Static point-to-set correlations in glass-forming liquids

Does the Naı̈ve Mode-Coupling Power Law Divergence Provide an Objective Determination of the Crossover Temperature in Glass Formation Behavior?

The glass formation temperature range is commonly divided into a weakly supercooled regime at higher temperatures and a deeply supercooled regime at lower temperatures, with a change in the physical mechanisms that govern dynamics often postulated to occur at the crossover between these regimes. This crossover temperature Tc is widely determined based on a fit of relaxation time vs temperature data to a power law divergence form predicted by the naı̈ve mode coupling theory (MCT). Here, we show, based on simulation data spanning polymeric, small molecule organic, metallic, and inorganic glass formers, that this approach does not yield an objective measure of a crossover temperature. Instead, the value of Tc is determined by the lowest temperature Tmin employed in the fit, and no regime of stationary or convergent Tc value is generally observed as Tmin is varied. Nor does the coefficient of determination R2 provide any robust means of selecting a fit range and thus a value of Tc. These results may require a re-evaluation of published results that have employed the fit MCT Tc value as a metric of temperature-dependent dynamics or a benchmark for depth of supercooling, and they highlight a need for the field to converge on a more objective determination of any posited crossover temperature between high and low temperature regimes of glass formation.

Collineations of particles in the Kob-Andersen system

Numerous indications suggest that subtle changes occurring in the structures of liquids on supercooling are connected to the phenomenon of the glass transition and that detailed understanding of these changes is crucial for the development of new glasses with desired properties. J. D. Bernal in his 1962 Bakerian lecture in particular reported about an observation of approximately linear chains of several particles, referred to as collineations. He found that in the studied hard sphere system, these collineations can contain up to eight particles. Since then the collineations of three particles have been discussed in many papers in the context of the splitting of the second peak in pair density functions of supercooled liquids and glasses. However, it appears that longer collineations involving more that three particles have not been systematically studied. Here we report on our study of such collineations for the Kob-Andersen system of particles on cooling for the parent and inherent structures. Contrary to intuition, our findings reveal that below the potential energy landscape crossover temperature, the number of collineations in the parent structures can exceed that of the corresponding inherent structures. We also introduce a model that connects long collineations with the pair density and angular density distribution functions and demonstrate that this model describes long collineations quite well. We also studied the diffusion of the particles forming collineations and demonstrated that these particles are slightly slower than the randomly chosen average particle. Preliminary investigation of the collineations' lifetimes suggests that there are vibrational and structural relaxation regimes in the decay of the considered correlation function. The second part of the paper explores potential connections between collineations and (1) the disclination lines associated with the geometric frustration approach, (2) low-energy clusters from the topological cluster classification approach, and (3) chainlike cooperative motion of particles in low-temperature supercooled liquids. For the studied system, according to the used methods, no clear connection was found between collineations and these phenomena.

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.

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.

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.

Glassy phases of the Gaussian core model

We present results from molecular dynamics simulations exploring the supercooled dynamics of the Gaussian Core Model in the low- and intermediate-density regimes. In particular, we analyse the transition from the low-density hard-sphere-like glassy dynamics to the high-density one. The dynamics at low densities is well described by the caging mechanism, giving rise to intermittent dynamics. At high densities, the particles undergo a more continuous motion in which the concept of cage loses its meaning. We elaborate on the idea that these different supercooled dynamics are in fact the precursors of two different glass states.

Relevance of structural defects to the mechanism of mechanical deformation in metallic glasses

It is known that deformation in disordered materials such as metallic glasses and supercooled liquids occurs via the cooperative rearrangement of atoms or constituent particles at dynamical heterogeneities, commonly regarded as point-like defects. We show via molecular-dynamics simulations that there is no apparent relationship between atomic rearrangements and the local atomic environment as measured by the atomic-level stresses, kinetic and potential energies, and the per-atom Voronoi volume. In addition, there is only a weak correlation between atomic rearrangements and the largest and smallest eigenvalues of the dynamical matrix. Our results confirm the transient nature of dynamical heterogeneities and suggest that the notion of defects may be less relevant than that of a propensity for rearrangement.

