Exact Poisson-Boltzmann solution for the interaction of dissimilar charge-regulating surfaces

An efficient method is proposed to calculate the electric double layer force between two flat surfaces of dissimilar composition and ionization properties. The approach is based on explicit expressions for the solution of the (nonlinear) Poisson-Boltzmann equation and allows for boundary conditions of charge regulation, i.e., chemical equilibrium of both surfaces with a bulk electrolyte at all surface separations. As an illustration, we discuss in some detail the interaction between a weakly acidic and a strongly acidic latex surface, and between an acidic (silica) surface and an amphoteric (rutile) surface.