Orientational ordering in a fluid of hard kites: A density-functional-theory study

TL;DR

This study uses density functional theory to analyze how the shape of hard kites influences their phase behavior, revealing the stabilization of various orientational phases and validating the new theoretical approach against simulations.

Contribution

The paper introduces a new approximation method within density functional theory that better predicts third virial coefficients for two-dimensional hard particles, applied to kites.

Findings

Kites can stabilize isotropic, nematic, tetratic, and triatic phases depending on shape.

The new theory aligns well with Monte Carlo simulations for specific kite shapes.

Certain kite geometries favor the stabilization of specific orientational phases.

Abstract

Using Density Functional Theory we theoretically study the orientational properties of uniform phases of hard kites -- two isosceles triangles joined by their common base. Two approximations are used: Scaled Particle Theory, and a new approach which better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to $90^{\circ}$, $60^{\circ}$ and $75^{\circ}$. Kites with one of their unequal angles fixed to $72^{\circ}$, which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilise the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to $60^{\circ}$ stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to $75^{\circ}$ have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to $72^{\circ}$. These particles also present phase diagrams with stable tetratic and triatic phases.