Frustration in bilayers and topologies of liquid crystals of amphiphilic molecules

Abstract

Amphiphilic molecules are well-known for their ability to build symmetric fluid films, or bilayers, most often organized in lamellar phases. The symmetric changes of curvatures of the two interfaces of a bilayer, as temperature and water content vary, may enter into conflict with the compactness of the bilayer core. We consider the possible role of such a stress as a structural factor promoting the transformation of lamellar phases into other liquid crystalline and micellar phases. We analyse this stress as a frustration which can be solved by the introduction of defects of rotation, or disclinations. We develop a geometrical approach and show that the possible solutions correspond to organizations of amphiphilic molecules whose topologies are similar to those of the liquid crystalline and micellar phases. We propose therefore to describe these phases as structures of disclinations. Such a geometrical approach puts forward the structural role of internal stresses within bilayers and provides the frame within which the other physical factors are to be considered