Lyotropic liquid crystals: The common skeleton of their phase diagrams

The polymorphism of lyotropic liquid crystals built by amphiphilic molecules is characterized by similar sequences of structures whatever the chemical details of the molecules. This suggests the existence of a very general framework, independent of these details but related to the common property of the molecules, which is the building of interfacial films. We therefore extend our recent analysis of lyotropic liquid crystals in terms of periodic systems of frustrated fluid films to this problem. In this analysis we showed that the frustration is totally relaxed if the system is organized in ideal structures built in curved spaces. Here, we use the fact that these ideal structures are submitted to packing constraints imposed by the particular geometries of their embedding spaces. The analysis of these constraints leads to localizations of ideal structures following a sequence similar to the observed ones. This shows that the dominant parameters of the sequence are those of the frustration, i.e. interfacial distances and spontaneous first curvature.