Energetic and Entropic Contributions to the Interaction of Unequal Spherical Double Layers

Abstract

The potential energy as a function of distance is obtained for the double-layer interaction of two spherical colloidal particles. The Poisson-Boltzmann equation is solved numerically, using a collocation technique, for two spheres having various sizes and for constant potential and constant charge boundary conditions. The potential distribution is determined and then used to find the change in the electrical energy, the entropy, and the chemical part of the free energy as the two particles are brought into contact from infinity. Various approximate methods used previously, depending on surface conditions and geometry, are found to work quite well for the constant potential case, but for the constant charge case, they are not adequate for most of the parameter space. The interaction energy profiles are found to be functions of the curvature of the interacting spheres, and the dependence is quite strong for the constant charge case, in which the relative magnitudes of the electrical energy and entropy change significantly as the radii of the interacting spheres are changed for a fixed Debye length.