Theory of Structural Glasses and Supercooled Liquids

Motility driven glassy dynamics in confluent epithelial monolayers

As wounds heal, embryos develop, cancer spreads, or asthma progresses, the cellular monolayer undergoes a glass transition between solid-like jammed and fluid-like flowing states. During some of these processes, the cells undergo an epithelial-to-mesenchymal transition (EMT): they acquire in-plane polarity and become motile. Thus, how motility drives the glassy dynamics in epithelial systems is critical for the EMT process. However, no analytical framework that is indispensable for deeper insights exists. Here, we develop such a theory inspired by a well-known glass theory. One crucial result of this work is that the confluency affects the effective persistence time-scale of active force, described by its rotational diffusivity, Deffr. Deffr differs from the bare rotational diffusivity, Dr, of the motile force due to cell shape dynamics, which acts to rectify the force dynamics: Deffr is equal to Dr when Dr is small and saturates when Dr is large. We test the theoretical prediction of Deffr and how it affects the relaxation dynamics in our simulations of the active Vertex model. This novel effect of Deffr is crucial to understanding the new and previously published simulation data of active glassy dynamics in epithelial monolayers.

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.

Role of anisotropy in understanding the molecular grounds for density scaling in dynamics of glass-forming liquids

Molecular Dynamics (MD) simulations of glass-forming liquids play a pivotal role in uncovering the molecular nature of the liquid vitrification process. In particular, much focus was given to elucidating the interplay between the character of intermolecular potential and molecular dynamics behaviour. This has been tried to achieve by simulating the spherical particles interacting via isotropic potential. However, when simulation and experimental data are analysed in the same way by using the density scaling approaches, serious inconsistency is revealed between them. Similar scaling exponent values are determined by analysing the relaxation times and pVT data obtained from computer simulations. In contrast, these values differ significantly when the same analysis is carried out in the case of experimental data. As discussed thoroughly herein, the coherence between results of simulation and experiment can be achieved if anisotropy of intermolecular interactions is introduced to MD simulations. In practice, it has been realized in two different ways: (1) by using the anisotropic potential of the Gay-Berne type or (2) by replacing the spherical particles with quasi-real polyatomic anisotropic molecules interacting through isotropic Lenard-Jones potential. In particular, the last strategy has the potential to be used to explore the relationship between molecular architecture and molecular dynamics behaviour. Finally, we hope that the results presented in this review will also encourage others to explore how 'anisotropy' affects remaining aspects related to liquid-glass transition, like heterogeneity, glass transition temperature, glass forming ability, etc.

Local and global expansivity in water

The supra-molecular structure of a liquid is strongly connected to its dynamics, which in turn control macroscopic properties such as viscosity. Consequently, detailed knowledge about how this structure changes with temperature is essential to understand the thermal evolution of the dynamics ranging from the liquid to the glass. Here, we combine infrared spectroscopy (IR) measurements of the hydrogen (H) bond stretching vibration of water with molecular dynamics simulations and employ a quantitative analysis to extract the inter-molecular H-bond length in a wide temperature range of the liquid. The extracted expansivity of this H-bond differs strongly from that of the average nearest neighbor distance of oxygen atoms obtained through a common conversion of mass density. However, both properties can be connected through a simple model based on a random loose packing of spheres with a variable coordination number, which demonstrates the relevance of supra-molecular arrangement. Furthermore, the exclusion of the expansivity of the inter-molecular H-bonds reveals that the most compact molecular arrangement is formed in the range of ∼316-331K (i.e., above the density maximum) close to the temperature of several pressure-related anomalies, which indicates a characteristic point in the supra-molecular arrangement. These results confirm our earlier approach to deduce inter-molecular H-bond lengths via IR in polyalcohols [Gabriel et al. J. Chem. Phys. 154, 024503 (2021)] quantitatively and open a new alley to investigate the role of inter-molecular expansion as a precursor of molecular fluctuations on a bond-specific level.

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in which a fraction (1-f_{R}) of the particles can perform pairwise exchange or "swap moves," while a fraction f_{P} of the particles can move only along restricted directions. We find that (i) the location of the glass transition varies greatly but smoothly as f_{P} and f_{R} change and (ii) it is governed by a linear combination of f_{P} and f_{R}. (iii) Dynamical heterogeneities (DHs) are not governed by the static structure of the material; their magnitude correlates instead with the relaxation time. (iv) We show that a recent theory for temporal growth of DHs based on thermal avalanches holds quantitatively throughout the (f_{R},f_{P}) diagram. These observations are negative items for some existing theories of the glass transition, particularly those reliant on growing thermodynamic order or locally favored structure, and open new avenues to test other approaches, as we illustrate.

