String model for the dynamics of glass-forming liquids

Stringlet excitation model of the boson peak

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density-density and hydrostatic pressure-pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. These results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

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.

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

We investigate a metallic glass-forming (GF) material (Al₉₀Sm₁₀) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, T_g. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the "hyperuniformity index" H of our liquid, which provides a quantitative measure of molecular "jamming". To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye-Waller parameter 〈u²〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u²〉 for heated crystalline Cu. This comparative analysis between H and 〈u²〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10^-3 as being analogous to the Lindemann criterion for both the melting of crystals and the "softening" of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.

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.

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.

Molecular basis of secondary relaxation in stiff-chain glassy polymers

Recent progress in establishing local order in polycarbonate-like glasses using rotational echo double resonance and centerband-only detection of exchange solid-state nuclear magnetic resonance (NMR) has stimulated a renewed attempt to connect molecular motion within glassy polymers and the mechanical properties of the glass. We have in fact established a correlation between molecular motion characterized by NMR and the mechanical secondary relaxation (tan δ) for nine polycarbonate-like glasses. All of the NMR and mechanical data are for T ≪ Tg. The resulting structural insights suggest that the chains of these polymers are simultaneously both Flory random coils and Vol'kenstein bundles. The cooperative motions of groups of bundles can be described qualitatively by a variety of constrained-kinetics models of the glass. All of the models share a common trait for large-amplitude motion: an exponential increase in the time required for an inter-bundle dilation event with a linear increase in bundle group size. This dependence and a locally ordered Vol'kenstein bundle lead to an understanding of the surprising 60° (K) shift of tan δ to higher temperature for ring-fluoro-polycarbonate relative to that of polycarbonate by the apparently minor substitution of a fluorine for a hydrogen on every fourth ring.

Local-Average Free Volume Correlates with Dynamics in Glass Formers

Glass formers exhibit a pronounced slowdown in dynamics, accompanied by progressive heterogeneity as they approach the glass transition. There is intense debate over whether the dramatic slowdown is caused by dynamical heterogeneity and whether the enhanced dynamical heterogeneity originates from structural causes. However, the connection between dynamical heterogeneity and the spatial distribution of the single-particle free volume (a purely static structural quantity) was found to be rather weak, which raises the question of whether dynamic heterogeneity has a purely structural origin. Here, by introducing the concept of local-average free volume, we present numerical evidence that long-time dynamic heterogeneity shows significantly enhanced correlation with the average local free volume over a length scale of a few neighboring shells. Our results resolve the long-standing controversy about whether free volume plays an important role in particle rearrangements associated with the activated hopping relaxation. The concept of "local average" can be applied to other local structural descriptors to better correlate with dynamic heterogeneity in glass-forming liquids.

Radical Diffusion Crossover Phenomenon in Glass-Forming Liquids

We studied the diffusivities of a nitroxide radical at various temperatures in six glass-forming molecular liquids by electron spin resonance. By comparing the radical diffusivities and solvent self-diffusivities, we found that the radical diffusivities are lower than the self-diffusivities at high temperatures and approach them at low temperatures in all liquids. This crossover behavior was considered as evidence that a single-molecule diffusion process transforms into a collective process with temperature lowering. The crossover phenomenon was analyzed by a novel, simple diffusion model, combining collective and single-molecule diffusion processes, and it was compared to the Arrhenius crossover phenomenon. The obtained results suggest that future studies of tracer diffusion could contribute to a better understanding of diffusion mechanisms in glass-forming liquids. The proposed diffusion model could be used to study the crossover phenomena of tracer diffusion measured by other techniques, and it could serve as a base for developing more advanced models.

Thermodynamic approach for the understanding of the kinetics of heat effects induced by structural relaxation of metallic glasses

We present a novel approach to the understanding of heat effects induced by structural relaxation of metallic glasses. The key idea consists in the application of a general thermodynamic equation for the entropy change due to the evolution of a non-equilibrium part of a complex system. This non-equilibrium part is considered as a defect subsystem of glass and its evolution is governed by local thermoactivated rearrangements with a Gibbs free energy barrier proportional to the high-frequency shear modulus. The only assumption on the nature of the defects is that they should provide a reduction of the shear modulus-a diaelastic effect. This approach allows to determine glass entropy change upon relaxation. On this basis, the kinetics of the heat effects controlled by defect-induced structural relaxation is calculated. A very good agreement between the calculation and specially performed calorimetric and shear modulus measurements on three metallic glasses is found.

