Periodic systems of frustrated fluid films and « micellar » cubic structures in liquid crystals

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Abstract
We examine the possible ordered configurations with cellular topology of the simply-connected type, solving the frustration in a periodic system of frustrated fluid films, such as those built by amphiphilic molecules in presence of water. We show that they are periodical organizations of amphiphilic and aqueous media in polyhedral cells, similar to type I and II structures of water clathrates. The walls of these cells support a self-intersecting film of one medium separating finite micelles of the other. This description applies well to liquid crystalline phases with cubic symmetries found in some phase diagrams, in between the hexagonal and micellar phases