Crossovers in the dynamics of supercooled liquids probed by an amorphous wall

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.

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.

Mixed equilibrium/nonequilibrium effects govern surface mobility in polymer glasses

Using angle-resolved X-ray photoelectron spectroscopy, sum-frequency generation vibrational spectroscopy, contact angle measurements, and molecular dynamics simulations, we verify that the glass transition temperature (Tg) of polymer glass is lower near the free surface. However, the experimental Tg-gradients showed a linear variation with depth (z) from the free surface, while the simulated equilibrium Tg-gradients exhibited a double exponential z-dependence. In typical simulations, Tg is determined based on the relaxation time of the system reaching a prescribed threshold value at equilibrium. Conversely, the experiments determined Tg by observing the unfreezing of molecular mobility during heating from a kinetically arrested, nonequilibrium glassy state. To investigate the impact of nonequilibrium effects on the Tg-gradient, we reduced the thermal annealing time in simulations, allowing the system to fall out of equilibrium. We observe a decrease in the relaxation time and the emergence of a modified z-dependence consistent with a linear Tg-gradient near the free surface. We further validate the impact of nonequilibrium effects by studying the dependence of the Tg on the heating/cooling rate for polymer films of varying thickness (h). Our experimental results reveal significant variations in the Tg-heating/cooling rate dependence with h below the bulk Tg, which are also observed in simulation when the simulated system is not equilibrated. We explain our findings by the reduction in mass density within the inner region of the system under nonequilibrium conditions, as observed in simulation, and recent research indicating a decrease in the local Tg of a polymer when placed next to a softer material.

Effect of the nature of the solid substrate on spatially heterogeneous activated dynamics in glass forming supported films

We extend the force-level elastically collective nonlinear Langevin equation theory to treat the spatial gradients of the alpha relaxation time and glass transition temperature, and the corresponding film-averaged quantities, to the geometrically asymmetric case of finite thickness supported films with variable fluid-substrate coupling. The latter typically nonuniversally slows down motion near the solid-liquid interface as modeled via modification of the surface dynamic free energy caging constraints that are spatially transferred into the film and which compete with the accelerated relaxation gradient induced by the vapor interface. Quantitative applications to the foundational hard sphere fluid and a polymer melt are presented. The strength of the effective fluid-substrate coupling has very large consequences for the dynamical gradients and film-averaged quantities in a film thickness and thermodynamic state dependent manner. The interference of the dynamical gradients of opposite nature emanating from the vapor and solid interfaces is determined, including the conditions for the disappearance of a bulk-like region in the film center. The relative importance of surface-induced modification of local caging vs the generic truncation of the long range collective elastic component of the activation barrier is studied. The conditions for the accuracy and failure of a simple superposition approximation for dynamical gradients in thin films are also determined. The emergence of near substrate dead layers, large gradient effects on film-averaged response functions, and a weak non-monotonic evolution of dynamic gradients in thick and cold films are briefly discussed. The connection of our theoretical results to simulations and experiments is briefly discussed, as is the extension to treat more complex glass-forming systems under nanoconfinement.

Understanding creep suppression mechanisms in polymer nanocomposites through machine learning

While recent efforts have shown how local structure plays an essential role in the dynamic heterogeneity of homogeneous glass-forming materials, systems containing interfaces such as thin films or composite materials remain poorly understood. It is known that interfaces perturb the molecular packing nearby, however, numerous studies show the dynamics are modified over a much larger range. Here, we examine the dynamics in polymer nanocomposites (PNCs) using a combination of simulations and experiments and quantitatively separate the role of polymer packing from other effects on the dynamics, as a function of distance from the nanoparticle surfaces. After showing good qualitative agreement between the simulations and experiments in glassy structure and creep compliance, we use a machine-learned structure indicator, softness, to decompose polymer dynamics in our simulated PNCs into structure-dependent and structure-independent processes. With this decomposition, the free energy barrier for polymer rearrangement can be described as a combination of packing-dependent and packing-independent barriers. We find both barriers are higher near nanoparticles and decrease with applied stress, quantitatively demonstrating that the slow interfacial dynamics is not solely due to polymer packing differences, but also the change of structure-dynamics relationships. Finally, we present how this decomposition can be used to accurately predict strain-time creep curves for PNCs from their static configuration, providing additional insights into the effects of polymer-nanoparticle interfaces on creep suppression in PNCs.

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.

