Generalized localization model of relaxation in glass-forming liquids

Do Specific Ion Effects on Collective Relaxation Arise from Perturbation of Hydrogen-Bonding Network Structure?

The change in the transport properties (i.e., water diffusivity, shear viscosity, etc.) when adding salts to water has been used to classify ions as either being chaotropic or kosmotropic, a terminology based on the presumption that this phenomenon arises from respective breakdown or enhancement of the hydrogen-bonding network structure. Recent quasi-elastic neutron scattering measurements of the collective structural relaxation time, τC, in aqueous salt solutions were interpreted as confirming this proposed origin of ion effects on the dynamics of water. However, we find similar changes in τC in the same salt solutions based on molecular dynamics (MD) simulations using a coarse-grained water model in which no hydrogen bonding exists, challenging this conventional interpretation of mobility change resulting from the addition of salts to water. A thorough understanding of specific ion effects should be useful in diverse material manufacturing and biomedical applications, where these effects are prevalent, but poorly understood.

Influence of swelling on the elasticity of polymer networks cross-linked in the melt state: Test of the localization model of rubber elasticity

The elasticity of polymer networks, formed by cross-linking high molecular mass polymers in the melt state and then swollen by a solvent, involves contributions from both the presence of cross-link network junctions and the interchain interactions associated with the combined effect of excluded volume interactions and topological constraints that become modified when the network is swollen. We test the capacity of the previously developed localization model of rubber elasticity, a mean field "tube model," to describe changes in elasticity observed in classical experimental studies of the mechanical properties of this type of network. In order to obtain a satisfactory comparison to the experiments, it was found to be necessary to account for the independently observed tendency of the network junctions to become localized in the network with appreciable swelling, as well as the interchain interactions emphasized in previous discussions of the localization model.

Unveiling the Structural Origins of Dynamic Diversity in Pd-Based Metallic Glasses

The β-relaxation is one of the major dynamic behaviors in metallic glasses (MGs) and exhibits diverse features. Despite decades of efforts, the understanding of its structural origin and contribution to the overall dynamics of MG systems is still unclear. Here two palladium-based Pd─Cu─P and Pd─Ni─P MGs are reported with distinct different β-relaxation behaviors and reveal the structural origins for the difference using the advanced X-ray photon correlation spectroscopy and absorption fine structure techniques together with the first-principles calculations. The pronounced β-relaxation and fast atomic dynamics in the Pd─Cu─P MG mainly come from the strong mobility of Cu atoms and their locally favored structures. In contrast, the motion of Ni atoms is constrained by P atoms in the Pd─Ni─P MG, leading to the weakened β-relaxation peak and sluggish dynamics. The correlation of atomic dynamics with microscopic structures provides a way to understand the structural origins of different dynamic behaviors as well as the nature of aging in disordered materials.

Local vs. cooperative: Unraveling glass transition mechanisms with SEER

Which phenomenon slows down the dynamics in supercooled liquids and turns them into glasses is a long-standing question of condensed matter. Most popular theories posit that as the temperature decreases, many events must occur in a coordinated fashion on a growing length scale for relaxation to occur. Instead, other approaches consider that local barriers associated with the elementary rearrangement of a few particles or "excitations" govern the dynamics. To resolve this conundrum, our central result is to introduce an algorithm, Systematic Excitation ExtRaction, which can systematically extract hundreds of excitations and their energy from any given configuration. We also provide a measurement of the activation energy, characterizing the liquid dynamics, based on fast quenching and reheating. We use these two methods in a popular liquid model of polydisperse particles. Such polydisperse models are known to capture the hallmarks of the glass transition and can be equilibrated efficiently up to millisecond time scales. The analysis reveals that cooperative effects do not control the fragility of such liquids: the change of energy of local barriers determines the change of activation energy. More generally, these methods can now be used to measure the degree of cooperativity of any liquid model.

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.

Energy renormalization for temperature transferable coarse-graining of silicone polymer

The bottom-up prediction of thermodynamic and mechanical behaviors of polymeric materials based on molecular dynamics (MD) simulation is of critical importance in polymer physics. Although the atomistically informed coarse-grained (CG) model can access greater spatiotemporal scales and retain essential chemical specificity, the temperature-transferable CG model is still a big challenge and hinders widespread application of this technique. Herein, we use a silicone polymer, i.e., polydimethylsiloxane (PDMS), having an incredibly low chain rigidity as a model system, combined with an energy-renormalization (ER) approach, to systematically develop a temperature-transferable CG model. Specifically, by introducing temperature-dependent ER factors to renormalize the effective distance and cohesive energy parameters, the developed CG model faithfully preserved the dynamics, mechanical and conformational behaviors compared with the target all-atomistic (AA) model from glassy to melt regimes, which was further validated by experimental data. With the developed CG model featuring tremendously improved computational efficiency, we systematically explored the influences of cohesive interaction strength and temperature on the dynamical heterogeneity and mechanical response of polymers, where we observed consistent trends with other linear polymers with varying chain rigidity and monomeric structures. This study serves as an extension of our proposed ER approach of developing temperature transferable CG models with diverse segmental structures, highlighting the critical role of cohesive interaction strength on CG modeling of polymer dynamics and thermomechanical behaviors.

