Morphology of Ionic Micelles as Studied by Numerical Solution of the Poisson Equation.

The existing concepts of the ionic micelle structure were specified. It was noted that the composition of dispersed phase particles in a liquid dispersion medium should necessarily include adsorbed counterions rigidly bound to these particles. By numerical solution of the Poisson equation for the two most often used approximations, the Poisson-Boltzmann (PB) model and the Jellium-approximation (JA), the electric potential decay from the Stern potential of dispersed phase particles was defined. A new methodological approach to analyze the reaction of micelle potential decay based on small variability of the CMC value was proposed. It made possible to determine the dimension parameter, which in the presence of weak thermal effects approximately corresponds to the micelle hydrodynamic radius, and to calculate the electrokinetic potential of micelles. The results of theoretical calculations were compared with our previous experimental data on the thickness of the SDS micelle hydrophilic layer obtained by SAXS. A good agreement between the calculated and measured values was obtained, and it was noted that for low concentrations the experimental values are more correctly described by the PB model, but for concentrations greater than 100 mM the JA model is more preferable. It was found that the slipping plane is located near the outer Stern plane and is separated from it only by a few molecular layers of water. The influence stronger than the thermal one can shift the slipping plane closer to the micelle core. Accordingly, the smallest hydrodynamic micelle size is determined by the outer Stern plane. The results of our work allowed us to conclude that the micelle is not something soft and watery, but according to its specified structure, it is a more solid-like particle than was previously assumed. The proposed approach can be extended to investigate other effects of a physicochemical nature, in particular, those observed with the addition of an external electrolyte or nanoparticles.