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel-Fulcher-Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

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

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

Unraveling the dynamic slowdown in supercooled water: The role of dynamic disorder in jump motions

When a liquid is rapidly cooled below its melting point without inducing crystallization, its dynamics slow down significantly without noticeable structural changes. Elucidating the origin of this slowdown has been a long-standing challenge. Here, we report a theoretical investigation into the mechanism of the dynamic slowdown in supercooled water, a ubiquitous yet extraordinary substance characterized by various anomalous properties arising from local density fluctuations. Using molecular dynamics simulations, we found that the jump dynamics, which are elementary structural change processes, deviate from Poisson statistics with decreasing temperature. This deviation is attributed to slow variables competing with the jump motions, i.e., dynamic disorder. The present analysis of the dynamic disorder showed that the primary slow variable is the displacement of the fourth nearest oxygen atom of a jumping molecule, which occurs in an environment created by the fluctuations of molecules outside the first hydration shell. As the temperature decreases, the jump dynamics become slow and intermittent. These intermittent dynamics are attributed to the prolonged trapping of jumping molecules within extended and stable low-density domains. As the temperature continues to decrease, the number of slow variables increases due to the increased cooperative motions. Consequently, the jump dynamics proceed in a higher-dimensional space consisting of multiple slow variables, becoming slower and more intermittent. It is then conceivable that with further decreasing temperature, the slowing and intermittency of the jump dynamics intensify, eventually culminating in a glass transition.

Protecting Proteins from Desiccation Stress Using Molecular Glasses and Gels

Faced with desiccation stress, many organisms deploy strategies to maintain the integrity of their cellular components. Amorphous glassy media composed of small molecular solutes or protein gels present general strategies for protecting against drying. We review these strategies and the proposed molecular mechanisms to explain protein protection in a vitreous matrix under conditions of low hydration. We also describe efforts to exploit similar strategies in technological applications for protecting proteins in dry or highly desiccated states. Finally, we outline open questions and possibilities for future explorations.

Metastability of Protein Solution Structures in the Absence of a Solvent: Rugged Energy Landscape and Glass-like Behavior

Native ion mobility/mass spectrometry is well-poised to structurally screen proteomes but characterizes protein structures in the absence of a solvent. This raises long-standing unanswered questions about the biological significance of protein structures identified through ion mobility/mass spectrometry. Using newly developed computational and experimental ion mobility/ion mobility/mass spectrometry methods, we investigate the unfolding of the protein ubiquitin in a solvent-free environment. Our data suggest that the folded, solvent-free ubiquitin observed by ion mobility/mass spectrometry exists in a largely native fold with an intact β-grasp motif and α-helix. The ensemble of folded, solvent-free ubiquitin ions can be partitioned into kinetically stable subpopulations that appear to correspond to the structural heterogeneity of ubiquitin in solution. Time-resolved ion mobility/ion mobility/mass spectrometry measurements show that folded, solvent-free ubiquitin exhibits a strongly stretched-exponential time dependence, which simulations trace to a rugged energy landscape with kinetic traps. Unfolding rate constants are estimated to be approximately 800 to 20,000 times smaller than in the presence of water, effectively quenching the unfolding process on the time scale of typical ion mobility/mass spectrometry measurements. Our proposed unfolding pathway of solvent-free ubiquitin shares substantial characteristics with that established for the presence of solvent, including a polarized transition state with significant native content in the N-terminal β-hairpin and α-helix. Our experimental and computational data suggest that (1) the energy landscape governing the motions of folded, solvent-free proteins is rugged in analogy to that of glassy systems; (2) large-scale protein motions may at least partially be determined by the amino acid sequence of a polypeptide chain; and (3) solvent facilitates, rather than controls, protein motions.

Glass transition of quantum hard spheres in high dimensions

We study the equilibrium thermodynamics of quantum hard spheres in the infinite-dimensional limit, determining the boundary between liquid and glass phases in the temperature-density plane by means of the Franz-Parisi potential. We find that as the temperature decreases from high values, the effective radius of the spheres is enhanced by a multiple of the thermal de Broglie wavelength, thus increasing the effective filling fraction and decreasing the critical density for the glass phase. Numerical calculations show that the critical density continues to decrease monotonically as the temperature decreases further, suggesting that the system will form a glass at sufficiently low temperatures for any density. The methods used in this paper can be extended to more general potentials, and also to other transitions such as the Kauzman/Replica Symmetry Breaking (RSB) transition, the Gardner transition, and potentially even jamming.

Determinants of viscoelasticity and flow activation energy in biomolecular condensates

The form and function of biomolecular condensates are intimately linked to their material properties. Here, we integrate microrheology with molecular simulations to dissect the physical determinants of condensate fluid phase dynamics. By quantifying the timescales and energetics of network relaxation in a series of heterotypic viscoelastic condensates, we uncover distinctive roles of sticker motifs, binding energy, and chain length in dictating condensate dynamical properties. We find that the mechanical relaxation times of condensate-spanning networks are determined by both intermolecular interactions and chain length. We demonstrate, however, that the energy barrier for network reconfiguration, termed flow activation energy, is independent of chain length and only varies with the strengths of intermolecular interactions. Biomolecular diffusion in the dense phase depends on a complex interplay between viscoelasticity and flow activation energy. Our results illuminate distinctive roles of chain length and sequence-specific multivalent interactions underlying the complex material and transport properties of biomolecular condensates.

Solid-that-Flows Picture of Glass-Forming Liquids

This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.

