Molecular-Thermodynamic Model of Solubilization in Direct Spherical Micelles of Nonionic Surfactants

A thermodynamic model has been formulated for the formation work of a molecular aggregate consisting of molecules of a nonionic surfactant and a solubilisate in a hydrocarbon–surfactant–water solution as a function of temperature, concentrations of the surfactant and hydrocarbon in the solution, and aggregation numbers of the surfactant and hydrocarbon in the aggregate. The model depends on the structural parameters and physical characteristics of surfactant and solubilisate molecules. Predictions of the model concerning the minimum and the saddle point of the aggregation work have been considered and the distributions of relative concentrations of aggregates over the aggregation numbers of the surfactant and solubilisate have been plotted at different concentrations of surfactant and hydrocarbon monomers in the solution. The fractions of the surfactant and solubilisate in the aggregates have been numerically estimated relative to the equilibrium concentrations of surfactant and solubilisate monomers, and the average aggregation numbers of the surfactant and solubilisate in the aggregates have been found. The possibility of the colossal accumulation of solubilisate molecules in the molecular aggregates has been shown. The aggregation and solubilization have been considered at equilibrium surfactant concentrations that are markedly lower than the critical micelle concentration in a pure surfactant solution. It has been found that the limiting concentrations of the nonionic surfactant and the solubilisate corresponding to the formation of stable nanoemulsions lie in rather narrow ranges, and it is unlikely to get into them as a result of the random search in laboratory experiments.