Stability and structure of a supercooled liquid mixture in two dimensions

Experimental measurements of the granular density of modes via impact

The jamming transition is an important feature of granular materials, with prior work showing an excess of low-frequency modes in the granular analog to the density of states, the granular density of modes. In this work, we present an experimental method for acoustically measuring the granular density of modes using a single impact event to excite vibrational modes in an experimental, three-dimensional, granular material. We test three different granular materials, all of which are composed of spherical beads. The first two systems are monodisperse collections of either 6 mm or 8 mm diameter beads. The third system is a bidisperse mixture of the previous two bead sizes. During data collection, the particles are confined to a box; on top of this box, and resting on the granular material, is a light, rigid sheet onto which pressure can be applied to the system. To excite the material, a steel impactor ball is dropped on top of the system. The response of the granular material to the impact pulse is recorded by piezoelectric sensors buried throughout the material, and the density of modes is computed from the spectrum of the velocity autocorrelation of these sensors. Our measurements of the density of modes show more low-frequency modes at low pressure, consistent with previous experimental and numerical results, as well as several low-frequency peaks in the density of modes that shift with applied pressure. Our method represents an experimentally simple technique for investigating the granular density of modes and may increase the accessibility and number of such measurements.

Fickian Non-Gaussian Diffusion in Glass-Forming Liquids

Fickian yet non-Gaussian diffusion (FnGD), a most intriguing open issue in soft matter, is generically associated with some dynamical and/or structural heterogeneity of the environment. Here we investigate the features of FnGD in glass-forming liquids, the epitome of dynamical heterogeneity, drawing on experiments on hard-sphere colloidal suspensions and simulations of a simple model of molecular liquid. We demonstrate that FnGD strengthens on approaching the glass transition, by identifying distinct timescales for Fickianity, τ_{F}, and for restoring of Gaussianity, τ_{G}>τ_{F}, as well as their associated length scales, ξ_{F} and ξ_{G}. We find τ_{G}∝τ_{F}^{γ} with γ≃1.8 for both systems. In the deep FnGD regime, the displacement distributions display exponential tails. We show that, in simulations, the time-dependent decay lengths l(t) at different temperatures all collapse onto a power-law master curve [l(t)/(ξ_{G})]∝(t/τ_{G})^{α}, with α=0.33. A similar collapse, if less sharp, is also found in experiments, seemingly with the same exponent α. We further discuss the connections of the timescales and length scales characterizing FnGD with structural relaxation and dynamic heterogeneity.

Translation-rotation decoupling of tracers reflects medium-range crystalline order in two-dimensional colloid glasses

The dynamic heterogeneity and the translation-rotation decoupling are the dynamic signatures of glasses and supercooled liquids. Whether and how the dynamic heterogeneity would relate to the local structure of glasses has been a puzzle for decades. In this work we perform molecular dynamics simulations for tracers in both two-dimensional polydisperse colloids (2DPC) and two-dimensional binary colloids (2DBC). In 2DPC glasses, hexatic local structures develop at low enough temperatures and grow quickly along with the dynamic correlation length of the 2DPC, which is well known as the medium-range crystalline order (MRCO). In 2DBC glasses, on the other hand, any explicit local structure has not been reported to grow significantly with the dynamic correlation length at low temperatures. We introduce two different types of tracers into colloidal systems: A diamond tracer that resembles the MRCO of 2DPC glasses and a square tracer that is dissimilar to any local structure of glasses. The translation-rotation decoupling of the diamond tracer in 2DPC glasses is much more significant than that of the square tracer in the same 2DPC glasses. On the other hand, such a tracer shape-dependence of the decoupling is not observed in 2DBC glasses where the local hexatic structure does not develop significantly. We introduce a shape-dependency parameter of the decoupling and find that the shape-dependency parameter grows along with the dynamic correlation length in 2DPC glasses but not in 2DBC glasses. This illustrates that the dynamic heterogeneity and the translation-rotation decoupling of tracers could reveal the local structure that develops in glasses.

Critical yielding rheology: from externally deformed glasses to active systems

We use extensive computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics and self-propelled dense active systems. In the active systems, a yielding transition toward an out-of-equilibrium flowing state known as the liquid phase is observed when self-propulsion is increased. The range of self-propulsions in which this pure liquid regime exists appears to vanish upon approaching the so-called 'jamming point' at which the solidity of soft-sphere packings is lost. Such an 'active yielding' transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed along the liquid regime in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existence of different universality classes for the yielding transition under different driving conditions. In addition, we present the direct measurements of growing length and time scales for both driving scenarios. A comparison with theoretical predictions from the recent literature reveals poor agreement with our numerical results.

