We present the dynamic propensity distribution as an explicit measure of the degree to which the dynamics in a liquid over the time scale of structural relaxation is determined by the initial configuration. We then examine, for a binary mixture of soft discs in two dimensions, the correlation between the spatial distribution of propensity and that of two localmeasures of configuration structure: the local composition and local free volume. While the small particles dominate the high propensity population,we find no strong correlation between either the local composition or the local free volume and the propensity. It is argued that this is a generic failure of purely local structural measures to capture the inherently non-local character of collective behaviour.
For a deeply supercooled liquid just above its glass transition temperature, we present a simple thermodynamic model, where the deeply supercooled liquid is assumed to be a mixture of solid-like and liquid-like micro regions. The mole fraction of the liquid-like regions controls the thermodynamic properties of the supercooled liquid while that of the solid-like regions controls its relaxation time or viscosity. From the universal temperature dependence of the molar excess entropy for the deeply supercooled liquids, we derive the temperature dependence of the mole fraction of the liquid-like re…
We propose deformations of inherent structures as a suitable tool for detecting structural changes underlying the onset of cooperativity in supercooled liquids. The non-affine displacement (NAD) field resulting from the applied deformation shows characteristic differences between the high temperature liquid and supercooled state, that are typically observed in dynamic quantities. The average magnitude of the NAD is very sensitive to temperature changes in the supercooled regime and is found to be strongly correlated with the inherent structure energy. In addition, the NAD field is characterize…
We introduce a supercooled liquid model and obtain parameter-free quantitative predictions that are in excellent agreement with numerical simulations, notably in the hard low-temperature region characterized by strong deviations from Mode-Coupling-Theory behavior. The model is the Fredrickson-Andersen Kinetically-Constrained-Model on the three-dimensional $M$-layer lattice. The agreement has implications beyond the specific model considered because the theory is potentially valid for many more systems, including realistic models and actual supercooled liquids.
In recent years it has become widely accepted that a dynamical length scale ξ_α plays an important role in supercooled liquids near the glass transition. We examine the implications of the interplay between the growing ξ_α and the size of the crystal nucleus, ξ_M, which shrinks on cooling. We argue that at low temperatures where ξ_α > ξ_M a new crystallization mechanism emerges enabling rapid development of a large scale web of sparsely connected crystallinity. Though we predict this web percolates the system at too low a temperature to be easily seen in the laboratory, there are noticeable re…
The use of the isoconfigurational ensemble to explore structure-dynamic correlations in supercooled liquids is examined. The statistical error of the dynamic propensity and its spatial distribution are determined. The authors present the spatial distribution of the particle non-Gaussian parameter as a measure of the intermittency with which particles exhibit their propensity for motion. The ensemble average of the direction of particle motion is introduced to establish the anisotropy of the dynamic propensity.
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. U.S.A., 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder char…
Stochastic-Beta-Relaxation (SBR) provides a characterisation of the glass crossover in discontinuous Spin-Glasses and Supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landa…
We study the transport and the relaxation properties of a molecular supercooled liquid by molecular-dynamics numerical simulations. The focus is on the translational motion. Jump motion is detected. At lower temperature the Stokes-Einstein law breaks down.
It is proposed that the rate of relaxation in a liquid is better described by the geometric mean of the van Hove distribution function, rather than the standard arithmetic mean used to obtain the mean squared displacement. The difference between the two means is shown to increase significantly with an increase in the non-Gaussian character of the displacement distribution. Preliminary results indicate that the geometric diffusion constant results in a substantial reduction of the deviation from Stokes-Einstein scaling.
Lecture notes for LES HOUCHES 2002 SUMMER SCHOOL - SESSION LXXVII on SLOW RELAXATIONS AND NONEQUILIBRIUM DYNAMICS IN CONDENSED MATTER; Les Houches: July 1-26, 2002
The dynamical heterogeneity in supercooled liquids measured by a molecular dynamics simulation has been quantified on the basis of the multifractal formalism. The singularity spectrum becomes broader as the glass transition is approached. This behavior is similar to that observed in the case of the Anderson-localization transition.
