Theories of glass formation and the glass transition

Classical route to ergodicity and scarring in collective quantum systems

Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.

Mean-field model for the Curie-Weiss temperature dependence of coherence length in metallic liquids

The coherence length of the medium-range order (MRO) in metallic liquids is known to display a Curie-Weiss temperature dependence; its inverse is linearly related to temperature, and when extrapolated from temperatures above the glass transition, the coherence length diverges at a negative temperature with a critical exponent of unity. We propose a mean-field pseudospin model that explains this behavior. Specifically, we model the atoms and their local environment as Ising spins with antiferromagnetic exchange interactions. We further superimpose an exchange interaction between dynamical heterogeneities, or clusters of atoms undergoing cooperative motion. The coherence length in the metallic liquid is thus the correlation length between dynamical heterogeneities. Our results reaffirm the idea that the MRO coherence length is a measure of point-to-set correlations, and that local frustrations in the interatomic interactions are prominent in metallic liquids.

Tagged-particle motion of Percus-Yevick hard spheres from first principles

We develop a first-principles-based generalized mode-coupling theory (GMCT) for the tagged-particle motion of glassy systems. This theory establishes a hierarchy of coupled integro-differential equations for self-multi-point density correlation functions, which can formally be extended up to infinite order. We use our GMCT framework to calculate the self-nonergodicity parameters and the self-intermediate scattering function for the Percus-Yevick hard-sphere system based on the first few levels of the GMCT hierarchy. We also test the scaling laws in the α- and β-relaxation regimes near the glass-transition singularity. Furthermore, we study the mean-square displacement and the Stokes-Einstein relation in the supercooled regime. We find that qualitatively our GMCT results share many similarities with the well-established predictions from standard mode-coupling theory, but the quantitative results change, and typically improve, by increasing the GMCT closure level. However, we also demonstrate on general theoretical grounds that the current GMCT framework is unable to account for violation of the Stokes-Einstein relation, underlining the need for further improvements in the first-principles description of glassy dynamics.

Multi-component generalized mode-coupling theory: predicting dynamics from structure in glassy mixtures

The emergence of glassy dynamics and the glass transition in dense disordered systems is still not fully understood theoretically. Mode-coupling theory (MCT) has shown to be effective in describing some of the non-trivial features of glass formation, but it cannot explain the full glassy phenomenology due to the strong approximations on which it is based. Generalized mode-coupling theory (GMCT) is a hierarchical extension of the theory, which is able to outclass MCT by carefully describing the dynamics of higher-order correlations in its generalized framework. Unfortunately, the theory has so far only been developed for single-component systems and as a result works poorly for highly polydisperse materials. In this paper, we solve this problem by developing GMCT for multi-component systems. We use it to predict the glassy dynamics of the binary Kob-Andersen Lennard-Jones mixture, as well as its purely repulsive Weeks-Chandler-Andersen analogue. Our results show that each additional level of the GMCT hierarchy gradually improves the predictive power of GMCT beyond its previous limit. This implies that our theory is able to harvest more information from the static correlations, thus being able to better understand the role of attraction in supercooled liquids from a first-principles perspective.

Dimensionality dependence of the Kauzmann temperature: A case study using bulk and confined water

