Solvation of a spherical cavity in simple liquids: interpolating between the limits

Dissolution of a solute molecule into a solvent necessitates the creation of a cavity devoid of solvent molecules. The cavity solvation free energy is exactly known at both very small and large length scales, but in between it can only be estimated by various approximations. Guided by simulation results for the solvation of small cavities and density functional theory, we analyze the size dependence of the solvation free energy, contact density of solvent molecules, and the interfacial tension for a spherical cavity in a Lennard-Jones fluid or a system of hard spheres. Unlike cavity formation in the hard-sphere system, a quadratic curvature expansion is insufficient to connect smoothly the exact results in the microscopic and macroscopic limits for the cavity surface tension (or equivalently, the contact solvent density) in Lennard-Jones fluids. Considering the sensitivity of solvation to molecular details at small length scales, we conjecture that, for practical purposes, a heuristic approach may be sufficient to link the thermodynamic limit at large length scales and the exact results of cavity formation at very small length scales.