Chain Configurations
S. F. Sun · 2004
Flory's influence on polymer chemistry is again detailed in this chapter. His interpretation of the polymer chain configurations in terms of the expansion factor α (or swelling ratio) constitutes the central point of general polymer chain dynamics. Before we introduce Flory's theory, we describe the random flight model of chain configurations; after we introduce Flory's theory, we describe the two parameter theory (α and z, z being the excluded volume parameter). We then focus on the new idea of complex dumping and internal movements of polymer chain molecules. This new challenge came from various related areas, among them the development of renormalization group theory, the modern concept of chaos, and the universality of critical exponents on scaling laws. Along with Flory's work, we discuss in detail de Gennes' work on chain configurations. It was de Gennes' theories that pointed to similarities between motion of long chains and magnetic movements undergoing a phase transition. His theories of semidilute solution and reptation in the entangled chain have stimulated new approaches and new ways of interpreting chain configurations. This chapter also covers many other important topics on chain configurations. As in our normal way of presentation, background materials are given first, namely, random walk statistics and a description of the Markov chain. In the appendices we provide the mathematics of the scaling relation and correlation function.