Nonanalytical equation of state of the hard sphere fluid

TL;DR

This paper proposes a nonanalytical equation of state for the hard sphere fluid that captures the pressure anomaly at high densities by integrating classical nucleation theory with the virial expansion.

Contribution

It introduces a novel nonanalytical term based on nucleation theory to model the hard sphere fluid's behavior near freezing density.

Findings

Successfully models pressure increase at high densities

Combines nucleation theory with virial expansion

Matches observed experimental data

Abstract

An equation of state of the hard sphere fluid which is not analytical at the freezing density is proposed and tested. The nonanalytical term is based on the the classical nucleation theory and is able to capture the observed ``anomalous increase'' of pressure at high densities. It is combined with the virial expansion at low densities.