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Theory of Polymer Dynamics
W.J. Briels
October 1998
Contents
Preface
The Rotational Isomeric State model
The model
The partition function
Some probabilities
The mean square end-to-end vector
The radius of gyration
Some results for polyethylene
Appendix A
Appendix B
Integral equations for polymer liquids
Flory's hypothesis
The radial distribution function
The Ornstein-Zernike equation and integral equations
Molecular liquids
Polymer RISM
Appendix A
The Gaussian chain
Simple models
The central limit theorem
The Gaussian chain
Green's function method
One Gaussian chain in a box
Appendix A
Appendix B
Appendix C
Stochastic processes
The Langevin equation
The Fokker-Planck equation
The Smoluchowski time scale
The Smoluchowski equation
Appendix A
Appendix B
Appendix C
Hydrodynamics
Introduction
Navier-Stokes equations
A moving sphere in a quiescent fluid
Hydrodynamic interaction in colloidal suspensions
The virial theorem, and the microscopic expressions for the stress tensor
A. General
B. Suspensions
The Rouse chain
Introduction
The Rouse chain
Normal mode analysis
Correlation of the end-to-end vector
Monomer motion
Viscosity of a dilute polymer solution and a polymer melt
A. Shear flow
B. The stress tensor in normal coordinates
C. Calculation of the stress tensor
Summary
Appendix A
The Zimm chain
Definition and equations of motion
Normal coordinates and the spectrum
Diffusion coefficient and viscosity
Appendix A
Dynamics of dense polymer systems: reptation
The tube model
Mathematical definition of the model
Monomer motion
Viscoelastic behavior
Index
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W.J. Briels
