Inner segment radial distribution functions at contact point for chain-like molecules

Here we present, by simple geometric arguments, a proposal to calculate the radial distribution function at the contact point (RDF) between inner chain segments for chain-like molecules. Segments are identified as disconnected spheres, dimmer segments, or inner chain segments according to the number of adjacent joined spheres. The RDF expressions are based on three main considerations: a) the segment-surface area available for contact is additive for the two segments correlated by the RDF; b) the RDFs between segments with the same segment-surface area are considered equal; c) the effect of chain length on the RDF is neglected. In order to test the proposed equations, canonical ensemble Monte Carlo simulations were performed in order to obtain the RDF of segments in mixtures involving monomers, dimers, and n-mer chains (n = 4, 8, and 16), where each chain is composed of freely-jointed tangent spheres interacting by the square-well potential. Even though we present very simple equations, the calculated RDFs are in very good agreement with those obtained from molecular simulations. The assumption that adjacent segments respond to the major contribution for the contact correlation function is confirmed at all conditions. The results indicate that the approach presented here can be useful for improving calculations of thermodynamic properties of chain molecules.