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

Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test

It has been recognized of late that even amorphous, glass-forming materials in two dimensions (2D) are affected by Mermin-Wagner-type long wavelength thermal fluctuation, which is inconsequential in three dimensions (3D). We consider the question of whether the effect of spatial dimension on dynamics is only limited to such fluctuations or if the nature of glassy dynamics is intrinsically different in 2D. To address it, we study the relationship between dynamics and thermodynamics using the Adam-Gibbs (AG) relation and the random first order transition (RFOT) theory. Using two model glass-forming liquids, we find that even after removing the effect of long wavelength fluctuations, the AG relation breaks down in two dimensions. Next, we consider the effect of anharmonicity of vibrational entropy-a second factor that affects the thermodynamics but not dynamics. Using the potential energy landscape formalism, we explicitly compute the configurational entropy, both with and without the anharmonic correction. We show that even with both the corrections, the AG relation still breaks down in 2D. The extent of deviation from the AG relation crucially depends on the attractive vs repulsive nature of interparticle interactions, choice of representative timescale (diffusion coefficient vs α-relaxation time), and implies that the RFOT scaling exponents also depend on these factors. Thus, our results suggest that some differences in the nature of glassy dynamics between 2D and 3D remain that are not explained by long wavelength fluctuations.

Predicting the pathways of string-like motions in metallic glasses via path-featurizing graph neural networks

String-like motions (SLMs)-cooperative, "snake"-like movements of particles-are crucial for dynamics in diverse glass formers. Despite their ubiquity, questions persist: Do SLMs prefer specific paths? If so, can we predict these paths? Here, in Al-Sm glasses, our isoconfigurational ensemble simulations reveal that SLMs do follow certain paths. By designing a graph neural network (GNN) to featurize the environment around directional paths, we achieve a high-fidelity prediction of likely SLM pathways, solely based on the static structure. GNN gauges a structural measure to assess each path's propensity to engage in SLMs, akin to a "softness" metric, but for paths rather than for atoms. Our GNN interpretation reveals the critical role of the bottleneck zone along a path in steering SLMs. By monitoring "path softness," we elucidate that SLM-favored paths transit from fragmented to interconnected upon glass transition. Our findings reveal that, beyond atoms or clusters, glasses have another dimension of structural heterogeneity: "paths."

Different glassy characteristics are related to either caging or dynamical heterogeneity

Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different. What leads to this difference is the central puzzle of the field. Even the primary defining glassy characteristics, their implications, and if they are related to a single mechanism remain unclear. This lack of clarity is a severe hindrance to theoretical progress. Here, we combine analytical arguments and simulations of various systems in different dimensions and address these questions. Our results suggest that the myriad of glassy features are manifestations of two distinct mechanisms. Particle caging controls the mean, and coexisting slow- and fast-moving regions govern the distribution of particle displacements. All the other glassy characteristics are manifestations of these two mechanisms; thus, the Fickian yet non-Gaussian nature of glassy liquids is not surprising. We discover a crossover, from stretched exponential to a power law, in the behavior of the overlap function. This crossover is prominent in simulation data and forms the basis of our analyses. Our results have crucial implications on how the glassy dynamics data are analyzed, challenge some recent suggestions on the mechanisms governing glassy dynamics, and impose strict constraints that a correct theory of glasses must have.

Method to probe the pronounced growth of correlation lengths in active glass-forming liquids using an elongated probe

The growth of correlation lengths in equilibrium glass-forming liquids near the glass transition is considered a critical finding in the quest to understand the physics of glass formation. These understandings helped us understand various dynamical phenomena observed in supercooled liquids. It is known that at least two different length scales exist; one is of thermodynamic origin, while the other is dynamical in nature. Recent observations of glassy dynamics in biological and synthetic systems where the external or internal driving source controls the dynamics, apart from the usual thermal noise, lead to the emergence of the field of active glassy matter. A question of whether the physics of glass formation in these active systems is also accompanied by growing dynamic and static lengths is indeed timely. In this article, we probe the growth of dynamic and static lengths in a model active glass system using rod-like elongated probe particles, an experimentally viable method. We show that the dynamic and static lengths in these nonequilibrium systems grow much more rapidly than their passive counterparts. We then offer an understanding of the violation of the Stokes-Einstein relation and Stokes-Einstein-Debye relation using these lengths via a scaling theory.