Understanding the glassy dynamics from melting temperatures in binary glass-forming liquids

It is natural to expect that small particles in binary mixtures move faster than large ones. However, in binary glass-forming liquids with soft-core particle interactions, we observe the counterintuitive dynamic reversal between large and small particles along with the increase of pressure by performing molecular dynamics simulations. The structural relaxation (dynamic heterogeneity) of small particles is faster (weaker) than large ones at low pressures, but becomes slower (stronger) above a crossover pressure. In contrast, this dynamic reversal never happens in glass-forming liquids with hard-core interactions. We find that the difference of the effective melting temperatures felt by large and small particles can be used to understand the dynamic reversal. In binary mixtures, we derive effective melting temperatures of large and small particles simply from the conversion of units and find that particles with a higher effective melting temperature usually undergo a slower and more heterogeneous relaxation. The presence (absence) of the dynamic reversal in soft-core (hard-core) systems is simply due to the non-monotonic (monotonic) behavior of the melting temperature as a function of pressure. Interestingly, by manipulating the relative softness between large and small particles, we obtain a special case of soft-core systems, in which large particles always have higher effective melting temperatures than small ones. As a result, the dynamic reversal is totally eliminated. Our work provides another piece of evidence of the underlying connections between the properties of non-equilibrium glass-formers and equilibrium crystal-formers.

Highly stable petroleum pitches provide access to the deep glassy state

Differential scanning calorimetry (DSC) was used to study the fast aging behavior of two petroleum pitch materials despite being only three to five years old. We observe that these highly aromatic pitches with broad distributions of both molecular weight and aromaticity exhibit large enthalpic relaxation endotherms in initial DSC heating scans, and 20-32 °C reductions in the fictive temperature and 0.35-0.87 of θK, which are indicative of aged glasses similar to ultrastable glasses and 20 MA aged amber. Quantifying the degree of thermodynamic stability relative to the Kauzmann temperature vs. the aging time demonstrates that these materials age just as quickly as low fragility metallic glasses. Additionally, we observe that pitches age faster than polymers reported in the literature when compared using down-jump experiments. We hypothesize that the fraction of higher aromaticity of pitch molecules plays a crucial role in faster dynamics. The unique aging behavior and the ability to produce pitches in bulk quantities using pilot-scale equipment, while being possible to tailor their molecular composition, make them a useful material for studying complex aging dynamics in the deep glassy state.

Different glassy characteristics are related to either caging or dynamical heterogeneity

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

Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies

The formation of the nematic to twist-bend nematic (NTB) phase has emerged as a fascinating phenomenon in the field of supramolecular chemistry, based on complex intermolecular interactions. Through a careful analysis of molecular structures and dynamics, we elucidate how these intermolecular interactions drive the complex twist-bend modulation observed in the NTB. The study employs broadband dielectric spectroscopy spanning frequencies from 10 to 2 × 109 Hz to investigate the molecular orientational dynamics within the glass-forming thioether-linked cyanobiphenyl liquid crystal dimers, namely, CBSC7SCB and CBSC7OCB. The experimental findings align with theoretical expectations, revealing the presence of two distinct relaxation processes contributing to the dielectric permittivity of these dimers. The low-frequency relaxation mode is attributed to an "end-over-end rotation" of the dipolar groups parallel to the director. The high-frequency relaxation mode is associated with precessional motions of the dipolar groups about the director. Various models are employed to describe the temperature-dependent behavior of the relaxation times for both modes. Particularly, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics in accordance with findings from infrared (IR) spectroscopy. Here, as the longitudinal correlations of dipoles intensify, the m1 mode experiences a sudden upsurge in enthalpy, while the m2 mode undergoes continuous changes, displaying critical mode coupling behavior. Interestingly, both types of molecular motion exhibit a strong cooperative interplay within the lower temperature range of the NTB phase, evolving in tandem as the material's temperature approaches the glass transition point. Consequently, both molecular motions converge to determine the glassy dynamics, characterized by a shared glass transition temperature, Tg.

Replica symmetry broken states of some glass models

We have studied in detail the M-p balanced spin-glass model, especially the case p=4. These types of model have relevance to structural glasses. The models possess two kinds of broken replica states; those with one-step replica symmetry breaking (1RSB) and those with full replica symmetry breaking (FRSB). To determine which arises requires studying the Landau expansion to quintic order. There are nine quintic-order coefficients, and five quartic-order coefficients, whose values we determine for this model. We show that it is only for 2≤M<2.4714⋯ that the transition at mean-field level is to a state with FRSB, while for larger M values there is either a continuous transition to a state with 1RSB (when M≤3) or a discontinuous transition for M>3. The Gardner transition from a 1RSB state at low temperatures to a state with FRSB also requires the Landau expansion to be taken to quintic order. Our result for the form of FRSB in the Gardner phase is similar to that found when 2≤M<2.4714⋯, but differs from that given in the early paper of Gross et al. [Phys. Rev. Lett. 55, 304 (1985)0031-900710.1103/PhysRevLett.55.304]. Finally we discuss the effects of fluctuations on our mean-field solutions using the scheme of Höller and Read [Phys. Rev. E 101, 042114 (2020)2470-004510.1103/PhysRevE.101.042114] and argue that such fluctuations will remove both the continuous 1RSB transition and discontinuous 1RSB transitions when 8>d≥6 leaving just the FRSB continuous transition. We suggest values for M and p which might be used in simulations to confirm whether fluctuation corrections do indeed remove the 1RSB transitions.

