Is there a fractional breakdown of the Stokes-Einstein relation in kinetically constrained models at low temperature?

Blondel, Oriane; Toninelli, Cristina

doi:10.1209/0295-5075/107/26005

Cited by 11 publications

(15 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…D now scales as τ −ζ where ζ relates to the characteristic spatio-temporal lengthscales involved in the hetergeneous dynamics, and a typical value has been found to be of about 0.82−0.85 for different glass formers [432,442,443]. Here, ζ has been proposed to derive from temperature dependent scaling exponents of both diffusivity and relaxation time, respectively [444].…”

Section: Stokes-einstein Breakdownmentioning

confidence: 99%

Relaxation and physical aging in network glasses: a review

Micoulaut

2016

Rep. Prog. Phys.

View full text Add to dashboard Cite

Abstract. Recent progresses in the description of glassy relaxation and ageing are reviewed for the wide class of network-forming materials such as GeO 2 , Ge x Se 1−x , silicates (SiO 2 -Na 2 O) or borates (B 2 O 3 -Li 2 O), all of them having an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspect of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit to calculate various structure-related functions in connection with glassy relaxation and the physics of ageing which reveals the off-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the picture of "dynamic heterogeneities", and recent results of this important topic for network glasses are also reviewed.PACS numbers: 61.43. Fs, 64.70.kj Relaxation and physical ageing in network glasses 2 Figure 1. Typical network-forming glasses: a) A stoichiometric glass former (SiO 2 , B 2 S 3 ) whose structure and network connectivity can be altered by the addition (b) of 2-fold coordinated atoms (usually chalcogens, S, Se) that lead to cross-linked chains. The structure can also be depolymerized (c) by the addition of a network modifier (alkali oxides or chalcogenides, Na 2 O, Li 2 S, etc.). Glassy dynamics depends strongly on the network topology, i.e. the way bonds and angles arrange to lead to a connected atomic network. Note that only chalcogenides can produce a mixture of these three kinds of basic networks, e.g. (1-x)Ge y Se 1−y -xAg 2 Se [2], and for the latter system x=0 corresponds to case (b), y=33% corresponds to case (c), and both conditions together (x=0,y=33 %) to case (a).

show abstract

Section: Stokes-einstein Breakdownmentioning

confidence: 99%

Relaxation and physical aging in network glasses: a review

Micoulaut

2016

Rep. Prog. Phys.

View full text Add to dashboard Cite

show abstract

“…Diffusion of a probe particle in the East model was also studied rigorously in Ref. [10]. There it was found that in the limit very low temperature the inequality c 2 ≤ Dτ ≤ 1/c α holds, where α > 0 and c is the equilibrium concentration of excited sites, c = (1 + e 1/T ) −1 .…”

Section: Dimensional Dependence Of the Breakdown Of The Stokes-ementioning

confidence: 99%

Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation

Kim

Thorpe

Noh

et al. 2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

We investigate the dimensional dependence of dynamical fluctuations related to dynamic heterogeneity in supercooled liquid systems using kinetically constrained models. The d-dimensional spinfacilitated East model with embedded probe particles is used as a representative super-Arrhenius glass forming system. We investigate the existence of an upper critical dimension in this model by considering decoupling of transport rates through an effective fractional Stokes-Einstein relation, D ∼ τ −1+ω , with D and τ the diffusion constant of the probe particle and the relaxation time of the model liquid, respectively, and where ω > 0 encodes the breakdown of the standard Stokes-Einstein relation. To the extent that decoupling indicates non mean-field behavior, our simulations suggest that the East model has an upper critical dimension which is at least above d = 10, and argue that it may be actually be infinite. This result is due to the existence of hierarchical dynamics in the East model in any finite dimension. We discuss the relevance of these results for studies of decoupling in high dimensional atomistic models.

show abstract

“…When µ(η(0)) = 1/2, for ε small enough, the sign of the velocity can be read from (13). When µ(η(0)) = 1/2, the scenario is more subtle.…”

Section: 2mentioning

confidence: 99%

“…the ones considered in [24]. A further study of random walks in kinetically constrained models is given in [13].…”

Section: Introductionmentioning

confidence: 99%

A Class of Random Walks in Reversible Dynamic Environments: Antisymmetry and Applications to the East Model

2016

View full text Add to dashboard Cite

Abstract. We introduce via perturbation a class of random walks in reversible dynamic environments having a spectral gap. In this setting one can apply the mathematical results derived in [2]. As first results, we show that the asymptotic velocity is antisymmetric in the perturbative parameter and, for a subclass of random walks, we characterize the velocity and a stationary distribution of the environment seen from the walker as suitable series in the perturbative parameter. We then consider as a special case a random walk on the East model that tends to follow dynamical interfaces between empty and occupied regions. We study the asymptotic velocity and density profile for the environment seen from the walker. In particular, we determine the sign of the velocity when the density of the underlying East process is not 1/2, and we discuss the appearance of a drift in the balanced setting given by density 1/2.

show abstract

Is there a fractional breakdown of the Stokes-Einstein relation in kinetically constrained models at low temperature?

Cited by 11 publications

References 43 publications

Relaxation and physical aging in network glasses: a review

Relaxation and physical aging in network glasses: a review

Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation

A Class of Random Walks in Reversible Dynamic Environments: Antisymmetry and Applications to the East Model

Contact Info

Product

Resources

About