THERMAL STABILITY OF AN ADSORBED ARRAY OF CHARGES IN THE EINSTEIN APPROXIMATION

For an infinite hexagonal array of ions adsorbed on a conducting plane of infinite extent, the thermal fluctuation from strict lattice ordering in the neighborhood of a given adion is considered. The ions are imaged in the uniform, conducting adsorbent and are assumed to move freely in the plane; they thus arrange themselves in a perfect hexagonal array at absolute zero temperature. By use of the accurate planar potential seen by one adion moving in the field arising from an infinite number of fixed hexagonally arrayed surrounding ions, the root-mean-square (r.m.s.) amplitude of planar vibration of the ion relative to its neighbors is approximately determined for several values of nearest neighbor distances between ions, r1. On the basis of these results, we find, for example, that for a distance, β, between the center of charge of an ion and the imaging plane of 3 Å, an ionic valence zv of unity, and an effective dielectric constant of ε, a hexagonal array with r1 = 15 Å is stable up to a temperature, T0, of approximately 1760/ε°K while one with r1 = 21 Å is stable up to about 760/ε°K. Results apply to adsorption from either a gas or liquid phase and, as well, to an array of real dipoles adsorbed on a nonconducting surface. The appropriate values for ε are of the order of 2 and 6, respectively, for adsorption from gas or from aqueous electrolytes. For various r1's, explicit expressions for T0 are obtained which depend on ε, β, and zv.