Anomalous segmental dynamics of supercooled polyrotaxane melts: A computer simulation study

Polyrotaxanes, which consist of mechanically interlocked bonds with rings threaded onto soft polymer chains, exhibit unique mechanical properties and find applications in diverse fields. In this study, we investigate the anomalous segmental dynamics of supercooled polyrotaxane melts using coarse-grained molecular dynamics simulations. Our simulations reveal that the presence of rings effectively reduces the packing efficiency, resulting in well-contained local motion even below the glass transition temperature. We also observe variations in dynamical free volume, characterized by the Debye-Waller factor, which shows a minimum at a ring coverage of 0.1 on threading chains. Such a non-monotonic dependence on coverage shows great consistency in structural relaxation time and dynamic heterogeneity. Specifically, the high segmental mobility of threading linear chains at large coverage can be attributed to the increased dynamical free volume due to supported rigid rings. However, such anomalous segmental dynamics is limited to length scales smaller than one ring size. Beyond this characteristic length scale, the diffusion is dominated by topological constraints, which significantly reduce the mobility of polyrotaxanes and enhance the dynamic heterogeneity. These findings offer microscopic insights into the unique packing structures and anomalous segmental dynamics of supercooled polyrotaxane melts, facilitating the design of advanced materials based on mechanical interlocking polymers for various applications.

Interplay between dynamic heterogeneity and interfacial gradients in a model polymer film

Glass-forming liquids exhibit long-lived, spatially correlated dynamical heterogeneity, in which some nm-scale regions in the fluid relax more slowly than others. In the nanoscale vicinity of an interface, glass-formers also exhibit the emergence of massive interfacial gradients in glass transition temperature Tg and relaxation time τ. Both of these forms of heterogeneity have a major impact on material properties. Nevertheless, their interplay has remained poorly understood. Here, we employ molecular dynamics simulations of polymer thin films in the isoconfigurational ensemble in order to probe how bulk dynamic heterogeneity alters and is altered by the large gradient in dynamics at the surface of a glass-forming liquid. Results indicate that the τ spectrum at the surface is broader than in the bulk despite being shifted to shorter times, and yet it is less spatially correlated. This is distinct from the bulk, where the τ distribution becomes broader and more spatially organized as the mean τ increases. We also find that surface gradients in slow dynamics extend further into the film than those in fast dynamics-a result with implications for how distinct properties are perturbed near an interface. None of these features track locally with changes in the heterogeneity of caging scale, emphasizing the local disconnect between these quantities near interfaces. These results are at odds with conceptions of the surface as reflecting simply a higher "rheological temperature" than the bulk, instead pointing to a complex interplay between bulk dynamic heterogeneity and spatially organized dynamical gradients at interfaces in glass-forming liquids.

Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt

In this work, we extend an approach to coarse-grained (CG) modeling for polymer melts in which the conservative potential is parametrized using the iterative Boltzmann inversion (IBI) method and the accelerated dynamics inherent to IBI are corrected using the dissipative Langevin thermostat with a single tunable friction parameter (J. Chem. Phys. 2021, 154, 084114). Diffusive measures from picoseconds to nanoseconds are used to determine the Langevin friction factor to apply to the CG model to recover all-atom (AA) dynamics; the resulting friction factors are then compared for consistency. Here, we additionally parametrize the CG dynamics using a material property, the zero-shear viscosity, which we measure using the Green-Kubo (GK) method. Two materials are studied, squalane as a function of temperature and the same polystyrene oligomers previously studied as a function of chain length. For squalane, the friction derived from the long-time diffusive measures and the viscosity all strongly increase with decreasing temperature, showing an Arrhenius-like dependence, and remain consistent with each other over the entire temperature range. In contrast, the friction required for the picosecond diffusive measurement, the Debye-Waller factor, is somewhat lower than the friction from long-time measures and relatively insensitive to temperature. A time-dependent friction would be required to exactly reproduce the AA measurements during the caging transition connecting these two extremes over the entire timespan at this level of coarse-graining. For the polystyrene oligomers for which we previously characterized the diffusive friction, the viscosity-parametrized frictions are consistent with the diffusive measures for the smallest chain length. However, for the longer chains, we find different trends based on measurement method with friction derived from rotational diffusion remaining nearly constant, friction derived from translational diffusion showing a modestly increasing trend, and viscosity-derived friction showing a modest decreasing trend. This seems to indicate that there is some sensitivity of the friction measurement method for systems with increased relaxation times and that in particular, the unsteady dynamics of the individual parametrization schemes plays a role in this. Increased difficulty in applying the GK method with increasing relaxation time of the longer chain systems is also discussed. Overall, we find that when the material is in a high-temperature melt state and the viscosity measurement is reliable, the friction parametrization from the diffusive friction measures is consistent and the lower cost diffusive parametrization is a reliable means for modeling viscosity. Our data give insight into the time-dependent friction one might compute using a non-Markovian approach to enable the recovery of AA dynamics over a wider range of time scales than can be computed using a single friction.

