Melting of polydisperse hard disks

Pronk, Sander; Frenkel, Daan

doi:10.1103/physreve.69.066123

Cited by 49 publications

(42 citation statements)

References 31 publications

(60 reference statements)

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“…For smaller Á, the ratio increases more rapidly with an increase in . We note that the system is ordered for Á 8% [11,25,26]. How the behavior of T > eff =T changes toward the critical Á, which separates the ordered and disordered region, is an interesting problem, but it is beyond the scope of this Letter.…”

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confidence: 96%

Apparent Violation of the Fluctuation-Dissipation Theorem due to Dynamic Heterogeneity in a Model Glass-Forming Liquid

Kawasaki

Tanaka

2009

Phys. Rev. Lett.

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Here we study the relation between the mobility and the translational diffusion in supercooled two-dimensional polydisperse colloidal liquids, using numerical simulations. We find an apparent violation of the Einstein-Smoluchowski (ES) relation D=kB T micro (D: diffusion constant; mu: mobility; kB; Boltzmann's constant; T: temperature). The violation is a direct consequence of the fact that it is difficult for a driven particle to enter a jammed region with high order due to its yield stress. The degree of this apparent ES violation is controlled solely by the characteristic size of slow jammed regions, xi. Our finding implies that the characteristic time of this problem is not the structural relaxation time tau alpha but the lifetime of dynamic heterogeneity, tau xi. A supercooled liquid can be regarded to be ergodic only over tau xi, which may be the slowest intrinsic time scale of the system.

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confidence: 96%

Apparent Violation of the Fluctuation-Dissipation Theorem due to Dynamic Heterogeneity in a Model Glass-Forming Liquid

Kawasaki

Tanaka

2009

Phys. Rev. Lett.

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“…We now boost thermalization by implementing a swap algorithm [18][19][20]. With probability α, we perform conventional Monte-Carlo moves where particles are translated, and with probability (1 − α) we perform a swap move where we pick two particles at random and attempt to exchange their diameters.…”

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confidence: 99%

“…The key enabling factor of our computational approach is the combination of swap Monte-Carlo moves to standard single-particle translations [18][19][20], which is a simple instance of a cluster move [21,22]. Swap moves enhance thermalization in simple mixtures [23], but their efficiency is significantly higher in continuously polydisperse systems [24][25][26].…”

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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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“…In the case of the polydisperse soft system, the particle size distribution was taken to be Gaussian [17,18]; for binary soft disk system the particle size distribution was composed of two Dirac delta functions of equal amplitudes. The Poisson's ratio of the polydisperse and binary soft disk crystalline phases were determined by Monte Carlo simulation using the analysis of box fluctuations in the constant pressure ensemble with variable box shape (NpT) [19][20][21].…”

Section: Simulation Detailsmentioning

confidence: 99%