Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation

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.

Unified Understanding of Nonlinear Rheology near the Jamming Transition Point

When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening or melting emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of athermal frictionless soft particles under quasistatic shear γ. We find the universal scaling behavior for the ratio of the shear stress σ and the pressure P, independent of the preparation protocol of the initial configurations. In particular, we reveal shear softening σ/P∼γ^{1/2} over an unprecedentedly wide range of strain up to the yielding point, which a simple scaling argument can rationalize.

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.

The distinguishable-particle lattice model of glasses in three dimensions

The nature of glassy states in realistic finite dimensions is still under fierce debate. Lattice models can offer valuable insights and facilitate deeper theoretical understanding. Recently, a disordered-interacting lattice model with distinguishable particles in two dimensions (2D) has been shown to produce a wide range of dynamical properties of structural glasses, including the slow and heterogeneous characteristics of the glassy dynamics, various fragility behaviors of glasses, and so on. These findings support the usefulness of this model for modeling structural glasses. An important question is whether such properties still hold in the more realistic three dimensions. In this study, we aim to extend the distinguishable-particle lattice model (DPLM) to three dimensions (3D) and explore the corresponding glassy dynamics. Through extensive kinetic Monte Carlo simulations, we found that the 3D DPLM exhibits many typical glassy behaviors, such as plateaus in the mean square displacement of particles and the self-intermediate scattering function, dynamic heterogeneity, variability of glass fragilities, and so on, validating the effectiveness of the DPLM in a broader realistic setting. The observed glassy behaviors of the 3D DPLM appear similar to those of its 2D counterpart, in accordance with recent findings in molecular models of glasses. We further investigate the role of void-induced motions in dynamical relaxations and discuss their relation to dynamic facilitation. As lattice models tend to keep the minimal but important modeling elements, they are typically much more amenable to analysis. Therefore, we envisage that the DPLM will benefit future theoretical developments, such as the configuration tree theory, towards a more comprehensive understanding of structural glasses.

Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain

Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.

Emerging exotic compositional order on approaching low-temperature equilibrium glasses

The ultimate fate of a glass former upon cooling has been a fundamental problem in condensed matter physics and materials science since Kauzmann. Recently, this problem has been challenged by a model with an extraordinary glass-forming ability effectively free from crystallisation and phase separation, two well-known fates of most glass formers, combined with a particle-size swap method. Thus, this system is expected to approach the ideal glass state if it exists. However, we discover exotic compositional order as the coexistence of space-spanning network-like structures formed by small-large particle connections and patches formed by medium-size particles at low temperatures. Therefore, the glass transition is accompanied unexpectedly by exotic compositional ordering inaccessible through ordinary structural or thermodynamic characterisations. Such exotic compositional ordering is found to have an unusual impact on structural relaxation dynamics. Our study thus raises fundamental questions concerning the role of unconventional structural ordering in understanding glass transition.

Dynamic Gardner cross-over in a simple glass

The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.

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.

Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a "universal" evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

Surface premelting and melting of colloidal glasses

The nature of liquid-to-glass transition is a major puzzle in science. A similar challenge exists in glass-to-liquid transition, i.e., glass melting, especially for the poorly investigated surface effects. Here, we assemble colloidal glasses by vapor deposition and melt them by tuning particle attractions. The structural and dynamic parameters saturate at different depths, which define a surface liquid layer and an intermediate glassy layer. The power-law growth of both layers and melting front behaviors at different heating rates are similar to crystal premelting and melting, suggesting that premelting and melting can be generalized to amorphous solids. The measured single-particle kinetics reveal various features and confirm theoretical predictions for glass surface layer.

BOTAN: BOnd TArgeting Network for prediction of slow glassy dynamics by machine learning relative motion

Recent developments in machine learning have enabled accurate predictions of the dynamics of slow structural relaxation in glass-forming systems. However, existing machine learning models for these tasks are mostly designed such that they learn a single dynamic quantity and relate it to the structural features of glassy liquids. In this study, we propose a graph neural network model, "BOnd TArgeting Network," that learns relative motion between neighboring pairs of particles, in addition to the self-motion of particles. By relating the structural features to these two different dynamical variables, the model autonomously acquires the ability to discern how the self motion of particles undergoing slow relaxation is affected by different dynamical processes, strain fluctuations and particle rearrangements, and thus can predict with high precision how slow structural relaxation develops in space and time.

