We develop the elastically collective nonlinear Langevin equation theory of bulk relaxation of glass-forming liquids to investigate molecular mobility under compression conditions. The applied pressure restricts more molecular motion and therefore significantly slows-down the molecular dynamics when increasing the pressure. We quantitatively determine the temperature and pressure dependence of the structural relaxation time. To validate our model, dielectric spectroscopy experiments for three rigid and non-polymeric supramolecules are carried out at ambient and elevated pressures. The numerical results quantitatively agree with experimental data.
This report proposes the solution of the long standing problem regarding the key property governing the pressure related dynamics in glass forming and complex systems: the determination of the apparent activation volume Va and its pressure dependence. Results are tested in the previtreous domain, up to P ~ 1.2 GPa, for glass forming diisobutyl phthalate (DIIP, low molecular weight liquid), isoctyloxycyanobiphenyl (8*OCB, liquid crystal), bisphenol A/epichlorohydrin (EPON 828, epoxy resin).
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…
The role of porous structure and glass density in response to compressive deformation of amorphous materials is investigated via molecular dynamics simulations. The disordered, porous structures were prepared by quenching a high-temperature binary mixture below the glass transition into the phase coexistence region. With decreasing average glass density, the pore morphology in quiescent samples varies from a random distribution of compact voids to a porous network embedded in a continuous glass phase. We find that during compressive loading at constant volume, the porous structure is linearly …
We theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulation. An external pressure restricts local motions of a single molecule within its cage and triggers the slowing down of cooperative mobility. While the ECNLE theory and simulation generally predict a monotonic increase of the glass transition temperature and dynamic fragility with pressure, the simulation indicates a decrease of fragility as pressure above 10…
A key property of glass forming alloys, the anomalously small volume difference with respect to the crystal, is shown to arise as a direct consequence of the soft repulsive potentials between metals. This feature of the inter-atomic potential is demonstrated to be responsible for a significant component of the glass forming ability of alloys due to the decrease in the enthalpy of fusion and the associated depression of the freezing point.
The glass-forming ability is an important material property for manufacturing glasses and understanding the long-standing glass transition problem. Because of the nonequilibrium nature, it is difficult to develop the theory for it. Here we report that the glass-forming ability of binary mixtures of soft particles is related to the equilibrium melting temperatures. Due to the distinction in particle size or stiffness, the two components in a mixture effectively feel different melting temperatures, leading to a melting temperature gap. By varying the particle size, stiffness, and composition ove…
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…
Bulk metallic glasses (BMGs) are produced by rapidly thermally quenching supercooled liquid metal alloys below the glass transition temperature at rates much faster than the critical cooling rate R_c below which crystallization occurs. The glass-forming ability of BMGs increases with decreasing R_c, and thus good glass-formers possess small values of R_c. We perform molecular dynamics simulations of binary Lennard-Jones (LJ) mixtures to quantify how key parameters, such as the stoichiometry, particle size difference, attraction strength, and heat of mixing, influence the glass-formability of m…
It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [S. P. Bierwirth \textit{et al.}, Phys. Rev. Lett. {\bf 119}, 248001 (2017)]. Inspired by these results we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing unit (GPU)-based molecular-dynamics simulations are presented. We find that the low-t…
We study signatures of the energy landscape's evolution through the crystal-to-glass transition by compressing 2D finite aggregates of oil droplets. Droplets of two distinct sizes are used to compose small aggregates in an aqueous environment. Aggregates range from perfectly ordered monodisperse single crystals to disordered bidisperse glasses. The aggregates are compressed between two parallel boundaries, with one acting as a force sensor. The compression force provides a signature of the aggregate composition and gives insight into the energy landscape. In particular, crystals dissipate all …
The effect of cyclic loading on relaxation dynamics and mechanical properties of metallic glasses is studied using molecular dynamics simulations. We consider the Kob-Andersen three-dimensional binary mixture rapidly cooled across the glass transition and subjected to thousands of tension-compression cycles in the elastic range. It was found that during cyclic loading at constant pressure, the system is relocated to progressively lower levels of the potential energy, thus promoting greater densification and higher strength. Furthermore, with increasing stress amplitude, the average glass densi…
In a recent article, Schmelzer and Tropin [Entropy 20 [2] 103 (2018)] presented an unfounded, confusing critique of several aspects of modern glass science. Relying on pre-Socratic Greek philosophy and state-of-the-art scientific understanding from the 1920s-1930s, Schmelzer and Tropin propagate an antiquated view of glass physics that is at odds with well-accepted knowledge in the field from both theory and experiments conducted in the post-World War II era. The objective of this short letter is to elucidate and extinguish their critique. This rebuttal is directed to our colleagues and especi…
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.