Nonmonotonic Dynamical Correlations beneath the Surface of Glass-Forming Liquids

Collective motion over increasing length scales is a signature of the vitrification process of liquids. We demonstrate how distinct static and dynamic length scales govern the dynamics of vitrifying films. In contrast to a monotonically growing static correlation length, the dynamical correlation length that measures the extent of surface-dynamics acceleration into the bulk displays a striking nonmonotonic temperature evolution that is robust also against changes in detailed interatomic interaction. This nonmonotonic change defines a crossover temperature T_{*} that is distinct from the critical temperature T_{c} of mode-coupling theory. We connect this nonmonotonic change to a morphological change of cooperative rearrangement regions of fast particles, and to the point where the decoupling of fast-particle motion from the bulk relaxation is most sensitive to fluctuations. We propose a rigorous definition of this new crossover temperature T_{*} within a recent extension of mode-coupling theory, the stochastic β-relaxation theory.

A β-NMR study of the depth, temperature, and molecular-weight dependence of secondary dynamics in polystyrene: Entropy–enthalpy compensation and dynamic gradients near the free surface

We investigated the depth, temperature, and molecular-weight (MW) dependence of the γ-relaxation in polystyrene glasses using implanted 8Li+ and β-detected nuclear magnetic resonance. Measurements were performed on thin films with MW ranging from 1.1 to 641 kg/mol. The temperature dependence of the average 8Li spin–lattice relaxation time [Formula: see text] was measured near the free surface and in the bulk. Spin–lattice relaxation is caused by phenyl ring flips, which involve transitions between local minima over free-energy barriers with enthalpic and entropic contributions. We used transition state theory to model the temperature dependence of the γ-relaxation, and hence [Formula: see text]. There is no clear correlation of the average entropy of activation [Formula: see text] and enthalpy of activation [Formula: see text] with MW, but there is a clear correlation between [Formula: see text] and [Formula: see text], i.e., entropy–enthalpy compensation. This results in the average Gibbs energy of activation, [Formula: see text], being approximately independent of MW. Measurements of the temperature dependence of [Formula: see text] as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to [Formula: see text] = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in [Formula: see text] near the free surface being lower than the bulk. Combining these observations results in a model where the average fluctuation rate of the γ-relaxation has a “double-exponential” depth dependence. This model can explain the depth dependence of [Formula: see text] in polystyrene films. The characteristic length of enhanced dynamics is ∼6 nm and approximately independent of MW near room temperature.

Confinement Effects on the Spatially Inhomogeneous Dynamics in Metallic Glass Films

This work develops the elastically collective nonlinear Langevin equation theory to investigate, for the first time, the glassy dynamics in capped metallic glass thin films. Finite-size effects on the spatial gradient of structural relaxation time and glass transition temperature (T_g) are calculated at different temperatures and vitrification criteria. Molecular dynamics is significantly slowed down near rough solid surfaces, and the dynamics at location far from the interfaces is sped up. In thick films, the mobility gradient normalized by the bulk value obeys the double-exponential form since interference effects between two surfaces are weak. Reducing the film thickness induces a strong dynamic coupling between two surfaces and flattens the relaxation gradient. The normalized gradient of the glass transition temperature is independent of vitrification time scale criterion and can be fitted by a superposition function as the films are not ultrathin. The local fragility is found to remain unchanged with location. This finding suggests that one can use Angell plots of bulk relaxation time and the T_g spatial gradient to characterize glassy dynamics in metallic glass films. Our computational results agree well with experimental data and simulation.

Super-Arrhenius diffusion in a binary colloidal mixture at low volume fraction: an effect of depletion interaction due to an asymmetric barrier

We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observed in the high density systems where the transient cages are present due to dense packing, e.g., supercooled liquids, jammed systems, diffusion through porous membranes, dynamics within the cellular environment, etc. This model can be applied to study the molecular transport across cell membranes, nano-, and micro-channels which are characterized by spatially asymmetric potentials.

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.

Dynamic phase transitions in freestanding polymer thin films

After more than two decades of study, many fundamental questions remain unanswered about the dynamics of glass-forming materials confined to thin films. Experiments and simulations indicate that free interfaces enhance dynamics over length scales larger than molecular sizes, and this effect strengthens at lower temperatures. The nature of the influence of interfaces, however, remains a point of significant debate. In this work, we explore the properties of the nonequilibrium phase transition in dynamics that occurs in trajectory space between high- and low-mobility basins in a set of model polymer freestanding films. In thick films, the film-averaged mobility transition is broader than the bulk mobility transition, while in thin films it is a variant of the bulk result shifted toward a higher bias. Plotting this transition's local coexistence points against the distance from the films' surface shows thick films have surface and film-center transitions, while thin films practically have a single transition throughout the film. These observations are reminiscent of thermodynamic capillary condensation of a vapor-liquid phase between parallel plates, suggesting they constitute a demonstration of such an effect in a trajectory phase transition in the dynamics of a structural glass former. Moreover, this transition bears similarities to several experiments exhibiting anomalous behavior in the glass transition upon reducing film thickness below a material-dependent onset, including the broadening of the glass transition and the homogenization of surface and bulk glass transition temperatures.

