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 proposed theory, we discuss the origin of two dynamic crossovers in a liquid: 1) the crossover from exponential to non-exponential and from Arrhenius to VFT relaxation at high temperature and 2) the crossover from the VFT to a more Arrhenius-like relaxation at low temperature. The corresponding values of $τ$ at the two crossovers are in quantitative parameter-free agreement with experiments. The origin of the second crossover allows us to reconcile the ongoing controversy surrounding the possible divergence of $τ$. The crossover to Arrhenius relaxation universally takes place when $d_{\rm el}$ reaches system size, thus avoiding divergence and associated theoretical complications such as identifying the nature of the phase transition and the second phase itself. Finally, we discuss the effect of volume on $τ$ and the origin of liquid fragility.
Glass-to-glass and liquid-to-liquid phase transitions were observed many years ago in bulk and confined water with or without applied pressure. It is shown that they result from the competition of two-liquid phases separated by an enthalpy difference depending on temperature. The model is based on the classical nucleation equation of these phases completed by this enthalpy saving existing at all temperatures and a pressure contribution. The thermodynamic parameters of amorphous water, the multiple glass transition temperatures, the enthalpy changes, and the temperature of maximum density under…
A liquid can exist under conditions of thermodynamic stability or metastability within boundaries defined by the liquid-gas spinodal and the glass transition line. The relationship between these boundaries has been investigated previously using computer simulations, the energy landscape formalism, and simplified model calculations. We calculate these stability boundaries semi-analytically for a model glass forming liquid, employing accurate liquid state theory and a first-principles approach to the glass transition. These boundaries intersect at a finite temperature, consistent with previous s…
In network glass including chalcogenides, the network topology of microscopic structures can be tuned by changing the chemical compositions. As the composition is varied, an intermediate phase (IP) singularly different from the adjacent floppy or rigid phases on sides has been revealed in the vicinity of the rigidity onset of the network. Glass formers in the IP appear to be reversible at glass transition and strong in dynamical fragility. Meanwhile, the calorimetry experiments indicate the existence of a first-order liquid-liquid transition (LLT) at a temperature above the glass transition in…
The specific heat of liquid helium confined under pressure in nanoporous material and the formation, in these conditions, of a glass phase accompanied by latent heat are known. These properties are in good agreement with a recent model predicting, in liquid elements, the formation of ultrastable glass having universal thermodynamic properties. The third law of thermodynamics involves that the specific heat decreases at low temperatures and consequently the effective transition temperature of the glass increases up to the temperature where the frozen enthalpy becomes equal to the predicted valu…
Incoherent neutron scattering experiments are simulated for simple dynamic models: a glass (with a smooth distribution of harmonic vibrations) and a viscous liquid (described by schematic mode-coupling equations). In most situations multiple scattering has little influence upon spectral distributions, but it completely distorts the wavenumber-dependent amplitudes. This explains an anomaly observed in recent experiments.
The fragility, that controls the temperature-dependent viscous properties of liquids as the glass transition is approached, in various glass-forming liquids with different atomic interactions and densities is investigated by molecular dynamic simulations. We show the landscape of fragility in purely repulsive systems can be separated into three regions with qualitatively disparate dynamic behaviors, suggesting that the density plays an unexpected role for understanding the repulsive steepness dependence of fragility. Furthermore, the vastly dissimilar influences of attractive interaction on fr…
The shapes of cooperatively rearranging regions in glassy liquids change from being compact at low temperatures to fractal or ``stringy'' as the dynamical crossover temperature from activated to collisional transport is approached from below. We present a quantitative microscopic treatment of this change of morphology within the framework of the random first order transition theory of glasses. We predict a correlation of the ratio of the dynamical crossover temperature to the laboratory glass transition temperature, and the heat capacity discontinuity at the glass transition, Delta C_p. The pr…
The dynamics of confined glassforming liquids is discussed on the basis of the recent extension of the mode coupling theory for the liquid-glass transition to the model of the quenched-annealed binary mixture. It is in particular shown that, in confinement, the density correlation functions always decay to a non-zero infinite time value, even in the fluid state, and some clarification is given about the question of the relation between structure and dynamics in confined fluids.
