Hydrodynamic theory of $p-$atic liquid crystals

TL;DR

This paper develops a hydrodynamic theory for two-dimensional p-atic liquid crystals, revealing how discrete rotational symmetry introduces new phenomena like flow alignment and shear-induced long-range order.

Contribution

It extends previous theories by incorporating discrete symmetry effects, predicting novel flow behaviors and shear-induced ordering in p-atic liquid crystals.

Findings

Flow alignment at high shear rates for p>2

Shear induces long-range orientational order

Order parameter scales as a non-universal power of shear rate

Abstract

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic $p-$fold rotational symmetry, also known as $p-$atics, of which mematics $(p=2)$ and hexatics $(p=6)$ are the two best known examples. Previous hydrodynamic theories of $p-$atics are characrerized by continuous ${\rm O}(2)$ rotational symmetry, which is higher than the discrete rotational symmetry of $p-$atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for $p>2$. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any $p-$atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a non-universal power of the applied shear rate at small shear rates.