An analytic Percus–Yevick approach to the RISM model of monodisperse, homopolymer melts

Abstract

The reference interaction site model is often used as a nonperturbative description of the equilibrium structure of monodisperse polymer melts on nanoscopical scales. Assuming that the single polymer chains in the melt have ideal (Gaussian) conformations, we derive for the melt a set of generalized Percus–Yevick (PY) equations which can be exactly reduced to a simple algebraic systems of equations. While in the case of the simple atomic sphere systems this involves cubic polynomials, in the analogous hard-sphere polymer system this leads to quintic polynomials. In the limit of infinitely long chains the exact, generalized PY static structure factors, the compressibility and the direct correlation functions are found as functions of the monomer density.