Below the onset temperature $T_\text{o}$, the equilibrium relaxation time of most glass-forming liquids exhibits glassy dynamics characterized by super-Arrhenius temperature dependence. In this supercooled regime, the relaxation dynamics also proceeds through localized elastic excitations corresponding to hopping events between inherent states, i.e., potential-energy minimizing configurations of the liquid. Despite its importance in distinguishing the supercooled regime from the high-temperature regime, the microscopic origin of $T_\text{o}$ is not yet known. Here, we construct a theory for the onset temperature in two dimensions and find that inherent-state melting transition, described by the binding-unbinding transition of dipolar elastic excitations, delineates the supercooled regime from the high-temperature regime. The corresponding melting transition temperature is in good agreement with the onset temperature found in various two-dimensional atomistic models of glass formers. We discuss the predictions of our theory on the displacement and density correlations of two-dimensional supercooled liquids, which are consistent with observations of the Mermin-Wagner fluctuations in recent experiments and molecular simulations.
In simulations of supercooled, high-density liquid silica we study a range of temperature T in which we find both crystal nucleation, as well as the characteristic dynamics of a glass forming liquid, including a breakdown of the Stokes-Einstein relation. We find that the liquid cannot be observed below a homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than it can equilibrate. We show that the HNL would occur at lower T, and perhaps not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy dynamics plays a central role in setting a crystallization…
We present a model for glassy dynamics in supercooled liquid mixtures. Given the relaxation behavior of individual supercooled liquids, the model predicts the relaxation times of their mixtures as temperature is decreased. The model is based on dynamical facilitation theory for glassy dynamics, which provides a physical basis for relaxation and vitrification of a supercooled liquid. This is in contrast to empirical linear interpolations such as the Gordon-Taylor equation typically used to predict glass transition temperatures of liquid mixtures. To understand the behavior of supercooled liquid…
We numerically investigate the metastable equilibrium structure of deep supercooled and glassy water under pressure, covering the range of densities corresponding to the experimentally produced high-density and very-high-density amorphous phases. At $T = 188$ K, a continuous increase in density is observed on varying pressure from $2.5$ to $13$ kbar, with no signs of first-order transitions. Exploiting a recently proposed approach to the analysis of the radial distribution function -- based on topological properties of the hydrogen-bond network -- we are able to identify well-defined local geo…
We use molecular simulation to study the structural and dynamic properties of glassy nanoclusters formed both through the direct condensation of the vapor below the glass transition temperature, without the presence of a substrate, and \textit{via} the slow supercooling of unsupported liquid nanodroplets. An analysis of local structure using Voronoi polyhedra shows that the energetic stability of the clusters is characterized by a large, increasing fraction of bicapped square antiprism motifs. We also show that nanoclusters with similar inherent structure energies are structurally similar, ind…
How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential energy landscape ensemble, it is possible to make direct connections between the geometry of the landscape and the long-time dynamical behaviors of systems such as supercooled liquids. We show, in particular, that the onset of slow dynamics in such systems is governed directly by the lengths of their geodesics - the shortest paths through their landscapes with…
There are deep analogies between the melting dynamics in systems with a first order phase transition and the dynamics from equilibrium in super-cooled liquids. For a class of Ising spin models undergoing a first order transition - namely p-spin models on the so-called Nishimori line - it can be shown that the melting dynamics can be exactly mapped to the equilibrium dynamics. In this mapping the dynamical -or mode-coupling- glass transition corresponds to the spinodal point, while the Kauzmann transition corresponds to the first order phase transition itself. Both in mean field and finite dime…
The following properties are in the present literature associated with the behavior of super-cooled glass-forming liquids: faster than exponential growth of the relaxation time, dynamical heterogeneities, growing point-to-set correlation length, crossover from mean field behavior to activated dynamics. In this paper we argue that these properties are also present in a much simpler situation, namely the melting of the bulk of an ordered phase beyond a first order phase transition point. This is a promising path towards a better theoretical, numerical and experimental understanding of the above …
Using Monte Carlo simulations we study crystallization in the three-dimensional Ising model with four-spin interaction. We monitor the morphology of crystals which grow after placing crystallization seeds in a supercooled liquid. Defects in such crystals constitute an intricate and very stable network which separate various domains by tensionless domain walls. We also show that the crystallization which occurs during the continuous heating of the glassy phase takes place at a heating-rate dependent temperature.
