Model of inverse “dry” micelles with coexisting spherical, globular and cylindrical aggregates

A new statistical thermodynamic model of inverse nonionic aggregates of surfactant molecules in nonpolar solvents is considered. This model admits the fluctuation coexistence of inverse spherical, globular, and spherocylindrical aggregates without activation barriers between them. The model is based on the assumption of a uniform bulk density of the number of molecular groups inside the core of an aggregate that can continuously transform into a sphere, a globule, and a spherocylinder. In this model, for any aggregation numbers, the work of aggregation depends not only on the aggregation numbers and the concentration of surfactant monomers, but also on two independent geometric parameters characterizing, at the same aggregation numbers, the deviation from the spherical form of the aggregate towards globular and spherocylindrical forms. Even in the range of small aggregation numbers, this fact leads to a significant difference between the equilibrium distribution function of aggregates, which depends on the aggregation number and two form parameters, and the one-dimensional distribution function in terms of aggregation numbers. It is shown that the optimal values of the form parameters, which minimize the work of aggregation, are in good agreement for spherocylindrical aggregates with the predictions of a purely geometric model of such aggregates under the additional assumption of a uniform surface density of molecular groups at the micelle core. The predictions of a new molecular thermodynamic model for the degrees of surfactant micellization in inverse aggregates of various forms at different surfactant concentrations are considered.