Long-Wavelength Fluctuations in Quasi-2D Supercooled Liquids

We use molecular simulation to characterize the dynamics of supercooled liquids confined in quasi-2D slit geometries. Similar to bulk supercooled liquids, the confined systems exhibit subdiffusive dynamics on intermediate time scales arising from particle localization inside their neighbor cages, followed by an eventual crossover to diffusive behavior as cage rearrangement occurs. The quasi-2D confined liquids also exhibit signatures of long-wavelength fluctuations (LWFs) in the lateral directions parallel to the confining walls, reminiscent of the collective displacements observed in 2D but not 3D systems. The magnitude of the LWFs increases with the lateral dimensions of systems with the same particle volume fraction and confinement length scale, consistent with the logarithmic scaling predicted for 2D Mermin-Wagner fluctuations. The amplitude of the fluctuations is a nonmonotonic function of the confinement length scale because of a competition between caging and strengthening LWFs upon approaching the 2D limit. Our findings suggest that LWFs may play an important role in understanding the behavior of confined supercooled liquids due to their prevalence over a surprisingly broad range of particle densities and confinement length scales.

Relevance of Shear Transformations in the Relaxation of Supercooled Liquids

While deeply supercooled liquids exhibit divergent viscosity and increasingly heterogeneous dynamics as the temperature drops, their structure shows only seemingly marginal changes. Understanding the nature of relaxation processes in this dramatic slowdown is key for understanding the glass transition. Here, we show by atomistic simulations that the heterogeneous dynamics of glass-forming liquids strongly correlate with the local residual plastic strengths along soft directions computed in the initial inherent structures. The correlation increases with decreasing temperature and is maximum in the vicinity of the relaxation time. For the lowest temperature investigated, this maximum is comparable with the best values from the literature dealing with the structure-property relationship. However, the nonlinear probe of the local shear resistance in soft directions provides here a real-space picture of relaxation processes. Our detection method of thermal rearrangements allows us to investigate the first passage time statistics and to study the scaling between the activation energy barriers and the residual plastic strengths. These results shed new light on the nature of relaxations of glassy systems by emphasizing the analogy between the thermal relaxations in viscous liquids and the plastic shear transformation in amorphous solids.

Evidence for growing structural correlation length in colloidal supercooled liquids

Using video microscopy, we measure the long-time diffusion coefficients of colloidal particles at different concentrations. The measured diffusion coefficients start to deviate from theoretical predictions based on random collision models upon entering the supercooled regime. The theoretical diffusion relation is recovered by assigning an effective mass proportional to the size of structurally correlated clusters to the diffusing particles, providing an indirect method to probe the growth of static correlation length scales approaching the glass transition. This method is tested and validated in the crystallization of mono-disperse colloids in quasi-two-dimensional experiments. The correlation length obtained for a binary colloidal liquid increases by a power law toward a critical packing fraction of ∼0.79. The system relaxation time exhibits a power-law dependence on the correlation length in agreement with dynamical facilitation theories.

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.

Disordered Collective Motion in Dense Assemblies of Persistent Particles

We explore the emergence of nonequilibrium collective motion in disordered nonthermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompanied by collective motion, whose nature evolves from near-equilibrium spatially heterogeneous dynamics at small persistence, to a qualitatively different intermittent dynamics when persistence is large. This latter regime involves a complex time evolution of the correlated displacement field.

Local Plastic Response and Slow Heterogeneous Dynamics of Supercooled Liquids

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

Are strongly confined colloids good models for two dimensional liquids?

Quasi-two-dimensional (quasi-2D) colloidal hard-sphere suspensions confined in a slit geometry are widely used as two-dimensional (2D) model systems in experiments that probe the glassy relaxation dynamics of 2D systems. However, the question to what extent these quasi-2D systems indeed represent 2D systems is rarely brought up. Here, we use computer simulations that take into account hydrodynamic interactions to show that dense quasi-2D colloidal bi-disperse hard-sphere suspensions exhibit much more rapid diffusion and relaxation than their 2D counterparts at the same area fraction. This difference is induced by the additional vertical space in the quasi-2D samples in which the small colloids can move out of the 2D plane, therefore allowing overlap between particles in the projected trajectories. Surprisingly, this difference in the dynamics can be accounted for if, instead of using the surface density, one characterizes the systems by means of a suitable structural quantity related to the radial distribution function. This implies that in the two geometries, the relevant physics for glass formation is essentially identical. Our results provide not only practical implications on 2D colloidal experiments but also interesting insights into the 3D-to-2D crossover in glass-forming systems.

