DOUBLE-LAYER FORCES BETWEEN HETEROGENEOUS CHARGED SURFACES

In this paper we study the double layer interaction between two hetero geneous surfaces of either constant charge or constant potential. The surface heterogeneities are assumed to be distributed on periodic latt ices of arbitrary structure. General expressions for the 3-D electrost atic potential distribution and the interaction free energy between th e two surfaces are given. Asymptotic forms and numerical examples for the interaction potential are provided for the symmetric lattice probl em. In general, the interaction potential or osmotic pressure decays e xponentially at large separations. When a nonuniform, but net neutral, surface interacts with a uniform surface (charged or uncharged), the interaction can be either attractive or repulsive depending on whether the surfaces are constant potential or constant charge. For two nonun iform net neutral surfaces, the interaction can be either attractive o r repulsive depending on whether the surfaces are constrained in confi gurations in which regions of unlike or like charge are in opposition. For this case, a statistical mechanical average over all relative lat eral displacements shows that asymptotically the interaction will alwa ys be attractive. The magnitude of the attraction is comparable to or can exceed the van der Waals interaction. The results given here would warrant inclusion in any interpretation of surface force measurements in systems involving adsorbing, neutralizing surfactants.