Chiral nematic liquid crystals in cylindrical cavities

We report a theoretical study of various structures of chiral nematic liquid crystals, confined to submicrometer cylindrical cavities with tangential anchoring conditions. The Frank-Oseen free energy with additional surface energy terms is used to find nematic director fields, free energies, and stability diagrams of relevant structures. The dependence of various chiral nematic structures on the chirality parameter, pore size, elastic constants, and polar and azimuthal surface anchoring strengths is studied. We are particularly interested in the influence of the saddle-splay elastic constant on the structures. For ordinary values of material parameters, only radially twisted and asymmetric conical structure are stable. The former is stable at low chiralities, while the latter is stable for high chiralities. The radially twisted structure is commonly known as double twisted structure, while the asymmetric conical structure has not been considered, to the authors' knowledge. The phase diagram including both structures is determined by comparing their free energies. Theoretical predictions are in agreement with available experimental data.