The Mesoscopic Theory of Polymer Dynamics

by Pokrovskii, Vladimir N.

• ISBN13: 9789048122301
• ISBN10: 9048122309
• Edition: 2nd
• Format: Hardcover
• Copyright: 2010-01-03
• Publisher: Springer Verlag

Summary

The theory presented in this book explains in a consistent manner all dynamics effects (diffusion, neutron scattering, viscoelasticity, optical birefringence) observed in very concentrated solutions and melts of linear polymers from a macromolecular point of view. This monograph reconciles different approaches to polymer dynamics and reflects the modern situation in understanding the relaxation behaviour of the polymer systems. The reader is invited to follow the way from dynamics of a separate macromolecule to the constitutive relations for both weakly and strongly entangled linear polymers. The contents can be related to the fields of molecular physics, fluid mechanics, polymer physics and materials science. This text provides material for one or two semester graduate-level course in polymer dynamics or for graduate students with some background in physics and mathematics. The monograph presents topics in a self-contained way that makes it a suitable reference book for professional researchers in the fields of polymer science, polymer engineering, and materials science.

Table of Contents

Preface to the Revised Edition	p. xi
Preface to the First Edition	p. xiii
Notations and Conventions	p. xv
Introduction: Macromolecular Systems in Equilibrium	p. 1
Microscopic Models of a Macromolecule	p. 1
Bead-and-Spring Model	p. 3
Normal Co-Ordinates	p. 5
Macromolecular Coil	p. 6
Excluded-Volume Effects	p. 8
Macromolecules in a Solvent	p. 11
Macromolecules in a Dilute Solution	p. 12
Weakly-Coupled Macromolecules	p. 13
Elasticity of Polymer Networks	p. 16
Crystalline and Glassy Systems	p. 19
Dynamics of a Macromolecule in a Viscous Liquid	p. 21
Equation of Macromolecular Dynamics	p. 21
Intramacromolecular Hydrodynamic Interactions	p. 22
Resistance-Drag Coefficient of a Macromolecular Coil	p. 24
Effective Resistance-Drag Coefficient of a Particle	p. 26
Intramolecular Friction	p. 28
The Cerf-Zimm-Rouse Modes	p. 31
The Moments of Linear Modes	p. 32
Equations for the Moments of Co-ordinates	p. 33
The Slowest Relaxation Processes	p. 33
Fourier-Transforms of Moments	p. 35
Dynamics of a Macromolecule in an Entangled System	p. 37
Admitted Approximations in the Many-Chain Problem	p. 38
Dynamics of Entangled Course-Grained Chains	p. 38
Dynamics of a Probe Macromolecule	p. 40
The General Form of Dynamic Equation	p. 42
The Linear Approximation	p. 43
A Non-Linear Approximation - Local Anisotropy	p. 45
Molecular Interpretation of the Dissipative Terms	p. 46
Concept of Microviscoelasticity	p. 46
External Friction	p. 48
Intramolecular Friction	p. 51
Fundamental Dynamical Parameters	p. 53
Markovian Form of Dynamic Equation	p. 54
Reptation-Tube Model	p. 56
Method of Numerical Simulation	p. 59
Non-Dimensional Form of Dynamic Equation	p. 59
Algorithm of Calculation	p. 61
Conformational Relaxation	p. 63
Correlation Functions for the Linear Dynamics	p. 63
Modified Cerf-Rouse Modes	p. 63
Equilibrium Correlation Functions	p. 66
One-Point Non-Equilibrium Correlation Functions	p. 68
Two-Point Non-Equilibrium Correlation Functions	p. 69
Relaxation of Macromolecular Coil	p. 71
Correlation Functions for Isotropic Motion	p. 71
Effect of Local Anisotropy	p. 73
Transition Point	p. 77
Conformational Relaxation Times	p. 78
Macromolecular Coil in a Flow	p. 79
Non-Equilibrium Correlation Functions	p. 79
Size and Form of the Macromolecular Coil	p. 80
The Localisation Effect	p. 83
Mobility of a Macromolecule	p. 83