Melting temperatures at ambient pressure of systems of isosceles Lennard-Jones trimers with angles ranging from 70 degrees to 100 degrees are determined. Two crystal structures are considered: a distorted body centered cubic structure and a distorted face centered cubic structure with preferred angles of 77 and 96 degrees, respectively. Liquid dynamics are slowed down when the angle is increased. A trimer angle of 83 degrees yields the largest distance between isochrones and the melting temperature, suggesting that this value gives the optimal glass-forming ability. It is conjectured that bett…
String Model Predicts Relaxation in Sheared Glass-Forming Liquids
Changchun Institute of Applied Chemistry, Chinese Academy of Sciences（中国科学院长春应用化学研究所）；University of Science and Technology of China（中国科学技术大学）；Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所）；University of Chinese Academy of Sciences（中国科学院大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Shanghai Jiao Tong University（上海交通大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
We consider the adiabatic evolution of glassy states under external perturbations. Although the formalism we use is very general, we focus here on infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e. compression or (volume preserving) shear-strain, and we compute the response of glassy states to such perturbations: pressure and shear-stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. F…
We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of backgammon or urn models to a non--constant number of particles, where entropic barriers are replaced by energy barriers, allowing for the existence of activated processes. We formulate a mean--field version of the models, which keeps most of the features of the finite dimensional ones, and solve analytically the out--of--equilibrium dynamics in the low tempe…
This article discusses recent attempts to provide a deeper understanding of the thermoreversible "gel" state of colloidal matter and to unravel the analogies between gels at the colloidal level and gels at the molecular level, commonly known as network-forming strong liquids. The connection between gel-forming patchy colloids and strong liquids is provided by the limited valence of the inter-particle interactions, i.e. by the presence of a limit in the number of bonded nearest neighbors.
The influence of static stress and alternating loading direction on the potential energy and mechanical properties of amorphous alloys is investigated using molecular dynamics simulations. The model glass is represented via a binary mixture which is first slowly annealed well below the glass transition temperature and then subjected to elastostatic loading either along a single direction or along two and three alternating directions. We find that at sufficiently large values of the static stress, the binary glass becomes rejuvenated via collective, irreversible rearrangements of atoms. Upon in…
For fundamentally characterizing the effect of hierarchical structure in granular matter, a set of compression-relaxation tests for dust particles and glass beads confined in a cylindrical cell was performed. Typical diameter of both grains is approximately 1~mm. However, dust particles are produced by binding tiny ($\sim 5$~{\textmu}m) glass beads. The granular columns were compressed with a piston until reaching a maximum load force of 20~N with a constant compression rate $v$ ($0.17 \leq v \leq 2000$~{\textmu}m~s$^{-1}$). After that, the piston was stopped and the relaxation process was qua…
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.
We study the four-point dynamic susceptibility $χ_4(t)$ obtained from Brownian dynamics computer simulations of the Kob-Andersen Lennard-Jones mixture. We compare the results of the simulations with qualitative predictions of the mode-coupling theory. In addition, we test an estimate of the four-point susceptibility recently proposed by Berthier \textit{et al.} [Science, \textbf{310}, 1797 (2005)].
A fascinating feature of metallic glasses is their ability to explore different configurations under mechanical deformations. This effect is usually observed through macroscopic observables, while little is known on the consequence of the deformation at atomic level. Using the new generation of synchrotrons, we probe the atomic motion and structure in a metallic glass under hydrostatic compression, from the onset of the perturbation up to a severely-compressed state. While the structure indicates reversible densification under compression, the dynamic is dramatically accelerated and exhibits a…
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents $1/3 \leq β\leq 1$ and the functional dependence of the structural relaxation time $τ_α$ and exponent $β$ on temperature, density, and wave number.
Dielectric spectroscopy is one of the most commonly used techniques for the investigation of the dynamic response of glass-forming materials. The tremendous slow-down of the particle motions when approaching the glass transition and especially the fast processes in glass-forming materials, which have come into the focus of scientific interest recently, make the investigation in a wide frequency range highly desirable. Recently, results from broadband dielectric spectroscopy on glass-forming materials in their liquid and supercooled-liquid state, covering more than 18 decades of frequency have …
In molecular dynamics simulations of soft glass-formers interacting via repulsions, we find that the glass transition temperature, dynamical heterogeneity, and glass fragility reach their maxima at the same crossover pressure $P_d$. Our analysis of the zero-temperature jammed states indicates that states at $P_d$ have the highest bond orientational order with the largest spatial fluctuation. Correspondingly, the low-frequency normal modes of vibration are the least localized and the average potential energy barrier along these modes are the highest for jammed states in the vicinity of $P_d$. T…
In this note we apply some theoretical predictions that arise in the mean field framework for a large class of infinite range models to structural glasses and we present a first comparison of these predictions with numerical results.
