Influence of planar anchoring on escaped-twisted configurations of liquid crystals in a cylindrical cavity

Lyotropic chromonic liquid crystals (LCLCs) confined in cylindrical cavity can form an escaped-twisted (ET) configuration, resulting from the saddle-splay elastic constant is great much than twist elastic constant. The thermotropic liquid crystal 5CB does not meet the conditions for the formation of ET configuration, but it can be achieved under the appropriate planar anchoring and the action of chiral dopant. The equilibrium configuration of nematic liquid crystals confined in cylindrical cavities with azimuthal and axial surface anchoring conditions respectively is studied by the elastic continuum theory and the difference iterative method. We obtain the analytical solution of the distribution of the director without chiral dopant and the numerical solution of the chiral dopant. We find that the planar anchoring, the saddle-splay elastic constant and the chirality determine whether an ET configuration is formed. Furthermore, the cavity radius and the bend elastic constant can affect the value of twist angle. It provides a good theoretical basis for the determination of anchoring energy and saddle-splay elastic constant.