Intermediate-range order governs dynamics in dense colloidal liquids

The conventional wisdom is that liquids are completely disordered and lack nontrivial structure beyond nearest-neighbor distances. Recent observations have upended this view and demonstrated that the microstructure in liquids is surprisingly rich and plays a critical role in numerous physical, biological, and industrial processes. However, approaches to uncover this structure are either system-specific or yield results that are not physically intuitive. Here, through single-particle resolved three-dimensional confocal microscope imaging and the use of a recently introduced four-point correlation function, we show that bidisperse colloidal liquids have a highly nontrivial structure comprising alternating layers with icosahedral and dodecahedral order, which extends well beyond nearest-neighbor distances and grows with supercooling. By quantifying the dynamics of the system on the particle level, we establish that it is this intermediate-range order, and not the short-range order, which has a one-to-one correlation with dynamical heterogeneities, a property directly related to the relaxation dynamics of glassy liquids. Our experimental findings provide a direct and much sought-after link between the structure and dynamics of liquids and pave the way for probing the consequences of this intermediate-range order in other liquid state processes.

Fractional Coupling of Primary and Johari-Goldstein Relaxations in a Model Polymer

A polymer model exhibiting heterogeneous Johari−Goldstein (JG) secondary relaxation is studied by extensive molecular-dynamics simulations of states with different temperature and pressure. Time−temperature−pressure superposition of the primary (segmental) relaxation is evidenced. The time scales of the primary and the JG relaxations are found to be highly correlated according to a power law. The finding agrees with key predictions of the Coupling Model (CM) accounting for the decay in a correlation function due to the relaxation and diffusion of interacting systems. Nonetheless, the exponent of the power law, even if it is found in the range predicted by CM (0<ξ<1), deviates from the expected one. It is suggested that the deviation could depend on the particular relaxation process involved in the correlation function and the heterogeneity of the JG process.

Enhanced short time peak in four-point dynamic susceptibility in dense active glass-forming liquids

Active glassy systems are simple model systems that imitate complex biological processes. Sometimes, it becomes crucial to estimate the amount of activity present in such biological systems, such as predicting the progression rate of the cancer cells or the healing time of the wound, etc. In this work, we study a model active glassy system to quantify the degree of activity from the collective, long-wavelength fluctuations in the system. These long-wavelength fluctuations present themselves as an additional peak in the four-point dynamic susceptibility (χ₄(t)) apart from the usual peak at structural relaxation time. We then show how the degree of the activity at such a small timescale can be obtained by measuring the variation in χ₄(t) due to changing activity. A Detailed finite size analysis of the peak height of χ₄(t) suggests the existence of an intrinsic dynamic length scale that grows with increasing activity. Finally, we show that this peak height is a unique function of effective activity across all system sizes, serving as a possible parameter for characterizing the degree of activity in a system.

Fragility in glassy liquids: A structural approach based on machine learning

The rapid rise of viscosity or relaxation time upon supercooling is a universal hallmark of glassy liquids. The temperature dependence of viscosity, however, is quite nonuniversal for glassy liquids and is characterized by the system's "fragility," with liquids with nearly Arrhenius temperature-dependent relaxation times referred to as strong liquids and those with super-Arrhenius behavior referred to as fragile liquids. What makes some liquids strong and others fragile is still not well understood. Here, we explore this question in a family of harmonic spheres that range from extremely strong to extremely fragile, using "softness," a structural order parameter identified by machine learning to be highly correlated with dynamical rearrangements. We use a support vector machine to identify softness as the same linear combination of structural quantities across the entire family of liquids studied. We then use softness to identify the factors controlling fragility.

Neural Networks Reveal the Impact of the Vibrational Dynamics in the Prediction of the Long-Time Mobility of Molecular Glassformers

Two neural networks (NN) are designed to predict the particle mobility of a molecular glassformer in a wide time window ranging from vibrational dynamics to structural relaxation. Both NNs are trained by information concerning the local structure of the environment surrounding a given particle. The only difference in the learning procedure is the inclusion (NN A) or not (NN B) of the information provided by the fast, vibrational dynamics and quantified by the local Debye–Waller factor. It is found that, for a given temperature, the prediction provided by the NN A is more accurate, a finding which is tentatively ascribed to better account of the bond reorientation. Both NNs are found to exhibit impressive and rather comparable performance to predict the four-point susceptibility χ4(t) at τα, a measure of the dynamic heterogeneity of the system.

Dynamics of liquids in the large-dimensional limit

In this paper we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation greatly simplifies the original path-integral-based route to these equations and provides insight into the physical features associated with high-dimensional liquids and glass formation. Most importantly, our construction provides a route to the exact dynamical analysis of important related dynamical problems, as well as a means to devise cluster generalizations of the exact solution in infinite dimensions. This latter fact opens the door to the construction of increasingly accurate theories of vitrification in three-dimensional liquids.

Finite size effect on the magnetic glass

The nature of glass formation and crystallization in structural glass is yet to be understood despite the intense studies of many decades. Analogous to the structural glasses, hindered first order magnetic transitions produce magnetic glasses, where the volume fraction of two phases having long range structural and magnetic order are frozen in time. Here, we have prepared Pr_0.5Ca_0.5Mn_0.975Al_0.025O₃nanoparticles of different size as a case study and investigated the formation and stability of the magnetic glass state at the length scale of a few nanometers. We have observed a profound interplay between the glass state and sample size: stability of the glass state highly increases and scales linearly with decrease in the sample size. Smaller the particle size, slower is the crystallization rate. The crystallization occurs through both homogeneous and heterogeneous nucleation and is controlled by the surface to volume ratio of the particles. Our results emphasize on an important fact that glass transition is not a phase transition in actual sense, rather it is a kinetic phenomena. The length scale associated with different nucleation processes is an important length scale and it controls the glass dynamics. Besides, apart from the intrinsic metastability due to magnetic glass, we also distinguish a secondary source of relaxation, which is dominant at low magnetic fields, predominantly arising due to surface spin disorder.

Spatial Dimensionality Dependence of Heterogeneity, Breakdown of the Stokes-Einstein Relation, and Fragility of a Model Glass-Forming Liquid

We investigate the heterogeneity of dynamics, the breakdown of the Stokes-Einstein relation and fragility in a model glass forming liquid, a binary mixture of soft spheres with a harmonic interaction potential for spatial dimensions from 3 to 8. The dynamical heterogeneity is quantified through the dynamical susceptibility χ₄ and the non-Gaussian parameter α₂. We find that the fragility, the degree of breakdown of the Stokes-Einstein relation, and the heterogeneity of the dynamics decrease with increasing spatial dimensionality. We briefly describe the dependence of fragility on the density and use it to resolve an apparent inconsistency with previous results.

Mutual Information in Molecular and Macromolecular Systems

The relaxation properties of viscous liquids close to their glass transition (GT) have been widely characterised by the statistical tool of time correlation functions. However, the strong influence of ubiquitous non-linearities calls for new, alternative tools of analysis. In this respect, information theory-based observables and, more specifically, mutual information (MI) are gaining increasing interest. Here, we report on novel, deeper insight provided by MI-based analysis of molecular dynamics simulations of molecular and macromolecular glass-formers on two distinct aspects of transport and relaxation close to GT, namely dynamical heterogeneity (DH) and secondary Johari–Goldstein (JG) relaxation processes. In a model molecular liquid with significant DH, MI reveals two populations of particles organised in clusters having either filamentous or compact globular structures that exhibit different mobility and relaxation properties. In a model polymer melt, MI provides clearer evidence of JG secondary relaxation and sharper insight into its DH. It is found that both DH and MI between the orientation and the displacement of the bonds reach (local) maxima at the time scales of the primary and JG secondary relaxation. This suggests that, in (macro)molecular systems, the mechanistic explanation of both DH and relaxation must involve rotation/translation coupling.

Translational dynamics of a rod-like probe in supercooled liquids: an experimentally realizable method to study Stokes-Einstein breakdown, dynamic heterogeneity, and amorphous order

The use of probe molecules to extract the local dynamical and structural properties of complex dynamical systems is an age-old technique both in simulations and in experiments. A lot of important information which is not immediately accessible from bulk measurements can be accessed via these local measurements. Still, a detailed understanding of how a probe particle dynamics is affected by the surrounding liquid medium is lacking, especially in the supercooled temperature regime. This work shows how the translational dynamics of a rod-like particle immersed in a supercooled liquid can give us information on the growth of the correlation length scales associated with dynamical heterogeneity and the multi-body static correlations in the medium. This work also provides an understanding of the breakdown of Stokes-Einstein and Stokes-Einstein-Debye relations in supercooled liquids along with a unified scaling theory that rationalizes all the observed results. Finally, this work proposes a novel yet simple method accessible in experiments to measure the growth of these important length scales in molecular glass-forming liquids.

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.

An alternative approach to evidence the structural conditioning in the dynamic slowdown in a polymer glass-former

Dynamic slowdown of liquids, leading to a breakdown of Arrhenius behavior of relaxation and Stokes-Einstein relationship (SER), as the glass transition is approached, is still not fully understood despite decades of study. They are usually associated to the emergence of dynamic heterogeneity, that is, regions or clusters of particles that have high or low mobilities. But the physical origin of these dynamic heterogeneity, and in particular, the question whether they have a structural origin or they are a purely dynamical phenomenon, is still under debate. In this work we study through molecular dynamics simulations in a polymer model the dynamic slowdown and the breakdown of SER, in connection with dynamic susceptibility calculated for an isoconfigurational ensemble, such that the effects of structure on dynamics can be discriminated. The onset of structure effects on dynamical behavior is found to be coincident with the onset of slow dynamics and SER breakdown.

Fast Vibrational Modes and Slow Heterogeneous Dynamics in Polymers and Viscous Liquids

Many systems, including polymers and molecular liquids, when adequately cooled and/or compressed, solidify into a disordered solid, i.e., a glass. The transition is not abrupt, featuring progressive decrease of the microscopic mobility and huge slowing down of the relaxation. A distinctive aspect of glass-forming materials is the microscopic dynamical heterogeneity (DH), i.e., the presence of regions with almost immobile particles coexisting with others where highly mobile ones are located. Following the first compelling evidence of a strong correlation between vibrational dynamics and ultraslow relaxation, we posed the question if the vibrational dynamics encodes predictive information on DH. Here, we review our results, drawn from molecular-dynamics numerical simulation of polymeric and molecular glass-formers, with a special focus on both the breakdown of the Stokes-Einstein relation between diffusion and viscosity, and the size of the regions with correlated displacements.

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.

Nuclear magnetic relaxation and diffusion study of the ionic liquids 1-ethyl- and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide confined in porous glass

The molecular dynamics of the room-temperature ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (Bmim Tf2N) confined in porous glass is studied by nuclear magnetic resonance (NMR) relaxometry and diffusometry and is compared with the bulk dynamics over a wide temperature range. The molecular reorientation processes for anions and cations alike are found to be significantly affected by the presence of the glass interface at high temperatures. In this respect, the ionic liquid behaves similarly to polar liquids where proton NMR relaxation is governed by reorientations mediated by translational displacements (RMTDs). This process becomes less significant towards lower temperatures when the characteristic translational correlation times of the ions approach a timescale comparable with those of the RMTD process, and the relaxation dispersions in bulk and in confinement become similar below a temperature corresponding to about 1.2T_g , a value where the onset of dynamic heterogeneity has been observed before. The self-diffusion coefficient, on the other hand, is found to be strongly reduced than the bulk within the accessible temperature range of 248 K and above and is significantly slower than expected from the tortuosity effect, suggesting that ion-surface interactions affect the macroscopic properties.

Static and dynamic correlation lengths in supercooled polymers

A key point to understand the glass transition is the relationship between structural and dynamic behavior experienced by a glass former when it approaches T_g. In this work, the relaxation in a simple bead-spring polymer system in the supercooled regime near its glass transition temperature was investigated with molecular dynamic simulations. We develop a new manner to look at the dynamic length scales in a supercooled polymeric system, focusing on correlated motion of particles in an isoconfigurational ensemble (that is, associated with the structure), as measured by Pearson's correlation coefficient. We found that while the usual dynamic four-point correlation length deviates from the structural (mosaic or point-to-set) length scale at low temperatures, Pearson's length behaves similarly to the static length in the whole temperature range. The results lead to a consensus of similar scaling of structural and dynamical length scales, reinforcing the idea of the theories of Adam-Gibbs and random first order transition.

