A model for the supercooled liquid is considered by taking into account its solid like properties. We focus on how the long time dynamics is affected due to the coupling between the slowly decaying density fluctuations and the local displacement variables in the frozen liquid. Results from our model agree with the recent observation of Novikov and Sokolov [Nature (London) {\bf 431}, 961 (2004)] that the fragility index $m$ of a glass forming material is linearly related to the corresponding ratio $K/G$ of the bulk and the shear moduli.
We reveal the existence of systematic variations of isobaric fragility in different supercooled Lennard-Jones binary mixtures by performing molecular dynamics simulations. The connection between fragility and local structures in the bulk is analyzed by means of a Voronoi construction. We find that clusters of particles belonging to locally preferred structures form slow, long-lived domains, whose spatial extension increases by decreasing temperature. As a general rule, a more rapid growth, upon supercooling, of such domains is associated to a more pronounced super-Arrhenius behavior, hence to …
We numerically investigated the connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile is the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states …
Master curves of the relaxation time, tau, or viscosity, eta, versus T^-1V^-x, where T is temperature, V the specific volume, and x a material constant, are used to deduce the effect of pressure on the dynamic crossover and the fragility. The crossover is determined from the change in slope of derivative plots of the relaxation times or viscosities. We confirm our previous findings that the value of tau or eta at the crossover is independent of both T and P; that is, the dynamic crossover is associated with a characteristic value of the relaxation time. Previous determinations were limited to …
We present an analytic scheme to connect the fragility and viscoelasticity of metallic glasses to the effective ion-ion interaction in the metal. This is achieved by an approximation of the short-range repulsive part of the interaction, combined with nonaffine lattice dynamics to obtain analytical expressions for the shear modulus, viscosity, and fragility in terms of the ion-ion interaction. By fitting the theoretical model to experimental data, we are able to link the steepness of the interionic repulsion to the Thomas-Fermi screened Coulomb repulsion and to the Born-Mayer valence-electron o…
Using molecular dynamics simulations, we study the slow dynamics of supercooled liquids confined in a random matrix of immobile obstacles. We study the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms of the density correlation function, the mean square displacement, the nonlinear dynamic susceptibility, the non-Gaussian parameter, and the fragility. Cooperative and spatially heterogeneous dynamics are suppressed as the obstacle density increases, which lead to the more Arrhenius-like behavior in the temperature dependence of the relaxation time. Our findings are quali…
A recently proposed expression to describe the temperature and volume dependences of the structural (or alpha) relaxation time is discussed. This equation satisfies the scaling law for the relaxation times, tau = f(TV^g), where T is temperature, V the specific volume, and g a material-dependent constant. The expression for the function f is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover, providing a description of the dynamics with a minimal number of parameters. The results herein can be reconc…
We address the question of the dependence of the fragility of glass forming supercooled liquids on the softness of an interacting potential by performing numerical simulation of a binary mixture of soft spheres with different power n of the interparticle repulsive potential. We show that the temperature dependence of the diffusion coefficients for various $n$ collapses onto a universal curve, supporting the unexpected view that fragility is not related to the hard core repulsion. We also find that the configurational entropy correlates with the slowing down of the dynamics for all studied n.
