Multi-scale Times and Modes of Fast and Slow Relaxation in Solutions with Coexisting Spherical and Cylindrical Micelles according to the Difference Becker-Doering Kinetic Equations

摘要

The eigenvalues and eigenvectors of the matrix of coefficients of thelinearized kinetic equations applied to aggregation in surfactant solutiondetermine the full spectrum of characteristic times and specific modes ofmicellar relaxation. The dependence of these relaxation times and modes on thetotal surfactant concentration has been analyzed for concentrations in thevicinity and well above the second critical micelle concentration (cmc2) forsystems with coexisting spherical and cylindrical micelles. The analysis hasbeen done on the basis of a discrete form of the Becker-Doering kineticequations employing the Smoluchowsky diffusion model for the attachment ratesof surfactant monomers to surfactant aggregates with matching the rates forspherical aggregates and the rates for large cylindrical micelles. Theequilibrium distribution of surfactant aggregates in solution has been modeledas having one maximum for monomers, another maximum for spherical micelles andwide slowly descending branch for cylindrical micelles. The results ofcomputations have been compared with the analytical ones known in the limitingcases from solutions of the continuous Becker-Doering kinetic equation. Theydemonstrated a fair agreement even in the vicinity of the cmc2 where theanalytical theory looses formally its applicability.