The random packing density of nearly spherical particles

Kallus, Yoav

doi:10.1039/c6sm00213g

Cited by 25 publications

(17 citation statements)

References 44 publications

(57 reference statements)

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“…Whether there is any deeper geometrical meaning to this remains an open question. Recent exact local expansions from the spherical RCP point to arbitrary shapes agree very well with our results and may shed further light on this question (Kallus, 2016). We also notice that the frictional and non-spherical branches are continuous at the spherical RCP point suggesting that a variation in fric-…”

Section: H Towards An Edwards Phase Diagram For All Jammed Mattersupporting

confidence: 88%

“…Extensions to mixtures and polydisperse packings can also be formulated. This might elucidate in particular the validity of Ulam's conjecture that the sphere is the worst packing object in 3d (Gardner, 2001), which has also been formulated in a random version (Jiao and Torquato, 2011) locally around the sphere shape (Kallus, 2016).…”

Section: Discussionmentioning

confidence: 98%

“…In fact, a conjecture attributed to Ulam (recorded in the book (Gardner, 2001)) in the context of regular packings, recently also formulated for random packings (Jiao and Torquato, 2011), states that the sphere is, indeed, the worst packing object among all convex shapes. In (Kallus, 2016) it has been shown for random packings that all sufficiently spherical shapes pack more densely than spheres. However, one should notice the local character of such a conjecture for random packings: Onsager already proved that elongated spaghettilike thin rods pack randomly much worse than spheres (Onsager, 1949).…”

Section: G Packing Of Non-spherical Particlesmentioning

confidence: 99%

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Edwards statistical mechanics for jammed granular matter

et al. 2018

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In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical mechanics, despite their inherent athermal features. Since then, the statistical mechanics approach for jammed matter -one of the very few generalizations of Gibbs-Boltzmann statistical mechanics to out of equilibrium matter -has garnered an extraordinary amount of attention by both theorists and experimentalists. Its importance stems from the fact that jammed states of matter are ubiquitous in nature appearing in a broad range of granular and soft materials such as colloids, emulsions, glasses, and biomatter. Indeed, despite being one of the simplest states of matter -primarily governed by the steric interactions between the constitutive particles -a theoretical understanding based on first principles has proved exceedingly challenging. Here, we review a systematic approach to jammed matter based on the Edwards statistical mechanical ensemble. We discuss the construction of microcanonical and canonical ensembles based on the volume function, which replaces the Hamiltonian in jammed systems. The importance of approximation schemes at various levels is emphasized leading to quantitative predictions for ensemble averaged quantities such as packing fractions and contact force distributions. An overview of the phenomenology of jammed states and experiments, simulations, and theoretical models scrutinizing the strong assumptions underlying Edwards' approach is given including recent results suggesting the validity of Edwards ergodic hypothesis for jammed states. A theoretical framework for packings whose constitutive particles range from spherical to non-spherical shapes like dimers, polymers, ellipsoids, spherocylinders or tetrahedra, hard and soft, frictional, frictionless and adhesive, monodisperse and polydisperse particles in any dimensions is discussed providing insight into an unifying phase diagram for all jammed matter. Furthermore, the connection between the Edwards' ensemble of metastable jammed states and metastability in spin-glasses is established. This highlights that the packing problem can be understood as a constraint satisfaction problem for excluded volume and force and torque balance leading to a unifying framework between the Edwards ensemble of equiprobable jammed states and out-of-equilibrium spin-glasses.

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Section: H Towards An Edwards Phase Diagram For All Jammed Mattersupporting

confidence: 88%

Section: Discussionmentioning

confidence: 98%

Section: G Packing Of Non-spherical Particlesmentioning

confidence: 99%

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Edwards statistical mechanics for jammed granular matter

et al. 2018

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“…It is notable that our analysis provides a clear systematic procedure to predict MRJ densities of other families of smooth particle shapes in both 2D and 3D, e.g., ellipses and ellipsoids. We note that after initial submission of our paper, we learned of a preprint that uses a local perturbation analysis to predict random close packing densities of the special case of smooth particle shapes that are very nearly spherical, which can continuously be deformed into a sphere 52 .…”

Section: Discussionmentioning

confidence: 99%

A Geometric-Structure Theory for Maximally Random Jammed Packings

Tian

Jiao

et al. 2015

Sci Rep

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Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density “random-close packing” polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.

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“…The range of the random packing fraction obtained for monosized frictionless spheres is between the random loose packing η RLP ∼ 0.55 and the random close packing η RCP ∼ 0.64. These values are significantly lower than the packing fraction η max ∼ 0.74 corresponding to the highly ordered close-packed configuration that is obtained for hexagonal compact packing [2,3], although the precise values of the packing density depend on the geometry of particles, dispersity, and intergrain friction [4][5][6].…”

Section: Introductionmentioning

confidence: 65%

Decompaction of wet granular materials under freeze-thaw cycling

2019

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The packing fraction dynamics of a wet granular material submitted to freeze-thaw cycling is investigated experimentally. The dynamics is strongly influenced by the liquid volume fraction ω in the considered range of 0.03 < ω < 0.32. This range of liquid contents covers different regimes of wetness from the creation of the capillary network until the formation of large clusters and finally close to the saturated case. For the liquid contents ω 0.15, the pile experiences a decompaction until a particular value of the packing fraction 0.56 corresponding to a random loose packing configuration for monosized spheres. Moreover, the decompaction starts after a cycling number that decreases exponentially with the liquid content. Finally, we show that the packing dynamics can be well modeled on the basis of a Landau potential with an asymmetric double-well structure. The onset of decompaction represents the tendency of the system to stay in a metastable state. After several cycles, the forces induced by the thermal cycling and local stochastic rearrangements of the grains can drive the system to overcome the energy barrier of the cohesive forces.

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The random packing density of nearly spherical particles

Cited by 25 publications

References 44 publications

Edwards statistical mechanics for jammed granular matter

Edwards statistical mechanics for jammed granular matter

A Geometric-Structure Theory for Maximally Random Jammed Packings

Decompaction of wet granular materials under freeze-thaw cycling

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