The term "fragility" describes the rate at which viscosity grows when a supercooled liquid approaches its putative glass transition temperature. The field of glassy materials is actively searching for a structural origin that governs this dynamical slowing down in the supercooled liquid, which occurs without any discernible change in structure. Our work shows clear evidence that growing many-body static amorphous order is intimately correlated with the kinetic fragility of glass-forming liquids. It confirms that the system's dynamical response to temperature is concealed in its micro-structure…
The thermal expansion coefficients, structure factors, and viscosities of twenty-five equilibrium and supercooled metallic liquids have been measured using an electrostatic levitation (ESL) facility. The structure factor was measured at the Advanced Photon Source, Argonne, using the ESL. A clear connection between liquid fragility and structural and volumetric changes at high temperatures is established; the observed changes are larger for the more fragile liquids. It is also demonstrated that the fragility of metallic liquids is determined to a large extent by the cohesive energy and is, ther…
A mesoscopic model is proposed to explain the anomalous dynamics in a supercooled liquid as its glass transition temperature is approached from above. The model is based on the assumption of $β$ organized $α$ process, with the requirement of coherent excitation of a minimum critical number $N_{c}$ of $β$ processes in the surroundings of a total $N_β$. Numerical evaluation of the model shows that the growth in this critical number in the background of a modest $N_β$ can lead to a severe entropic bottleneck and slow down the dynamics to an extent observed near real glass transition. The fragilit…
We propose a microscopic picture for understanding the nonlinear rheology of supercooled liquids with soft-repulsive potentials. Based on Brownian dynamics simulations of supercooled charge-stabilized colloidal suspensions, our analysis shows that the shear thinning of viscosity (eta) at large enough shear rates (sr), expressed as eta~sr^(-lambda), originates from the evolution of the localized elastic region (LER). An LER is a transient region composed of the first several coordination shells of a reference particle. In response to the external shear, particles within LER undergo nearly affin…
We study the effect of heavy impurities on the dynamics of supercooled liquids. When a small fraction of particles in the supercooled liquid is made heavier, they exhibit slower dynamics than the original particles and also make the overall system slower. If one looks at the overlap correlation function to quantify dynamics in the system, it has different behavior for the heavy and the light particles. In particular, at the relaxation time of the overall system, the degree of relaxation achieved by the heavier particles is lesser on average than that achieved by the light particles. This diffe…
Polydispersity is found to have a significant effect on the potential energy landscape; the the average inherent structure energy with temperature decreases with polydispersity. Increasing polydispersity at fixed volume fraction decreases the glass transition temperature and the fragility of glass formation analogous to the antiplasticization seen in some polymeric melts. An interesting temperature dependent crossover of heterogeneity with polydispersity is observed at low temperature due to the faster build-up of dynamic heterogeneity at lower polydispersity.
We demonstrate, via numerical simulations, that the relaxation dynamics of supercooled liquids correlates well with a plastic length scale measuring a particle's response to impulsive localized perturbations and weakly to measures of local elasticity. We find that the particle averaged plastic length scale vanishes linearly in temperature and controls the super-Arrhenius temperature dependence of the relaxation time. Furthermore, we show that the plastic length scale of individual particles correlates with their typical displacement at the relaxation time. In contrast, the local elastic respon…
Glass formers exhibit a viscoelastic behavior: at the laboratory timescale, they behave like (glassy) solids at low temperatures, and like liquids at high temperatures. Based on this observation, elastic models relate the long time supercooled dynamics to short time elastic properties of the supercooled liquid. In the present work, we assess the validity of elastic models for the shear viscosity and the $α$-relaxation time of supercooled water, using molecular dynamics simulations with the TIP4P/2005f force field over a wide range of temperatures. We show that elastic models provide a good des…
In the present work, a detailed analysis of the glassy behavior and the relaxation dynamics of the liquid crystal dimer α-(4-cyanobiphenyl-4'-yloxy)-ω-(1-pyrenimine-benzylidene-4'-oxy) heptane (CBO7O.Py) throughout both nematic and smectic A mesophases by means of broadband dielectric spectroscopy has been performed. CBO7O.Py shows three different dielectric relaxation modes and two glass transition (Tg) temperatures: the higher Tg is due to the freezing of the molecular motions responsible of the relaxation mode with the lowest frequency (μ1L); the lower Tg is due to the motions responsible o…
We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction, to address the effects of particle deformation on the collective response of the system. In particular, we compare three different models: (i) a recently investigated model [Gnan \& Zaccarelli, Nat. Phys. 15, 683 (2019)], where an inner hertzian field providing the internal elasticity acts on the monomers of the ring, (ii) the same model where the effect of such a field on the center of mass is balanced…
