The van der Waals interactions in sphere-shell and cone-shell configurations.

This work introduces two expressions for the integration of the van der Waals interactions in geometries that are relevant to determining oil solubilization in micelles and the interaction among surfactants in micelles. The first integral applies to the interaction between a sphere and a spherical shell that surrounds the sphere. The second integral calculates the interaction between a truncated cone and the rest of a spherical shell that contains the cone. The new sphere-shell integration method was validated via a comparison between fully predicted and experimental surface tensions of alkanes at room temperature and reproduced the near zero surface tension values that are obtained close to the critical point. The cone-shell integration method was validated, in association with the sphere-shell expression, using a comparison between predicted and experimental cohesive energies for alkanes.