The Equilibrium Theory of Inhomogeneous Polymers

Abstract This book provides an introduction to the field-theoretic methods and computer simulation techniques used in the design of structured polymeric fluids for a wide variety of applications. By such methods, the principles that dictate equilibrium self-assembly in systems ranging from block and graft copolymers, to polyelectrolytes, liquid crystalline polymers, and polymer nanocomposites can be established. Building on an introductory discussion of single-polymer statistical mechanics, the book provides a detailed treatment of analytical and numerical techniques for addressing the statistical properties of polymers subjected to spatially-varying potential fields. This problem is shown to be central to the field-theoretic description of interacting polymeric fluids, and models for a number of important polymer systems are elaborated. Self-consistent field theory is treated in detail, which is a collection of analytical and numerical techniques for obtaining solutions of polymer field theory models in the mean-field approximation. The book concludes with a discussion of analytical methods for going beyond the mean-field approximation and an introduction to the exciting new field of field-theoretic polymer simulations — the direct numerical simulation of polymer field theory models.