Electrostatics of Diffuse Anisotropic Interfaces. III. Point Charge and Dipole Image Potentials for Air-Water and Metal-Water Interfaces

Abstract

Within the framework of macroscopic continuum theory, the point charge and point dipole image potentials in the presence of a diffuse dielectric interface are calculated. We consider the cases of both short and long range diffuseness for air-water interfaces. In the first category we propose a model profile for which the charge image potential is devoid of singularities and is an integral over elementary functions. The calculated image potential goes through a maximum and minimum as the charge is taken from the high to the low dielectric constant medium. The heights of the maximum and minimum may be estimated in terms of a physical cutoff, characteristic of the gradient of the dielectric constant, D, in the diffuse region, using the crude model of an abrupt interface. For a diffuse layer, the very large but finite electrostatic barrier for an ion is determined by the ratio of a distance characteristic of the bulk electrolyte and a distance characteristic of the maximum gradient of D. The image potential for a point dipole, normal or tangential to the diffuse interface, is exhibited in the repulsive region, for the long range diffuse interface. For metal-water interfaces, encountered in electrochemistry, the effects of diffuseness of the inner region, adjacent to the metal, are examined. One effect of diffuseness is to remove singularities in the image potential and to increase it in the relevant part of the inner region. The other effect is to decrease the effective attractive interaction between charges. For both the air-water and metal-water interfaces, the limitations of the commonly used constant dielectric profile are discussed.