Thermal-fluctuation approach to Fréedericksz transitions in nematic liquid crystals

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Abstract
The boundary effects on the thermal fluctuations of the director in a planar nematic-liquid-crystal cell with strong anchoring conditions in the presence of an electric field, coupled to the dielectric anisotropy and to flexoelectric polarization, are theoretically studied. The conditions for second-order Fréedericksz-type transitions and the actual shape of the distortion above the threshold are analyzed by considering the critical eigenmodes of the fluctuations. A phase diagram for the different types of distortions, periodic or aperiodic, is obtained through a fully analytic calculation. These results allow for a better interpretation of the light-scattering experiments and give a unified picture of the instabilities, induced by the flexoelectricity and by the elastic constant anisotropy, which give static periodic structures.