Probing a liquid to glass transition in equilibrium

Static lengths in glass-forming monodisperse hard-sphere fluids from periodic array pinning

We explore the static length in glass-forming hard-sphere liquids revealed by the response of dynamical properties (diffusion coefficient D and α relaxation time τα) to a regular array of pinned particles. By assuming a universal scaling form, we find data can be excellently collapsed onto a master curve, from which relative length scales can be extracted. By exploiting a crystal-avoiding simulation method that suppresses crystallization while preserving dynamics, we can study monodisperse as well as polydisperse systems. The static length obtained from dynamical property Q (τα and D) scales as log Q ∼ ξ, with ψ ≈ 1.

Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics

We consider thermodynamic and dynamic phase transitions in plaquette spin models of glasses. The thermodynamic transitions involve coupled (annealed) replicas of the model. We map these coupled-replica systems to a single replica in a magnetic field, which allows us to analyze the resulting phase transitions in detail. For the triangular plaquette model (TPM), we find for the coupled-replica system a phase transition between high- and low-overlap phases, occurring at a coupling ɛ*(T), which vanishes in the low-temperature limit. Using computational path sampling techniques, we show that a single TPM also displays "space-time" transitions between active and inactive dynamical phases. These first-order dynamical transitions occur at a critical counting field sc(T)≳0 that appears to vanish at zero temperature in a manner reminiscent of the thermodynamic overlap transition. In order to extend the ideas to three dimensions, we introduce the square pyramid model, which also displays both overlap and activity transitions. We discuss a possible common origin of these various phase transitions, based on long-lived (metastable) glassy states.

Dynamics of Glass Forming Liquids with Randomly Pinned Particles

It is frequently assumed that in the limit of vanishing cooling rate, the glass transition phenomenon becomes a thermodynamic transition at a temperature T_K. However, with any finite cooling rate, the system falls out of equilibrium at temperatures near T_g(>T_K), implying that the very existence of the putative thermodynamic phase transition at T_K can be questioned. Recent studies of systems with randomly pinned particles have hinted that the thermodynamic glass transition may be observed for liquids with randomly pinned particles. This expectation is based on the results of approximate calculations that suggest that the thermodynamic glass transition temperature increases with increasing concentration of pinned particles and it may be possible to equilibrate the system at temperatures near the increased transition temperature. We test the validity of this prediction through extensive molecular dynamics simulations of two model glass-forming liquids in the presence of random pinning. We find that extrapolated thermodynamic transition temperature T_K does not show any sign of increasing with increasing pinning concentration. The main effect of pinning is found to be a rapid decrease in the kinetic fragility of the system with increasing pin concentration. Implications of these observations for current theories of the glass transition are discussed.

Equilibrium phase diagram of a randomly pinned glass-former

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 [Formula: see text] at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, i.e., [Formula: see text] 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 [Formula: see text]. The two temperatures [Formula: see text] and [Formula: see text] 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.

Assessing the role of static length scales behind glassy dynamics in polydisperse hard disks

The possible role of growing static order in the dynamical slowing down toward the glass transition has recently attracted considerable attention. On the basis of random first-order transition theory, a new method to measure the static correlation length of amorphous order, called "point-to-set" (PTS) length, has been proposed and used to show that the dynamic length grows much faster than the static length. Here, we study the nature of the PTS length, using a polydisperse hard-disk system, which is a model that is known to exhibit a growing hexatic order upon densification. We show that the PTS correlation length is decoupled from the steeper increase of the correlation length of hexatic order and dynamic heterogeneity, while closely mirroring the decay length of two-body density correlations. Our results thus provide a clear example that other forms of order can play an important role in the slowing down of the dynamics, casting a serious doubt on the order-agnostic nature of the PTS length and its relevance to slow dynamics, provided that a polydisperse hard-disk system is a typical glass former.

Critical dynamical heterogeneities close to continuous second-order glass transitions

We analyze, using inhomogeneous mode-coupling theory, the critical scaling behavior of the dynamical susceptibility at a distance ε from continuous second-order glass transitions. We find that the dynamical correlation length ξ behaves generically as ε(-1/3) and that the upper critical dimension is equal to six. More surprisingly, we find that ξ grows with time as ln²t exactly at criticality. All of these results suggest a deep analogy between the glassy behavior of attractive colloids or randomly pinned supercooled liquids and that of the random field Ising model.