The Kauzmann temperature (T_K) of a supercooled liquid is defined as the temperature at which the liquid entropy becomes equal to that of the crystal. The excess entropy, the difference between liquid and crystal entropies, is routinely used as a measure of the configurational entropy, whose vanishing signals the thermodynamic glass transition. The existence of the thermodynamic glass transition is a widely studied subject, and of particular recent interest is the role of dimensionality in determining the presence of a glass transition at a finite temperature. The glass transition in water has been investigated intensely and is challenging as the experimental glass transition appears to occur at a temperature where the metastable liquid is strongly prone to crystallization and is not stable. To understand the dimensionality dependence of the Kauzmann temperature in water, we study computationally bulk water (three-dimensions), water confined in the slit pore of the graphene sheet (two-dimensions), and water confined in the pore of the carbon nanotube of chirality (11,11) having a diameter of 14.9 Å (one-dimension), which is the lowest diameter where amorphous water does not always crystallize into nanotube ice in the supercooled region. Using molecular dynamics simulations, we compute the entropy of water in bulk and under reduced dimensional nanoscale confinement to investigate the variation of the Kauzmann temperature with dimension. We obtain a value of T_K (133 K) for bulk water in good agreement with experiments [136 K (C. A. Angell, Science 319, 582-587 (2008) and K. Amann-Winkel et al., Proc. Natl. Acad. Sci. U. S. A. 110, 17720-17725 (2013)]. However, for confined water, in two-dimensions and one-dimension, we find that there is no finite temperature Kauzmann point (in other words, the Kauzmann temperature is 0 K). Analysis of the fluidicity factor, a measure of anharmonicity in the oscillation of normal modes, reveals that the Kauzmann temperature can also be computed from the difference in the fluidicity factor between amorphous and ice phases.

Translational and rotational critical-like behaviors in the glass transition of colloidal ellipsoid monolayers

Critical-like behaviors have been found in translational degrees of freedom near the glass transition of spherical particle systems mainly with local polycrystalline structures, but it is not clear if criticality exists in more general glassy systems composed of nonspherical particles without crystalline structures. Here, through experiments and simulations, we show critical-like behaviors in both translational and rotational degrees of freedom in monolayers of monodisperse colloidal ellipsoids in the absence of crystalline orders. We find rich features of the Ising-like criticality in structure and slow dynamics at the ideal glass transition point ϕ₀, showing the thermodynamic nature of glass transition at ϕ₀ A dynamic criticality is found at the mode-coupling critical point ϕ_c for the fast-moving clusters whose critical exponents increase linearly with fragility, reflecting a dynamic glass transition. These results cast light on the glass transition and explain the mystery that the dynamic correlation lengths diverge at two different temperatures.

Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres

Mode-coupling theory (MCT) constitutes one of the few first-principles-based approaches to describe the physics of the glass transition, but the theory's inherent approximations compromise its accuracy in the activated glassy regime. Here, we show that microscopic generalized mode-coupling theory (GMCT), a recently proposed hierarchical framework to systematically improve upon MCT, provides a promising pathway toward a more accurate first-principles description of glassy dynamics. We present a comprehensive numerical analysis for Percus-Yevick hard spheres by performing explicitly wavenumber- and time-dependent GMCT calculations up to sixth order. Specifically, we calculate the location of the critical point, the associated non-ergodicity parameters, and the time-dependent dynamics of the density correlators at both absolute and reduced packing fractions, and we test several universal scaling relations in the α- and β-relaxation regimes. It is found that higher-order GMCT can successfully remedy some of MCT's pathologies, including an underestimation of the critical glass transition density and an overestimation of the hard-sphere fragility. Furthermore, we numerically demonstrate that the celebrated scaling laws of MCT are preserved in GMCT and that the predicted critical exponents manifestly improve as more levels are incorporated in the GMCT hierarchy. Although formally the GMCT equations should be solved up to infinite order to reach full convergence, our finite-order GMCT calculations unambiguously reveal a uniform convergence pattern for the dynamics. We thus argue that GMCT can provide a feasible and controlled means to bypass MCT's main uncontrolled approximation, offering hope for the future development of a quantitative first-principles theory of the glass transition.