A Macromolecule in a Viscous Liquid	p. 84
A Macromolecule in an Entangled System	p. 85
Quasi-Elastic Neutron Scattering	p. 93
The Scattering Function	p. 94
An Estimation of Intermediate Length	p. 96
Linear Viscoelasticity	p. 99
Stresses in the Flow System	p. 99
The Stress Tensor	p. 99
Oscillatory Deformation	p. 102
Macromolecules in a Viscous Liquid	p. 103
The Stress Tensor	p. 103
Dynamic Characteristics	p. 105
Initial Intrinsic Viscosity	p. 107
On the Effect of Internal Viscosity	p. 109
Macromolecules in a Viscoelastic Liquid	p. 111
The Stress Tensor	p. 111
Dynamic Characteristics	p. 112
Entangled Macromolecules	p. 115
The Stress Tensor	p. 116
Dynamic Modulus and Relaxation Branches	p. 118
Self-Consistency of the Mesoscopic Approach	p. 122
Modulus of Elasticity and the Intermediate Length	p. 124
Concentration and Macromolecular Length Dependencies	p. 125
Frequency-Temperature Superposition	p. 127
Dilute Blends of Linear Polymers	p. 128
Relaxation of Probe Macromolecule	p. 129
Characteristic Quantities	p. 130
Terminal Relaxation Time	p. 132
A Pinal Remark	p. 134
Equations of Relaxation	p. 135
Normal-Modes Form of Dynamic Equation	p. 135
Transition to the Normal Modes	p. 135
Anisotropy of Particle Mobility	p. 137
Equations for the Non-Equilibrium Moments	p. 139
Relaxation of the Macromolecular Conformation	p. 143
Diffusive Relaxation	p. 143
Reptation Relaxation	p. 145
Relaxation of Orientational Variables	p. 146
Weakly Entangled Systems	p. 148
Strongly Entangled Systems	p. 148
Relaxation, of the Segment Orientation	p. 149
Rubber Elasticity and Mean Orientation of Segments	p. 149
Elementary Theory of Dielectric Relaxation	p. 151
Relaxation Processes in the Phenomenological Theory	p. 155
The Laws of Conservation of Momentum and Angular Momentum	p. 155
The Law of Conservation of Energy and the Balance of Entropy	p. 158
Thermodynamic Fluxes and Relaxation Processes	p. 160
The Principle of Relativity for Slow Motions	p. 163
Constitutive Relations for Non-Linear Viscoelastic Fluids	p. 164
Different Forms of Constitutive Relation	p. 167
Non-Linear Effects of Viscoelasticity	p. 171
Dilute Polymer Solutions	p. 171
Constitutive Relations	p. 172
Non-Linear Effects in Simple Shear Flow	p. 173
Non-Steady-State Shear Flow	p. 175
Non-Linear Effects in Oscillatory Shear Motion	p. 176
Many-Mode Description of Entangled Systems	p. 178
Constitutive Relations	p. 178
Linear Approximation	p. 180
Steady-State Simple Shear Flow	p. 184
Single-Mode Description of Entangled System	p. 186
Weakly Entangled Systems	p. 187
Strongly Entangled Systems	p. 189
Vinogradov Constitutive Relation	p. 191
Relation between Shear and Elongational Viscosities	p. 194
Recoverable Strain	p. 196
Optical Anisotropy	p. 199
The Relative Permittivity Tensor	p. 199
The Permittivity Tensor for Polymer Systems	p. 202
Dilute Solutions	p. 203
Entangled Systems	p. 204
Optical Birefringence	p. 206
Simple Elongation	p. 206
Simple Shear	p. 207
Oscillatory Deformation	p. 208
Anisotropy in a Simple Steady-State Shear Flow	p. 209
Dilute Solutions	p. 209
Entangled Systems	p. 211
Oscillatory Birefringence	p. 211
Dilute Solutions	p. 211
Entangled Systems	p. 212
Conclusion	p. 215
Appendices	p. 217
The Random Walk Problem	p. 217
Equilibrium Deformation of a Non-Linear Elastic Body	p. 219
The Tensor of Hydrodynamic Interaction	p. 222
Resistance Force of a Particle in a Viscoelastic Fluid	p. 223
Resistance Coefficient of a Particle in Non-Local Fluid	p. 225
Dynamics of Suspension of Dumbbells	p. 228
Estimation of Some Series	p. 239
References	p. 241
Index	p. 253
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