By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at…
We have performed dielectric spectroscopy on the molecular glass-formers glycerol, propylene carbonate (PC) and the ionic melts CKN and CRN. The frequency range covers almost 20 decades from some micro-Hz to some THz. The meausrement results are compared to neutron and light scattering data and analysed with mode coupling theory.
In this Comment, we argue that the behavior of the overlap functions reported in the commented paper can be fully understood in terms of the physics of simple liquids in contact with disordered substrates, without appealing to any particular glassy phenomenology. This suggestion is further supported by an analytic study of the one-dimensional Ising model provided as Supplementary Material.
We explore the smectic liquid crystal order in a cell with a "dirty" substrate imposing random pinnings. Within harmonic elasticity we find a subtle three-dimensional surface disorder-driven transition into a pinned smectic-glass, controlled by a three-dimensional Cardy-Ostlund-like fixed line, akin to a super-rough phase of a two-dimensional xy model. We compute the associated random substrate-driven distortions of the smectic-glass state, identify the characteristic length scales on the heterogeneous substrate and in the bulk, and discuss a variety of experimental signatures.
The point-to-set correlation function has proved to be a very valuable tool to probe structural correlations in disordered systems, but more than that, its detailed behavior has been used to try to draw information on the mechanisms leading to glassy behavior in supercooled liquids. For this reason it is of primary importance to discern which of those details are peculiar to glassy systems, and which are general features of confinement. Within the present response we provide an answer to the concerns raised in [J. Chem. Phys. 144, 227101 (2016)].
Supercooled liquids give rise, by homogeneous nucleation, to solid superclusters acting as building blocks of glass, ultrastable glass, and glacial glass phases before being crystallized. Liquid-to-liquid phase transitions begin to be observed above the melting temperature Tm as well as critical undercooling depending on critical overheating (Tm-T)/Tm. Solid nuclei exist above Tm and melt by homogeneous nucleation of liquid instead of surface melting. The Gibbs free energy change predicted by the classical nucleation equation is completed by an additional enthalpy which stabilize these solid e…
Glass-to-glass and liquid-to-liquid phase transitions are observed in bulk and confined water, with or without applied pressure. They result from the competition of two liquid phases separated by an enthalpy difference depending on temperature. The classical nucleation equation of these phases is completed by this quantity existing at all temperatures, a pressure contribution, and an enthalpy excess. This equation leads to two homogeneous nucleation temperatures in each liquid phase, the first one being the formation temperature of an ordered liquid phase below the melting temperature and the …
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…
The rapid rise of viscosity or relaxation time upon supercooling is universal hallmark of glassy liquids. The temperature dependence of the viscosity, however, is quite non universal for glassy liquids and is characterized by the system's "fragility," with liquids with nearly Arrhenius temperature-dependent relaxation times referred to as strong liquids and those with super-Arrhenius behavior referred to as fragile liquids. What makes some liquids strong and others fragile is still not well understood. Here we explore this question in a family of glassy liquids that range from extremely strong…
The behaviour of a model glass forming liquid is analyzed for a range of densities, with a focus on the temperature interval where the liquid begins to display non-Arrhenius temperature dependence of relaxation times. Analyzing the dynamics along with properties of local potential energy minima sampled by the liquid, a crossover or onset temperature $T_s$ is identified below which the liquid manifests {\it slow dynamics}, and a change in the character of typical local potential energy minima.
The liquid-gas spinodal and the glass transition define ultimate boundaries beyond which substances cannot exist as (stable or metastable) liquids. The relation between these limits is analyzed {\it via} computer simulations of a model liquid. The results obtained indicate that the liquid - gas spinodal and the glass transition lines intersect at a finite temperature, implying a glass - gas mechanical instability locus at low temperatures. The glass transition lines obtained by thermodynamic and dynamic criteria agree very well with each other.
