PHASE-DIAGRAM AND STRUCTURE OF THE BICONTINUOUS PHASE IN A 3-DIMENSIONAL LATTICE MODEL FOR OIL-WATER-SURFACTANT MIXTURES

The regions of stability of the bicontinuous, lamellar, oil-rich, water-rich, and disordered phases and the phase equilibria are determined for a three-dimensional lattice model of surfactant mixtures. Analytical expressions for the density distributions in the bicontinuous phase are obtained in the vicinity of the critical temperature T(c). A tricritical point is calculated analytically, and is found to be located either on the transition between the disordered phase and the bicontinuous phase or on the transition between the disordered phase and coexisting oil- and water-rich phases, depending on the interaction strengths. A structure factor in the bicontinuous phase is calculated. Connection with microemulsions is discussed.