In the last few decades, theoretical and experimental studies of glass-forming liquids have revealed presence of universal regularities in the viscosity-temperature data. In the present work, we propose a viscosity model for scaling description of experimental viscosity data. A feature of this model is presence of only two adjustable parameters and high accuracy of experimental data approximation by this model for a wide temperature range. The basis of the scaling description is an original temperature scale. Within this scaling description we obtain the transformed Angell plot, in which the a…
Glass forming ability (GFA) is a property of utmost importance in glass science and technology. In this paper, we used a statistical methodology---involving bootstrap sampling and the Wilcoxon test---to find out which glass stability parameters can better predict the glass forming ability. We collected or measured the necessary data for twelve stoichiometric oxide glasses that underwent predominant heterogeneous nucleation (the most common case). We found that some GS parameters could predict the GFA of these oxide glasses quite well, whereas others perform poorly. Parameter $K_w$ was the top …
All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system. Most prior work has considered the mean values of liquid or glass properties, such as the average number of topological degrees of freedom per atom; however, the localized fluctuations in properties also play a key role in governing the macroscopic characteristics of any glass-forming system. This paper proposes a generalized approach for modeling topological …
This review deals with the kinetic and thermodynamic fragility of bulk metallic glass forming liquids. The experimental methods to determine the kinetic fragility, relaxation behavior and thermodynamic functions of undercooled metallic liquids are introduced. Existing data are assessed and discussed using the Vogel-Fulcher-Tammann equation and in the frameworks of the Adam-Gibbs as well as the Cohen-Turnbull free volume approach. In contrast to pure metals and most non glass forming alloys, bulk glass formers are moderately strong liquids. In general the fragility parameter $D^{*} $ increases …
We introduce a new theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed.
The local organisation of a simulated glass-forming mixture due to Kob and Andersen is analysed. Evidence is presented for a structural transition from triangulated coordination polyhedra to cubic as the number fraction of the smaller species B increases towards equimolar. The impact of the change on the partial radial distribution function g-{BB}(r) is established. The dependence of the crystallisation rate on the composition is determined and the related to the observed structural changes.
Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. The short-time $β$-relaxation is generally attributed to spatially local processes involving the rattling motion of a particle in the transient cage formed by its neighbors. Using molecular dynamics simulations for three model glass-forming liquids, we show that the $β$-relaxation is actually cooperative in nature. Using finite-size scaling analysis, we extract a growing length-scale associated with $β$-relaxation from the observed dependence of the $β$-relaxation time on the …
If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a …
Bulk metallic glasses (BMGs) are amorphous alloys with desirable mechanical properties and processing capabilities. To date, the design of new BMGs has largely employed empirical rules and trial-and-error experimental approaches. Ab initio computational methods are currently prohibitively slow to be practically used in searching the vast space of possible atomic combinations for bulk glass formers. Here, we perform molecular dynamics simulations of a coarse-grained, anisotropic potential, which mimics interatomic covalent bonding, to measure the critical cooling rates for metal-metalloid alloy…
Motivated by recent experimental studies probing i) the existence of a mobile layer at the free surface of glasses, and ii) the capillary leveling of polymer nanofilms, we study the evolution of square-wave patterns at the free surface of a generic glass-forming binary Lennard-Jones mixture over a wide temperature range, by means of molecular dynamics simulations. The pattern's amplitude is monitored and the associated decay rate is extracted. The evolution of the latter as a function of temperature exhibits a crossover between two distinct behaviours, over a temperature range typically bounde…
There is growing evidence that slow dynamics and dynamic heterogeneity possess structural signatures in glass-forming liquids. However, even in the weakly frustrated glass-forming liquids, whether or not the dynamic heterogeneity has a structural origin is a matter of debate. Via molecular dynamics simulation, we present a study of examining the connection between dynamic heterogeneity and bond orientational order in a weakly frustrated glass-forming liquid in two dimensions by taking advantage of assessing the effect of attractions on the correlation length scales. We find that attractions ca…
Translational dynamics of two-dimensional glass forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation and well developed plateaus are observed in orientational correlation functions. It has been suggested that by monitoring translational motion …
We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero temperature dynamical critical point. To support our proposal, we derive from simple physical assumptions a dynamic field theory for supercooled liquids, which we study using the renormalization group (RG). Its long time behaviour is dominated by a zero temperature critical point, which for dimensions d > 2 belongs to the directed percolation universality class. Molecular dynamics simulations confirm the existence of dynamic scaling behaviour consistent with the RG pr…
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…
Existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems l…
We discuss the relaxation dynamics of a simple lattice gas model for glass-forming systems and show that with increasing density of particles this dynamics slows down very quickly. By monitoring the trajectory of tagged particles we find that their motion is very heterogeneous in space and time, leading to regions in space in which there is a fast dynamics and others in which it is slow. We determine how the geometric properties of these quickly relaxing regions depend on density and time. Motivated by this heterogeneous hopping dynamics, we use a simple model, a variant of a continuous time r…
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…
We speculate that glass-forming liquids may contain fairly large and well-defined crystallites. This is based on arguing that the slowly relaxing "frozen-in" stresses characterizing ultraviscous liquids increase the barrier for nucleation, thus allowing for larger unstable crystallites than otherwise possible. The frozen-in stresses also deform the crystallites, making their observation difficult; specifically it is argued that a situation where 1/N of the molecules form N X N X N crystallites would be hard to detect by standard X-ray or neutron scattering experiments.
