A model for calculating electrostatic interactions between colloidal particles of arbitrary surface topology

A numerical model for calculating the electrostatic interaction between two particles of arbitrary shape and topology is described. A key feature of t he model is a generalized discretization program, capable of simulating any desired analytical shape as a set of flat, triangular elements. The relati ve sizes of the elements are adjusted using a density function to better ma tch the desired shape and the spatial variation of the electrical surface p roperties on each particle. The distribution of either surface potential or surface charge density is then calculated using a boundary element approac h to solve the linearized Poisson-Boltzmann equation. Example interaction e nergy profiles are calculated for three different types of roughness-bumps, pits, and surface waves. It is found that the interaction energy between r ough particles remains different from that between two equivalent smooth sp heres at all separations, even for gap widths much larger than either the s olution Debye length or the characteristic roughness size. This behavior at large gap widths arises from the nature of the decay of the electric poten tial away from each particle. In addition, the magnitude of the roughness e ffect is found to depend greatly on the size and shape of the nonuniformity as well as the electrostatic boundary conditions. For example, for a spher e containing asperities of height equal to 0.2 times the particle radius, t he interaction energy can be as much as 50% greater than that between two e quivalent spheres under the condition of constant surface potential. At con stant surface charge density, the ratio of the interaction energies between rough and smooth spheres was found to either diverge or become zero as con tact between the two particles is approached, depending on the nature of th e roughness. Changes of this magnitude could clearly have a substantial imp act on the stability behavior of a dispersion of such particles. (C) 2001 A cademic Press.