Maximally dense random packings of cubes and cuboids via a novel inverse packing method

Liu, Lufeng; Li, Zhuoran; Jiao, Yang; Li, Shuixiang

doi:10.1039/c6sm02065h

Cited by 34 publications

(26 citation statements)

References 53 publications

(75 reference statements)

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“…For f larger than B0.6, we observe akin to ref. [39][40][41][42] that ordering and orientational correlations start manifesting themselves (for f Z 0.57, crystallization behaviour has been observed). It can hence be discussed whether these configurations are random and to what extent; herein, it suffices to conclude that our algorithm will create crystals for high solid volume fractions.…”

Section: Resultsmentioning

confidence: 94%

“…Just to give a brief account, studies performed include the random close packing of ellipsoids, 27 monodisperse and polydisperse hard spheres, 28,29 polyhedra including platonic solids, [30][31][32][33] superballs and superellipsoids, [34][35][36] cubes with round edges, 37 and monodisperse and polydisperse cubes and cuboids. [38][39][40][41][42] Hard cubes and cuboids and their packing and phase behavior have been studied both as limiting cases of superballs and superellipsoids, 35,36 and modeled exactly as cubes and cuboids. [39][40][41] The true nature of their behavior is somewhat elusive; as stated by Jiao and Torquato, 31 attempts to create random close packings (or rather maximally random jammed packings) of cubes easily lead to high degrees of order, raising questions concerning the appropriateness of some of the algorithms suggested so far to generate these packings.…”

Section: Introductionmentioning

confidence: 99%

“…Nonetheless, random sequential addition [39][40][41] can produce packings with a high degree of randomness, as can the order-constrained stochastic optimization method described in ref. 42.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Shape-dependent effective diffusivity in packings of hard cubes and cuboids compared with spheres and ellipsoids

Röding

2017

Soft Matter

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We performed computational screening of effective diffusivity in different configurations of cubes and cuboids compared with spheres and ellipsoids. In total, more than 1500 structures are generated and screened for effective diffusivity. We studied simple cubic and face-centered cubic lattices of spheres and cubes, random configurations of cubes and spheres as a function of volume fraction and polydispersity, and finally random configurations of ellipsoids and cuboids as a function of shape. We found some interesting shape-dependent differences in behavior, elucidating the impact of shape on the targeted design of granular materials.

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Section: Resultsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Shape-dependent effective diffusivity in packings of hard cubes and cuboids compared with spheres and ellipsoids

Röding

2017

Soft Matter

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“…41 The MDRP is defined as the densest packing in the random state in which the particle positions and orientations are randomly distributed. [31][32][33]42 The packing density of the MDRP corresponds to a sharp transition in the order map, which characterizes the onset of nontrivial spatial correlations among the particles. 33,42 The MDRP is also regarded as a glass state of hard particle systems with an artificial constraint and is always random.…”

Section: Introductionmentioning

confidence: 99%

“…33,42 The MDRP is also regarded as a glass state of hard particle systems with an artificial constraint and is always random. 31 The jammed or mechanically stable condition is emphasized in the MRJ state, while the random condition is emphasized in the MDRP state. For the particle shapes which are difficult to crystalize, the packing density of the MDRP is close to that of the RCP or MRJ packing, such as the spheroids, 32 spherocylinders, 33 octahedra, 42 and superellipsoids with small surface shape parameters.…”

Section: Introductionmentioning

confidence: 99%

Evolutions of packing properties of perfect cylinders under densification and crystallization

