Andriyenko D. Orientational ordering in the liquid crystal cells with controlled boundary conditions

Surface-mediated effects in liquid crystals attract more and more attention since liquid crystal devices are mostly based on the liquid crystal sandwiched between aligning substrates or confined in some volume. Orienting surfaces change the structure of the surface liquid crystal layer as well as influence bulk properties of the liquid crystal cell such as dynamics of the director reorientation, amplitudes of the director fluctuations, sensitivity to the external fields. In this work studied influence of the confinement on the variety of electro-optical effects specific for the liquid-crystalline systems. In particular, we considered light-induced Freederiksz transition in the mixture of liquid crystal and chiral dopant. It was shown that the value of the light-induced threshold decreases in the mixture with chiral molecules as compared to the pure liquid crystal. Dependencies of the threshold on the anchoring coefficient, polarization state of the incident light, and concentration of the chiral dopant have been obtained analytically. This result generalizes the well-known expression for the light-induced threshold on the case of weak anchoring, presence of chiral dopant and arbitrary polarization of the incident light. The second chapter deals with interaction of the liquid crystal director with angular momentum of incident light. The cell geometry has been chosen to fit the particular experimental conditions favoring the director orientation. Namely, we consider combined planar cell with one surface with strong anchoring providing planar orientation of the director in the cell. The other surface has degenerate planar orientation with zero azimuthal anchoring energy. Because of the interaction of the director with the electromagnetic field of the incident light wave the director rotates in the bulk and at the surface with weak anchoring. We obtained the amplitude of the surface director deviation as a function of the polarization state of the incident light and parameters of the liquid crystals. It turned out that the character of the director profile in the cell bulk depends on the polarization state. For circularly polarized light wave deviation angle growths monotonically in the cell bulk. At the same time linear polarization of the incident light gives modulated structure of the director in the cell. The phenomenon has been explained in terms of the light angular momentum transfer to the liquid crystal bulk. Estimations show that this phenomenon can be effectively used for recording surface-based holographic director gratings. Third chapter is devoted to studies of the director diffraction gratings in the LC cell bulk. These gratings are being formed because of the variation of the surface parameters. Both the easy axis direction and amplitude of the surface order parameter have been allowed to alternate. In the case of the easy axis modulation we consider both homeotropic and planar geometry of the director deviations, as well as influence of the weak anchoring energy on the formation of the bulk directo r grating. It has been shown that for the initially homeotropic cell phase diffraction is formed in the cell as a result of the easy axis deviation. The diffraction efficiency of such a grating is proportional to the forth power of the surface director deviation angle and is quite small. For planar cell, the polarization grating is formed in the cell with the diffraction efficiency proportional to the squared deviation of the director angle at the surface and is much more efficient than corresponding homeotropic grating. In the cell with modulated surface order parameter the diffraction efficiency is rather small but can be enhanced significantly near the nematic-isotropic transition point. The obtained diffraction efficiencies allow us to select the most effective geometry for the recording of the surface holographic gratings. In the last chapter we consider surface-induced orientational transitions in the hybrid LC cell. It was shown that smooth variations of the director anchoring with bounding surfaces c ould lead to the threshold reorientation of the director in the LC bulk. The orientational transition is accompanied with growth of the director fluctuations, the amplitude of which has been calculated. The increase in the director fluctuations results in the light scattering by the LC cell, providing a powerful method to study anchoring transitions using common scattered-light-measurement techniques.