Role of α and β relaxations in collapsing dynamics of a polymer chain in supercooled glass-forming liquid

Understanding the effect of glassy dynamics on the stability of bio-macromolecules and investigating the underlying relaxation processes governing degradation processes of these macromolecules are of immense importance in the context of bio-preservation. In this work, we have studied the stability of a model polymer chain in a supercooled glass-forming liquid at different amounts of supercooling in order to understand how dynamics of supercooled liquids influence the collapse behavior of the polymer. Our systematic computer simulation studies find that, apart from long time relaxation processes (α relaxation), short time dynamics of the supercooled liquid, known as β relaxation, is also correlated with the stability of the model polymer. We also show that anti-plasticizing effect found in this context can be rationalized using the β-relaxation process and how it is modified due to changes in the specific interactions between the biomolecules and the solvent molecules or changes in the local packing around the biomolecules. Our results corroborate with other recent results which suggest that it is important to take in to account both the α and β relaxation times while choosing appropriate bio-preservatives. We believe that our results will have implications in understanding the primary factors in protein stabilization in the context of bio-preservation.

Glass forming phase diagram and local structure of Kob-Andersen binary Lennard-Jones nanoparticles

Molecular dynamics simulation is used to study glass formation in Kob-Andersen binary Lennard-Jones nanoparticles and determine the glass forming phase diagram for the system as a function of composition. The radial distribution function, a Steinhardt bond-orientational order parameter, and favored local structure analysis are used to distinguish between glassy and ordered systems. We find that surface enrichment of the large atoms alters the nanoparticle core composition, leading to an overall shift of the glass forming region to lower small atom mole fractions, relative to the bulk system. At small atom mole fraction, x_B = 0.1, the nanoparticles form a solid with an amorphous core, enriched with the small atoms, surrounded by a partially ordered surface region, enriched with the large atom component. The most disordered glass nanoparticles occur at x_B ≈ 0.3, but the surface-core enrichment leads to the crystallization of the nanoparticle to the CsCl crystal above x_B ≈ 0.35, which is lower than observed in the bulk. The glass transition temperatures of the nanoparticles are also significantly reduced. This allows the liquid to remain dynamic to low temperatures and sample the low energy inherent structure minima on the potential energy surface containing a high abundance of favoured local structures.

Long-range stress correlations in viscoelastic and glass-forming fluids

A simple and rigorous approach to obtain stress correlations in viscoelastic liquids (including supercooled liquid and equilibrium amorphous systems) is proposed. The long-range dynamical correlations of local shear stress are calculated and analyzed in 2-dimensional space. It is established how the long-range character of the stress correlations gradually emerges as the relevant dynamical correlation length l grows in time. The correlation range l is defined by momentum propagation due to acoustic waves and vorticity diffusion which are the basic mechanisms for transmission of shear stress perturbations. We obtain the general expression defining the time- and distance-dependent stress correlation tensor in terms of material functions (generalized relaxation moduli). The effect of liquid compressibility is quantitatively analyzed; it is shown to be important at large distances and/or short times. The revealed long-range stress correlation effect is shown to be dynamical in nature and unconnected with static structural correlations in liquids (correlation length ξ_s). Our approach is based on the assumption that ξ_s is small enough as reflected in weak wave-number dependencies of the generalized relaxation moduli. We provide a simple physical picture connecting the elucidated long-range fluctuation effect with anisotropic correlations of the (transient) inherent stress field, and discuss its implications.

Glass Transition in Supercooled Liquids with Medium-Range Crystalline Order

The origin of the rapid dynamical slowdown in glass forming liquids in the growth of static length scales, possibly associated with identifiable structural ordering, is a much debated issue. Growth of medium range crystalline order (MRCO) has been observed in various model systems to be associated with glassy behavior. Such observations raise the question of whether molecular mechanisms for the glass transition in liquids with and without MRCO are the same. In this study we perform extensive molecular dynamics simulations of a number of glass forming liquids and show that the static and dynamic properties of glasses with MRCO are different from those of other glass forming liquids with no predominant local order. We also resolve an important issue regarding the so-called point-to-set method for determining static length scales, and demonstrate it to be a robust method for determining static correlation lengths in glass formers.

Power law relationship between diffusion coefficients in multi-component glass forming liquids

The slow down of dynamics in glass forming liquids as the glass transition is approached has been characterised through the Adam-Gibbs relation, which relates relaxation time scales to the configurational entropy. The Adam-Gibbs relation cannot apply simultaneously to all relaxation times scales unless they are coupled, and exhibit closely related temperature dependences. The breakdown of the Stokes-Einstein relation presents an interesting situation to the contrary, and in analysing it, it has recently been shown that the Adam-Gibbs relation applies to diffusion coefficients rather than to viscosity or structural relaxation times related to the decay of density fluctuations. However, for multi-component liquids --the typical cases considered in computer simulations, metallic glass formers, etc.-- such a statement raises the question of which diffusion coefficient is described by the Adam-Gibbs relation. All diffusion coefficients can be consistently described by the Adam-Gibbs relation if they bear a power law relationship with each other. Remarkably, we find that for a wide range of glass formers, and for a wide range of temperatures spanning the normal and the slow relaxation regimes, such a relationship holds. We briefly discuss possible rationalisations of the observed behaviour.

Growing length scale accompanying vitrification: A perspective based on nonsingular density fluctuations

A model for describing growing length scale accompanying the vitrification is introduced, in which we assume that in a subsystem whose density is above a certain threshold value, ρ_{c}, due to steric constraints, particle rearrangements are highly suppressed for a sufficiently long time period (∼structural relaxation time). We regard such a subsystem as a glassy cluster. With this assumption and without introducing any complicated thermodynamic arguments, we predict that with compression (increasing average density ρ) at a fixed temperature T in supercooled states, the characteristic length of the clusters, ξ, diverges as ξ∼(ρ_{c}-ρ)^{-2/d}, where d is the spatial dimensionality. This ξ measures the average persistence length of the steric constraints in blocking the rearrangement motions and is determined by the subsystem density. Additionally, with decreasing T at a fixed ρ, the length scale diverges in the same manner as ξ∼(T-T_{c})^{-2/d}, for which ρ is identical to ρ_{c} at T=T_{c}. The exponent describing the diverging length scale is the same as the one predicted by some theoretical models and indeed has been observed in some simulations and experiments. However, the basic mechanism for this divergence is different; that is, we do not invoke thermodynamic anomalies associated with the thermodynamic phase transition as the origin of the growing length scale. We further present arguements for the cooperative properties of the structural relaxation based on the clusters.

The role of local-geometrical-orders on the growth of dynamic-length-scales in glass-forming liquids

The precise nature of complex structural relaxation as well as an explanation for the precipitous growth of relaxation time in cooling glass-forming liquids are essential to the understanding of vitrification of liquids. The dramatic increase of relaxation time is believed to be caused by the growth of one or more correlation lengths, which has received much attention recently. Here, we report a direct link between the growth of a specific local-geometrical-order and an increase of dynamic-length-scale as the atomic dynamics in metallic glass-forming liquids slow down. Although several types of local geometrical-orders are present in these metallic liquids, the growth of icosahedral ordering is found to be directly related to the increase of the dynamic-length-scale. This finding suggests an intriguing scenario that the transient icosahedral connectivity could be the origin of the dynamic-length-scale in metallic glass-forming liquids.

Block Analysis for the Calculation of Dynamic and Static Length Scales in Glass-Forming Liquids

We present block analysis, an efficient method of performing finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves considering blocks of varying sizes embedded in a system of a fixed (large) size. The length scale associated with dynamic heterogeneity is obtained from a finite-size scaling analysis of the dependence of the four-point dynamic susceptibility on the block size. The block size dependence of the variance of the α relaxation time yields the static point-to-set length scale. The values of the obtained length scales agree quantitatively with those obtained from other conventional methods. This method provides an efficient experimental tool for studying the growth of length scales in systems such as colloidal glasses for which performing finite-size scaling by carrying out experiments for varying system sizes may not be feasible.

Structural rearrangements governing Johari-Goldstein relaxations in metallic glasses

The Johari-Goldstein secondary (β) relaxations are an intrinsic feature of supercooled liquids and glasses. They are crucial to many properties of glassy materials, but the underlying mechanisms are still not established. In a model metallic glass, we study the atomic rearrangements by molecular dynamics simulations at time scales of up to microseconds. We find that the distributions of single-particle displacements exhibit multiple peaks, whose positions quantitatively match the pair distribution function. These are identified as the structural signature of cooperative string-like excitations. Furthermore, the most probable time of the string-like motions coincides with the β-relaxation time as probed by dynamical mechanical simulations over a wide temperature range and is consistent with a theoretical model. Our results provide insights into the long-standing puzzle regarding the structural origin of β relaxations in glassy metallic materials.