Role of Attractive Interactions in Structure Ordering and Dynamics of Glass-Forming Liquids

A key question in glass physics is what the origin of slow glassy dynamics is. The liquid structure is a natural candidate; however, an apparently severe counterexample has been known. Two model glass-forming liquids, with the standard Lennard-Jones interaction potential and its Weeks-Chandler-Andersen variation without the attractive tail, exhibit very similar structures at the two-body level but drastically different dynamical behaviors in the supercooled states. Here we look at the liquid structure through a (many-body) structural order parameter Θ characterizing the packing capability of local particle arrangements. We show that the structures of these two systems seen by Θ are actually very different at a many-body level, but, quite surprisingly, the macroscopic structure (Θ)-dynamics (τ_{α}) relationships commonly follow a Vogel-Fulcher-Tammann-like function. Furthermore, the mutual information analysis reveals strong local structure-dynamics correlations. Therefore, we conclude that attractive interactions affect the liquid structure in a nonperturbative manner, but a general structural origin of slow dynamics holds for these systems.

A simple mean-field model of glassy dynamics and glass transition

We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.

Active glasses

Active glassy matter has recently emerged as a novel class of non-equilibrium soft matter, combining energy-driven, active particle movement with dense and disordered glass-like behavior. Here we review the state-of-the-art in this field from an experimental, numerical, and theoretical perspective. We consider both non-living and living active glassy systems, and discuss how several hallmarks of glassy dynamics (dynamical slowdown, fragility, dynamical heterogeneity, violation of the Stokes-Einstein relation, and aging) are manifested in such materials. We start by reviewing the recent experimental evidence in this area of research, followed by an overview of the main numerical simulation studies and physical theories of active glassy matter. We conclude by outlining several open questions and possible directions for future work.

Configurational entropy of glass-forming liquids

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 fraught 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 why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.

Spatiotemporal intermittency and localized dynamic fluctuations upon approaching the glass transition

We introduce a robust approach for characterizing spatially and temporally heterogeneous behavior within a system based on the evolution of dynamic fluctuations averaged over different space lengths and timescales. We apply it to investigate the dynamics in two canonical systems as the glass transition is approached: simulated Lennard-Jones liquids and experimental dense colloidal suspensions. In both cases the onset of glassiness is marked by spatially localized dynamic fluctuations originating in regions of correlated mobile particles. By removing the trivial system size dependence we show that the spatial heterogeneity of the dynamics extends to large length scales containing tens to hundreds of particles, corresponding to the timescale of maximally non-Gaussian dynamics.

Glass transition memorized by the enthalpy-entropy compensation in the shear thinning of supercooled metallic liquids

To unravel the true nature of glass transition, broader insights into glass forming have been gained by examining the stress-driven glassy systems, where strong shear thinning, i.e. a reduced viscosity under increasing shear rate, is encountered. It is argued that arbitrarily small stress-driven shear rates would 'melt' the glass and erase any memory of its thermal history. In this work, we report a glass transition memorized by the enthalpy-entropy compensation in strongly shear-thinned supercooled metallic liquids, which coincides with the thermal glass transition in both the transition temperature and the activation Gibbs free energy. Our findings provide distinctive insights into both glass forming and shear thinning, and enrich current knowledge on the ubiquitous enthalpy-entropy compensation empirical law in condensed matter physics.

Melting of superheated molecular crystals

Melting dynamics of micrometer scale, polycrystalline samples of isobutane, dimethyl ether, methyl benzene, and 2-propanol were investigated by fast scanning calorimetry. When films are superheated with rates in excess of 10⁵ K s^-1, the melting process follows zero-order, Arrhenius-like kinetics until approximately half of the sample has transformed. Such kinetics strongly imply that melting progresses into the bulk via a rapidly moving solid-liquid interface that is likely to originate at the sample's surface. Remarkably, the apparent activation energies for the phase transformation are large; all exceed the enthalpy of vaporization of each compound and some exceed it by an order of magnitude. In fact, we find that the crystalline melting kinetics are comparable to the kinetics of dielectric α-relaxation in deeply supercooled liquids. Based on these observations, we conclude that the rate of non-isothermal melting for superheated, low-molecular-weight crystals is limited by constituent diffusion into an abnormally dense, glass-like, non-crystalline phase.

