The role of capillary wave fluctuations in determining the liquid-vapour interface

Abstract

We investigate the role played by capillary-wave like fluctuations in the determination of the equilibrium density profile and the intermolecular correlation functions of various models of a planar liquid-vapour interface in an external gravitational field. We show that the interfacial profile calculated from the van der Waals model, which is the simplest (squaregradient) approximation in a density functional theory of inhomogeneous fluids, is stable against capillary-wave fluctuations and therefore cannot be used to describe the ‘bare’ interface in a capillary wave model. The density-density correlation function of the van der Waals model exhibits long-ranged correlations in the interface. These are of precisely the same form as those predicted by Wertheim and can be associated with capillary-wave like fluctuations of the Gibbs dividing surface. These fluctuations do not lead to a ‘diffuse’ interfacial profile in the limits of infinite interfacial area and zero gravity; the interfacial thickness remains ...