Strain-Controlled Critical Slowing Down in the Rheology of Disordered Networks

Networks and dense suspensions frequently reside near a boundary between soft (or fluidlike) and rigid (or solidlike) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.

A geometry-enhanced graph neural network for learning the smoothness of glassy dynamics from static structure

Modeling the dynamics of glassy systems has been challenging in physics for several decades. Recent studies have shown the efficacy of Graph Neural Networks (GNNs) in capturing particle dynamics from the graph structure of glassy systems. However, current GNN methods do not take the dynamic patterns established by neighboring particles explicitly into account. In contrast to these approaches, this paper introduces a novel dynamical parameter termed "smoothness" based on the theory of graph signal processing, which explores the dynamic patterns from a graph perspective. Present graph-based approaches encode structural features without considering smoothness constraints, leading to a weakened correlation between structure and dynamics, particularly on short timescales. To address this limitation, we propose a Geometry-enhanced Graph Neural Network (Geo-GNN) to learn the smoothness of dynamics. Results demonstrate that our method outperforms state-of-the-art baselines in predicting glassy dynamics. Ablation studies validate the effectiveness of each proposed component in capturing smoothness within dynamics. These findings contribute to a deeper understanding of the interplay between glassy dynamics and static structure.

Spatiotemporal observation of quantum crystallization of electrons

Liquids crystallize as they cool; however, when crystallization is avoided in some way, they supercool, maintaining their liquidity, and freezing into glass at low temperatures, as ubiquitously observed. These metastable states crystallize over time through the classical dynamics of nucleation and growth. However, it was recently found that Coulomb interacting electrons on charge-frustrated triangular lattices exhibit supercooled liquid and glass with quantum nature and they crystallize, raising fundamental issues: what features are universal to crystallization at large and specific to that of quantum systems? Here, we report our experimental challenges that address this issue through the spatiotemporal observation of electronic crystallization in an organic material. With Raman microspectroscopy, we have successfully performed real-space and real-time imaging of electronic crystallization. The results directly capture strongly temperature-dependent crystallization profiles indicating that nucleation and growth proceed at distinctive temperature-dependent rates, which is common to conventional crystallization. However, the growth rate is many orders of magnitude larger than that in the conventional case. The temperature characteristics of nucleation and growth are universal, whereas unusually fast growth kinetics features quantum crystallization where a quantum-to-classical catastrophe occurs in interacting electrons.

Depicting Defects in Metallic Glasses by Atomic Vibrational Entropy

Due to the chaotic structure of amorphous materials, it is challenging to identify defects in metallic glasses. Here we tackle this problem from a thermodynamic point of view using atomic vibrational entropy, which represents the inhomogeneity of atomic contributions to vibrational modes. We find that the atomic vibrational entropy is correlated to the vibrational mean-square displacement and polyhedral volume of atoms, revealing the critical role of vibrational entropy in bridging dynamics, thermodynamics, and structure. On this method, the local vibrational entropy obtained by coarse-graining the atomic vibrational entropy in space can distinguish more effectively between liquid-like and solid-like atoms in metallic glasses and establish the correlation between the local vibrational entropy and the structure of metallic glasses, offering a route to predict the plastic events from local vibrational entropy. The local vibration entropy is a good indicator of thermally activated and stress-driven plastic events, and its predictive ability is better than that of the structural indicators.

Dielectric Study of Liquid Crystal Dimers: Probing the Orientational Order and Molecular Interactions in Nematic and Twist-Bend Nematic Phases

Dielectric spectroscopy in frequencies that range from 10 Hz to 1 GHz has been used to study the molecular orientational dynamics of the two types of dimers that form the twist-bend nematic phase over a wide range of temperatures for both nematic and twist-bend nematic phases. The symmetrical and asymmetrical liquid crystal dimers with the cyanobiphenyl mesogenic groups were investigated. The results were analyzed within the framework of the molecular theory of dielectric permittivity for nematogens. The two molecular processes can be assigned to the reorientation of the monomeric unit: the high frequency one to the precessional rotation of the longitudinal components of the cyanobiphenyl groups (CN) and the second (low frequency) to the end-over-end rotation of the CN dipole around the short molecular axis. The precession mode, which is determined by the local order and is almost unaffected by the phase transition from the nematic to the twist-bend phase, while the end-over-end rotation clearly slowed down at the transition, as it is affected by the growth of the intermolecular interactions. The latter corresponds well to the fact revealed by IR spectroscopy about the longitudinal correlation of the molecular dipoles.

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.