Universal Density of Low-Frequency States in Amorphous Solids at Finite Temperatures

It has been established that the low frequency quasilocalized modes of amorphous solids at zero temperature exhibit universal density of states, depending on the frequencies as D(ω)∼ω^{4}. It remains an open question whether this universal law extends to finite temperatures. In this Letter we show that well quenched model glasses at temperatures as high as T_{g}/3 possess the same universal density of states. The only condition required is that average particle positions stabilize before thermal diffusion destroys the cage structure of the material. The universal density of quasilocalized low frequency modes refers then to vibrations around the thermally averaged configuration of the material.

Pattern detection in colloidal assembly: A mosaic of analysis techniques

Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.

Bidisperse Nanospheres Jammed on a Liquid Surface

Jammed packings of bidisperse nanospheres were assembled on a nonvolatile liquid surface and visualized to the single-particle scale by using an in situ scanning electron microscopy method. The PEGylated silica nanospheres, mixed at different number fractions and size ratios, had large enough in-plane mobilities prior to jamming to form uniform monolayers reproducibly. From the collected nanometer-resolution images, local order and degree of mixing were assessed by standard metrics. For equimolar mixtures, a large-to-small size ratio of about 1.5 minimized correlated metrics for local orientational and positional order, as previously predicted in simulations of bidisperse disk jamming. Despite monolayer uniformity, structural and depletion interactions caused spheres of a similar size to cluster, a feature evident at size ratios above 2. Uniform nanoparticle monolayers of high packing disorder are sought in many liquid interface technologies, and these experiments outlined key design principles, buttressing extensive theory/simulation literature on the topic.

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

Instabilities of time-averaged configurations in thermal glasses

In amorphous solids at finite temperatures the particles follow chaotic trajectories which, at temperatures sufficiently lower than the glass transition, are trapped in "cages." Averaging their positions for times shorter than the diffusion time, one can define a time-averaged configuration. Under strain or stress, these average configurations undergo sharp plastic instabilities. In athermal glasses the understanding of plastic instabilities is furnished by the Hessian matrix and its eigenvalues and eigenfunctions. Here we propose an uplifting of Hessian methods to thermal glasses, with the aim of understanding the plastic responses in the time-averaged configuration. We discuss a number of potential definitions of Hessians and identify which of these can provide eigenvalues and eigenfunctions which can explain and predict the instabilities of the time-averaged configurations. The conclusion is that the nonaffine changes in the average configurations during an instability is accurately predicted by the eigenfunctions of the low-lying eigenvalues of the chosen Hessian.

Evidence of a two-dimensional glass transition in graphene: Insights from molecular simulations

Liquids exhibit a sudden increase in viscosity when cooled fast enough, avoiding thermodynamically predicted route of crystallization. This phenomenon, known as glass transition, leads to the formation of non-periodic structures known as glasses. Extensive studies have been conducted on model materials to understand glass transition in two dimensions. However, despite the synthesis of disordered/amorphous single-atom thick structures of carbon, little attention has been given to glass transition in realistic two-dimensional materials such as graphene. Herein, using molecular dynamics simulation, we demonstrate the existence of glass transition in graphene leading to a realistic two-dimensional glassy structure, namely glassy graphene. We show that the resulting glassy structure exhibits excellent agreement with experimentally realized disordered graphene. Interestingly, this glassy graphene exhibits a wrinkled but stable structure, with reduced thermal vibration in comparison to its crystalline counterpart. We suggest that the topological disorder induced by glass transition governs the unique properties of this structure.

