Information-theoretic measurements of coupling between structure and dynamics in glass formers

Unsupervised learning of structural relaxation in supercooled liquids from short-term fluctuations

Unraveling the relationship between structural information and the dynamic properties of supercooled liquids is one of the great challenges of physics. Dynamic heterogeneity, characterized by the propensity of particles, is often used as a proxy for dynamic slowing. Over the years, significant efforts have been made to capture the structural variations linked to dynamic heterogeneity in supercooled liquids. In this work, we present an innovative unsupervised machine learning protocol based on time-lagged canonical correlation analysis or time-lagged autoencoder to autonomously identify a key order parameter (OP) for the amorphous structures of the Kob-Andersen glass former. The OP is constructed by integrating numerous classical structural descriptors and represents the component with the strongest short-term correlation on a timescale thousands of times shorter than the relaxation time. Strikingly, this OP demonstrates a remarkable correlation with the propensity at long times, significantly outperforming traditional unsupervised models and rivaling supervised models. This demonstrates that fluctuations of structural descriptors contain sufficient information about the long-time dynamic heterogeneity. The most important structural features are the density distributions at mid-range. As a consequence, the OP also exhibits excellent transferability in capturing dynamic heterogeneity across a wide temperature range and greatly facilitates the evaluation of descriptor importance, highlighting its potential for broader application to other glassy systems.

The role of excitations in supercooled liquids: Density, geometry, and relaxation dynamics

Low-energy excitations play a key role in all condensed-matter systems, yet there is limited understanding of their nature in glasses, where they correspond to local rearrangements of groups of particles. Here, we introduce an algorithm to systematically uncover these excitations up to the activation energy scale relevant to structural relaxation. We use it in a model system to measure the density of states on a scale never achieved before, confirming that this quantity shifts to higher energy under cooling, precisely as the activation energy does. Second, we show that the excitations' energetic and spatial features allow one to predict with great accuracy the dynamic propensity, i.e., the location of future relaxation dynamics. Finally, we find that excitations have a primary field whose properties, including the displacement of the most mobile particle, scale as a power-law of their activation energy and are independent of temperature. Additionally, they exhibit an outer deformation field that depends on the material's stability and, therefore, on temperature. We build a scaling description of these findings. Overall, our analysis supports that excitations play a crucial role in regulating relaxation dynamics near the glass transition, effectively suppressing the transition to dynamical arrest predicted by mean-field theories while also being strongly influenced by it.

Structural Origin of Dynamic Heterogeneity in Supercooled Liquids

As a liquid is supercooled toward the glass transition point, its dynamics slow significantly, provided that crystallization is avoided. With increased supercooling, the particle dynamics become more spatially heterogeneous, a phenomenon known as dynamic heterogeneity. Since its discovery, this characteristic of metastable supercooled liquids has garnered considerable attention in glass science. However, the precise physical origins of dynamic heterogeneity remain elusive and widely debated. In this perspective, we examine the relationship between dynamic heterogeneity and structural order, based on numerical simulations of fragile liquids with isotropic potentials and strong liquids with directional interactions. We demonstrate that angular ordering, arising from many-body steric interactions, plays a crucial role in the slow dynamics and dynamic cooperativity of fragile liquids. Additionally, we explore how the growth of static order correlates with slower dynamics. In fragile liquids exhibiting super-Arrhenius behavior, the spatial extent of regions with high angular order grows upon cooling, and the sequential propagation of particle rearrangements within these ordered regions increases the activation energy for particle motion. In contrast, strong liquids with spatially constrained local ordering display a distinct "two-state" dynamic characteristic, marked by a transition between two Arrhenius-type behaviors. We argue that dynamic heterogeneity, irrespective of a liquid's fragility, arises from underlying structural order, with its spatial extent determined by static ordering. This perspective aims to deepen our understanding of the interplay between structural and dynamic properties in metastable supercooled liquids.

Selecting relevant structural features for glassy dynamics by information imbalance

We numerically investigate the identification of relevant structural features that contribute to the dynamical heterogeneity in a model glass-forming liquid. By employing the recently proposed information imbalance technique, we select these features from a range of physically motivated descriptors. This selection process is performed in a supervised manner (using both dynamical and structural data) and an unsupervised manner (using only structural data). We then apply the selected features to predict future dynamics using a machine learning technique. One of the advantages of the information imbalance technique is that it does not assume any model a priori, i.e., it is a non-parametric method. Finally, we discuss the potential applications of this approach in identifying the dominant mechanisms governing the glassy slow dynamics.