Aging or DEAD: Origin of the non-monotonic response to weak self-propulsion in active glasses

Among amorphous states, glass is defined by relaxation times longer than the observation time. This nonergodic nature makes the understanding of glassy systems an involved topic, with complex aging effects or responses to further out-of-equilibrium external drivings. In this respect, active glasses made of self-propelled particles have recently emerged as a stimulating systems, which broadens and challenges our current understanding of glasses by considering novel internal out-of-equilibrium degrees of freedom. In previous experimental studies we have shown that in the ergodicity broken phase, the dynamics of dense passive particles first slows down as particles are made slightly active, before speeding up at larger activity. Here, we show that this nonmonotonic behavior also emerges in simulations of soft active Brownian particles and explore its cause. We refute that the deadlock by emergence of active directionality model we proposed earlier describes our data. However, we demonstrate that the nonmonotonic response is due to activity enhanced aging and thus confirm the link with ergodicity breaking. Beyond self-propelled systems, our results suggest that aging in active glasses is not fully understood.

Multiscale heterogeneous dynamics in two-dimensional glassy colloids

On approaching the glass transition, a dense colloid exhibits a dramatic slowdown with minute structural changes. Most microscopy experiments directly follow the motion of individual particles in real space, whereas scattering experiments typically probe the collective dynamics in reciprocal space, at variable wavevector q. Multiscale studies of glassy dynamics are experimentally demanding and thus seldom performed. By using two-dimensional hard-sphere colloids at various area fractions φ, we show here that Differential Dynamic Microscopy (DDM) can be effectively used to measure the collective dynamics of a glassy colloid in a range of q within a single experiment. As φ is increased, the single decay of the intermediate scattering functions is progressively replaced by a more complex relaxation that we fit to a sum of two stretched-exponential decays. The slowest process, corresponding to the long-time particle escapes from caging, has a characteristic time τs = 1/(DLq2 ) with diffusion coefficient DL ∼ (φc −φ)2.8 , and φc ≈ 0.81. The fast process exhibits, instead, a non-Brownian scaling of the characteristic time τf(q) and a relative amplitude a(q) that monotonically increases with q. Despite the non-Brownian nature of τf(q), we succeed in estimating the short-time diffusion coefficient Dcage, whose φ-dependence is practically negligible compared to the one of DL. Finally, we extend DDM to measure the q-dependent dynamical susceptibility χ4(q,t), a powerful yet hard-to-access multiscale indicator of dynamical heterogeneities. Our results show that DDM is a convenient tool to study the dynamics of colloidal glasses over a broad range of time and length-scales.

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

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

Tracer dynamics in crowded active-particle suspensions

We discuss the dynamics of active Brownian particles (ABPs) in crowded environments through the mean-squared displacement (MSD) of active and passive tracer particles in both active and passive host systems. Exact equations for the MSD are derived using a projection operator technique, extending to dense systems the known solution for a single ABP. The interaction of the tracer particle with the host particles gives rise to strong memory effects. Evaluating these approximately in the framework of a recently developed mode-coupling theory for active Brownian particles (ABP-MCT), we discuss the various dynamical regimes that emerge: While self-propelled motion gives rise to super-diffusive MSD, at high densities, this competes with an interaction-induced sub-diffusive regime. The predictions of the theory are shown to be in good agreement with results obtained from an event-driven Brownian dynamics (ED-BD) simulation scheme for the dynamics of two-dimensional active Brownian hard disks.

Mode-coupling theory for tagged-particle motion of active Brownian particles

We derive a mode-coupling theory (MCT) to describe the dynamics of a tracer particle that is embedded in a dense system of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian motion and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density-correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a single active particle in a glass-forming passive host suspensions, that of a passive colloidal particle in a suspension of ABP, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We confirm in the simulations a peculiar feature of the transient and stationary dynamical density-correlation functions regarding their lack of symmetry under time reversal, demonstrating the nonequilibrium nature of the system and how it manifests itself in the theory.

Breakdown of the Stokes-Einstein relation in supercooled liquids: A cage-jump perspective

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio τ_ατ_D between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that τ_ατ_D∝⟨t_p⟩⟨t_c⟩, where ⟨t_p⟩ and ⟨t_c⟩ are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations τ_α∝⟨t_p⟩⟨Δr_J ²⟩ and τ_D∝⟨t_c⟩⟨Δr_J ²⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨Δr_J ²⟩ shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.

Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses

Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak (BP). For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige,et al2019,Sci. Rep.919514], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the BP scales only with that of the global shear modulus. This observation suggests that the spatial heterogeneity of the local shear modulus distribution is insensitive to changes in the bending rigidity. Here, we demonstrate the insensitivity of elastic heterogeneity by directly measuring the local shear modulus distribution. We also study transverse sound wave propagation, which is also shown to scale only with the global shear modulus. Through these analyses, we conclude that the bending rigidity does not alter the spatial heterogeneity of the local shear modulus distribution, which yields vibrational and acoustic properties that are controlled solely by the global shear modulus of a polymer glass.

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

Active microrheology of a bulk metallic glass

The glass transition remains unclarified in condensed matter physics. Investigating the mechanical properties of glass is challenging because any global deformation that might result in shear rejuvenation would require a prohibitively long relaxation time. Moreover, glass is well known to be heterogeneous, and a global perturbation would prevent exploration of local mechanical/transport properties. However, investigation based on a local probe, i.e., microrheology, may overcome these problems. Here, we establish active microrheology of a bulk metallic glass, via a probe particle driven into host medium glass. This technique is amenable to experimental investigations via nanoindentation tests. We provide distinct evidence of a strong relationship between the microscopic dynamics of the probe particle and the macroscopic properties of the host medium glass. These findings establish active microrheology as a promising technique for investigating the local properties of bulk metallic glass.

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

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

Power laws in pressure-induced structural change of glasses

Many glasses exhibit fractional power law (FPL) between the mean atomic volume v_a and the first diffraction peak position q₁, i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{\mathrm{a}} \propto q_1^{ - d}$$\end{document}va∝q1−d with d ≃ 2.5 deviating from the space dimension D = 3, under compression or composition change. What structural change causes such FPL and whether the FPL and d are universal remain controversial. Here our simulations show that the FPL holds in both two- and three-dimensional glasses under compression when the particle interaction has two length scales which can induce nonuniform local deformations. The exponent d is not universal, but varies linearly with the deformable part of soft particles. In particular, we reveal an unexpected crossover regime with d > D from crystal behavior (d = D) to glass behavior (d < D). The results are explained by two types of bond deformation. We further discover FPLs in real space from the radial distribution functions, which correspond to the FPLs in reciprocal space.

A puzzle in metallic glass research is the existence of the fractional power law in reciprocal space, whilst its origin remains controversial. Zhang et al. show that nonuniform local deformations under compression induce this phenomenon and quantify the power law exponent at both two and three dimensions.

Metallic glass-formers in 2D exhibit the same scaling as in 3D between vibrational dynamics and structural relaxation

Glass-forming systems approaching their glass transition exhibit universal correlations between picosecond vibrational dynamics and long-time structural relaxation, which can be described by the same master curve in the bulk or confined conditions. In this work, we study at a fundamental level the effects of the reduction of spatial dimensionality on this phenomenon. We perform molecular dynamics simulations of a metallic glass-formers in two dimensions (2D). We show that in the supercooled regime particle localization in the cage and structural relaxation are blurred by long-wavelength fluctuations specific to low-dimensional systems. Once these effects are properly removed, we demonstrate that the fast dynamics and slow relaxation comply, without any adjustment, with same scaling between the structural relaxation time and the Debye-Waller factor, originally observed in three-dimensions (3D).

Local Density Fluctuation Governs the Divergence of Viscosity Underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid

If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a logarithmically diverging diffusivity in the long-time limit.

Boson peak, elasticity, and glass transition temperature in polymer glasses: Effects of the rigidity of chain bending

The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decrease of the density and the increase of the rigidity, show a non-monotonic dependence on the rigidity of the polymer chain that arises from the non-affine component. Moreover, a clear boson peak is observed in the vibrational density of states, which depends on the macroscopic shear modulus G. In particular, the boson peak frequency ω_BP is proportional to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{G}$$\end{document}G. These results provide a positive correlation between the boson peak, shear elasticity, and the glass transition temperature.

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

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

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

Long-wavelength fluctuations and anomalous dynamics in 2-dimensional liquids

In 2-dimensional systems at finite temperature, long-wavelength Mermin-Wagner fluctuations prevent the existence of translational long-range order. Their dynamical signature, which is the divergence of the vibrational amplitude with the system size, also affects disordered solids, and it washes out the transient solid-like response generally exhibited by liquids cooled below their melting temperatures. Through a combined numerical and experimental investigation, here we show that long-wavelength fluctuations are also relevant at high temperature, where the liquid dynamics do not reveal a transient solid-like response. In this regime, these fluctuations induce an unusual but ubiquitous decoupling between long-time diffusion coefficient D and structural relaxation time τ, where [Formula: see text], with [Formula: see text] Long-wavelength fluctuations have a negligible influence on the relaxation dynamics only at extremely high temperatures in molecular liquids or at extremely low densities in colloidal systems.

