Self-assembly of a space-tessellating structure in the binary system of hard tetrahedra and octahedra

Cadotte, Andrew T.; Dshemuchadse, Julia; Damasceno, Pablo F.; Newman, Richmond S.; Glotzer, Sharon C.

doi:10.1039/c6sm01180b

Cited by 20 publications

(17 citation statements)

References 39 publications

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“…ref. [1][2][3][4][5][6]. Several sub-problems have to be distinguished, among them is the question of the maximum density and other characteristics of a randomly packed arrangement, the so-called random close packing, or the quest for the maximum achievable packing density in regular structures.…”

Section: Introductionmentioning

confidence: 99%

Frustrated packing in a granular system under geometrical confinement

et al. 2018

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Optimal packings of uniform spheres are solved problems in two and three dimensions. The main difference between them is that the two-dimensional ground state can be easily achieved by simple dynamical processes while in three dimensions, this is impossible due to the difference in the local and global optimal packings. In this paper we show experimentally and numerically that in 2 + ε dimensions, realized by a container which is in one dimension slightly wider than the spheres, the particles organize themselves in a triangular lattice, while touching either the front or rear side of the container. If these positions are denoted by up and down the packing problem can be mapped to a 1/2 spin system. At first it looks frustrated with spin-glass like configurations, but the system has a well defined ground state built up from isosceles triangles. When the system is agitated, it evolves very slowly towards the potential energy minimum through metastable states. We show that the dynamics is local and is driven by the optimization of the volumes of 7-particle configurations and by the vertical interaction between touching spheres.

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Section: Introductionmentioning

confidence: 99%

Frustrated packing in a granular system under geometrical confinement

et al. 2018

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“…Environments of particles i and j are only compared if M i = M j , and thus, a one-to-one mapping is possible; otherwise, particles i and j are automatically deemed nonmatching. The threshold t = 0.2 r cut was chosen for all systems because 0.2 or 0.3 times the approximate nearest-neighbor distance ( r cut ) has proven appropriate—neither too stringent nor too lenient—in other contexts ( 67 , 68 ). Figure S2 explores the impact of threshold choice on crystallinity characterization as we explain next.…”

Section: Methodsmentioning

confidence: 99%

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

et al. 2021

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The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material’s memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.

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“…Here, the entropy of the individual configurations comes into play. In simulations, one can force the system by repeated growth and shrinking of the ensemble [43], or by adding Brownian motion [44][45][46][47]. In many respects, these systems can be considered as analogues of colloidal crystals.…”

Section: Introductionmentioning

confidence: 99%

On regular and random two-dimensional packing of crosses

Stannarius

Schulze

2021

Granular Matter

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Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packing structures are known. The packing of 2D crosses does not yet belong to the category of solved problems. We demonstrate in experiments with crosses of different aspect ratios (arm width to length) which packing fractions are actually achieved by random packing, and we compare them to densest regular packing structures. We determine local correlations of the orientations and positions after ensembles of randomly placed crosses were compacted in the plane until they jam. Short-range orientational order is found over 2 to 3 cross lengths. Similarly, correlations in the spatial distributions of neighbors extend over 2 to 3 crosses. There is no simple relation between the geometries of the crosses and the peaks in the spatial correlation functions, but some features of the orientational correlations can be traced to typical local configurations.

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Self-assembly of a space-tessellating structure in the binary system of hard tetrahedra and octahedra

Cited by 20 publications

References 39 publications

Frustrated packing in a granular system under geometrical confinement

Frustrated packing in a granular system under geometrical confinement

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

On regular and random two-dimensional packing of crosses

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