The Lamellar-to-Isotropic Transition in Ternary Amphiphilic Systems

We study the dependence of the phase behavior of ternary amphiphilic systems on composition and temperature. Our analysis is based on a curvature elastic model of the amphiphile film with sufficiently large spontaneous curvature c0 and sufficiently negative saddle-splay modulus κ̄ that the stable phases are the lamellar phase and a droplet microemulsion. In addition to the curvature energy, we consider the contributions to the free energy of the long-ranged van der Waals interaction and of the undulation modes. We find that for bending rigidities of order kBT , the lamellar phase extends further and further into the water apex of the phase diagram as the phase inversion temperature is approached, in good agreement with experimental results. PACS numbers: 64.70.Ja, 64.75.+g, 82.70.-y