Emergence and percolation of rigid domains during the colloidal glass transition

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

Revealing Inherent Structural Characteristics of Jammed Particulate Packings

We look for inherent structural characteristics hidden behind amorphous solid formation by using zero-temperature jammed packings of frictionless particles as models. Differently from previous geometrical approaches, we introduce a microscopic mechanical or vibrational order parameter Ψ, which characterizes the susceptibility of particle motion to infinitesimal thermal excitation. We show that (i) the distribution of Ψ has a power-law tail toward high Ψ and (ii) the spatial organization of Ψ is characterized by a nontrivial scale-free correlation. Both findings (i) and (ii) are regarded as a real-space manifestation of marginal stability due to critical self-organization of jammed packings toward mechanical equilibrium. Furthermore, we find that the power-law exponent of the Ψ distribution tail shows a critical-like scaling behavior toward the unjamming transition, which unveils an intriguing interplay between jamming criticality and marginal stability. Our microscopic order parameter provides new structural insights into the marginal stability and instability of jammed packings and may shed light on the important common structural feature of amorphous solids.

Long-wavelength fluctuations and static correlations in quasi-2D colloidal suspensions

Dimensionality strongly affects thermal fluctuations and critical dynamics of equilibrium systems. These influences persist in amorphous systems going through the nonequilibrium glass transition. Here, we experimentally study the glass transition of quasi-2D suspensions of spherical and ellipsoidal particles under different degrees of circular confinement. We show that the strength of the long-wavelength fluctuations increases logarithmically with system sizes and displays the signature of the Mermin-Wagner fluctuations. Moreover, using confinement as a tool, we also measure static structural correlations and extract a growing static correlation length in 2D supercooled liquids. Finally, we explore the influence of the Mermin-Wagner fluctuations on the translational and orientational relaxations of 2D ellipsoidal suspensions, which leads to a new interpretation of the two-step glass transition and the orientational glass phase of anisotropic particles. Our study reveals the importance of long-wavelength fluctuations in 2D supercooled liquids and provides new insights into the role of dimensionality in the glass transition.

Zero-temperature glass transition in two dimensions

Liquids cooled towards the glass transition temperature transform into amorphous solids that have a wide range of applications. While the nature of this transformation is understood rigorously in the mean-field limit of infinite spatial dimensions, the problem remains wide open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we develop Monte Carlo methods for two-dimensional glass-forming liquids that allow us to access equilibrium states at sufficiently low temperatures to directly probe the glass transition in a regime inaccessible to experiments. We find that the liquid state terminates at a thermodynamic glass transition which occurs at zero temperature and is associated with an entropy crisis and a diverging static correlation length. Our results thus demonstrate that a thermodynamic glass transition can occur in finite dimensional glass-formers.

The thermal jamming transition of soft harmonic disks in two dimensions

By exploring the properties of the energy landscape of a bidisperse system of soft harmonic disks in two dimensions we determine the thermal jamming transition. To be specific, we study whether the ground state of the system where the particles do not overlap can be reached within a reasonable time. Starting with random initial configurations, the energy landscape is probed by energy minimization steps as in case of athermal jamming and in addition steps where an energy barrier can be crossed with a small but non-zero probability. For random initial conditions we find that as a function of packing fraction the thermal jamming transition, i.e. the transition from a state where all overlaps can be removed to an effectively non-ergodic state where one cannot get rid of the overlaps, occurs at a packing fraction of [Formula: see text], which is smaller than the transition packing fraction of athermal jamming at [Formula: see text]. Furthermore, we show that the thermal jamming transition is in the universality class of directed percolation and therefore is fundamentally different from the athermal jamming transition.

