Lamellar phases and disordered phases of fluid bilayer membranes

Statistical ensembles of random geometrical shapes pervade complex fluid physics. Initially one-dimensional curves in space were most thoroughly studied due to the many applications of such ensembles to the conformation and dynamics of polymers. But today, ensembles of two-dimensional membranes also attract much attention. Physical realizations of such surfaces include surfactant bilayers which spontaneously self assemble from amphiphilic molecules in solution. At the present time, two different dilute phases of fluid membranes have been well characterized which correspond to different large scale arrangements for the surfaces: the swollen lamellar phase (L alpha ) and the sponge phase (L 3 ). In this brief review, the author sums up what is understood at the present time of these phases of surfaces. The role of the bending elasticity of the membrane in the phase stability is particularly emphasized.