Random Flight Model in the Theory of the Second Virial Coefficient of Polymer Solutions

Abstract

The theory of the second virial coefficient, A₂(M₂,T), for dilute polymer solutions is investigated from the point of view, first developed by Zimm, of the Ursell‐Mayer‐like development in terms which successively represent increasing numbers of contacts between molecular subunits of flexible chain molecules. The methods used by Fixman in treating excluded volume problems in the random flight model are here employed. Evaluation is carried out to the triple contact approximation. A formal analysis of all higher terms is presented and the contribution of one class of terms is evaluated exactly. The remaining terms appear to be inaccessible to numerical evaluation by ordinary methods so that a rigorous discussion of the asymptotic behavior of A₂ is precluded. Semiquantitative arguments, however, indicate favorable agreement with experiment, provided intramolecular excluded volume effects are considered.