A Novel Chiral Phase of Achiral Hard Triangles and an Entropy-Driven Demixing of Enantiomers

TL;DR

This study reveals that achiral hard triangles can form chiral phases and undergo entropy-driven demixing of enantiomers, with phase transitions characterized through Monte Carlo simulations in two dimensions.

Contribution

It uncovers a novel entropy-driven chiral symmetry breaking and enantiomer demixing in a system of achiral hard triangles, expanding understanding of phase behavior in simple particle systems.

Findings

Achiral triangles exhibit spontaneous chiral symmetry breaking at high packing fractions.

Enantiomeric demixing occurs spontaneously due to entropy considerations.

Distinct phase transitions are observed from isotropic to liquid crystal and then to crystal phases.

Abstract

We investigate the phase behavior of a system of hard equilateral and right-angled triangles in two dimensions using Monte Carlo simulations. Hard equilateral triangles undergo a continuous isotropic-triatic liquid crystal phase transition at packing fraction $\phi=0.7$. Similarly, hard right-angled isosceles triangles exhibit a first-order phase transition from an isotropic fluid phase to a rhombic liquid crystal phase with a coexistence region $\phi \in \left[0.733,0.782\right]$. Both these liquid crystal phases undergo a continuous phase transition to their respective close-packed crystal structures at high pressures. Although the particles and their close-packed crystals are both achiral, the solid phases of equilateral and right-angled triangles exhibit spontaneous chiral symmetry breaking at sufficiently high packing fractions. The colloidal triangles rotate either in clockwise or anti-clockwise direction with respect to one of the lattice vectors for packing fractions higher than $\phi_\chi$. As a consequence, these triangles spontaneously form a regular lattice of left- or right-handed chiral holes which are surrounded by six triangles in the case of equilateral triangles and four or eight triangles for right-angled triangles. Moreover, our simulations show a spontaneous entropy-driven demixing transition of the right- and left-handed "enantiomers".