A General Approach to Describing Fast Relaxation with Regard to Specific Features of Micellar Models

Abstract

It has been shown that, when passing from the Becker–Döring finite-difference equations to the differential kinetic equation for the function of aggregate distribution over aggregation numbers, the value of the error in the calculation of the times of fast relaxation in a micellar solution is primarily determined by the approximation used for the behavior of the aggregation work in the vicinity of the minimum of the work. The approach developed in this study on the basis of the perturbation theory enables one to take into account the features of a specific micellar model and, in particular, the possible essential asymmetry of the aggregation work in the vicinity of its minimum already in the principal order. The values of some characteristic times of fast relaxation obtained in terms of the proposed approach show a markedly improved accuracy (in the sense of the closeness to “exact” solutions) as compared with recently obtained results at all considered concentrations. This approach is undoubtedly advantageous in the simplicity of its application, universality, and the feasibility to use it for spherical normal and reverse micelles, as well as for cylindrical micelles. Therewith, the complexity of the method is independent of the explicit specification of employed aggregation work and attachment coefficient as functions of aggregation number.