Entropic timescales of dynamic heterogeneity in supercooled liquid

Non-Gaussian displacement distributions are universal predictors of dynamic heterogeneity in slowly varying environments. Here, we explore heterogeneous dynamics in supercooled liquid using molecular dynamics simulations and show the efficiency of the relative-entropy based measure, negentropy, in quantifying dynamic heterogeneity over the widely used non-Gaussian parameter. Our analysis shows that the heterogeneity quantified by the negentropy is significantly different from the one obtained using the conventional moment-based definition that considers deviation from Gaussianity up to lower-order moments. We extract the timescales of dynamic heterogeneity using the two methods and show that the differential changes diverge as the system experiences strong intermittency near the glass transition. Further, we interpret the entropic timescales and discuss the general implications of our work.

Information decomposition in complex systems via machine learning

One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of linking variation across scales of a system due to its independence of functional relationship between observables. However, characterizing the manner in which information is distributed across a set of observables is computationally challenging and generally infeasible beyond a handful of measurements. Here, we propose a practical and general methodology that uses machine learning to decompose the information contained in a set of measurements by jointly optimizing a lossy compression of each measurement. Guided by the distributed information bottleneck as a learning objective, the information decomposition identifies the variation in the measurements of the system state most relevant to specified macroscale behavior. We focus our analysis on two paradigmatic complex systems: a Boolean circuit and an amorphous material undergoing plastic deformation. In both examples, the large amount of entropy of the system state is decomposed, bit by bit, in terms of what is most related to macroscale behavior. The identification of meaningful variation in data, with the full generality brought by information theory, is made practical for studying the connection between micro- and macroscale structure in complex systems.

Rearrangements during slow compression of a jammed two-dimensional emulsion

As amorphous materials get jammed, both geometric and dynamic heterogeneity are observed. We investigate the correlation between the local geometric heterogeneity and local rearrangements in a slowly compressed bidisperse quasi-two-dimensional emulsion system. The compression is driven by evaporation of the continuous phase and causes the area packing fraction to increase from 0.88 to 0.99. We quantify the structural heterogeneity of the system using the radical Voronoi tessellation following the method of Rieser et al. [Phys. Rev. Lett. 116, 088001 (2016)]0031-900710.1103/PhysRevLett.116.088001. We define two structural quantities characterizing local structure, the first of which considers nearest neighbors and the second of which includes information from second-nearest neighbors. We find that droplets in heterogeneous local regions are more likely to have local rearrangements. These rearrangements are generally T1 events where two droplets converge toward a void, and two droplets move away from the void to make room for the converging droplets. Thus, the presence of the voids tends to orient the T1 events. The presence of a correlation between the structural quantities and the rearrangement dynamics remains qualitatively unchanged over the entire range of packing fractions observed.

Solid-that-Flows Picture of Glass-Forming Liquids

This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.

Heterogeneous attenuation of sound waves in three-dimensional amorphous solids

Sound waves are attenuated as they propagate in amorphous materials. We investigate the mechanism driving sound attenuation in the Rayleigh scattering regime by resolving the dynamics of an excited phonon in time and space via numerical simulations. We find sound attenuation is spatiotemporally heterogeneous. It starts in localized regions, which identify soft regions within the material and correlate with low-frequency vibrational modes. As time progresses, the regions where sound is primarily attenuated invade the system via an apparent diffusive process.

Anomalous temperature dependence of elastic limit in metallic glasses

Understanding the atomistic mechanisms of inelastic deformation in metallic glasses (MGs) remains challenging due to their amorphous structure, where local carriers of plasticity cannot be easily defined. Using molecular dynamics (MD) simulations, we analyzed the onset of inelastic deformation in CuZr MGs, specifically the temperature dependence of the elastic limit, in terms of localized shear transformation (ST) events. We find that although the ST events initiate at lower strain with increasing temperature, the elastic limit increases with temperature in certain temperature ranges. We explain this anomalous behavior through the framework of an energy-strain landscape (ESL) constructed from high-throughput strain-dependent energy barrier calculations for the ST events identified in the MD simulations. The ESL reveals that the anomalous behavior is caused by the transition of ST events from irreversible to reversible with increasing temperature. An analytical formulation is developed to predict this transition and the temperature dependence of the elastic limit.

