Model of the quasi-monodisperse micelles with application to the kinetics of micellization, adsorption and diffusion in surfactant solutions and thin liquid films

The micelles in a water surfactant solution are considered as quasi-monodisperse aggregates of two kinds: large and small. They give rise to two micellization processes, fast and slow, in response to any external perturbation. During the fast process the bigger micelles release a certain number of monomers to transfer into the smaller ones, while the total micelle concentration remains constant. During the slow process both types of micelle decrease in number until the effect of perturbation is compensated. Using an asymptotic mathematical procedure, we derive analytical expressions for the concentrations of species and the characteristic time constants of relaxation. The time constants obtained are consistent with the experimental data for the micellization kinetics and also with their counterparts known from the polydisperse micelle model. The advantage of the quasi-monodisperse model dealing with only two micelle fractions is further exploited to solve a more complicated diffusion problem for the kinetics of adsorption. It turns out that the micellization process is important for surfactant mass transfer; because the time constant of this process is commensurable with the characteristic time of diffusion. The set of coupled equations derived for the diffusion of free monomers and micelles contains source terms accounting for the exchange of material among the species. The equations are solved for a semi-infinite micellar solution and the analytical expression for the dynamic surface tension is compared with experimental data for different surfactants, measured by various methods. In all cases the slow micellization process predetermines the adsorption kinetics, i.e. the micelles have to be destroyed in order to fill the adsorption layer with monomers. In contrast to this observation, the fast relaxation process affects the adsorption on the two opposite surfaces of a thin liquid film, because the diffusion in the film is much faster than in a semi-infinite medium. For this reason the micelles can compensate the surface tension gradients created in the course of film thinning by simply releasing monomers. The calculated velocity of thinning is effectively increasing above the critical micelle concentration, which is in accord with existing experimental data. The thin him hydrodynamics turns out to be affected by the bulk diffusion of monomers enhanced by the micellization kinetics. This is opposite to the mechanism accepted for films without micelles, whose hydrodynamics is governed by the surface diffusion in the adsorbed layer. (C) 1998 Elsevier Science B.V. All rights reserved.