The rotational dynamics of a supercooled molecular liquid is investigated by a molecular-dynamics numerical study. We detect rotational jumps with a waiting-time distribution which is well fitted by a truncated power law. At lower temperatures the rotational correlation times are decoupled from the viscosity.
In this paper, we discuss theoretically the behavior of the four point nonlinear susceptibility and its associated correlation length for supercooled liquids close to the Mode Coupling instability temperature $T_c$. We work in the theoretical framework of the glass transition as described by mean field theory of disordered systems, and the hypernetted chain approximation. Our results give an interpretation framework for recent numerical findings on heterogeneities in supercooled liquid dynamics.
In these lectures, which were presented at "Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow" University of St. Andrews, 8 July - 22 July, 1999, I give an introduction to the physics of supercooled liquids and glasses and discuss some computer simulations done to investigate these systems.
Because of the isotropic and disordered nature of liquids, the anisotropy hidden in intermolecular interactions are often neglected. Accordingly, the order parameter describing a simple liquid has so far been believed to be only density. In contrast to this common sense, we propose that two order parameters, namely, density and bond order parameters, are required to describe the phase behavior of liquids since they intrinsically tend to form local bonds. This model gives us clear physical explanations for two poorly-understood phenomena in supercooled liquids: (i) large-scale density fluctuati…
We investigate to what extend the replica-exchange Monte Carlo method is able to equilibrate a simple liquid in its supercooled state. We find that this method does indeed allow to generate accurately the canonical distribution function even at low temperatures and that its efficiency is about 10-100 times higher than the usual canonical molecular dynamics simulation.
Reply to "Comment on 'Fickian non-Gaussian diffusion in glass-forming liquids' ". In [ArXiv:2210.07119v1], Berthier et al. questioned the findings of our letter [Phys. Rev. Lett. 128, 168001 (2022)], concerning the existence and the features of Fickian non-Gaussian diffusion in glass-forming liquids. Here we demonstrate that their arguments are either wrong, or not meaningful to our scope. Thus, we fully confirm the validity and novelty of our results.
We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory (MCT) originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the $q$-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different appr…
We determine the phase diagram of liquid supercooled water by extensive computer simulations using the TIP5P-E model [J. Chem. Phys. {\bf 120}, 6085 (2004)]. We find that the transformation of water into a low density liquid in the supercooled range strongly enhances the solubility of hydrophobic particles. The transformation of water into a tetrahedrally structured liquid is accompanied by a minimum in the hydration entropy and enthalpy. The corresponding change in sign of the solvation heat capacity indicates a loss of one characteristic signature of hydrophobic hydration. The observed behav…
A metastable state, characterized by a low degree of mass localization is identified using Density Functional Theory. This free energy minimum, located through the proper evaluation of the competing terms in the free energy functional, is independent of the specific form of the DFT used. Computer simulation results on particle motion indicate that this heterogeneous state corresponds to the supercooled state.
