Dynamical susceptibility of glass formers: contrasting the predictions of theoretical scenarios

Collective dynamic length increases monotonically in pinned and unpinned glass forming systems

The Random First-Order Transition (RFOT) theory predicts that transport proceeds by the cooperative movement of particles in domains, whose sizes increase as a liquid is compressed above a characteristic volume fraction, ϕd. The rounded dynamical transition around ϕd, which signals a crossover to activated transport, is accompanied by a growing correlation length that is predicted to diverge at the thermodynamic glass transition density (>ϕd). Simulations and imaging experiments probed the single particle dynamics of mobile particles in response to pinning all the particles in a semi-infinite space or randomly pinning (RP) a fraction of particles in a liquid at equilibrium. The extracted dynamic length increases non-monotonically with a peak around ϕd, which not only depends on the pinning method but is also different from ϕd of the actual liquid. This finding is at variance with the results obtained using the small wavelength limit of a four-point structure factor for unpinned systems. To obtain a consistent picture of the growth of the dynamic length, one that is impervious to the use of RP, we introduce a multiparticle structure factor, Smpc(q,t), that probes collective dynamics. The collective dynamical length, calculated from the small wave vector limit of Smpc(q,t), increases monotonically as a function of the volume fraction in a glass-forming binary mixture of charged colloidal particles in both unpinned and pinned systems. This prediction, which also holds in the presence of added monovalent salt, may be validated using imaging experiments.

Displacement correlations in a two-dimensional colloidal liquid and their relationship with shear strain correlations

Correlations of the displacement field in a two-dimensional model colloidal liquid are studied numerically and analytically. By calculating the displacement correlations and the shear strain correlations from the numerical data of particle simulations, the displacement field is shown to have nontrivial correlations, even in liquids that are only slightly glassy with the area fraction as low as 0.5. It is suggested analytically and demonstrated numerically that the displacement correlations are more informative than the shear correlations: the former behaves logarithmically with regard to the spatial distance at shorter scales, while the corresponding information is missing from the shear correlations. The logarithmic behavior of the displacement correlations is interpreted as manifesting a long-lived aspect of the cage effect.

Characterizing the Slow Dynamics of the Swap Monte Carlo Algorithm

The swap Monte Carlo algorithm introduces nonphysical dynamic rules to accelerate the exploration of the configuration space of supercooled liquids. Its success raises deep questions regarding the nature and physical origin of the slow dynamics of dense liquids and how it is affected by swap moves. We provide a detailed analysis of the slow dynamics generated by the swap Monte Carlo algorithm at very low temperatures in two glass-forming models. We find that the slowing down of the swap dynamics is qualitatively distinct from its local Monte Carlo counterpart, with considerably suppressed dynamic heterogeneity at both single-particle and collective levels. Our results suggest that local kinetic constraints are drastically reduced by swap moves, leading to nearly Gaussian and diffusive dynamics and weakly growing dynamic correlation length scales. The comparison between static and dynamic fluctuations shows that swap Monte Carlo is a nearly optimal local equilibrium algorithm, suggesting that further progress should necessarily involve collective or driven algorithms.

Sequence complexity and monomer rigidity control the morphologies and aging dynamics of protein aggregates

Understanding the biophysical basis of protein aggregation is important in biology because of the potential link to several misfolding diseases. Although experiments have shown that protein aggregates adopt a variety of morphologies, the dynamics of their formation are less well characterized. Here, we introduce a minimal model to explore the dependence of the aggregation dynamics on the structural and sequence features of the monomers. Using simulations, we demonstrate that sequence complexity (codified in terms of word entropy) and monomer rigidity profoundly influence the dynamics and morphology of the aggregates. Flexible monomers with low sequence complexity (corresponding to repeat sequences) form liquid-like droplets that exhibit ergodic behavior. Strikingly, these aggregates abruptly transition to more ordered structures, reminiscent of amyloid fibrils, when the monomer rigidity is increased. In contrast, aggregates resulting from monomers with high sequence complexity are amorphous and display nonergodic glassy dynamics. The heterogeneous dynamics of the low and high-complexity sequences follow stretched exponential kinetics, which is one of the characteristics of glassy dynamics. Importantly, at nonzero values of the bending rigidities, the aggregates age with the relaxation times that increase with the waiting time. Informed by these findings, we provide insights into aging dynamics in protein condensates and contrast the behavior with the dynamics expected in RNA repeat sequences. Our findings underscore the influence of the monomer characteristics in shaping the morphology and dynamics of protein aggregates, thus providing a foundation for deciphering the general rules governing the behavior of protein condensates.

