Effect of Surface Roughness on the Interaction Energy between a Colloidal Sphere and a Flat Plate

Abstract

A set of analytical equations are developed for calculating the van der Waals and electrostatic interaction energies between a rough spherical particle and a smooth plate. The particle roughness is modeled as hemispherical asperities of fixed radius, in agreement with SEM micrographs of polystyrene latex spheres. The van der Waals energy is calculated using a pairwise summation technique for both nonretarded and retarded cases. The electrostatic energy is calculated using the linear superposition approximation and assuming the asperity-plate and particle-plate interactions are additive. We find that at large separations, the increased electrostatic repulsion produced by the roughness results in a shallower secondary potential well. At closer separations, however, the increased van der Waals attraction produces a dramatically lower repulsive barrier (as much as two orders of magnitude smaller in the example presented). This lower barrier would yield much larger capture rates than predicted by DLVO theory for smooth surfaces, in qualitative agreement with experimental observations.