Liu

Yuan

Deng

et al. 2018

The Journal of Chemical Physics

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Cylindrical particles are ubiquitous in nature and industry, and a cylinder is a representative shape of rod-like particles. However, the disordered packing results of cylinders in previous studies are quite inconsistent with each other. In this work, we obtain the MRJ (maximally random jammed) packings and the MDRPs (maximally dense random packings) of perfect cylinders with the aspect ratio (height/diameter) 0.2 ≤ ≤ 6.0 using the ASC (adaptive shrinking cell) algorithm and the IMC (inverse Monte Carlo) method, respectively. The optimal aspect ratio corresponding to the maximal packing density is = 0.9 in the MRJ state, while the value is = 1.2 in the MDRP state. Then we investigate the evolutions of packing properties of perfect cylinders under densification and crystallization. We compare the different final packing states generated via the two methods with different compression rates and order constraints. In the densification procedure, we generate jammed and random packings of cylinders with various compression rates via the ASC and IMC method, respectively. When decreasing the compression rate, we find that the packing density increases but the optimal remains the same in both methods. In the crystallization procedure, the order constraint in the IMC method is gradually released which means the degree of order in the packings is allowed to increase, and we find that the optimal shifts from 1.2 to 0.9 while the packing density increases as well. Meanwhile, the random packings evolve into the jammed packings in the crystallization procedure which reflects the competition mechanism between the randomness and jamming. These results also indicate that the optimal is solely related to the degree of order in the cylinder packings but not determined by the protocol or packing density. Furthermore, a uniform shape elongation effect on the random-packing densities of various shaped particles is found via a new proposed definition of the scaled aspect ratio. Finally, a rough linear relationship between the mean and standard deviation of the reduced Voronoi cell volumes is obtained only for the random packings. Our findings should lead to a better understanding toward the jammed and random packings and are helpful in guiding the granular material design.

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Review on the structure of random packed‐beds

Seckendorff

Hinrichsen

2021

Can J Chem Eng

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Independent from their intended purpose, the understanding of structural characteristics of random packings of particles having defined shapes is important to understand and optimize fluid dynamic behaviour, heat, and mass transfer. The packing structure can be described by the coordination number, local porosity profiles, the average porosity, and pore characteristics, which are influenced by the wall and thickness effect; the material, shape, and size distribution of the packing particles; the packing and compaction mode; and the shape and material of the packing's containing walls. Therefore, existing knowledge on the structure of randomly packed mono-sized particles is reviewed to provide an updated selection of relevant parameters and their derived correlations obtained by experimental, numerical, and analytical means.packed-bed reactor, porosity, random particle packings, review, structure | INTRODUCTIONRandom packings of particles having defined shapes are deployed in all kinds of industrial applications and come in all orders of magnitude. The most prominent examples comprise micro-sized particle beds as commonly used in chromatography packed columns, [1][2][3] packed-bed reactors filled with catalytic shaped bodies having millimetre size, [4,5] packed columns used in separation processes such as distillation incorporating particles in the lower centimetre range, [6,7] and the pebble-bed reactor, which is a gas-cooled nuclear reactor, moderated by a packing of graphite spheres. [8][9][10] In addition to those, numerous less-known applications of packed-beds exist, ranging from powder-bed 3D printers, [11] solar-energy storage systems, [12] earth science, [13] civil engineering, [14,15] and pharmaceutical processing, [16] to the pyrolysis of pelletized wood fuels, [17] to name but a few.Irrespective of its intended purpose, the extent of a packed-bed is limited by a confining wall of commonly cylindrical shape, though flat plates and other container geometries are possible. Despite its generally random nature, close to this confinement the particles' placement is naturally forced to align with the wall's geometry. This imposed order reaches a couple of particle diameters into the packing and is usually named the wall effect. Its influence on the overall packed-bed characteristics decreases with increasing tube-to-particle diameter ratio λ = D d p . While most applications operate in an only sparsely affected λ-range, this effect becomes dominant, for instance, in catalytic multitubular reactors, typically performing at λ = 4-7 [18] or a single-pellet-string reactor with a λ < 2. [19] Moreover, some packed-bed utilizations, especially chromatography columns, have very delicate requirements regarding bed homogeneity and its derived characteristics.Abbreviations: DEM, discrete element method; Erfc, error function; J 0 , Bessel function of first kind and zero order; MRJ, maximally random jammed; RCP, random close packing; RLP, random loose packing.

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Maximally dense random packings of cubes and cuboids via a novel inverse packing method

Cited by 34 publications

References 53 publications

Shape-dependent effective diffusivity in packings of hard cubes and cuboids compared with spheres and ellipsoids

Shape-dependent effective diffusivity in packings of hard cubes and cuboids compared with spheres and ellipsoids

Evolutions of packing properties of perfect cylinders under densification and crystallization

Review on the structure of random packed‐beds

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