In ref. cond-mat/0005372, Sastry studies by numerical simulations the phase diagram of a simple fragile glass-forming liquid, presenting very interesting and clear results. We apply to this system, at various density values, the analytic approach to structural glass thermodynamics recently introduced and we compare our theoretical predictions on the liquid-glass transition temperature with Sastry's data.
In order to point out the influence of thermal history (fictive temperature) and OH content on the elastic properties of silica glass, we have performed high resolution in situ Brillouin spectra of SiO2 glass from room temperature to the supercooled liquid at 1773K across the glass transition. The well known anomalous increase of elastic modulus in the glassy state and in the supercooled liquid regime is observed. No change of slope in the elastic moduli of silica appears as a characteristic of glass transition, on the contrary to what happens in various other glasses. We show that thermal his…
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…
We study numerically a monodisperse model of interacting classical particles predicted to exhibit a static liquid-glass transition. Using a dynamical Monte Carlo method we show that the model does not freeze into a glassy phase at low temperatures. Instead, depending on the choice of the hard-core radius for the particles the system either collapses trivially or a polycrystalline hexagonal structure emerges.
Generally there are two strategies in fitting the measured structural relaxation time of glass-forming liquids: the single-formula approach e.g. the Vogel-Tammann-Fulcher equation,and the multi-branch approach. In this note, a two-branch method was presented. By analyzing existing single- and multi-branch approaches, I am trying to recall the attention of researchers in this field to the possibilities of the multi-branch approach.
The liquid state is one of the fundamental and essential states of matter, but its physical understanding is far behind the other states, such as the gas and solid states, due to the difficulties associated with the high density causing many-body correlations and the lack of long-range order. Significant open problems in liquid science include glass transition, crystallization, and water's anomalies. Austen Angell has contributed tremendously to these problems and proposed many new concepts of fundamental importance. In this article, we review how these concepts have influenced our work on liq…
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 that the origin of the Vogel-Fulcher-Tammann law is the increase of the range of elastic interaction between local relaxation events in a liquid. In this picture, we discuss the origin of cooperativity of relaxation, the absence of divergence of relaxation time at a finite temperature and the crossover to a more Arrhenius behaviour at low temperature.
We propose that glass-forming liquids are intrinsically under the influences of both fluctuating interactions and random fields well-known in the field of spin systems. This is due to the frustration between the isotropic and anisotropic parts of effective intermolecular interactions. Our model indicates the existence of two key temperatures relevant to glass transition, the density ordering point T^*_m and the Vogel-Fulcher temperature T_0. Between T^*_m and T_0, a system has features similar to the `Griffiths phase', while below $T_0$ it has those peculiar to the `spin-glass phase'. This pic…
We introduce an approach to derive an effective scalar field theory for the glass transition; the fluctuating field is the overlap between equilibrium configurations. We apply it to the case of constrained liquids for which the introduction of a conjugate source to the overlap field was predicted to lead to an equilibrium critical point. We show that the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model. The quenched disorder is provided here by a reference equilibrium liquid c…
Glass-forming liquids display strong fluctuations -- dynamical heterogeneities -- near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and timescale, we investigate the probability distributions of two kinds of local fluctuations in the non-equilibrium (aging) regime and in the equilibrium regime; and find them to be very similar in the two regimes and across temperatures. We also observe that, when appropriately rescaled, the integrated dynamic susceptibility is very weakly dependent on temperature and very similar in both…
Based on experimental evidences we present a phenomenological description of the thermal glass transition as a dynamical phase transition. Different susceptibilities calculated on the basis of this description are in good qualitative agreement with experimental data. As an essential feature this novel view of the glass transition reflects the kinetic as well as the transition aspect of the thermal glass transition.
