Nonanalytic curvature contributions to solvation free energies: influence of drying

We investigate the solvation of a hard spherical cavity, of radius R, immersed in a fluid for which the interparticle forces are short ranged. For thermodynamic states lying close to the liquid binodal, where the chemical potential deviation deltamu is identical with mu-muco(T) is very small and positive, complete wetting by gas (drying) occurs and two regimes of interfacial behavior can be identified. These are characterized by the length scale Rc=2gamma(gl)infinity/(Deltarhodeltamu), where gamma(gl)infinity is the planar gas-liquid surface tension and Deltarho is the difference in coexisting densities at temperature T. For R>Rc, the interfacial free energy and the density profile of the fluid near the hard wall can be expanded in powers of the curvature R(-1), in keeping with the analysis of Stillinger and Cotter [J. Chem. Phys. 55, 3449 (1971)]. In the other regime, R0, of the work of formation of a hard spherical cavity and of the Gibbs adsorption and the fluid density at contact with the wall. Our analysis, which is based on an effective interfacial Hamiltonian combined with exact statistical mechanical sum rules, is confirmed fully by the results of microscopic density functional calculations for a square-well fluid. We discuss the repercussions of our results for solvation phenomena, emphasizing that nonanalytic behavior equivalent to that we find for complete drying in solvophobic systems will also arise in the case of complete wetting, i.e. when liquid films are adsorbed on the surface of large (colloidal) particles or at curved substrates. We reassess various results in the important but neglected Stillinger-Cotter paper, where drying was not considered explicitly, in the light of our present analysis.