Microemulsion model with oil-water anisotropy

We consider a spin model for applications to oil-water-amphiphilic-surfactant mixtures near the region where those phases coexist. We analyze this model assuming that oil and water molecules cannot be treated symmetrically, given that they do exhibit different chemical potentials. Using a mean-field approximation, we find that the modulated phase assumes two possible arrangements, such as sheets (lamellar phase) or rods (hexagonal phase). Due to fluctuations, the lamellar phase is present when the difference between the chemical potential of oil and the chemical potential of water is not too high. Both lamellar and hexagonal phases are present when this difference exceeds a certain value. This value specifies the triple point where the two modulated. phases coexist with the disordered phase. This point is present even for small values of the critical wave vector, indicating that the mean-field Lifshitz point is actually a Buctuation-induced end point