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It is commonly considered that the frustration between the curvature energyand the chain stretching energy plays an important role in the formation oflyotropic liquid crystals in bicontinuous cubic phases. Theoretic and numericcalculations were performed for two extreme cases: Parallel surfaces eliminatethe variance of the chain length; constant mean curvature surfaces eliminatethe variance of the mean curvature. We have implemented a model with Brakke'sSurface Evolver which allows a competition between the two variances. Theresult shows a compromise of the two limiting geometries. With data from realsystems, we are able to recover the G--D--P phase sequence which was observedin experiments.

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Competition brings out the best: Modeling the frustration between  curvature energy and chain stretching energy of lyotropic liquid crystals in  bicontinuous cubic phases