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The volume exclusion effect in a chain of small impenetrable spheres is treated by two methods—one based on derivation of a Fokker-Planck equation by consideration of the number of ways in which a chain can be extended by adding another sphere without violating the volume exclusion condition, and the other based on the calculation of the number of excluded configurations as a function of chain extension. Both approaches lead, in the first approximation, to the same simple analytic form for the distribution of chain extensions r, and to the prediction that 〈r2〉 will increase faster than the number of spheres in the chain. Volume exclusion does not merely change the distribution function by a scale factor, as is assumed in the theory of Flory; there is a relatively large decrease in the probability of small extensions. The present theory is compared in detail with that of Hermans, Klamkin, and Ullman, which is superficially similar in appearance, but fundamentally quite different in character and result.
Hubert M. James (Thu,) studied this question.