ENERGETIC AND ENTROPIC CONTRIBUTIONS TO THE INTERACTION OF UNEQUAL SPHERICAL DOUBLE-LAYERS

The potential energy as a function of distance is obtained for the dou ble-layer interaction of two spherical colloidal particles. The Poisso n-Boltzmann equation is solved numerically, using a collocation techni que, for two spheres having various sizes and for constant potential a nd 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 parti cles are brought into contact from infinity. Various approximate metho ds 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 th e curvature of the interacting spheres, and the dependence is quite st rong for the constant charge case, in which the relative magnitudes of the electrical energy and entropy change significantly as the radii o f the interacting spheres are changed for a fixed Debye length. (C) 19 94 Academic Press, Inc.