Primary relaxation in a hard-sphere system

Fuchs, Matthias; Hofacker, Ivo L.; Latz, Arnulf

doi:10.1103/physreva.45.898

Cited by 162 publications

(202 citation statements)

References 44 publications

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“…The studies for the hard sphere colloids [29] have shown that the data are in agreement with equation (14), where the predicted HSS-master-functionsφ q [58] were used. In addition, it was demonstrated [29] that the small-t corrections to the leading-order result (14) agreed with the terms expected from the β-process.…”

Section: The Second Scaling Law and Kohlrausch's Lawsupporting

confidence: 67%

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The Essentials of the Mode-Coupling Theory for Glassy Dynamics

Gotze¹

1998

Condens. Matter Phys.

101

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The essential results of the mode-coupling theory for the evolution of structural relaxation in simple liquids such as the Debye-Waller-factor anomaly, the critical decay, von Schweidler's law, the α -and β -relaxation scaling, the appearance of two divergent time scales, and Kohlrausch's law for the α -process are explained, and their relevance to the understanding of experiments in glass-forming systems is described. : 64.70.Pf, 61.20.Lc In memoriam: I first met Dmitrii Nikolaevich Zubarev in 1969, when I came to Moscow to work with his team at the Steklov-Institute. Since then we met regularly. I always enjoyed discussing with him many open problems in statistical physics and I learned a lot from his unbiased and well contemplated views on various issues. I like to remember his gentleness, his warm hospitality, and the conversations with him on non-scientific matters. I dedicate this article to the memory of Dmitrii Nikolaevich with gratitude. Key words: mode-coupling theory, structural relaxation, glassy dynamics, bifurcation dynamics PACS

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Section: The Second Scaling Law and Kohlrausch's Lawsupporting

confidence: 67%

“…It is also shown there that rather simple schematic models produce master spectra in perfect agreement with the presented experimental findings. A detailed discussion of the theoretical α-relaxation master functions for the HSS is presented in [58].…”

Section: The Second Scaling Law and Kohlrausch's Lawmentioning

confidence: 99%

The Essentials of the Mode-Coupling Theory for Glassy Dynamics

Gotze¹

1998

Condens. Matter Phys.

101

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“…Then h q s presents a maximum at qa ≈ 12, whereas h q oscillates at low wavevectors and coincides with h q s for large q. Contrary to f q , the oscillations in the amplitude h q are out of phase with respect to S(q), as predicted by MCT for other systems 36 (forming repulsive glasses).…”

Section: Resultsmentioning

confidence: 72%

Mode Coupling and Dynamical Heterogeneity in Colloidal Gelation: A Simulation Study

2005

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We present simulation results addressing the dynamics of a colloidal system with attractive interactions close to gelation. Our interaction also has a soft, long-range repulsive barrier that suppresses liquid-gas type phase separation at long wavelengths. The new results presented here lend further weight to an intriguing picture emerging from our previous simulation work on the same system. Whereas mode coupling theory (MCT) offers quantitatively good results for the decay of correlators, closer inspection of the dynamics reveals a bimodal population of fast and slow particles with a very long exchange time scale. This population split represents a particular form of dynamic heterogeneity (DH). Although DH is usually associated with activated hopping and/or facilitated dynamics in glasses, the form of DH observed here may be more collective in character and associated with static (i.e., structural) heterogeneity.

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“…Note, however, that the de Gennes narrowing is a phenomenon observed at short times and thus cannot be used to explain the τ (q) dependence on the time scale of the α-relaxation. Finally we mention that this type of dependence has also been found in a MCT calculation for a hard sphere system [28] and recently in a neutron scattering experiment of Toluene and m-Toluidine [41].…”

Section: Resultsmentioning

confidence: 97%

Relaxation dynamics of a viscous silica melt: The intermediate scattering functions

2001

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We use molecular dynamics computer simulations to study the relaxation dynamics of a viscous melt of silica. The coherent and incoherent intermediate scattering functions, F d (q, t) and F s (q, t), show a crossover from a nearly exponential decay at high temperatures to a two-step relaxation at low temperatures. Close to the critical temperature of mode-coupling theory (MCT) the correlators obey in the α-regime the time temperature superposition principle (TTSP) and show a weak stretching. We determine the wave-vector dependence of the stretching parameter and find that for F d (q, t) it shows oscillations which are in phase with the static structure factor. The temperature dependence of the α-relaxation times τ shows a crossover from an Arrhenius law at low temperatures to a weaker T -dependence at intermediate and high temperatures. At the latter temperatures the T -dependence is described well by the power law proposed by MCT with the same critical temperature that has previously been found for the diffusion constant D and the viscosity. We find that the exponent γ of the power law for τ are significantly larger than the one for D. The wave-vector dependence of the α-relaxation times for F d (q, t) oscillates around τ (q) for F s (q, t) and is in phase with the structure factor. Due to the strong vibrational component of the dynamics at short times the TTSP is not valid in the β-relaxation regime. We show, however, that in this time window the shape of the curves is independent of the correlator and is given by a functional form proposed by MCT. We find that the value of the von Schweidler exponent and the value of γ for finite q are compatible with the expression proposed by MCT. Finally we discuss the q-dependence of the critical amplitude and the correction term and find that they are qualitatively similar to the ones for simple liquids and the prediction of MCT. We conclude that, in the temperature regime where the relaxation times are mesoscopic, many aspects of the dynamics of this strong glass former can be rationalized very well by MCT.

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Primary relaxation in a hard-sphere system

Cited by 162 publications

References 44 publications

The Essentials of the Mode-Coupling Theory for Glassy Dynamics

The Essentials of the Mode-Coupling Theory for Glassy Dynamics

Mode Coupling and Dynamical Heterogeneity in Colloidal Gelation: A Simulation Study

Relaxation dynamics of a viscous silica melt: The intermediate scattering functions

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