Sponge phases and balanced microemulsions: What determines their stability?

Abstract

We discuss the criteria for the thermodynamic stability of the L 3 (sponge) phase and its monolayer analogue, the balanced microemulsion, in the framework of the flexible surface model. In particular, we emphasize that a parameter which plays a controlling role in the behavior of these phases is the monolayer spontaneous curvature, which, depending on the system being considered, may be tuned by ionic strength, temperature or interfacial composition. With this connection made, the phase behavior of many experimental systems can be understood. In the case of the sponge, this phase is preferred over its competitors (for example, lamellae) in a very narrow region of the phase diagram where it best meets the energetic constraint of matching the negative monolayer spontaneous curvature. The balanced microemulsion, in contrast, is found at zero spontaneous curvature, and the criteria for its stability can then be argued from a consideration of the scaling behavior of the free energy.