Axially twisted chiral nematic structures in cylindrical cavities

Abstract

Here we report a theoretical study of chiral nematic liquid crystals, confined to cylindrical cavities with planar anchoring conditions. Three different model structures are considered: radially twisted, eccentric radially twisted, and axially twisted structure. The Frank-Oseen free energy with additional surface energy terms is used to find nematic director fields and free energies of the structures in different ranges of material parameters. We are particularly interested in the influence of chirality, anchoring strength, and the saddle-splay elastic constant on the stability regions of the described structures. For low chiralities the radially twisted structure is stable, while for high chiralities the axially twisted structure is stable. The stability region of the eccentric radially twisted structure is confined to a limited intervals of anchoring strengths and chiralities. Most of our attention is devoted to details of the axially twisted structure. In the high chirality limit the axially twisted structure resembles a simpler model structure which in our previous work we called an asymmetric conical structure. The tilt of the nematic director of the axially twisted structure out of the plane perpendicular to the cylinder axis is small except in the layer at the cylinder boundary. Polarization microscopy simulations of the three structures are also shown.