Discreteness-of-Charge Adsorption Micropotentials. II. Single Imaging

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Abstract
Methods are developed for calculating exact potentials and fields arising from discrete hexagonal arrays of monopoles imaged by a perfect conductor. They allow calculation of the potential and field at any point outside a plane electrode upon which such a hexagonal array of charges (of infinite extent) is adsorbed, and are applied to the problem of determining various electrical properties of such adsorbed arrays. We give particular attention to the micropotential and energy of adsorption for ionic adsorption in both electrolytic and gaseous systems and consider further application of the results to electron emission from metals. Detailed comparison with earlier approximate treatments is made, and when appropriate, errors appearing there are corrected. For example, we find that the rearrangement energy on incremental adsorption of ions does not vanish, as previously suggested, except for a nonphysical limit. Exact results are obtained for the rearrangement energy, and it is usually found to be a significant contribution to the total adsorption energy. Sufficient graphical and numerical results are given for all computed quantities so as to be of direct use to the worker in this general area.