Direct Numerical Analysis of Dynamic Facilitation in Glass-Forming Liquids

We propose a computational strategy to quantify the temperature evolution of the timescales and length scales over which dynamic facilitation affects the relaxation dynamics of glass-forming liquids at low temperatures, which requires no assumption about the nature of the dynamics. In two glass models, we find that dynamic facilitation depends strongly on temperature, leading to a subdiffusive spreading of relaxation events which we characterize using a temperature-dependent dynamic exponent. We also establish that this temperature evolution represents a major contribution to the increase of the structural relaxation time.

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic-subdiffusive-diffusive crossover MSD behaviors commonly found in supercooled liquids.

Dynamics and fluctuations of minimally structured glass formers

The mean-field theory (MFT) of simple structural glasses, which is exact in the limit of infinite spatial dimensions, d→∞, offers theoretical insight as well as quantitative predictions about certain features of d=3 systems. In order to more systematically relate the behavior of physical systems to MFT, however, various finite-d effects need to be accounted for. Although some efforts along this direction have already been undertaken, theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally structured models whose behavior smoothly converges to that described by the MFT as d increases, so as to permit a controlled dimensional extrapolation. Using this approach, we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable, the non-Gaussian parameter α_{2}. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.

Viscoelastic relaxation and topological fluctuations in glass-forming liquids

A method for characterizing the topological fluctuations in liquids is proposed. This approach exploits the concept of the weighted gyration tensor of a collection of particles and permits the definition of a local configurational unit (LCU). The first principal axis of the gyration tensor serves as the director of the LCU, which can be tracked and analyzed by molecular dynamics simulations. Analysis of moderately supercooled Kob-Andersen mixtures suggests that orientational relaxation of the LCU closely follows viscoelastic relaxation and exhibits a two-stage behavior. The slow relaxing component of the LCU corresponds to the structural, Maxwellian mechanical relaxation. Additionally, it is found that the mean curvature of the LCUs is approximately zero at the Maxwell relaxation time with the Gaussian curvature being negative. This observation implies that structural relaxation occurs when the configurationally stable and destabilized regions interpenetrate each other in a bicontinuous manner. Finally, the mean and Gaussian curvatures of the LCUs can serve as reduced variables for the shear stress correlation, providing a compelling proof of the close connection between viscoelastic relaxation and topological fluctuations in glass-forming liquids.

How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

Collective Relaxation Dynamics in a Three-Dimensional Lattice Glass Model

We numerically elucidate the microscopic mechanisms controlling the relaxation dynamics of a three-dimensional lattice glass model that has static properties compatible with the approach to a random first-order transition. At low temperatures, the relaxation is triggered by a small population of particles with low-energy barriers forming mobile clusters. These emerging quasiparticles act as facilitating defects responsible for the spatially heterogeneous dynamics of the system, whose characteristic length scales remain strongly coupled to thermodynamic fluctuations. We compare our findings both with existing theoretical models and atomistic simulations of glass formers.

How the Presence of Crystalline Phase Affects Structural Relaxation in Molecular Liquids: The Case of Amorphous Indomethacin

The influence of partial crystallinity on the structural relaxation behavior of low-molecular organic glasses is, contrary to, e.g., polymeric materials, a largely unexplored territory. In the present study, differential scanning calorimetry was used to prepare a series of amorphous indomethacin powders crystallized to various extents. The preparations stemmed from the two distinct particle size fractions: 50-125 µm and 300-500 µm. The structural relaxation data from the cyclic calorimetric measurements were described in terms of the phenomenological Tool-Narayanaswamy-Moynihan model. For the 300-500 µm powder, the crystalline phase forming dominantly on the surface led to a monotonous decrease in the glass transition by ~6 °C in the 0-70% crystallinity range. The activation energy of the relaxation motions and the degree of heterogeneity within the relaxing matrix were not influenced by the increasing crystallinity, while the interconnectivity slightly increased. This behavior was attributed to the release of the quenched-in stresses and to the consequent slight increase in the structural interconnectivity. For the 50-125 µm powder, distinctly different relaxation dynamics were observed. This leads to a conclusion that the crystalline phase grows throughout the bulk glassy matrix along the internal micro-cracks. At higher crystallinity, a sharp increase in Tg, an increase in interconnectivity, and an increase in the variability of structural units engaged in the relaxation motions were observed.

