Long-range orientational order, local-field anisotropy, and mean molecular polarizability in liquid crystals

Abstract

The problems on the relation of the mean effective molecular polarizability to the long-range ori- entational order of molecules (the optical anisotropy of the medium) in uniaxial and biaxial liquid crystals, the local anisotropy on mesoscopic scales, and the anisotropy of the Lorentz tensor L and the local-field tensor f are formulated and solved. It is demonstrated that the presence of the long-range orientational order of molecules in liquid crystals imposes limitations from below on the molecular polarizability , which differs for uniaxial and biaxial liquid crystals. The relation between the local anisotropy and the molecular polarizability is inves- tigated for calamitic and discotic uniaxial liquid crystals consisting of lath- and disk-shaped molecules. These liquid crystals with identical macroscopic symmetry differ in the local anisotropy and the relationships between the components L || L ⊥ , f || > f ⊥ (discotic) for an electric field oriented parallel and perpendicular to the director. The limitations from below and above on the molecular polarizability due to the anisotropy of the tensors L and f are established for liquid crystals of both types. These limitations indi- cate that the molecular polarizability depends on the phase state and the temperature. The factors responsible for the nonphysical consequences of the local-field models based on the approximation = const are revealed. The theoretical inferences are confirmed by the experimental data for a number of calamitic nematic liquid crys- tals with different values of birefringence and the discotic liquid crystal .