Irreversible Statistical Mechanics of Polymer Chains. I. Fokker–Planck Diffusion Equation

Abstract

A theory of the irreversible statistical mechanics of flexible polymer chains is developed on the basis of new ideas. The Brownian motion of polymer chains is assumed to be a Markoff random transition among their rotational isomeric states. The theory is described for ringpolymer chains, for which the “normal coordinates” can be determined by the consideration of their symmetry alone. First, we derive the master equation which describes the discrete Brownian motion of a ringpolymer chain. The master equation is averaged over all the configurations, fixed several normal coordinates to certain values. This averaging process is called “coarse graining.” By Taylor expansion of the coarse‐grained master equation, we get a Fokker–Planck diffusion equation which is specified by two kinds of molecular constants, the diffusion constant D α and the expansion parameter γ α , both of which depend on the suffix α of the normal coordinates. For slow relaxation phenomena, the diffusion equation is reduced to that of the spring‐bead modeltheory. The general behaviors of D α and γ α are discussed: The reduced diffusion constant D̃ α (= D α / D 0 ) decreases rapidly as α increases, whereas γ α 2 / α 2 remains roughly constant.