Enhanced Phosphorus Locking by Novel Lanthanum/Aluminum-Hydroxide Composite: Implications for Eutrophication Control

Lanthanum (La) bearing materials have been widely used to remove phosphorus (P) in water treatment. However, it remains a challenge to enhance phosphate (PO₄) adsorption capacity and La usage efficiency. In this study, La was coprecipitated with aluminum (Al) to obtain a La/Al-hydroxide composite (LAH) for P adsorption. The maximum PO₄ adsorption capacities of LAH (5.3% La) were 76.3 and 45.3 mg P g^-1 at pH 4.0 and 8.5, which were 8.5 and 5.3 times higher than those of commercially available La-modified bentonite (Phoslock, 5.6% La), respectively. P K-edge X-ray absorption near edge structure analysis showed that PO₄ was preferentially bonded with Al under weakly acid conditions (pH 4.0), while tended to associate with La under alkaline conditions (pH 8.5). La L_III-edge extended X-ray absorption fine structure analysis indicated that PO₄ was bonded on La sites by forming inner sphere bidentate-binuclear complexes and oxygen defects exhibited on LAH surfaces, which could be active adsorption sites for PO₄. The electrostatic interaction, ligand exchange, and oxygen defects on LAH surfaces jointly facilitated PO₄ adsorption but with varied contribution under different pH conditions. The combined contribution of two-component of La and Al may be an important direction for the next generation of commercial products for eutrophication mitigation.

The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero

Rapid cooling of liquids below a certain temperature range can result in a transition to glassy states. The traditional understanding of glasses includes their thermodynamic metastability with respect to crystals. However, here we present specific examples of interactions that eliminate the possibilities of crystalline and quasicrystalline phases, while creating mechanically stable amorphous glasses down to absolute zero temperature. We show that this can be accomplished by introducing a new ideal state of matter called a "perfect glass". A perfect glass represents a soft-interaction analog of the maximally random jammed (MRJ) packings of hard particles. These latter states can be regarded as the epitome of a glass since they are out of equilibrium, maximally disordered, hyperuniform, mechanically rigid with infinite bulk and shear moduli, and can never crystallize due to configuration-space trapping. Our model perfect glass utilizes two-, three-, and four-body soft interactions while simultaneously retaining the salient attributes of the MRJ state. These models constitute a theoretical proof of concept for perfect glasses and broaden our fundamental understanding of glass physics. A novel feature of equilibrium systems of identical particles interacting with the perfect-glass potential at positive temperature is that they have a non-relativistic speed of sound that is infinite.

Applicability of Dynamic Facilitation Theory to Binary Hard Disk Systems

We numerically investigate the applicability of dynamic facilitation (DF) theory for glass-forming binary hard disk systems where supercompression is controlled by pressure. By using novel efficient algorithms for hard disks, we are able to generate equilibrium supercompressed states in an additive nonequimolar binary mixture, where microcrystallization and size segregation do not emerge at high average packing fractions. Above an onset pressure where collective heterogeneous relaxation sets in, we find that relaxation times are well described by a "parabolic law" with pressure. We identify excitations, or soft spots, that give rise to structural relaxation and find that they are spatially localized, their average concentration decays exponentially with pressure, and their associated energy scale is logarithmic in the excitation size. These observations are consistent with the predictions of DF generalized to systems controlled by pressure rather than temperature.

Nonaffine displacements and the nonlinear response of a strained amorphous solid

We demonstrate that irreversible structural reorganization is not necessary for the observation of yield behavior in an amorphous solid. While the majority of solids strained to their yield point do indeed undergo an irreversible reorganization, we find that a significant fraction of solids exhibits yield via a reversible strain. We also demonstrate that large instantaneous strains in excess of the yield stress can result in complete stress relaxation, a result of the large nonaffine motions driven by the applied strain. The empirical similarity of the dependence of the ratio of stress over strain on the nonaffine mean-square displacement to that for the shear modulus obtained from quiescent liquid at nonzero temperature supports the proposition that rigidity depends on the size of the sampled configurational space only and is insensitive to how this space is sampled.

Rigidity in Condensed Matter and Its Origin in Configurational Constraint

Motivated by the formal argument that a nonzero shear modulus is the result of averaging over a constrained configuration space, we demonstrate that the shear modulus calculated over a range of temperatures and averaging times can be expressed (relative to its infinite frequency value) as a single function of the mean squared displacement. This result is shown to hold for both a glass-liquid and a crystal-liquid system.