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

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

Dynamic heterogeneity in polydisperse systems: A comparative study of the role of local structural order parameter and particle size

In polydisperse systems, describing the structure and any structural order parameter (SOP) is not trivial as it varies with the number of species we use to describe the system, M. Depending on the degree of polydispersity, there is an optimum value of M = M0 where we show that the mutual information of the system increases. However, surprisingly, the correlation between a recently proposed SOP and the dynamics is highest for M = 1. This effect increases with polydispersity. We find that the SOP at M = 1 is coupled with the particle size, σ, and this coupling increases with polydispersity and decreases with an increase in M. Careful analysis shows that at lower polydispersities, the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on σ. Since the coupling between the SOP and σ is higher for M = 1, it appears to be a better predictor of the dynamics. We also study the Vibrality, an order parameter independent of structural information. Compared to SOP, at high polydispersity, we find Vibrality to be a marginally better predictor of the dynamics. However, this high predictive power of Vibrality, which is not there at lower polydispersity, appears to be due to its stronger coupling with σ. Therefore, our study suggests that for systems with high polydispersity, the correlation of any order parameter and σ will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter.

Cooperative activated hopping dynamics in binary glass-forming liquids: effects of the size ratio, composition, and interparticle interactions

Slow dynamics in supercooled and glassy liquids is an important research topic in soft matter physics. Compared to the traditionally focused one-component systems, glassy dynamics in mixture systems adds in a rich set of new complexities, which are fundamentally interesting and also relevant for many technological applications. In this paper, we apply the recently developed self-consistent cooperative hopping theory (SCCHT) to systematically investigate the effects of the size ratio, composition and interparticle interactions on the cooperative activated hopping dynamics of matrix (in larger size) and penetrant (in smaller size) particles in varied binary sphere mixture model systems, with a specific focus on ultrahigh mixture packing fractions that mimic the deeply supercooled glass transition conditions for molecular/polymeric mixture materials. Analysis shows that in these high activation barrier cases, the long-range elastic distortion associated with a matrix particle hopping over its cage confinement always generates an elastic barrier of a nonnegligible magnitude, although the ratio between the elastic barrier and local barrier contribution is sensitively dependent on all three mixture-specific system factors considered in this work. SCCHT predicts two general scenarios of penetrant-matrix cooperative activated hopping dynamics: matrix/penetrant co-hopping (regime 1) or the penetrant mean barrier hopping time shorter than that of the matrix (regime 2). Increasing the penetrant-to-matrix size ratio or the penetrant-matrix cross-attraction strength is found to universally enlarge the composition window of regime 1. Diverse dynamical properties characterising different aspects of the cooperative activated hopping process, including the penetrant and matrix transient localization lengths, penetrant and matrix hopping jump distances, different types of local and elastic activated barriers, and matrix long-time diffusivity, relaxation time and dynamic fragility are quantitatively studied against a wide range of variations over the three system factors. Of particular interest is the universal "anti-plasticization" phenomenon achievable for sufficiently strong cross-attractive interactions. The prospects this work opens for the exploration of a wide variety of polymer-based mixture materials are briefly discussed at the end.

Pressure-induced nonmonotonic cross-over of steady relaxation dynamics in a metallic glass

Relaxation dynamics, as a key to understand glass formation and glassy properties, remains an elusive and challenging issue in condensed matter physics. In this work, in situ high-pressure synchrotron high-energy X-ray photon correlation spectroscopy has been developed to probe the atomic-scale relaxation dynamics of a cerium-based metallic glass during compression. Although the sample density continuously increases, the collective atomic motion initially slows down as generally expected and then counterintuitively accelerates with further compression (density increase), showing an unusual nonmonotonic pressure-induced steady relaxation dynamics cross-over at ~3 GPa. Furthermore, by combining in situ high-pressure synchrotron X-ray diffraction, the relaxation dynamics anomaly is evidenced to closely correlate with the dramatic changes in local atomic structures during compression, rather than monotonically scaling with either sample density or overall stress level. These findings could provide insight into relaxation dynamics and their relationship with local atomic structures of glasses.

Thickness Dependence of Segmental Dynamics in Free-Standing Thin Films Predicted by a Dynamically Correlated Network Model

The anomalous dynamics and glass transition behaviors of supercooled liquids under nanoconfinement, such as ultrathin polymer films, have attracted much attention in recent decades. However, a complete elucidation of this mechanism has not yet been achieved. For the dynamics of bulk materials without confinement, we previously proposed a dynamically correlated network (DCN) model, which was found to agree well with the experimental data. The model assumes that segments with thermal fluctuations are dynamically correlated to their neighbors to form string-like clusters, which eventually grow into networks as temperature decreases. In this study, we applied the DCN model to nanoconfined free-standing films by using a simple cubic lattice sandwiched between two free surface layers consisting of virtual "uncorrelated" segments. The average size of DCNs at lower temperatures decreased with decreasing thickness because of confinement. This trend was associated with a decrease in the percolation temperature at which the size of DCN diverges. It was also revealed that the fractal dimension of the generated DCNs exhibits a peak with respect to temperature. The segmental relaxation time for free-standing polystyrene films was evaluated, and the predicted thickness dependence of the glass transition temperature qualitatively agreed with the experimental data. The results suggest that the concept of DCN is compatible with the dynamics of free-standing thin films.

