Curvature elasticity of smectic-C liquid crystals and formation of stripe domains along thickness gradients in menisci of free-standing films.

Abstract

Smectic liquid crystals with a layering order of rodlike molecules can be drawn in the form of free standing films across holes. Extensive experimental studies have shown that smectic-C (SmC) liquid crystals (LCs) with tilted molecules form periodic stripes in the thinner parts of the meniscus, which persist over a range of temperatures above the transition of the bulk medium to the SmA phase in which the tilt angle is zero. The prevailing theoretical models cannot account for all the experimental observations. We propose a model in which we argue that the negative curvature of the surface of the meniscus results in an energy cost when the molecules tilt at the surface. The energy can be reduced by exploiting the allowed (∇·k)(∇·c) deformation which couples the divergence of k, the unit vector along the layer normal, with that of c, the projection of the tilted molecular director on the layer plane. We propose a structure with periodic bending of layers with opposite curvatures, in which the c-vector field itself has a continuous deformation. Calculations based on the theoretical model can qualitatively account for all the experimental observations. It is suggested that detailed measurements on the stripes may be useful for getting good estimates of a few curvature elastic constants of SmC LCs.