Structural evolution in the aging process of supercooled colloidal liquids

Structural Origin of Dynamic Heterogeneity in Supercooled Liquids

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

Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of machine learning

A computational approach by an implementation of the principle component analysis (PCA) withK-means and Gaussian mixture (GM) clustering methods from machine learning algorithms to identify structural and dynamical heterogeneities of supercooled liquids is developed. In this method, a collection of the average weighted coordination numbers (WCNs‾) of particles calculated from particles' positions are used as an order parameter to build a low-dimensional representation of feature (structural) space forK-means clustering to sort the particles in the system into few meso-states using PCA. Nano-domains or aggregated clusters are also formed in configurational (real) space from a direct mapping using associated meso-states' particle identities with some misclassified interfacial particles. These classification uncertainties can be improved by a co-learning strategy which utilizes the probabilistic GM clustering and the information transfer between the structural space and configurational space iteratively until convergence. A final classification of meso-states in structural space and domains in configurational space are stable over long times and measured to have dynamical heterogeneities. Armed with such a classification protocol, various studies over the thermodynamic and dynamical properties of these domains indicate that the observed heterogeneity is the result of liquid-liquid phase separation after quenching to a supercooled state.

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.

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.

Local symmetry predictors of mechanical stability in glasses

The mechanical properties of crystals are controlled by the translational symmetry of their structures. But for glasses with a disordered structure, the link between the symmetry of local particle arrangements and stability is not well established. In this contribution, we provide experimental verification that the centrosymmetry of nearest-neighbor polyhedra in a glass strongly correlates with the local mechanical stability. We examine the distribution of local stability and local centrosymmetry in a glass during aging and deformation using microbeam x-ray scattering. These measurements reveal the underlying relationship between particle-level structure and larger-scale behavior and demonstrate that spatially connected, coordinated local transformations to lower symmetry structures are fundamental to these phenomena. While glassy structures lack obvious global symmetry breaking, local structural symmetry is a critical factor in predicting stability.

Screening toward the Development of Fingerprints of Atomic Environments Using Bond-Orientational Order Parameters

A combination of atomic numbers and bond-orientational order parameters is considered a candidate for a simple representation that involves information on both the atomic species and their positional relation. The 504 candidates are applied as the fingerprint of the molecules stored in QM9, a data set of computed geometric, energetic, electronic, and thermodynamic properties for 133 885 stable small organic molecules made up of carbon, hydrogen, oxygen, nitrogen, and fluorine atoms. To screen the fingerprints, a regression analysis of the atomic charges given by Open Babel was performed by supervised machine learning. The regression results indicate that the 60 fingerprints successfully estimate Open Babel charges. The results of the dipole moments, an example of a property expressed by charge and position, also had a high accuracy in comparison with the values computed from Open Babel charges. Therefore, the screened 60 fingerprints have the potential to precisely describe the chemical and structural information on the atomic environment of molecules.

Towards Glasses with Permanent Stability

Unlike crystals, glasses age or devitrify over time, reflecting their nonequilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that the devitrification of quasi-hard-sphere glasses is prevented by suppressing volume-fraction inhomogeneities. A monodisperse glass known to devitrify with "avalanchelike" intermittent dynamics is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this entirely prevents structural relaxation and devitrification over aging time scales, even in the presence of crystallites. There is a dramatic homogenization in the number of load-bearing nearest neighbors each particle has, indicating that ultrastable glasses may be formed via "mechanical homogenization." Our finding provides a physical principle for glass stabilization and opens a novel route to the formation of mechanically stabilized glasses.

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.

Weak temperature dependence of ageing of structural properties in atomistic model glassformers

Ageing phenomena are investigated from a structural perspective in two binary Lennard-Jones glassformers, the Kob-Andersen and Wahnström mixtures. In both, the geometric motif assumed by the glassformer upon supercooling, the locally favoured structure (LFS), has been established. The Kob-Andersen mixture forms bicapped square antiprisms; the Wahnström model forms icosahedra. Upon ageing, we find that the structural relaxation time has a time-dependence consistent with a power law. However, the LFS population and potential energy increase and decrease, respectively, in a logarithmic fashion. Remarkably, over the time scales investigated, which correspond to a factor of 10⁴ change in relaxation times, the rate at which these quantities age appears almost independent of temperature. Only at temperatures far below the Vogel-Fulcher-Tamman temperature do the ageing dynamics slow.