Necking and failure of a particulate gel strand: signatures of yielding on different length scales

"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.

A comparative study of the correlation between the structure and the dynamics for systems interacting via attractive and repulsive potentials

We present the study of the structure-dynamics correlation for systems interacting via attractive Lennard-Jones (LJ) and its repulsive counterpart, the Weeks-Chandler-Andersen (WCA) potentials. The structural order parameter (SOP) is related to the microscopic mean-field caging potential. At a particle level, the SOP shows a distribution. Although the two systems have similar pair structures, their average SOP differs. However, this difference alone is insufficient to explain the well known slowing down of the dynamics in the LJ system at low temperatures. The slowing down can be explained in terms of a stronger coupling between the SOP and the dynamics. To understand the origin of this system specific coupling, we study the difference in the microscopic structure between the hard and soft particles. We find that for the LJ system, the structural differences of the hard and soft particles are more significant and have a much stronger temperature dependence compared to the WCA system. Thus, the study suggests that attractive interaction creates more structurally different communities. This broader difference in the structural communities is probably responsible for stronger coupling between the structure and dynamics. Thus, the system specific structure-dynamics correlation, which also leads to a faster slowing down in the dynamics, appears to have a structural origin. A comparison of the predictive power of our SOP with the local energy and two body excess entropy in determining the dynamics shows that in the LJ system, the enthalpy plays a dominant role and in the WCA system, the entropy plays a dominant role, and our SOP can capture both these contributions.

Dynamic heterogeneity in polydisperse systems: A comparative study of the role of local structural order parameter and particle size

In polydisperse systems, describing the structure and any structural order parameter (SOP) is not trivial as it varies with the number of species we use to describe the system, M. Depending on the degree of polydispersity, there is an optimum value of M = M0 where we show that the mutual information of the system increases. However, surprisingly, the correlation between a recently proposed SOP and the dynamics is highest for M = 1. This effect increases with polydispersity. We find that the SOP at M = 1 is coupled with the particle size, σ, and this coupling increases with polydispersity and decreases with an increase in M. Careful analysis shows that at lower polydispersities, the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on σ. Since the coupling between the SOP and σ is higher for M = 1, it appears to be a better predictor of the dynamics. We also study the Vibrality, an order parameter independent of structural information. Compared to SOP, at high polydispersity, we find Vibrality to be a marginally better predictor of the dynamics. However, this high predictive power of Vibrality, which is not there at lower polydispersity, appears to be due to its stronger coupling with σ. Therefore, our study suggests that for systems with high polydispersity, the correlation of any order parameter and σ will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter.

Dimensionality reduction of local structure in glassy binary mixtures

We consider unsupervised learning methods for characterizing the disordered microscopic structure of supercooled liquids and glasses. Specifically, we perform dimensionality reduction of smooth structural descriptors that describe radial and bond-orientational correlations and assess the ability of the method to grasp the essential structural features of glassy binary mixtures. In several cases, a few collective variables account for the bulk of the structural fluctuations within the first coordination shell and also display a clear connection with the fluctuations of particle mobility. Fine-grained descriptors that characterize the radial dependence of bond-orientational order better capture the structural fluctuations relevant for particle mobility but are also more difficult to parameterize and to interpret. We also find that principal component analysis of bond-orientational order parameters provides identical results to neural network autoencoders while having the advantage of being easily interpretable. Overall, our results indicate that glassy binary mixtures have a broad spectrum of structural features. In the temperature range we investigate, some mixtures display well-defined locally favored structures, which are reflected in bimodal distributions of the structural variables identified by dimensionality reduction.

Local Plastic Response and Slow Heterogeneous Dynamics of Supercooled Liquids

We demonstrate, via numerical simulations, that the relaxation dynamics of supercooled liquids correlates well with a plastic length scale measuring a particle's response to impulsive localized perturbations and weakly to measures of local elasticity. We find that the particle averaged plastic length scale vanishes linearly in temperature and controls the super-Arrhenius temperature dependence of the relaxation time. Furthermore, we show that the plastic length scale of individual particles correlates with their typical displacement at the relaxation time. In contrast, the local elastic response only correlates with the dynamics on the vibrational timescale.

