STABILITY AND INSTABILITY OF AN UNIAXIAL ALIGNMENT AGAINST BIAXIAL DISTORTIONS IN THE ISOTROPIC AND NEMATIC PHASES OF LIQUID-CRYSTALS

The nonlinear relaxation equation for the five components of the (2nd rank) alignment tensor is used to analyze the stability or instability of its uniaxial stationary solutions against biaxial distortions. The equation is valid for both the isotropic and nematic phases of a liquid crystal. The influence of an external field is taken into account. For liquid crystals with positive dielectric anisotropy in the presence of an electric field, the uniaxial state is stable against biaxial distortions. The situation is different for the case of a negative dielectric anisotropy. At temperatures above the field-free transition temperature isotropic-nematic. application of an electric field leads to a uniaxial state which becomes unstable against biaxial distortions if the strength of the field exceeds a critical value. Properties of the biaxial state which can exist in a limited range of temperatures are also presented.