Curvatures of smectic liquid crystals and their applications

Curvature is an important concept for understanding layering structures in soft matters, ranging from complex macromolecular self-assembled structures to simple lipid bilayers. Among the various kinds of soft matters, smectic liquid crystal (LC) phases have been widely studied because of their periodic featured curvatures under various external forces. Generally, their curvatures are on the micron-scale due to the bulk elasticity of smectic LC materials. In this review, a combination of sublimation and recondensation of smectic LC materials generates a variety of curvatures at the nanometer scale, which cannot be achieved by self-assembly under thermal equilibrium conditions. In particular, we have focused on the change of curvatures in focal conic domains under non-equilibrium conditions, in which negative and zero Gaussian curvatures in the micron-scale transform to positive Gaussian curvatures in the micron- and nanometer scales. Finally, the review closes with applications using such non-equilibrium self-assembly of smectics.