Failure of standard density functional theory to describe the phase behavior of a fluid of hard right isosceles triangles

TL;DR

This paper shows that standard density functional theory fails to predict the complex high-symmetry phases of a fluid of hard right isosceles triangles, highlighting the need for theories that incorporate higher-order correlations.

Contribution

It demonstrates the limitations of existing density functional theory in capturing exotic liquid-crystal phases in a specific two-dimensional particle system.

Findings

Monte Carlo simulations predict tetratic and octatic phases.

Standard DFT predicts only uniaxial nematic phase.

Failure of DFT suggests need for incorporating high-order correlations.

Abstract

A fluid of hard right isosceles triangles was studied using an extension of Scaled-Particle Density-Functional Theory which includes the exact third virial coefficient. We show that the only orientationally ordered stable liquid-crystal phase predicted by the theory is the uniaxial nematic phase, in agreement with the second-order virial theory. By contrast, Monte Carlo simulations predict exotic liquid-crystal phases exhibiting tetratic and octatic correlations, with orientational distribution functions having four and eight equivalent peaks, respectively. This demonstrates the failure of the standard Density Functional Theory based on two and three-body correlations to describe high-symmetry orientational phases in two-dimensional hard right-triangle fluids, and points to the necessity to reformulate the theory to take into account high-order body correlations and ultimately particle self-assembling and clustering effects. This avenue may represent a great challenge for future research, and we discuss some fundamental ideas to construct a modified version of Density-Functional Theory to account for these clustering effects.