THERMAL-FLUCTUATION APPROACH TO FREEDERICKSZ TRANSITIONS IN NEMATIC LIQUID-CRYSTALS

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 anisotro py and to flexoelectric polarization, are theoretically studied. The c onditions for second-order Fredericksz-type transitions and the actual shape of the distortion above the threshold are analyzed by consideri ng the critical eigenmodes of the fluctuations. A phase diagram for th e different types of distortions, periodic or aperiodic, is obtained t hrough 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 t he elastic constant anisotropy, which give static periodic structures.