Terahertz wave modulation enhanced by laser processed PVA film on Si substrate

An optically pumped ultrasensitive broadband terahertz (THz) wave modulator based on polyvinyl alcohol (PVA) film on Si wafer was demonstrated in this work. The THz time domain spectroscopy experiments confirm that the PVA/Si can drastically enhance the photo-induced THz wave modulation on the Si surface, especially when the PVA film is heated by a high-power laser. A modulation depth of 72% can be achieved only under 0.55 W/cm² modulated laser power, which is superior significantly to the bare Si. The numerical simulations indicate that the laser processed PVA (LP-PVA) film increases the photo-generated carrier concentration on the Si surface in two orders of magnitude higher than that of bare Si. Moreover, the modulation mechanism and the dynamic process of laser heating on the PVA/Si have been discussed. This highly efficient THz modulation mechanism and its simple fabrication method have great application potentials in THz modulators.

Equation of state of polydisperse hard-disk mixtures in the high-density regime

A proposal to link the equation of state of a monocomponent hard-disk fluid to the equation of state of a polydisperse hard-disk mixture is presented. Event-driven molecular dynamics simulations are performed to obtain data for the compressibility factor of the monocomponent fluid and of 26 polydisperse mixtures with different size distributions. Those data are used to assess the proposal and to infer the values of the compressibility factor of the monocomponent hard-disk fluid in the metastable region from those of mixtures in the high-density region. The collapse of the curves for the different mixtures is excellent in the stable region. In the metastable regime, except for two mixtures in which crystallization is present, the outcome of the approach exhibits a rather good performance. The simulation results indicate that a (reduced) variance of the size distribution larger than about 0.01 is sufficient to avoid crystallization and explore the metastable fluid branch.

Study on the Glass Transition Process of Polymer System Using Differential Scanning Calorimetry and Fourier Transform Infrared Spectroscopy

The change in the infrared spectrum of polymer samples with temperature and their differential scanning calorimetry (DSC) experimental results are analyzed. According to the van't Hoff equation at constant pressure, the changes in the absorbance ratio corresponding to high and low vibrational states are calculated, and the apparent enthalpy differences of the vibration energy states transformation of the characteristic group can be obtained. From the experimental results, we can find that characteristic vibration modes of a chemical group in a polymer are under the influence of the glass transition process of the polymer with a different extent. The characteristic vibration modes of the same chemical group behave differently due to the influence of the polymer system at which the chemical moiety is situated.

Impact of spatial dimension on structural ordering in metallic glass

Metallic glasses (MGs) have so far attracted considerable attention for their applications as bulk materials. However, new physics and applications often emerge by dimensional reduction from three dimensions (3D) to two dimensions (2D). Here, we study, by molecular dynamics simulations, how the liquid-to-glass transition of a binary Cu_{50}Zr_{50} MG is affected by spatial dimensionality. We find clear evidence that crystal-like structural ordering controls both dynamic heterogeneity and slow dynamics, and thus plays a crucial role in the formation of the 2DMG. Although the 2DMG reproduces the dynamical behaviors of its 3D counterpart by considering Mermin-Wagner-type fluctuations specific to 2D, this atomic-scale structural mechanism is essentially different from that for the 3DMG in which icosahedral clusters incompatible with crystallographic symmetry play a key role in glassy behaviors. Our finding provides a structural mechanism for the formation of 2DMGs, which cannot be inferred from the knowledge of 3DMGs. The results suggest a structural basis for the glass transition in 2DMG and provide possible explanations for some previous experimental observations in ultrathin film MGs.

