From the Authors Introduction
Diffusion is one of the few manageable nonequilibrium pro- cesses during which matter is transported through a system. Traditionally, diffusion is studied in physical chemistry; however, the fundamental understanding of diffusion processes is not possible without involving statistical physics.
Diffusion in disordered systems, such as in polymers, has sometimes unexpected features, the nature of which has not yet been determined. Since modern technology involves more and more complex materials which rely on a subtle balance of microscopic effects, the understanding of diffusion processes in these materials is of paramount importance from the practical point of view.
A renewed interest in the basic principles of diffusion is a direct result of new experimental data. This was a contributing factor in the preparation of this text.
In the first chapter, the phenomenological thermodynamic basics of diffusion is reviewed, and the diffusion equation is derived from the principles of irreversible thermodynamics. The basic mathematical apparatus for solving diffusion equations is reviewed in the second chapter. The third chapter deals mainly with the vast amount of experimental data dealing with diffusion in polymers. . . . A reader interested in particular polymeric systems can use the . . . material as a useful introduction. The last chapter contains basic information concerning random walks and their application to the diffusion in disordered systems. The theory of random walks is widely used in polymer physics where it is usually combined with statistical mechanics to formulate various models of polymeric systems.
Finally, useful mathematical formulas and references to the original sources of some mathematical methods are [provided] in the appendices. Some physical constants associated with several polymer solvent systems are also presented.
Basic Thermodynamic Concepts
Equation of State
Reversible and Irreversible Processes
The Second Thermodynamic Principle
Thermodynamics of Irreversible Processes
The Diffusion Equation
Basic Properties of Linear Partial Differential Equations
Separation of Variables
Diffusion in Polymers
Diffusion in Polymeric Membranes
Diffusion-Continuum Mechanics Picture
Controlled Release Systems
Basic Concepts of the Random Walk
Correlated and Self-Avoiding Walks
Ideal Polymer Chains
Laplace Equation in Curvilinear Coordinates
Vectors, Vector Operators, and Integral Theorems
Some Special Functions
Associated Legendre Functions
Transport Properties: Diffusion, Solubility, Permeation, and Swelling Data for Some Systems
" . . . it is a good resource for a reader looking for an introduction into the area of diffusion in polymers and its mathematical modeling using random walks. The references listed after every chapter provide a good compilation of contemporary work in this field."
Arvind M. Mather and Alec B. Scranton
University of Michigan, East Lansing