We study a calcium aluminosilicate glass of composition (SiO2)0.60(Al2O3)0.10(CaO)0.30 by means of molecular dynamics. To this end, we conduct parallel simulations, following a consistent methodology, but using three different potentials. Structural and elastic properties are analyzed and compared to available experimental data. This allows assessing the respective abilities of the potentials to produce a realistic glass. We report that, although all these potentials offer a reasonable glass structure, featuring tricluster oxygen atoms, their respective vibrational and elastic predictions diff…
Due to nonuniform aggregation in liquid state, from the thermodynamic point of view any glass-forming liquid in the vicinity of the liquid-to-solid phase transition temperature, irrespective of its actual chemical composition, shall be described in terms of a complex multicomponent solution whose comprised of the same chemical elements components have characteristic atomic arrangement deviating to various extent from the thermodynamic ground state with respect to the size, shape, density, structure, and stoichiometry. Therefore, glass transition appears to be a process of non-equilibrium solid…
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 review the phenomena of dynamical heterogeneity in glass-forming systems and its description within replica and mean-field theories of the glass transition.
Raman scattering, IR reflectance and modulated DSC measurements are performed on specifically prepared dry (AgI)x(AgPO3)1-x glasses over a wide range of compositions 0 < x < 0.60. A reversibility window is observed in the 0.095< x < 0.378 range, which fixes the elastically rigid but unstressed regime also known as the Intermediate Phase. Glass compositions at x < 0.095 are stressed-rigid, while those at x > 0.378 elastically flexible. Raman optical elasticity power-laws, trends in the nature of the glass transition endotherms corroborate the three elastic phase assignments. Ionic conductivitie…
The relationship between spatially heterogeneous dynamics (SHD) and jamming is studied in a glass-forming binary Lennard-Jones system via molecular dynamics simulations. It has been suggested that the probability distribution of interparticle forces $P(F)$ develops a peak at the glass transition temperature $T_g$, and that the large force inhomogeneities, responsible for structural arrest in granular materials, are related to dynamical heterogeneities in supercooled liquids that form glasses. It has been further suggested that ``force chains'' present in granular materials may exist in superco…
If quenched fast enough, a liquid is able to avoid crystallization and will remain in a metastable supercooled state down to the glass transition, with an important increase in viscosity upon further cooling. There are important differences in the way liquids relax as they approach the glass transition, rapid or slow variation in dynamic quantities under moderate temperature changes, and a simple means to quantify such variations is provided by the concept of "fragility". Here, we report molecular dynamics simulations of a typical network-forming glass, Ge-Se, and find that the relaxation beha…
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
A microscopically motivated theory of glassy dynamics based on an underlying random first order transition is developed to explain the magnitude of free energy barriers for glassy relaxation. A variety of empirical correlations embodied in the concept of liquid "fragility" are shown to be quantitatively explained by such a model. The near universality of a Lindemann ratio characterizing the maximal amplitude of thermal vibrations within an amorphous minimum explains the variation of fragility with a liquid's configurational heat capacity density. Furthermore the numerical prefactor of this cor…
Dynamic heterogeneity as one of the most important properties in supercooled liquids has been found for several decades. However, its structural origin remains open for many systems. Here, we propose a new structural parameter to characterize local atomic packing in metallic liquids. It is found that the new parameter in a simulated metallic glass-forming liquid is closely correlated with potential energy and atomic mobility. It also exhibits significant spatial heterogeneities and these structural fluctuations show close correlation with the spatial distribution of the long-time dynamic prope…
The relation between Poisson's ratio of a glass and fragility of a liquid recently proposed is re-examined in light of evaluation of a large number of data available in the literature
The ratio between the couplings of a relaxational process to compression and shear, respectively, is calculated in the Eshelby picture of structural rearrangements within a surrounding elastic matrix, assuming a constant density of stable structures in distortion space. The result is compared to experimental data for the low-temperature tunneling states in glasses and to Prigogine-Defay data at the glass transition from the literature.
A lattice model of spinless interacting electrons is used to formulate the Landau theory of the Fermi liquid to electron glass quantum phase transition. We demonstrate that the presence of additional random site energies does not affect the character of the transition, once the replica symmetry breaking is considered self-consistently at the mean-field level. Inside the glass phase, the low temperature conductivity assumes a non-Fermi liquid ~ T^{3/2} form, in agreement with recent experiments.
