Computer simulation study of the closure relations in hard sphere fluids

TL;DR

This study uses Monte Carlo simulations to analyze the behavior of cavity and bridge functions in various hard sphere fluids, challenging assumptions of local dependency in integral equation theories.

Contribution

It provides numerical evidence that the local dependency assumption of bridge functions can be violated in certain regions, especially at higher coupling.

Findings

Violations occur around the first and second neighbor shells.

Violations are amplified with increased system coupling.

Duh-Haymet plots clearly show these violations.

Abstract

We study, using Monte Carlo simulations, the cavity and the bridge functions of various hard sphere fluids: one component system, equimolar additive and non additive binary mixtures. In particular, we numerically check the assumption of local dependency of the bridge functions from the indirect correlation functions, on which most of the existing integral equation theories hinge. We find that this condition can be violated either in the region around the first and second neighbors shell, or inside the hard core, for the systems here considered. The violations manifest themselves clearly in the so called Duh-Haymet plots of the bridge functions versus the indirect correlation functions and become amplified as the coupling of the system increases.