The Essentials of the Mode-Coupling Theory for Glassy Dynamics

Gotze,

doi:10.5488/cmp.1.4.873

Cited by 76 publications

(104 citation statements)

References 68 publications

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“…In this theory, developed to elucidate the properties related to the glass transition phenomenon (Gotze 1998), the key role is played by the imaginary part of the dynamic susceptibility, which is related to the dynamic structure factor via the fluctuation dissipation theorem x 00 (q,v)¼p S(q,v)/(n(v)þ1) (Lovesey 1986), where n(v) is the Bose factor. In this representation, the quasi-elastic scattering is composed of two terms: the fast local motions (b relaxation) of particles caged in a heat bath of nearest neighbours and the slow collective motions (a relaxation) arising from the rearrangement of the cages.…”

Section: Resultsmentioning

confidence: 99%

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Coupled relaxations at the protein–water interface in the picosecond time scale

Paciaroni

Cornicchi

Marconi

et al. 2009

J. R. Soc. Interface.

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The spectral behaviour of a protein and its hydration water has been investigated through neutron scattering. The availability of both hydrogenated and perdeuterated samples of maltose-binding protein (MBP) allowed us to directly measure with great accuracy the signal from the protein and the hydration water alone. Both the spectra of the MBP and its hydration water show two distinct relaxations, a behaviour that is reminiscent of glassy systems. The two components have been described using a phenomenological model that includes two Cole -Davidson functions. In MBP and its hydration water, the two relaxations take place with similar average characteristic times of approximately 10 and 0.2 ps. The common time scales of these relaxations suggest that they may be a preferential route to couple the dynamics of the water hydrogen-bond network around the protein surface with that of protein fluctuations.

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Section: Resultsmentioning

confidence: 99%

“…The two relaxations we mentioned above can be represented in an alternative way as the sum of two power-law components, respectively, also called Von Schweidler and critical decays (Gotze 1998): S638 Coupled relaxations at the protein -water interface A. Paciaroni et al…”

Section: ð3:1þmentioning

confidence: 99%

Coupled relaxations at the protein–water interface in the picosecond time scale

Paciaroni

Cornicchi

Marconi

et al. 2009

J. R. Soc. Interface.

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“…Mode Coupling Theory 16,17,18 is perhaps the most successful theoretical approach to the dynamics of the supercooled liquid state. It predicts the existence of relevant regimes for relaxation, like the beta and alpha relaxations, and make quantitative predictions for temperatures above the glass transition.…”

Section: Introductionmentioning

confidence: 99%

Fickian crossover and length scales from two point functions in supercooled liquids

Stariolo

Fabricius

2006

The Journal of Chemical Physics

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Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The lengthscale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characterisitic timescale is several times larger than the alpha relaxation time. A second crossover lengthscale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back in the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.

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“…From a theoretical point of view, our understanding of supercooled liquids owes much to the Mode-Coupling Theory (MCT) of the glass transition. Although approximate in nature, MCT has achieved many qualitative and quantitative successes in explaining various experimental and numerical results [11,12]. In spite of early insights [13], the freezing predicted by MCT was repeatedly argued to be a small scale caging phenomenon, without any diverging collective length scale.…”

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confidence: 99%

Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids

et al. 2006

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We extend Mode-Coupling Theory (MCT) to inhomogeneous situations, relevant for supercooled liquid in pores, close to a surface, or in an external field. We compute the response of the dynamical structure factor to a static inhomogeneous external potential and provide the first direct evidence that the standard formulation of MCT is associated with a diverging length scale. We find in particular that the so called "cages" are in fact extended objects. Although close to the transition the dynamic length grows as |T − Tc| −1/4 in both the β and α regimes, our results suggest that the fractal dimension of correlated clusters is larger in the α regime. We also derive inhomogeneous MCT equations valid to second order in gradients.It is becoming increasingly clear that the viscous slowing down of supercooled liquids, jammed colloids or granular assemblies is accompanied by a growing dynamic length scale, whereas all static correlation functions remain short-ranged. This somewhat unusual scenario, suggested by the experimental discovery of strong dynamical heterogeneities in glass-formers [1], has been substantiated by detailed numerical simulations [2,3,4,5,6], explicit solution of simplified models [9,10] and very recent direct experiments [7,8] where four-point spatiotemporal correlators are measured. From a theoretical point of view, our understanding of supercooled liquids owes much to the Mode-Coupling Theory (MCT) of the glass transition. Although approximate in nature, MCT has achieved many qualitative and quantitative successes in explaining various experimental and numerical results [11,12]. In spite of early insights [13], the freezing predicted by MCT was repeatedly argued to be a small scale caging phenomenon, without any diverging collective length scale. This, however, is rather surprising from a physical point of view, since one expects on general grounds that a diverging relaxation time should involve an infinite number of particles [15]. Building upon the important work of Franz and Parisi [14], two of us (BB) [16] suggested a way to reconcile MCT with physical intuition. Within a field theory formulation of MCT, BB showed that the four-point density correlation function is given by the so-called 'ladder' diagrams that indeed lead, upon resummation, to a diverging dynamical correlation length and spatio-temporal scaling laws. BB also proposed a Ginzburg criterion that delineates the region of validity of MCT, which breaks down in low dimensions. Still, the field theory language used in [16] is not trivially related to the standard, liquid theory formulation of MCT [11]. Indeed recent work has shown that the field theory is laden with subtleties [17,18,19], in particular related to the Fluctuation-Dissipation relation. The aim of the present letter is twofold. First, we show how the results of BB may be recovered and extended to obtain testable, quantitative predictions on absolute dynamic length scales, entirely within via the standard, projection-operator based MCT [11]. Our detailed analysis predicts...

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The Essentials of the Mode-Coupling Theory for Glassy Dynamics

Cited by 76 publications

References 68 publications

Coupled relaxations at the protein–water interface in the picosecond time scale

Coupled relaxations at the protein–water interface in the picosecond time scale

Fickian crossover and length scales from two point functions in supercooled liquids

Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids

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