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

The excess chemical potential mu(ex)(sigma, eta) of a test hard spherical particle of diameter sigma in a fluid of hard spheres of diameter sigma(0) and packing fraction eta can be computed with high precision using Widom's particle insertion method [B. Widom, J. Chem. Phys. 39, 2808 (1963)] for sigma between 0 and just larger than 1 and/or small eta. Heyes and Santos [J. Chem. Phys. 145, 214504 (2016)] analytically showed that the only polynomial representation of mu(ex) consistent with the limits of sigma at zero and infinity has a cubic form. On the other hand, through the solvation free energy relationship between mu(ex) and the surface free energy gamma of hard-sphere fluids at a hard spherical wall, we can obtain precise measurements of mu(ex) for large sigma, 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 mu(ex) that combine the two methods to obtain high-precision results for the full range of sigma values from zero to infinity, which show statistically significant deviations from the cubic polynomial form. We propose an empirical functional form for the mu(ex) dependence on sigma and eta, which better fits the measurement data while remaining consistent with the analytical limiting behavior at zero and infinite sigma. Published under an exclusive license by AIP Publishing.