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density-density and hydrostatic pressure-pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. These results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

Spectroscopic and Chemical Properties of Ionic Liquids: Computational Study

A brief account is given of highlights of our computational efforts - often in collaboration with experimental groups - to understand spectroscopic and chemical properties of ionic liquids (ILs). Molecular dynamics, including their inhomogeneous character, responsible for key spectral features observed in dielectric absorption, infra-red (IR) and fluorescence correlation spectroscopy (FCS) measurements are elucidated. Mechanisms of chemical processes involving imidazolium-based ILs are illustrated for CO2 capture and related reactions, transesterification of cellulose, and Au nanocluster-catalyzed Suzuki cross-coupling reaction with attention paid to differing roles of IL ions. A comparison with experiments is also made.

Controlling crystallization: what liquid structure and dynamics reveal about crystal nucleation mechanisms

Over recent years, molecular simulations have provided invaluable insights into the microscopic processes governing the initial stages of crystal nucleation and growth. A key aspect that has been observed in many different systems is the formation of precursors in the supercooled liquid that precedes the emergence of crystalline nuclei. The structural and dynamical properties of these precursors determine to a large extent the nucleation probability as well as the formation of specific polymorphs. This novel microscopic view on nucleation mechanisms has further implications for our understanding of the nucleating ability and polymorph selectivity of nucleating agents, as these appear to be strongly linked to their ability in modifying structural and dynamical characteristics of the supercooled liquid, namely liquid heterogeneity. In this perspective, we highlight recent progress in exploring the connection between liquid heterogeneity and crystallization, including the effects of templates, and the potential impact for controlling crystallization processes. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Predicting Dynamic Heterogeneity in Glass-Forming Liquids by Physics-Inspired Machine Learning

We introduce GlassMLP, a machine learning framework using physics-inspired structural input to predict the long-time dynamics in deeply supercooled liquids. We apply this deep neural network to atomistic models in 2D and 3D. Its performance is better than the state of the art while being more parsimonious in terms of training data and fitting parameters. GlassMLP quantitatively predicts four-point dynamic correlations and the geometry of dynamic heterogeneity. Transferability across system sizes allows us to efficiently probe the temperature evolution of spatial dynamic correlations, revealing a profound change with temperature in the geometry of rearranging regions.

Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids

We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.

Structure ordering and glass transition in size-asymmetric ternary mixtures of hard spheres: Variation from fragile to strong glasses

We investigate the structure and activated dynamics of a binary mixture of colloidal particles dispersed in a solvent of much smaller-sized particles. The solvent degrees of freedom are traced out from the grand partition function of the colloid-solvent mixture which reduces the system from ternary to effective binary mixture of colloidal particles. In the effective binary mixture colloidal particles interact via effective potential that consists of bare potential plus the solvent-induced interaction. Expressions for the effective potentials and pair correlation functions are derived. We used the result of pair correlation functions to determine the number of particles in a cooperatively reorganizing cluster (CRC) in which localized particles form "long-lived" nonchemical bonds with the central particle. For an event of relaxation to take place these bonds have to reorganize irreversibly, the energy involved in the processes is the effective activation energy of relaxation. Results are reported for hard sphere colloidal particles dispersed in a solvent of hard sphere particles. Our results show that the concentration of solvent can be used as a control parameter to fine-tune the microscopic structural ordering and the size of CRC that governs the glassy dynamics. We show that a small variation in the concentration of solvent creates a bigger change in the kinetic fragility which highlights a wide variation in behavior, ranging from fragile to strong glasses. We conclude that the CRC which is determined from the static pair correlation function and the fluctuations embedded in the system is probably the sole player in the physics of glass transition.