Despite decades of intense study, the mechanisms underlying the extraordinary dynamics of supercooled liquids as they approach the glass transition remain, at best, mis-characterized, and at worst, misunderstood. A long standing endeavor is to understand the remarkable increase of the viscosity with supercooling. Recently, a new theory of supercooled liquids has been proposed that starts from first principles, using elementary statistical mechanics arguments, to derive a form for the viscosity that contains only a single fitting parameter in its simplest form. In this we demonstrate that this …
We apply microcanonical ensemble considerations to suggest that, whenever it may thermalize, a general disorder-free many-body Hamiltonian of a typical atomic system has solid-like eigenstates at low energies and fluid-type (and gaseous, plasma) eigenstates associated with energy densities exceeding those present in the melting (and, respectively, higher energy) transition(s). In particular, the lowest energy density at which the eigenstates of such a clean many body atomic system undergo a non-analytic change is that of the melting (or freezing) transition. We invoke this observation to analy…
In the absence of disorder, electrons can display glassy behavior through supercooling the liquid state, avoiding the solidification into a charge ordered state. Such supercooled electron liquids are experimentally found in organic $θ$-$MM'$ compounds. We present theoretical results that qualitatively capture the experimental findings. At intermediate temperatures, the conducting state crosses over into a weakly insulating pseudogap phase. The stripe order phase transition is first order, so that the liquid phase is metastable below $T_s$. In the supercooled liquid phase the resistivity increa…
We numerically study the interplay between heterogeneous dynamics and properties of negatively curved regions of the potential energy surface in a model glassy system. We find that the unstable modes of saddles and quasi-saddles undergo a localization transition close to the Mode-Coupling critical temperature. We also find evidence of a positive spatial correlation between clusters of particles having large displacements in the unstable modes and dynamical heterogeneities.
In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move - an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ens…
The connectivity of the potential energy landscape in supercooled atomic liquids is investigated through the calculation of the instantaneous normal modes spectrum and a detailed analysis of the unstable directions in configuration space. We confirm the hypothesis that the mode-coupling critical temperature is the $T$ at which the dynamics crosses over from free to activated exploration of configuration space. We also report the observed changes in the local connectivity of configuration space sampled during aging, following a temperature jump from a liquid to a glassy state.
We show that a generalized fluctuation-dissipation relation applies upon instantaneously increasing the temperature of a deeply supercooled liquid. This has the same two-step shape of the relation found upon cooling the liquid, but with opposite violation, indicating an effective temperature that is lower than bath temperature. We show that the effective temperature exhibits some sensible time-dependence and that it retains its connection with the partitioned phase space visited in ageing. We underline the potential relevance of our numerical results for experimental studies of the fluctuation…
Molecular dynamics simulations are performed for a polymer melt composed of short chains in quiescent and sheared conditions. The stress relaxation function $G(t)$ exhibits a stretched exponential form in a relatively early stage and ultimately follows the Rouse function in quiescent supercooled state. Transient stress evolution after application of shear obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 and then saturates into a non-Newtonian viscosity. In steady states, strong shear-thinning and elongation of chains into ellipsoidal shapes are found at extremely small shea…
We have analyzed a non-randomly frustrated spin model which exhibits behavior remarkably similar to the phenomenology of structural glasses. The high-temperature disordered phase undergoes a strong first-order transition to a long-range ordered structure. Using Monte Carlo simulations, we have studied the behavior of the supercooled state by quenching to temperatures below this transition temperature. For a range of supercooling, the system remains ergodic and exhibits dynamics characteristic of supercooled liquids. Below a certain characteristic temperature, however, the system freezes into a…
The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation, however, it is difficult to define measures of spatial heterogeneities in the dynamics, as particles move in and out of any one given region within long enough times. It is also non-transparent how to make connections between the structural glass and the spin glass problems within the Lagrangian formulation. We propose an Eulerian formulation of supercooled liquids…
