Lamellar versus isotropic structures in dilute phases of fluid membranes

In recent years, considerable attention has been focused on dilute phases of fluid membranes in surfactant systems. At the present time, the structure of two different phases have been well characterized. The lamellar phase (Lα) shows long range smectic order and consists of a regular stack of parallel bilayers. At high dilution, its long range order has been shown to be stabilized by the steric interaction between adjacent undulating membranes. The other phase (L3) is isotropic and shows no long range positional order. Scattering patterns and transport properties strongly suggest that its structure consists of a randomly multiconnected bilayer separating two equivalent subvolumes of solvent. We here discuss the relative stability of these two structures in connection with the elastic properties of the amphiphilic membrane. A general scaling law for the free energy of the L3 phase as function of the degree of dilution is proposed and is checked against experimental measurements of some of its static and dynamic physical properties.