Dynamic Heterogeneity and Kovacs' Memory Effects in Supercooled Water

Understanding the properties of supercooled water is important for developing a comprehensive theory for liquid water and amorphous ices. Because of rapid crystallization for deeply supercooled water, experiments on it are typically carried out under conditions in which the temperature and/or pressure are rapidly changing. As a result, information on the structural relaxation kinetics of supercooled water as it approaches (metastable) equilibrium is useful for interpreting results obtained in this experimentally challenging region of phase space. We used infrared spectroscopy and the fast time resolution obtained by transiently heating nanoscale water films to investigate relaxation kinetics (aging) in supercooled water. When the structural relaxation of the water films was followed using a temperature jump protocol analogous to the classic experiments of Kovacs, similar memory effects were observed. In particular, after suitable aging at one temperature, water's structure displayed an extremum versus the number of heat pulses upon changing to a second temperature before eventually relaxing to a steady-state structure characteristic of that temperature. A random double well model based on the idea of dynamic heterogeneity in supercooled water accounts for the observations.

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

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

Difference in "Supercooling" Affinity between (Acetamide + Na/KSCN) Deep Eutectics: Reflections in the Simulated Anomalous Motions of the Constituents and Solution Microheterogeneity Features

Deep depression of freezing points of ionic amide deep eutectic solvents (DESs) is known to exhibit a significant dependence on the identity of ions present in those systems and the nature of the functional group attached to the host amide. This deep depression of the freezing point is sometimes termed as "supercooling". For (acetamide + electrolyte) DESs, experiments have revealed signatures of ion-dependent spatiotemporal heterogeneity features. The focus of this work is to provide microscopic explanations of these experimentally observed macroscopic system properties in terms of particle jumps and insights about the origin of the cation dependence. For this purpose, extensive molecular dynamics simulations have been performed employing (acetamide + Na/KSCN) deep eutectics as representative ionic systems at 303, 318, 333, and 348 K. The individual translational motions of acetamide and the ions are followed, and their connections to solution heterogeneity are explored. The center-of-mass motion for Na⁺ has been found to be more anomalous than that for K⁺. This difference corroborates well with experimental reports on heterogeneous relaxations in these systems. Simulated viscosity coefficients and dynamic heterogeneity features also reflect this difference. Moreover, simulated reorientational relaxations of acetamide molecules in these ionic DESs suggest that a Na⁺-containing DES is more heterogeneous than the corresponding K⁺-containing system. Estimated void and neck distributions for acetamide molecules differ as the alkali metal ions differ. In brief, this study provides a detailed microscopic view of the cation dependence of the microheterogeneous relaxation dynamics of these DESs reported repeatedly by different experiments.

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.

An Ising Model for Supercooled Liquids and the Glass Transition

We describe the behavior of an Ising model with orthogonal dynamics, where changes in energy and changes in alignment never occur during the same Monte Carlo (MC) step. This orthogonal Ising model (OIM) allows conservation of energy and conservation of (angular) momentum to proceed independently, on their own preferred time scales. The OIM also includes a third type of MC step that makes or breaks the interaction between neighboring spins, facilitating an equilibrium distribution of bond energies. MC simulations of the OIM mimic more than twenty distinctive characteristics that are commonly found above and below the glass temperature, Tg. Examples include a specific heat that has hysteresis around Tg, out-of-phase (loss) response that exhibits primary (α) and secondary (β) peaks, super-Arrhenius T dependence for the α-response time (τα), and fragilities that increase with increasing system size (N). Mean-field theory for energy fluctuations in the OIM yields a critical temperature (Tc) and a novel expression for the super-Arrhenius divergence as T→Tc: ln(τα)~1/(1−Tc/T)2. Because this divergence is reminiscent of the Vogel-Fulcher-Tammann (VFT) law squared, we call it the “VFT2 law”. A modified Stickel plot, which linearizes the VFT2 law, shows that at high T where mean-field theory should apply, only the VFT2 law gives qualitatively consistent agreement with measurements of τα (from the literature) on five glass-forming liquids. Such agreement with the OIM suggests that several basic features govern supercooled liquids. The freezing of a liquid into a glass involves an underlying 2nd-order transition that is broadened by finite-size effects. The VFT2 law for τα comes from energy fluctuations that enhance the pathways through an entropy bottleneck, not activation over an energy barrier. Values of τα vary exponentially with inverse N, consistent with the distribution of relaxation times deduced from measurements of α response. System sizes found via the T dependence of τα from simulations and measurements are similar to sizes of independently relaxing regions (IRR) measured by nuclear magnetic resonance (NMR) for simple-molecule glass-forming liquids. The OIM elucidates the key ingredients needed to interpret the thermal and dynamic properties of amorphous materials, while providing a broad foundation for more-detailed models of liquid-glass behavior.

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.