Theory of activated dynamics and glass transition of hard colloids in two dimensions

The microscopic nonlinear Langevin equation theory is applied to study the localization and activated hopping of two-dimensional hard disks in the deeply supercooled and glass states. Quantitative comparisons of dynamic characteristic length scales, barrier, and their dependence on the reduced packing fraction are presented between hard-disk and hard-sphere suspensions. The dynamic barrier of hard disks emerges at higher absolute and reduced packing fractions and correspondingly, the crossover size of the dynamic cage which correlates to the Lindemann length for melting is smaller. The localization lengths of both hard disks and spheres decrease exponentially with packing fraction. Larger localization length of hard disks than that of hard spheres is found at the same reduced packing fraction. The relaxation time of hard disks rises dramatically above the reduced packing fraction of 0.88, which leads to lower reduced packing fraction at the kinetic glass transition than that of hard spheres. The present work provides a foundation for the subsequent study of the glass transition of binary or polydisperse mixtures of hard disks, normally adopted in experiments and simulations to avoid crystallization, and further, the rheology and mechanical response of the two-dimensional glassy colloidal systems.

Molecular dynamics study of one-component soft-core system: thermodynamic properties in the supercooled liquid and glassy states

Molecular dynamics simulations were performed to study the thermal properties of a supercooled liquid near the glass transition regime and of glasses in a one-component soft-core system with the pair potential φn(r) = ɛ(σ/r)(n), in which n = 12. The results are examined along a phase diagram, in which the compressibility factor defined by [Formula: see text] is plotted against the reduced density ρ* = ρ(ɛ/kBT)(3/n) (or the reduced temperature T* = ρ*(-n/3)). Similarly, a time-dependent dynamical compressibility factor can be plotted against the time-dependent reduced density [Formula: see text] (or the reduced time-dependent temperature). Analytical expressions of the specific heats CV and CP and of the entropy, S, were obtained as a function of [Formula: see text] or of the scaled potential U*. Even for a rapid cooling process, the CV values are found to be affected by non-equilibrium relaxations in the [Formula: see text] region, where [Formula: see text] is the given initial value of [Formula: see text]. The problem of the Kauzmann paradox is discussed using these expressions. The fluctuation of the time-dependent temperature, Tt*, which determines CV, is characterized by the spectra that are obtained by multitaper methods. The thermal fluctuation along the non-equilibrium relaxation under NVE conditions was also examined.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

Tuning jammed frictionless disk packings from isostatic to hyperstatic

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates r and initial packing fractions followed by compression and decompression in small steps to reach packing fractions φ(J) at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to φ(J). Using these protocols, we generate more than 10(4) static packings over a wide range of packing fraction, contact number, and compositional and positional order. We find that disordered, isostatic packings exist over a finite range of packing fractions in the large-system limit. In agreement with previous calculations, the most dilute mechanically stable packings with φ min ≈ 0.84 are obtained for r > r*, where r* is the rate above which φ(J) is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, several order parameters, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered (with only small changes in a number of order parameters), whereas bond-orientational and compositional order increase strongly with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies (in the harmonic approximation) of the static packings to understand the extent to which the mechanical properties of disordered, isostatic packings differ from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.

Structural signature of slow dynamics and dynamic heterogeneity in two-dimensional colloidal liquids: glassy structural order

Glassy states are formed if crystallization is avoided upon cooling or increasing density. However, the physical factors controlling the ease of vitrification and the nature of glass transition remain elusive. Among various glass-forming systems, colloidal liquids are one of the most ideal glass-forming systems because of the simplicity and controllability of the interactions. We use numerical simulations of two-dimensional polydisperse and binary hard discs to tackle both of these longstanding questions. For polydisperse systems, we systematically control the polydispersity, which can be regarded as the strength of frustration effects on crystallization. We reveal that crystal-like hexatic order grows in size and lifetime with an increase in the colloid volume fraction or with a decrease in polydispersity (or frustration). We stress that hexatic ordering in hard disc systems is a direct consequence of dense packing and a manifestation of low configurational entropy. Our study suggests an intriguing scenario that the strength of frustration controls both the ease of vitrification and the nature of the glass transition. Vitrification may be a process of hidden crystal-like ordering under frustration for this system. This may provide not only a physical basis for glass formation, but also an answer to another longstanding question on the structure of amorphous materials: 'order in disorder' may be an intrinsic feature of a glassy state of many materials. For binary mixtures, on the other hand, the relevant structural feature linked to slow dynamics is not hexatic order, but an amorphous structure of low structural entropy. These results suggest that slow dynamics is associated with bond orientational order linked to the crystal for a weakly frustrated system, whereas to amorphous structures of low configurational entropy for a strongly frustrated system. This suggests an intrinsic link between structure and dynamics in glass-forming materials: slow dynamics is linked to structuring ('glassy ordering') towards low configurational entropy. We discuss the nature of 'glassy order' responsible for slow dynamics.

