Analytical expression for radial distribution function of hard sphere system: density derivative and application to perturbation theories

TL;DR

This paper develops an explicit analytical expression for the radial distribution function of hard sphere fluids, including its density derivative, facilitating thermodynamic calculations and applications in perturbation theories.

Contribution

It introduces a new analytical form of the radial distribution function and derives its density derivative and perturbation terms, improving theoretical modeling of liquids.

Findings

Analytical expression agrees well with simulation data

Derived density derivative and perturbation terms are accurate

Facilitates thermodynamic and fluid modeling applications

Abstract

Model of hard sphere system is important part of modern theories of liquids. Radial distribution function of hard sphere fluid represented in form of explicit analytical expression allows to obtain thermodynamic potentials in analytical form, which is very helpful for further analysis and applications. A new analytical expression of radial distribution function of hard sphere fluid is developed. The density derivative of the radial distribution function and the first two terms of Barker-Henderson perturbation theory are derived as analytical expressions. The obtained results agree well with published simulation data. These results have important implications for real fluid modeling using density functional theory and perturbation theories.