Tethered hard spheres: A bridge between the fluid and solid phases

The thermodynamics of hard spheres tethered to a Face-Centered Cubic (FCC) lattice is investigated using event-driven molecular-dynamics. The particle-particle and the particle-tether collision rates are related to the phase space geometry and are used to study the FCC and fluid states. In tethered systems, the entropy can be determined by at least two routes: (i) through integration of the tether collision rates with the tether length $r_T$ or (ii) through integration of the particle-particle collision rates with the hard-sphere diameter $\sigma$ (or, equivalently, the density). If the entropy were an entirely analytic function of $r_T$ and $\sigma$, these two methods for calculating the entropy should lead to the same results; however, a non-analytic region exists as an extension of the solid-fluid phase transition of the untethered hard-sphere system, and integration paths that cross this region will lead to values for the entropy that depend on the particular path chosen. The difference between the calculated entropies appears to be related to the communal entropy, and the location of the non-analytic region appears to be related to conditions where the regions of phase space associated with the FCC configuration become separated from those associated with the disordered fluid. The non-analytic region is finite in extent, vanishing below $r_T/a\approx0.55$, where $a$ is the lattice spacing, and there are many continuous paths that connect the fluid and solid phases that can be used to determine the crystal free energy with respect to the fluid.

Disentangling the Calorimetric Glass-Transition Trace in Polymer/Oligomer Mixtures from the Modeling of Dielectric Relaxation and the Input of Small-Angle Neutron Scattering

We have disentangled the contributions to the glass transition as observed by differential scanning calorimetry (DSC) on simplified systems of industrial interest consisting of blends of styrene–butadiene rubber (SBR) and polystyrene (PS) oligomer. To do this, we have started from a model previously proposed to describe the effects of blending on the equilibrium dynamics of the α-relaxation as monitored by broadband dielectric spectroscopy (BDS). This model is based on the combination of self-concentration and thermally driven concentration fluctuations (TCFs). Considering the direct insight of small-angle neutron scattering on TCFs, blending effects on the α-relaxation can be fully accounted for by using only three free parameters: the self-concentration of the components φ_self^SBR and φ_self^PS) and the relevant length scale of segmental relaxation, 2R_c. Their values were determined from the analysis of the BDS results on these samples, being that obtained for 2R_c ≈ 25Å in the range usually reported for this magnitude in glass-forming systems. Using a similar approach, the distinct contributions to the DSC experiments were evaluated by imposing the dynamical information deduced from BDS and connecting the component segmental dynamics in the blend above the glass-transition temperature T_g (at equilibrium) and the way the equilibrium is lost when cooling toward the glassy state. This connection was made through the α-relaxation characteristic time of each component at T_g, τ_g. The agreement of such constructed curves with the experimental DSC results is excellent just assuming that τ_g is not affected by blending.

Equilibrium fluctuations in mean-field disordered models

Mean-field models of glasses that present a random first order transition exhibit highly nontrivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for all equilibrium conditions. By means of the replica method we evaluate Gaussian fluctuations of the overlaps around the thermodynamic limit, decomposing them in thermal fluctuations inside each state and heterogeneous fluctuations between different states. We first test and compare our analytical results with numerical simulation results for the p-spin spherical model and the random orthogonal model, and then analyze the random Lorentz gas. In all cases, a strong quantitative agreement is obtained. Our analysis thus provides a robust scheme for identifying the key finite-size (or finite-dimensional) corrections to the mean-field treatment of these paradigmatic glass models.

Annealing glasses by cyclic shear deformation

A major challenge in simulating glassy systems is the ability to generate configurations that may be found in equilibrium at sufficiently low temperatures, in order to probe static and dynamic behavior close to the glass transition. A variety of approaches have recently explored ways of surmounting this obstacle. Here, we explore the possibility of employing mechanical agitation, in the form of cyclic shear deformation, to generate low energy configurations in a model glass former. We perform shear deformation simulations over a range of temperatures, shear rates, and strain amplitudes. We find that shear deformation induces faster relaxation toward low energy configurations, or overaging, in simulations at sufficiently low temperatures, consistently with previous results for athermal shear. However, for temperatures at which simulations can be run until a steady state is reached with or without shear deformation, we find that the inclusion of shear deformation does not result in any speed up of the relaxation toward low energy configurations. Although we find the configurations from shear simulations to have properties indistinguishable from an equilibrium ensemble, the cyclic shear procedure does not guarantee that we generate an equilibrium ensemble at a desired temperature. In order to ensure equilibrium sampling, we develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial generation step and has acceptance probabilities that depend not only on the change in internal energy but also on the heat dissipated (equivalently, work done). We show that such an algorithm, indeed, generates an equilibrium ensemble.

A general structural order parameter for the amorphous solidification of a supercooled liquid

The persistent problem posed by the glass transition is to develop a general atomic level description of amorphous solidification. The answer proposed in this paper is to measure a configuration's capacity to restrain the motion of the constituent atoms. Here, we show that the instantaneous normal modes can be used to define a measure of atomic restraint that accounts for the difference between fragile and strong liquids and the collective length scale of the supercooled liquid. These results represent a significant simplification of the description of amorphous solidification and provide a powerful systematic treatment of the influence of microscopic factors on the formation of an amorphous solid.