Viscoelastic shear stress relaxation in two-dimensional glass-forming liquids

Translational dynamics of 2D glass-forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean-squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation, and well-developed plateaus are observed in orientational correlation functions. It has been suggested that, by monitoring translational motion of particles relative to that of their neighbors, one can recover characteristic features of glassy dynamics and thus disentangle the Mermin-Wagner fluctuations from the 2D glass transition. Here we use molecular dynamics simulations to study viscoelastic relaxation in two and three dimensions. We find different behavior of the dynamic modulus below the onset of slow dynamics (determined by the orientational or cage-relative correlation functions) in two and three dimensions. The dynamic modulus for 2D supercooled fluids is more stretched than for 3D supercooled fluids and does not exhibit a plateau, which implies the absence of glassy viscoelastic relaxation. At lower temperatures, the 2D dynamic modulus starts exhibiting an intermediate time plateau and decays similarly to the 2D dynamic modulus. The differences in the glassy behavior of 2D and 3D glass-forming fluids parallel differences in the ordering scenarios in two and three dimensions.

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.

Glassy dynamics of dense particle assemblies on a spherical substrate

We study by molecular dynamics simulation a dense one-component system of particles confined on a spherical substrate. We more specifically investigate the evolution of the structural and dynamical properties of the system when changing the control parameters, the temperature and the curvature of the substrate. We find that the dynamics become glassy at low temperature, with a strong slowdown of the relaxation and the emergence of dynamical heterogeneity. The prevalent local 6-fold order is frustrated by curvature and we analyze in detail the role of the topological defects in the statics and the dynamics of the particle assembly.

Isolating long-wavelength fluctuation from structural relaxation in two-dimensional glass: cage-relative displacement

It has recently been revealed that long-wavelength fluctuation exists in two-dimensional (2D) glassy systems, having the same origin as that given by the Mermin-Wagner theorem for 2D crystalline solids. In this paper, we discuss how to characterise quantitatively the long-wavelength fluctuation in a molecular dynamics simulation of a lightly supercooled liquid. We employ the cage-relative mean-square displacement (MSD), defined on relative displacement to its cage, to quantitatively separate the long-wavelength fluctuation from the original MSD. For increasing system size the amplitude of acoustic long wavelength fluctuations not only increases but shifts to later times causing a crossover with structural relaxation of caging particles. We further analyse the dynamic correlation length using the cage-relative quantities. It grows as the structural relaxation becomes slower with decreasing temperature, uncovering an overestimation by the four-point correlation function due to the long-wavelength fluctuation. These findings motivate the usage of cage-relative MSD as a starting point for analysis of 2D glassy dynamics.

Anomalous vibrational properties in the continuum limit of glasses

The low-temperature thermal properties of glasses are anomalous with respect to those of crystals. These thermal anomalies indicate that the low-frequency vibrational properties of glasses differ from those of crystals. Recent studies revealed that, in the simplest model of glasses, i.e., the harmonic potential system, phonon modes coexist with soft localized modes in the low-frequency (continuum) limit. However, the nature of low-frequency vibrational modes of more realistic models is still controversial. In the present work, we study the Lennard-Jones (LJ) system using large-scale molecular-dynamics (MD) simulation and establish that the vibrational property of the LJ glass converges to coexistence of the phonon modes and the soft localized modes in the continuum limit as in the case of the harmonic potential system. Importantly, we find that the low-frequency vibrations are rather sensitive to the numerical scheme of potential truncation, which is usually implemented in the MD simulation, and this is the reason why contradictory arguments have been reported by previous works. We also discuss the physical origin of this sensitiveness by means of a linear stability analysis.

Elastic moduli of a Brownian colloidal glass former

The static, dynamic and flow-dependent shear moduli of a binary mixture of Brownian hard disks are studied by an event-driven molecular dynamics simulation. Thereby, the emergence of rigidity close to the glass transition encoded in the static shear modulus [Formula: see text] is accessed by three methods. Results from shear stress auto-correlation functions, elastic dispersion relations, and the elastic response to strain deformations upon the start-up of shear flow are compared. This enables one to sample the time-dependent shear modulus [Formula: see text] consistently over several decades in time. By that a very precise specification of the glass transition point and of [Formula: see text] is feasible. Predictions by mode coupling theory of a finite shear modulus at the glass transition, of α-scaling in fluid states close to the transition, and of shear induced decay in yielding glass states are tested and broadly verified.

Translationally invariant colloidal crystal templates

We show that dynamic, feed-back controlled optical traps, whose positions depend on the instantaneous local configuration of particles in a pre-determined way, can stabilise colloidal particles in finite lattices of any given symmetry. Unlike in a static template, the crystal so formed is invariant under uniform translations and retains all possible zero energy modes. We demonstrate this in silico by stabilising the unstable two-dimensional square lattice in a model soft solid with isotropic interactions.

Continuum limit of the vibrational properties of amorphous solids

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.