SUPERCOOLING OF A NEMATIC LIQUID-CRYSTAL

We investigate the supercooling of a nematic liquid crystal using fluctuating nonlinear hydrodynamic equations. The Martin-Siggia-Rose formalism [Phys. Rev. A 8, 423 (1973)] is used to calculate renormalized transport coefficients to one-loop order. Similar theories for isotropic liquids have shown substantial increases of the viscosities as the liquid is supercooled or compressed due to feedback from the density fluctuations which are freezing. We find similar results here for the longitudinal and various shear viscosities of the nematic phase. However, the two viscosities associated with the nematic-director motion do not grow in any dramatic way; i.e., there is no apparent freezing of the director modes within this hydrodynamic formalism. Instead a glassy state of the nematic phase may arise from a ''random-anisotropy'' coupling of the director to the frozen density.