Cell theories for the chiral crystal phase of hard equilateral triangles

TL;DR

This paper develops cell theories for the chiral crystal phase of hard equilateral triangles, predicting equations of state that match simulations and exploring the stability of chiral versus achiral phases.

Contribution

It introduces new analytical cell theories for chiral crystal phases and evaluates their accuracy in predicting equations of state and phase stability.

Findings

The equations of state agree well with simulations for both crystal and liquid-crystal phases.

Chiral configurations are less stable than achiral ones according to free-energy calculations.

Clustering effects do not account for the observed chirality in simulations.

Abstract

We derive several versions of the cell theory for a crystal phase of hard equilateral triangles. To that purpose we analytically calculated the free area of a frozen oriented or freely rotating particle inside the cavity formed by its neighbours in a chiral configuration of their orientations. From the most successful versions of the theory we predict an equation of state which, despite being derived from a crystal configuration of particles, describes very reasonably the equation of state of the 6-atic liquid-crystal phase at packing fractions not very close from the isotropic-6-atic bifurcation. Also, the same equation of state performs well when compared to that from MC simulations for the stable crystal phase. The agreement can even be improved by selecting adequate values for the angle of chirality.Despite the success of two of the versions of the theory for the pressure, we show that the free-energy is an increasing function of the angle of chirality, implying that the most stable phase is the achiral phase. Furthermore, we show that possible clustering effects, such as the formation of perfect chiral hexagonal clusters, which in turn crystallize into an hexagonal lattice, cannot explain the presence of the chirality observed in simulations.