TEMPERATURE-DEPENDENCE OF CRITICAL MICELLE CONCENTRATIONS AND HEAT-CAPACITIES OF MICELLIZATION FOR IONIC SURFACTANTS

When the critical micelle concentration of an ionic surfactant has a minimal value, cmc*, occurring at a temperature T*, the cmc at other temperatures depends on cmc*, T/T*, and DELTAC(p)/(1 + alpha). DELTAC(p) is the change in heat capacity for micellization, and alpha is the fractional degree of counterion binding. When DELTAC(p)/(1 + alpha) is treated as a constant, a simple equation for this relation is readily obtained. It is tested on 20 sets of experimental data and found to fit with root mean square deviations less than 1 % for 19 of them and 1.6% for the other. The possibility that DELTAC(p) varies with temperature is not ruled out, but the fits are not significantly improved by assuming a linear dependence. Approximate best-fit parameters are presented and used to find values of DELTAC(p) and other changes in thermodynamic variables of micellization for each surfactant. Most of the results are consistent with a suggestion of Evans and Ninham that (1 + alpha)RT In cmc is equal to the contribution of hydrocarbon chain-water interactions to the Gibbs energy of micellization, but there are several anomalies remaining to be resolved.