A new connection between structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as $J_σ$, is obtained as a function of inherent-state elastic moduli and radial distribution function. The energy barrier from the current theory is compared to one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations.
Zero-temperature Avalanche Criticality Governing Dynamical Heterogeneity in Supercooled Liquids
Toyota Central R&D Labs., Inc.（丰田中央研究所）；D3 Center, The University of Osaka（大阪大学D3中心）；Department of Physics, The University of Osaka（大阪大学物理系）；Department of Physics, Nagoya University（名古屋大学物理系）；Division of Chemical Engineering, Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科化学工程专修）
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…
First principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below $T_c\approx 1232K$. The low density phase is nearly tetra-coordinated, with a pseudogap at the Fermi surface, while the high density phase is more highly coordinated and metallic in nature. The transition is observed through the formation of van der Waals loops in pressure-volume isotherms below $T_c$.
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 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.
A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Max…
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.
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.
Using computer simulations, we show that the localized low frequency normal modes of a configuration in a supercooled liquid are strongly correlated with the irreversible structural reorganization of the particles within that configuration. Establishing this correlation constitutes the identification of the aspect of a configuration that determines the heterogeneity of the subsequent motion. We demonstrate that the spatial distribution of the summation over the soft local modes can persist in spite of particle reorganization that produces significant changes in individual modes. Along with spa…
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 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…
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.
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…
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…
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…
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…
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.
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 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.
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 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.
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…
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…
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 …
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 …
The dielectric response of supercooled liquids is phenomenologically modeled by a set of Asymmetric Double Wells (ADW), where each ADW contains a dynamical heterogeneity of $N_{corr}$ molecules. We find that the linear macroscopic susceptibility $χ_1$ does not depend on $N_{corr}$ contrary to all higher order susceptibilities $χ_{2k+1}$. We show that $χ_{2k+1}$ is proportional to the $k^{th}$ moment of $N_{corr}$, which could pave the way for new experiments on glass transition. In particular, as predicted by Bouchaud and Biroli on general grounds [Phys. Rev. B, {\bf 72}, 064204 (2005)], we fi…
Enormous enhancement in the viscosity of a liquid near its glass transition is generally connected to the growing many-body static correlations near the transition, often coined as `amorphous ordering'. Estimating the length scales of such correlations in different glass-forming liquids is highly important to unravel the physics of glass formation. Experiments on molecular glass-forming liquids become pivotal in this scenario as the viscosity grows several folds ($\sim 10^{14}$), simulations or colloidal glass experiments fail to access the long-time scales required. Here we design an experime…
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…
In the present work we present a fractal model for the beta relaxation in supercooled liquids. The macroscopic dynamics is obtained by superposition of relaxation of independent mesoscopic regions (cages). Scaling relations and exponents are assumed for the distribution of cage sizes and for the size dependent response of the independent cages. In this way we obtain some scaling relations for the average response, in the time and frequency domain. For a particular choice of the scaling exponents we obtain the scaling relations predicted by the MCT. The comparison with recent light scattering d…
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 (…
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…
We introduce a semi-schematic mode-coupling model to describe the slow dynamics in molecular liquids, retaining explicitly only the description of the center of mass degrees of freedom. Angular degrees of freedom are condensed in a q-vector independent coupling parameter. We compare the time and q-dependence of the density fluctuation correlators with numerical data from a 250 ns long molecular dynamics simulation. Notwithstanding the choice of a network-forming liquid as a model for comparing theory and simulation, the model describes the main static and dynamic features of the relaxation in …
We numerically obtain the first quantitative demonstration that development of spatial correlations of mobility as temperature is lowered is responsible for the ``decoupling'' of transport properties of supercooled liquids. This result further demonstrates the necessity of a spatial description of the glass formation and therefore seriously challenges a number of popular alternative theoretical descriptions.
We propose a method to analyze the dynamics of systems exhibiting slow relaxation which is based on mesoscopic non-equilibrium thermodynamics. The method allows us to obtain kinetic equations of the Fokker-Planck type for the probability functional and their corresponding Langevin equations. Our results are compared with the ones obtained by other authors.
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.
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…
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
We study supercooled dynamics in quantum hard-sphere liquid using quantum mode-coupling formulation. In the moderate quantum regime, classical cage effects lead to slower dynamics compared to strongly quantum regime, where tunneling overcomes classical caging, leading to faster relaxation. As a result, the glass transition critical density can become significantly higher than for the classical liquids. Perturbative approach is used to solve time dependent quantum mode-coupling equations to study in detail the dynamics of the supercooled liquid in moderate quantum regime. Similar to the classic…
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.
