Electrostatic Interaction between Two Dissimilar Spheres: Image-Interaction Correction to the Linear Superposition Approximation

Abstract

The leading term of the electrostatic interaction energy between two colloidal spheres in an electrolyte solution is given by a screened Coulomb interaction due to a simple linear superposition of the unperturbed potentials of the respective spheres. We have previously shown that the next-order correction to the linear superposition approximation corresponds to the interaction between one sphere and its image with respect to the other sphere. The image interaction depends strongly on the type of boundary conditions on the interacting spheres. In the present paper we consider the image-interaction energy for three cases on the basis of the linearized Poisson–Boltzmann equation: (a) the constant surface potential case, (b) the constant surface charge density case, and (c) the mixed case in which one sphere has a constant surface potential and the other has a constant surface charge density. It is shown that the image interaction is always attractive for case (a) but may be either attractive or repulsive for case (b). The change in sign of the interaction force or the appearance of the extremum in the interaction energy may occur when the image-interaction correction term and the leading term are of the opposite sign and the former exceeds the latter.