General features of lattices of point dipoles against a charged wall

Abstract

Some general properties of monolayers and multilayers of point dipoles against a charged wall, which do not depend on the discrete or infinite number of allowed orientations nor on the statistical-mechanical procedure employed, are derived. These properties stem directly from purely electrostatic considerations on the regular lattice structure of the layer and from the very definition of a statistical-mechanical average. The ‘‘effective coordination number’’ ce, frequently employed in monolayer models, is shown not to be an adjustable parameter, but rather a well-defined lattice sum. The implications of the use of erroneously high ce values are pointed out. Finally, the general features of monolayer models of point dipoles with an infinite number of orientations in the framework of the mean-field approximation are stressed, together with the limitations of this widely employed approximate statistical-mechanical procedure.