Double layer forces between heterogeneous charged surfaces: The effect of net surface charge

Abstract

In this paper a theoretical analysis is outlined which describes forces between macroscopic heterogeneous surfaces that bear a significant residual charge after, say, the nonuniform adsorption of large, oppositely charged macromolecules. Quite unlike the case of uniform surface charges, extremely strong and long-ranged attractive forces of electrostatic origin can exist between surfaces with regularly spaced charge distributions. However, when a residual surface charge is present, this attractive component is reduced, compared with the case of net uncharged nonuniform surfaces, due to screening of the surface charges by electrolyte which has accumulated in double layers adjacent to each surface. Exact analytical formulas for the free energy expressed in terms of elliptic functions show that to leading order the asymptotic decay of the interaction is independent of average surface charge, while the magnitude is affected by both this charge and amount of bulk electrolyte present. Full numerical calculations of the disjoining pressure show that under conditions of low net surface charge and low electrolyte the influence of nonuniformities can be of some significance. However, because of the different decay rates, this influence is invariably limited to separations smaller than the Debye length. At moderate to high concentrations, the decay rates become similar and although the magnitude of the nonuniform term is diminished there is a regime of surface charge for which it does influence the interaction. The relative strength of the heterogeneous contribution, however, rapidly diminishes as the net surface charge increases. It is concluded that even in this ideal case of regularly spaced charge distributions, the effect of inhomogeneities is not important when there is a significant net surface charge.