Critical-like behaviour of glass-forming liquids

Recently it has been revealed that when approaching the glass-transition temperature, T(g), the dynamics of a liquid not only drastically slows down, but also becomes progressively more heterogeneous. From our simulations and experiments of six different glass-forming liquids, we find that the heterogeneous dynamics is a result of critical-like fluctuations of static structural order, contrary to a common belief that it is purely of dynamic origin. The static correlation length and susceptibility of a structural order parameter show Ising-like power-law divergence towards the ideal glass-transition point. However, this structural ordering accompanies little density change, which explains why it has not been detected by the static structure factor so far. Our results suggest a far more direct link than thought before between glass transition and critical phenomena. Indeed, the glass transition may be a new type of critical phenomenon where a structural order parameter is directly linked to slowness.

Second-order dynamic transition in a p=2 spin-glass model

We consider the dynamics of a disordered p -spin model with p=2 , analyzing the dynamics within Ruelle's thermodynamic formalism, We use an indicator of the dynamical activity to construct the relevant dynamical Gibbs ensemble. We prove that the dynamics in the low-temperature (spin-glass) phase of the model take place at a second-order phase transition between dynamically active and inactive trajectories. We also show that the same behavior is found in a related model of a three-dimensional ferromagnet.

Central role of thermal collective strain in the relaxation of structure in a supercooled liquid

The spatial distribution of structural relaxation in a supercooled liquid is studied using molecular dynamics simulations of a two-dimensional binary mixture. It is shown that the spatial heterogeneity of the relaxation along with the time scale of the relaxation is determined, not by the frequency with which particles move a distance pi/2kBragg, but by the frequency with which particles can achieve persistent displacements. We show that these persistent displacements are achieved through the coupled action of local reorganizations and unrecoverable thermal strains.

Partial clustering prevents global crystallization in a binary 2D colloidal glass former

A mixture of two types of super-paramagnetic colloidal particles with long-range dipolar interaction is confined by gravity to the flat interface of a hanging water droplet. The particles are observed by video microscopy and the dipolar interaction strength is controlled via an external magnetic field. The system is a model system to study the glass transition in 2D, and it exhibits partial clustering of the small particles (N. Hoffmann et al., Phys. Rev. Lett. 97, 078301 (2006)). This clustering is strongly dependent on the relative concentration [Formula: see text] of big and small particles. However, changing the interaction strength [Formula: see text] reveals that the clustering does not depend on the interaction strength. The partial clustering scenario is quantified using Minkowski functionals and partial structure factors. Evidence that partial clustering prevents global crystallization is discussed.

Statistical mechanics and dynamics of a three-dimensional glass-forming system

In the context of a classical example of glass formation in three dimensions, we exemplify how to construct a statistical-mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of upscaled quasispecies that allow the construction of a theory with a finite number of "states." Once constructed, the theory identifies a typical scale xi that increases rapidly with lowering the temperature and which determines the alpha-relaxation time tau(alpha) as tau(alpha) approximately exp(muxi/T), with mu a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.

Glass transitions in one-, two-, three-, and four-dimensional binary Lennard-Jones systems

We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T = 0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning rate dependence of the area and height of the hysteresis can be described using power laws. The one-dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the D≥2 results in the supercooled liquid regime above the glass transition. As D increases, the radial distribution functions reflect reduced geometric constraints. Nearest neighbor distances become smaller with increasing D due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing D crystallization becomes increasingly more difficult.

Nonuniversality of the specific heat in glass forming systems

We present new simulation results for the specific heat in a classical model of a binary mixture glass former in two dimensions. We show that in addition to the formerly observed specific heat peak, there is a second peak at lower temperatures which was not observable in earlier simulations. This is a surprise, as most texts on the glass transition expect a single specific heat peak. We explain the physics of the two specific heat peaks by the micromelting of two types of clusters. While this physics is easily accessible, the consequences are that one should not expect any universality in the temperature dependence of the specific heat in glass formers.