Solid-State NMR Characterization of Lyophilized Formulations of Monoclonal Antibody Therapeutics

Monoclonal antibodies (mAbs) are an important and growing class of biotherapeutic drugs. Method development for the characterization of critical quality attributes, including higher-order structure (HOS), of mAbs remains an area of active inquiry. Recently, solution-state nuclear magnetic resonance (NMR) spectroscopy has received increased attention and is a means for reliable, high-resolution HOS characterization of aqueous-based preparations of mAbs. While mAbs are predominantly formulated in solution, up to 20% are prepared as solid amorphous powders and techniques for the robust characterization of HOS in the solid state remain limited. We propose here the use of solid-state NMR (ssNMR) fingerprinting to inform directly on the HOS of solid preparations of mAbs. Using lyophilized samples of the NISTmAb reference material prepared with different formulation conditions, we demonstrate that ¹H-¹³C cross-polarization (hC-CP) buildup spectral series at natural isotopic abundance mAb samples are sensitive to differences in formulation. We also demonstrate that principal component analysis (PCA) can be used to differentiate the samples from one another in a user-independent manner while also highlighting areas where expert analysis can provide structural details about important molecular interactions in solid-phase protein formulations. Results from this study contribute to establishing the foundation for the use of ssNMR for HOS characterization of solid-phase biotherapeutics.

Long-Wavelength Fluctuations in Quasi-2D Supercooled Liquids

We use molecular simulation to characterize the dynamics of supercooled liquids confined in quasi-2D slit geometries. Similar to bulk supercooled liquids, the confined systems exhibit subdiffusive dynamics on intermediate time scales arising from particle localization inside their neighbor cages, followed by an eventual crossover to diffusive behavior as cage rearrangement occurs. The quasi-2D confined liquids also exhibit signatures of long-wavelength fluctuations (LWFs) in the lateral directions parallel to the confining walls, reminiscent of the collective displacements observed in 2D but not 3D systems. The magnitude of the LWFs increases with the lateral dimensions of systems with the same particle volume fraction and confinement length scale, consistent with the logarithmic scaling predicted for 2D Mermin-Wagner fluctuations. The amplitude of the fluctuations is a nonmonotonic function of the confinement length scale because of a competition between caging and strengthening LWFs upon approaching the 2D limit. Our findings suggest that LWFs may play an important role in understanding the behavior of confined supercooled liquids due to their prevalence over a surprisingly broad range of particle densities and confinement length scales.

Excitations follow (or lead?) density scaling in propylene carbonate

Structural excitations that enable interbasin (IB) barrier crossings on a potential energy landscape are thought to play a facilitating role in the relaxation of liquids. Here, we show that the population of these excitations exhibits the same density scaling observed for α relaxation in propylene carbonate, even though they are heavily influenced by intramolecular modes. We also find that IB crossing modes exhibit a Gr[Formula: see text]neisen parameter ( γ G) that is approximately equivalent to the density scaling parameter γ TS. These observations suggest that the well-documented relationship between γ G and γ TS may be a direct result of the pressure dependence of the frequency of unstable (relaxation) modes associated with IB motion.

Relative effects of polymer composition and sample preparation on glass dynamics

Modern design of common adhesives, composites and polymeric parts makes use of polymer glasses that are stiff enough to maintain their shape under a high stress while still having a ductile behavior after the yield point. Typically, material compositions are tuned with co-monomers, polymer blends, plasticizers, or other additives to arrive at a tradeoff between the elastic modulus and toughness. In contrast, strong changes to the mechanics of a glass are possible by changing only the molecular packing during vitrification or even deep in the glassy state. For example, physical aging or processing techniques such as physical vapor deposition increase the density, embrittle the material, and increase elastic modulus. Here, we use molecular simulations, validated by positron annihilation lifetime spectroscopy (PALS) and quasi-elastic neutron scattering, to understand the free volume distribution and the resulting dynamics of glassy co-polymers where the composition is systemically varied between polar 5-norbornene-2-methanol (NBOH) and non-polar ethylidene norbornene (ENB) monomers. In these polymer glasses, we analyze the structural features of the unoccupied volume using clustering analysis, where the clustering is parameterized to reproduce experimental measurements of the same features from PALS. Further, we analyze the dynamics, quantified by the Debye-Waller factor, and compare the results with softer, lower density states. Our findings indicate that faster structural relaxations and potentially improved ductility are possible through changes to the geometric structure and fraction of the free volume, and that the resulting changes to the glass dynamics are comparable to large changes in the monomer composition.

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature T_g, whether there is an underlying thermodynamic transition at some finite temperature below T_g, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

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.