Implanted muon spin spectroscopy on 2-O-adamantane: a model system that mimics the liquid[Formula: see text]glasslike transitions

The transition taking place between two metastable phases in 2-O-adamantane, namely the [Formula: see text] cubic, rotator phase and the lower temperature P2₁/c, Z  =  4 substitutionally disordered crystal is studied by means of muon spin rotation and relaxation techniques. Measurements carried out under zero, weak transverse and longitudinal fields reveal a temperature dependence of the relaxation parameters strikingly similar to those exhibited by structural glass[Formula: see text]liquid transitions (Bermejo et al 2004 Phys. Rev. B 70 214202; Cabrillo et al 2003 Phys. Rev. B 67 184201). The observed behaviour manifests itself as a square root singularity in the relaxation rates pointing towards some critical temperature which for amorphous systems is located some tens of degrees above that shown as the characteristic transition temperature if studied by thermodynamic means. The implications of such findings in the context of current theoretical approaches concerning the canonical liquid-glass transition are discussed.

The role of liquid–liquid transition in glass formation of CuZr alloys

The structure evolution during LLTs is beneficial to the glass forming ability (GFA) of Cu–Zr systems.

Vapor Condensed and Supercooled Glassy Nanoclusters

We use molecular simulation to study the structural and dynamic properties of glassy nanoclusters formed both through the direct condensation of the vapor below the glass transition temperature, without the presence of a substrate, and via the slow supercooling of unsupported liquid nanodroplets. An analysis of local structure using Voronoi polyhedra shows that the energetic stability of the clusters is characterized by a large, increasing fraction of bicapped square antiprism motifs. We also show that nanoclusters with similar inherent structure energies are structurally similar, independent of their history, which suggests the supercooled clusters access the same low energy regions of the potential energy landscape as the vapor condensed clusters despite their different methods of formation. By measuring the intermediate scattering function at different radii from the cluster center, we find that the relaxation dynamics of the clusters are inhomogeneous, with the core becoming glassy above the glass transition temperature while the surface remains mobile at low temperatures. This helps the clusters sample the highly stable, low energy structures on the potential energy surface. Our work suggests the nanocluster systems are structurally more stable than the ultrastable glassy thin films, formed through vapor deposition onto a cold substrate, but the nanoclusters do not exhibit the superheating effects characteristic of the ultrastable glass states.

Anomalously slow relaxation of interacting liquid nanoclusters confined in a porous medium

Anomalously slow relaxation of clusters of a liquid confined in a disordered system of pores has been studied for the (water-L23 nanoporous medium) system. The evolution of the system of confined liquid clusters consists of a fast formation stage followed by slow relaxation of the system and its decay. The characteristic time for the formation of the initial state is τ(p)∼10 s after the reduction of excess pressure after complete filling. Anomalously slow relaxation has been observed for times of 10(1)-10(5) s, and decay has been observed at times of >10(5) s. The time dependence of the volume fraction θ of pores filled with the confined liquid is described by a power law θ∼t(-α) with the exponent α<0.15. The exponent α and temperature dependence α(T) are qualitatively described theoretically for the case of a slightly polydisperse medium in a mean-field approximation with the inclusion of the interaction of liquid clusters and averaging over various degenerate local configurations of clusters. In this approximation, slow relaxation is represented as a continuous transition through a sequence of metastable states of the system of clusters with a decreasing barrier.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

Soft matter food physics--the physics of food and cooking

This review discusses the (soft matter) physics of food. Although food is generally not considered as a typical model system for fundamental (soft matter) physics, a number of basic principles can be found in the interplay between the basic components of foods, water, oil/fat, proteins and carbohydrates. The review starts with the introduction and behavior of food-relevant molecules and discusses food-relevant properties and applications from their fundamental (multiscale) behavior. Typical food aspects from 'hard matter systems', such as chocolates or crystalline fats, to 'soft matter' in emulsions, dough, pasta and meat are covered and can be explained on a molecular basis. An important conclusion is the point that the macroscopic properties and the perception are defined by the molecular interplay on all length and time scales.

Microscopic Dynamics of Supercooled Liquids from First Principles

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 a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a glass-forming system over a broad density range. Our approach requires only simple static structural information as input and is based entirely on first principles. Owing to its ab initio nature, the framework offers a unique platform to study the relation between structure and dynamics in glass-forming matter, and paves the way towards a systematically correctable and ultimately fully quantitative theory of microscopic glassy dynamics.

