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

The inhomogeneous structure of a fluid at a wall can be characterised 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 parameterisations show significant deviation at high density. In this work, we propose new parameterisations for gamma and Gamma that agree with the simulation data within statistical error over the entire fluid density range.