Local Plastic Response and Slow Heterogeneous Dynamics of Supercooled Liquids

We demonstrate, via numerical simulations, that the relaxation dynamics of supercooled liquids correlates well with a plastic length scale measuring a particle's response to impulsive localized perturbations and weakly to measures of local elasticity. We find that the particle averaged plastic length scale vanishes linearly in temperature and controls the super-Arrhenius temperature dependence of the relaxation time. Furthermore, we show that the plastic length scale of individual particles correlates with their typical displacement at the relaxation time. In contrast, the local elastic response only correlates with the dynamics on the vibrational timescale.

Temperature dependence of aging dynamics in highly non-equilibrium model polymer glasses

A central feature of the non-equilibrium glassy “state” is its tendency to age toward equilibrium, obeying signatures identified by Kovacs over 50 years ago. The origin of these signatures, their fate far from equilibrium and at high temperatures, and the underlying nature of the glassy “state” far from equilibrium remain unsettled. Here, we simulate physical aging of polymeric glasses, driven much farther from equilibrium and at much higher temperatures than possible in experimental melt-quenched glasses. While these glasses exhibit Kovacs’ signatures of glassy aging at sufficiently low temperatures, these signatures disappear above the onset TA of non-Arrhenius equilibrium dynamics, suggesting that TA demarcates an upper bound to genuinely glassy states. Aging times in glasses after temperature up-jumps are found to obey an Arrhenius law interpolating between equilibrium dynamics at TA and at the start of the temperature up-jump, providing a zero-parameter rule predicting their aging behavior and identifying another unrecognized centrality of TA to aging behavior. This differs qualitatively from behavior of our glasses produced by temperature down-jumps, which exhibit a fractional power law decoupling relation with equilibrium dynamics. While the Tool–Narayanaswamy–Moynihan model can predict the qualitative single-temperature behavior of these systems, we find that it fails to predict the disappearance of Kovacs signatures above TA and the temperature dependence of aging after large temperature up-jumps. These findings highlight a need for new theoretical insights into the aging behavior of glasses at ultra-high fictive temperatures and far from equilibrium.

Explaining the Sensitivity of Polymer Segmental Relaxation to Additive Size Based on the Localization Model

We use molecular simulations to examine how the dynamics of a coarse-grained polymer melt are altered by additives of variable size and interaction strength with the polymer matrix. The effect of diluent size σ on polymer dynamics changes significantly when its size is comparable to the polymer segment size. For each σ, we show that the localization model (LM) quantitatively describes the dependence of the segmental relaxation time τ on temperature T in terms of dynamic free volume, quantified by the Debye-Waller factor ⟨u^{2}⟩. Within this model, we show that the additive size alone controls the functional form of the T dependence. The LM parameters reach asymptotic values when the diluent size exceeds the monomer size, converging to a limit applicable to macroscopic interfaces.

Construction of a quantitative relation between structural relaxation and dynamic heterogeneity by vibrational dynamics in glass-forming liquids and polymers

The structural relaxation slows down drastically upon approaching the glass transition, accompanied by the significant growth of dynamic heterogeneity. The fundamental question of elusiveness and interest is whether there exists an underlying quantitative relationship between structural relaxation and dynamic heterogeneity. Here, we reveal that b̃ which is related to the reduced mean square displacements to overcome the energy barriers of activated jumps, instead of the kinetic fragility m, is the genuine key parameter connecting dynamic heterogeneity with structural relaxation for varying types of glass formers. Furthermore, based on the dependence of dynamic heterogeneity on the Debye-Waller factor we obtained a direct quantitative relation between dynamic heterogeneity and structural relaxation is built for different glass-forming liquids. More importantly, a scaling collapse of structural relaxation and dynamic heterogeneity is achieved by the important parameter b̃. These results are of fundamental and critical importance for developing a unified theory of glassy dynamics.

Systematic Coarse-graining of Epoxy Resins with Machine Learning-Informed Energy Renormalization

A persistent challenge in predictive molecular modeling of thermoset polymers is to capture the effects of chemical composition and degree of crosslinking (DC) on dynamical and mechanical properties with high computational efficiency. We established a new coarse-graining (CG) approach that combines the energy renormalization method with Gaussian process surrogate models of the molecular dynamics simulations. This allows a machine-learning informed functional calibration of DC-dependent CG force field parameters. Taking versatile epoxy resins consisting of Bisphenol A diglycidyl ether combined with curing agent of either 4,4-Diaminodicyclohexylmethane or polyoxypropylene diamines, we demonstrated excellent agreement between all-atom and CG predictions for density, Debye-Waller factor, Young's modulus and yield stress at any DC. We further introduce a surrogate model enabled simplification of the functional forms of 14 non-bonded calibration parameters by quantifying the uncertainty of a candidate set of high-dimensional/flexible calibration functions. The framework established provides an efficient methodology for chemistry-specific, large-scale investigations of the dynamics and mechanics of epoxy resins.

