Percus-Yevick integral equation theory for athermal hard-sphere chains.

Abstract

Equations for three intermolecular correlation functions for athermal hardsphere chain fluids are derived in the context of the Percus-Yevick (PY) integral equation theory. The approach employed here is based on a particle-particle description of chain molecules developed in part I of this series. Specifically, we obtained equations for the site-site total correlation function h _αβ(r), the single index average total correlation function h _α(r), and the average total correlation function h(r) for m-mer homonuclear hard-sphere chains. It is found that the PY theory does not yield a closed equation for the average total correlation function h(r). Solving h(r) requires additional information on the chain-end correlation functions. Two approximations (beyond the PY theory) which yield a single closed equation for h(r) are proposed and examined. Analytic expressions for these average correlation functions at contact are obtained as a function of the chain length m and hard-sphere site volume fraction η. Numerical solutions for g(r) are obtained for 4-mer and 8-mer chains and compared with computer simulation data. It is found that the PY theory is able to predict g(r) for 4-mer chains accurately; however, only qualitative agreement is obtained for 8-mer chains.