Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres

TL;DR

This paper introduces a new Percus-Yevick equation of state for hard spheres derived via the chemical potential route, which outperforms traditional methods and improves accuracy for polydisperse systems.

Contribution

A novel Percus-Yevick equation of state for hard spheres derived from the chemical potential route, enhancing accuracy over conventional approaches.

Findings

New PY equation of state better than virial route

Interpolations improve accuracy over Carnahan-Starling

Extension to polydisperse systems demonstrated

Abstract

The chemical potential of a hard-sphere fluid can be expressed in terms of the contact value of the radial distribution function of a solute particle with a diameter varying from zero to that of the solvent particles. Exploiting the explicit knowledge of such a contact value within the Percus--Yevick (PY) theory, and using standard thermodynamic relations, a hitherto unknown PY equation of state, $p/\rho k_BT=-(9/\eta)\ln(1-\eta)-(16-31\eta)/2(1-\eta)^2$, is unveiled. This equation of state turns out to be better than the one obtained from the conventional virial route. Interpolations between the chemical-potential and compressibility routes are shown to be more accurate than the widely used Carnahan--Starling equation of state. The extension to polydisperse hard-sphere systems is also presented.