Tetratic Phase in the Planar Hard Square System?

Wojciechowski, Krzysztof W.; Frenkel, Daan

doi:10.12921/cmst.2004.10.02.235-255

Cited by 112 publications

(133 citation statements)

References 30 publications

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“…[30][31][32] For hard squares and rectangles, a tetratic phase with quasi-long-range orientational order was observed in simulations. 34,36 Contrary to the simulation results, a hexagonal plastic-crystal (rotator) phase appeared in experiments of square colloidal particles under confinement. 37 This finding could be explained by the roundness of particles.…”

Section: Introductioncontrasting

confidence: 86%

“…The mesophase behavior of convex anisotropic particles in quasi-2D, such as rods and polygonal (e.g., square and pentagonal) particles, has for instance been studied in experiments and by simulations. [29][30][31][32][33][34][35][36][37][38] a) Electronic mail: W.Qi@uu.nl b) Electronic mail: M.Dijkstra1@uu.nl For rods, theoretical investigations 29,31 suggested a possible Kosterlitz-Thouless (KT) isotropic-nematic phase transition, when the aspect ratio exceeded 7.0, and its existence was confirmed by simulations and experiments. [30][31][32] For hard squares and rectangles, a tetratic phase with quasi-long-range orientational order was observed in simulations.…”

Section: Introductionmentioning

confidence: 99%

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Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

Graaf

Qiao

et al. 2013

The Journal of Chemical Physics

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Recently, we reported the formation of crystalline monolayers consisting of octapod-shaped nanocrystals (so-called octapods) that had arranged in a square-lattice geometry through drop deposition and fast evaporation on a substrate [W. Qi, J. de Graaf, F. Qiao, S. Marras, L. Manna, and M. Dijkstra, Nano Lett. 12, 5299 (2012)]. In this paper we give a more in-depth exposition on the Monte Carlo simulations in a quasi-two-dimensional (quasi-2D) geometry, by which we modelled the experimentally observed crystal structure formation. Using a simulation model for the octapods consisting of four hard interpenetrating spherocylinders, we considered the effect of the pod length-to-diameter ratio on the phase behavior and we constructed the full phase diagram. The methods we applied to establish the nature of the phase transitions between the various phases are discussed in detail. We also considered the possible existence of a Kosterlitz-Thouless-type phase transition between the isotropic liquid and hexagonal rotator phase for certain pod lengthto-diameter ratios. Our methods may prove instrumental in guiding future simulation studies of similar anisotropic nanoparticles in confined geometries and monolayers.

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Section: Introductioncontrasting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

Graaf

Qiao

et al. 2013

The Journal of Chemical Physics

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“…Of particular interest is the case of hard rectangular particles, which might exhibit a so-called tetratic phase (N t ) in the one-component fluid [30,31,32,33,34]. The tetratic phase possesses two equivalent directors pointing along mutually orthogonal directions; it exhibits a symmetry higher than that of the particles making up the fluid.…”

Section: Introductionmentioning

confidence: 99%

Demixing and orientational ordering in mixtures of rectangular particles

2007

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Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyse the stability of phases with orientational order and the demixing phase behaviour of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first-or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture.The second component of the mixture has been chosen to be hard discs or disco-rectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behaviour, or simply rectangles of different aspect ratio but with the same particle area, or different particle area but with the same aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic-tetratic or tetratic-tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.

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“…1 and 2 differ in their interpretation of the phase that ref. 3 system, translational order extends throughout the system-and this is why a discussion in terms of a simple cubic crystal is justified. To know what happens in the thermodynamic limit, a full-scale finite-size scaling analysis would be required.…”

mentioning

confidence: 99%

“…Ref. 3 did not explore the presence of vacancies-and yet vacancies are likely to be just as important in two dimensions as in three. Moreover vacancies make the system highly compressible, and this may facilitate the formation of bond-ordered phases.…”

mentioning

confidence: 99%

Colloidal crystals full of invisible vacancies

Frenkel

2012

Proc. Natl. Acad. Sci. U.S.A.

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Tetratic Phase in the Planar Hard Square System?

Cited by 112 publications

References 30 publications

Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

Demixing and orientational ordering in mixtures of rectangular particles

Colloidal crystals full of invisible vacancies

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