Collective dynamics in a glass-former with Mari-Kurchan interactions

We numerically study the equilibrium relaxation dynamics of a two-dimensional Mari-Kurchan glass model. The tree-like structure of particle interactions forbids both non-trivial structural motifs and the emergence of a complex free-energy landscape leading to a thermodynamic glass transition, while the finite-dimensional nature of the model prevents the existence of a mode-coupling singularity. Nevertheless, the equilibrium relaxation dynamics is shown to be in excellent agreement with simulations performed in conventional glass-formers. Averaged time-correlation functions display a phenomenology typical of supercooled liquids, including the emergence of an excess signal in relaxation spectra at intermediate frequencies. We show that this evolution is accompanied by strong signatures of collective and heterogeneous dynamics which cannot be interpreted in terms of single particle hopping and emerge from dynamic facilitation. Our study demonstrates that an off-lattice interacting particle model with extremely simple structural correlations displays quantitatively realistic glassy dynamics.

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Single-particle fluctuations dominate the long-time dynamic susceptibility in glass-forming liquids

Liquids near the glass transition exhibit dynamical heterogeneity, i.e., correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by measurements of a dynamic susceptibility χ_{4}(t), which is sometimes interpreted in terms of the size of those relaxing regions and the intensity of the fluctuations. We show that the results of those measurements can be affected not only by the collective fluctuations in the relaxation rate, but also by density fluctuations in the initial state and by single-particle fluctuations. We also show that at very long times the average overlap C(t) probing the similarity between an initial and a final state separated by a time interval t decays as a power law C(t)∼t^{-d/2}. This is much slower than the stretched exponential behavior C(t)∼e^{-(t/τ)^{β}} previously observed at times within one or two orders of magnitude of the α-relaxation time τ_{α}. We find that for times longer than 10-100τ_{α}, the dynamic susceptibility χ_{4}(t) is dominated by single-particle fluctuations, and that χ_{4}(t)≈C(t)∼t^{-d/2}. Finally, we introduce a method to extract the collective relaxation contribution to the dynamic susceptibility χ_{4}(t) by subtracting the effects of single-particle fluctuations and initial state density fluctuations. We apply this method to numerical simulations of two glass-forming models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system. This allows us to extend the analysis of numerical data to timescales much longer than previously possible, and opens the door for further future progress in the study of dynamic heterogeneities, including the determination of the exchange time.

Multiple evidences of dynamic heterogeneity in hydrophobic deep eutectic solvents

Hydrophobic deep eutectic solvents (HDESs) have gained immense popularity because of their promising applications in extraction processes. Herein, we employ atomistic molecular dynamics simulations to unveil the dynamics of DL-menthol (DLM) based HDESs with hexanoic (C6), octanoic (C8), and decanoic (C10) acids as hydrogen bond donors. The particular focus is on understanding the nature of dynamics with changing acid tail length. For all three HDESs, two modes of hydrogen bond relaxations are observed. We observe longer hydrogen bond lifetimes of the inter-molecular hydrogen bonding interactions between the carbonyl oxygen of the acid and hydroxyl oxygen of menthol with hydroxyl hydrogen of both acids and menthol. We infer strong hydrogen bonding between them compared to that between hydroxyl oxygen of acids and hydroxyl hydrogens of menthol and acids, marked by a faster decay rate and shorter hydrogen bond lifetime. The translational dynamics of the species in the HDES becomes slower with increasing tail length of the organic acid. Slightly enhanced caging is also observed for the HDES with a longer tail length of the acids. The evidence of dynamic heterogeneity in the displacements of the component molecules is observed in all the HDESs. From the values of the α-relaxation time scale, we observe that the molecular displacements become random in a shorter time scale for DLM-C6. The analysis of the self-van Hove function reveals that the overall distance covered by DLM and acid molecules in the respective HDES is more than what is expected from ideal diffusion. As marked by the shorter time scale associated with hole filling, the diffusion of the oxygen atom of menthol and the carbonyl oxygen of acid from one site to the other is fastest for hexanoic acid containing HDES.