World beyond the nearest neighbors

The structure beyond the nearest neighbor atoms in liquid and glass is characterized by the medium-range order (MRO). In the conventional approach, the MRO is considered to result directly from the short-range order (SRO) in the nearest neighbors. To this bottom-up approach starting with the SRO, we propose to add a top-down approach in which global collective forces drive liquid to form density waves. The two approaches are in conflict with each other, and the compromise produces the structure with the MRO. The driving force to produce density waves provides the stability and stiffness to the MRO, and controls various mechanical properties. This dual framework provides a novel perspective for description of the structure and dynamics of liquid and glass.

End-Tethered Chains Increase the Local Glass Transition Temperature of Matrix Chains by 45 K Next to Solid Substrates Independent of Chain Length

The local glass transition temperature T_g of pyrene-labeled polystyrene (PS) chains intermixed with end-tethered PS chains grafted to a neutral silica substrate was measured by fluorescence spectroscopy. To isolate the impact of the grafted chains, the films were capped with bulk neat PS layers eliminating competing effects of the free surface. Results demonstrate that end-grafted chains strongly increase the local T_g of matrix chains by ≈45 K relative to bulk T_g, independent of grafted chain molecular weight from M_n = 8.6 to 212 kg/mol and chemical end-group, over a wide range of grafting densities σ = 0.003 to 0.33 chains/nm² spanning the mushroom-to-brush transition regime. The tens-of-degree increase in local T_g resulting from immobilization of the chain ends by covalent bonding in this athermal system suggests a mechanism that substantially increases the local activation energy required for cooperative rearrangements.

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.

Jammed solids with pins: Thresholds, force networks, and elasticity

The role of fixed degrees of freedom in soft or granular matter systems has broad applicability and theoretical interest. Here we address questions of the geometrical role that a scaffolding of fixed particles plays in tuning the threshold volume fraction and force network in the vicinity of jamming. Our two-dimensional simulated system consists of soft particles and fixed "pins," both of which harmonically repel overlaps. On the one hand, we find that many of the critical scalings associated with jamming in the absence of pins continue to hold in the presence of even dense pin latices. On the other hand, the presence of pins lowers the jamming threshold in a universal way at low pin densities and a geometry-dependent manner at high pin densities, producing packings with lower densities and fewer contacts between particles. The onset of strong lattice dependence coincides with the development of bond-orientational order. Furthermore, the presence of pins dramatically modifies the network of forces, with both unusually weak and unusually strong forces becoming more abundant. The spatial organization of this force network depends on pin geometry and is described in detail. Using persistent homology, we demonstrate that pins modify the topology of the network. Finally, we observe clear signatures of this developing bond-orientational order and broad force distribution in the elastic moduli which characterize the linear response of these packings to strain.

Structural and Dynamical Properties of Liquids in Confinements: A Review of Molecular Dynamics Simulation Studies

Molecular dynamics (MD) simulations are a powerful tool for detailed studies of altered properties of liquids in confinement, in particular, of changed structures and dynamics. They allow, on one hand, for perfect control and systematic variation of the geometries and interactions inherent in confinement situations and, on the other hand, for type-selective and position-resolved analyses of a huge variety of structural and dynamical parameters. Here, we review MD simulation studies on various types of liquids and confinements. The main focus is confined aqueous systems, but also ionic liquids and polymer and silica melts are discussed. Results for confinements featuring different interactions, sizes, shapes, and rigidity will be presented. Special attention will be given to situations in which the confined liquid and the confining matrix consist of the same type of particles and, hence, disparate liquid-matrix interactions are absent. Findings for the magnitude and the range of wall effects on molecular positions and orientations and on molecular dynamics, including vibrational motion and structural relaxation, are reviewed. Moreover, their dependence on the parameters of the confinement and their relevance to theoretical approaches to the glass transition are addressed.

Mean-field model for the Curie-Weiss temperature dependence of coherence length in metallic liquids

The coherence length of the medium-range order (MRO) in metallic liquids is known to display a Curie-Weiss temperature dependence; its inverse is linearly related to temperature, and when extrapolated from temperatures above the glass transition, the coherence length diverges at a negative temperature with a critical exponent of unity. We propose a mean-field pseudospin model that explains this behavior. Specifically, we model the atoms and their local environment as Ising spins with antiferromagnetic exchange interactions. We further superimpose an exchange interaction between dynamical heterogeneities, or clusters of atoms undergoing cooperative motion. The coherence length in the metallic liquid is thus the correlation length between dynamical heterogeneities. Our results reaffirm the idea that the MRO coherence length is a measure of point-to-set correlations, and that local frustrations in the interatomic interactions are prominent in metallic liquids.

Revealing the characteristic length of random close packing via critical-like random pinning

By randomly pinning particles in fluidized states and finding the local energy minima, we form static packings of mono-disperse disks that resemble random close packing, when only n_c = 2.6% of the particles are pinned. The packings are isostatic and exhibit typical critical scalings of the jamming transition. The non-triviality of n_c is manifested mainly in two aspects. First, n_c acts as a critical point, leading to bifurcated critical scalings in its vicinity. The criticality of n_c is also demonstrated in the packings of weakly polydisperse disks. Second, n_c sets a length scale in agreement with the characteristic length of random close packing. With robust evidence, we show that this agreement is generally true for both mono- and poly-disperse particles and in both two and three dimensions. The randomness inherited from fluidized states by random pinning thus interprets the randomness of random close packing from a unique perspective.

Medium-range atomic correlation in simple liquids. I. Distinction from short-range order

Physical properties of liquids and glasses are controlled not only by the short-range order (SRO) in the nearest-neighbor atoms but also by the medium-range order (MRO) observed for atoms beyond the nearest neighbors. In this article the nature of the MRO as the descriptor of point-to-set atomic correlation is discussed focusing on simple liquids, such as metallic liquids. Through the results of x-ray diffraction and simulation with classical potentials we show that the third peak of the pair-distribution function, which describes the MRO, shows a distinct change in temperature dependence at the glass transition, whereas the first peak, which represents the SRO, changes smoothly through the glass transition. The result suggests that the glass transition is induced by the freezing of the MRO rather than that of the SRO, implying a major role of the MRO on the viscosity of supercooled liquid.

Medium-range atomic correlation in simple liquids. II. Theory of temperature dependence

The spatial atomic correlations in liquids and glasses extend often significantly beyond the nearest neighbors. Such correlations, called the medium-range order (MRO), affect many physical properties, but their nature is not well understood. In this article the variation of the MRO with temperature is calculated based upon the concept of the atomic-level pressure, focusing on simple liquids, such as metallic liquids. It is shown that the structural coherence length that characterizes MRO follows the Curie-Weiss law with a negative Curie temperature as observed by experiment and simulation. It is also shown that the glass transition is induced by freezing of the MRO, rather than the freezing of the nearest-neighbor shell. The implications of these results are discussed.

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

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

The microscopic origins of stretched exponential relaxation in two model glass-forming liquids as probed by simulations in the isoconfigurational ensemble

The origin of stretched exponential relaxation in supercooled glass-forming liquids is one of the central questions regarding the anomalous dynamics of these fluids. The dominant explanation for this phenomenon has long been the proposition that spatial averaging over a heterogeneous distribution of locally exponential relaxation processes leads to stretching. Here, we perform simulations of model polymeric and small-molecule glass-formers in the isoconfigurational ensemble to show that stretching instead emerges from a combination of spatial averaging and locally nonexponential relaxation. The results indicate that localities in the fluid exhibiting faster-than-average relaxation tend to exhibit locally stretched relaxation, whereas slower-than-average relaxing domains exhibit more compressed relaxation. We show that local stretching is predicted by loose local caging, as measured by the Debye-Waller factor, and vice versa. This phenomenology in the local relaxation of in-equilibrium glasses parallels the dynamics of out of equilibrium under-dense and over-dense glasses, which likewise exhibit an asymmetry in their degree of stretching vs compression. On the basis of these results, we hypothesize that local stretching and compression in equilibrium glass-forming liquids results from evolution of particle mobilities over a single local relaxation time, with slower particles tending toward acceleration and vice versa. In addition to providing new insight into the origins of stretched relaxation, these results have implications for the interpretation of stretching exponents as measured via metrologies such as dielectric spectroscopy: measured stretching exponents cannot universally be interpreted as a direct measure of the breadth of an underlying distribution of relaxation times.

On the overlap between configurations in glassy liquids

The overlap, or similarity, between liquid configurations is at the core of the mean-field description of the glass transition and remains a useful concept when studying three-dimensional glass-forming liquids. In liquids, however, the overlap involves a tolerance, typically of a fraction a/σ of the inter-particle distance, associated with how precisely similar two configurations must be for belonging to the same physically relevant "state." Here, we systematically investigate the dependence of the overlap fluctuations and of the resulting phase diagram when the tolerance is varied over a large range. We show that while the location of the dynamical and thermodynamic glass transitions (if present) is independent of a/σ, that of the critical point associated with a transition between a low- and a high-overlap phase in the presence of an applied source nontrivially depends on the value of a/σ. We rationalize our findings by using liquid-state theory and the hypernetted-chain approximation for correlation functions. In addition, we confirm the theoretical trends by studying a three-dimensional glass-former by computer simulations. We show, in particular, that a range of a/σ below what is commonly considered maximizes the temperature of the critical point, pushing it up in a liquid region where viscosity is low and computer investigations are easier due to a significantly faster equilibration.

Fragile-to-strong crossover, growing length scales, and dynamic heterogeneity in Wigner glasses

Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition theories. In these systems glassy behavior arises as the density of the particles is increased. Thus, soft colloidal particles with varying degree of softness capture diverse glass-forming properties, observed normally in molecular glasses. Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions show that tuning the softness of the interaction potential, achievable by changing the monovalent salt concentration results in a continuous transition from fragile to strong behavior. Remarkably, this is found in a system where the well characterized interaction potential between the colloidal particles is isotropic. We also show that the predictions of the random first-order transition (RFOT) theory quantitatively describes the universal features such as the growing correlation length, ξ∼(ϕ_{K}/ϕ-1)^{-ν} with ν=2/3 where ϕ_{K}, the analog of the Kauzmann temperature, depends on the salt concentration. As anticipated by the RFOT predictions, we establish a causal relationship between the growing correlation length and a steep increase in the relaxation time and dynamic heterogeneity as the system is compressed. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular and polymer glasses. The large variations in the fragility are normally found only when the temperature dependence of the viscosity is examined for a large class of diverse glass-forming materials. In sharp contrast, this is vividly illustrated in a single system that can be experimentally probed. Our work also shows that the RFOT predictions are accurate in describing the dynamics over the entire density range, regardless of the fragility of the glasses.

Do String-like Cooperative Motions Predict Relaxation Times in Glass-Forming Liquids?

The Adam-Gibbs theory of glass formation posits that the growth in the activation barrier of fragile liquids on cooling emerges from a loss of configurational entropy and concomitant growth in "cooperatively rearranging regions" (CRRs). A body of literature over 2 decades has suggested that "string-like" cooperatively rearranging clusters observed in molecular simulations may be these CRRs-a scenario that would have profound implications for the understanding of the glass transition. The central element of this postulate is the report of an apparent zero-parameter relationship between the mass of string-like CRRs and the relaxation time. Here, we show, based on molecular dynamics simulations of multiple glass-forming liquids, that this finding is the result of an implicit adjustable parameter-a "replacement distance". This parameter is equivalent to an adjustable exponent within a generalized Adam-Gibbs relation, such that it tunes the entire functional form of the relation. Moreover, we are unable to find any objective criterion, based on the radial distribution function or the cluster fractal dimension, for selecting this replacement distance across multiple systems. We conclude that the present data do not establish that string-like cooperative rearrangements, as presently defined, are predictive of segmental relaxation via an Adam-Gibbs-like physical model.

Progress towards a phenomenological picture and theoretical understanding of glassy dynamics and vitrification near interfaces and under nanoconfinement

The nature of alterations to dynamics and vitrification in the nanoscale vicinity of interfaces-commonly referred to as "nanoconfinement" effects on the glass transition-has been an open question for a quarter century. We first analyze experimental and simulation results over the last decade to construct an overall phenomenological picture. Key features include the following: after a metrology- and chemistry-dependent onset, near-interface relaxation times obey a fractional power law decoupling relation with bulk relaxation; relaxation times vary in a double-exponential manner with distance from the interface, with an intrinsic dynamical length scale appearing to saturate at low temperatures; the activation barrier and vitrification temperature T_g approach bulk behavior in a spatially exponential manner; and all these behaviors depend quantitatively on the nature of the interface. We demonstrate that the thickness dependence of film-averaged T_g for individual systems provides a poor basis for discrimination between different theories, and thus we assess their merits based on the above dynamical gradient properties. Entropy-based theories appear to exhibit significant inconsistencies with the phenomenology. Diverse free-volume-motivated theories vary in their agreement with observations, with approaches invoking cooperative motion exhibiting the most promise. The elastically cooperative nonlinear Langevin equation theory appears to capture the largest portion of the phenomenology, although important aspects remain to be addressed. A full theoretical understanding requires improved confrontation with simulations and experiments that probe spatially heterogeneous dynamics within the accessible 1-ps to 1-year time window, minimal use of adjustable parameters, and recognition of the rich quantitative dependence on chemistry and interface.

Relation between Heterogeneous Frozen Regions in Supercooled Liquids and Non-Debye Spectrum in the Corresponding Glasses

Recent numerical studies on glassy systems provide evidence for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states D(ω). Similarly to Goldstone modes (GMs), i.e., phonons in solids, NGMs are soft low-energy excitations. However, differently from GMs, NGMs are localized excitations. Here we first show that the parental temperature T^{*} modifies the GM/NGM ratio in D(ω). In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent s(T^{*}) in the low-frequency power law D(ω)∼ω^{s(T^{*})}, with 2≤s(T^{*})≤4. Second, by comparing s(T^{*}) with s(p), i.e., the same quantity obtained by pinning a p particle fraction, we suggest that s(T^{*}) reflects the presence of dynamical heterogeneous regions of size ξ^{3}∝p. Finally, we provide an estimate of ξ as a function of T^{*}, finding a mild power law divergence, ξ∼(T^{*}-T_{d})^{-α/3}, with T_{d} the dynamical crossover temperature and α falling in the range α∈[0.8,1.0].

Static and dynamic correlation lengths in supercooled polymers

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

Effects of confinement on supercooled tetrahedral liquids

We use molecular dynamics simulations to ascertain the effects of geometrical restriction on glass-forming tetrahedral liquids. Striving for a broad approach, we study families of waterlike and silicalike liquids, for which we systematically scale the partial charges and, hence, the relevance of the tetrahedral networks. The confined liquids and the confining matrices consist of the same type of particles to avoid disruptive interactions and distorted structures at the interfaces. Spatially resolved analyses show that these neutral confinements still impose static mobility gradients and density correlations on the liquids. We quantify the increasing degree and range of the altered properties upon cooling. For both families of models, common relations describe the confinement effects of all systems with tetrahedral order, while deviations occur for systems with lower polarities and different structures. The observations are rationalized by considering the fact that a pinned wall imprints a static energy landscape to a neighboring liquid. We explore the properties of this landscape based on changes in vibrational motion and structural relaxation and find that typical barrier heights amount to two to three times the activation energy of bulk dynamics. Combining the present and previous results, we predict the evolution of confinement effects down to the glass transition temperature for liquids without fragile-to-strong crossover. In addition, it is found for silicalike liquids that the temperature dependence of dynamic and static correlation lengths from confinement studies is not affected when cooling through fragile-to-strong transitions of the bulk materials, casting doubt on the relevance of these length scales for the glassy slowdown.

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.

Configurational entropy of glass-forming liquids

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraught with difficulties, misconceptions, and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.

Ideal Glass States Are Not Purely Vibrational: Insight from Randomly Pinned Glasses

We use computer simulations to probe the thermodynamic and dynamic properties of a glass former that undergoes an ideal glass transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass state, the system relaxes to some extent because of the presence of localized excitations that allow the system to access different inherent structures, thus giving rise to a nontrivial contribution to the entropy. By calculating with high accuracy the vibrational part of the entropy, we show that also in the equilibrium glass state thermodynamics and dynamics give a coherent picture, and that glasses should not be seen as a disordered solid in which the particles undergo just vibrational motion but instead as a system with a highly nonlinear internal dynamics.

The race to the bottom: approaching the ideal glass?

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

Translational and Rotational Dynamical Heterogeneities in Granular Systems

We use x-ray tomography to investigate the translational and rotational dynamical heterogeneities of a three dimensional hard ellipsoid granular packing driven by oscillatory shear. We find that particles which translate quickly form clusters with a size distribution given by a power law with an exponent that is independent of the strain amplitude. Identical behavior is found for particles that are translating slowly, rotating quickly, or rotating slowly. The geometrical properties of these four different types of clusters are the same as those of random clusters. Different cluster types are considerably correlated or anticorrelated, indicating a significant coupling between translational and rotational degrees of freedom. Surprisingly, these clusters are formed already at time scales that are much shorter than the α-relaxation time, in stark contrast to the behavior found in glass-forming systems.