The temperature dependence of the non-ergodicity factor of vitreous GeO$_2$, $f_{q}(T)$, as deduced from elastic and quasi-elastic neutron scattering experiments, is analyzed. The data are collected in a wide range of temperatures from the glassy phase, up to the glass transition temperature, and well above into the undercooled liquid state. Notwithstanding the investigated system is classified as prototype of strong glass, it is found that the temperature- and the $q$-behavior of $f_{q}(T)$ follow some of the predictions of Mode Coupling Theory. The experimental data support the hypothesis of…
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.
A theory which uses data of the static pair-correlation function is developed to calculate quantities associated with the viscous slowing down of supercooled liquids. We calculate value of the energy fluctuations that determine the number of stable bonds a particle forms with neighbors from data of the structural relaxation time. The number of bonds and the activation energy for relaxation are shown to increase sharply in a narrow temperature range close to the glass temperature. The configurational entropy calculated from values of the configurational fluctuations is found in good agreement w…
We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field $p$-spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a non-trivial universal exponent at high temperatures crossing over to a harmoni…
Via molecular dynamics simulations of a generic glass former in the supercooled and normal liquid states, it is shown that spatial correlations of strain fluctuations exhibit a crossover from the well-established power-law $\sim 1/r^3$-decay at long wavelengths to an exponential behavior, $\sim \exp(-r/l_{\text {c}})$ at intermediate distances. The characteristic length of the exponential decay grows both with temperature and time via, $l_{\text {c}}^2 \propto D(T)\, t$, with $D(T)$ being the temperature-dependent diffusion coefficient. This suggests that the crossover between the power-law an…
We theoretically investigate physical properties of the pressure-induced activation volume and dynamic decoupling of ternidazole, glycerol, and probucol by the Elastically Collective Nonlinear Langevin Equation theory. Based on the predicted temperature dependence of activated relaxation under various compression, the activation volume is determined to characterize effects of pressure on molecular dynamics of materials. We find that the decoupling of the structural relaxation time of compressed systems from their bulk uncompressed value is governed by the power-law rule. The decoupling exponen…
We examine the relation between the free volume per particle and the variance of the particle position, equivalent to a local Debye-Waller (DW) factor for a 2D glass-forming alloy using molecular dynamics simulations. We find that the latter quantity exhibits significant spatial heterogeneity despite involving trajectories two orders of magnitude shorter than those typically used to measure such heterogeneities. We find that the free volume exhibits no significant spatial correlation with the local DW factor. We conclude that the spatial variation in local free volume is not the cause of the s…
Analysis of temperature dependence of structural relaxation time in supercooled liquids revealed a qualitatively distinct feature - a sharp, cusp-like maxumum in the second derivative of its logarithm. It suggests that the super-Arrhenius behavior of the structural relaxation time in glass-forming liquids eventually crosses over to the Arrhenius behavior below the temperature of maximum, and there is no divergence of the relaxation time at non-zero temperature. The position of the maximum can be both above or below glass transition temperature, depending on the sensitivity of the structural re…
Mixtures of glass-forming fluids sometimes exhibit glass-glass phase separation at low temperatures. Here, we use a molecular dynamics simulation to study one of the simplest examples of the glass-glass phase separation. We consider a mixture composed of type A and B particles, in which the A-A and B-B interactions are the identical Lennard-Jones interactions and the A-B interaction is repulsive only. To avoid crystallization, we also introduce the polydispersity in the particle sizes for each component. We study the phase separation kinetics of this model at a 50:50 concentration at various t…
The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain w…
We propose and use a novel, hybrid Monte Carlo algorithm that combines configurational bias particle swaps with parallel tempering. We use this new method to simulate a standard model of a glass forming binary mixture above and below the so-called mode-coupling temperature, Tmct. We find that an ansatz that was used previously to extrapolate thermodynamic quantities to temperatures below Tmct breaks down in the vicinity of the mode-coupling temperature. Thus, previous estimates of the so-called Kauzmann temperature need to be reexamined. Also, we find that the Adam-Gibbs relations D ~ exp(-a/T…