The anomalous properties of water in the supercooled state are numerous and well-known. Particularly striking are the strong changes in dynamic properties that appear to display divergences at temperatures close to -- but beyond -- the lowest temperatures attainable either experimentally or in computer simulations. Recent work on slow or glassy dynamics in water suggests analogies with simple liquids not previously appreciated, and at the same time highlights some aspects that remain peculiar to water. A comparison of the behavior of water with normal liquids, with respect to its dynamic, ther…
Freezing is a fundamental physical phenomenon that has been studied over many decades; yet the role played by surfaces in determining nucleation has remained elusive. Here we report direct computational evidence of surface induced nucleation in supercooled systems with a negative slope of their melting line (dP/dT < 0). This unexpected result is related to the density decrease occurring upon crystallization, and to surface tension facilitating the initial nucleus formation. Our findings support the hypothesis of surface induced crystallization of ice in the atmosphere, and provide insight, at …
Dynamical heterogeneity in a system of Gay-Berne ellipsoids near its isotropic-nematic (I-N) transition and also in an equimolar mixture of Lennard-Jones spheres and Gay-Berne ellipsoids in deeply supercooled regime is probed by the time evolution of non-Gaussian parameter (NGP). The appearance of a dominant second peak in the rotational NGP near the I-N transition signals the growth of pseudonematic domains. Surprisingly such a second peak is instead observed in the translational NGP for glassy binary mixture. Localization of orientational motion near the I-N transition is found to be respons…
We formulate a microscopic, no adjustable parameter, theory of activated relaxation in supercooled liquids directly in terms of the repulsive and attractive forces within the framework of pair correlations. Under isochoric conditions, attractive forces can nonperturbatively modify slow dynamics, but at high enough density their influence vanishes. Under isobaric conditions, attractive forces play a minor role. High temperature apparent Arrhenius behavior and density-temperature scaling are predicted. Our results are consistent with recent isochoric simulations and isobaric experiments on a dee…
We investigate a minimal model for non-crystalline water, defined on a Husimi lattice. The peculiar random-regular nature of the lattice is meant to account for the formation of a random 4-coordinated hydrogen-bond network. The model turns out to be consistent with most thermodynamic anomalies observed in liquid and supercooled-liquid water. Furthermore, the model exhibits two glassy phases with different densities, which can coexist at a first-order transition. The onset of a complex free-energy landscape, characterized by an exponentially large number of metastable minima, is pointed out by …
Glasses are solid materials whose constituent atoms are arranged in a disordered manner. The transition from a liquid to a glass remains one of the most poorly understood phenomena in condensed matter physics, and still no fully microscopic theory exists that can describe the dynamics of supercooled liquids in a quantitative manner over all relevant time scales. Here we present such a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a supercooled system over a broad density range. Our approach requires only simple static structural in…
Supercooled water is a metastable phase of liquid water below the melting temperature. An interesting discussion recently developed on the relationship between crystallization rate and the time scales of equilibration within the liquid phase. Calculations using a coarse grained monatomic model of water, the mW model, suggested that equilibration of the liquid below the temperature of homogeneous nucleation $T_H\approx225$ K is slower than ice nucleation. Here, a 3 $μ$s long molecular dynamics simulation of the TIP4P-Ew water model is presented to investigate the relaxation properties of an ato…
Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally-relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, we introduce a novel way to account for a pu…
Many successful theories of liquids near the melting temperature assume that small length scale density fluctuations follow Gaussian statistics. In this paper I present numerical investigations of fluctuations in the supercooled viscous regime using an enhance sampling method. I present results for the single component Lennard-Jones liquid, the Kob-Andersen binary mixture, the Wahnström binary mixture, the Lewis-Wahnström model of ortho-terphenyl and for the TIP4P/Ice model of water. Results show that the Gaussian approximation persist to a good degree into the supercooled viscous regime, howe…
