Kinetic description of the relaxation of surfactant solutions in the absence of activation barrier between spherical and cylindrical micelles

Abstract

The realistic situation, where there is no potential barrier of aggregation work between the spherical and cylindrical micelles, is analyzed within the framework of the kinetic description of the relaxation of nonionic surfactant solution containing spherical and cylindrical micelles. The variations in the sum of the total concentrations of spherical and cylindrical micelles caused by the total flux of molecular aggregates over the potential barrier of aggregation work between the monomers and spherical micelles is taken into account; it is also accounted for that, in the absence of the potential barrier of aggregation work between the spherical and cylindrical micelles, they are present in the mutual quasi-equilibrium. The closed linearized relaxation equation determining the variations (with time) in the total concentrations of spherical and cylindrical micelles in a materially isolated surfactant solution is derived and solved. The variations (with time) of the total concentrations of spherical and cylindrical micelles, the concentration of surfactant monomers, as well as the total amount of surfactant in cylindrical micelles, in the process of approach of a materially isolated micellar solution to the final equilibrium state are described analytically. It is disclosed that, at the mutual quasi-equilibrium of spherical and cylindrical micelles, the opposite-sign deviations of the total amount of substance in cylindrical micelles and the total amount of cylindrical micelles from their values in the final equilibrium state of a materially isolated solution is attributed to the relatively large cylindrical micelles. The agreement between the results obtained and analogous results of the description of micellar relaxation in the presence of the potential barrier of aggregation work between spherical and cylindrical micelles whose relative height is at least slightly lower than that between monomers and spherical micelles is demonstrated. Comparison is performed for the cases of the absence of either spherical or cylindrical micelles. Analytical expressions, which are accessible for experimental verification, for the ratios of relaxation times of surfactant solutions containing spherical and cylindrical micelles to those of surfactant solutions containing either spherical or cylindrical micelles alone are derived.