Theory of specific heat in glass-forming systems

Experimental measurements of the specific heat in glass-forming systems are obtained from the linear response to either slow cooling (or heating) or to oscillatory perturbations with a given frequency about a constant temperature. The latter method gives rise to a complex specific heat with the constraint that the zero frequency limit of the real part should be identified with thermodynamic measurements. Such measurements reveal anomalies in the temperature dependence of the specific heat, including the so called "specific heat peak" in the vicinity of the glass transition. The aim of this paper is to provide theoretical explanations of these anomalies in general and a quantitative theory in the case of a simple model of glass formation. We first present interesting simulation results for the specific heat in a classical model of a binary mixture glass former. We show that in addition to the formerly observed specific heat peak there is a second peak at lower temperatures which was not observable in earlier simulations. Second, we present a general relation between the specific heat, a caloric quantity, and the bulk modulus of the material, a mechanical quantity, and thus offer a smooth connection between the liquid and amorphous solid states. The central result of this paper is a connection between the micromelting of clusters in the system and the appearance of specific heat peaks; we explain the appearance of two peaks by the micromelting of two types of clusters. We relate the two peaks to changes in the bulk and shear moduli. We propose that the phenomenon of glass formation is accompanied by a fast change in the bulk and the shear moduli, but these fast changes occur in different ranges of the temperature. Last, we demonstrate how to construct a theory of the frequency dependent complex specific heat, expected from heterogeneous clustering in the liquid state of glass formers. A specific example is provided in the context of our model for the dynamics of glycerol. We show that the frequency dependence is determined by the same alpha -relaxation mechanism that operates when measuring the viscosity or the dielectric relaxation spectrum. The theoretical frequency dependent specific heat agrees well with experimental measurements on glycerol. We conclude the paper by stating that there is nothing universal about the temperature dependence of the specific heat in glass formers-unfortunately, one needs to understand each case by itself.

Quantitative theory of a relaxation function in a glass-forming system

We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) that are long-lived but each of which relaxes as a simple function of time. Without the clusters, the relaxation of the background is simply determined by one typical length, which we deduce from an elementary statistical mechanical argument. The total relaxation function (which depends on time in a nontrivial manner) is quantitatively determined as a weighted sum over the clusters and the background. The "fragility" in this system can be understood quantitatively since it is determined by the temperature dependence of the number fractions of the locally favored regions.

Ergodicity and slowing down in glass-forming systems with soft potentials: no finite-temperature singularities

The aim of this paper is to discuss some basic notions regarding generic glass-forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction, we discuss the so-called glass transition in which a supercooled amorphous state is formed, accompanied by a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length scales, we show the following. (i) The system remains ergodic at all temperatures. (ii) The number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the small world property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0 .

Aging and relaxation in glass-forming systems

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to aging occur where the local shear modulus is low (even negative) and result in an increase in the size of local patches of relative order. We examine the aging events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass-forming systems to the reduction in relative volume of the amorphous material which is liquidlike. While we agree with the well-known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulas that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most superexponentially when the temperature is lowered.

Local crystalline order in a 2D colloidal glass former

A mixture of two types of super-paramagnetic colloidal particles with long-range dipolar interaction is confined by gravity to a flat interface of a hanging water droplet. The particles are observed by video microscopy and the dipolar interaction strength is controlled by an external magnetic field. The local structure as obtained by pair correlation functions and bond order statistics is investigated as a function of system temperature and relative concentration. Although the system has no long-range order and exhibits glassy dynamics, different types of stable crystallites coexist. The local order of the globally disordered structure is explained by a small set of specific crystal structures. The statistics of crystal unit cells show a continuous increase of local order with decreasing system temperature as well as a dependence on sample history and local composition.

Correlation between dynamic heterogeneity and medium-range order in two-dimensional glass-forming liquids

A glassy state of matter results if crystallization is avoided upon cooling or increasing density. However, the physical factors controlling the ease of vitrification and nature of the glass transition remain elusive. Using numerical simulations of polydisperse hard disks, we find a direct relation between medium-range crystalline ordering and the slow dynamics which characterizes the glass transition. This suggests an intriguing scenario that the strength of frustration controls both the ease of vitrification and nature of the glass transition. Vitrification may be a process of hidden crystalline ordering under frustration, at least in our system.

Mechanical properties of glass forming systems

We address the interesting temperature range of a glass forming system where the mechanical properties are intermediate between those of a liquid and a solid. We employ an efficient Monte Carlo method to calculate the elastic moduli, and show that in this range of temperatures the moduli are finite for short times and vanish for long times, where short and long depend on the temperature. By invoking some exact results from statistical mechanics we offer an alternative method to compute shear moduli using molecular dynamics simulations, and compare those to the Monte Carlo method. The final conclusion is that these systems are not "viscous fluids" in the usual sense, as their actual time-dependence concatenates solid-like materials with varying local shear moduli.

