Statistical mechanics of random-flight chains. V Excluded volume expansion and second virial coefficient for linear chains of varying shape

Abstract

The excluded‐volume expansion factor of a flexible chain is calculated with a smooth‐density model providing for a distribution of both sizes and shapes of the segment cloud. From the known average moments of the inertial tensor found previously by Monte Carlo methods, an approximate empirical function is constructed to describe the distribution of ellipsoidal dimensions. With a suitably related pseudopotential representing the excluded‐volume forces, an expansion factor ${\alpha }_s^2$ for the mean square radius is obtained which requires very little scale adjustment to match first‐order perturbation theory and which also gives a good representation at higher values of the interaction parameter. The empirical function approach is supplemented with a Monte Carlo study to remove bias inherent in the choice of the functional form. Because of the small increase in asymmetry with increasing excluded volume, the direct effect of shape variation on the expansion factor is less important than that of size variation. A calculation of the interaction of two chains and the resulting second virial coefficient is carried out, and in this case both shape and size variations are important.