  The eigenvalues and eigenvectors of the matrix of coefficients of the
linearized kinetic equations applied to aggregation in surfactant solution
determine the full spectrum of characteristic times and specific modes of
micellar relaxation. The dependence of these relaxation times and modes on the
total surfactant concentration has been analyzed for concentrations in the
vicinity and well above the second critical micelle concentration (cmc2) for
systems with coexisting spherical and cylindrical micelles. The analysis has
been done on the basis of a discrete form of the Becker-Doering kinetic
equations employing the Smoluchowsky diffusion model for the attachment rates
of surfactant monomers to surfactant aggregates with matching the rates for
spherical aggregates and the rates for large cylindrical micelles. The
equilibrium distribution of surfactant aggregates in solution has been modeled
as having one maximum for monomers, another maximum for spherical micelles and
wide slowly descending branch for cylindrical micelles. The results of
computations have been compared with the analytical ones known in the limiting
cases from solutions of the continuous Becker-Doering kinetic equation. They
demonstrated a fair agreement even in the vicinity of the cmc2 where the
analytical theory looses formally its applicability.

Soft Condensed Matter