Geometrical Basis of Cubic Structures

Abstract

We consider cubic liquid crystalline phases formed by amphiphilic molecules in the presence of water and which can be found in some phase diagrams in the immediate vicinity of lamellar phases [1,2]. These cubic phases have symmetries [2] and topolooies [3] strikingly different from those of lamellar phases. However we argue here that the basis of these structures can be understood in the same geometrical terms. They are periodic systems of fluid films separated by interfaces: lamellar phases are periodical stackings of flat interfaces at constant distances and cubic phases can be seen as periodical stackings of symmetrically curved interfaces at optimized distances.