ABSTRACT
Lyotropic liquid crystalline phases can be formed in concentrated mixtures of amphiphilic molecules and water [1-6]. The normal hexagonal (H
) and lamellar (L
) are two such liquid crystalline phases that are well characterized [7]. The H
phase has been shown to consist of infinite cylindrical micellar rods, which possess a right circular cross section, hexagonally close packed onto a lattice that has p6m symmetry [7-9]. The rod radius in the phase is usually constant and always less than the fully extended hydrophobic chain of the amphiphilic entity [2]. The structural building block of the L
phase is a bilayer, the thickness of which is never greater than 1.5 times the length of the fully extended hydrophobic moiety of the surfactant [2,7,10-12]. In this phase the bilayers are stacked one on
top of another, with water in the inter bilayer region, to form a phase that possesses one-dimensional periodicity. These two phases are ubiquitous to many systems that form lyotropic liquid crystalline phases, with the H
phase always occurring at lower amphiphilic volume fractions than the L
α phase. The transition between these phases upon increasing surfactant concentration is marked both by a topological transition, with the mesogenic units going from discrete micellar aggregates having positive interfacial curvature to continuous bilayers with zero curvature, and a commensurate change in the symmetry of the resultant phase. The topological transformation at the H
to L
α transition requires an alteration in the packing of the amphiphilic molecules at the mesogen-water interface. If an interfacial organization of the amphiphilic monomers other than that required to form a continuous bilayer minimizes the interactions in the system and possesses a lower interfacial curvature than the H
, that organization will be stabilized prior to the formation of the L
α. Two types of phases can be formed in this H
–L
α region. The first is a phase with a bicontinuous structure that possesses longrange three-dimensional cubic symmetry, the V
phase [2,13-15]. Such phases are viscous, isotropic, and therefore optically inactive. The properties of these phases are detailed extensively in other chapters of this book. The mesogenic unit of this phase is a surfactant bilayer that separates two distinct continuous solvent networks. This bilayer decorates a triply periodic surface, the midplane of which possesses cubic symmetry. This surface is locally highly curved, but the overall curvature of the phase is zero. The interfacial curvature of the V
phases is therefore uniform and smoothly varying over its unit cell. Three cubic symmetries for the V
phase have been observed from extensive x-ray scattering studies: Ia3d, Pn3m, and Im3m [16].