Theory of Spatial Gradients of Relaxation, Vitrification Temperature and Fragility of Glass-Forming Polymer Liquids Near Solid Substrates

We employ a new force-level statistical mechanical theory to predict spatial gradients of the structural relaxation time and T_g of polymer liquids near microscopically rough and smooth hard surfaces and contrast the results with vapor interface systems. Repulsive rough (smooth) surfaces induce large slowing down (modest speeding up) of the relaxation time compared to the bulk. Nevertheless, a remarkable degree of universality of distinctive dynamical behaviors is predicted for different polymer chemistries and all interfaces, including a double exponential form of the alpha time gradient, power law decoupling of the relaxation time from its bulk value with exponential spatial variation of the exponent, exponential spatial gradient of T_g, weak dependence of normalized T_g gradients on vitrification criterion, and near linear growth with cooling of the slowed down layer thickness near a rough hard interface. The results appear consistent with simulations and experiments, and multiple testable predictions are made.

Continuous time random walk concepts applied to extended mode coupling theory: a study of the Stokes-Einstein breakdown

In an attempt to extend the mode coupling theory (MCT) to lower temperatures, some years back an Unified theory was proposed which within the MCT framework incorporated the activated dynamics via the random first order transition theory (RFOT). The theory successfully showed that there is hopping induced diffusive dynamics and the modified MCT coupled to the activated motion continues till low temperatures. Here we show that the theory although successful in describing other properties of supercooled liquids is unable to capture the Stokes-Einstein breakdown. We then show using continuous time random work (CTRW) formalism that the Unified theory is equivalent to a CTRW dynamics in presence of two waiting time distributions. It is known from earlier work on CTRW that in such cases the total dynamics is dominated by the fast motion. This explains the failure of the Unified theory in predicting the SE breakdown as both the structural relaxation and the diffusion process are described by the comparatively fast MCT like dynamics. The study also predicts that other forms of extended MCT with Markovian hopping kernel will face a similar issue. We next modify the Unified theory by applying the concept of renewal theory, usually used in CTRW models where the distribution has a long tail. According to this theory the first jump given by the persistent time is slower than the subsequent jumps given by the exchange time. We first show that for systems with two waiting time distributions even when both the distributions are exponential the persistent time is larger than the exchange time. We also identify the persistent time with the slower activated process. The extended Unified theory can now explain the SE breakdown. In this extended theory at low temperatures the structural relaxation is described by the activated dynamics whereas the diffusion is primarily determined by the MCT like dynamics leading to a decoupling between them. We also calculate a dynamic lengthscale from the wavenumber dependence of the relaxation time. We find that this dynamic length scale grows faster than the static length scale.

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.

Molecular Dynamics Simulation of the Capillary Leveling of a Glass-Forming Liquid

Motivated by recent experimental studies probing (i) the existence of a mobile layer at the free surface of glasses and (ii) the capillary leveling of polymer nanofilms, we study the evolution of square-wave patterns at the free surface of a generic glass-forming binary Lennard-Jones mixture over a wide temperature range, by means of molecular dynamics simulations. The pattern's amplitude is monitored, and the associated decay rate is extracted. The evolution of the latter as a function of temperature exhibits a crossover between two distinct behaviors, over a temperature range typically bounded by the glass-transition temperature and the mode-coupling critical temperature. Layer-resolved analysis of the film particles' mean-squared displacements further shows that diffusion at the surface is considerably faster than in the bulk, below the glass-transition temperature. The diffusion coefficient of the surface particles is larger than its bulk counterpart by a factor that reaches 10⁵ at the lowest temperature studied. This factor decreases upon heating, in agreement with recent experimental studies.

Theory of the spatial transfer of interface-nucleated changes of dynamical constraints and its consequences in glass-forming films

