Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid

TL;DR

This paper introduces a universal approach to determine contact values of radial distribution functions in polydisperse hard-sphere fluids, using a cubic model and consistency conditions, validated against Monte Carlo simulations.

Contribution

It proposes a universal cubic model for contact values in polydisperse hard-sphere fluids based on a dimensionless parameter and consistency conditions, extending previous theories.

Findings

The model accurately predicts contact values compared to Monte Carlo data.

The approach unifies the treatment of particle-particle and wall-particle correlations.

Consistency conditions effectively constrain the model parameters.

Abstract

The contact values $g(\sigma,\sigma')$ of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution $f(\sigma)$ are considered. A ``universality'' assumption is introduced, according to which, at a given packing fraction $\eta$, $g(\sigma,\sigma')=G(z(\sigma,\sigma'))$, where $G$ is a common function independent of the number of components (either finite or infinite) and $z(\sigma,\sigma')=[2 \sigma \sigma'/(\sigma+\sigma')]\mu_2/\mu_3$ is a dimensionless parameter, $\mu_n$ being the $n$-th moment of the diameter distribution. A cubic form proposal for the $z$-dependence of $G$ is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express $G(z)$ in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations.