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Computer simulations give precious insight into the microscopic behavior of supercooled liquids and glasses, but their typical time scales are orders of magnitude shorter than the experimentally relevant ones. We recently closed this gap for a class of models of size polydisperse fluids, which we successfully equilibrate beyond laboratory time scales by means of the swap Monte Carlo algorithm. In this contribution, we study the interplay between compositional and geometric local orders in a model of polydisperse hard spheres equilibrated with this algorithm. Local compositional order has a weak state dependence, while local geometric order associated to icosahedral arrangements grows more markedly but only at very high density. We quantify the correlation lengths and the degree of sphericity associated to icosahedral structures and compare these results to those for the Wahnström Lennard-Jones mixture. Finally, we analyze the structure of very dense samples that partially crystallized following a pattern incompatible with conventional fractionation scenarios. The crystal structure has the symmetry of aluminum diboride and involves a subset of small and large particles with size ratio approximately equal to 0.5.

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We numerically study the jamming transition of frictionless polydisperse spheres in three dimensions. We use an efficient thermalisation algorithm for the equilibrium hard sphere fluid and generate amorphous jammed packings over a range of critical jamming densities that is about three times broader than in previous studies. This allows us to reexamine a wide range of structural properties characterizing the jamming transition. Both isostaticity and the critical behavior of the pair correlation function hold over the entire range of jamming densities. At intermediate length scales, we find a weak, smooth increase of bond orientational order. By contrast, distorted icosahedral structures grow rapidly with increasing the volume fraction in both fluid and jammed states. Surprisingly, at large scale we observe that denser jammed states show stronger deviations from hyperuniformity, suggesting that the enhanced amorphous ordering inherited from the equilibrium fluid competes with, rather than enhances, hyperuniformity. Finally, finite size fluctuations of the critical jamming density are considerably suppressed in the denser jammed states, indicating an important change in the topography of the potential energy landscape. By considerably stretching the amplitude of the critical "J-line", our work disentangles physical properties at the contact scale that are associated with jamming criticality, from those occurring at larger length scales, which have a different nature.

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Liquids relax extremely slowly upon approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally-relevant timescales. In this work we not only close the colossal gap between experiments and simulations but manage to create in-silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the new observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

Commentaires: 4+23 pages, 3+12 figures; v2: final version, with various changes made. Data relevant to this work can be accessed at http://dx.doi.org/10.7924/G8ZG6Q9T. Réf Journal: PNAS 114, 11356-11361 (2017)

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Computer simulations give precious insight into the microscopic behavior of disordered and amorphous materials, but their typical time scales are orders of magnitude shorter than the experimentally relevant ones. In particular, simulations of supercooled liquids cover at most 4-5 decades of viscous slowing down, which falls far short of the 13 decades commonly accessible in experimental studies. We close this enormous gap for a class of realistic models of liquids, which we successfully equilibrate beyond laboratory time scales by means of the swap Monte Carlo algorithm. We show that combined optimization of selected features of the interaction potential, such as particle softness, polydispersity and non-additivity, leads to computer models with excellent glass-forming ability. For such models, we achieve over 10 orders of magnitude speedup in equilibration time scale. This numerical advance allows us to address some outstanding questions concerning glass formation, such as the role of local structure and the relevance of an entropy crisis, in a dynamical range that remains inaccessible in experiments. Our results support the view that non-trivial static correlations continue to build up steadily in supercooled liquids even below the laboratory glass temperature.

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Successful computer studies of glass-forming materials need to overcome both the natural tendency to structural ordering and the dramatic increase of relaxation times at low temperatures. We present a comprehensive analysis of eleven glass-forming models to demonstrate that both challenges can be efficiently tackled using carefully designed models of size polydisperse supercooled liquids together with an efficient Monte Carlo algorithm where translational particle displacements are complemented by swaps of particle pairs. We study a broad range of size polydispersities, using both discrete and continuous mixtures, and we systematically investigate the role of particle softness, attractivity and non-additivity of the interactions. Each system is characterized by its robustness against structural ordering and by the efficiency of the swap Monte Carlo algorithm. We show that the combined optimisation of the potential's softness, polydispersity and non-additivity leads to novel computer models with excellent glass-forming ability. For such models, we achieve over ten orders of magnitude gain in the equilibration timescale using the swap Monte Carlo algorithm, thus paving the way to computational studies of static and thermodynamic properties under experimental conditions. In addition, we provide microscopic insights into the performance of the swap algorithm which should help optimizing models and algorithms even further.