Activation free energy gradient controls interfacial mobility gradient in thin polymer films

We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH₀ and entropy ΔS₀ as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH₀ in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u²(z)^-3/2, where u²(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH₀(z) and that ΔS₀(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.

Fast Surface Dynamics on a Metallic Glass Nanowire

The dynamics near the surface of glasses can be much faster than in the bulk. We studied the surface dynamics of a Pt-based metallic glass using electron correlation microscopy with sub-nanometer resolution. Our studies show an ∼20 K suppression of the glass transition temperature at the surface. The enhancement in surface dynamics is suppressed by coating the metallic glass with a thin layer of amorphous carbon. Parallel molecular dynamics simulations on Ni₈₀P₂₀ show a similar temperature suppression of the surface glass transition temperature and that the enhanced surface dynamics are arrested by a capping layer that chemically binds to the glass surface. Mobility in the near-surface region occurs via atomic caging and hopping, with a strong correlation between slow dynamics and high cage-breaking barriers and stringlike cooperative motion. Surface and bulk dynamics collapse together as a function of temperature rescaled by their respective glass transition temperatures.

Experimental test of a predicted dynamics-structure-thermodynamics connection in molecularly complex glass-forming liquids

Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different "order parameters" including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local-nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply supercooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

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.

Energy barriers and cooperative motion at the surface of freestanding glassy polystyrene films

We investigate the near-surface relaxation of freestanding atactic polystyrene films with molecular dynamics simulations. As in previous coarse-grained simulations, relaxation times for backbone segments and phenyl rings are linked to their bulk relaxation times via a power-law coupling relation. Variation of the coupling exponent with distance from the surface is consistent with depth-dependent activation barriers. We also quantify a reduction in dynamical heterogeneity at the interface, which can be interpreted in the framework of cooperative models for glassy dynamics.

Exploring a unified description of the super-Arrhenius region above and below the glass transition temperature

A new approach is presented in order to check whether the hypothesis of an Arrhenius component surviving in the α-relaxation region is consistent with experimental data. The temperature dependence of the dynamics in the whole glassy regime is described by an equation which assumes an Arrhenius component in the cooperative diffusion. Based on thermodynamic arguments, the dynamic heterogeneities close to the glass transition region are related to structural heterogeneities in a manner consistent with the idea of a sigmoidal shape in the cohesion energy. By doing so, a characteristic temperature which can be identified as the glass transition temperature (T_g) emerges, while an additional parameter for the extension of the super-Arrhenius region is introduced. In the analysis of experimental data, the activation energy parameter, determined from the temperature dependence of the β-relaxation, is fixed, and the relation between the experimental and the predicted glass transition temperature is examined. The results of this comparison support the idea that dynamics above and below T_g can be described in a unified manner. The proposed model is tested against experimental data of glass-forming liquids, polymers and polymer composites. In the latter systems, it is shown that the Arrhenius-like behavior characterizing the dynamics of the polymeric bound-layer can be accounted for by such an extension of the super-Arrhenius region.

Cooperative strings and glassy dynamics in various confined geometries

Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, by canceling and restarting any cooperative-chain realization reaching the boundary with a smaller number of steps than the bulk cooperativity, we account for a purely attractive substrate, and explore the impact of the latter in the previous geometries.

Predictive relation for the α-relaxation time of a coarse-grained polymer melt under steady shear

We examine the influence of steady shear on structural relaxation in a simulated coarse-grained unentangled polymer melt over a wide range of temperature and shear rates. Shear is found to progressively suppress the α-relaxation process observed in the intermediate scattering function, leading ultimately to a purely inertially dominated β-relaxation at high shear rates, a trend similar to increasing temperature. On the basis of a scaling argument emphasizing dynamic heterogeneity in cooled liquids and its alteration under material deformation, we deduce and validate a parameter-free scaling relation for both the structural relaxation time τα from the intermediate scattering function and the "stretching exponent" β quantifying the extent of dynamic heterogeneity over the entire range of temperatures and shear rates that we can simulate.