Relations Between Dynamic Localization and Solute Diffusion in Polymers

Various public health concerns can arise from the unintended leaching of additives and impurities from polymeric medical devices or food packaging, which is directly related to each solute's diffusivity D. Both experimental and simulation methods can be used to quantify D, but slow diffusion at physiologic temperature in glassy polymers can render these approaches impractical. Here, we investigate a simulation approach with the potential to more rapidly calculate D. Specifically, we examine links between dynamic localization, characterized by the Debye-Waller factor, ⟨u²⟩, and D in a variety of polymer/solute systems using atomistic molecular dynamics (MD) simulations. Using short, high-temperature MD simulations to estimate D at physiologic temperature, we find that the relation ln D ∝ 1/⟨u²⟩ quantitatively predicts D for small solutes and produces an upper-bound estimate of D for larger solutes. Upper-bound estimates are useful in certain contexts, and we compare our results with another approach for determining upper bounds, the Piringer model, to show where each method may be useful. Then, we examine a modified relation where the Debye-Waller factor is rescaled by the mode coupling temperature T_c, which can produce better estimates of D if T_c is carefully chosen. Last, we compare our approach with several other models that relate temperature or localized dynamics with diffusivity. Although each of these approaches can be used to model D across wide temperature ranges using one or more adjustable parameters, none of them are truly predictive in glassy polymers. Further developments are needed to predict the optimal values of the adjustable parameters a priori.

Waiting-time dependent non-equilibrium phase diagram of simple glass- and gel-forming liquids

Under numerous circumstances, many soft and hard materials are present in a puzzling wealth of non-equilibrium amorphous states, whose properties are not stationary and depend on preparation. They are often summarized in unconventional "phase diagrams" that exhibit new "phases" and/or "transitions" in which time, however, is an essential variable. This work proposes a solution to the problem of theoretically defining and predicting these non-equilibrium phases and their time-evolving phase diagrams, given the underlying molecular interactions. We demonstrate that these non-equilibrium phases and the corresponding non-stationary (i.e., aging) phase diagrams can indeed be defined and predicted using the kinetic perspective of a novel non-equilibrium statistical mechanical theory of irreversible processes. This is illustrated with the theoretical description of the transient process of dynamic arrest into non-equilibrium amorphous solid phases of an instantaneously quenched simple model fluid involving repulsive hard-sphere plus attractive square well pair interactions.

Dynamical properties across different coarse-grained models for ionic liquids

Room-temperature ionic liquids (RTILs) stand out among molecular liquids for their rich physicochemical characteristics, including structural and dynamic heterogeneity. The significance of electrostatic interactions in RTILs results in long characteristic length- and timescales, and has motivated the development of a number of coarse-grained (CG) simulation models. In this study, we aim to better understand the connection between certain CG parameterization strategies and the dynamical properties and transferability of the resulting models. We systematically compare five CG models: a model largely parameterized from experimental thermodynamic observables; a refinement of this model to increase its structural accuracy; and three models that reproduce a given set of structural distribution functions by construction, with varying intramolecular parameterizations and reference temperatures. All five CG models display limited structural transferability over temperature, and also result in various effective dynamical speedup factors, relative to a reference atomistic model. On the other hand, the structure-based CG models tend to result in more consistent cation-anion relative diffusion than the thermodynamic-based models, for a single thermodynamic state point. By linking short- and long-timescale dynamical behaviors, we demonstrate that the varying dynamical properties of the different CG models can be largely collapsed onto a single curve, which provides evidence for a route to constructing dynamically-consistent CG models of RTILs.

Localization model description of the interfacial dynamics of crystalline Cu and [Formula: see text] metallic glass nanoparticles

Many of the special properties of nanoparticles (NPs) and nanomaterials broadly derive from the significant fraction of particles (atoms, molecules or segments of polymeric molecules) in the NP interfacial region in which the interparticle interactions are characteristically highly anharmonic in comparison to the bulk material. This leads to relatively large mean square particle displacements relative to the material interior, often resulting in a strong increase interfacial mobility and reactivity in both crystalline and glass NPs. The 'Debye-Waller factor', or the mean square particle displacement [Formula: see text] on a ps 'caging' timescale relative to the square of the average interparticle distance [Formula: see text], provides an often experimentally accessible measure of the strength of this anharmonic interaction. The Localization Model (LM) of the dynamics of condensed materials relates this thermodynamic property to the structural relaxation time [Formula: see text], determined from the intermediate scattering function, without any free parameters. Moreover, the LM allows for the prediction of the diffusion coefficient D when combined with the 'decoupling' or Fractional Stokes-Einstein relation linking [Formula: see text] to D. In the current study, we employed classical molecular dynamics simulation to investigate the structural relaxation and diffusion of model [Formula: see text] metallic glass and Cu crystalline NPs with different sizes. As with previous studies validating the LM on model bulk and crystalline materials, and for the interfacial dynamics of thin crystalline and metallic glass films, we find the LM model also describes the interfacial dynamics of model crystalline metal (Cu) and metallic glass ([Formula: see text] NPs to a good approximation, further confirming the generality of the model.

