Van der Waals free energy model for solubilization of oil in micelles

This work introduces the first of a two part thermodynamic framework to estimate the solubilization of nonpolar oils in micelles conformed by nonionic surfactants with linear alkyl tails, considering their configuration and the molecular properties of the constituents. This first part introduces a formal approach to account for the lipophilic (van der Waals) contributions to the free energy of solubilization in spherical micelles. To this end, this work uses two recently developed integration methods for sphere-shell and cone-shell VDW interactions that allow the calculation of surfactant-oil and surfactant-surfactant interactions that take place within the micelles of the solubilization process studied here. The method consists in calculating the free energy of transferring a normal alkane from its continuum, and surfactants monomers from empty micelles to produce an oil swollen micelle. The lipophilic interactions are estimated using the microscopic approach of Hamaker with Lifshitz-based Hamaker constants. The influence of n-alkane and surfactant tail length on the solubilization capacity predicted by the van der Walls free energy model (VDW-FEM) are consistent with experimental trends and it is also consistent with the lipophilic terms included in the semi-empirical Hydrophilic-Lipophilic-Difference + Net-Average-Curvature's (HLD-NAC) equation that predicts the phase behavior of microemulsions. As a result, these lipophilic terms can now be defined in terms of molecular interactions and molecular properties.