Water in biodegradable glucose–water–urea deep eutectic solvent: modifications of structure and dynamics in a crowded environment

Molecular dynamics simulations have been performed on a highly viscous (η ∼ 255 cP) naturally abundant deep eutectic solvent (NADES) composed of glucose, urea and water in a weight ratio of 6 : 4 : 1 at 328 K.

Interplay of structural and dynamical heterogeneity in the nucleation mechanism in Ni

Gaining fundamental understanding of crystal nucleation processes in metal alloys is crucial for the development and design of high-performance materials with targeted properties. Yet, crystallizationis a complex non-equilibrium process and,...

Coarse-graining strategy for modeling effective, highly diffusive fluids with reduced polydispersity: A dynamical study

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of application, we chose the bidisperse Lennard-Jones-like mixture, discovered by Kob and Andersen [Phys. Rev. Lett. 73, 1376 (1994)], possessing a slow dynamics due to the fluid's multi-component character with its apparently unconventional choice for the pair potential of the type-A-type-B arrangement. We further established in a so-formed coarse-grained and temperature-independent monodisperse system an equilibrium structure with a radial distribution function resembling its mixture counterpart. This one-component system further possesses similar dynamic features such as glass transition temperature and critical exponents while subjected to Newtonian mechanics. This strategy may finally lead to the manufacturing of new nanoparticle/colloidal fluids by experimentally modeling only the outcoming effective pair potential(s) and no other macroscopic quantity.

Lattice Glass Model in Three Spatial Dimensions

The understanding of thermodynamic glass transition has been hindered by the lack of proper models beyond mean-field theories. Here, we propose a three-dimensional lattice glass model on a simple cubic lattice that exhibits the typical dynamics observed in fragile supercooled liquids such as two-step relaxation, super-Arrhenius growth in the relaxation time, and dynamical heterogeneity. Using advanced Monte Carlo methods, we compute the thermodynamic properties deep inside the glassy temperature regime, well below the onset temperature of the slow dynamics. The specific heat has a finite jump towards the thermodynamic limit with critical exponents close to those expected from the hyperscaling and the random first-order transition theory for the glass transition. We also study an effective free energy of glasses, the Franz-Parisi potential, as a function of the overlap between equilibrium and quenched configurations. The effective free energy indicates the existence of a first-order phase transition, consistent with the random first-order transition theory. These findings strongly suggest that the glassy dynamics of the model has its origin in thermodynamics.

Microscopic pathways for stress relaxation in repulsive colloidal glasses

Residual stresses are well-known companions of all glassy materials. They affect and, in many cases, even strongly modify important material properties like the mechanical response and the optical transparency. The mechanisms through which stresses affect such properties are, in many cases, still under study, and their full understanding can pave the way to a full exploitation of stress as a primary control parameter. It is, for example, known that stresses promote particle mobility at small length scales, e.g., in colloidal glasses, gels, and metallic glasses, but this connection still remains essentially qualitative. Exploiting a preparation protocol that leads to colloidal glasses with an exceptionally directional built-in stress field, we characterize the stress-induced dynamics and show that it can be visualized as a collection of "flickering," mobile regions with linear sizes of the order of ≈20 particle diameters (≈2 μm here) that move cooperatively, displaying an overall stationary but locally ballistic dynamics.

Universal nature of dynamic heterogeneity in glass-forming liquids: A comparative study of metallic and polymeric glass-forming liquids

Glass-formation is a ubiquitous phenomenon that is often observed in a broad class of materials ranging from biological matter to commonly encountered synthetic polymer, as well as metallic and inorganic glass-forming (GF) materials. Despite the many regularities in the dynamical properties of GF materials, the structural origin of the universal dynamical properties of these materials has not yet been identified. Recent simulations of coarse-grained polymeric GF liquids have indicated the coexistence of clusters of mobile and immobile particles that appear to be directly linked, respectively, to the rate of molecular diffusion and structural relaxation. The present work examines the extent to which these distinct types of "dynamic heterogeneity" (DH) arise in metallic GF liquids (Cu-Zr, Ni-Nb, and Pd-Si alloys) having a vastly different molecular structure and chemistry. We first identified mobile and immobile particles and their transient clusters and found the DH in the metallic alloys to be remarkably similar in form to polymeric GF liquids, confirming the "universality" of the DH phenomenon. Furthermore, the lifetime of the mobile particle clusters was found to be directly related to the rate of diffusion in these materials, while the lifetime of immobile particles was found to be proportional to the structural relaxation time, providing some insight into the origin of decoupling in GF liquids. An examination of particles having a locally preferred atomic packing, and clusters of such particles, suggests that there is no one-to-one relation between these populations of particles so that an understanding of the origin of DH in terms of static fluid structure remains elusive.

