Statistical physics of polymer gels - Physics Report 269 by Panyukov & Rabin

Description

A comprehensive analysis of the statistical mechanics of randomly cross-linked polymer gels, starting from a microscopic model of a network made of instantaneously cross-linked Gaussian chains with excluded volume, and ending with the derivation of explicit expressions for the thermodynamic functions and for the density correlation functions which can be tested by experiments.

Contents
1. Introduction
2. The model
2.1. Pre-cross-linked polymer
2.2. Instantaneous cross-linking and cross-link
saturation threshold
2.3. Edwards formulation
2.4. Field theory
3. Mean-field solution
3.1. The mean-field equation
3.2. Homogeneous solution
3.3. Inhomogeneous solution
3.4. Mean-field free energy
3.5. Stability of the mean-field solution
3.6. Uniqueness of the ground state
3.1. Local deviations from affinity
4. Static inhomogeneities and thermal fluctuations
4.1. RPA free energy density functional
4.2. Inhomogeneous equilibrium density profile
4.3. Thermal and structure averages
4.4. Density correlation functions
4.5. Analytical expressions for the correlators
4.6. Gels in polymeric solvents
5. Gels in good solvents
5.1. Renormalization and scaling
5.2. Thermodynamics
5.3. Interpenetration and desinterpenetration of
network chains
5.4. Density correlation functions
6. Connection with continuum theory of elasticity
6.1. Anisotropic moduli of homogeneous
deformed networks
6.2. Equilibrium state of deformed inhomo-
geneous gels and the butterfly effect
7. Discussion

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