CRITICAL COAGULATION CONCENTRATION OF CATIONS FOR NEGATIVELY CHARGED-PARTICLES WITH AN ION-PENETRABLE SURFACE-LAYER

The critical coagulation concentration (CCC) of cations in a suspension of negatively charged colloidal particles and arbitrary a:b electrolyte is derived. Here, a particle comprises a rigid core and an ion-penetrable surface layer. The latter contains fixed charges due to either the dissociation of the functional groups it bears or the adsorption of ions in the liquid phase. We show that, if the potential in the surface layer is high, the CCC ratio of cations follows that predicted by the Schulze-Hardy rule. On the other hand, if the potential in the surface layer is low, the CCC ratio deviates appreciably from this rule, in general. On possible exception is that the fixed charges arise from the exchange of cations in the liquid phase with the protons of the functional groups in the surface layer to form a metal complex, and the subsequent dissociation of this complex. The binding of the cations with dissociated functional groups needs to be strong enough, and there are sufficiently many functional groups. (C) 1995 Academic Press, Inc