QUANTIFYING PACKING FRUSTRATION ENERGY IN INVERSE LYOTROPIC MESOPHASES

In this paper we investigate a simple model of inverse lyotropic mesop hase energetics. The total energy is constructed by first minimizing t he curvature elastic energy for the interface and then calculating the energy tied up in the chain extension variations that result for the various interfacial shapes and crystallographic space groups. We have calculated the chain packing energy in the harmonic approximation and find that we can separate this into two distinct terms. The first of t hese we call the packing factor, which is a constant for each interfac ial shape and its associated crystallographic space group. The second term describes the variation in the packing frustration energy with me an curvature and monolayer thickness for the different interfacial sha pes, i.e. spherical, cylindrical, and hyperbolic. Using this formalism and optimizing the mean interfacial curvature, we are able to build a global phase diagram in terms of the spontaneous mean curvature and t he molecular length. The phase diagram we construct from the model pla ces the phase boundaries between the inverse bicontinuous cubic, inver se hexagonal, and inverse micellar cubic phases in the expected region s of the diagram. This gives some encouragement to the widely held not ion that the competition between interfacial curvature and hydrocarbon packing constraints can be used to explain lyotropic mesomorphism. Ho wever, the model is overly simplistic and breaks down in the regimes w here the average interfacial curvature is at its greatest. Specificall y it predicts that a body-centered cubic arrangement of inverse micell es is of lower energy than an Fd3m packing, but the latter are the onl y arrangements which have been found to date.