Demixing and tetratic ordering in some binary mixtures of hard superellipses

Mizani, Sakine; Gurin, Péter; Aliabadi, Roohollah; Salehi, Hadi; Varga, Szabolcs

doi:10.1063/5.0009705

Cited by 12 publications

(11 citation statements)

References 105 publications

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“…After substitution into Eqs. ( 1) and (10), the total free energy per particle ϕ = ϕ I + ϕ is obtained, with ϕ I calculated from (17). The excess part over the isotropic contribution, ϕ, is now…”

Section: Minimizationmentioning

confidence: 99%

“…Experiments with particles of square sections did not find the T phase [3], but this was due to the roundness of the corners, as proved by Monte Carlo (MC) simulations [4]. The stability of T [5][6][7][8][9][10] and T R [11][12][13] phases as a function of particle shape was also confirmed by theoretical and simulation works on two-dimensional hard-particle fluids. Experiments on monolayers of vibrated granular cylinders [14][15][16][17] and squares [18] also showed the presence of stationary nonequilibrium T -like textures in the arrangement of particles.…”

Section: Introductionmentioning

confidence: 95%

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

Martı́nez-Ratón

Velasco

2021

Phys. Rev. E

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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.

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Section: Minimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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

Martı́nez-Ratón

Velasco

2021

Phys. Rev. E

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“…The ideal free-energy density functional per particle is, as usual, (10) where the thermal volume term has been dropped. Therefore our theory is completely defined as ϕ…”

Section: Third-virial Dftmentioning

confidence: 99%

“…Experiments with particles of square sections did not find the T phase [3], but this was due to the roundness of the corners, as proved by Monte Carlo (MC) simulations [4]. The stability of T [5][6][7][8][9][10] and TR [11,12] phases as a function of particle shape was also confirmed by theoretical and simulation works on two-dimensional hard particle fluids. Experiments on monolayers of vibrated granular cylinders [19][20][21][22] and squares [23] also showed the presence of stationary nonequilibrium T-like textures in the arrangement of particles.…”

Section: Introductionmentioning

confidence: 96%

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

Martinez-Raton,

Velasco

2021

Preprint

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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.

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“…In the case of hexagons with rounded corners a transition occurs between an hexagonal rotator crystal and an hexagonal crystal 32 . DFT studies revealed that nonpolygonal particles such as hard rectangles [25][26][27] or superellipses close enough to the rectangular shape 33 can stabilize the T phase when the aspect ratio is below a certain critical value.…”

Section: Introductionmentioning

confidence: 99%

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

Martı́nez-Ratón

Velasco

2020

Phys. Rev. E

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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 • , 60 • and 75 • . Kites with one of their unequal angles fixed to 72 • , 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 • 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 • 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 • . These particles also present a phase diagram with stable tetratic and triatic phases.

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Demixing and tetratic ordering in some binary mixtures of hard superellipses

Cited by 12 publications

References 105 publications

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

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

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

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

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