Phase diagram of hard tetrahedra

Haji-Akbari, Amir; Engel, Michael; Glotzer, Sharon C.

doi:10.1063/1.3651370

Cited by 86 publications

(115 citation statements)

References 60 publications

(100 reference statements)

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“…[26], and simulations are essential to answering theoretical questions including "What is the densest packing of perfectly hard tetrahedra?" [27,28].…”

Section: Predicting Morphologymentioning

confidence: 99%

Computationally connecting organic photovoltaic performance to atomistic arrangements and bulk morphology

Jones

Jankowski

2017

Molecular Simulation

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Rationally designing roll-to-roll printed organic photovoltaics requires a fundamental understanding of active layer morphologies optimized for charge separation and transport, and which ingredients can be used to self-assemble those morphologies. In this review article we discuss advances in three areas of computational modeling that provide insight into active layer morphology and the charge transport properties that result. We explain the computational bottlenecks prohibiting atomistically-detailed simulations of device-scale active layers and the coarse-graining and hardware acceleration strategies for overcoming them. We review coarse-grained simulations of organic photovoltaic active layers and show that high throughput simulations of experimentally-relevant length scales are now accessible. We describe a new Python package diffractometer that permits grazing-incidence X-ray scattering patterns of simulated active layers to be compared against experiments. We explain the accurate calculation of charge-carrier mobilities from coarse-grained active layer morphologies by using atomistic backmapping, quantum chemical calculations, and kinetic Monte Carlo simulations. We employ these simulations to show that ordering of poly(3-hexylthiophene-2,5-diyl) explains a factor of 1000 improvement in charge mobility. In concert, we present a suite of computational tools enabling large-scale electronic properties of organic photovoltaics to be studied and screened for by molecular simulations.

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“…[26], and simulations are essential to answering theoretical questions including "What is the densest packing of perfectly hard tetrahedra?" [27,28].…”

Section: Predicting Morphologymentioning

confidence: 99%

Computationally connecting organic photovoltaic performance to atomistic arrangements and bulk morphology

Jones

Jankowski

2017

Molecular Simulation

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“…While initial studies focused understandably on dense packing of uniform spheres research has since been extended to objects with complex, anisotropic shapes (Donev et al, 2006;Frenkel et al, 1988;Haji-Akbari et al, 2013, 2011a, 2011bJiao et al, 2009;Jiao and Torquato, 2011;Torquato and Jiao, 2009;Veerman and Frenkel, 1991;Xu et al, 2005;Zeravcic et al, 2009). Athermal polymer packings (of hard-sphere chains) fall in the latter category: while the constituent monomers are well-defined, nonoverlapping spheres (of uniform size), the global shape and size of each molecule are highly non-trivial, fluctuate over time, and are distinctly different from one chain to the other.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Foteinopoulou

Karayiannis

Laso

2015

Chemical Engineering Science

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HIGHLIGHTS• Identification of the maximally random jammed state for polymer packings.• Molecular simulation of the phase transition in hard-sphere chains.• Molecular modelling of the effect of confinement in densely-packed athermal polymers.• Numerical calculation of the topological constraints in polymeric systems.• First-principles calculation of the scaling regimes in flexible polymers. ABSTRACTWe review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder-order transition). In addition, we observe how these properties are affected by confinement realized by fiat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

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“…At lower packing fractions, hard tetrahedra assemble into a dodecagonal quasicrystal [19], in which the tetrahedra form a decorated square-triangle tiling [20]. Degenerate phases are impossible in the TBP crystal because the contacts between neighboring tetrahedra in different TBPs are highly imperfect [21], but are possible in the quasicrystal due to the almost-perfect face-to-face contacts between arXiv:1106.5561v2 [cond-mat.stat-mech] …”

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confidence: 99%

Degenerate Quasicrystal of Hard Triangular Bipyramids

2011

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We report a degenerate quasicrystal in Monte Carlo simulations of hard triangular bipyramids each composed of two regular tetrahedra sharing a single face. The dodecagonal quasicrystal is similar to that 1 recently reported for hard tetrahedra [Haji-Akbari et al., Nature (London) 462, 773 (2009)] but degenerate in the pairing of tetrahedra, and self-assembles at packing fractions above 54%. This notion of degeneracy differs from the degeneracy of a quasiperiodic random tiling arising through phason flips. Free energy calculations show that a triclinic crystal is preferred at high packing fractions.Hard disks and spheres order into hexagonal and facecentered cubic crystals, respectively, above a certain packing fraction. A more complex phase behavior is observed if the disks or spheres are rigidly bonded into dimers (dumbbells) [1][2][3][4]. A solid phase, disordered in the orientation of dimers while ordered on the monomer level, forms if the distance between monomers within a dimer is roughly the diameter of a monomer. This equilibrium solid phase can be alternatively understood as a random pairing of neighboring monomers within the native monomer crystal. The resulting thermodynamic ensemble of ground states is degenerate and the structure is therefore called a degenerate crystal. As shown by Wojciechowski et al.[1] for hard disks, the entropy associated with the degeneracy exceeds the entropy from excluded volume effects, which by itself is sufficient to drive the crystallization of hard monomers. Other consequences of the pairing of monomers into dimers include topological defects [5], a restricted, glassy dislocation motion [6,7], and unusual elastic properties [8]. Similar degenerate phases have also been observed for freely-joined chains of hard spheres [9,10].Although degenerate crystals can potentially assemble from dimers of hard shapes other than disks and spheres, few examples have been reported. One reason is the competition between degenerate crystals and the liquid crystalline phases frequently observed for particles with large aspect ratios. For example, elongated tetragonal parallelepipeds, which for an aspect ratio of 2:1 can be viewed as dimers of face-sharing cubes, form a degenerate parquet phase at intermediate densities before transforming into a smectic liquid crystal that eventually crystallizes [11]. Another simple dimer is the triangular bipyramid (TBP), which consists of two face-sharing, regular tetrahedra (Fig. 1a). The TBP is the simplest face-transitive bipyramid and the twelfth of the 92 Johnson solids. The lack of inversion symmetry of the TBP, however, makes lattice packings non-optimal [12], and thus it is potentially more interesting as a dimer than dimers of spheres and cubes. Moreover, the recent synthesis of TBP-shaped nanoparticles and colloids [13][14][15][16] relevance. In both of the known ordered phases of hard, regular tetrahedra, each tetrahedron is in almost-perfect face-to-face contact with at least one other tetrahedron. The densest known packing of tetrahedr...

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Phase diagram of hard tetrahedra

Cited by 86 publications

References 60 publications

Computationally connecting organic photovoltaic performance to atomistic arrangements and bulk morphology

Computationally connecting organic photovoltaic performance to atomistic arrangements and bulk morphology

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Degenerate Quasicrystal of Hard Triangular Bipyramids

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