Intermolecular site–site correlation functions of athermal hard-sphere chains: Analytic integral equation theory

The intermolecular site–site correlation function gij(r) of freely jointed athermal tangent hard-sphere chains (HSC) are determined based on a particle–particle description of the chain system. We developed a mathematical framework through which the functions gij(r) can be obtained within the context of the Percus–Yevick (PY) integral equation theory. The computational scheme involves the analytic solution to the structure of a multicomponent particle mixture that is subject to some specified connectivity constraints. In particular, we determined the site–site correlation functions gij(r) of homonuclear 4-mer chains, and homonuclear 4-mer chains in a hard-sphere solvent. Analytic expressions for the site–site and site–solvent correlation functions at contact, i.e., gij(σ+), are obtained. Site–site correlation functions determined from the PY theory show the ‘‘correlation hole’’ behavior at low density. Comparison of the PY results with computer simulation data shows that the theory yields accurate values for an averaged ‘‘total’’ correlation function, and captures the essential features of the site–site correlation functions gij(r). In addition the effect of hard-sphere solvent particles on the structure of HSC molecules is also investigated.