Dynamic Heterogeneities in Colloidal Supercooled Liquids: Experimental Tests of Inhomogeneous Mode Coupling Theory

The dynamics in supercooled liquids slow enormously upon approaching the glass transition, albeit without significant change of liquid structure. This empirical observation has stimulated development of many theoretical models which attempt to elucidate microscopic mechanisms in glasses and glass precursors. Here, quasi-two-dimensional colloidal supercooled liquids and glasses are employed to experimentally test predictions of widely used models: mode coupling theory (MCT) and its important extension, inhomogeneous MCT (IMCT). We measure two-point dynamic correlation functions in the glass forming liquids to determine structural relaxation times, τ_α, and mode coupling exponents, a, b, and γ; these parameters are then used to extract the mode coupling dynamic crossover packing area-fraction, ϕ _c. This information, along with our measurements of supercooled liquid spatiotemporal dynamics, permits characterization of dynamic heterogeneities in the samples and facilitates direct experimental tests of the scaling predictions of IMCT. The time scales at which dynamic heterogeneities are largest, and their spatial sizes, exhibit power law growth on approaching ϕ _c. Within experimental error, the exponents of the measured power laws are close to the predictions of IMCT.

Spurious violation of the Stokes-Einstein-Debye relation in supercooled water

The theories of Brownian motion, the Debye rotational diffusion model, and hydrodynamics together provide us with the Stokes–Einstein–Debye (SED) relation between the rotational relaxation time of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\ell }}$$\end{document}ℓ-th degree Legendre polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ, and viscosity divided by temperature, η/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓk_BT/η and D_t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ, where D_t is the translational diffusion constant. However, the SED relations break down, and its molecular origin remains elusive. Here, we assess the validity of the SED relations in TIP4P/2005 supercooled water using molecular dynamics simulations. Specifically, we demonstrate that the higher-order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ values exhibit a temperature dependence similar to that of η/T, whereas the lowest-order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ values are decoupled with η/T, but are coupled with the translational diffusion constant D_t. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.

Random close packing from hard-sphere Percus-Yevick theory

The Percus-Yevick theory for monodisperse hard spheres gives very good results for the pressure and structure factor of the system in a whole range of densities that lie within the liquid phase. However, the equation seems to lead to a very unacceptable result beyond that region. Namely, the Percus-Yevick theory predicts a smooth behavior of the pressure that diverges only when the volume fraction η approaches unity. Thus, within the theory there seems to be no indication for the termination of the liquid phase and the transition to a solid or to a glass. In the present article we study the Percus-Yevick hard-sphere pair distribution function, g_{2}(r), for various spatial dimensions. We find that beyond a certain critical volume fraction η_{c}, the pair distribution function, g_{2}(r), which should be positive definite, becomes negative at some distances. We also present an intriguing observation that the critical η_{c} values we find are consistent with volume fractions where onsets of random close packing (or maximally random jammed states) are reported in the literature for various dimensions. That observation is supported by an intuitive argument. This work may have important implications for other systems for which a Percus-Yevick theory exists.

Microstructure and Soft Glassy Dynamics of an Aqueous Laponite Dispersion

Synthetic hectorite clay Laponite RD/XLG is composed of disk-shaped nanoparticles that acquire dissimilar charges when suspended in an aqueous medium. Owing to their property to spontaneously self-assemble, Laponite is used as a rheology modifier in a variety of commercial water-based products. In particular, an aqueous dispersion of Laponite undergoes a liquid-to-solid transition at about 1 vol % concentration. The evolution of the physical properties as the dispersion transforms to the solid state is reminiscent of physical aging in molecular as well as colloidal glasses. The corresponding soft glassy dynamics of an aqueous Laponite dispersion, including the rheological behavior, has been extensively studied in the literature. In this feature article, we take an overview of recent advances in understanding soft glassy dynamics and various efforts taken to understand the peculiar rheological behavior. Furthermore, the continuously developing microstructure that is responsible for the eventual formation of a soft solid state that supports its own weight against gravity has also been a topic of intense debate and discussion. In particularly, extensive experimental and theoretical studies lead to two types of microstructures for this system: an attractive gel-like or a repulsive glass-like structure. We carefully examine and critically analyze the literature and propose a state (phase) diagram that suggests an aqueous Laponite dispersion to be present in an attractive gel state.

