Lyotropic Liquid Crystals as Structures of Defects

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Abstract
The most representative lyotropic liquid crystals are those formed by amphiphilic molecules, such as soaps, detergents and lipids, in presence of water. These molecules are able to build structures exhibiting a long range crystalline order, although they are disordered in a liquid-like manner at the local level. This clearly shows that the individual molecules can not be the building blocks of the structures and that the elements of structures are indeed the interfaces built by the molecules or, better, the symmetric films built by two facing interfaces. These structures can therefore be described as crystals of fluid films. In order to bring out a general basis for the understanding of this new class of crystals we develop a model for studying periodic configurations of symmetric films. Its basic hypothesis is the existence of a geometrical frustration resulting from the conflict between forces normal to the interfaces and forces parallel to the interfaces. We determine its possible solutions following a geometrical approach similar to those developed for other cases of frustration in condensed matter physics. The solutions optimizing the frustration appear to be in a satisfying agreement with the observed structures. This leads to consider crystals of films as structures of disclinations.