Approximate expression for the interaction of diffuse electrical double layers at constant charge

Abstract

A new approximation for the repulsive energy between two flat, diffuse electrical double layers is derived for the condition that the double layer charge remains constant. The main assumption is that the potential of the isolated double layers is fairly small, but, during interaction, the potential can take any value. Comparison with exact computations for the constant charge case shows good agreement, even when the double layers interact strongly and when the results differ most widely from those based on the constant potential assumption. A simpler expression, based on the linear Poisson-Boltzmann equation, is shown to be a rather poor approximation in the constant charge case.