Discreteness‐of‐Charge Adsorption Micropotentials: III . Dielectric‐Conductive Imaging

Abstract

A convenient general method for calculating potentials and fields arising from planar arrays of discrete adions under a variety of imaging conditions is described and illustrated. Adions are perfectly imaged by one conducting plane (single imaging) and are also imaged by a dielectric constant discontinuity at a plane on their other side. The method employs only solutions of the single imaging problem, is readily applied without a computer, and is pertinent to the usual electrolyte compact layer adjoining either an electrode or a dielectric material, which may be air. The single image solutions used in calculating more complex imaging results may be exact values obtained from a previous rather complicated approach, or for ease in calculation, may frequently be approximate but quite accurate values calculated by a simple method described herein. Using the exact approach, one can calculate, for the full range of the dielectric reflection parameter, fields and potentials along any line perpendicular to the conducting plane. Here we are primarily concerned with potentials and fields along the line through a removed adion, and the approximate single imaging solution is especially useful. Although we apply the method to regular hexagonal arrays, in the latter case it is equally applicable to arrays described by Grahame's partially smeared, cut‐off model for single imaging. Some comparison with the results of this model is presented. In addition to calculating and illustrating the variation of field and potential within the compact layer and the adjoining dielectric medium, we have examined in detail the difference between the micropotential and the macropotential for many different imaging situations. The present study includes the previously treated single conductive plane imaging and also the (infinite) conductive‐conductive imaging situations as special cases. It is found that special care is needed to describe the latter situation by the present model. Finally, the effect of possible conductive imaging by the electrolyte diffuse layer is considered qualitatively.