Random Interface Model of Sponge Phases

Abstract

We present a coherent structural and thermodynamic approach to sponge phases of surfactant solutions based on the curvature energy of the surfactant film characterized by the bending moduli κ, , the surfactant concentration _s and the inside/outside ratio . We find that an entropy-driven transition between symmetric (S) and asymmetric (A) sponge phases with a critical _s ~ κ^-1/3 is possible. Film and bulk scattering are given consistently, in terms of the correlation length ξ(κ, , _s) and the structural wave vector k₀(κ, , _s). The film scattering at small wave vectors has approximately an arctangent form and—depending on the value of k₀ ξ—a more or less pronounced irregularity at about 2k₀.