Theory of Banana Liquid Crystal Phases and Phase Transitions

TL;DR

This paper develops a comprehensive theoretical framework for banana-shaped liquid crystal phases, introducing a third-rank tensor order parameter, predicting new phases, and analyzing their phase transitions and symmetries.

Contribution

It introduces a third-rank tensor order parameter for bent-core liquid crystals, catalogs possible phases, and predicts novel chiral and tetrahedratic phases with their transition characteristics.

Findings

Identification of new liquid crystal phases including chiral nematic and tetrahedratic phases.

Prediction that the isotropic-tetrahedratic transition can be continuous or first-order.

Characterization of phase transition universality classes and symmetry properties.

Abstract

We study phases and phase transitions that can take place in the newly discovered banana (bow-shaped or bent-core) liquid crystal molecules. We show that to completely characterize phases exhibited by such bent-core molecules a third-rank tensor $T^{ijk}$ order parameter is necessary in addition to the vector and the nematic (second-rank) tensor order parameters. We present an exhaustive list of possible liquid phases, characterizing them by their space-symmetry group and order parameters, and catalog the universality classes of the corresponding phase transitions that we expect to take place in such bent-core molecular liquid crystals. In addition to the conventional liquid-crystal phases such as the nematic phase, we predict the existence of novel liquid phases, including the spontaneously chiral nematic $(N_T + 2)^*$ and chiral polar $(V_T + 2)^*$ phases, the orientationally-ordered but optically isotropic tetrahedratic $T$ phase, and a novel nematic $N_T$ phase with $D_{2d}$ symmetry that is neither uniaxial nor biaxial. Interestingly, the Isotropic-Tetrahedratic transition is {\em continuous} in mean-field theory, but is likely driven first-order by thermal fluctuations. We conclude with a discussion of smectic analogs of these phases and their experimental signatures.