CHARGE-REGULATION MODELING OF THE SCHULZE-HARDY RULE AND RELATED COAGULATION EFFECTS

The DLVO theory of colloid stability provided an explanation of the long-standing Schulze-Hardy rule, i.e. that the critical coagulation concentration (c.c.c.) is proportional to some inverse power of the counter-ion valency (z). For particular limiting cases the inverse power exponent was calculated to be either 2 or 6. By using the charge-regulation approach to double-layer interaction for real surfaces with identifiable surface sites, dissociation equilibria, new insights into the link between physiochemical parameters and the Schulze-Hardy exponent are obtained. The model also produces an important result, viz. that the total double-layer potential for the isolated particle at the c.c.c. solution condition, while different for each of a series of real materials, is independent of counter-ion valency (z).