Liquid-liquid and liquid-vapor coexistence regions of various water models were determined by MC simulations of isotherms of density fluctuation restricted systems and by Gibbs ensemble MC simulations. All studied water models show multiple liquid-liquid phase transitions in the supercooled region: we observe two transitions of the TIP4P, TIP5P and SPCE model and three transitions of the ST2 model. The location of these phase transitions with respect to the liquid-vapor coexistence curve and the glass temperature is highly sensitive to the water model and its implementation. We suggest, that t…
We present a quantitative description of the thermodynamics in a supercooled binary Lennard Jones liquid via the evaluation of the degeneracy of the inherent structures, i.e. of the number of potential energy basins in configuration space. We find that for supercooled states, the contribution of the inherent structures to the free energy of the liquid almost completely decouples from the vibrational contribution. An important byproduct of the presented analysis is the determination of the Kauzmann temperature for the studied system. The resulting quantitative picture of the thermodynamics of t…
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…
When we lower the temperature of a liquid, at some point we meet a first order phase transition to the crystal. Yet, under certain conditions it is possible to keep the system in its metastable phase and to avoid crystallization. In this way the liquid enters in the supercooled phase. Supercooled liquids have a very rich phenomenology, which is still far from being completely understood. To begin with, there is the problem of how to prevent crystallization and how deeply the liquid can be supercooled before a metastability limit is hit. But by far the most interesting feature of supercooled li…
We consider the relationship between the temperature at which averaged energy landscape properties change sharply ($T_{o}$), and the breakdown of mean-field treatments of the dynamics of supercooled liquids. First, we show that the solution of the wavevector dependent mode-coupling equations undergoes an ergodic-nonergodic transition consistently close to $T_{o}$. Generalizing the landscape concept to include hard-sphere systems, we show that the property of inherent structures that changes near $T_{o}$ is governed more fundamentally by packing and free volume than potential energy. Lastly, we…
The predictions of a class of phenomenological trap models of supercooled liquids are tested via computer simulation of a model glass-forming liquid. It is found that a model with a Gaussian distribution of trap energies provides a good description of the landscape dynamics, even at temperatures above $T_{c}$, the critical temperature of mode-coupling theory. A scenario is discussed whereby deep traps are composed of collections of inherent structures above $T_{c}$ and single inherent structures below $T_{c}$. Deviations from the simple Gaussian trap picture are quantified and discussed.
The manner in which the intermolecular potential u(r) governs structural relaxation in liquids is a long standing problem in condensed matter physics. Herein we show that diffusion coefficients for simulated Lennard-Jones m-6 liquids (8<m<36) in normal and moderately supercooled states are a unique function of the variable rho^g/T, where rho is density and T is temperature. The scaling exponent g is a material specific constant whose magnitude is related to the steepness of the repulsive part of u(r), evaluated around the distance of closest approach between particles probed in the supercooled…
In two recent interesting letters evidence was presented for the existence of a growing dynamic correlation length when we approach the glass transition from the liquid phase (a similar divergence is present also in the off-equilibrium dynamics below $T_c$). Here we would like to point out that this phenomenon can be easily predicted using the replica approach.
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.
Liquid is represented as complicated system of disclinations according to defect description of liquids and glasses. The expressions for the linear disclination field of an arbitrary form and energy of inter-disclination interaction are derived in the framework of gauge theory of defects. It allows us to describe liquid as a disordered system of topological moments and reduce this model to the Edwards--Anderson model with large-range interaction. Within the framework of this approach vitrifying is represented as a "hierarchical" phase transition. The suggested model allows us to explain the pr…
A theoretical treatment of deeply supercooled liquids is difficult because their properties emerge from spatial inhomogeneities that are self-induced, transient, and nanoscopic. I use computer simulations to analyse self-induced static and dynamic heterogeneity in equilibrium systems approaching the experimental glass transition. I characterise the broad sample-to-sample fluctuations of salient dynamic and thermodynamic properties in elementary mesoscopic systems. Findings regarding local lifetimes and distributions of dynamic heterogeneity are in excellent agreement with recent single molecul…
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…
We compute critical exponents governing universal features of supercooled liquids through the effective theory of an overlap field. The correlation length diverges with the Ising exponent; the size of dynamically heterogeneous patches grows more rapidly; and the relaxation time obeys a generalized Vogel-Fulcher-Tammann relation.
