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 An Introduction to Polymer Physics David I Bower Formerly at the University of Leeds Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge , United Kingdom Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521631372 © D I Bower 2002 This book is in copyright Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published in print format 2002 - - ---- eBook (NetLibrary) --- eBook (NetLibrary) - - ---- hardback --- hardback - - ---- paperback --- paperback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Contents Preface Acknowledgements xii xv Introduction 1.1 Polymers and the scope of the book 1.2 A brief history of the development of synthetic polymers 1.3 The chemical nature of polymers 1.3.1 Introduction 1.3.2 The classification of polymers 1.3.3 ‘Classical’ polymerisation processes 1.3.4 Newer polymers and polymerisation processes 1.4 Properties and applications 1.5 Polymer processing 1.5.1 Introduction 1.5.2 Additives and composites 1.5.3 Processing methods 1.6 Further reading 1.6.1 Some general polymer texts 1.6.2 Further reading specifically for chapter 1 8 12 17 18 21 21 22 23 25 25 26 Some physical techniques for studying polymers 2.1 Introduction 2.2 Differential scanning calorimetry (DSC) and differential thermal analysis (DTA) 2.3 Density measurement 2.4 Light scattering 2.5 X-ray scattering 2.5.1 Wide-angle scattering (WAXS) 2.5.2 Small-angle scattering (SAXS) 2.6 Infrared and Raman spectroscopy 2.6.1 The principles of infrared and Raman spectroscopy 2.6.2 Spectrometers for infrared and Raman spectroscopy 2.6.3 The infrared and Raman spectra of polymers 2.6.4 Quantitative infrared spectroscopy – the Lambert–Beer law 27 27 27 31 32 33 33 38 38 38 41 42 43 v vi Contents 2.7 Nuclear magnetic resonance spectroscopy (NMR) 2.7.1 Introduction 2.7.2 NMR spectrometers and experiments 2.7.3 Chemical shifts and spin–spin interactions 2.7.4 Magic-angle spinning, dipolar decoupling and cross polarisation 2.7.5 Spin diffusion 2.7.6 Multi-dimensional NMR 2.7.7 Quadrupolar coupling and 2H spectra 2.8 Optical and electron microscopy 2.8.1 Optical microscopy 2.8.2 Electron microscopy 2.9 Further reading 44 44 46 49 Molecular sizes and shapes and ordered structures 3.1 Introduction 3.2 Distributions of molar mass and their determination 3.2.1 Number-average and weight-average molar masses 3.2.2 Determination of molar masses and distributions 3.3 The shapes of polymer molecules 3.3.1 Bonding and the shapes of molecules 3.3.2 Conformations and chain statistics 3.3.3 The single freely jointed chain 3.3.4 More realistic chains – the excluded-volume effect 3.3.5 Chain flexibility and the persistence length 3.4 Evidence for ordered structures in solid polymers 3.4.1 Wide-angle X-ray scattering – WAXS 3.4.2 Small-angle X-ray scattering – SAXS 3.4.3 Light scattering 3.4.4 Optical microscopy 3.5 Further reading 3.6 Problems 63 63 63 63 65 66 66 72 72 76 80 81 81 82 83 84 85 85 Regular chains and crystallinity 4.1 Regular and irregular chains 4.1.1 Introduction 4.1.2 Polymers with ‘automatic’ regularity 4.1.3 Vinyl polymers and tacticity 4.1.4 Polydienes 4.1.5 Helical molecules 4.2 The determination of crystal structures by X-ray diffraction 87 87 87 89 90 96 96 98 50 52 52 54 55 55 58 62 Contents 4.3 4.4 4.5 4.6 4.2.1 Introduction 4.2.2 Fibre patterns and the unit cell 4.2.3 Actual chain conformations and crystal structures Information about crystal structures from other methods Crystal structures of some common polymers 4.4.1 Polyethylene 4.4.2 Syndiotactic poly(vinyl chloride) (PVC) 4.4.3 Poly(ethylene terephthalate) (PET) 4.4.4 The nylons (polyamides) Further reading Problems Morphology and motion 5.1 Introduction 5.2 The degree of crystallinity 5.2.1 Introduction 5.2.2 Experimental determination of crystallinity 5.3 Crystallites 5.3.1 The fringed-micelle model 5.3.2 Chain-folded crystallites 5.3.3 Extended-chain crystallites 5.4 Non-crystalline