A simple mean-field model of glassy dynamics and glass transition

We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.

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.

Two-step relaxation and the breakdown of the Stokes-Einstein relation in glass-forming liquids

It is well known that glass-forming liquids exhibit a number of anomalous dynamical phenomena, most notably a two-step relaxation in the self-intermediate scattering function and the breakdown of the Stokes-Einstein (SE) relation, as they are cooled toward the glass transition temperature. While these phenomena are generally ascribed to dynamic heterogeneity, specifically to the presence of slow- and fast-moving particles, a quantitative elucidation of the two-step relaxation and the violation of the SE relation in terms of these concepts has not been successful. In this work, we propose a classification of particles according to the rank order of their displacements (from an arbitrarily defined origin of time), and we divide the particles into long-distance (LD), medium-distance, and short-distance (SD) traveling particle groups. Using molecular-dynamics simulation data of the Kob-Andersen model, we show quantitatively that the LD group is responsible for the fast relaxation in the two-step relaxation process in the intermediate scattering function, while the SD group gives rise to the slow (α) relaxation. Furthermore, our analysis reveals that τ_{α} is controlled by the SD group, while the ensemble-averaged diffusion coefficient D is controlled by both the LD and SD groups. The combination of these two features provides a natural explanation for the breakdown in the SE relation at low temperature. In addition, we find that the α-relaxation time, τ_{α}, of the overall system is related to the relaxation time of the LD particles, τ_{LD}, as τ_{α}=τ_{0}exp(Ωτ_{LD}/k_{B}T).

What does the instantaneous normal mode spectrum tell us about dynamical heterogeneity in glass-forming fluids?

We examine the instantaneous normal mode spectrum of model metallic and polymeric glass-forming liquids. We focus on the localized modes in the unstable part of the spectrum [unstable localized (UL) modes] and find that the particles making the dominant contribution to the participation ratio form clusters that grow upon cooling in a fashion similar to the dynamical heterogeneity in glass-forming fluids, i.e., highly mobile (or immobile) particles form clusters that grow upon cooling; however, a comparison of the UL mode clusters to the mobile and immobile particle clusters indicates that they are distinct entities. We also show that the cluster size provides an alternate method to distinguish localized and delocalized modes, offering a significant practical advantage over the finite-size scaling approach. We examine the trajectories of particles contributing most to the UL modes and find that they have a slightly enhanced mobility compared to the average, and we determine a characteristic time quantifying the persistence time of this excess mobility. This time scale is proportional to the structural relaxation time τ_α of the fluid, consistent with a prediction by Zwanzig [Phys. Rev. 156, 190 (1967)] for the lifetime of collective excitations in cooled liquids. Evidently, these collective excitations serve to facilitate relaxation but do not actually participate in the motion associated with barrier crossing events governing activated transport. They also serve as a possible concrete realization of the "facilitation" clusters postulated in previous modeling of glass-forming liquids.

Universal nature of dynamic heterogeneity in glass-forming liquids: A comparative study of metallic and polymeric glass-forming liquids

Glass-formation is a ubiquitous phenomenon that is often observed in a broad class of materials ranging from biological matter to commonly encountered synthetic polymer, as well as metallic and inorganic glass-forming (GF) materials. Despite the many regularities in the dynamical properties of GF materials, the structural origin of the universal dynamical properties of these materials has not yet been identified. Recent simulations of coarse-grained polymeric GF liquids have indicated the coexistence of clusters of mobile and immobile particles that appear to be directly linked, respectively, to the rate of molecular diffusion and structural relaxation. The present work examines the extent to which these distinct types of "dynamic heterogeneity" (DH) arise in metallic GF liquids (Cu-Zr, Ni-Nb, and Pd-Si alloys) having a vastly different molecular structure and chemistry. We first identified mobile and immobile particles and their transient clusters and found the DH in the metallic alloys to be remarkably similar in form to polymeric GF liquids, confirming the "universality" of the DH phenomenon. Furthermore, the lifetime of the mobile particle clusters was found to be directly related to the rate of diffusion in these materials, while the lifetime of immobile particles was found to be proportional to the structural relaxation time, providing some insight into the origin of decoupling in GF liquids. An examination of particles having a locally preferred atomic packing, and clusters of such particles, suggests that there is no one-to-one relation between these populations of particles so that an understanding of the origin of DH in terms of static fluid structure remains elusive.

