STRUCTURED PHASES OF A 3-DIMENSIONAL VECTOR LATTICE MODEL FOR OIL-WATER-SURFACTANT MIXTURES

A three-dimensional vector lattice model for a mixture of water, oil a nd amphiphile is considered on the simple cubic lattice. For a balance d system with equal water and oil concentrations the ground state exhi bits, when the surfactant is strong, an ordered bicontinuous structure in addition to pure oil/water and pure surfactant states. The model i s transformed, integrating out exactly the surfactant orientational de grees of freedom, in an effective spin-1 model with two-, three-, five - and seven-body interactions with temperature dependent interaction s trengths. This effective model is then investigated using the local me an-field approximation. The phase diagram of the model is derived and discussed, with particular attention to the structured ordered phase. In the disordered phase a microemulsion region is also found.