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 combine Creutz energy conservation with Kawasaki spin exchange to simulate the microcanonical dynamics of a system of interacting particles. Relaxation occurs via Glauber spin-flip activation using a self-consistent temperature. Heterogeneity in the dynamics comes from finite-size constraints on the spin exchange that yield a distribution of correlated regions. The simulation produces a high-frequency response that can be identified with the boson peak, and a lower-frequency peak that contains non-Debye relaxation and non-Arrhenius activation, similar to the primary response of supercooled …
Using molecular dynamics simulations we investigate the relaxation dynamics of a supercooled liquid close to a rough as well as close to a smooth wall. For the former situation the relaxation times increase strongly with decreasing distance from the wall whereas in the second case they strongly decrease. We use this dependence to extract various dynamical length scales and show that they grow with decreasing temperature. By calculating the frequency dependent average susceptibility of such confined systems we show that the experimental interpretation of such data is very difficult.
We propose a quantitative measure of a time scale on which Fickian diffusion sets in for supercooled liquids and use Brownian Dynamics computer simulations to determine the temperature dependence of this onset time in a Lennard-Jones binary mixture. The time for the onset of Fickian diffusion ranges between 6.5 and 31 times the $α$ relaxation time (the $α$ relaxation time is the characteristic relaxation time of the incoherent intermediate scattering function). The onset time increases faster with decreasing temperature than the $α$ relaxation time. Mean squared displacement at the onset time …
Computer simulations of a model glass-forming system are presented, which are particularly sensitive to the correlation between the dynamics and the topography of the potential energy landscape. This analysis clearly reveals that in the supercooled regime the dynamics is strongly influenced by the presence of deep valleys in the energy landscape, corresponding to long-lived metastable amorphous states. We explicitly relate non-exponential relaxation effects and dynamic heterogeneities to these metastable states and thus to the specific topography of the energy landscape.
Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.
Glass formation is encountered in diverse materials. Experiments have revealed that dynamic relaxation spectra of supercooled liquids generically become asymmetric near the glass transition temperature, $T_g$, where an extended power law emerges at high frequencies. The microscopic origin of this "wing" remains unknown, and was so far inaccessible to simulations. Here, we develop a novel computational approach and study the equilibrium dynamics of model supercooled liquids near $T_g$. We demonstrate the emergence of a power law wing in numerical spectra, which originates from relaxation at rar…
Despite the absence of consensus on a theory of the transition from supercooled liquids to glasses, the experimental observations suggest that a detail-independent theory should exist.
Using a novel thermodynamic integration scheme, we compute the excess free energy, $γ$, of a glass-forming, binary Lennard-Jones liquid in contact with a frozen amorphous wall, formed by particles frozen into a similar structure as the liquid. We find that $γ$ is non-zero, becoming negative at low temperature. This indicates that the thermodynamics of the system is perturbed by the effect of the amorphous wall.
We examine structural relaxation in a supercooled glass-forming liquid simulated by NVE molecular dynamics. Time correlations of the total kinetic energy fluctuations are used as a comprehensive measure of the system's approach to the ergodic equilibrium. We find that, under cooling, the total structural relaxation becomes delayed as compared with the decay of the component of the intermediate scattering function corresponding to the main peak of the structure factor. This observation can be explained by collective movements of particles preserving many-body structural correlations within comp…
We present molecular dynamics results for a two component, two-dimensional Lennard-Jones supercooled liquid near the glass transition. We find that the supercooled liquid is spatially heterogeneous and that there are long-lived clusters whose size distribution satisfies a scaling relation up to a cutoff. The similarity of several properties of the supercooled liquid to those of a mean-field glass-forming fluid near the spinodal suggests that the glass transition in the supercooled liquid is associated with an underlying thermodynamic instability.
