APPLICATION OF THE INTEGRAL-EQUATION THEORY OF POLYMERS - DISTRIBUTION FUNCTION, CHEMICAL-POTENTIAL, AND MEAN EXPANSION COEFFICIENT

A recursive integral equation for the intramolecular correlation funct ion of an isolated linear polymer of N bonds is derived from the integ ral equations presented in the preceding paper. The derivation basical ly involves limiting the density of the polymer to zero so that polyme rs do not interact with each other, and thus taking into account the i ntramolecular part only. The integral equation still has the form of a generalized Percus-Yevick integral equation. The intramolecular corre lation function of a polymer of N bonds is recursively generated by me ans of it from those of polymers of 2, 3,..., (N-1) bonds. The end-to- end distance distribution functions are computed by using the integral equation for various chain lengths, temperatures, and bond lengths in the case of a repulsive soft-sphere potential. Numerical solutions of the recursive integral equation yield universal exponents for the mea n square end-to-end distance in two and three dimensions with values w hich are close to the Flory results: 0.77 and 0.64 vs Flory's values 0 .75 and 0.6 for two and three dimensions, respectively. The intramolec ular correlation functions computed can be fitted with displaced Gauss ian forms. The N dependence of the internal chemical potential is foun d to saturate after some value of N depending on the ratio of the bond length to the bead radius.