INTEGRAL-EQUATION THEORY OF POLYMERS - TRANSLATIONAL INVARIANCE APPROXIMATION AND PROPERTIES OF AN ISOLATED LINEAR POLYMER IN SOLUTION

In this paper, we continue investigations on the solution methods for the generalized Percus-Yevick equations for the pair correlation funct ions of polymers, which were formulated in the previous papers of this series [J. Chem. Phys. 99, 4084, 4103 (1993)]. Previously, they were reduced to recursive integral equations and solved numerically. In thi s paper, a translational invariance approximation is used to reduce th e number of integral equations to solve. In this approximation, only N integral equations out of N2 integral equations are required for a po lymer consisting of N beads (monomers). The behavior of an isolated po lymer is studied with three different potential models, a soft sphere, a hard sphere, and a Lennard-Jones potential. The main motivation for considering these three potential models is in testing the idea of un iversality commonly believed to hold for some properties of polymers. We find that the universality holds for the power law exponent for the expansion factor of polymers at high temperatures. The end-to-end dis tance distribution functions, intermediate distribution functions, che mical potentials, the density distributions, and various expansion fac tors of the polymer chain are computed from the solutions of the integ ral equations in the case of coiled, ideal, and collapsed states of th e polymer. The expansion factors in the collapsed regime are found to obey power laws with respect to the length of the polymer and [B(T) - B(theta)BAR], where B(T) is the second virial coefficient and thetaBAR is a modified thetaBAR temperature. The values of these exponents app roach those from the known theories of polymer collapse as the chain l ength becomes long and the ratio of bond length to bead radius becomes large.