The isotropic (“Sponge”) to lamellar transition in dilute surfactant systems

We study the transition from an L3 “symmetric sponge” phase to a dilute lamellar phase Lα, in a bilayer-forming surfactant solution. The coupling of the smectic order parameter to the volume fraction of surfactant φ ensures that there is always a finite miscibility gap between the L3 and Lα phases. In contrast to block copolymer/solvent systems, the relative charge in composition at the transition is not small but of order unity, so that the usual Brazovskii approximation is only marginally applicable. This coupling should also have some interesting consequences for the phase separation and hysteresis behaviour of shear-induced lamellar phases. The unusual symmetry of the isotropic phase means that the amplitude of smectic order, as measured in scattering experiments, should vary linearly with the distance from the transition in the mean field regime, rather than as the usual square root.