First-principles study of the specific heat of glass at the glass transition with a case study on glycerol

The standard method to determine the transition temperature (T_g) of glasses is the jump in the specific heat,ΔCp. Despite its importance, standard theory for this jump is lacking. The difficulties include lack of proper treatment of the specific heat of liquids, hysteresis, and the timescale issue. The first part of this paper provides a non-empirical method for calculating the specific heat in the glass transition. The method consists of molecular dynamics (MD) simulations based on density-functional theory (DFT) and thermodynamics methods. Calculation of the total energy, which is the heart of DFT, is the most general method for obtaining specific heat for any state of matters. The influence of energy dissipation processes on specific heat is treated by adiabatic MD simulations. The problems of hysteresis and the timescale are alleviated by restricting the scope of calculations to equilibrium states only. The second part of this paper demonstrates the validity and usefulness of the methods by applying to the specific-heat jump of glycerol. By decomposingΔCpinto contributions of the structural, phonon, and thermal expansion energies, an appropriate interpretation for the specific-heat jump has been established: the major contribution toΔCpis the change in the structural energy. From this, a neat energy diagram about the glass transition is obtained. An outcome of this study is verification of the empirical relationship between the fragility and the specific-heat jump. These two quantities scale to the ratiok=Tg/ΔTg, whereΔTgis the width of the transition, through which the two quantities are interrelated.

Understanding the Fragile-to-Strong Transition in Silica from Microscopic Dynamics

In this work, we revisit the fragile-to-strong transition (FTS) in the simulated BKS silica from the perspective of microscopic dynamics in an effort to elucidate the dynamical behaviors of fragile and strong glass-forming liquids. Softness, which is a machine-learned feature from local atomic structures, is used to predict the microscopic activation energetics and long-term dynamics. The FTS is found to originate from a change in the temperature dependence of the microscopic activation energetics. Furthermore, results suggest there are two diffusion channels with different energy barriers in BKS silica. The fast dynamics at high temperatures is dominated by the channel with small energy barriers (<∼1  eV), which is controlled by the short-range order. The rapid closing of this diffusion channel when lowering temperature leads to the fragile behavior. On the other hand, the slow dynamics at low temperatures is dominated by the channel with large energy barriers controlled by the medium-range order. This slow diffusion channel changes only subtly with temperature, leading to the strong behavior. The distributions of barriers in the two channels show different temperature dependences, causing a crossover at ∼3100  K. This transition temperature in microscopic dynamics is consistent with the inflection point in the configurational entropy, suggesting there is a fundamental correlation between microscopic dynamics and thermodynamics.

Structural origin of excitations in a colloidal glass-former

Despite decades of intense research, whether the transformation of supercooled liquids into glass is a kinetic phenomenon or a thermodynamic phase transition remains unknown. Here, we analyzed optical microscopy experiments on 2D binary colloidal glass-forming liquids and investigated the structural links of a prominent kinetic theory of glass transition. We examined a possible structural origin for localized excitations, which are building blocks of the dynamical facilitation theory—a purely kinetic approach for the glass transition. To accomplish this, we utilize machine learning methods to identify a structural order parameter termed “softness” that has been found to be correlated with reorganization events in supercooled liquids. Both excitations and softness qualitatively capture the dynamical slowdown on approaching the glass transition and motivated us to explore spatial and temporal correlations between them. Our results show that excitations predominantly occur in regions with high softness and the appearance of these high softness regions precedes excitations, thus suggesting a causal connection between them. Thus, unifying dynamical and thermodynamical theories into a single structure-based framework may provide a route to understand the glass transition.

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.

An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids

We propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function that is local in time and is similar in spirit to the equation of motion for the average non-uniform density profile derived within the dynamic density functional theory. We identify the Franz-Parisi free energy functional as the non-equilibrium free energy for the evolution of the density correlation function. An appearance of a local minimum of this functional leads to a dynamic arrest. Thus, the ergodicity breaking transition predicted by our theory coincides with the dynamic transition of the static approach based on the same non-equilibrium free energy functional.

Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope

We propose and numerically implement a local probe of the static self-induced heterogeneity characterizing glass-forming liquids. This method relies on the equilibrium statistics of the overlap between pairs of configurations measured in mesoscopic cavities with unconstrained boundaries. By systematically changing the location of the probed cavity, we directly detect spatial variations of the overlap fluctuations. We provide a detailed analysis of the statistics of a local estimate of the configurational entropy, and we infer an estimate of the surface tension between amorphous states, ingredients that are both at the basis of the random first-order transition theory of glass formation. Our results represent the first direct attempt to visualize and quantify the self-induced heterogeneity underpinning the thermodynamics of glass formation. They pave the way for the development of coarse-grained effective theories and for a direct assessment of the role of thermodynamics in the activated dynamics of deeply supercooled liquids.

Mean-field description for the architecture of low-energy excitations in glasses

In amorphous materials, groups of particles can rearrange locally into a new stable configuration. Such elementary excitations are key as they determine the response to external stresses, as well as to thermal and quantum fluctuations. Yet, understanding what controls their geometry remains a challenge. Here we build a scaling description of the geometry and energy of low-energy excitations in terms of the distance to an instability, as predicted, for instance, at the dynamical transition in mean-field approaches of supercooled liquids. We successfully test our predictions in ultrastable computer glasses, with a gapped spectrum and an ungapped (regular) spectrum. Overall, our approach explains why excitations become less extended, with a higher energy and displacement scale upon cooling.