An Introduction to Polymer Physics

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1 An Introduction to Polymer Physics David I. Bower Formerly at the University of Leeds (CAMBRIDGE UNIVERSITY PRESS

Preface Acknowledgements xii xv 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.

2 Preface Acknowledgements xii xv 1 Introduction Polymers and the scope of the book A brief history of the development of synthetic polymers The chemical nature of polymers Introduction The classification of polymers 'Classical' polymerisation processes Newer polymers and polymerisation processes Properties and applications Polymer processing Introduction Additives and composites Processing methods Further reading Some general polymer texts Further reading specifically for chapter Some physical techniques for studying polymers Introduction Differential scanning calorimetry (DSC) and differential thermal analysis (DTA) Density measurement Light scattering X-ray scattering Wide-angle scattering (WAXS) Small-angle scattering (SAXS) Infrared and Raman spectroscopy The principles of infrared and Raman spectroscopy Spectrometers for infrared and Raman spectroscopy The infrared and Raman spectra of polymers 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.

3 2.7 Nuclear magnetic resonance spectroscopy (NMR) Introduction NMR spectrometers and experiments Chemical shifts and spin-spin interactions Magic-angle spinning, dipolar decoupling and cross polarisation Spin diffusion Multi-dimensional NMR Quadrupolar coupling and 2 H spectra Optical and electron microscopy Optical microscopy Electron microscopy Further reading 62 3 Molecular sizes and shapes and ordered structures Introduction Distributions of molar mass and their determination Number-average and weight-average molar masses Determination of molar masses and distributions The shapes of polymer molecules Bonding and the shapes of molecules Conformations and chain statistics The single freely jointed chain More realistic chains - the excluded-volume effect Chain flexibility and the persistence length Evidence for ordered structures in solid polymers Wide-angle X-ray scattering - WAXS Small-angle X-ray scattering - SAXS Light scattering Optical microscopy Further reading Problems 85 4 Regular chains and crystallinity Regular and irregular chains Introduction Polymers with 'automatic' regularity Vinyl polymers and tacticity Polydienes Helical molecules 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 4.2.1 Introduction Fibre patterns and the unit cell Actual chain conformations and crystal structures Information about crystal structures from other methods Crystal structures of some common polymers Polyethylene Syndiotactic polyvinyl chloride) (PVC) Polyethylene terephthalate) (PET) The nylons (polyamides) Further reading Problems Morphology and motion Introduction The degree of crystallinity Introduction Experimental determination of crystallinity Crystallites The fringed-micelle model Chain-folded crystallites Extended-chain crystallites Non-crystalline regions and polymer macro-conformations Non-crystalline regions Polymer macro-conformations Lamellar stacks Spherulites and other polycrystalline structures Optical microscopy of spherulites Light scattering by spherulites Other methods for observing spherulites Axialites and shish-kebabs Crystallisation and melting The melting temperature The rate of crystallisation Theories of chain folding and lamellar thickness Molecular motion Introduction NMR, mechanical and electrical relaxation The site-model theory Three NMR studies of relaxations with widely different values of r c Further NMR evidence for various motions in polymers 156

viii Contents 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.

5 viii Contents 5.8 Further reading Problems Mechanical properties I - time-independent elasticity Introduction to the mechanical properties of polymers Elastic properties of isotropic polymers at small strains The elastic constants of isotropic media at small strains The small-strain properties of isotropic polymers The phenomenology of rubber elasticity Introduction The transition to large-strain elasticity Strain-energy functions The neo-hookeian solid The statistical theory of rubber elasticity Introduction The fundamental mechanism of rubber elasticity The thermodynamics of rubber elasticity Development of the statistical theory Modifications of the simple molecular and phenomenological theories Further reading Problems Mechanical properties П - linear viscoelasticity Introduction and definitions Introduction Creep Stress-relaxation The Boltzmann superposition principle (BSP) Mechanical models Introduction The Maxwell model The Kelvin or Voigt model The standard linear solid Real materials - relaxation-time and retardation-time spectra Experimental methods for studying viscoelastic behaviour Transient measurements Dynamic measurements - the complex modulus and compliance Dynamic measurements; examples 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.

6 7.5 The glass transition in amorphous polymers The determination of the glass-transition temperature The temperature dependence of the shift factor: the VFT and WLF equations Theories of the glass transition Factors that affect the value of T g Relaxations for amorphous and crystalline polymers Introduction Amorphous polymers Crystalline polymers Final remarks Further reading Problems Yield and fracture of polymers Introduction Yield Introduction The mechanism of yielding - cold drawing and the Considere construction Yield criteria The pressure dependence of yield Temperature and strain-rate dependences of yield Fracture Introduction Theories of fracture; toughness parameters Experimental determination of fracture toughness Crazing Impact testing of polymers Further reading Problems Electrical and optical properties Introduction Electrical polarisation The dielectric constant and the refractive index Molecular polarisability and the low-frequency dielectric constant Bond polarisabilities and group dipole moments Dielectric relaxation The dielectric constants and relaxations of polymers Conducting polymers 267

$4.2 Transparency and colourlessness ъ 284 9.4.3 The refractive index 285 9.5 Further reading 288 9.6 Problems 288 10 Oriented polymers I - production and characterisation 290 10.$

7 9.3.1 Introduction Ionic conduction Electrical conduction in metals and semiconductors Electronic conduction in polymers Optical properties of polymers Introduction Transparency and colourlessness ъ The refractive index Further reading Problems Oriented polymers I - production and characterisation Introduction - the meaning and importance of orientation The production of orientation in synthetic polymers Undesirable or incidental orientation Deliberate orientation by processing in the solid state Deliberate orientation by processing in the fluid state Cold drawing and the natural draw ratio The mathematical description of molecular orientation Experimental methods for investigating the degree of orientation Measurement of optical refractive indices or birefringence Measurement of infrared dichroism Polarised fluorescence Raman spectroscopy Wide-angle X-ray scattering The combination of methods for two-phase systems Methods of representing types of orientation Triangle diagrams Pole figures Limitations of the representations Further reading Problems Oriented polymers II - models and properties Introduction Models for molecular orientation The affine rubber deformation scheme The aggregate or pseudo-afline deformation scheme Comparison between theory and experiment 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.

8 The affine rubber model and 'frozen-in' orientation The affine rubber model and the stress-optical coefficient The pseudo-affine aggregate model Comparison between predicted and observed elastic properties Introduction The elastic constants and the Ward aggregate model Takayanagi composite models Highly oriented polymers and ultimate moduli Ultimate moduli Models for highly oriented polyethylene Further reading Problems Polymer blends, copolymers and liquid-crystal polymers Introduction Polymer blends Introduction Conditions for polymer-polymer miscibility Experimental detection of miscibility Compatibilisation and examples of polymer blends Morphology Properties and applications Copolymers Introduction and nomenclature Linear copolymers: segregation and melt morphology Copolymers combining elastomeric and rigid components Semicrystalline block copolymers Liquid-crystal polymers Introduction Types of mesophases for small molecules Types of liquid-crystal polymers The theory of liquid-crystal alignment The processing of liquid-crystal polymers The physical structure of solids from liquid-crystal polymers The properties and applications of liquid-crystal polymers 386 1=2.5 Further reading Problems 391 Appendix: Cartesian tensors 393 Solutions to problems 397 Index 425

Mechanical Properties of Polymers. Scope. MSE 383, Unit 3-1. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept.

Mechanical Properties of Polymers Scope MSE 383, Unit 3-1 Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Structure - mechanical properties relations Time-dependent mechanical