We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the dynamic free energy concept of the Nonlinear Langevin Equation (NLE) theory approach. The dynamic free energy at any mean location (cage center) involves contributions from two adjacent layers where confining forces are not the same. At the most fundamental level of the theory, the caging component of the dynamic free energy varies essentially exponentially with distance from the interface, saturating deep enough into the film with a correlation length of modest size and weak sensitivity to the thermodynamic state. This imparts a roughly exponential spatial variation of all the key features of the dynamic free energy required to compute gradients of dynamical quantities including the localization length, jump distance, cage barrier, collective elastic barrier, and alpha relaxation time. The spatial gradients are entirely of dynamical, not structural or thermodynamic, origin. The theory is implemented for the hard sphere fluid and diverse interfaces which can be a vapor, a rough pinned particle solid, a vibrating (softened) pinned particle solid, or a smooth hard wall. Their basic description at the level of the spatially heterogeneous dynamic free energy is identical, with the crucial difference arising from the first layer where dynamical constraints can be weakened, softened, or hardly changed depending on the specific interface. Numerical calculations establish the spatial dependence and fluid volume fraction sensitivity of the key dynamical property gradients for five different model interfaces. A comparison of the theoretical predictions for the dynamic localization length and glassy modulus with simulations and experiments for systems with a vapor interface reveals good agreement. The present advance sets the stage for using the Elastically Collective NLE theory to make quantitative predictions for the alpha relaxation time gradient, decoupling phenomena, T_g gradient, and many film-averaged properties of both model and experimental (colloids, molecules, and polymers) systems with diverse interfaces and chemical makeup.

Determination of onset temperature from the entropy for fragile to strong liquids

In this paper, we establish a connection between the onset temperature of glassy dynamics with the change in the entropy for a wide range of model systems. We identify the crossing temperature of pair and excess entropies as the onset temperature. Below the onset temperature, the residual multiparticle entropy, the difference between excess and pair entropies, becomes positive. The positive entropy can be viewed as equivalent to the larger phase space exploration of the system. The new method of onset temperature prediction from entropy is less ambiguous, as it does not depend on any fitting parameter like the existing methods.

Structural-dynamical transition in the Wahnström mixture

In trajectory space, dynamical heterogeneities in glass-forming liquids correspond to the emergence of a dynamical phase transition between an active phase poor in local structure and an inactive phase which is rich in local structure. We support this scenario with the study of a model additive mixture of Lennard-Jones particles, quantifying how the choice of the relevant structural and dynamical observable affects the transition in trajectory space. We find that the low mobility, structure-rich phase is dominated by icosahedral order. Applying a non-equilibrium rheological protocol, we connect local order to the emergence of mechanical rigidity.

Aging near rough and smooth boundaries in colloidal glasses

We use a confocal microscope to study the aging of a bidisperse colloidal glass near rough and smooth boundaries. Near smooth boundaries, the particles form layers, and particle motion is dramatically slower near the boundary as compared to the bulk. Near rough boundaries, the layers nearly vanish, and particle motion is nearly identical to that of the bulk. The gradient in dynamics near the boundaries is demonstrated to be a function of the gradient in structure for both types of boundaries. Our observations show that wall-induced layer structures strongly influence aging.

Disconnecting structure and dynamics in glassy thin films

Nanometrically thin glassy films depart strikingly from the behavior of their bulk counterparts. We investigate whether the dynamical differences between a bulk and thin film polymeric glass former can be understood by differences in local microscopic structure. Machine learning methods have shown that local structure can serve as the foundation for successful, predictive models of particle rearrangement dynamics in bulk systems. By contrast, in thin glassy films, we find that particles at the center of the film and those near the surface are structurally indistinguishable despite exhibiting very different dynamics. Next, we show that structure-independent processes, already present in bulk systems and demonstrably different from simple facilitated dynamics, are crucial for understanding glassy dynamics in thin films. Our analysis suggests a picture of glassy dynamics in which two dynamical processes coexist, with relative strengths that depend on the distance from an interface. One of these processes depends on local structure and is unchanged throughout most of the film, while the other is purely Arrhenius, does not depend on local structure, and is strongly enhanced near the free surface of a film.

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.

Point-to-set lengths, local structure, and glassiness

The growing sluggishness of glass-forming liquids is thought to be accompanied by growing structural order. The nature of such order, however, remains hotly debated. A decade ago, point-to-set (PTS) correlation lengths were proposed as measures of amorphous order in glass formers, but recent results raise doubts as to their generality. Here, we extend the definition of PTS correlations to agnostically capture any type of growing order in liquids, be it local or amorphous. This advance enables the formulation of a clear distinction between slowing down due to conventional critical ordering and that due to glassiness, and provides a unified framework to assess the relative importance of specific local order and generic amorphous order in glass formation.

Nonlinear dynamic response of glass-forming liquids to random pinning

We use large scale computer simulations of a glass-forming liquid in which a fraction c of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on c. This result can be rationalized by assuming that the configurational entropy of the pinned liquid decreases linearly upon increasing of c. This behavior is discussed in the context of thermodynamic theories for the glass transition, notably the Adam-Gibbs picture and the random first order transition theory. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing c, results which indicate that in glass-forming liquids there is a dynamic crossover at which the shape of the relaxing entities changes.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.