Phase ordering of zig-zag and bow-shaped hard needles in two dimensions

TL;DR

This study uses Monte Carlo simulations to explore the phase behavior of two-dimensional bent hard-needle models, revealing multiple stable phases and transition mechanisms influenced by molecular geometry.

Contribution

It provides the first detailed phase diagrams for zig-zag and bow-shaped hard needles, identifying novel modulated-nematic phases and analyzing their transition densities.

Findings

Identification of isotropic, quasi-nematic, smectic-C, and other phases.

Discovery of a modulated-nematic phase with periodic polarity modulation.

Confirmation of the isotropic--quasi-nematic transition as a Kosterlitz-Thouless transition.

Abstract

We perform extensive Monte Carlo simulations of a two-dimensional bent hard-needle model in both its chiral zig-zag and its achiral bow-shape configurations and present their phase diagrams. We find evidence for a variety of stable phases: isotropic, quasi-nematic, smectic-C, anti-ferromorphic smectic-A, and modulated-nematic. This last phase consists of layers formed by supramolecular arches. They create a periodic modulation of the molecular polarity whose period is sensitively controlled by molecular geometry. We identify transition densities using correlation functions together with appropriately defined order parameters and compare them with predictions from Onsager theory. The contribution of the molecular excluded area to deviations from Onsager theory and simple liquid crystal phase morphology is discussed. We demonstrate the isotropic--quasi-nematic transition to be consistent with a Kosterlitz-Thouless disclination unbinding scenario.