Non-Gaussianity of the van Hove function and dynamic-heterogeneity length scale

Non-Gaussian nature of the probability distribution of particles' displacements in the supercooled temperature regime in glass-forming liquids are believed to be one of the major hallmarks of glass transition. It has already been established that this probability distribution, which is also known as the van Hove function, shows universal exponential tail. The origin of such an exponential tail in the distribution function is attributed to the hopping motion of particles observed in the supercooled regime. The non-Gaussian nature can also be explained if one assumes that the system has heterogeneous dynamics in space and time. Thus exponential tail is the manifestation of dynamic heterogeneity. In this work we directly show that non-Gaussianity of the distribution of particles' displacements occur over the dynamic heterogeneity length scale and the dynamical behavior course grained over this length scale becomes homogeneous. We study the non-Gaussianity of the van Hove function by systematically coarse graining at different length scales and extract the length scale of dynamic heterogeneity at which the shape of the van Hove function crosses over from non-Gaussian to Gaussian. The obtained dynamic heterogeneity scale is found to be in very good agreement with the scale obtained from other conventional methods.

Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overtaking, correlated motion with a diffusively growing length scale is observed. By allowing the particles to overtake each other, the short-range correlation is destroyed, but the long-range weak correlation remains almost intact. These results describe nested space–time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes.

Spatiotemporal intermittency and localized dynamic fluctuations upon approaching the glass transition

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

Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy

Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of crystals from the liquid. Here, we report direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution. An experimental four-point space-time correlation function demonstrates a growing dynamic correlation length, ξ, upon cooling of the liquid toward the glass transition temperature. ξ as a function of the relaxation time τ are in good agreement with Adam-Gibbs theory, inhomogeneous mode-coupling theory and random first-order transition theory of the glass transition. The same experiments demonstrate the existence of a nanometer thickness near-surface layer with order of magnitude shorter relaxation time than inside the bulk.

Study of dynamical heterogeneities in colloidal nanoclay suspensions approaching dynamical arrest

The dynamics of aqueous Laponite clay suspensions slow down with increasing sample waiting time (t w ). This behavior, and the material fragility that results, closely resemble the dynamical slowdown in fragile supercooled liquids with decreasing temperature, and are typically ascribed to the increasing sizes of distinct dynamical heterogeneities in the sample. In this article, we characterize the dynamical heterogeneities in Laponite suspensions by invoking the three-point dynamic susceptibility formalism. The average time-dependent two-point intensity autocorrelation and its sensitivity to t w are probed in dynamic light scattering experiments. Distributions of relaxation time scales, deduced from the Kohlrausch-Williams-Watts equation, are seen to widen with increasing t w . The calculated three-point dynamic susceptibility of Laponite suspensions exhibits a peak, with the peak height increasing with evolving t w at fixed volume fraction or with increasing volume fraction at fixed t w , thereby signifying the slowdown of the sample dynamics. The number of dynamically correlated particles, calculated from the peak-height, is seen to initially increase rapidly with increasing t w , before eventually slowing down close to the non-ergodic transition point. This observation is in agreement with published reports on supercooled liquids and hard sphere colloidal suspensions and offers a unique insight into the colloidal glass transition of Laponite suspensions.

