Hard superellipse phases: particle shape anisotropy &amp; curvature

Torres‐Díaz, Isaac; Hendley, Rachel S.; Mishra, Akhilesh C.; Yeh, Alexander; Bevan, Michael A.

doi:10.1039/d1sm01523k

Cited by 9 publications

(51 citation statements)

References 50 publications

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“…We have solved a subset of Eqns. (20), together with the pressure equality, p (c) = p (s) , between cloud and shadow phases, to find the set of moments {m (k,α) i } in both coexisting phases and at the parent number density ρ 0 . As will be shown in Sec.…”

Section: A Coexistence Calculationsmentioning

confidence: 99%

“…As will be shown in Sec. A, we need to solve a total number of equations less than that in (20), which is a direct consequence of the peculiar form of the spt-area (3).…”

Section: A Coexistence Calculationsmentioning

confidence: 99%

“…This is very important because taking into account the expression for f (l) from Eq. ( 21), the integration over l in the coexistence set of equations (20) can be computed analytically. Defining the new variables y…”

Section: Appendix A: Explicit Equations For Coexistence and Bifurcati...mentioning

confidence: 99%

“…The value of κ * predicted by scaled particle theory (SPT) [16], a version of DFT, and a more sophisticated DFT based on the second and third virial coefficients [17], are 2.21 and 3.23, respectively. Recent simulations have shown that κ * ≈ 5 [20] while experiments on monolayers of quasi-two-dimensional granular cylinders indicate the presence of T correlations for aspect ratios as large as κ c ≈ 7 [22,23]. However, some care should be taken to compare the results from experiments on non-equilibrium dissipative granular rods to those obtained by theoretical models based on equilibrium statistical mechanics.…”

Section: Introductionmentioning

confidence: 99%

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The effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

Martı́nez-Ratón¹,

Velasco²

2022

Preprint

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We introduce a model for a fluid of polydisperse rounded hard rectangles where the length and width of the rectangular core are fixed, while the roundness is taken into account by the convex envelope of a disk displaced along the perimeter of the core. The diameter of the disk has a continuous polydispersity described by a Schultz distribution function. We implemented the scaled particle theory for this model with the aim to studying: (i) the effect of roundness on the phase behavior of the one-component hard-rectangle fluid, and (ii) how polydispersity affects phase transitions between isotropic, nematic and tetratic phases. We found that roundness greatly affects the tetratic phase, whose region of stability in the phase diagram strongly decreases as the roundness parameter is increased. Also the interval of aspect ratios where the tetratic-nematic and isotropicnematic phase transitions are of first order considerably reduces with roundness, both transitions becoming weaker. Polydispersity induces strong fractionation between the coexisting phases, with the nematic phase enriched in particles of lower roundness. Finally, for high enough polydispersity and certain mean aspect ratios, the isotropic-to-nematic transition can change from second (for the one-component fluid) to first order. We also found a packing-fraction inversion phenomenon for large polydispersities: the coexisting isotropic phase has a higher packing fraction than the nematic.

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Section: A Coexistence Calculationsmentioning

confidence: 99%

“…As will be shown in Sec. A, we need to solve a total number of equations less than that in (20), which is a direct consequence of the peculiar form of the spt-area (3).…”

Section: A Coexistence Calculationsmentioning

confidence: 99%

Section: Appendix A: Explicit Equations For Coexistence and Bifurcati...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

Martı́nez-Ratón¹,

Velasco²

2022

Preprint

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“…The latter, in the case of HR of κ = 2, also exhibits 4-atic ordering with square dimers at perpendicular orientations, tesseling the whole area at close packing. Recent simulations showed that the 4-atic phase is stable up to κ ∼ 5 [40], while experiments on monolayers of granular cylinders of aspect ratios as large as 7 showed the existence of stationary states exhibiting 4-atic textures [22,26].…”

Section: A One-component Fluidsmentioning

confidence: 99%

Exotic liquid crystalline phases in monolayers of vertically vibrated granular particles

Martı́nez-Ratón¹,

Velasco²

2022

Preprint

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Recently two-dimensional (2D) hard particles have enjoyed a renewed interest in the liquid-crystal community. Their reduced dimensionality leads to peculiar properties of their phase transitions (nonexistence of long-ranged order and defect-mediated phase transitions), but the possibility that these particles stabilise mesogenic (hence fluid) phases with high-order orientational symmetries ('exotic' nematic phases) has attracted much attention [7]. Schlacken et al.[8] used the Scaled-Particle Theory (SPT) version of DFT, based on two-particle correlations via the second virial coefficient, to analyse fluids of hard rectangles, and an intermediate tetratic phase, with four-fold symmetry, was predicted to stabilise for relatively low aspect ratios. This is in contrast to the standard uniaxial nematic phase with twofold symmetry in systems of rods with head-tail symmetry. Later, a more complete fluid phase diagram was obtained using the same theory [9], and the effect of three-body correlations was assessed [10] and seen to reinforce tetratic order. 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]. Focussing on hard or quasi-hard particles of convex polygonal shape, phases with tetratic phases were initially studied in squares [14] and then confirmed by several studies [15][16][17]. 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

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Stripes polymorphism and water-like anomaly in hard core-soft corona dumbbells

Nogueira,

Bordin

2023

Journal of Molecular Liquids

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Hard superellipse phases: particle shape anisotropy & curvature

Abstract: We report computer simulations of two-dimensional convex hard superellipse particle phases vs. particle shape parameters including aspect ratio, corner curvature, and sidewall curvature. Shapes investigated include disks, ellipses, squares, rectangles,...

Cited by 9 publications

References 50 publications

The effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

The effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

Exotic liquid crystalline phases in monolayers of vertically vibrated granular particles

Stripes polymorphism and water-like anomaly in hard core-soft corona dumbbells

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