regions and polymer macro-conformations 5.4.1 Non-crystalline regions 5.4.2 Polymer macro-conformations 5.4.3 Lamellar stacks 5.5 Spherulites and other polycrystalline structures 5.5.1 Optical microscopy of spherulites 5.5.2 Light scattering by spherulites 5.5.3 Other methods for observing spherulites 5.5.4 Axialites and shish-kebabs 5.6 Crystallisation and melting 5.6.1 The melting temperature 5.6.2 The rate of crystallisation 5.6.3 Theories of chain folding and lamellar thickness 5.7 Molecular motion 5.7.1 Introduction 5.7.2 NMR, mechanical and electrical relaxation 5.7.3 The site-model theory 5.7.4 Three NMR studies of relaxations with widely different values of c 5.7.5 Further NMR evidence for various motions in polymers 98 99 106 109 111 111 111 111 113 115 115 117 117 118 118 119 120 121 122 127 127 127 129 129 133 133 135 136 136 137 138 139 141 145 145 146 148 150 156 vii viii Contents 5.8 Further reading 5.9 Problems 160 160 Mechanical properties I – time-independent elasticity 6.1 Introduction to the mechanical properties of polymers 6.2 Elastic properties of isotropic polymers at small strains 6.2.1 The elastic constants of isotropic media at small strains 6.2.2 The small-strain properties of isotropic polymers 6.3 The phenomenology of rubber elasticity 6.3.1 Introduction 6.3.2 The transition to large-strain elasticity 6.3.3 Strain–energy functions 6.3.4 The neo-Hookeian solid 6.4 The statistical theory of rubber elasticity 6.4.1 Introduction 6.4.2 The fundamental mechanism of rubber elasticity 6.4.3 The thermodynamics of rubber elasticity 6.4.4 Development of the statistical theory 6.5 Modifications of the simple molecular and phenomenological theories 6.6 Further reading 6.7 Problems 162 162 164 164 166 169 169 170 173 174 176 176 178 179 181 Mechanical properties II – linear viscoelasticity 7.1 Introduction and definitions 7.1.1 Introduction 7.1.2 Creep 7.1.3 Stress-relaxation 7.1.4 The Boltzmann superposition principle (BSP) 7.2 Mechanical models 7.2.1 Introduction 7.2.2 The Maxwell model 7.2.3 The Kelvin or Voigt model 7.2.4 The standard linear solid 7.2.5 Real materials – relaxation-time and retardation-time spectra 7.3 Experimental methods for studying viscoelastic behaviour 7.3.1 Transient measurements 7.3.2 Dynamic measurements – the complex modulus and compliance 7.3.3 Dynamic measurements; examples 7.4 Time–temperature equivalence and superposition 187 187 187 188 190 191 193 193 194 195 196 184 184 185 197 198 198 199 201 204 Contents 7.5 The glass transition in amorphous polymers 7.5.1 The determination of the glass-transition temperature 7.5.2 The temperature dependence of the shift factor: the VFT and WLF equations 7.5.3 Theories of the glass transition 7.5.4 Factors that affect the value of Tg 7.6 Relaxations for amorphous and crystalline polymers 7.6.1 Introduction 7.6.2 Amorphous polymers 7.6.3 Crystalline polymers 7.6.4 Final remarks 7.7 Further reading 7.8 Problems Yield and fracture of polymers 8.1 Introduction 8.2 Yield 8.2.1 Introduction 8.2.2 The mechanism of yielding – cold drawing and the Conside`re construction 8.2.3 Yield criteria 8.2.4 The pressure dependence of yield 8.2.5 Temperature and strain-rate dependences of yield 8.3 Fracture 8.3.1 Introduction 8.3.2 Theories of fracture; toughness parameters 8.3.3 Experimental determination of fracture toughness 8.3.4 Crazing 8.3.5 Impact testing of polymers 8.4 Further reading 8.5 Problems Electrical and optical properties 9.1 Introduction 9.2 Electrical polarisation 9.2.1 The dielectric constant and the refractive index 9.2.2 Molecular polarisability and the low-frequency dielectric constant 9.2.3 Bond polarisabilities and group dipole moments 9.2.4 Dielectric relaxation 9.2.5 The dielectric constants and relaxations of polymers 9.3 Conducting polymers 206 206 208 209 211 212 212 213 213 217 217 217 220 220 223 223 223 226 231 232 234 234 235 239 240 243 246 246 248 248 249 249 252 254 256 260 267 ix