Effective free energies for cholesteric shells

Abstract

We propose a continuum two-dimensional model to describe the molecular alignment in thin cholesteric shells. Effective two-dimensional free energies, aimed at describing the physics of thin cholesteric films deposited on curved substrates, are deduced from the three-dimensional Frank theory for cholesteric liquid crystals. Based on the ratio between the natural helical pitch and the shell thickness, we distinguish between weakly and strongly twisted cholesterics. In the former class of cholesterics, the reduced energy exhibits either chiral and achiral terms. In the latter one, the achiral terms are ruled out. Basically, this enables the manipulation of the helical pitch to control the curvature effects of a soft surface. We also illustrate the molecule alignments on special classes of rigid shells.