Pinning susceptibility: a novel method to study growth of amorphous order in glass-forming liquids

The existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and has also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems like colloidal glasses and simulations of model glass-forming liquids. In this work, we propose an experimentally realizable yet simple susceptibility to study the growth of amorphous order. We then demonstrate the validity of this approach for a few well-studied model supercooled liquids and obtain results which are consistent with other conventional methods.

Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its thermodynamics via the configurational entropy and is of fundamental importance in descriptions of glassy behavior. The breakdown of the Stokes-Einstein relation (SEB) between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.

Nonlinear response theory for Markov processes. II. Fifth-order response functions

The nonlinear response of stochastic models obeying a master equation is calculated up to fifth order in the external field, thus extending the third-order results obtained earlier [G. Diezemann, Phys. Rev. E 85, 051502 (2012)PLEEE81539-375510.1103/PhysRevE.85.051502]. For sinusoidal fields the 5ω component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurrence of such a hump as compared to a single characteristic regime in the case of the third-order response. In the case of the trap model the results strongly depend on the variable coupled to the field. As for the third-order response, the low-frequency limit of the susceptibility plays a crucial role with respect to the occurrence of a hump. The findings are discussed in light of recent experimental results obtained for supercooled liquids. The differences found for the third-order and the fifth-order response indicate that nonlinear response functions might serve as a powerful tool to discriminate among the large number of existing models for glassy relaxation.

Role of density modulation in the spatially resolved dynamics of strongly confined liquids

Confinement by walls usually produces a strong modulation in the density of dense liquids near the walls. Using molecular dynamics simulations, we examine the effects of the density modulation on the spatially resolved dynamics of a liquid confined between two parallel walls, using a resolution of a fraction of the interparticle distance in the liquid. The local dynamics is quantified by the relaxation time associated with the temporal autocorrelation function of the local density. We find that this local relaxation time varies in phase with the density modulation. The amplitude of the spatial modulation of the relaxation time can be quite large, depending on the characteristics of the wall and thermodynamic parameters of the liquid. To disentangle the effects of confinement and density modulation on the spatially resolved dynamics, we compare the dynamics of a confined liquid with that of an unconfined one in which a similar density modulation is induced by an external potential. We find several differences indicating that density modulation alone cannot account for all the features seen in the spatially resolved dynamics of confined liquids. We also examine how the dynamics near a wall depends on the separation between the two walls and show that the features seen in our simulations persist in the limit of large wall separation.

Glass susceptibility: Growth kinetics and saturation under shear

We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function χ_{C}(t,t_{w}) with time t and waiting time t_{w}. From the complete wave-vector-dependent equations of motion for domain growth, we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value χ_{C}^{P} of χ_{C}(t,t_{w}), which can be viewed as a correlation volume, grows as t_{w}^{0.5}, and the relaxation time as t_{w}^{0.8}, following a quench to a point deep in the glassy state. These results constitute a theoretical explanation of the simulation findings of Parisi [J. Phys. Chem. B 103, 4128 (1999)JPCBFK1520-610610.1021/jp983967m] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)PRLTAO0031-900710.1103/PhysRevLett.78.4581], and they are also in qualitative agreement with Parsaeian and Castillo [Phys. Rev. E 78, 060105(R) (2008)PLEEE81539-375510.1103/PhysRevE.78.060105]. On the other hand, if the quench is to a point on the liquid side, the correlation volume grows to saturation. We present a similar calculation for the growth kinetics in a p-spin spin glass mean-field model where we find a slower growth, χ_{C}^{P}∼t_{w}^{0.13}. Further, we show that a shear rate γ[over ̇] cuts off the growth of glassy correlations when t_{w}∼1/γ[over ̇] for quench in the glassy regime and t_{w}=min(t_{r},1/γ[over ̇]) in the liquid, where t_{r} is the relaxation time of the unsheared liquid. The relaxation time of the steady-state fluid in this case is ∝γ[over ̇]^{-0.8}.