Electrostatics of Diffuse Anisotropic Interfaces. I. Planar Layer Model

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Abstract
In problems involving the electrostatic potential due to charges in the presence of a diffuse interface, for simplicity it is assumed that the interface is an abrupt one. We have investigated the effects of relaxing this assumption. By a procedure related to the method of invariant imbedding, we have formulated, within the regime of macroscopic continuum theory, the calculation of the electrostatic potential for a charge in the presence of an anisotropic diffuse layer. For distances far from the interface, the leading term in the image potential is the same as that for an abrupt interface, but referred to an origin which is determined by the components of the dielectric tensor. The next term arising from an induced quadrupole moment is negligible in representative cases. Close to the interface, divergences in the image potential can only be avoided if the values and first derviatives of the dielectric parameter are continuous. These results are illustrated by model dielectric profiles for the diffuse layer for which analytic expressions are derived for the electrostatic potential. It is found that as the dielectric profile becomes smoother, the value of image potential decreases.

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