The Mesoscopic Theory of Polymer Dynamics

by Pokrovskii, Vladimir N.

• ISBN13: 9780792366829
• ISBN10: 0792366824
• Format: Hardcover
• Copyright: 2001-02-01
• Publisher: Kluwer Academic Pub

Summary

A monograph presenting the fundamentals of the mesoscopic theory of polymer dynamics, giving a concise view of the various relaxation phenomena that occur in very concentrated solutions and melts of certain polymers. A textbook and reference for graduate students and researchers in rheology, polymer science, polymer engineering, and materials science.

Table of Contents

Preface	ix
Notations and Conventions	xi
Introduction: Macromolecular Systems in Equilibrium	1	(20)
Microscopic Models of a Macromolecule	1	(2)
Bead-and-Spring Model	3	(3)
Normal Co-Ordinates	6	(1)
Excluded-Volume Effects	7	(3)
Macromolecules in Solvent	10	(1)
Weakly-Coupled Macromolecules	11	(4)
The Elasticity of Polymer Networks	15	(3)
Crystalline and Glassy Systems	18	(3)
Dynamics of a Macromolecule in a Viscous Liquid	21	(16)
Equation of Macromolecular Dynamics	21	(1)
Hydrodynamic Interactions inside a Macromolecular Coil	22	(3)
Resistance-Drag Coefficient of a Macromolecular Coil	25	(1)
Effective Resistance-Drag Coefficient of a Particle	26	(2)
Intramolecular Friction	28	(3)
Linear Modes	31	(2)
The Moments of Linear Modes	33	(4)
Dynamics of a Macromolecule in an Entangled System	37	(14)
Many-Chain Problem	38	(3)
Single-Chain Problem	41	(3)
Heuristic Speculations for the Memory Functions	44	(4)
Dynamics of a Reptating Macromolecule	48	(3)
Low-Frequency Modes for Weakly-Coupled Macromolecules	51	(13)
Modes of Motion in Linear Approximation	51	(3)
Correlation Functions	54	(5)
Relaxation of the Macromolecular Coil	59	(5)
The Localisation Effect	64	(17)
Mobility of a Macromolecule	64	(4)
The Localisation of a Macromolecule	68	(3)
The Mobility of a Macromolecule through Reptation	71	(2)
Quasi-Elastic Neutron Scattering	73	(3)
The Slowest Relaxation Processes	76	(2)
The Fundamental Dynamical Parameters	78	(3)
Linear Viscoelasticity	81	(33)
Stresses in the Flow System	81	(7)
Macromolecules in a Viscous Liquid	88	(7)
Macromolecules in a Viscoelastic Liquid	95	(5)
Dynamic Modulus and Relaxation Branches	100	(4)
Self-Consistency of the Mesoscopic Approach	104	(2)
Modulus of Elasticity and the Intermediate Length	106	(2)
Concentration and Macromolecular Length Dependencies	108	(1)
Frequency-Temperature Superposition	109	(2)
Viscoelasticity of Dilute Blends of Polymers	111	(3)
Equations of Relaxation	114	(16)
The Anisotropy of Particle Mobility	114	(2)
Markovian Form of the Equation of Macromolecular Dynamics	116	(3)
Equations for the Non-Equilibrium Moments	119	(4)
Relaxation of the Macromolecular Conformation	123	(2)
Relaxation of Orientation	125	(3)
The Size and Form of the Macromolecular Coil in a Flow	128	(2)
Relaxation Processes in the Phenomenological Theory	130	(17)
The Laws of Conservation of Momentum and Angular Momentum	130	(3)
The Law of Conservation of Energy and the Balance of Entropy	133	(3)
Thermodynamic Fluxes and Relaxation Processes	136	(2)
The Principle of Relativity for Slow Motions	138	(2)
Constitutive Relation for Non-Linear Viscoelastic Fluids	140	(3)
Different Forms of Constitutive Relation	143	(4)
Non-Linear Effects of Viscoelasticity	147	(20)
Constitutive Relation for Dilute Polymer Solutions	147	(2)
Constitutive Relation for Entangled Systems	149	(2)
Steady-State Simple Shear Flow	151	(3)
A Single-Mode Simplification	154	(3)
Single-Relaxation Constitutive Relation	157	(1)
Vinogradov Constitutive Relation	158	(2)
Relation between Shear and Elongational Viscosities	160	(4)
Recoverable Strain	164	(3)
Optical Anisotropy	167	(22)
The Relative Permittivity Tensor	167	(3)
The Permittivity Tensor for Polymer Systems	170	(5)
Optical Birefringence	175	(3)
Anisotropy in a Simple Steady-State Shear Flow	178	(2)
Oscillatory Birefringence of Dilute Solutions	180	(1)
Oscillatory Birefringence of Concentrated Solutions	181	(8)
Conclusion	185	(4)
APPENDICES	189	(26)
A. The Random Walk Problem	189	(2)
B. Equilibrium Deformation of a Non-Linear Elastic Body	191	(3)
C. The Tensor of Hydrodynamic Interaction	194	(2)
D. Resistance Force of a Particle in a Viscoelastic Fluid	196	(2)
E. Resistance Coeffcient of a Particle in Non-Local Fluid	198	(3)
F. Dynamics of Suspension of Dumbbells	201	(12)
G. Estimation of some Series	213	(2)
References	215	(14)
Subject Index	229