A Novel Approach to Determine the Critical Coagulation Concentration of a Colloidal Dispersion with Plate-like Particles

The critical coagulation concentration (ccc) of counterions is commonly described by the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory on the basis of a static force balance. It can, however, also be estimated from a kinetic point of view by studying the process of colloidal coagulation, or from a dynamic point of view by considering colloidal transport in nonequilibrium systems where other processes such as diffusion and the influence of gravity come into play. In particular, in a test tube where colloidal expansion takes place, the ccc can be interpreted as the electrolyte concentration below which expansion of colloids would always lead to full access to the entire volume of the test tube and above which a sharp boundary is established between a colloidal gel and pure water. On the basis of this perception and the dynamic force balance model that we developed to describe colloidal expansion in a test tube, accounting for the effects of particle diffusion and gravity in contrast to the DLVO theory, we propose an alternative way to assess the ccc of counterions. We also derive an approximate expression for the case of homointeraction at constant charge for montmorillonite. The estimated ccc values agree quite well with those observed experimentally for both Na+ and Ca2+ counterions for montmorillonite dispersions, at pH similar to 6.5. This is in contrast to the DLVO theory, which overpredicts the ccc by about 2 orders of magnitude. In addition, the detailed analyses suggest that the ccc of counterions decreases with increasing surface area and with the thickness of the particles. For montmorillonite, the ccc is nearly independent of the surface charge density of the particles for the range of typical charge densities.