We propose a new method to measure time-dependent linear susceptibilities in molecular simulations, which does not require the use of nonequilibrium simulations, subtraction techniques, or fluctuation-dissipation theorems. The main idea is an exact reformulation of linearly perturbed quantities in terms of observables accessible in unperturbed trajectories. We have applied these ideas to two supercooled liquids in their nonequilibrium aging regime. We show that previous work had underestimated deviations from fluctuation-dissipation relations in the case of a Lennard-Jones system, while our re…
Breakdown of Stokes-Einstein relation in supercooled liquids is believed to be one of the hallmarks of glass transition. The phenomena is studied in depth over many years to understand the microscopic mechanism without much success. Recently it was found that violation of Stokes-Einstein relation in supercooled liquids can be tuned very systematically by pinning randomly a set of particles in their equilibrium positions. This observation suggested a possible framework where breakdown of Stokes-Einstein relation in the dynamics of supercooled liquids can be studied with precise control. We have…
We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity allows us to perform a finite-size scaling (FSS) analysis, which indicates that the peak persists at a finite temperature in the thermodynamic limit. We attempt to collapse the data onto a FSS curve according to different theoretical scenarios, obtaining reasonable results in two cases: a "not-so-simple" liquid with nonstandard values of the exponents α and ν, a…
We unveil the existence of non-affinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of two- and three-dimensional model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of rather large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of non-affinely rearranging …
The use of probe molecules to extract the local dynamical and structural properties of complex dynamical systems is an age-old technique both in simulations and experiments. A lot of important information which is not immediately accessible from the bulk measurements can be accessed via these local measurements. Still, a detailed understanding of how a probe particle's dynamics are affected by the surrounding liquid medium is not very well understood, especially in the supercooled temperature regime. This work shows how translational dynamics of a rod-like particle immersed in a supercooled li…
Importance of nuclear quantum effects on the structure of supercooled water around its liquid--liquid critical point
Center for Advanced Systems Understanding (CASUS)（先进系统理解中心）；Helmholtz Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；Paderborn University（帕德博恩大学）；Technische Universität Dresden（德累斯顿工业大学）
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…
I employ the van der Waals theory of Baus and coworkers to analyze the fast, adiabatic decay of a supercooled liquid in a closed vessel with which the solidification process usually starts. By imposing a further constraint on either the system volume or pressure, I use the maximum-entropy method to quantify the fraction of liquid that is transformed into solid as a function of undercooling and of the amount of a foreign gas that could possibly be also present in the test tube. Upon looking at the implications of thermal and mechanical insulation for the energy cost of forming a solid droplet w…
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…
A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid sees a sharp rise in its viscosity over a narrow temperature range, eventually becoming frozen on laboratory timescales. Explaining this immense increase in viscosity is one of the principle goals of condensed matter physicists. To that end, numerous theoretical frameworks have been proposed which explain and reproduce the temperature dependence of the visco…
We present a direct comparison of the number of dynamically correlated molecules in the shear-mechanical and dielectric relaxations of the following seven supercooled organic liquids: triphenylethylene, tetramethyl-tetraphenyl-trisiloxane, polyphenyl ether, perhydrosqualene, polybutadiene, decahydroisoquinoline, and tripropylene glycol. For each liquid we observe that the numbers of dynamically correlated molecules in the shear and in the dielectric relaxation are proportional. We show that this proportionality can be explained by the constancy of the decoupling index of the shear and dielectr…
We report that the local Debye-Waller factor in a simulated 2D glass-forming mixture exhibits significant spatial heterogeneities and that these short time fluctuations provide an excellent predictor of the spatial distribution of the long time dynamic propensities [Phys.Rev.Lett. 93, 135701 (2004)]. In contrast, the potential energy per particle of the inherent structure does not correlate well with the spatially distributed dynamics.
A model for the slow dynamics of the supercooled liquid is formulated in terms of the standard equations of fluctuating nonlinear hydrodynamics (FNH) with the inclusion of an extra diffusive mode for the collective density fluctuations. If the compressible nature of the liquid is completely ignored, this diffusive mode sets the longest relaxation times in the supercooled state and smooths off a possible sharp ergodicity-nonergodicity (ENE) transition predicted in a mode coupling theory. The scenario changes when the complete dynamics is considered with the inclusion of $1/ρ$ nonlinearities in …
