Phase behavior of hard circular arcs

TL;DR

This study uses Monte Carlo simulations to explore the phase behavior of two-dimensional systems of hard circular arcs, revealing various phases including isotropic, nematic, filamentary, and cluster hexagonal phases based on arc aperture and density.

Contribution

It provides new insights into the phase transitions and self-assembly of hard circular arcs, especially the formation of filamentary and cluster phases depending on arc angle and density.

Findings

Filamentous clusters form at small aperture angles and high density.

Roundish clusters form at larger aperture angles and high density.

Distinct phases include isotropic, nematic, filamentary, and cluster hexagonal.

Abstract

By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally-thin circular arcs, from an aperture angle $\theta \rightarrow 0$ to an aperture angle $\theta \rightarrow 2 \pi$, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase that solely forms for sufficiently small values of $\theta$ and at intermediate values of density, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally-thin circular arcs auto-assemble to form clusters. These clusters are either filamentous, for smaller values of $\theta$, or roundish, for larger values of $\theta$. Provided density is sufficiently high, the filaments lengthen, merge and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.