Why is Random Close Packing Reproducible?

Kamien, Randall D.; Liu, Andrea J.

doi:10.1103/physrevlett.99.155501

Cited by 192 publications

(182 citation statements)

References 43 publications

Supporting

Mentioning

165

Contrasting

Order By: Relevance

“…that there is a single packing fraction at which jamming occurs in the large system limit [17,18]. Since amorphous, isostatic packings can exist over a finite range of packing fractions, the onset of jamming should not be classified as a point in the jamming phase diagram, but rather as a region of finite extent.…”

Section: Introductionmentioning

confidence: 99%

Tuning jammed frictionless disk packings from isostatic to hyperstatic

2011

View full text Add to dashboard Cite

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates r and initial packing fractions followed by compression and decompression in small steps to reach packing fractions φJ at jamming onset. For the second, we seed the system with initial configurations that promote microand macrophase-separated packings followed by compression and decompression to φJ . Using these protocols, we generate more than 10 4 static packings over a wide range of packing fraction, contact number, and compositional and positional order. We find that amorphous, isostatic packings exist over a finite range of packing fractions from φmin ≤ φJ ≤ φmax in the large-system limit, with φmax ≈ 0.853. In agreement with previous calculations, we obtain φmin ≈ 0.84 for r > r * , where r * is the rate above which φJ is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, bond orientational order, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered, whereas bondorientational and compositional order increase with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies of the static packings to understand the extent to which the mechanical properties of amorphous, isostatic packings are different from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.PACS numbers: 83.80.

show abstract

Section: Introductionmentioning

confidence: 99%

Tuning jammed frictionless disk packings from isostatic to hyperstatic

2011

View full text Add to dashboard Cite

show abstract

“…This observation led to the proposal that "typical" amorphous packings should have common structure and density; the latter has been denoted Random Close Packing (RCP) density. The definition of RCP has been intensively debated in the last few years, in connection with the progresses of numerical simulations [1,10].Nevertheless, the empirical evidence, that amorphous packings produced according to very different protocols have common structural properties, is striking and call for an explanation. This is all the more true for binary or multicomponent mixtures, where in addition to the usual structural observables, such as the structure factor, one can investigate other quantities such as the coordination between spheres of different type, and study their variation with the composition of the mixture.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

et al. 2009

View full text Add to dashboard Cite

We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.Amorphous packings of hard spheres are ubiquitous in physics: they have been used as models for liquids, glasses, colloidal systems, granular systems, and powders. They are also related to important problems in mathematics and information theory, such as digitalization of signals, error correcting codes, and optimization problems. Moreover, the structure and density (or porosity) of amorphous multicomponent packings is important in many branches of science and technology, ranging from oil extraction to storage of grains in silos.Despite being empirically studied since at least sixty years, amorphous packings still lack a precise mathematical definition, due to the intrinsic difficulty of quantifying "randomness" [1]. Indeed, even if a sphere packing is a purely geometrical object, in practice dense amorphous packings always result from rather complicated dynamical protocols: for instance, spheres can be thrown at random in a box that is subsequently shaken to achieve compactification [2], or they can be deposited onto a random seed cluster [3]. In numerical simulations, one starts from a random distribution of small spheres and inflates them until a jammed state is reached [4,5]; alternatively, one starts from large overlapping spheres and reduces the diameter in order to eliminate the overlaps [6][7][8][9]. In principle, each of these dynamical prescriptions produces an ensemble of final packings that depends on the details of the procedure used. Still, very remarkably, if the presence of crystalline regions is avoided, the structural properties of amorphous packings turn out to be very similar. This observation led to the proposal that "typical" amorphous packings should have common structure and density; the latter has been denoted Random Close Packing (RCP) density. The definition of RCP has been intensively debated in the last few years, in connection with the progresses of numerical simulations [1,10].Nevertheless, the empirical evidence, that amorphous packings produced according to very different protocols have common structural properties, is striking and call for an explanation. This is all the more true for binary or multicomponent mixtures, where in addition to the usual structural observables, such as the structure factor, one can investigate other quantities such as the coordination between spheres of different type, and study their variation with the composition of the mixture.In earlier attempts to build statistical models of ...

show abstract

“…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.…”

mentioning

confidence: 99%

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

et al. 2016

View full text Add to dashboard Cite

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...

show abstract

Why is Random Close Packing Reproducible?

Cited by 192 publications

References 43 publications

Tuning jammed frictionless disk packings from isostatic to hyperstatic

Tuning jammed frictionless disk packings from isostatic to hyperstatic

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

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

Contact Info

Product

Resources

About