ON THE FLEXIBLE SURFACE MODEL OF SPONGE PHASES AND MICROEMULSIONS

We investigate the flexible surface model of sponge phases and microemulsions where the local curvature (free) energy, expanded to second order, leads to a total free energy per unit volume that is proportional to the area/volume (A/V) ratio to the third power. This is a general result applicable to lamellar phases, sponge phases, and balanced microemulsions. A number of conclusions follow from this simple relation, the most significant being the following: (i) For the majority of sponge or L3 phases we conclude that the coefficient for the (A/V)3 term in the free energy is negative. To account for the stability of the phase at finite concentration, one has to introduce fourth-order terms in the curvature energy. (ii) lt is suggested that also for a balanced microemulsion the (A/V)3 term is negative, and this provides a simple and direct explanation of the existence of the three-phase triangle with a microemulsion in equilibrium with almost pure oil and water phases.