Jamming Transition and Inherent Structures of Hard Spheres and Disks

Ozawa, Masakuni; Kuroiwa, Takeshi; Ikeda, Atsushi; Miyazaki, Kunimasa

doi:10.1103/physrevlett.109.205701

Cited by 96 publications

(113 citation statements)

References 41 publications

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“…The value of φ c,∞ is consistent with previous studies of the same bi-disperse systems [11,25]. For finite size systems, σ y (φ, N ) deviates from Eq.…”

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confidence: 81%

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Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential

Liu

Xie

2014

Phys. Rev. Lett.

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By finding local minima of an enthalpy-like energy, we can generate jammed packings of frictionless spheres under constant shear stress σ and obtain the yield stress σy by sampling the potential energy landscape. For three-dimensional systems with harmonic repulsion, σy satisfies the finite size scaling with the limiting scaling relation σy ∼ φ − φ c,∞ , where φ c,∞ is the critical volume fraction of the jamming transition at σ = 0 in the thermodynamic limit. The width or uncertainty of the yield stress decreases with decreasing φ and decays to zero in the thermodynamic limit. The finite size scaling implies a length ξ ∼ (φ − φ c,∞ ) −ν with ν = 0.81 ± 0.05, which turns out to be a robust and universal length scale exhibited as well in the finite size scaling of multiple quantities measured without shear and independent of particle interaction. Moreover, comparison between our new approach and quasi-static shear reveals that quasi-static shear tends to explore low-energy states.PACS numbers: 61.43. Bn,61.43.Fs At zero temperature and shear stress, a packing of frictionless spheres interacting via repulsions jams into a disordered solid when its volume fraction φ exceeds a critical value φ c at the so-called Point J [1][2][3]. As a simplified model to understand the noncrystalline liquid-solid transition of various materials including granular materials, foams, colloids, emulsions, and glasses, jammed packings of frictionless spheres exhibit interesting but unusual critical behaviors at Point J [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].In addition to the volume fraction, shear stress σ and temperature T have been proposed as the other two control parameters to cause generalized jamming transition, i.e. yielding and glass transition [1]. A jammed solid remains rigid when subject to a shear stress smaller than the yield stress σ y , while it unjams and flows otherwise. It has been shown that the yield stress of the T = 0 jammed solids decreases with decreasing the volume fraction and vanishes at Point J [7,12,18,19]. This is different from the glass transition temperature at which a supercooled liquid is supposed to freeze into a glass, through the fact that in the T = 0 limit glass transition occurs at a volume fraction lower than φ c [20][21][22][23][24][25][26]. Therefore, Point J is more relevant to the volume fraction and shear stress than to the temperature. Jammed packings of frictionless spheres under applied shear stress thus serve as typical systems to study the criticality of Point J [7,8,12].In most of the previous simulations, the yield stress of a jammed solid has been defined as either the average shear stress of the quasi-static shear flow in which the shear stress is not a controllable parameter [18,19,27,28] or the critical shear stress extrapolated from nonequilibrium molecular dynamics simulations above which the system loses shear rigidity and flows forever [18,28]. In the potential energy landscape perspective, the yield stress corresponds to the critical shear stress above whic...

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“…The value of φ c,∞ is consistent with previous studies of the same bi-disperse systems [11,25]. For finite size systems, σ y (φ, N ) deviates from Eq.…”

supporting

confidence: 81%

“…As a simplified model to understand the noncrystalline liquid-solid transition of various materials including granular materials, foams, colloids, emulsions, and glasses, jammed packings of frictionless spheres exhibit interesting but unusual critical behaviors at Point J [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

mentioning

confidence: 99%

Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential

Liu

Xie

2014

Phys. Rev. Lett.

