Chemical potential and surface free energy of a hard spherical particle in hard-sphere fluid over the full range of particle diameters

Abstract

The excess chemical potential μex(σ, η) of a test hard spherical particle of diameter σ in a fluid of hard spheres of diameter σ0 and packing fraction η can be computed with high precision using Widom’s particle insertion method [B. Widom, J. Chem. Phys. 39, 2808 (1963)] for σ between 0 and just larger than 1 and/or small η. Heyes and Santos [J. Chem. Phys. 145, 214504 (2016)] analytically showed that the only polynomial representation of μex consistent with the limits of σ at zero and infinity has a cubic form. On the other hand, through the solvation free energy relationship between μex and the surface free energy γ of hard-sphere fluids at a hard spherical wall, we can obtain precise measurements of μex for large σ, extending up to infinity (flat wall) [R. L. Davidchack and B. B. Laird, J. Chem. Phys. 149, 174706 (2018)]. Within this approach, the cubic polynomial representation is consistent with the assumptions of morphometric thermodynamics. In this work, we present the measurements of μex that combine the two methods to obtain high-precision results for the full range of σ values from zero to infinity, which show statistically significant deviations from the cubic polynomial form. We propose an empirical functional form for the μex dependence on σ and η, which better fits the measurement data while remaining consistent with the analytical limiting behavior at zero and infinite σ.