Theory of Excluded Volume Effect in Polymer Chains

Abstract

The excluded volume effect of linear chain polymer is investigated with the aid of the method of cluster expansion theory which has been developed in the theory of imperfect gases. Three prototypes of simple clusters, their generalizations and their complex combinations are considered. The linear expansion factor α of the effect is obtained in a double series with respect to the number of segments N in a chain polymer. The series are summed with the help of Hankel’s integral representation of the Gamma function. Using the method of the steepest descent, the factor is evaluted for large N. It approaches monotonically to a finite value with increasing N, and does not show the behaviors given by ordinary two parameter theories.