Toward a Theory of Diffusion of a Nonionic Surfactant with Variable Aggregation Number in a Micellar System

Since the aggregation number of micelles always grows with concentration, and, in some cases this dependence is noticeable even for spherical micelles, there is a need to revise the theory of micellization, in which the aggregation number is assumed to be constant. This work reformulates the theory of diffusion of nonionic surfactants in micellar solutions with regard to the variability of the aggregation number. A new formula, which expresses the diffusion coefficient of a surfactant via the diffusion coefficients of monomers and micelles, contains an additional factor capable of increasing the diffusion coefficient with the surfactant concentration. However, this factor is not overly strong, and the “old” part of the formula acts in the opposite direction; as a result, the conventional decrease in the diffusion coefficient of a nonionic surfactant remains prevailing. The analytical consideration has been supplemented with numerical calculations, the results of which are presented in the tables.