Polymers are remarkable molecules with a particularly rich behavior and a wealth of interesting properties. Statistical mechanical arguments may be used to understand these properties. In this chapter, we present an elementary theory of polymer configurations and polymer dynamics. We also offer a brief exposition of the theory of Brownian dynamics. This is a powerful theoretical formalism for studying the motion of molecules in a solution.

Polymers

The study of conformations and conformational motions of flexible polymer chains in solution is of great scientific and technological importance. Understanding the physics of macromolecules at the molecular level helps the synthesis and design of commercial products. It also provides insight into the structure and functions of biological systems. Flexible polymers have therefore been the subject of extensive theoretical treatments, a wide variety of experiments, and computer simulations (see Further reading at the end of the chapter).

Historically, theoretical treatments have resorted to simple phenomenological models of polymeric materials. In the framework of statistical mechanics, polymeric chains are at a first stage considered to consist of independent elements or segments. The principal property of macromolecular behavior taken into account with this representation is the flexibility of the chains. With non-interacting monomeric units having uncorrelated directions, it is straightforward to show that the chains acquire random-walk behavior.