Surfactants in the two gradient theory of phase transitions

We investigate the influence of surfactants on stabilizing the formation of interfaces in solid-solid phase transitions. The analysis focuses on singularly perturbed van der Waals-Cahn-Hillard-type energies for gradient vector fields, supplemented with a term that accounts for the interaction between the surfactant and the solid. Assuming the potential term to have only two rank-$ 1 $ connected wells, we prove that the effective energy for the formation of an interface decreases when the surfactant segregate to the interface.