and D. J. Read. In addition, Drs P. Hine and A.
all the examples and problems. Without the efforts of all these people many
obscurities and errors would not have been removed. For any that remain
and for sometimes not taking the advice offered, I am, of course,
responsible.
Dr W. F. Maddams, my co-author for an earlier book, The Vibrational
Spectroscopy of Polymers (CUP 1989), kindly permitted me to use or adapt
materials from that book, for which I thank him. I have spent considerable
time trying to track down the copyright holders and originators of the
other figures and tables not drawn or compiled by me and I am grateful
to those who have given permission to use or adapt material. If I have
inadvertently not given due credit for any material used I apologise. I have
generally requested permission to use material from only one of a set of coauthors
and I hope that I shall be excused for using material without their
explicit permission by those authors that I have not contacted and authors
that I have not been able to trace. Brief acknowledgements are given in the
figure captions and fuller versions are listed on p. xv. This list may provide
useful additional references to supplement the books cited in the further
reading sections of each chapter. I am grateful to The University of Leeds
for permission to use or adapt some past examination questions as
problems.
Finally, I should like to thank my wife for her support during the
writing of this book.
D. I. B., Leeds, November 2001
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