Nonlinear dynamic response of glass-forming liquids to random pinning

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.

Determination of dynamical parameters in liquids by homodyne transient grating spectroscopy at large angles

We report on the possibility of extracting fast dynamical relaxation times from homodyne transient grating measurements. We demonstrate the validity of our approach by experimental measurements on liquid acetonitrile and by comparison with literature. This approach would be of tremendous help in the case of free-electron-laser-based transient grating experiments due to the overcoming of technical difficulties, such as large-angle geometries.

Growing dynamical facilitation on approaching the random pinning colloidal glass transition

Despite decades of research, it remains to be established whether the transformation of a liquid into a glass is fundamentally thermodynamic or dynamic in origin. Although observations of growing length scales are consistent with thermodynamic perspectives, the purely dynamic approach of the Dynamical Facilitation (DF) theory lacks experimental support. Further, for vitrification induced by randomly freezing a subset of particles in the liquid phase, simulations support the existence of an underlying thermodynamic phase transition, whereas the DF theory remains unexplored. Here, using video microscopy and holographic optical tweezers, we show that DF in a colloidal glass-forming liquid grows with density as well as the fraction of pinned particles. In addition, we observe that heterogeneous dynamics in the form of string-like cooperative motion emerges naturally within the framework of facilitation. Our findings suggest that a deeper understanding of the glass transition necessitates an amalgamation of existing theoretical approaches.

Pressure-induced transformations in computer simulations of glassy water

Glassy water occurs in at least two broad categories: low-density amorphous (LDA) and high-density amorphous (HDA) solid water. We perform out-of-equilibrium molecular dynamics simulations to study the transformations of glassy water using the ST2 model. Specifically, we study the known (i) compression-induced LDA-to-HDA, (ii) decompression-induced HDA-to-LDA, and (iii) compression-induced hexagonal ice-to-HDA transformations. We study each transformation for a broad range of compression/decompression temperatures, enabling us to construct a "P-T phase diagram" for glassy water. The resulting phase diagram shows the same qualitative features reported from experiments. While many simulations have probed the liquid-state phase behavior, comparatively little work has examined the transitions of glassy water. We examine how the glass transformations relate to the (first-order) liquid-liquid phase transition previously reported for this model. Specifically, our results support the hypothesis that the liquid-liquid spinodal lines, between a low-density and high-density liquid, are extensions of the LDA-HDA transformation lines in the limit of slow compression. Extending decompression runs to negative pressures, we locate the sublimation lines for both LDA and hyperquenched glassy water (HGW), and find that HGW is relatively more stable to the vapor. Additionally, we observe spontaneous crystallization of HDA at high pressure to ice VII. Experiments have also seen crystallization of HDA, but to ice XII. Finally, we contrast the structure of LDA and HDA for the ST2 model with experiments. We find that while the radial distribution functions (RDFs) of LDA are similar to those observed in experiments, considerable differences exist between the HDA RDFs of ST2 water and experiment. The differences in HDA structure, as well as the formation of ice VII (a tetrahedral crystal), are a consequence of ST2 overemphasizing the tetrahedral character of water.

Investigating amorphous order in stable glasses by random pinning

We investigate stable glassy states that are found when glass-forming liquids are biased to lower than average dynamical activity. By pinning the positions of randomly chosen particles, we show that many-body correlations in these states are relatively strong and long ranged compared to equilibrium reference states. The presence of strong many-body correlations in these apparently disordered systems supports the idea that stable glassy states exhibit a kind of "amorphous order," which helps to explain their stability.

Crossovers in the dynamics of supercooled liquids probed by an amorphous wall

We study the relaxation dynamics of a binary Lennard-Jones liquid in the presence of an amorphous wall generated from equilibrium particle configurations. In qualitative agreement with the results presented by Kob et al. [Nat. Phys. 8, 164 (2012).] for a liquid of harmonic spheres, we find that our binary mixture shows a saturation of the dynamical length scale close to the mode-coupling temperature T(c). Furthermore we show that, due to the broken symmetry imposed by the wall, signatures of an additional change in dynamics become apparent at a temperature well above T(c). We provide evidence that this modification in the relaxation dynamics occurs at a recently proposed dynamical crossover temperature T(s) > T(c), which is related to the breakdown of the Stokes-Einstein relation. We find that this dynamical crossover at T(s) is also observed for the harmonic spheres as well as a WCA liquid, showing that it may be a general feature of glass-forming systems.