Common mechanism of thermodynamic and mechanical origin for ageing and crystallization of glasses

The glassy state is known to undergo slow structural relaxation, where the system progressively explores lower free-energy minima which are either amorphous (ageing) or crystalline (devitrification). Recently, there is growing interest in the unusual intermittent collective displacements of a large number of particles known as ‘avalanches’. However, their structural origin and dynamics are yet to be fully addressed. Here, we study hard-sphere glasses which either crystallize or age depending on the degree of size polydispersity, and show that a small number of particles are thermodynamically driven to rearrange in regions of low density and bond orientational order. This causes a transient loss of mechanical equilibrium which facilitates a large cascade of motion. Combined with previously identified phenomenology, we have a complete kinetic pathway for structural change which is common to both ageing and crystallization. Furthermore, this suggests that transient force balance is what distinguishes glasses from supercooled liquids.

Glass is characterized by stochastic and slow structural relaxation dynamics, whose details remain elusive due to its complicated kinetic processes. Here, the authors show that avalanche-like dynamics in both ageing and devitrifying glasses are governed by thermodynamic initiation and a transient loss in mechanical stability.

Introduction to the Colloidal Glass Transition

Colloids are suspensions of small solid particles in a liquid and exhibit glassy behavior when the particle concentration is high. In these samples, the particles are roughly analogous to individual molecules in a traditional glass. This model system has been used to study the glass transition since the 1980s. In this Viewpoint I summarize some of the intriguing behaviors of the glass transition in colloids and discuss open questions.

Relationship between local structure and relaxation in out-of-equilibrium glassy systems

The dynamical glass transition is typically taken to be the temperature at which a glassy liquid is no longer able to equilibrate on experimental timescales. Consequently, the physical properties of these systems just above or below the dynamical glass transition, such as viscosity, can change by many orders of magnitude over long periods of time following external perturbation. During this progress toward equilibrium, glassy systems exhibit a history dependence that has complicated their study. In previous work, we bridged the gap between structure and dynamics in glassy liquids above their dynamical glass transition temperatures by introducing a scalar field called "softness," a quantity obtained using machine-learning methods. Softness is designed to capture the hidden patterns in relative particle positions that correlate strongly with dynamical rearrangements of particle positions. Here we show that the out-of-equilibrium behavior of a model glass-forming system can be understood in terms of softness. To do this we first demonstrate that the evolution of behavior following a temperature quench is a primarily structural phenomenon: The structure changes considerably, but the relationship between structure and dynamics remains invariant. We then show that the relaxation time can be robustly computed from structure as quantified by softness, with the same relation holding both in equilibrium and as the system ages. Together, these results show that the history dependence of the relaxation time in glasses requires knowledge only of the softness in addition to the usual state variables.

Direct visualization of free-volume-triggered activation of β relaxation in colloidal glass

β relaxation, which is predicted by mode coupling theory and involves the localized motions of particles, initiates in a supercooled liquid and continues into glassy state. It correlates essentially with many fundamental properties of amorphous materials. Despite its importance, the underlying mechanisms leading to the β relaxation have remained elusive. As natural heterogeneity, the original distributed free volume has been supposed to be associated with the activation of β relaxation in amorphous solids. However, there has been no direct experimental proof for this hypothesis. Here we used a colloidal glass to directly observe the β relaxation and free-volume distribution. We found a spatial correlation between the β relaxation and free volume. The large free volume regions were observed to possess a low-energy cost of relaxation-induced strain, indicating that the large free volume region presenting a low-energy barrier for structural relaxation benefits the β relaxation.

Anomalously slow relaxation of interacting liquid nanoclusters confined in a porous medium

Anomalously slow relaxation of clusters of a liquid confined in a disordered system of pores has been studied for the (water-L23 nanoporous medium) system. The evolution of the system of confined liquid clusters consists of a fast formation stage followed by slow relaxation of the system and its decay. The characteristic time for the formation of the initial state is τ(p)∼10 s after the reduction of excess pressure after complete filling. Anomalously slow relaxation has been observed for times of 10(1)-10(5) s, and decay has been observed at times of >10(5) s. The time dependence of the volume fraction θ of pores filled with the confined liquid is described by a power law θ∼t(-α) with the exponent α<0.15. The exponent α and temperature dependence α(T) are qualitatively described theoretically for the case of a slightly polydisperse medium in a mean-field approximation with the inclusion of the interaction of liquid clusters and averaging over various degenerate local configurations of clusters. In this approximation, slow relaxation is represented as a continuous transition through a sequence of metastable states of the system of clusters with a decreasing barrier.