Parameterizing the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall

TL;DR

This paper develops new parameterizations for the surface free energy and excess adsorption of a hard-sphere fluid at a planar wall, achieving high accuracy across all densities by comparing with precise simulation data.

Contribution

It introduces novel parameterizations for surface free energy and excess adsorption that match simulation data more accurately than previous models.

Findings

New parameterizations agree with simulation data within statistical error.

Existing models deviate at high densities, but the new ones maintain accuracy.

Enhanced understanding of fluid-wall interactions at various densities.

Abstract

he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Within a thermodynamic description the surface free energy $\gamma$ and the excess adsorption $\Gamma$ are of central importance. For theoretical studies closed expression of $\gamma$ and $\Gamma$ can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for $\gamma$ and $\Gamma$, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for $\gamma$ and $\Gamma$ to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterizations show significant deviation at high density. In this work, we propose new parameterizations for $\gamma$ and $\Gamma$ that agree with the simulation data within statistical error over the entire fluid density range.