Dynamically consistent coarse-grain simulation model of chemically specific polymer melts via friction parameterization

Coarse-grained (CG) models of polymers involve grouping many atoms in an all-atom (AA) representation into single sites to reduce computational effort yet retain the hierarchy of length and time scales inherent to macromolecules. Parameterization of such models is often via "bottom-up" methods, which preserve chemical specificity but suffer from artificially accelerated dynamics with respect to the AA model from which they were derived. Here, we study the combination of a bottom-up CG model with a dissipative potential as a means to obtain a chemically specific and dynamically correct model. We generate the conservative part of the force-field using the iterative Boltzmann inversion (IBI) method, which seeks to recover the AA structure. This is augmented with the dissipative Langevin thermostat, which introduces a single parameterizable friction factor to correct the unphysically fast dynamics of the IBI-generated force-field. We study this approach for linear polystyrene oligomer melts for three separate systems with 11, 21, and 41 monomers per chain and a mapping of one monomer per CG site. To parameterize the friction factor, target values are extracted from the AA dynamics using translational monomer diffusion, translational chain diffusion, and rotational chain motion to test the consistency of the parameterization across different modes of motion. We find that the value of the friction parameter needed to bring the CG dynamics in line with AA target values varies based on the mode of parameterization with short-time monomer translational dynamics requiring the highest values, long-time chain translational dynamics requiring the lowest values, and rotational dynamics falling in between. The friction ranges most widely for the shortest chains, and the span narrows with increasing chain length. For longer chains, a practical working value of the friction parameter may be derived from the rotational dynamics, owing to the contribution of multiple relaxation modes to chain rotation and a lack of sensitivity of the translational dynamics at these intermediate levels of friction. A study of equilibrium chain structure reveals that all chains studied are non-Gaussian. However, longer chains better approximate ideal chain dimensions than more rod-like shorter chains and thus are most closely described by a single friction parameter. We also find that the separability of the conservative and dissipative potentials is preserved.

MD simulations of charged binary mixtures reveal a generic relation between high- and low-temperature behavior

Experimental studies of the glassy slowdown in molecular liquids indicate that the high-temperature activation energy E_∞ of glass-forming liquids is directly related to their glass transition temperature T_g. To further investigate such a possible relation between high- and low-temperature dynamics in glass-forming liquids, we analyze the glassy dynamics of binary mixtures using molecular dynamics simulations. We consider a binary mixture of charged Lennard-Jones particles and vary the partial charges of the particles and, thus, the high-temperature activation energy and the glass transition temperature of the system. Based on previous results, we introduce a phenomenological model describing relaxation times over the whole temperature regime from high temperatures to temperatures well inside the supercooled regime. By investigating the dynamics of both particle species on molecular and diffusive length scales along isochoric and isobaric pathways, we find a quadratic charge dependence of both E_∞ and T_g, resulting in an approximately constant ratio of both quantities independent of the underlying observable, the thermodynamic ensemble, and the particle species, and this result is robust against the actual definition of T_g. This generic relation between the activation energy and the glass transition temperature indicates that high-temperature dynamics and the glassy slowdown are related phenomena, and the knowledge of E_∞ may allow us to approximately predict T_g.

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.

Localization model description of the interfacial dynamics of crystalline Cu and Cu64Zr36 metallic glass films

Recent studies of structural relaxation in Cu-Zr metallic glass materials having a range of compositions and over a wide range of temperatures and in crystalline UO₂ under superionic conditions have indicated that the localization model (LM) can predict the structural relaxation time τ_α of these materials from the intermediate scattering function without any free parameters from the particle mean square displacement ⟨r²⟩ at a caging time on the order of ps, i.e., the "Debye-Waller factor" (DWF). In the present work, we test whether this remarkable relation between the "fast" picosecond dynamics and the rate of structural relaxation τ_α in these model amorphous and crystalline materials can be extended to the prediction of the local interfacial dynamics of model amorphous and crystalline films. Specifically, we simulate the free-standing amorphous Cu₆₄Zr₃₆ and crystalline Cu films and find that the LM provides an excellent parameter-free prediction for τ_α of the interfacial region. We also show that the Tammann temperature, defining the initial formation of a mobile interfacial layer, can be estimated precisely for both crystalline and glass-forming solid materials from the condition that the DWFs of the interfacial region and the material interior coincide.

How to "measure" a structural relaxation time that is too long to be measured?

It has recently become possible to prepare ultrastable glassy materials characterized by structural relaxation times, which vastly exceed the duration of any feasible experiment. Similarly, new algorithms have led to the production of ultrastable computer glasses. Is it possible to obtain a reliable estimate of a structural relaxation time that is too long to be measured? We review, organize, and critically discuss various methods to estimate very long relaxation times. We also perform computer simulations of three dimensional ultrastable hard spheres glasses to test and quantitatively compare some of these methods for a single model system. The various estimation methods disagree significantly, and non-linear and non-equilibrium methods lead to a strong underestimate of the actual relaxation time. It is not yet clear how to accurately estimate extremely long relaxation times.