We have carried out extensive molecular dynamics simulations of a supercooled polydisperse Lennard-Jones liquid with large variations in temperature at a fixed pressure. The particles in the system are considered to be polydisperse both in size and mass. The temperature dependence of the dynamical properties such as the viscosity ($η$) and the self-diffusion coefficients ($D_i$) of different size particles is studied. Both viscosity and diffusion coefficients show super-Arrhenius temperature dependence and fit well to the well-known Vogel-Fulcher-Tammann (VFT) equation. Within the temperature …
Under an applied traction, highly concentrated suspensions of solid particles in fluids can turn from a state in which they flow to a state in which they counteract the traction as an elastic solid: a shear-jammed state. Remarkably, the suspension can turn back to the flowing state simply by inverting the traction. A tensorial model is presented and tested in paradigmatic cases. We show that, to reproduce the phenomenology of shear jamming in generic geometries, it is necessary to link this effect to the elastic response supported by the suspension microstructure rather than to a divergence of…
In an attempt to quantitatively characterize the recently observed slow dynamics in the isotropic and nematic phase of liquid crystals, we investigate the single-particle orientational dynamics of rodlike molecules across the isotropic-nematic transition in computer simulations of a family of model systems of thermotropic liquid crystals. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. In order to obtain a quantitative measure of glassy dyn…
The relationship between the microscopic arrangement of molecules in a supercooled liquid and its slow dynamics at low temperature near glass transition is studied by Molecular Dynamics (MD) simulations. A Lennard-Jones liquid with polydispersity in size and mass of constituent particles is chosen as the model system. Our studies reveal that the local structure (that varies with polydispersity) plays a crucial role both in the slowing down of dynamics and in the growth of the dynamic heterogeneities, besides determining the glass forming ability (GFA) of the system. Increasing polydispersity a…
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 show that the fragility $m$, the steepness of the viscosity and relaxation time close to the vitrification, increases with the degree of elastic softening, i.e. the decrease of the elastic modulus with increasing temperature, in universal way. This provides a novel connection between the thermodynamics, via the modulus, and the kinetics. The finding is evidenced by numerical simulations and comparison with the experimental data of glassformers with widely different fragilities ($33 \le m \le 115$), leading to a fragility-independent elastic master curve extending over eighteen decades in vi…
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…
We report a thorough characterization of the glassy phases of mixtures of succinonitrile and glutaronitrile via dielectric spectroscopy and differential scanning calorimetry. This system is revealed to be one of the rare examples where both glassy states of matter, a structurally disordered supercooled liquid and an orientationally disordered plastic crystal, can be prepared in the same material. Both disordered states can be easily supercooled, finally arriving at a structural-glass or a glassy-crystal state. Detailed investigations using broadband dielectric spectroscopy enable a comparison …
Dynamics of a coarse-grained model for the room-temperature ionic liquid, 1-ethyl-3-methylimidazolium hexafluorophosphate, couched in the united-atom site representation are studied via molecular dynamics simulations. The dynamically heterogeneous behavior of the model resembles that of fragile supercooled liquids. At or close to room temperature, the model ionic liquid exhibits slow dynamics, characterized by nonexponential structural relaxation and subdiffusive behavior. The structural relaxation time, closely related to the viscosity, shows a super-Arrhenius behavior. Local excitations, def…
Investigations of strain correlations at the glass transition reveal unexpected phenomena. The shear strain fluctuations show an Eshelby-strain pattern ($\,\sim \cos{(4θ)}/r^2\,$), characteristic for elastic response, even in liquids at long times [1]. We address this using a mode-coupling theory for the strain fluctuations in supercooled liquids and data from both, video microscopy of a two-dimensional colloidal glass former and simulations of Brownian hard disks. We show that long-ranged and long-lived strain-signatures follow a scaling law valid close to the glass transition. For large enou…
The thermodynamic and kinetic anomalies of supercooled liquids are analyzed from the perspective of energy landscapes. A mean field model, a generalized random energy model of liquids is developed, which exhibits a dynamical transition of the onset of slow dynamics at T_0, alteration of the nature of motion from the saddle-to-saddle to minimum-to-minimum motion at T_c, and an ideal glass transition at T_k. If the energy spectrum of the configurations has a low energy tail, the model also allows a thermodynamic liquid-liquid transition at T_l. The liquid-liquid transition of the model is correl…
We report the observation of a distinct correlation between the kinetic fragility index $m$ and the reduced Arrhenius crossover temperature $θ_A = T_A/T_g$ in various glass-forming liquids, identifying three distinguishable groups. In particular, for 11 glass-forming metallic liquids, we universally observe a crossover in the mean diffusion coefficient from high-temperature Arrhenius to low-temperature super-Arrhenius behavior at approximately $θ_A \approx 2$ which is in the stable liquid phases. In contrast, for fragile molecular liquids, this crossover occurs at much lower $θ_A \approx 1.4$ …