Revisiting the single-saddle model for the β-relaxation of supercooled liquids

The dynamics of glass-forming liquids display several outstanding features, such as two-step relaxation and dynamic heterogeneities, which are difficult to predict quantitatively from first principles. In this work, we revisit a simple theoretical model of the β-relaxation, i.e., the first step of the relaxation dynamics. The model, first introduced by Cavagna et al. [J. Phys. A: Math. Gen. 36, 10721 (2003)], describes the dynamics of the system in the neighborhood of a saddle point of the potential energy surface. We extend the model to account for density–density correlation functions and for the four-point dynamic susceptibility. We obtain analytical results for a simple schematic model, making contact with related results for p-spin models and with the predictions of inhomogeneous mode-coupling theory. Building on recent computational advances, we also explicitly compare the model predictions against overdamped Langevin dynamics simulations of a glass-forming liquid close to the mode-coupling crossover. The agreement is quantitative at the level of single-particle dynamic properties only up to the early β-regime. Due to its inherent harmonic approximation, however, the model is unable to predict the dynamics on the time scale relevant for structural relaxation. Nonetheless, our analysis suggests that the agreement with the simulations may be largely improved if the modes’ spatial localization is properly taken into account.

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.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids

We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress, which correspond to atomic rearrangement events. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation gradient tensor F_α associated with each triangle α. To understand the spatio-temporal evolution of the displacement fields during shear stress drops, we calculate F_α along minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop. We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops. We then perform local perturbations (rotation, dilation, simple and pure shear) to single triangles and measure the resulting displacement fields. We find that local pure shear deformations of single triangles give rise to mostly quadrupolar displacement fields, and thus pure shear strain is the primary type of local strain that is activated by bulk, athermal quasistatic simple shear. Other local perturbations, e.g. rotations, dilations, and simple shear of single triangles, give rise to vortex-like and dipolar displacement fields that are not frequently activated by bulk AQS. These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.

A structural study and its relation to dynamic heterogeneity in a polymer glass former

The relationship between structure and dynamical behavior (super-Arrhenius temperature dependence of relaxation time accompanied by heterogeneous dynamics) in glassy materials remains an open issue in the physics of condensed matter. The question of whether this dynamic phenomena have a thermodynamic origin or not still remains unanswered. In this work we analyze several dynamic and structural parameters in a polymer glass-former by means of molecular dynamics simulations. The results obtained in this work indicate that the structure does affect dynamic behavior, whereas structural conditioning becomes noticeable below the temperature at which the non-Arrhenius behavior manifests and increases as the system approaches the glass transition temperature. Moreover, we observed that the short-range order parameters are related to local dynamics at the single-particle level. These results reinforce the idea of a connection between the structure and dynamics and that could indicate the thermodynamic nature of glass transition.

Inferring the particle-wise dynamics of amorphous solids from the local structure at the jamming point

Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their static critical properties with a unified approach. However, the dynamics occurring in the vicinity of the jamming point has received little attention and the problem of finding a connection with the local structure of the configuration remains unexplored. Here we address this issue by constructing physically well defined structural variables using the information contained in the network of contacts of jammed configurations, and then showing that such variables yield a resilient statistical description of the particle-wise dynamics near this critical point. Our results are based on extensive numerical simulations of systems of spherical particles that allow us to statistically characterize the trajectories of individual particles in terms of their first two moments. We first demonstrate that, besides displaying a broad distribution of mobilities, particles may also have preferential directions of motion. Next, we associate each of these features with a structural variable computed uniquely in terms of the contact vectors at jamming, obtaining considerably high statistical correlations. The robustness of our approach is confirmed by testing two types of dynamical protocols, namely molecular dynamics and Monte Carlo, with different types of interaction. We also provide evidence that the dynamical regime we study here is dominated by anharmonic effects and therefore it cannot be described properly in terms of vibrational modes. Finally, we show that correlations decay slowly and in an interaction-independent fashion, suggesting a universal rate of information loss.

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.

