Towards an understanding of phase transitions between inverse bicontinuous cubic lyotropic liquid crystalline phases

The inverse bicontinuous cubic phases that form in some lipid-water mixtures are both important structural elements in cells and emerging vehicles for nanotechnological applications. We model the relative phase behaviour of the three known inverse bicontinuous cubic lyotropic phases as the sum of the curvature elastic and chain packing energy of the membrane, under the assumption that the membranes form interfaces of constant mean curvature. The model correctly predicts a number of apparently universal, qualitative features of the relative phase behaviour of the gyroid (Q(II)(G)), double diamond (Q(II)(D)) and primitive (Q(II)(P)) inverse bicontinuous cubic phases. These are: the phase sequence Q(II)(G) -> Q(II)(D) -> Q(II)(P) with increasing water composition; the absence in certain cases of Q(II)(P) from the phase diagram; the destabilisation of Q(II)(P) with an increase in the temperature and the negative slope of phase boundaries with respect to temperature. Unexpectedly the model predicts the potential existence of a re-entrant Q(II)(G) at high water dilutions that swells indefinitely. This has yet to be reported, which may reflect the difficulty of stabilising and then detecting such swollen, fluid interfacial structures. However, in the model the presence of the highly swollen Q(II)(G) phase causes the adjacent phase to exhibit an almost vertical phase boundary, a phenomenon which should be more readily detectable.