Structural relaxation of polydisperse hard spheres: Comparison of the mode-coupling theory to a Langevin dynamics simulation

Weysser, Fabian; Puertas, Antonio M.; Fuchs, Matthias; Voigtmann, Thomas

doi:10.1103/physreve.82.011504

Cited by 111 publications

(199 citation statements)

References 69 publications

(103 reference statements)

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“…Standard MCT predicts a diverging relaxation time above ϕ MCT c ¼ 0.566 [29], as seen in our N ¼ 2 results in Figs. 1(c) and 1(d).…”

supporting

confidence: 82%

“…The predicted curves for kd ¼ 13.0 also develop a small shoulder at intermediate times that is absent in the simulated data. This slightly poorer agreement for kd > 7.4 was also noted by Weysser et al [29] for the standard-MCT case, even after rescaling of the data. The origin of the discrepancy may be related to the fact that the use of a density-mode basis neglects some short-time correlations, which are expected to be more pronounced away from the first peak of SðkÞ.…”

supporting

confidence: 67%

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Microscopic Dynamics of Supercooled Liquids from First Principles

2015

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The transition from a liquid to a glass remains one of the most poorly understood phenomena in condensed matter physics, and still no fully microscopic theory exists that can describe the dynamics of supercooled liquids in a quantitative manner over all relevant time scales. Here we present a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a glass-forming system over a broad density range. Our approach requires only simple static structural information as input and is based entirely on first principles. Owing to its ab initio nature, the framework offers a unique platform to study the relation between structure and dynamics in glass-forming matter, and paves the way towards a systematically correctable and ultimately fully quantitative theory of microscopic glassy dynamics.

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“…Standard MCT predicts a diverging relaxation time above ϕ MCT c ¼ 0.566 [29], as seen in our N ¼ 2 results in Figs. 1(c) and 1(d).…”

supporting

confidence: 82%

supporting

confidence: 67%

Microscopic Dynamics of Supercooled Liquids from First Principles

2015

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“…We also compare with numerical data obtained in [87] using Molecular Dynamics (MD) for a polydisperse system of hard spheres. The agreement of our results with MCT and with numerics is rather good, although the VW approximation at ϕ d gives more pronounced oscillations with in particular a lower value of f (q) at the local minima.…”

Section: Three Dimensional Results: Non-ergodicity Factormentioning

confidence: 97%

“…MCT results using the PY structure for the liquid at ϕ = ϕ PY MCT = 0.516 [86] are reported as a red long-dashed line. Numerical results from MD [87] for polydisperse hard spheres at ϕ = 0.585, which is estimated to be close to ϕ d for this system, are reported as a blue dashed line.…”

Section: B Three Dimensional Results: Thermodynamicsmentioning

confidence: 99%

Quantitative approximation schemes for glasses

Mangeat

Zamponi

2016

Phys. Rev. E

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By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode-Coupling approximation scheme. Our scheme becomes exact, by construction, in dimension d → ∞ and it can be improved systematically by adding more terms in the expansion. ContentsI. Introduction A. The exact solution of infinite-dimensional glassy hard spheres B. Extension to finite dimension: state of the art C. Aim and structure of this paper II. Derivation of the equations A. The variational problem B. "Small cage" expansion C. Determination of G(r), and the final set of equations D. Discussion III. Connections with previous work A. Mézard-Parisi 1999 B. Parisi-Zamponi 2005 C. Berthier-Jacquin-Zamponi 2011 IV. Extracting physical quantities from the replicated free energy A. A convenient expression of q m,A (r) B. The equation for A and the complexity C. The equilibrium transition densities: dynamical transition and Kauzmann transition D. The jamming line E. Correlation functions and non-ergodicity factor V. Numerical methods A. Integral equations of liquid theory B. Discrete Fourier transformation C. Algorithm for g liq D. More accurate expressions for three-dimensional hard spheres E. Non-ergodicity factor F. Summary VI. Results: hard spheres A. HNC and PY results as a function of dimension B. Three dimensional results: thermodynamics C. Three dimensional results: non-ergodicity factor VII. Conclusions2. The dynamical transition density [8,12], at which the liquid phase becomes infinitely viscous and ergodicity is broken by the emergence of many metastable states. This transition is similar to the one of Mode-Coupling Theory (MCT) [23] and is thus characterized by MCT critical dynamical scaling, controlled by the so-called MCT parameter λ that can be also computed [8,12]. The Kauzmann transition [6], where the number of metastable states becomes sub-exponential, giving rise to an "entropy crisis" and a second order equilibrium phase transition.4. The Gardner transition line, that separates a region where glass basins are stable from a region where they are broken in a complex structure of metabasins [8,10,11].5. The density region where jammed packings exist (also known as "jamming line" or "J-line" [6,24,25]), which is delimited by the threshold density and the glass close packing density [6].6. The equation of state of glassy states, computed by compression and decompression of equilibrium glasses [11].7. The response of the glass state to a shear strain [11,26]. 8. The long time limit of the mean square displacement in the glass (the so-called Edwards-Anderson order parameter) [9]. 9. The behavior of correlation function, structural g(r) and non-ergodicity factor of the glass [6,9,12].10. The probability distribution of the for...

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“…with Brownian dynamics the description by an effective monodisperse system breaks down in the q→0 limit. 55 In many cases, for example in liquid Ni-Zr alloy 56 and a binary Lennard-Jones system, 57 the self-diffusion coefficients for the two species vary in parallel with changing temperature.…”

Section: A Mean Square Displacement (Msd) and Diffusion Coefficientmentioning

confidence: 99%

Transport properties and Stokes-Einstein relation in a computer-simulated glass-forming Cu33.3Zr66.7

Han

Schober

2011

Phys. Rev. B

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Molecular dynamics simulation with a modified embedded atom potential was used to study transport properties and the Stokes-Einstein relation of a glass-forming Cu 33.3 Zr 66.7 metallic melt. Upon cooling, at high temperatures, the self-diffusion coefficients of the two species evolve nearly parallel, whereas they diverge below 1600K. The viscosity as function of temperature is calculated from the Green-Kubo equation. The critical temperature of mode coupling theory, T c , is found as 1030K, both, from the transport properties and the α-relaxation time. It is found that the Stokes-Einstein relation between viscosity and diffusivity breaks down at around 1600K, far above T c and even above the melting temperature. The temperature dependence of the effective diameter in the Stokes-Einstein relation correlates closely with the first derivative of the ratio of the self-diffusion coefficients of the two components. We propose that the onset of Stokes-Einstein relation breakdown could be predicted quantitatively by the divergence behavior of diffusion coefficients, and the breakdown of Stokes-Einstein relation is ascribed to the sudden increase of the dynamics heterogeneity.

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Structural relaxation of polydisperse hard spheres: Comparison of the mode-coupling theory to a Langevin dynamics simulation

Cited by 111 publications

References 69 publications

Microscopic Dynamics of Supercooled Liquids from First Principles

Microscopic Dynamics of Supercooled Liquids from First Principles

Quantitative approximation schemes for glasses

Transport properties and Stokes-Einstein relation in a computer-simulated glass-forming Cu33.3Zr66.7

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