Long Range Order and Thermal Fluctuations in Liquid Crystals

Abstract

Some recent applications of the Oseen-Zocher-Frank elastic theory of nematic and cholesteric liquid crystals are reviewed. (1) The effects of a static magnetic field H are calculated in detail. In particular, for a cholesteric system, the spiral structure is distorted by the field and the period increases with H, up to a critical field H_c at which a nematic phase is expected. H_c is inversely proportional to the pitch of the unperturbed helix, and should be observable in systems with long periods. A cholesteric → nematic transition of this type has in fact been qualitatively observed. (2) The optical striations which are observed when a cholesteric liquid is inserted in a region of variable thickness have been shown by Cano to correspond to discontinuities of the torsion. The transition region between regions of different pitch has been analyzed in terms of a “disclination line” normal to the helical axis. (3) In a nematic liquid crystal the long wavelength thermal fluctuations of orientation can be analyzed from macroscopic elastic considerations: these large fluctuations are responsible for the strong scattering and depolarization of light measured by Ch[acaron]telain. The angular dependence of the scattering intensity can thus be explained without any assumption on “swarms”.