Geometric signatures of jamming in the mechanical vacuum

Jamming has traditionally been studied as a mechanical phenomenon and characterized with mechanical order parameters. However, this approach is not meaningful in the "mechanical vacuum" of systems below jamming in which all mechanical properties are precisely zero. We find that the network of nearest neighbors and the geometric structure of the Voronoi cell contain well-defined and meaningful order parameters for jamming, which exist on both sides of the transition. We observe critical exponents in these order parameters and an upper critical dimension of 3. Further, we present evidence for a new incipient-jamming phase below the jamming transition marked by additional symmetry in the Voronoi tessellation.

Counting metastable states in a kinetically constrained model using a patch repetition analysis

We analyze metastable states in the East model, using a recently proposed patch repetition analysis based on time-averaged density profiles. The results reveal a hierarchy of states of varying lifetimes, consistent with previous studies in which the metastable states were identified and used to explain the glassy dynamics of the model. We establish a mapping between these states and configurations of systems of hard rods, which allows us to analyze both typical and atypical metastable states. We discuss connections between the complexity of metastable states and large-deviation functions of dynamical quantities, both in the context of the East model and more generally in glassy systems.

Manifestation of random first-order transition theory in Wigner glasses

We use Brownian dynamics simulations of a binary mixture of highly charged spherical colloidal particles to test some of the predictions of the random first-order transition (RFOT) theory [Phys. Rev. Lett. 58, 2091 (1987); Phys. Rev. A 40, 1045 (1989)]. In accord with mode-coupling theory and RFOT, we find that as the volume fraction of the colloidal particles ϕ approaches the dynamical transition value ϕ(A), three measures of dynamics show an effective ergodic to nonergodic transition. First, there is a dramatic slowing down of diffusion, with the translational diffusion constant decaying as a power law as ϕ→ϕ(A)(-). Second, the energy metric, a measure of ergodicity breaking in classical many-body systems, shows that the system becomes effectively nonergodic as ϕ(A) is approached. Finally, the time t(*), at which the four-point dynamical susceptibility achieves a maximum, also increases as a power law near ϕ(A). Remarkably, the translational diffusion coefficients, ergodic diffusion coefficient, and (t(*))(-) all vanish as (ϕ(-1)-ϕ(A)(-1))(γ) with both ϕ(A)(≈0.1) and γ being the roughly the same for all three quantities. Above ϕ(A), transport involves crossing free energy barriers. In this regime, the density-density correlation function decays as a stretched exponential [exp-(t/τ(α))(β)] with β≈0.45. The ϕ dependence of the relaxation time τ(α) could be fit using the Vogel-Tamman-Fulcher law with the ideal glass transition at ϕ(K)≈0.47. By using a local entropy measure, we show that the law of large numbers is not obeyed above ϕ(A), and gives rise to subsample to subsample fluctuations in all physical observables. We propose that dynamical heterogeneity is a consequence of violation of law of large numbers.

Dynamical correlations in a glass former with randomly pinned particles

The effects of randomly pinning particles in a model glass-forming fluid are studied, with a focus on the dynamically heterogeneous relaxation in the presence of pinning. We show how four-point dynamical correlations can be analyzed in real space, allowing direct extraction of a length scale that characterizes dynamical heterogeneity. In the presence of pinning, the relaxation time of the glassy system increases by up to two decades, but there is almost no increase in either the four-point correlation length or the strength of the four-point correlations. We discuss the implications of these results for theories of the glass transition.

Overlap fluctuations in glass-forming liquids

We analyze numerically thermal fluctuations of the static overlap between equilibrium configurations in a glass-forming liquid approaching the glass transition. We find that the emergence of slow dynamics near the onset temperature correlates with the development of non-Gaussian probability distributions of overlap fluctuations, measured using both annealed and quenched definitions. Below a critical temperature, a thermodynamic field conjugate to the overlap induces a first-order phase transition, whose existence we numerically demonstrate in the annealed case. These results establish that the approach to the glass transition is accompanied by profound changes in the nature of thermodynamic fluctuations, deconstructing the view that glassy dynamics occurs with little structural evolution.