Critical Micelle Concentration
The critical micelle concentration (CMC) is the surfactant concentration above which surfactant molecules self-assemble into micelles. Because solubilization of oily or nonpolar species requires micelles, the CMC is a key property of any surfactant formulation. It can be measured by surface tension, conductivity, capillary electrophoresis, spectroscopy, or dye solubilization, in which a dye that fluoresces or absorbs differently in a nonpolar environment reports the appearance of micelle cores as an abrupt change in signal with concentration.
Practical formulations usually mix surfactants, and mixtures are generally non-ideal. A widely used description is regular solution theory, which expresses the mixed CMC in terms of the pure-component CMCs, the bulk and micellar compositions, and one empirical interaction parameter beta. A value of zero means ideal mixing; negative values mean attractive interactions and synergism, where micelles form at lower total concentration than for either pure surfactant. Anionic and nonionic pairs typically show small negative beta, anionic and cationic pairs can reach about -20, and some fluorocarbon surfactants give positive values. More complex activity coefficient and packing models also exist.
Mapping binary CMCs by classification (2025)
Chilkunda, Kitchin and Tilton determined the composition-dependent CMC of SDS and C8E4 mixtures from a single 96-well plate of Nile Red fluorescence measurements (Chilkunda et al. 2025). Instead of extracting a CMC along each composition line and fitting a model through those points, they labeled every well as below or above the CMC and chose the regular solution beta whose boundary minimized misclassifications, obtaining beta = -3.6 +/- 0.5 against a literature value of -3.1. In 0.5 M NaCl they found beta = -3.1 +/- 0.4, with the smaller magnitude attributed to salt screening of the sulfate headgroups. A conventional two-step leaky ReLU analysis of the same plate gave -2.8 +/- 0.2 but was more sensitive to local noise. The plate design is discussed under design of experiments and high-throughput experimentation. Summary: chilkunda2025.