Tilt model of inverted amphiphilic mesophases

We present an alternative model of structure and energetics of the inverted amphiphilic mesophases. The previous studies of the inverted hexagonal, H-II, and inverted micellar cubic, Q(II), phases considered the amphiphilic monolayers to be homogeneously bent. In contrast, we assume a unit cell of an inverted mesophase to consist of flat fragments of monolayer. Hence, the unit cells of the H-II and Q(II) phases are represented by a hexagonal rod and a polyhedron, respectively. Our model is motivated by Turner and Gruner's X-ray, diffraction reconstruction of structure of the H-II phase. The only deformation of the amphiphilic monolayers we consider is tilt of the hydrocarbon chains with respect to the monolayer surface, determined by the packing constraints imposed in the mesophases. Applying our recent model for the elastic energy of tilt in liquid membranes [23], we show that: i) tilt accounts in a natural way for the frustration energy of mesophases resulting from filling by the hydrocarbon chains the corners of the unit cells, ii) the energy of tilt variation along the membrane surface is analogous to the bending energy. We compute the energetics of the H-II, Q(IIsc) and Q(IIfcc) phases and obtain a hypothetical phase diagram in terms of the elastic constants of monolayers. Moreover, we calculate the structural dimensions of the mesophases. We verify the model showing that the obtained phase diagram describes the recent data for the glycolipids/water systems; the predicted dimensions of the Q(II) phase are in accord with the measured values; the model treats quantitatively the structural features observed for the H-II phase.