Introduction

The single chain constitutes the basic building block of elastomers and understanding its structure and properties is necessary before going into the study of rubberlike elasticity. The original picture of a polymer chain as an isolated entity was by Guth and Mark (Guth and Mark, 1934) and Kuhn (Kuhn, 1934). According to this picture, the polymer chain consisted of freely jointed beads. Further developments elucidating the real nature of the single chain and its departure from the simple freely jointed model were made by several authors, notably by Volkenstein (Volkenstein, 1963) and Flory (Flory, 1953, 1969). The elastic properties such as the force–deformation relations of the single chain, to be used in constructing the elasticity theory, then followed through the use of thermodynamic relations. However, after the advance of experiments such as the atomic force microscope (AFM) and optical tweezers, direct experimental observation of the single chain behavior became possible (Chu, 1991; Granzier and Pollack, 2000; Janshoff et al., 2000; Hugel and Seitz, 2001; Strick et al., 2001; Zhang and Zhang, 2003; Hummer and Szabo, 2005; Barbara et al., 2005; Schuler, 2005). In this chapter, we will first outline the theoretical model of the single chain for a few simplified cases, and then relate this to experimental work on single chains.

Different models of the single chain, the end-to-end vector distribution and force–deformation relations

A simplified picture of the single chain is sketched in Figure 1.1, where the projection of the chain to the x-z coordinates is shown.