THE EFFECT OF DISCRETE SURFACE-CHARGE ON POTENTIAL-ENERGY OF REPULSION BETWEEN COLLOIDAL SURFACES

The linear Poisson-Boltzmann equation is extended in three dimensions to account for the discreteness of potential-determining ions, in a system of two parallel surfaces. A planar square lattice of disk type surface ions is considered. Solutions based on double Fourier series are obtained, which permit the computation of potential energy of repulsion using concepts of DLVO theory. Results are presented for the limiting cases of constant mean surface charge and constant mean surface potential. In both cases the discrete charges appear to generate greater interaction potential compared to uniformly charged surfaces. Under constant mean surface charge this effect tends to vanish with increasing separation distance between surfaces. In the case of constant mean potential, however, there is a nearly constant deviation (when surfaces with discrete and uniform charges are compared) even for large separation distances. © 1992.