We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behaviors found in amorphous materials does not necessarily result from the diversity of particle interactions or microscopic dynamics but is instead unified by carefully considering the role of the initial stability of the system.

We implement and optimize a particle-swap Monte-Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly-large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct non-equilibrium protocols. We demonstrate that equilibrium fluid and non-equilibrium jammed states can have the same density, showing that the jamming transition cannot be the end-point of the fluid branch.PACS numbers: 05.20.Jj,We clarify the behavior of non-crystalline states of hard spheres at very large densities where both a glass transition (in colloidal systems) and a jamming transition (in non-Brownian systems) are observed [1][2][3]. Glass and jamming transitions are usually studied through distinct protocols, and understanding the relation between these two broad classes of phase transformations and the resulting amorphous arrested states is an important research goal [1][2][3][4][5]. These questions impact a wide range of fields, from the rheological properties of soft materials to optimization problems in computer science [1,6].Let us first consider Brownian hard spheres. When size polydispersity is introduced, crystallization can be prevented and the thermodynamic properties of the fluid studied at increasing density until a glass transition takes place, where particle diffusivity becomes very small [7]. Upon further compression, the pressure of the glass increases until a jamming transition occurs, where particles come at close contact and the pressure diverges [8]. Because the laboratory glass transition arises from using a finite observation timescale, two scenarios were proposed to describe the hypothetical situation where thermalization is no longer an issue [9]. A first possibility is that slower compressions reveal an ideal glass transition density, ϕ 0 , above which the equilibrium state is a glass, not a fluid [2]. Jamming would then be observed upon further non-equilibrium compression of these glass states [10]. Alternatively, it may be that slower compressions continuously shift the kinetic glass transition to higher densities. In this view, it is plausible that jamming becomes the end-point of the equilibrium fluid branch [11,12].Distinguishing between these two scenarios by direct numerical measurements is challenging. For a wellstudied binary mixture of hard spheres, for instance, thermalization can be achieved up to ϕ max ≈ 0.60 [9,13]. The location of the glass transition must be extrapolated using empirical fits based on activated relaxation. Values in the range ϕ 0 = 0.615 − 0.635 were obtained [9], depending on the fitting function. Fitting the relaxation times to a power law yields ϕ mct ≈ 0.59 < ϕ max , so that the associated mode-coupling transition [14] corresponds to an avoided singularity. For the same system, jamming transitions were located in the range ϕ J = 0.648 − 0.662 depending on the chosen protocol [15][1...

Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, because of 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 observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

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We use computer simulations to study the thermodynamic properties of a glass-former in which a fraction c of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature T K (c) at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, i.e., T K (c) is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, i.e., the order parameter that signals the glass state. We find that the transition line obtained from the overlap coincides with that obtained from the thermodynamic integration, thus showing that the two approaches give the same transition line. Finally, we determine the geometrical properties of the potential energy landscape, notably the T-and c dependence of the saddle index, and use these properties to obtain the dynamic transition temperature T d (c). The two temperatures T K (c) and T d (c) cross at a finite value of c and indicate the point at which the glass transition line ends. These findings are qualitatively consistent with the scenario proposed by the random first-order transition theory.ideal glass transition | computer simulations | random first-order transition theory | Kauzmann temperature | configurational entropy U pon cooling, glass-forming liquids show a dramatic increase of their viscosities and relaxation times before they eventually fall out of equilibrium at low temperatures (1, 2). This laboratory glass transition is a purely kinetic effect because it occurs at the temperature at which the relaxation time of the system crosses the time scale imposed by the experiment, e.g., via the cooling rate. Despite the intensive theoretical, numerical, and experimental studies of the last five decades, the mechanism responsible for the slowing down and thus for the (kinetic) glass transition is still under debate and hence a topic of intense research. From a fundamental point of view the ultimate goal of these studies is to find an answer to the big question in the field: Does a finite temperature exist at which the dynamics truly freezes and, if so, is this ideal glass transition associated with a thermodynamic singularity or is it of kinetic origin (3-6)?Support for the existence of a kinetic transition comes from certain lattice gas models with a "facilitated dynamics" (6). In these models, the dynamics is due to the presence of "defects" and hence for such systems the freezing is not related to any thermodynamic singularity. However, the first evidence that there does indeed exist a thermodynamic singularity goes back to Kauzmann, who found that the residual entropy (the difference of the entropy of the liquid state from that of the crystalline state) vanishes at a finite temperature T K if it is extrapolated to temperatures below the laboratory glass transition (7). Subsequently many theoretical scenarios that invoke the presence of a thermodynamic transition have been proposed (8-10). One of these is the so-called ...

Recent studies show that volume fractions φ(J) at the jamming transition of frictionless hard spheres and disks are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate the dependence of φ(J) on the initial configurations of the parent fluid equilibrated at a volume fraction φ(eq), before compressing to generate a jammed packing. We find that φ(J) remains constant when φ(eq) is small but sharply increases as φ(eq) exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of φ(J) is accompanied with subtle but distinct changes of local orders, a static length scale, and an exponent of the finite-size scaling. These results are consistent with the scenario of the random first-order transition theory of the glass transition.

Liquids cooled towards the glass transition temperature transform into amorphous solids that have a wide range of applications. While the nature of this transformation is understood rigorously in the mean-field limit of infinite spatial dimensions, the problem remains wide open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we develop Monte Carlo methods for two-dimensional glass-forming liquids that allow us to access equilibrium states at sufficiently low temperatures to directly probe the glass transition in a regime inaccessible to experiments. We find that the liquid state terminates at a thermodynamic glass transition which occurs at zero temperature and is associated with an entropy crisis and a diverging static correlation length. Our results thus demonstrate that a thermodynamic glass transition can occur in finite dimensional glass-formers.