On the Problem of Determining Aggregation Numbers from Surface Tension Measurements

In view of the recent discovery of variable aggregation numbers in the vicinity of the critical micelle concentration (CMC), the mass-action-law theory of the surface tension isotherm of a micellar solution with variable aggregation numbers is formulated both for nonionic and ionic surfactants. It is shown that the shape of the surface tension isotherm should be concave in the logarithmic scale above the CMC. Considering a change in the isotherm slope at the CMC apparent break point, the problems of determining the aggregation number for nonionic micelles and the degree of counterion binding for ionic micelles are discussed. In case of the aggregation number variability near the CMC, finding the aggregation number above the CMC apparent break point is considered and a computational scheme is elaborated, requiring a higher precision for experiment. Some experimental data from the literature are analyzed, and the method of estimating the degree of counterion binding is improved.