Using Monte Carlo simulations we show that the three-dimensional Ising model with four-spin (plaquette) interactions has some characteristic glassy features. The model dynamically generates diverging energy barriers, which give rise to slow dynamics at low temperature. Moreover, in a certain temperature range the model possesses a metastable (supercooled liquid) phase, which is presumably supported by certain entropy barriers. Although extremely strong, metastability in our model is only a finite-size effect and sufficiently large droplets of stable phase divert evolution of the system toward …
We compare dynamical heterogeneities in equilibrated supercooled liquids and in the nonequilibrium glassy state within the framework of the random first order transition theory. Fluctuating mobility generation and transport in the glass are treated by numerically solving stochastic continuum equations for mobility and fictive temperature fields that arise from an extended mode coupling theory containing activated events. Fluctuating spatiotemporal structures in aging and rejuvenating glasses lead to dynamical heterogeneity in glasses with characteristics distinct from those found in the equili…
Translational dynamics of two-dimensional glass forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation and well developed plateaus are observed in orientational correlation functions. It has been suggested that by monitoring translational motion …
The formal structure of glass singularities in the mode-coupling theory (MCT) of supercooled liquids dynamics is closely related to that appearing in the analysis of heterogeneous bootstrap percolation on Bethe lattices, random graphs and complex networks. Starting from this observation one can build up microscopic on lattice realizations of schematic MCT based on cooperative facilitated spin mixtures. I discuss a microscopic implementation of the F13 schematic model including multiple glassy states and the glass-glass transition. Results suggest that our approach is flexible enough to bridge …
In an effort to understand the glass transition, the dynamics of a non-randomly frustrated spin model has been analyzed. The phenomenology of the spin model is similar to that of a supercooled liquid undergoing the glass transition. The slow dynamics can be associated with the presence of extended string-like structures which demarcate regions of fast spin flips. An entropy-vanishing transition, with the string density as the order parameter, is related to the observed glass transition in the spin model.
The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations we show that glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles upon approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlati…
Tackling the low-temperature fate of supercooled liquids is challenging due to the immense timescales involved, which prevent equilibration and lead to the operational glass transition. Relating glassy behaviour to an underlying, thermodynamic phase transition is a long-standing open question in condensed matter physics. Like experiments, computer simulations are limited by the small time window over which a liquid can be equilibrated. Here we address the challenge of low temperature equilibration using trajectory sampling in a system undergoing a nonequilibrium phase transition. This transiti…
Understanding the effect of glassy dynamics on the stability of bio-macromolecules and investigating the underlying relaxation processes governing degradation processes of these macromolecules are of immense importance in the context of bio-preservation. In this work we have studied the stability of a model polymer chain in a supercooled glass-forming liquid at different amount of supercooling in order to understand how dynamics of supercooled liquids influence the collapse behavior of the polymer. Our systematic computer simulation studies find that apart from long time relaxation processes (…
An analysis of diffusion in a supercooled liquid based solely in the density of diffusive directions and the value of energy barriers shows how the potential energy landscape (PEL) approach is capable of explaining the $α$ and $β$ relaxations and the fragility of a glassy system. We find that the $β$ relaxation is directly related to the search for diffusive directions. Our analysis shows how in strong liquids diffusion is mainly energy activated, and how in fragile liquids the diffusion is governed by the density of diffusive directions. We describe the fragile-to-strong crossover as a change…
In this work, we study the nature of transitions between inherent structures of a two-dimensional model supercooled liquid. We demonstrate that these transitions occur predominately along a small number of directions on the energy landscape. Moreover, we show that the number of such directions decreases as the temperature of the liquid is decreased in the mildly supercooled regime, in concert with earlier studies on an athermal jamming system. We show that this decrease happens in parallel with a change in character of the transitions as dynamics in the system become more heterogeneous and loc…
