Irreversible Statistical Mechanics of Polymer Chains. I. Fokker–Planck Diffusion Equation
1971; American Institute of Physics; Volume: 54; Issue: 1 Linguagem: Inglês
10.1063/1.1674580
ISSN1520-9032
Autores Tópico(s)Polymer crystallization and properties
ResumoA 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 ring polymer 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 ring polymer 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 Dα and the expansion parameter γα, 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 model theory. The general behaviors of Dα and γα are discussed: The reduced diffusion constant D̃α(= Dα / D0) decreases rapidly as α increases, whereas γα2 / α2 remains roughly constant.
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