Statistical mechanics of the glass transition in one-component liquids with an anisotropic potential

We study a recently introduced model of one-component glass-forming liquids whose constituents interact with an anisotropic potential. This system is interesting per se and as a model of liquids such as glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasiparticles (36 of them). The theory provides a full explanation of the glass transition phenomenology, including the identification of a diverging length scale and a relation between the structural changes and the diverging relaxation times.

Configurational entropy of binary hard-disk glasses: Nonexistence of an ideal glass transition

We study the thermodynamics of a binary hard-disk mixture in which the ratio of disk diameters is kappa=1.4. We use a recently developed molecular dynamics algorithm to calculate the free-volume entropy of glassy configurations and obtain the configurational entropy (degeneracy) of the supercompressed liquid as a function of density. We find that the configurational entropy of the glasses near the kinetic glass transition is very close to the mixing entropy, suggesting that the degeneracy is zero only for the phase-separated crystal. We explicitly construct an exponential number of jammed packings with densities spanning the spectrum from the accepted "amorphous" glassy state to the phase-separated crystal, thus showing that there is no ideal glass transition in binary hard-disk mixtures. This construction also demonstrates that the ideal glass, defined as having zero configurational entropy, is not amorphous, but instead is nothing more than a phase-separated crystal. This critique of the presumed existence of an ideal glass parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)]. We also perform free-energy calculations to determine the equilibrium phase behavior of the system. The calculations predict a first-order freezing transition at a density below the kinetic glass transition. However, this transition appears to be strongly kinetically suppressed and is not observed directly. New simulation techniques are needed in order to gain a more complete understanding of the thermodynamic and kinetic behavior of the binary disk mixture and, in particular, of the demixing process during crystallization.

Connecting microscopic simulations with kinetically constrained models of glasses

Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of this "mobility" field has remained elusive due to the lack of coarse-graining procedures to obtain these models from a more microscopic point of view. Here we exhibit a scheme to map the dynamics of a two-dimensional soft disk glass former onto a kinetically constrained spin model, providing an attempt at bridging these two approaches.

Dynamic glass transition in two dimensions

The question of the existence of a structural glass transition in two dimensions is studied using mode coupling theory (MCT). We determine the explicit d dependence of the memory functional of mode coupling for one-component systems. Applied to two dimensions we solve the MCT equations numerically for monodisperse hard disks. A dynamic glass transition is found at a critical packing fraction phi(c)d=2 approximately equal 0.697 which is above phi(c)d=3 approximately equal 0.516 by about 35%. Phi(c)d scales approximately with phi(rcp)d, the value for random close packing, at least for d=2, 3. Quantities characterizing the local, cooperative "cage motion" do not differ much for d=2 and d=3, and we, e.g., find the Lindemann criterion for the localization length at the glass transition. The final relaxation obeys the superposition principle, collapsing remarkably well onto a Kohlrausch law. The d=2 MCT results are in qualitative agreement with existing results from Monte Carlo and molecular dynamics simulations. The mean-squared displacements measured experimentally for a quasi-two-dimensional binary system of dipolar hard spheres can be described satisfactorily by MCT for monodisperse hard disks over four decades in time provided the experimental control parameter Gamma (which measures the strength of dipolar interactions) and the packing fraction phi are properly related to each other.

Experimental observation of structural crossover in binary mixtures of colloidal hard spheres

Using confocal microscopy, we investigate the structure of binary mixtures of colloidal hard spheres with size ratio q=0.61. As a function of the packing fraction of the two particle species, we observe a marked change of the dominant wavelength in the pair-correlation function. This behavior is in excellent agreement with a recently predicted structural crossover in such mixtures. In addition, the repercussions of structural crossover on the real-space structure of a binary fluid are analyzed. We suggest a relation between crossover and the lateral extension of networks containing only equally-sized particles that are connected by nearest-neighbor bonds. This is supported by Monte Carlo simulations which are performed at different packing fractions and size ratios.

Statistical mechanics of the glass transition as revealed by a Voronoi tesselation

The statistical mechanics of simple glass forming systems in two dimensions is worked out. The glass disorder is encoded via a Voronoi tesselation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, T(g) and T(c) , the first associated with jamming and the second associated with crystallization at very low temperatures.