Effect of the polydispersity of diffusing micelles on the surface elasticity

Abstract

The effect of the polydispersity of the micelles on the surface elasticity modulus of surfactant solutions subjected to periodical oscillations is studied theoretically. By using the results of a previous theoretical study (C.D. Dushkin, I.B. Ivanov and P.A. Kralchevsky, Colloids Surfaces, 60 (1991) 235) two important cases of surfactant diffusion are considered. First, diffusion affected by the slow relaxation process of micellization. Expressions for the elasticity modulus and its oscillation-retarding phase are derived. They appear as a special case of the equations of Lucassen for monodisperse micelles (J. Lucassen, J. Chem. Soc., Faraday Trans. 1, 72 (1976) 76). The parameters of the micelle size distribution (mean aggregation number and dispersion) are computed from the data of Lucassen. The values of the calculated parameters are in agreement with their experimental values for different surfactants, obtained by chemical relaxation techniques. Second, diffusion affected by the fast relaxation process of micellization. The equations for the surface elasticity modulus derived here cannot be obtained in the frame of Lucassen's model because the fast relaxation process is a net result of the polydispersity of the micelles. In both cases, the micelles enhance the exchange of monomers between the adsorption layer and the solution. Hence, the effective viscous behavior of the adsorption layer becomes more pronounced.