Abstract
On the basis of the linearized analytical and numerical kinetic description of stepwise aggregation of surfactant aggregates, the hierarchical relaxation times have been found for a polydisperse micellar system close and above the critical micellar concentration. The description was based on the difference and differential Becker–Döring kinetic equations with using a specific boundary condition and improved models for the attachment rates of surfactant monomers to cylindrical aggregates. Two models have been considered: the linear model for cylindrical aggregates and the attachment rate to elongated spheroidal aggregates. The rate of attachment of monomers to an elongated spheroidal aggregate was found explicitly as a function of the aggregation number. With applying the truncation techniques, the analytical solution of differential kinetic equations for fast relaxation of polydisperse micellar systems has been obtained for a linear model of the aggregation rate. In the case of the attachment rate for an elongated spheroidal aggregate, the semi-analytical solution has been found.
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