Slow Water Dynamics near a Glass Transition or a Solid Interface: A Common Rationale

Performing molecular dynamics simulations, we investigate the enormous slowdowns of water dynamics when approaching a glass transition or a solid interface. We show that both effects can be described on common grounds within a theoretical framework, which was recently proposed by Schweizer et al. and considers coupled local hopping and elastic distortion. For confined water, we correctly describe the variation of the α-relaxation time, τα, as a function of both temperature and position with respect to the interface. Exploiting our knowledge of a cooperative length scale ξ(T) from the confinement studies, we quantitatively rationalize the glassy slowdown, τα(T), and the Stokes-Einstein breakdown of bulk water. For both confined and bulk liquid, variations of the α-relaxation time are intimately related to changes of the cage-rattling amplitude.

Correlation between crystalline order and vitrification in colloidal monolayers

We investigate experimentally the relationship between local structure and dynamical arrest in a quasi-2d colloidal model system which approximates hard discs. We introduce polydispersity to the system to suppress crystallisation. Upon compression, the increase in structural relaxation time is accompanied by the emergence of local hexagonal symmetry. Examining the dynamical heterogeneity of the system, we identify three types of motion: 'zero-dimensional' corresponding to β-relaxation, 'one-dimensional' or stringlike motion and '2D' motion. The dynamic heterogeneity is correlated with the local order, that is to say locally hexagonal regions are more likely to be dynamically slow. However, we find that lengthscales corresponding to dynamic heterogeneity and local structure do not appear to scale together approaching the glass transition.

On the mechanism of activated transport in glassy liquids

We explore several potential issues that have been raised over the years regarding the "entropic droplet" scenario of activated transport in liquids, due to Wolynes and co-workers, with the aim of clarifying the status of various approximations of the random first-order transition theory (RFOT) of the structural glass transition. In doing so, we estimate the mismatch penalty between alternative aperiodic structures, above the glass transition; the penalty is equal to the typical magnitude of free energy fluctuations in the liquid. The resulting expressions for the activation barrier and the cooperativity length contain exclusively bulk, static properties; in their simplest form they contain only the bulk modulus and the configurational entropy per unit volume. The expressions are universal in that they do not depend explicitly on the molecular detail. The predicted values for the barrier and cooperativity length and, in particular, the temperature dependence of the barrier are in satisfactory agreement with observation. We thus confirm that the entropic droplet picture is indeed not only internally consistent but is also fully constructive, consistent with the apparent success of its many quantitative predictions. A simple view of a glassy liquid as a locally metastable, degenerate pattern of frozen-in stress emerges in the present description. Finally, we derive testable relationships between the bulk modulus and several characteristics of glassy liquids and peculiarities in low-temperature glasses.

Structural evolution in the aging process of supercooled colloidal liquids

When a liquid is rapidly quenched to a temperature below the glass-transition point, it is driven out of equilibrium; it then slowly relaxes to a (quasi)equilibrium state. This slow relaxation process is called aging. By definition, any glasses are inevitably in the process of aging and actually slowly evolving with time. Thus the study of aging phenomena is of fundamental importance for understanding not only the nonequilibrium nature of the glass transition, but also the stability of glassy materials. Here we consider aging after a rather shallow quench, for which a system is still able to reach (metastable) equilibrium. By using polydisperse colloidal liquids as a model, we show the validity of dynamical scaling that there is only one relevant length scale not only for a quasiequilibrium supercooled state but also for a nonequilibrium process of aging, which is reminiscent of dynamical critical phenomena. Our finding indicates that the aging toward (metastable) equilibrium may be regarded as the growth process of critical-like fluctuations of static order associated with low-free-energy configurations, further suggesting that this ordering is the origin of cooperative slow dynamics in the systems studied. The generality of this statement for other glass-forming systems remains for a future study.