Dramatic Increase in Polymer Glass Transition Temperature under Extreme Nanoconfinement in Weakly Interacting Nanoparticle Films

Properties of polymers in polymer nanocomposites and nanopores have been shown to deviate from their respective bulk properties due to physical confinement as well as polymer-particle interfacial interactions. However, separating the confinement effects from the interfacial effects under extreme nanoconfinement is experimentally challenging. Capillary rise infiltration enables polymer infiltration into nanoparticle (NP) packings, thereby confining polymers within extremely small pores and dramatically increasing the interfacial area, providing a good system to systematically distinguish the role of each effect on polymer properties. In this study, we investigate the effect of spatial confinement on the glass transition temperature ( T_g) of polystyrene (PS) infiltrated into SiO₂ NP films. The degree of confinement is tuned by varying the molecular weight of polymers, the size of NPs (diameters between 11 and 100 nm, producing 3-30 nm average pore sizes), and the fill-fraction of PS in the NP films. We show that in these dense NP packings the T_g of confined PS, which interacts weakly with SiO₂ NPs, significantly increases with decreasing pore size such that for the two molecular weights of PS studied the T_g increases by up to 50 K in 11 nm NP packings, while T_g is close to the bulk T_g in 100 nm NP packings. Interestingly, as the fill-fraction of PS is decreased, resulting in the accumulation of the polymer in the contacts between nanoparticles, hence an increased specific interfacial area, the T_g further increases relative to the fully filled films by another 5-8 K, indicating the strong role of geometrical confinement as opposed to the interfacial effects on the measured T_g values.

Molecular Dynamics Simulations of Water, Silica, and Aqueous Mixtures in Bulk and Confinement

Aqueous systems are omnipresent in nature and technology. They show complex behaviors, which often originate in the existence of hydrogen-bond networks. Prominent examples are the anomalies of water and the non-ideal behaviors of aqueous solutions. The phenomenology becomes even richer when aqueous liquids are subject to confinement. To this day, many properties of water and its mixtures, in particular, under confinement, are not understood. In recent years, molecular dynamics simulations developed into a powerful tool to improve our knowledge in this field. Here, our simulation results for water and aqueous mixtures in the bulk and in various confinements are reviewed and some new simulation data are added to improve our knowledge about the role of interfaces. Moreover, findings for water are compared with results for silica, exploiting that both systems form tetrahedral networks.

Atomic clusters with addressable complexity

A general formulation for constructing addressable atomic clusters is introduced, based on one or more reference structures. By modifying the well depths in a given interatomic potential in favour of nearest-neighbour interactions that are defined in the reference(s), the potential energy landscape can be biased to make a particular permutational isomer the global minimum. The magnitude of the bias changes the resulting potential energy landscape systematically, providing a framework to produce clusters that should self-organise efficiently into the target structure. These features are illustrated for small systems, where all the relevant local minima and transition states can be identified, and for the low-energy regions of the landscape for larger clusters. For a 55-particle cluster, it is possible to design a target structure from a transition state of the original potential and to retain this structure in a doubly addressable landscape. Disconnectivity graphs based on local minima that have no direct connections to a lower minimum provide a helpful way to visualise the larger databases. These minima correspond to the termini of monotonic sequences, which always proceed downhill in terms of potential energy, and we identify them as a class of biminimum. Multiple copies of the target cluster are treated by adding a repulsive term between particles with the same address to maintain distinguishable targets upon aggregation. By tuning the magnitude of this term, it is possible to create assemblies of the target cluster corresponding to a variety of structures, including rings and chains.

Experimental determination of configurational entropy in a two-dimensional liquid under random pinning

A quasi two-dimensional colloidal suspension is studied under the influence of immobilisation (pinning) of a random fraction of its particles. We introduce a novel experimental method to perform random pinning and, with the support of numerical simulation, we find that increasing the pinning concentration smoothly arrests the system, with a cross-over from a regime of high mobility and high entropy to a regime of low mobility and low entropy. At the local level, we study fluctuations in area fraction and concentration of pins and map them to entropic structural signatures and local mobility, obtaining a measure for the local entropic fluctuations of the experimental system.