Tetrahedrality Dictates Dynamics in Hard Sphere Mixtures

The link between local structure and dynamical slowdown in glassy fluids has been the focus of intense debate for the better part of a century. Nonetheless, a simple method to predict the dynamical behavior of a fluid purely from its local structural features is still missing. Here, we demonstrate that the diffusivity of perhaps the most fundamental family of glass formers-hard sphere mixtures-can be accurately predicted based on just the packing fraction and a simple order parameter measuring the tetrahedrality of the local structure. Essentially, we show that the number of tetrahedral clusters in a hard sphere mixture is directly linked to its global diffusivity. Moreover, the same order parameter is capable of locally pinpointing particles in the system with high and low mobility. We attribute the power of the local tetrahedrality for predicting local and global dynamics to the high stability of tetrahedral clusters, the most fundamental building and densest-packing building blocks for a disordered fluid.

Elucidation of the Nature of Structural Relaxation in Glassy d-Sorbitol

The nature and origin of the glass transition is one of the great unsolved problems of condensed-matter science. With the rapid increase of viscosity upon cooling the liquid near the glass-transition temperature, a range of dynamical motifs are observed, revealing the sheer complexity of interactions between the amorphous units. Yet, the causal link between those motifs and the solidification process remains unclear. Here, we apply a novel approach for exploring nontrivial interactions between structural units in d-sorbitol, a canonical example of a hydrogen-bonded organic glass, by introducing a dihedral-rearrangement-indicator analysis to shed light on relaxation processes and dynamical heterogeneity, which are known for their association with the stability of a glass. We find that both α- and β-relaxation processes are governed by cooperative and heterogeneous changes in hydrogen-bond dynamics that can be described by spatial and dihedral-angle-rearrangement indicators. The methodology and findings are of general applicability to other glass-forming systems.

Structural order as a genuine control parameter of dynamics in simple glass formers

Glass transition is characterised by drastic dynamical slowing down upon cooling, accompanied by growing spatial heterogeneity. Its rationalisation by subtle changes in the liquid structure has been long debated but remains elusive, due to intrinsic difficulty in detecting the underlying complex structural ordering. Here we report that structural order parameter characterising local packing capability can well describe the glassy dynamics not only macroscopically but also microscopically, no matter whether it is driven by temperature or density. A Vogel-Fulcher-Tammann (VFT)-like relation is universally identified between the structural relaxation time and the order parameter for supercooled liquids with isotropic interactions. More importantly, we find such an intriguing VFT-like relation to be statistically valid even at a particle level, between spatially coarse-grained structural order and microscopic particle-level dynamics. Such a unified description of glassy dynamics based solely on structural order is expected to contribute to the ultimate understanding of the long-standing glass-transition problem.

The glass-forming materials exhibit dynamical slowing down together with spatial heterogeneity at microscales, but their origin remains debated. Tong and Tanaka show that this phenomenon can be unified based on a structural order parameter capable of detecting subtle ordering in instantaneous liquid states.

Vibrational scaling of the heterogeneous dynamics detected by mutual information

The correlations detected by the mutual information in the propensities of a molecular viscous liquid are studied by molecular-dynamics simulations. Dynamic heterogeneity is evidenced and two particle fractions with different mobility and relaxation identified. The two fractions exhibit the scaling of their relaxation in terms of the rattling amplitude of the particle trapped in the cage of the first neighbours 〈u²〉 . The scaling master curve does not differ from the one found for bulk systems, thus confirming identical results previously reported in other systems with strong dynamic heterogeneity as thin molecular films. The excitation of planar and globular structures at short and long times with respect to structural relaxation, respectively, is revealed. Some of the globular structures are different from the ones evidenced in atomic mixtures. States with equal 〈u²〉 are found to have identical time dependence of several quantities, referring to both bulk and the two fractions with heterogeneous dynamics, at least up to the structural relaxation time [Formula: see text].

Mutual information does not detect growing correlations in the propensity of a model molecular liquid

The dynamical spatial correlations detected by the mutual information (MI) in the isoconfigurational particle displacements of a monodisperse molecular viscous liquid are studied via molecular-dynamics simulations by changing considerably both the molecular mobility and the degree of dynamical heterogeneity. Different from atomic liquids, the MI correlation length does not grow on approaching the glass transition by considering the liquid both in full detail as a collection of monomers and as a coarse-grained ensemble of molecular centers of mass. In the detailed picture, it is found that: (i) the MI correlations between monomers are largely due to inter-molecular correlations, (ii) the MI length scale is numerically identical, within the errors, to the correlation length scale of the displacement direction, as drawn by conventional correlation functions. The time evolution of the MI spatial correlations complies with the scaling between the fast vibrational dynamics and the long-time relaxation. Our findings suggest that the characteristics of the MI length scale are markedly system-dependent and not obviously related to dynamical heterogeneity.