Interstitial clustering in metallic systems as a source for the formation of the icosahedral matrix and defects in the glassy state

The paper presents molecular dynamics and -statics simulations of a prototypical mono-atomic metallic system (aluminum) and its defects in the crystalline and glassy states. It is shown that there is a thermodynamic driving force for the association of dumbbell interstitials in the crystalline lattice into clusters consisting of different amounts of defects. Clusters containing seven interstitials constitute perfect icosahedra. Within the general framework of the interstitialcy theory, melting of simple metallic crystals is intrinsically related to a rapid increase of the concentration of dumbbell interstitials, which remain identifiable structural units in the liquid state. Then, the glass produced by rapid melt quenching contains interstitial-type defects. The idea of the present work is to argue that the major structural feature of many metallic glasses-icosahedral ordering-originates from the clustering of interstitial-type defects frozen-in upon melt quenching. Separate defects and their small clusters represent the defect part of the glassy structure.

A comparative study on the dynamic heterogeneity of supercooled polymers under nanoconfinement

Dynamic heterogeneity (DH) is a universal property of glass transition phenomena. In this work, we perform a comparative analysis of DH for pure polymer and polymer/nanoparticle composite systems in both film and bulk states via molecular dynamics simulations. We find that the dynamic gradient and the faster average dynamics due to the presence of a free surface are two leading factors, resulting from a nanoconfinement effect, which influence different parts of DH in a film system. The dynamic gradient results from differences in dynamics at different distances from the mobile surface, which induces a large deviation from the Gaussian distribution for the displacement distribution in the film. At the same time, the maximum string size which describes the region size for cooperative motion (dynamic correlation) can also be influenced by the dynamic gradient, although this influence is much weaker than that on the displacement distribution. On the other hand, reflecting temporal fluctuations of dynamics or temporal parts of DH, characteristic peak times of the non-Gaussian parameter and string size, and the ratio between persistent times and exchange times which describe the dynamic exchange properties, are mainly influenced by the faster dynamics on average. Our results demonstrate that measuring different properties (dynamic distribution, dynamic correlation or dynamic exchange) place an emphasis on distinct temporal and spatial parts of DH. It is necessary to use combinational measurements of these properties to give a complete picture of DH in nanoconfinement environments.

Collective Motion in the Interfacial and Interior Regions of Supported Polymer Films and Its Relation to Relaxation

To understand the role of collective motion in the often large changes in interfacial molecular mobility observed in polymer films, we investigate the extent of collective motion in the interfacial regions of a thin supported polymer film and within the film interior by molecular dynamics simulation. Contrary to commonly stated expectations, we find that the extent of collective motion, as quantified by string-like molecular exchange motion, is similar in magnitude in the polymer-air interfacial layer as the film interior and distinct from the bulk material. This finding is consistent with Adam-Gibbs description of the segmental dynamics within mesoscopic film regions, where the extent of collective motion is related to the configurational entropy of the film as a whole rather than a locally defined extent of collective motion or configurational entropy.

Metallic Glasses: A New Approach to the Understanding of the Defect Structure and Physical Properties

The work is devoted to a brief overview of the Interstitialcy Theory (IT) as applied to different relaxation phenomena occurring in metallic glasses upon structural relaxation and crystallization. The basic hypotheses of the IT and their experimental verification are shortly considered. The main focus is given on the interpretation of recent experiments on the heat effects, volume changes and their link with the shear modulus relaxation. The issues related to the development of the IT and its relationship with other models on defects in metallic glasses are discussed.