The “fine structure” of the slow micellar relaxation mode and the aggregation rates in the range between a potential hump and well in the work of aggregation

An analytical expression has been derived for the quasi-stationary size distribution of surfactant aggregates in a micellar system approaching the final equilibrium state. In contrast to previously known relations, the derived expression takes into account variations in the concentration of monomers during the slow relaxation and enables one to determine the previously unknown fine structure of the linearized mode of slow relaxation, i.e., its dependence on the aggregation numbers in the range between the maximum and minimum of the work of aggregation. This dependence has been reliably confirmed by the numerical solution of the set of linearized Becker–Doering difference equations, which describe the molecular mechanism of the kinetics of micellization and micellar relaxation. In turn, the expression found for the relaxation mode makes it possible to refine the analogous “fine structure” of aggregation rates at different points of the same range between the maximum and minimum of the work of aggregation, in which the aggregation rates appear to be low but exhibit a nonmonotonic behavior. This behavior is also confirmed by the numerical solution of the Becker–Doering difference kinetic equations.