Virial Equation-of-State for Hard Spheres

TL;DR

This paper develops a convergent virial equation-of-state for hard spheres using coefficients up to B12, revealing divergence at maximum packing and deviations from molecular dynamics data near the freezing point.

Contribution

It introduces a closed-form virial equation-of-state for hard spheres based on high-order coefficients, extending understanding of fluid behavior at high densities.

Findings

The virial series converges for all densities up to maximum packing.

Divergence occurs at maximum close packing, indicating a physical limit.

Deviations from MD data start at the fluid freezing density.

Abstract

Recent values for virial coefficients up to B12, when expressed in powers of density relative to maximum close packing,lead to a closed equation-of-state for the equilibrium fluid. The series obtained converges for all densities;it becomes negative and diverges to a negative pole at maximum packing. MD data for 64000 spheres in the metastable region shows the virial pressure begins to deviate at the fluid freezing density.