Emergence and percolation of rigid domains during the colloidal glass transition

Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints and demonstrate a percolation transition near the glass transition, accompanied by the emergence of dynamical heterogeneities. Our results show that spatial constraint instead of the geometry of amorphous structures is the key that connects the complex spatial-temporal correlations in disordered materials.

Heterogeneous Activation, Local Structure, and Softness in Supercooled Colloidal Liquids

We experimentally characterize heterogeneous nonexponential relaxation in bidisperse supercooled colloidal liquids utilizing a recent concept called "softness" [Phys. Rev. Lett. 114, 108001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.108001]. Particle trajectory and structure data enable classification of particles into subgroups with different local environments and propensities to hop. We determine residence times t_{R} between particle hops and show that t_{R} derived from particles in the same softness subgroup are exponentially distributed. Using the mean residence time t[over ¯]_{R} for each softness subgroup, and a Kramers' reaction rate model, we estimate the activation energy barriers E_{b} for particle hops, and show that both t[over ¯]_{R} and E_{b} are monotonic functions of softness. Finally, we derive information about the combinations of large and small particle neighbors that determine particle softness, and we explicitly show that multiple exponential relaxation channels in the supercooled liquid give rise to its nonexponential behavior.

The race to the bottom: approaching the ideal glass?

Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an 'ideal glass', an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations give equally good descriptions of the data available, so it is hard to determine which-if any-is correct. Recently however this situation has begun to change. A consensus has emerged that one powerful means to resolve this longstanding question is to approach the putative thermodynamic transition sufficiently closely, and a number of techniques have emerged to meet this challenge. Here we review the results of some of these new techniques and discuss the implications for the existence-or otherwise-of the thermodynamic transition to an ideal glass.

Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations

Glasses are among the most widely used of everyday materials, yet the process by which a liquid's viscosity increases by 14 decades to become a glass remains unclear, as often contradictory theories provide equally good descriptions of the available data. Knowledge of emergent lengthscales and higher-order structure could help resolve this, but this requires time-resolved measurements of dense particle coordinates-previously only obtained over a limited time interval. Here we present an experimental study of a model colloidal system over a dynamic window significantly larger than previous measurements, revealing structural ordering more strongly linked to dynamics than previously found. Furthermore we find that immobile regions and domains of local structure grow concurrently with density, and that these regions have low configurational entropy. We thus show that local structure plays an important role at deep supercooling, consistent with a thermodynamic interpretation of the glass transition rather than a principally dynamic description.

Yielding of a model glass former: An interpretation with an effective system of icosahedra

We consider the yielding under simple shear of a binary Lennard-Jones glass former whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. We recast this glass former as an effective system of icosahedra [Pinney et al., J. Chem. Phys. 143, 244507 (2015)JCPSA60021-960610.1063/1.4938424]. Looking at the small-strain region of sheared simulations, we observe that shear rates affect the shear localization behavior particularly at temperatures below the glass transition as defined with a fit to the Vogel-Fulcher-Tamman equation. At higher temperature, shear localization starts immediately on shearing for all shear rates. At lower temperatures, faster shear rates can result in a delayed start in shear localization, which begins close to the yield stress. Building from a previous work which considered steady-state shear [Pinney et al., J. Chem. Phys. 143, 244507 (2015)JCPSA60021-960610.1063/1.4938424], we interpret the response to shear and the shear localization in terms of a local effective temperature with our system of icosahedra. We find that the effective temperatures of the regions undergoing shear localization increase significantly with increasing strain (before reaching a steady-state plateau).

Local yield stress statistics in model amorphous solids

We develop and extend a method presented by Patinet, Vandembroucq, and Falk [Phys. Rev. Lett. 117, 045501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.045501] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.

Structure and Liquid Fragility in Sodium Carbonate

The relationship between local structure and dynamics is explored for molten sodium carbonate. A flexible fluctuating-charge model, which allows for changes in the shape and charge distribution of the carbonate molecular anion, is developed. The system shows the evolution of highly temperature-dependent complex low-dimensional structures which control the dynamics (and hence the liquid fragility). By varying the molecular anion charge distribution, the key interactions responsible for the formation of these structures can be identified and rationalized. An increase in the mean charge separation within the carbonate ions increases the connectivity of the emerging structures and leads to an increase in the system fragility.