Metallic glass-formers in 2D exhibit the same scaling as in 3D between vibrational dynamics and structural relaxation

Glass-forming systems approaching their glass transition exhibit universal correlations between picosecond vibrational dynamics and long-time structural relaxation, which can be described by the same master curve in the bulk or confined conditions. In this work, we study at a fundamental level the effects of the reduction of spatial dimensionality on this phenomenon. We perform molecular dynamics simulations of a metallic glass-formers in two dimensions (2D). We show that in the supercooled regime particle localization in the cage and structural relaxation are blurred by long-wavelength fluctuations specific to low-dimensional systems. Once these effects are properly removed, we demonstrate that the fast dynamics and slow relaxation comply, without any adjustment, with same scaling between the structural relaxation time and the Debye-Waller factor, originally observed in three-dimensions (3D).

Glass transition temperature from the chemical structure of conjugated polymers

The glass transition temperature (Tg) is a key property that dictates the applicability of conjugated polymers. The Tg demarks the transition into a brittle glassy state, making its accurate prediction for conjugated polymers crucial for the design of soft, stretchable, or flexible electronics. Here we show that a single adjustable parameter can be used to build a relationship between the Tg and the molecular structure of 32 semiflexible (mostly conjugated) polymers that differ drastically in aromatic backbone and alkyl side chain chemistry. An effective mobility value, ζ, is calculated using an assigned atomic mobility value within each repeat unit. The only adjustable parameter in the calculation of ζ is the ratio of mobility between conjugated and non-conjugated atoms. We show that ζ correlates strongly to the Tg, and that this simple method predicts the Tg with a root-mean-square error of 13 °C for conjugated polymers with alkyl side chains.

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.

Vibrational scaling of the heterogeneous dynamics detected by mutual information

The correlations detected by the mutual information in the propensities of a molecular viscous liquid are studied by molecular-dynamics simulations. Dynamic heterogeneity is evidenced and two particle fractions with different mobility and relaxation identified. The two fractions exhibit the scaling of their relaxation in terms of the rattling amplitude of the particle trapped in the cage of the first neighbours 〈u²〉 . The scaling master curve does not differ from the one found for bulk systems, thus confirming identical results previously reported in other systems with strong dynamic heterogeneity as thin molecular films. The excitation of planar and globular structures at short and long times with respect to structural relaxation, respectively, is revealed. Some of the globular structures are different from the ones evidenced in atomic mixtures. States with equal 〈u²〉 are found to have identical time dependence of several quantities, referring to both bulk and the two fractions with heterogeneous dynamics, at least up to the structural relaxation time [Formula: see text].

Fast Vibrational Modes and Slow Heterogeneous Dynamics in Polymers and Viscous Liquids

Many systems, including polymers and molecular liquids, when adequately cooled and/or compressed, solidify into a disordered solid, i.e., a glass. The transition is not abrupt, featuring progressive decrease of the microscopic mobility and huge slowing down of the relaxation. A distinctive aspect of glass-forming materials is the microscopic dynamical heterogeneity (DH), i.e., the presence of regions with almost immobile particles coexisting with others where highly mobile ones are located. Following the first compelling evidence of a strong correlation between vibrational dynamics and ultraslow relaxation, we posed the question if the vibrational dynamics encodes predictive information on DH. Here, we review our results, drawn from molecular-dynamics numerical simulation of polymeric and molecular glass-formers, with a special focus on both the breakdown of the Stokes-Einstein relation between diffusion and viscosity, and the size of the regions with correlated displacements.

Mutual information does not detect growing correlations in the propensity of a model molecular liquid

The dynamical spatial correlations detected by the mutual information (MI) in the isoconfigurational particle displacements of a monodisperse molecular viscous liquid are studied via molecular-dynamics simulations by changing considerably both the molecular mobility and the degree of dynamical heterogeneity. Different from atomic liquids, the MI correlation length does not grow on approaching the glass transition by considering the liquid both in full detail as a collection of monomers and as a coarse-grained ensemble of molecular centers of mass. In the detailed picture, it is found that: (i) the MI correlations between monomers are largely due to inter-molecular correlations, (ii) the MI length scale is numerically identical, within the errors, to the correlation length scale of the displacement direction, as drawn by conventional correlation functions. The time evolution of the MI spatial correlations complies with the scaling between the fast vibrational dynamics and the long-time relaxation. Our findings suggest that the characteristics of the MI length scale are markedly system-dependent and not obviously related to dynamical heterogeneity.