We combine the swap Monte Carlo algorithm to long multi-CPU molecular dynamics simulations to analyse the equilibrium relaxation dynamics of model supercooled liquids over a time window covering ten orders of magnitude for temperatures down to the experimental glass transition temperature $T_g$. The analysis of \rev{several} time correlation functions coupled to spatio-temporal resolution of particle motion allow us to elucidate the nature of the equilibrium dynamics in deeply supercooled liquids. We find that structural relaxation starts at early times in rare localised regions characterised …
Motivated by recent experimental results on glassy polymer nanoparticles, we develop a minimal theoretical framework for the glass transition in spherical confinement. This is accomplished using our cooperative-string model for supercooled dynamics, that was successful at recovering the bulk phenomenology and describing the thin-film anomalies. In particular, we obtain predictions for the mobile-layer thickness as a function of temperature, and for the effective glass-transition temperature as a function of the radius of the spherical nanoparticle - including the existence of a critical partic…
We present Monte Carlo simulation results on the equilibrium relaxation of the two dimensional lattice Coulomb gas with fractional charges, which exhibits a close analogy to the primary relaxation of fragile supercooled liquids. Single particle and collective relaxation dynamics show that the Stokes-Einstein relation is violated at low temperatures, which can be characterized by a fractional power law relation between the self-diffusion coefficient and the characteristic relaxation time. The microscopic spatially heterogeneous structure responsible for the violation is identified.
We perform path integral Monte Carlo simulations to study the imaginary time dynamics of metastable supercooled superfluid states and nearly superglassy states of a one component fluid of spinless bosons square wells. Our study shows that the identity of the particles and the exchange symmetry is crucial for the frustration necessary to obtain metastable states in the quantum regime. Whereas the simulation time has to be chosen to determine whether we are in a metastable state or not, the imaginary time dynamics tells us if we are or not close to an arrested glassy state.
The origins of rapid dynamical slow down in glass forming liquids in the growth of static length scales, possibly associated with identifiable structural ordering, is a much debated issue. Growth of medium range crystalline order (MRCO) has been observed in various model systems to be associated with glassy behaviour. Such observations raise the question about the eventual state reached by a glass former, if allowed to relax for sufficiently long times. Is a slowly growing crystalline order responsible for slow dynamics? Are the molecular mechanisms for glass transition in liquids with and wit…
Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slow down under cooling. The specific pattern of slowing-down depends on the material considered. This dependence is poorly understood, in particular, it remains generally unclear which aspects of the microscopic structures control the dynamics and other macroscopic properties. Attacking this question is one of the two main aspects of this dissertation. We have introduced a new class of models of supercooled liquids, which captures the central aspects of the correspo…
The dynamics of iterates at the transition to chaos in one-dimensional unimodal maps is shown to exhibit the characteristic elements of the glass transition, e.g. two-step relaxation and aging. The properties of the bifurcation gap induced by external noise, including a relationship between relaxation time and entropy, are seen to be comparable to those of a supercooled liquid above a glass transition temperature. Universal time evolution obtained from the Feigenbaum RG transformation is expressed analytically via $q$-exponentials, and interpreted in terms of nonextensive statistics.
We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that …
Glasses feature a broad distribution of relaxation times and activation energies without an obvious characteristic scale. At the same time, macroscopic quantities such as Newtonian viscosity and nonlinear plastic deformation, are interpreted in terms of a characteristic energy scale, e.g. an effective temperature-dependent activation energy in Arrhenius relations. Nevertheless, despite its fundamental importance, such a characteristic energy scale has not been robustly identified. Inspired by the accumulated evidence regarding the crucial role played by soft quasilocalized excitations in glass…
We consider the problem of slow activation dynamics in glassy systems undergoing a random first order phase transition. Using an effective potential approach to supercooled liquids, we determine the spectrum of activation barriers for entropic droplets. We demonstrate that fluctuations of the configurational entropy and of the liquid glass surface tension are crucial to achieve an understanding of the barrier fluctuations in glassy systems and thus are ultimatively responsible for the broad spectrum of excitations and heterogeneous dynamics in glasses. In particular we derive a relation betwee…
We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well-described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement…
