Universal fluctuation-induced corrections to the Kelvin equation for capillary condensation

Abstract

Interfacial fluctuations in complete wetting films give rise to important corrections to the macroscopic Kelvin equation for the location of the shifted first-order (condensation) transition that occurs when a fluid (or an Ising magnet) is confined between two parallel adsorbing walls. The wall separation L that enters the usual Kelvin equation must be replaced by L- phi l( mu *), where l is the thickness of the wetting film at the chemical potential mu * at which capillary condensation occurs and phi is an amplitude. For pure systems with short-ranged forces thermal wandering is insufficient to renormalize the simple geometric result phi =2 for bulk dimensions d>or=3. However, in d=2, where fluctuations are much stronger, the authors predict phi =3 throughout the weak fluctuation regime of complete wetting which includes long-ranged dispersion forces as well as short-ranged forces. Their prediction is supported by an explicit analysis of a d=2 interfacial Hamiltonian. This shows that pseudo-phase coexistence, characterized by an exponentially large transverse correlation length, occurs for an exponentially narrow range of mu * determined by the corrected Kelvin equation with phi =3.