Résumé:

The competition between order and disorder in dense states of matter (liquids, crystals, glasses) is one of the most fascinating aspects of statistical physics. The microscopic mechanisms that allow us to transform some liquids into glass with ease, while others crystallize quickly when cooled or compressed, are subtle and still remain poorly understood. To try to understand how the collective behavior of these systems emerges from the interactions between the atoms, physicists often build on simple theoretical models, whose prototype is a system of purely repulsive hard spheres. These models, which were introduced during the second half of the twentieth century, have recently found important applications in glass transition studies, soft matter modeling, as well as in packing problems. The generalization to different spatial dimensions - from the Euclidean plane to the infinite dimensional limit - brings additional insight into which microscopic features stabilize disordered phases of matter and into the interplay between structure and dynamics. In reviewing these recent advances, I will emphasize the crucial role of numerical simulations, which help interpreting the experiments and provide stringent tests of theoretical models. I will discuss how to exploit powerful yet cheap architectures, such as graphics cards, and efficient algorithms to dramatically accelerate the sampling of configurational space.

Ref HAL: hal-01218876_v1
Ref Arxiv: 1504.06221
DOI: 10.1080/00268976.2015.1039089
WoS: 000362544000038
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6 Citations
Résumé:

We perform Monte-Carlo simulations to analyse the structure and microscopic dynamics of a viscous Lennard-Jones liquid coupled to a quenched reference configuration of the same liquid. The coupling between the two replicas is introduced via a field epsilon conjugate to the overlap Q between the two particle configurations. This allows us to study the evolution of various static and dynamic correlation functions across the (epsilon, T) equilibrium phase diagram. As the temperature is decreased, we identify increasingly marked precursors of a first-order phase transition between a low-Q and a high-Q phase induced by the field epsilon. We show in particular that both static and dynamic susceptibilities have a maximum at a temperature-dependent value of the coupling field, which defines a `Widom line'. We also show that, in the high-overlap regime, diffusion and structural relaxation are strongly decoupled because single particle motion mostly occurs via discrete hopping on the sites defined by the reference configuration. These results, obtained using conventional numerical tools, provide encouraging signs that an equilibrium phase transition exists in coupled viscous liquids, but also demonstrate that important numerical challenges must be overcome to obtain more conclusive numerical evidence.

Commentaires: 14 pages, 8 figures. Accepted for publication in Molecular Physics (Special Issue in honour of J.-P. Hansen). Réf Journal: Mol. Physics 113, 2707 (2015)

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Résumé:

The dynamics of glass-forming liquids is heterogeneous and displays growing spatial correlations upon cooling. Whether such behavior arises from heterogeneities in the local structure or more complex forms of amorphous order is a highly debated question. To clarify this issue, we study several model liquids within a coherent simulation framework based on the iso-configurational ensemble. We find that the correlation between the preferred local structure and the propensity of motion is pronounced in systems that deviate markedly from the mean-field picture of glassy dynamics and weak in models that adhere to it to a good extent. We conclude that the degree to which structural correlations affect the dynamics around the dynamic crossover is, in general, system-dependent.

Ref HAL: hal-01158440_v1
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PMID 25679615
Ref Arxiv: 1410.5683
DOI: 10.1103/PhysRevE.91.012203
WoS: 000348681000006
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49 Citations
Résumé:

We use large scale computer simulations and finite size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size, and study carefully the asymptotic limits of large system sizes and infinitely hard particle repulsion. Extending earlier analysis by about two orders of magnitude, we first study the asymptotic behavior of the shear viscosity in the hard particle limit. We confirm its asymptotic power law divergence at the jamming transition, but show that a precise determination of the critical density and critical exponent is difficult due to the `multiscaling' behavior of the viscosity. Additionally, finite-size scaling analysis suggests that this divergence is accompanied by a growing correlation length scale, which also diverges algebraically. We then study the effect of soft repulsion, and propose a natural extension of the standard granular rheology to account for softness effects, which we validate from simulations. Close to the jamming transition, this `soft granular rheology' offers a detailed description of the non-linear rheology of soft particles, which differs from earlier empirical scaling forms.

Commentaires: 12 pages, 9 figs. Réf Journal: Phys. Rev. E 91, 012203 (2015)

Ref HAL: hal-01114308_v1
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Résumé:

The dynamics of glass-forming liquids is heterogeneous and displays growing spatial correlations upon cooling. Whether such behavior arises from heterogeneities in local structure or more complex forms of amorphous order is a highly debated question. To clarify this issue, we study several model liquids within a coherent simulation framework based on the iso-configurational ensemble. We find that the correlation between the preferred local structure and dynamic heterogeneity is strongly system dependent. The correlation is pronounced in systems that deviate markedly from the mean-field picture of glassy dynamics and weak in models that adhere to it to a good extent. In the model that adheres best to the mean-field paradigm, namely a dense fluid of Gaussian particles, than nature of dynamic heterogeneity differs strikingly from the other liquids: on approaching the mode Coupling critical temperature the fluid develops giant dynamic fluctuations accompanied by nearly Gaussian single-particle dynamics. The observed differences between the models are qualitatively explained in terms of their potential energy landscapes.

Ref HAL: hal-01101053_v1
PMID 25493794
Ref Arxiv: 1403.3519
DOI: 10.1103/PhysRevE.90.052305
WoS: 000345539100004
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26 Citations
Résumé:

We use large scale computer simulations of a glass-forming liquid in which a fraction c of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on c. This result can be rationalized by assuming that the configurational entropy of the pinned liquid decreases linearly upon increasing of c. This behavior is discussed in the context of thermodynamic theories for the glass transition, notably the Adam-Gibbs picture and the random first order transition theory. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing c, results which indicate that in glass-forming liquids there is a dynamic crossover at which the shape of the relaxing entities changes.