Structural Origin of Enhanced Dynamics at the Surface of a Glassy Alloy

The enhancement of mobility at the surface of an amorphous alloy is studied using a combination of molecular dynamic simulations and normal mode analysis of the nonuniform distribution of Debye-Waller factors. The increased mobility at the surface is found to be associated with the appearance of Arrhenius temperature dependence. We show that the transverse Debye-Waller factor exhibits a peak at the surface. Over the accessible temperature range, we find that the bulk and surface diffusion coefficients obey the same empirical relationship with the respective Debye-Waller factors. Extrapolating this relationship to lower T, we argue that the observed decrease in the constraint at the surface is sufficient to account for the experimentally observed surface enhancement of mobility.

Local thermal energy as a structural indicator in glasses

Identifying heterogeneous structures in glasses-such as localized soft spots-and understanding structure-dynamics relations in these systems remain major scientific challenges. Here, we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change caused by thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses-an intrinsic signature of glassy frustration-anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal [Formula: see text] density of states of quasilocalized low-frequency vibrational modes. When the spatial thermal energy field-a "softness field"-is considered, this power law tail manifests itself by highly localized spots, which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal modes-based approach. These results offer a general, system/model-independent, physical/observable-based approach to identify structural properties of quiescent glasses and relate them to glassy dynamics.

Role of structure in the α and β dynamics of a simple glass-forming liquid

The elusive connection between dynamics and local structure in supercooled liquids is an important piece of the puzzle in the unsolved problem of the glass transition. The Johari-Goldstein β relaxation, ubiquitous in glass-forming liquids, exhibits mean properties that are strongly correlated to the long-time α dynamics. However, the former comprises simpler, more localized motion, and thus has perhaps a more straightforward connection to structure. Molecular dynamics simulations were carried out on a two-dimensional, rigid diatomic molecule (the simplest structure exhibiting a distinct β process) to assess the role of the local liquid structure on both the Johari-Goldstein β and the α relaxation. Although the average properties for these two relaxations are correlated, there is no connection between the β and α properties of a given (single) molecule. The propensity for motion at long times is independent of the rate or strength of a molecule's β relaxation. The mobility of a molecule averaged over many initial energies, a measure of the influence of structure, was found to be heterogeneous, with clustering at both the β and α time scales. This heterogeneity is less extended spatially for the β than for the α dynamics, as expected; however, the local structure is the more dominant control parameter for the β process. In the glassy state, the arrangement of neighboring molecules determines entirely the relaxation properties, with no discernible effect from the particle momenta.

Connecting Local Yield Stresses with Plastic Activity in Amorphous Solids

In model amorphous solids produced via differing quench protocols, a strong correlation is established between local yield stress measured by direct local probing of shear stress thresholds and the plastic rearrangements observed during remote loading in shear. This purely local measure shows a higher predictive power for identifying sites of plastic activity when compared with more conventional structural properties. Most importantly, the sites of low local yield stress, thus defined, are shown to be persistent, remaining predictive of deformation events even after fifty or more such plastic rearrangements. This direct and nonperturbative approach gives access to relevant transition pathways that control the stability of amorphous solids. Our results reinforce the relevance of modeling plasticity in amorphous solids based on a gradually evolving population of discrete and local zones preexisting in the structure.

Divergence of Voronoi Cell Anisotropy Vector: A Threshold-Free Characterization of Local Structure in Amorphous Materials

Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, where positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with the packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.

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.

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.

Disordered surface vibrations in jammed sphere packings

We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale ω*. This frequency is controlled by ΔZ = 〈Z〉 - 2d, the difference between the average coordination of the spheres and twice the spatial dimension, d, of the system, which vanishes at the jamming transition. In the presence of a free surface we find that there is a density of disordered vibrational modes associated with the surface that extends far below ω*. The total number of these low-frequency surface modes is controlled by ΔZ, and the profile of their decay into the bulk has two characteristic length scales, which diverge as ΔZ(-1/2) and ΔZ(-1) as the jamming transition is approached.

Identifying structural flow defects in disordered solids using machine-learning methods

We use machine-learning methods on local structure to identify flow defects-or particles susceptible to rearrangement-in jammed and glassy systems. We apply this method successfully to two very different systems: a two-dimensional experimental realization of a granular pillar under compression and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials.