Nonlinear kinetics of fast relaxation in solutions with short and lengthy micelles.

An analytical treatment of the nonlinear kinetic equations for fast relaxation of coexisting short and lengthy micelles in surfactant solutions is presented. The kinetic equations can be written as a hierarchical set of differential equations for the moments of the aggregation number distribution function of micelles. It is shown that the moment equations can be successively integrated. As examples of the general approach, particular cases of short spherical micelles, lengthy cylindrical micelles, and coexisting short and lengthy micelles have been considered and compared to the results of linear kinetic theory of micellar fast relaxation. The results show that there is a strong interplay between coexisting short and lengthy micelles, even in the case when the total number of surfactant molecules aggregated in short micelles is small in comparison with that in lengthy micelles.