Identifying time scales for violation/preservation of Stokes-Einstein relation in supercooled water

The violation of the Stokes-Einstein (SE) relation D ~ (η/T)^-1 between the shear viscosity η and the translational diffusion constant D at temperature T is of great importance for characterizing anomalous dynamics of supercooled water. Determining which time scales play key roles in the SE violation remains elusive without the measurement of η. We provide comprehensive simulation results of the dynamic properties involving η and D in the TIP4P/2005 supercooled water. This enabled the thorough identification of the appropriate time scales for the SE relation Dη/T. In particular, it is demonstrated that the temperature dependence of various time scales associated with structural relaxation, hydrogen bond breakage, stress relaxation, and dynamic heterogeneities can be definitely classified into only two classes. That is, we propose the generalized SE relations that exhibit "violation" or "preservation." The classification depends on the examined time scales that are coupled or decoupled with the diffusion. On the basis of the classification, we explain the physical origins of the violation in terms of the increase in the plateau modulus and the nonexponentiality of stress relaxation. This implies that the mechanism of SE violation is attributed to the attained solidity upon supercooling, which is in accord with the growth of non-Gaussianity and spatially heterogeneous dynamics.

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.

Evidence for Anomalous Dynamic Heterogeneities in Isostatic Supercooled Liquids

Upon cooling, the dynamics of supercooled liquids exhibits a growing transient spatial distribution of relaxation times that is known as dynamic heterogeneities. The relationship between this now well-established crucial feature of the glass transition and some underlying liquid properties remains challenging and elusive in many respects. Here we report on computer simulations of liquids with a changing network structure (densified silicates), and show that there is a deep and important link between the mechanical nature characterized by topological constraints and the spatial extent of such fluctuations. This is not only revealed by a maximum in the dynamic correlation length ξ_{4} for fluctuations when the liquid becomes isostatically rigid, but also by a contraction of the volume of relaxing structural correlations upon the onset of stressed rigidity.

Interplay between the static ordering and dynamical heterogeneities determining the dynamics of rotation and ordinary liquid phases in 1,6-anhydro-β-D-glucose

In this letter, we reported thorough the structural and molecular dynamics studies on 1,6-anhydro-β-D-glucose, the second compound reported so far that is capable to form rotator and supercooled liquid phases. In contrast to the data presented for ethanol, temperature dependences of structural dynamics in both phases are very comparable. On the other hand, X ray measurements revealed unusually long range ordering/correlations between molecules in the ODIC (d ≈ 95 Å) and supercooled phases (d ≈ 30-40 Å) of this carbohydrate. Our consideration clearly demonstrated that the interplay between length scales of static range ordering and dynamical heterogeneities as well as internal molecular arrangement seem to be the key to understanding the molecular dynamics of different materials characterized by varying degree of disorder in the vicinity of the glass transition temperature.

How Heterogeneous Are Trehalose/Glycerol Cryoprotectant Mixtures? A Combined Time-Resolved Fluorescence and Computer Simulation Investigation

Heterogeneity and molecular motions in representative cryoprotectant mixtures made of trehalose and glycerol are investigated in the temperature range 298 ≤ T (K) ≤ 353, via time-resolved fluorescence Stokes shift and anisotropy measurements, and molecular dynamics simulations of four-point density-time correlations and H-bond relaxations. Mixtures containing 5 and 20 wt % of trehalose along with neat glycerol are studied. Viscosity coefficients for these systems lie in the range 0.30 < η (P) < 23. Measured solute (Coumarin 153) rotation and solvation times reveal a substantial departure from the hydrodynamic viscosity dependence, suggesting the strong microheterogeneous nature of these systems. Fluorescence anisotropy decays are highly nonexponential, reflecting a non-Markovian character of the medium friction. A complete missing of the Stokes shift dynamics in these systems at 298 K but partial detection of it at other higher temperatures (shift magnitude being ∼400-600 cm^-1) indicates rigid solute environments. An amorphous solid-like feature emerges in the simulated radial distribution functions at these temperatures. Analyses of mean squared displacements reveal rattling-in-a-cage motion, non-Gaussian displacement distributions, and strong dynamic heterogeneity features. Simulated dynamic structure factors and four-point correlations hint, respectively, at very long α-relaxation and correlated time scales at 298 K. This explains the long solute rotation times (∼80-200 ns) measured at 298 K. Stretched exponential decay of the simulated H-bond relaxations with long time scales further highlights the strong temporal heterogeneity and slow dynamics inherent to these systems. In summary, this work provides the first insight into the molecular motions and interspecies interaction in a representative cryoprotectant mixture, and stimulates further study to investigate the interconnection between cryoprotection and dynamic heterogeneity.