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“…Growth of the dynamical and static lengths with increasing reduced pressure (or density). For both the 6:5 (left) and the 7:5 (right) binary mixtures, the static (point-to-set) length ξ p (dotted line) grows much slower than the dynamical length ξ dyn (dash-dotted line) relative to their value at ϕ * = 0.52, the onset of nontrivial dynamics [65]. The static length saturates and follows the bound given by Eq.…”

Section: Resultsmentioning

confidence: 94%

“…7, this is true even when restricting the analysis to densities above ϕ = 0.55. (Note that the "onset" value above which nontrivial glassy dynamics is reported to be around 0.52 [65].) It should be stressed that the span of relaxation times described in Ref.…”

Section: Resultsmentioning

confidence: 99%

Decorrelation of the static and dynamic length scales in hard-sphere glass formers

Charbonneau

Tarjus

2013

Phys. Rev. E

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We show that, in the equilibrium phase of glass-forming hard-sphere fluids in three dimensions, the static length scales tentatively associated with the dynamical slowdown and the dynamical length characterizing spatial heterogeneities in the dynamics unambiguously decorrelate. The former grow at a much slower rate than the latter when density increases. This observation is valid for the dynamical range that is accessible to computer simulations, which roughly corresponds to that accessible in colloidal experiments. We also find that, in this same range, no one-to-one correspondence between relaxation time and point-to-set correlation length exists. These results point to the coexistence of several relaxation mechanisms in the dynamically accessible regime of three-dimensional hard-sphere glass formers.

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“…Fitting the relaxation times to a power law yields ϕ mct ≈ 0.59 < ϕ max , so that the associated mode-coupling transition [14] corresponds to an avoided singularity. For the same system, jamming transitions were located in the range ϕ J = 0.648 − 0.662 depending on the chosen protocol [15][16][17]. The relation between glass and jamming transitions is left unresolved, as thermalization stops long before any of the singularities can be crossed, ϕ max ≪ ϕ 0 , ϕ J , and because estimates of ϕ 0 and ϕ J are too close to favor any of the above scenarios.…”

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confidence: 99%

Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond

et al. 2016

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We implement and optimize a particle-swap Monte-Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly-large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct non-equilibrium protocols. We demonstrate that equilibrium fluid and non-equilibrium jammed states can have the same density, showing that the jamming transition cannot be the end-point of the fluid branch.PACS numbers: 05.20.Jj,We clarify the behavior of non-crystalline states of hard spheres at very large densities where both a glass transition (in colloidal systems) and a jamming transition (in non-Brownian systems) are observed [1][2][3]. Glass and jamming transitions are usually studied through distinct protocols, and understanding the relation between these two broad classes of phase transformations and the resulting amorphous arrested states is an important research goal [1][2][3][4][5]. These questions impact a wide range of fields, from the rheological properties of soft materials to optimization problems in computer science [1,6].Let us first consider Brownian hard spheres. When size polydispersity is introduced, crystallization can be prevented and the thermodynamic properties of the fluid studied at increasing density until a glass transition takes place, where particle diffusivity becomes very small [7]. Upon further compression, the pressure of the glass increases until a jamming transition occurs, where particles come at close contact and the pressure diverges [8]. Because the laboratory glass transition arises from using a finite observation timescale, two scenarios were proposed to describe the hypothetical situation where thermalization is no longer an issue [9]. A first possibility is that slower compressions reveal an ideal glass transition density, ϕ 0 , above which the equilibrium state is a glass, not a fluid [2]. Jamming would then be observed upon further non-equilibrium compression of these glass states [10]. Alternatively, it may be that slower compressions continuously shift the kinetic glass transition to higher densities. In this view, it is plausible that jamming becomes the end-point of the equilibrium fluid branch [11,12].Distinguishing between these two scenarios by direct numerical measurements is challenging. For a wellstudied binary mixture of hard spheres, for instance, thermalization can be achieved up to ϕ max ≈ 0.60 [9,13]. The location of the glass transition must be extrapolated using empirical fits based on activated relaxation. Values in the range ϕ 0 = 0.615 − 0.635 were obtained [9], depending on the fitting function. Fitting the relaxation times to a power law yields ϕ mct ≈ 0.59 < ϕ max , so that the associated mode-coupling transition [14] corresponds to an avoided singularity. For the same system, jamming transitions were located in the range ϕ J = 0.648 − 0.662 depending on the chosen protocol [15][1...

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Jamming Transition and Inherent Structures of Hard Spheres and Disks

Cited by 96 publications

References 41 publications

Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential

Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential

Decorrelation of the static and dynamic length scales in hard-sphere glass formers

Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond

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