Variational approach to the conformation of flexible polymers in solution

Abstract

Approximate solutions to the self-consistent reference interaction-site model (RISM) integral equation theory of polymer liquids are employed to study the conformational properties of flexible polymers as a function of density and chain length. The nonlinear nature of the expression describing the medium-induced potential between two sites along the polymer chain necessitates the use of approximate methods to determine the intrachain pair-correlation function consistent with the interchain packing. In the limiting case where the polymer segment hard-core diameter approaches zero and the number of interaction sites comprising the chain goes to infinity, with the segment volume fraction held fixed, the intrachain pair correlation function is determined through a Feynman variational procedure for the effective free energy of a single chain in solution. The screening of the excluded volume interactions and the corresponding reduction of the polymer dimensions as a function of both polymer density and chain length is systematically studied with the results being in good agreement with scaling predictions. In addition, the variational method is successfully extended to chains having finite hard-core diameters, with the predictions of the theory comparing favorably with existing theories for polymer solutions based on field theoretic approaches.