Tetrahedral symmetry in nematic liquid crystals.

Abstract

By means of symmetry consideration the order parameter ${\mathit{U}}_{\mathit{i}\mathit{j}\mathit{k}}$ of a tetrahedral nematic liquid crystal (LC) was derived. In contrast to other nematic LC's (including uniaxial, biaxial, cubic, and icosahedral phases) the odd rank (=3) of ${\mathit{U}}_{\mathit{i}\mathit{j}\mathit{k}}$ permits the phase transition of both the first and second order from isotropic liquid into tetrahedral nematic LC's and leads to the appearance of one of two possible helical structures in the chiral T phase of this nematic LC. In the framework of the mean-field approximation the contribution of the orientational part of the LC order parameter to the polarizability of LC with different symmetries was found and the existence of the second order phase transition from isotropic liquid into nonchiral tetrahedral nematic LC's has been predicted. The Fr\'eedericksz transition in the nonchiral ${\mathit{T}}_{\mathit{d}}$ phase was considered: the peculiarities of the bifurcation tree crucially depended on the direction of the external field with respect to the rotational ${\mathit{C}}_{3}$ and screw C${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{4}$ axes of the unperturbed tetrahedral phase. The untwisting and deviation of the helical T phase in external fields were discussed. The structure of the disclination core in a tetrahedral nematic LC was analyzed.