Localization model description of diffusion and structural relaxation in superionic crystalline UO2

We test the Localization Model (LM) prediction of a parameter-free relationship between the α-structural relaxation time τ_α and the oxygen ion diffusion coefficient D_O with the Debye-Waller factor ⟨u²⟩ for crystalline UO₂ under superionic conditions where large anharmonic interactions lead to non-Arrhenius relaxation and high ion mobility. As in a previous study of structural relaxation in Cu-Zr metallic glass materials having a range of compositions, we find that the LM relationship between the picosecond atomic dynamics ("fast" beta relaxation) and the long-time structural relaxation time and oxygen ion diffusion coefficient holds to an excellent approximation without any free parameters over the full range of temperatures and pressures investigated in our simulations.

Universal behavior of the apparent fragility in ultraslow glass forming systems

Despite decades of studies on the grand problem of the glass transition the question of well-defined universal patterns, including the key problem of the previtreous behavior of the primary (structural) relaxation time, remains elusive. This report shows the universal previtreous behavior of the apparent fragility, i.e. the steepness index mP (T > Tg) = d log10τ(T)/d( Tg/T). It is evidenced that mP(T) = 1(T - T*), for T → Tg and  T*= Tg - Δ T*. Basing on this finding, the new 3-parameter dependence for portraying the previtreous behavior of the primary relaxation time has been derived: τ(T) = CΩ((T - T*)/T)-Ω × [exp((T - T*)/T)]Ω. The universality of obtained relations is evidenced for glass formers belonging to low molecular weight liquids, polymers (melt and solid), plastic crystals, liquid crystals, resins and relaxors. They exhibit clear preferences either for the VFT or for the critical-like descriptions, if recalled already used modeling. The novel relation can obey even above the dynamic crossover temperature, with the power exponent Ω ranging between ~17 (liquid crystals) to ~57 (glycerol), what may indicate the impact of symmetry on the previtreous effect. Finally, the emerging similarity to the behavior in the isotropic phase of nematic liquid crystals is recalled.

Energy renormalization for coarse-graining polymers having different segmental structures

Multiscale coarse-grained (CG) modeling of soft materials, such as polymers, is currently an art form because CG models normally have significantly altered dynamics and thermodynamic properties compared to their atomistic counterparts. We address this problem by exploiting concepts derived from the generalized entropy theory (GET), emphasizing the central role of configurational entropy s c in the dynamics of complex fluids. Our energy renormalization (ER) method involves varying the cohesive interaction strength in the CG models in such a way that dynamic properties related to s c are preserved. We test this ER method by applying it to coarse-graining polymer melts (i.e., polybutadiene, polystyrene, and polycarbonate), representing polymer materials having a relatively low, intermediate, and high degree of glass "fragility". We find that the ER method allows the dynamics of the atomistic polymer models to be faithfully described to a good approximation by CG models over a wide temperature range.

Universal localization transition accompanying glass formation: insights from efficient molecular dynamics simulations of diverse supercooled liquids

The origin of the precipitous dynamic arrest known as the glass transition is a grand open question of soft condensed matter physics. It has long been suspected that this transition is driven by an onset of particle localization and associated emergence of a glassy modulus. However, progress towards an accepted understanding of glass formation has been impeded by an inability to obtain data sufficient in chemical diversity, relaxation timescales, and spatial and temporal resolution to validate or falsify proposed theories for its physics. Here we first describe a strategy enabling facile high-throughput simulation of glass-forming liquids to nearly unprecedented relaxation times. We then perform simulations of 51 glass-forming liquids, spanning polymers, small organic molecules, inorganics, and metallic glass-formers, with longest relaxation times exceeding one microsecond. Results identify a universal particle-localization transition accompanying glass formation across all classes of glass-forming liquid. The onset temperature of non-Arrhenius dynamics is found to serve as a normalizing condition leading to a master collapse of localization data. This transition exhibits a non-universal relationship with dynamic arrest, suggesting that the nonuniversality of supercooled liquid dynamics enters via the dependence of relaxation times on local cage scale. These results suggest that a universal particle-localization transition may underpin the glass transition, and they emphasize the potential for recent theoretical developments connecting relaxation to localization and emergent elasticity to finally explain the origin of this phenomenon. More broadly, the capacity for high-throughput prediction of glass formation behavior may open the door to computational inverse design of glass-forming materials.

Molecular layers in thin supported films exhibit the same scaling as the bulk between slow relaxation and vibrational dynamics

We perform molecular-dynamics simulations of a supported molecular thin film. By varying thickness and temperature, we observe anisotropic mobility as well as strong gradients of both the vibrational motion and the structural relaxation through film layers with monomer-size thickness. We show that the gradients of the fast and the slow dynamics across the layers (except the adherent layer to the substrate) comply, without any adjustment, with the same scaling between the structural relaxation time and the Debye-Waller factor originally observed in the bulk [Larini et al., Nat. Phys., 2008, 4, 42]. The scaling is not observed if the average dynamics of the film is inspected. Our results suggest that the solidification process of each layer may be tracked by knowing solely the vibrational properties of the layer and the bulk.