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

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 it 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.

Sedimentation of colloidal plate-sphere mixtures and inference of particle characteristics from stacking sequences

“…Note that in the low density limit we recover the second virial coefficient, like in the original Onsager expression [36], since (η → 0) = 1/2. Onsager-like density functional theories rely on two-body correlations and can fail to describe the bulk if the symmetries of the stable bulk phases are the result of three-and higher-body correlations [66]. This is not the case here since the excluded volume between two cylinders is minimal if both particles are parallel to each other, i.e., like in the uniaxial nematic phase.…”

Exotic liquid crystalline phases in monolayers of vertically vibrated granular particles

“…However, there are strong indications that systems of particles made of nonregular polygonal shapes may form intermediate orientational phases of nontrivial symmetries due to clustering mechanisms [12]. In equilibrium the clustering tendency is driven by entropic forces [29,30], and additionally dissipation may contribute in vibrated monlayers [27].…”

“…Other convex hard particles with polygonal shape have been examined using the same theoretical approach, and phases with triatic, or sixfold, symmetry, were predicted in fluids of particles with isosceles triangular shape close to the equilateral condition [11]. More recently, fluids of hard right-angled triangles (HRT) have been seen to present evidences of strong octatic, or eightfold, orientational correlations, which constitutes a challenge for the standard DFT theories [12].On the simulation side, orientational order in fluids made of anisotropic hard particles has been studied by many authors. Nematic phases have quasi-long-range order and are obtained from the isotropic through a continuous transition driven by a Kosterlitz-Thouless mechanism [13].…”

“…Hard rectangles have also been studied but with not so much emphasis on the tetratic phase [18,19]. Recently fluids of HRT particles have been seen to exhibit peculiar orientational properties [12,20], with strong indications of quasi-eightfold symmetry. Other particle shapes such as pentagons and hexagons have been analysed…”

“…Other convex hard particles with polygonal shape have been examined using the same theoretical approach, and phases with triatic, or sixfold, symmetry, were predicted in fluids of particles with isosceles triangular shape close to the equilateral condition [11]. More recently, fluids of hard right-angled triangles (HRT) have been seen to present evidences of strong octatic, or eightfold, orientational correlations, which constitutes a challenge for the standard DFT theories [12].…”