Towards a practical WCA theory for chain molecules: eliminating the density-dependent hard-sphere diameter from the description of the radial distribution function at contact

Using first-order Mayer-f perturbation theory and a self-consistent procedure for calculating the pressure from the virial and free-energy routes, we develop a simple analytic approximation for the radial distribution function of fluids comprising particles interacting by the WCA repulsive part of a Mie pair potential (WCA-Mie). The approximation is valid near contact, r=σ, where σ is the distance at which the Mie potential is zero. The accuracy of the approximation is shown to surpass that of the original WCA approximation, using only temperature-dependent hard-sphere diameters. By eliminating the density-dependent hard-sphere diameter from the description of the radial distribution function, our approach enables a reformulation of WCA theory that is more suitable for developing practical equation-of-state models for chain molecules. As a first step towards this goal, we apply the new model for the radial distribution function within the first-order thermodynamic perturbation theory of polymerisation (TPT1) of Wertheim and calculate the thermodynamic properties of chains comprising freely-jointed WCA-Mie segments. Compared to other approximations for the radial distribution function, the results are shown to compare favourably with Monte Carlo simulation results for the pressure and internal energy. We further show that typical inaccuracies inherent to a TPT1 approach can be mitigated using extensions to TPT1 (TPT1-v and TPT1-y) previously developed for chains comprising hard-sphere segments.