Smectic Liquid Crystals

Abstract

As we have already mentioned, the smectic phase of liquid crystals is a phase where the translational invariance is spontaneously broken along one of the directions along which the density is periodically modulated (De Gennes, 1974; Prost, 1984). In other words, smectics have a layered structure. In equilibrium all layers are parallel and equidistant (naturally, in the absence of dislocations and with the boundary effects neglected). Henceforth, we will assume that in equilibrium the z-axis is directed along the normal to the layers. At a deviation from equilibrium smectic layers deform, therefore in the macroscopic description of smectics it is necessary to use a vector of layer displacement. Unlike crystals, this vector has only one component u along the z-axis, that is why it stands to reason to consider the displacement of a layer only in the direction perpendicular to the layer. In the macroscopic dynamics of smectics the presence of an extra degree of freedom, associated with u, gives rise to the existence of two types of acoustic oscillations—the first and second sound, to some extent, analogous to the first and second sound in superfluid helium.