Crystals of fluid films

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Abstract
Crystals are classically described as periodic organizations of point objects, atoms or molecules, regularly disposed at the knots of lattices of various symmetries. Their long range crystalline order is generally considered as resulting from the propagation of the short range order of the individual point objects, which are therefore the building blocks of the structures. However, recent studies show that a long range crystalline order can exist without any‘affine’molecular order at short range. Such a situation was encountered investigating liquid crystalline materials, particularly those formed by amphiphailic molecules such as soaps, detergents and lipids, in presence of water. These molecules build crystalline structures although they have a short range disorder of liquid-like type. Clearly the building blocks of these structures can not be the individual molecules and their understanding requires the definition of more operative elements of structures. If it is remembered that amphiphiles stabilize liquid/liquid interfaces, an obvious candidate is the infinite fluid film built by two facing amphiphile/water interfaces. This direction leads to consider a new class of crystals, where the element of structure is no longer a point object but a bi-dimensional one. We shall examine successively: the geometrical foundation of the organization of films in space, the basis of their thermodynamics, the departures from the perfect order, the processes taking place at the phase transitions between structures of different topologies.