Geometry of (non smectic) hexagonal mesophases

Abstract

An hexagonal order is frequent in liquid crystals, namely in many smectic phases. We consider here the non smectic phases formed by hexagonally packed, indefinite and flexible rods. The Volterra method enables three main components of the translation defects to be defined : transverse edge and screw dislocations and longitudinal edge dislocations. One also defines disclinations. Those formed about axes normal to rods must be frequent. The other disclinations about axes parallel to rods have little chance of existing. However, they can be involved in the architecture of the core of certain translation defects. In the absence of dislocations, the layers of rods of the hexagonal system form developable surfaces in the continuously distorted mesophases. Such domains must be limited by developable caustics, which often degenerate into axes. The rods then form coaxial circles or parallel arcs about these axes. Certain comparisons can be made with smectics. The presence of an hexagonal order in certain lyotropic cholesterics explains the general absence of focal lines in such phases