Dense Random Packing of Binary Mixtures of Spheres

Yerazunis, S.; Cornell, S. W.; Wintner, B.

doi:10.1038/207835a0

Cited by 140 publications

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“…(5) is an exact result [23,26,27,51] in the regime η > (1 − φ rcp )/(2 − φ rcp ) ≃ 0.26 where all particles participate to the jammed structure (in contrast to the complementary regime where the small particles "rattle" in the voids made by the big particles). Thus, Eq.…”

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Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

et al. 2014

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A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction φJ of the polydisperse system as a simple function of M1M3/M 2 2 , where M k is the kth moment of the size distribution. An analysis of experimental and simulation data of φJ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the highdensity region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures. Due to its simplicity and versatility, the hard-sphere (HS) system is considered as a prototype model in statistical physics [1], being also essential in studies in biological systems, granular matter, colloids, engineering, and materials science [2,3]. In an equilibrium monodisperse HS system the only control parameter is the packing fraction φ ≡ π 6 ρσ 3 (ρ and σ being the number density and the diameter of the spheres, respectively), i.e., the volume occupied by the spheres, relative to the total volume V . It is well established that the equilibrium system is in a stable fluid phase from φ = 0 to the freezing packing fraction φ f ≃ 0.492 [4,5], undergoes a fluid-solid transition from φ f to the crystal melting point φ m ≃ 0.543 [5,6], and finally is in a stable solid (crystalline) phase from φ m to the close-packing fraction φ cp = π 6 √ 2 ≃ 0.7405, corresponding to face-centered-cubic close-packing [7,8]. However, beyond the freezing point φ f there is also a region of metastable fluid states that is supposed to end at the glass transition point φ g ≃ 0.58 [2,8]. At even higher densities the system becomes a metastable amorphous solid until it jams at a random close-packing value * andres@unex.es;

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“…This has allowed us to obtain educated estimates of pressure values in a density range where, due to technical difficulties, no simulation experimental data from Ref. [51]; (b) simulation data from Ref. [22]; (c) simulation data from Ref.…”

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Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

et al. 2014

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“…Then, the total entropy of the system of m copies is given by S(m, ϕ|s) = ms + Σ(ϕ, s); the first term gives the entropy of the m copies in a state of entropy s, while the second term is due to the multiplicity of possible states. The total entropy of the system at fixed density [30]. Lines are predictions from theory, obtained fixing Σj = 1.7.…”

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“…[30], and the theoretical results. Note that a single "fitting" parameter Σ j , that is strongly constrained, allows to describe different sets of independent numerical and experimental data.…”

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Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

et al. 2009

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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 ...

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“…Approximating a uniform filling fraction of φ=0.65 for all hybrids, [161] which is admittedly a bit arguable especially for the extreme ratios, one can estimate that for the infiltrated opal the effective longitudinal sound velocity c ef f should be higher by about 6.3% or 8.5%, applying the EMT of Gaunaurd and Wertman [142] or Wood's law, [105] respectively (cf. section 5.2) -in reasonable agreement with the experimental c ef f .…”

Section: The Influence Of the Composition In Disordered Colloidal Sysmentioning

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High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

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Dense Random Packing of Binary Mixtures of Spheres

Cited by 140 publications

References 5 publications

Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

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