Thermodynamics of the L (Sponge) Phase in the Flexible Surface Model

(Received 5 August 1994, revised 17 October 1994, accepted 9 November 1994)

Abstract
The thermodynamics of the L ₃ (sponge) phase is investigated within the flexible surface model. The well-established leading-order scaling for the free energy density (where is the surfactant volume fraction) requires modification in order to describe the narrow character of the phase and the observed sequence of phase transitions. We find that higher order contributions to the free energy density from the local curvature energy provide a straightforward mechanism to account for these features. The phase equilibria with the dilute solution on one side of the phase and the lamellar phase on the other are evaluated for a model binary (surfactant-solvent) system, and calculated phase diagrams are presented. Experimental evidence in support of the model comes from static light scattering experiments on the pseudo-binary system AOT-NaNO ₃-water. We calculate the forward scattering intensity along chosen dilution lines within the phase using the model, and predict that the scattering intensity varies significantly as we move from one phase boundary to the other at constant . The experimental results confirm these predictions, and provide strong evidence in support of the proposed model.