Periodic surfaces and cubic phases in mixtures of oil, water, and surfactant

We study a ternary mixture of oil, water, and surfactant in the case of equal volume fractions of oil and water using the Landau–Ginzburg model derived from a lattice model of this ternary mixture. We concentrate on a phase region close to a coexistence line between microemulsion and cubic phases. In our model the bicontinuous cubic phases exist in a narrow window of the volume fraction of surfactant ρs≈0.6. The sequence of phase transitions is L→G→D→P→C as we increase ρs along the cubic-microemulsion bifurcation line. Here L stands for the lamellar phase and C for the cubic micellar phase. The gyroid G, primitive P, and diamond D phases are all bicontinuous. The transitions weakly depend on the temperature. The increase of ρs is accompanied by the increase of the surface area per unit volume. In the case of fluctuating monolayers the interface is diffused and the average area of the monolayer per unit volume is larger than the “projected area,” i.e., the area of the surface describing the average positio...

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