Thermodynamics of a liquid wetting film on a spherical particle with an adsorbed ion

Abstract

A thermodynamic description has been formulated for a wetting film formed on a spherical solid dielectric particle with a discrete electric charge adsorbed on its surface. The description is based on differential equations for the equilibrium nonspherical profile of the film and electric potentials in the particle, film, and a vapor-gas medium. By combining these equations and taking into account the action of disjoining pressure in the film, the film shape in a noncentral electric field has been determined and an expression has been derived for the chemical potential of condensate molecules in the film as a function of the effective curvature radius of the film external surface, this radius being predetermined by the number of condensate molecules in the film. The magnitude of the adsorbed electric charge, its characteristic size and its location with respect to the center of the solid particle, dielectric permittivities of the liquid in the film and the material of the particle, particle size, and the characteristics of the isotherm of the disjoining pressure represent parameters of the problem. Three characteristic disjoining pressure isotherms corresponding to films that wet and partly wet the particle in the absence of the electric charge have been considered. It has been shown that the noncentral position of an adsorbed ion at small particle sizes strongly affects the surface profile of a thin film and the chemical potential of its molecules.