A simple method for ionic and molecular adsorption electrical calculations

Abstract

The usual methods for calculating potentials and fields arising from a regular, adsorbed plane array of ions or dipoles are complex and time consuming to apply. We present here a method based on a modification of Grahame's cut-off model which allows several such quantities to be calculated accurately but rapidly from simple closed formulas. The method is applied to hexagonal arrays of ideal and non-ideal dipoles. Non-ideal dipoles are assumed to arise from imaging of an array of adions in a conducting adsorbent. Results of the simple, approximate formulas are compared in detail with very accurate results obtained from lengthy computer calculations. We believe the latter will be unnecessary hereafter, whenever the field or potential is desired on a line perpendicular to the plane adsorbent through a removed dipole or ion. With proper normalization, potential-distance curves for ideal and non-ideal (finite-length) dipoles are found to be nearly the same. Finally, the present results are employed to yield an improved formula for the change of work function of a conducting surface, when a hexagonal array of polarizable molecules or atoms is adsorbed on it. The formula is illustrated and shows that adsorbed uncharged elements, with sufficiently high but still physical polarizability, must either ionize or their polarizability decrease upon adsorption.