Mean-field theory of random close packings of axisymmetric particles

Baule, Adrian; Mari, Romain; Lin, Bo; Portal, Louis; Makse, Hernán A.

doi:10.1038/ncomms3194

Cited by 146 publications

(167 citation statements)

References 53 publications

(118 reference statements)

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“…Moreover, it occurs that the highest packing were found for particles (ellipsoids, spherocylinders or dimers) of long-to-short axis ratio around 1.5, which is similar as for RSA in two dimensions. These results were confirmed both: numerically 24,26,27 and theoretically 28 .…”

Section: Introductionsupporting

confidence: 70%

Shapes for maximal coverage for two-dimensional random sequential adsorption

Cieśla

Pajk

Ziff

2015

Phys. Chem. Chem. Phys.

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The random sequential adsorption of various particle shapes is studied in order to determine the influence of particle anisotropy on the saturated random packing. For all tested particles there is an optimal level of anisotropy which maximizes the saturated packing fraction. It is found that a concave shape derived from a dimer of disks gives a packing fraction of 0.5833, which is comparable to the maximum packing fraction of ellipsoids and spherocylinders and higher than other studied shapes. Discussion why this shape is beneficial for random sequential adsorption is given.

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Section: Introductionsupporting

confidence: 70%

Shapes for maximal coverage for two-dimensional random sequential adsorption

Cieśla

Pajk

Ziff

2015

Phys. Chem. Chem. Phys.

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“…We relate this transition to the emergence of a coupling between translations and rotations at t ¼ 1, which is also responsible for similar nonanalyticities in structural properties of jammed granular packings of ellipsoids [6,8,14], ellipses [44], and spherocylinders [45]. Moreover, fingerprints of such nonanalyticities seem also to show up in critical temperatures and concentrations of liquid-vapour transitions in attractive liquids [46], emphasizing the importance of the simpler athermal systems studied in our present work.…”

Section: -4supporting

confidence: 60%

“…We demonstrate that the critical dependence of this coupling on ϵ ≡ jt − 1j, for ϵ → 0, gives rise to a dramatic nondifferentiable variation of some structural and thermodynamic fluid properties. Strikingly, a similar nonanalytic behavior has been observed for the densities of jammed amorphous zero-temperature packings of frictionless ellipsoids [6,8,14], ellipses, and spherocylinders. Our observations suggest that vestiges of the jamming transition are present in thermodynamically equilibrated fluids, down to very low densities.…”

supporting

confidence: 68%

Structural Transition in a Fluid of Spheroids: A Low-Density Vestige of Jamming

et al. 2016

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A thermodynamically equilibrated fluid of hard spheroids is a simple model of liquid matter. In this model, the coupling between the rotational degrees of freedom of the constituent particles and their translations may be switched off by a continuous deformation of a spheroid of aspect ratio t into a sphere (t ¼ 1). We demonstrate, by experiments, theory, and computer simulations, that dramatic nonanalytic changes in structure and thermodynamics of the fluids take place, as the coupling between rotations and translations is made to vanish. This nonanalyticity, reminiscent of a second-order liquid-liquid phase transition, is not a trivial consequence of the shape of an individual particle. Rather, free volume considerations relate the observed transition to a similar nonanalyticity at t ¼ 1 in structural properties of jammed granular ellipsoids. This observation suggests a deep connection to exist between the physics of jamming and the thermodynamics of simple fluids. DOI: 10.1103/PhysRevLett.116.098001 The thermodynamics of a fluid of simple spheres is wellknown and almost completely understood [1,2]. However, the constituents of real matter are typically nonspherical. Their translational degrees of freedom are coupled to their rotations [3]. A system of spheroids, ellipsoids of revolution, is arguably the simplest model of matter, where such a coupling exists. This model has recently been realized in colloidal and granular matter experiments, providing an important insight onto the local bulk structure of fluids [4,5] and jammed packings [6]. While a very good agreement between experiment and theory has been achieved for the fluids [5,7], these studies dealt with only one specific particle aspect ratio, t ¼ 1.6. The dependence of the fluid structure on the aspect ratio of the constituent particles has not been tested, so that the fundamental role played in these fluids by rotational degrees of freedom remains unknown. The understanding of jammed packings of ellipsoids is incomplete, as well. Many common order metrics are minimized for the, so-called, "maximally random jammed" (MRJ) packings [8]. Yet, it remains unclear, how the various protocols of compression, commonly starting from a fluidlike initial state, explore the available phase space and whether any fundamental physical reason exists for the convergence of many common compression protocols towards packings with densities close to that of the MRJ state [8][9][10][11][12][13].In this work, we study the dependence of the bulk structure in fluids of ellipsoids on the aspect ratio t ¼ a=b of the constituent particles, where a and b are the polar and the equatorial diameters, respectively. We combine experiments, theory, and Monte Carlo (MC) simulations, to explore the fundamental role of the rotational degrees of freedom in these fluids, in the vicinity of the so-called "sphere point" (t ¼ 1), where the coupling between rotations and translations vanishes. We demonstrate that the critical dependence of this coupling on ϵ ≡ jt − 1j, for ϵ → 0, gives rise...

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“…Dense disordered packings of lenses, among other hard axisymmetric particles, have been recently studied using a mean-field theory. 66 It would be of interest to test the predictions made there: a knowledge of dense ordered packings and equilibrium phase behavior is a pre-requisite for such a study. Given today's developments in colloidal particle synthesis, we envision that colloidal lenses could be readily produced.…”

Section: Introductionmentioning

confidence: 99%

Hard convex lens-shaped particles: Densest-known packings and phase behavior

Cinacchi

Torquato

2015

The Journal of Chemical Physics

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By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the highdensity crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom. C 2015 AIP Publishing LLC. [http://dx

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Mean-field theory of random close packings of axisymmetric particles

Cited by 146 publications

References 53 publications

Shapes for maximal coverage for two-dimensional random sequential adsorption

Shapes for maximal coverage for two-dimensional random sequential adsorption

Structural Transition in a Fluid of Spheroids: A Low-Density Vestige of Jamming

Hard convex lens-shaped particles: Densest-known packings and phase behavior

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