STABILITY OF THE AXIAL DIRECTOR CONFIGURATION IN NEMATIC LIQUID-CRYSTALS CONFINED IN A CYLINDRICAL CAVITY AND THE SURFACE-LIKE ELASTIC-CONSTANT PROBLEM

Nematic liquid crystals confined in a cylindrical cavity under the anc horing conditions of various type are examined. The influence of the s addle - splay and splay - bend terms (the K-24-term and the K-13-term) on the axial director configuration stability is investigated. By usi ng the Fourier expansion of director fluctuations over the azimuth ang le our analytical method of attack enables the stability conditions to be found in terms of the stability of each fluctuation mode. Two meth ods of stabilizing the structure are explored: stabilization by a magn etic field and by the action of the boundary conditions. The restricti ons imposed on the constants are determined to make the stabilization possible. The dependence of the resultant stability threshold on the s urface-like elastic constants is calculated. The experimentally detect able effects due to the presence of the K-13-term are discussed in det ail. It is shown that the escaped-radial director structure exhibits s ome special features which are induced by the K-13-term.