Diffusion in micellar systems: theory and molecular modelling

Recent development of experimental methods of investigation of diffusion in micellar systems and rethinking of the available material led to an increase in the number of theoretical studies in this field. This review summarizes the achievements in the general theory of micellization based on the law of mass action and in its applications to migration of surfactants in micellar systems. The law of mass action itself is modified to describe aggregative systems not only at low but also at moderate concentrations. New methods for calculating the concentrations of monomers and micelles in nonionic and ionic micellar systems are presented. Methods for estimating the micellar diffusion coefficient and the aggregation number from experimental data on surfactant diffusion are described. The theory of diffusion of electrically neutral micelles in concentrated ionic micellar solutions is developed. Computer simulation is an important tool complementing analytical and experimental methods of investigation of diffusion processes in micellar systems. The review addresses modern methods of molecular modelling of micellar systems, such as the all-atom molecular dynamics, molecular dynamics within coarse-grained models, and Brownian dynamics, which allow one to obtain a most detailed description of the structural and transport properties of micellar solutions. Various versions of cluster analysis and the role of this approach in calculations of surfactant diffusion coefficients in micellar solutions are discussed. The results of calculations of the diffusion coefficients of aggregates with different aggregation numbers, ions and water molecules from the data of all-atom molecular dynamics simulations at different total surfactant concentrations in the presence and in the absence of electrolyte are presented.