Scaling of hydrophobic solvation free energies

We have calculated the free energy of solvation for hard sphere solutes, as large as 20 A in diameter, in two simple-point-charge models of water. These results were obtained using umbrella sampling of ensembles with fixed, ambient temperature and pressure. For the same water models, we have also calculated the surface tension of a liquid-vapor interface at room temperature. Analogous calculations were carried out for three thermodynamic states of the Lennard-Jones (LJ) fluid near liquid-vapor coexistence. For both water and the LJ fluid at the conditions we have simulated. extrapolation of our results suggests that the planar interface between coexisting liquid and vapor phases has the same surface tension as the planar limit of hard sphere solvation. We expect this correspondence to be a general result for fluids at thermodynamic states close to phase coexistence, as measured by the difference in chemical potential between bulk liquid and vapor phases, and far from the critical point. The solvation free energies we have computed for water and the LJ fluid cross over at microscopic solute sizes from a dependence on solute volume to an approximate dependence on solute surface area, as predicted by Lum et al.