The Supercooling of a Nematic Liquid Crystal

TL;DR

This paper models the supercooling behavior of nematic liquid crystals using advanced hydrodynamic equations, revealing viscosity increases similar to isotropic liquids but no dramatic freezing of director modes, suggesting a possible glassy state.

Contribution

It applies the Martin-Siggia-Rose formalism to nematic liquid crystals, extending supercooling theories from isotropic liquids to anisotropic systems.

Findings

Viscosities increase as nematic liquid is supercooled.

No dramatic growth in viscosities related to nematic director motion.

Potential emergence of a glassy state due to random anisotropy coupling.

Abstract

We investigate the supercooling of a nematic liquid crystal using fluctuating non-linear hydrodynamic equations. The Martin-Siggia-Rose formalism 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. 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 may arise from a ``random anisotropy" coupling of the director to the frozen density.