Liquid crystals of hard rectangles on flat and cylindrical manifolds

TL;DR

This study investigates the phase behavior of hard rectangles on flat and cylindrical surfaces using density functional theory and simulations, revealing various liquid crystalline phases and the influence of external fields.

Contribution

It introduces a combined theoretical and simulation analysis of hard rectangles on curved manifolds, including external field effects, which is novel in the study of liquid crystals on such geometries.

Findings

Identification of stable isotropic, nematic, tetratic, and smectic phases.

External field significantly shifts phase transition lines.

Observation of tilted smectic-like order on cylindrical surfaces.

Abstract

Using the classical density functional theory of freezing and Monte Carlo computer simulations, we explore the liquid-crystalline phase behavior of hard rectangles on flat and cylindrical manifolds. Moreover, we study the effect of a static external field which couples to the rectangles' orientations, aligning them towards a preferred direction. In the flat and field-free case, the bulk phase diagram involves stable isotropic, nematic, tetratic, and smectic phases depending on the aspect ratio and number density of the particles. The external field shifts the transition lines significantly and generates a binematic phase at the expense of the tetratic phase. On a cylindrical manifold, we observe tilted smectic-like order, as obtained by wrapping a smectic layer around a cylinder. We find in general good agreement between our density functional calculations and particle-resolved computer simulations and mention possible setups to verify our predictions in experiments.