By confining water in nanopores, so narrow that the liquid cannot freeze, it is possible to explore its properties well below its homogeneous nucleation temperature TH ~ 235 K. In particular, the dynamical parameters of water can be measured down to 180 K approaching the suggested glass transition temperature Tg ~ 165 K. Here we present experimental evidence, obtained from Nuclear Magnetic Resonance and Quasi-Elastic Neutron Scattering spectroscopies, of a well defined decoupling of transport properties (the self-diffusion coefficient and the average translational relaxation time), which impli…
Both local geometry and collective, extended excitations drive the moves of a particle in the cage of its neighbours in dense liquids. The strength of their influence is investigated by Molecular Dynamics simulations of a supercooled liquid of fully-flexible trimers with semirigid or rigid bonds. The rattling in the cage is investigated on different length scales. First, the rattling anisotropy due to local order is characterized by two order parameters sensing the monomers succeeding or failing to escape from the cage. Then, the collective response of the surroundings excited by the monomer-m…
Molecular origin of the well-known specific heat anomaly in supercooled liquid water is investigated here by using extensive computer simulations and theoretical analyses. A rather sharp increase in the values of isobaric specific heat with lowering temperature and the weak temperature dependence of isochoric specific heat in the same range are reproduced in simulations. We calculated the spatiotemporal correlation among temperature fluctuations and examined the frequency dependent specific heat. The latter shows a rapid growth in the low frequency regime as temperature is cooled below 270 K. …
Theories of the Glass Transition Based on Local Excitations
Nanyang Technological University（南洋理工大学）；Consiglio Nazionale delle Ricerche（意大利国家研究委员会）；Roskilde University（罗斯基勒大学）；University of Amsterdam（阿姆斯特丹大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；EPFL（洛桑联邦理工学院）
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 minim…
Random first order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first order transition theory, is used to treat individual glassy configurations, while the liquid phase is treated using common liquid state approximations. The transition temperature $T^{*}_{A} $, the temperature where the onset of activated behavior is predicted by mean field theory, the lower crossover temperature $T_{c}^{*}$ where barrierless motions actu…
The random first order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of ``entropic droplets'' in terms of libraries of local energy landscapes is introduced which treats in a uniform way the supercooled liquid (reproducing earlier results) and glassy regimes. The resulting microscopic theory of aging makes contact with the Nayaranaswamy-Moynihan-Tool nonlinear relaxation formalism and the Hodge-Scherer extrapolation of the Adam-Gibbs formula, but deviations from both approaches are…
We review the recently proposed elastic approach to glass transition. This approach is based on a simple and a physically transparent idea of elastic interactions between local relaxation events in a liquid. Central to this picture is the range of this interaction. Its increase on lowering the temperature explains several important open questions in the area of glass transition, including universal relaxation laws and dynamic crossovers. In particular, we show how the proposed theory explains (1) the physical origin of cooperativity of relaxation; (2) the origin of the crossover from exponenti…
A recently published analytical model, describing and predicting elasticity, viscosity, and fragility of metallic melts, is applied for the analysis of about 30 nonmetallic glassy systems, ranging from oxide network glasses to alcohols, low-molecular-weight liquids, polymers, plastic crystals, and even ionic glass formers. The model is based on the power-law exponent lambda representing the steepness parameter of the repulsive part of the inter-atomic or -molecular potential and the thermal-expansion parameter alpha_T determined by the attractive anharmonic part of the effective interaction. I…
Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the…
In this work, we investigate the ageing behavior of soft glassy solids of aqueous suspension of laponite under shear flow. We observe that when an imposed time is normalized by a dominating relaxation time of the system, the rheological response at different ages shows superposition. Analysis of this behavior suggests that the structural evolution with age under a deformation field, as represented by the dependence of dominant relaxation mode on age, becomes weaker as the system becomes progressively less homogeneous due to enhanced attractive interactions caused by addition of salt. Creep-rec…
We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory. By invoking a high temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron scattering measurements. In contrast, in the same format strongly non-universal behavior is found for the activation barrier that controls lo…
We propose that the properties of glass transition can be understood on the basis of elastic waves. Elastic waves originating from atomic jumps in a liquid propagate local expansion due to the anharmonicity of interatomic potential. This creates dynamic compressive stress, which increases the activation barrier for other events in a liquid. The non-trivial point is that the range of propagation of high-frequency elastic waves, $d_{\rm el}$, increases with liquid relaxation time $τ$. A self-consistent calculation shows that this increase gives the Vogel-Fulcher-Tammann (VFT) law. In the propose…
Building on the elastically collective nonlinear Langevin equation theory developed for hard spheres in the preceding paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermal liquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility. The result is a zero adjustable parameter theory that can quantitatively address in a unified manner the alpha relaxation time over 14 or more decades. The theory has no singularities above zero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a r…