We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass forming liquid consisting of a two component mixture of soft spheres in three dimensions. As the temperature is lowered, the generalized compressibility drops sharply at the glass transition. Our results are consistent with the kinetic view of the glass transition, but not with an underlying second order phase transition.
We discuss two main universal dynamic crossovers in a liquid that correspond to relaxation times of 1 ps and 10^{-7}--10^{-6} s. We introduce the concept of liquid elasticity length $d_{\rm el}$. At room temperature, $d_{\rm el}$ is several Åin water and increases to 0.01 mm in honey and 1 mm in tar. We discuss that on temperature decrease, $d_{\rm el}=d_{\rm m}$ and $d_{\rm el}=L$ correspond to the two dynamic crossovers, where $d_{\rm m}$ is the medium-range order and L is system size. The second crossover defines all kinetic aspects of the glass transition whereas ``thermodynamic'' glass tr…
Amorphous solids under mechanical strains are prone to plastic responses. Recent work showed that in amorphous granular system these plastic events, that are typically quadrupolar in nature, can screen the elastic response. When the density of the quadrupoles is high, the gradients of the quadrupole field act as emergent dipole sources, leading to qualitative changes in the mechanical response, as seen for example in the displacement field. In this paper we examine the effect of screening in classical glass formers. These are made of point particles that interact via binary forces. Both invers…
We study the thermodynamic and dynamic phase transitions in two-dimensional polydisperse hard disks using Monte Carlo methods. A conventional local Monte Carlo algorithm allows us to observe a dynamic liquid-glass transition at a density, which depends very little on the degree of polydispersity. We furthermore apply Monte Carlo methods which sample the Boltzmann equilibrium distribution at any value of the density and polydispersity, and remain ergodic even far within the glass. We find that the dynamical transition is not accompanied by a thermodynamic transition in this two-dimensional syst…
We use computer simulations to investigate the static properties of a simple glass-forming fluid in which the positions of a finite fraction of the particles has been frozen in. By probing the equilibrium distribution of the overlap between independent configurations of the liquid, we find strong evidence that this random pinning induces a glass transition. At low temperatures, our numerical findings are consistent with the existence of a random first order phase transition rounded by finite size effects.
This is our reply to the comment by Sausset and Tarjus (arXiv:0802.1631) on our paper titled "Correlation between Dynamic Heterogeneity and Medium-Range Order in Two-Dimensional Glass-Forming Liquids" [Phys. Rev. Lett. Vol. 99, No. 21, 215701 (2007)].
We divide glass and viscous liquid sciences into two major research areas, the first dealing with how to avoid crystals and so access the viscous liquid state, and the second dealing with how liquids behave when no crystals form. We review some current efforts to elucidate each area, looking at strategies for vitrification of monatomic metals in the first, and the origin of the property fragility in the second. Essential here is the non- trivial behavior of the glassformer thermodynamics. We explore the findings on nonexponential relaxationand dynamic heterogeneities in viscous liquids, emphas…
Super-cooled liquids are characterized by their fragility: the slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass -- a purely local property of the free energy landscape -- is a good predictor of fragility. In particular, materials presenting a la…
We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact solution on a completely connected lattice demonstrates that for large enough M it belongs to the class of mean-field systems solved by a one step replica symmetry breaking Ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behaviour similar to the one of glass-forming liquids. The …
Some facets of the way sound waves travel through glasses are still unclear. Recent works have shown that in the low-temperature harmonic limit a crucial role in controlling sound damping is played by local elastic heterogeneity. Sound waves propagation has been demonstrated to be strongly affected by inhomogeneous mechanical features of the materials, which add to the anharmonic couplings at finite temperatures. We describe the interplay between these two effects by molecular dynamics simulation of a model glass. In particular, we focus on the transverse components of the vibrational excitati…
