Mesophase behaviour of polyhedral particles

Agarwal, Umang; Escobedo, Fernando A.

doi:10.1038/nmat2959

Cited by 302 publications

(387 citation statements)

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“…Additionally, predicting the densest packings of hard polyhedra has intrigued mathematicians since the time of the early Greek philosophers, such as Plato and Archimedes [28,29]. Modern computer platforms have made it possible to perform simulations of these systems, which has resulted not only in an improved understanding of the experimentally observed phenomenology in colloidal suspensions of such particles, but also in improved Ansätze for the morphology of their closepacked configurations [24,[30][31][32][33][34][35].The self-assembly of the basic building blocks at finite pressures may differ substantially from the packings achieved at high (sedimentation and solvent-evaporation) pressures. For instance, liquid-crystal, plastic-crystal, vacancy-rich simple-cubic, and quasicrystalline mesophases are stabilized by entropy alone under non-closepacked conditions of hard anisotropic particle systems [30][31][32][33][34]36,37].…”

mentioning

confidence: 99%

“…Modern computer platforms have made it possible to perform simulations of these systems, which has resulted not only in an improved understanding of the experimentally observed phenomenology in colloidal suspensions of such particles, but also in improved Ansätze for the morphology of their closepacked configurations [24,[30][31][32][33][34][35].…”

mentioning

confidence: 99%

“…Predicting the phase behavior from the shape of the building blocks alone is therefore a major challenge in materials science and is crucial for the design of new functional materials. It is thus not surprising that numerous studies have been devoted to providing simple guidelines for predicting the self-assembly from the particle shape alone [32][33][34].…”

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confidence: 99%

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Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States

et al. 2013

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Using Monte Carlo simulations and free-energy calculations, we determine the phase diagram of a family of truncated hard cubes, where the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. A remarkable diversity in crystal phases and close-packed structures is found, including a fully degenerate crystal structure, several plastic crystals, as well as vacancy-stabilized crystal phases, all depending sensitively on the precise particle shape. Our results illustrate the intricate relation between phase behavior and building-block shape, and can guide future experimental studies on polyhedral-shaped nanoparticles. DOI: 10.1103/PhysRevLett.111.015501 PACS numbers: 61.46.Df, 64.70.MÀ, 64.75.Yz, 82.70.Dd Recent advances in experimental techniques to synthesize polyhedron-shaped particles, such as faceted nanocrystals and colloids [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and the ability to perform self-assembly experiments with these particles [15][16][17][18][19][20][21][22], have attracted the interest of physicists, mathematicians, and computer scientists [23][24][25][26][27]. Additionally, predicting the densest packings of hard polyhedra has intrigued mathematicians since the time of the early Greek philosophers, such as Plato and Archimedes [28,29]. Modern computer platforms have made it possible to perform simulations of these systems, which has resulted not only in an improved understanding of the experimentally observed phenomenology in colloidal suspensions of such particles, but also in improved Ansätze for the morphology of their closepacked configurations [24,[30][31][32][33][34][35].The self-assembly of the basic building blocks at finite pressures may differ substantially from the packings achieved at high (sedimentation and solvent-evaporation) pressures. For instance, liquid-crystal, plastic-crystal, vacancy-rich simple-cubic, and quasicrystalline mesophases are stabilized by entropy alone under non-closepacked conditions of hard anisotropic particle systems [30][31][32][33][34]36,37]. Predicting the phase behavior from the shape of the building blocks alone is therefore a major challenge in materials science and is crucial for the design of new functional materials. It is thus not surprising that numerous studies have been devoted to providing simple guidelines for predicting the self-assembly from the particle shape alone [32][33][34].Recently, Henzie et al.[15] reported the shapecontrolled synthesis of truncated cubes. In their research, the close-packed crystals of these particles were studied using sedimentation experiments and simulations. They created exotic superlattices, and their results also tested several conjectures on the densest packings of hard polyhedra [23,[25][26][27]. However, Henzie et al. did not examine the finite-pressure behavior of the system. Mapping the full phase diagram for the system of truncated cubes is thus important, not only from a fundamental perspective but also to guide future experimental self-assembly studies to fabricate new func...

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Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States

et al. 2013

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“…28 This has led to particular interest from the materials science community in these overlap algorithms to perform simulations on nanoparticle and colloid systems. [63][64][65][66][67][68][69][70][71] A. The method of separating axes…”

Section: Hard-particle Overlap Algorithmsmentioning

confidence: 99%

“…This is particularly relevant, since densest-packed candidate crystal structure need not be thermodynamically stable at all pressures for which the system crystallizes. 28,51,66,67,95 It is important to realize that there are strong finite-size effects for the prediction of candidates at finite pressure. The pressure P at which we perform the FBMC simulations only sets a range from which we sample crystal structures.…”

Section: Close-packed Crystal Structures For Anisotropic Particlesmentioning

confidence: 99%

Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

Graaf

Filion

Maréchal

et al. 2012

The Journal of Chemical Physics

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In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009)] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011)] were based. Finally, we comment on the process of crystalstructure prediction itself and the choices that can be made in these simulations.

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Entropy‐Driven Phase Transitions in Colloids: From spheres to anisotropic particles

Dijkstra¹

2014

Advances in Chemical Physics

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Mesophase behaviour of polyhedral particles

Cited by 302 publications

References 37 publications

Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States

Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States

Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

Entropy‐Driven Phase Transitions in Colloids: From spheres to anisotropic particles

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