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

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

Measurements of growing surface tension of amorphous-amorphous interfaces on approaching the colloidal glass transition

There is mounting evidence indicating that relaxation dynamics in liquids approaching their glass transition not only become increasingly cooperative, but the relaxing regions also become more compact in shape. Of the many theories of the glass transition, only the random first-order theory—a thermodynamic framework—anticipates the surface tension of relaxing regions to play a role in deciding both their size and morphology. However, owing to the amorphous nature of the relaxing regions, even the identification of their interfaces has not been possible in experiments hitherto. Here, we devise a method to directly quantify the dynamics of amorphous–amorphous interfaces in bulk supercooled colloidal liquids. Our procedure also helped unveil a non-monotonic evolution in dynamical correlations with supercooling in bulk liquids. We measure the surface tension of the interfaces and show that it increases rapidly across the mode-coupling area fraction. Our experiments support a thermodynamic origin of the glass transition.

The existence of interfaces, separating distinct relaxing regions, has been predicted in glass  theory, but a direct proof remains challenging due to the amorphous nature of glasses. Ganapathi et al. identify and measure the surface tension of these interfaces in bulk supercooled colloidal liquids.

From Glass Formation to Icosahedral Ordering by Curving Three-Dimensional Space

Geometric frustration describes the inability of a local molecular arrangement, such as icosahedra found in metallic glasses and in model atomic glass formers, to tile space. Local icosahedral order, however, is strongly frustrated in Euclidean space, which obscures any causal relationship with the observed dynamical slowdown. Here we relieve frustration in a model glass-forming liquid by curving three-dimensional space onto the surface of a 4-dimensional hypersphere. For sufficient curvature, frustration vanishes and the liquid "freezes" in a fully icosahedral structure via a sharp "transition." Frustration increases upon reducing the curvature, and the transition to the icosahedral state smoothens while glassy dynamics emerge. Decreasing the curvature leads to decoupling between dynamical and structural length scales and the decrease of kinetic fragility. This sheds light on the observed glass-forming behavior in Euclidean space.

Nonmonotonic dynamic correlations in quasi-two-dimensional confined glass-forming liquids

It has been broadly accepted that the behavior of glass-forming liquids, where their relaxation dynamics exhibit a pronounced slowdown as they are cooled toward the glass transition temperature, is caused by the increase in one or more correlation lengths. However, the role of length scales in the dynamics of glass-forming liquids is not clearly established, and past simulation work that suggests a surprising nonmonotonic temperature evolution of spatial dynamical correlations near the mode-coupling crossover temperature has been both questioned and supported by subsequent work. Here, using molecular dynamics simulation, we also show a striking maximum in the dynamic length scale ξ_{c}^{dyn} at a given temperature, but the temperature of this maximum is found to shift as the size of the confined system increases. Furthermore, we find that such a maximum disappears for all geometry sizes considered when a rough wall is replaced with a smooth, hard wall, suggesting that the nature of the nonmonotonic temperature dependence of ξ_{c}^{dyn} does not reflect an intrinsic property of bulk liquids, but originates from wall effects. Our results provide new insights into the dynamics of glass-forming liquids, particularly for quasi-two-dimensional systems.

Self-diffusion in two-dimensional binary colloidal hard-sphere fluids

We present a systematic experimental study of the dynamic behavior of monodisperse and bidisperse two-dimensional colloidal hard-sphere fluids. We consider the diffusive behavior of the two types of particles for systems with a variety of compositions and total area fractions. In particular, we measure the short- and long-time diffusion coefficients for both species independently. We find that the short-time self-diffusion coefficients show an approximately linear dependence on the area fraction and that the long-time self-diffusion coefficients are well described by an expression dependent upon only the area fraction and contact value of the radial distribution function. Finally, we consider the effect of composition change and find some variation in the long-time self-diffusion coefficients, which we ascribe to the complex packing effects exhibited by binary systems.

Significant difference in the dynamics between strong and fragile glass formers

Glass-forming liquids are often classified into strong glass formers with nearly Arrhenius behavior and fragile ones with super-Arrhenius behavior. We reveal a significant difference in the dynamics between these two types of glass formers through molecular dynamics simulations: In strong glass formers, the relaxation dynamics of density fluctuations is nondiffusive, whereas in fragile glass formers it exhibits diffusive behavior. We demonstrate that this distinction is a direct consequence of the fundamental difference in the underlying elementary relaxation process between these two dynamical classes of glass formers. For fragile glass formers, a density-exchange process proceeds the density relaxation, which takes place locally at the particle level in normal states but is increasingly cooperative and nonlocal as the temperature is lowered in supercooled states. On the other hand, in strong glass formers, such an exchange process is not necessary for density relaxation due to the presence of other local relaxation channels. Our finding provides a novel insight into Angell's classification scheme from a hydrodynamic perspective.