Topological defects in bicontinuous phases

Laboratoire de Physique des Solides, Université Paris-Sud - Bât. 510, 91405 Orsay, France

Received: 13 December 2007
Accepted: 23 January 2008

Abstract

It is shown that in balanced bicontinuous cubic lyotropic crystals two types of dislocations are possible. The first, trivial type of dislocations preserves the orientability of the surfactant bilayer. Dislocations of the second, Möbius type make the bilayer non-orientable. Upon melting of the cubic phase into the sponge phase, crystal order is destroyed but Möbius dislocations persist by virtue of topological continuity as disorientation: a new kind of topological defects which, by definition, alter the orientability of the bilayer.