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.

Glass formation and dynamics of model polymer films with one versus two active interfaces.

Polymers and other glass-forming liquids can exhibit profound alterations in dynamics in the nanoscale vicinity of interfaces, over a range appreciably exceeding that of typical interfacial thermodynamic gradients. The understanding of these dynamical gradients is particularly complicated in systems with internal or external nanoscale dimensions, where a gradient nucleated at one interface can impinge on a second, potentially distinct, interface. To better understand the interactions that govern system dynamics and glass formation in these cases, here we simulate the baseline case of a glass-forming polymer film, over a wide range of thickness, supported on a dynamically neutral substrate that has little effect on nearby dynamics. We compare these results to our prior simulations of freestanding films. Results indicate that dynamical gradients in our simulated systems, as measured based upon translational relaxation, are simply truncated when they impinge on a secondary surface that is locally dynamically neutral. Altered film behavior can be described almost entirely by gradient effects down to the thinnest films probed, with no evidence for finite-size effects sometimes posited to play a role in these systems. Finally, our simulations predict that linear gradient overlap effects in the presence of symmetric dynamically active interfaces yield a non-monotonic variation of the whole free standing film stretching exponent (relaxation time distribution breadth). The maximum relaxation time distribution breadth in simulation is found at a film thickness of 4-5 times the interfacial gradient range. Observation of this maximum in experiment would provide an important validation that the gradient behavior observed in simulation persists to experimental timescales. If validated, observation of this maximum would potentially also enable determination of the dynamic gradient range from experimental mean-film measurements of film dynamics.

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.

Mobility gradients yield rubbery surfaces on top of polymer glasses.

Many emerging materials, such as ultrastable glasses1,2 of interest for phone displays and OLED television screens, owe their properties to a gradient of enhanced mobility at the surface of glass-forming liquids. The discovery of this surface mobility enhancement3-5 has reshaped our understanding of the behaviour of glass formers and of how to fashion them into improved materials. In polymeric glasses, these interfacial modifications are complicated by the existence of a second length scale-the size of the polymer chain-as well as the length scale of the interfacial mobility gradient6-9. Here we present simulations, theory and time-resolved surface nano-creep experiments to reveal that this two-scale nature of glassy polymer surfaces drives the emergence of a transient rubbery, entangled-like surface behaviour even in polymers comprised of short, subentangled chains. We find that this effect emerges from superposed gradients in segmental dynamics and chain conformational statistics. The lifetime of this rubbery behaviour, which will have broad implications in constraining surface relaxations central to applications including tribology, adhesion, and surface healing of polymeric glasses, extends as the material is cooled. The surface layers suffer a general breakdown in time-temperature superposition (TTS), a fundamental tenet of polymer physics and rheology. This finding may require a reevaluation of strategies for the prediction of long-time properties in polymeric glasses with high interfacial areas. We expect that this interfacial transient elastomer effect and TTS breakdown should normally occur in macromolecular systems ranging from nanocomposites to thin films, where interfaces dominate material properties5,10.

Nature of dynamic gradients, glass formation, and collective effects in ultrathin freestanding films.

Molecular, polymeric, colloidal, and other classes of liquids can exhibit very large, spatially heterogeneous alterations of their dynamics and glass transition temperature when confined to nanoscale domains. Considerable progress has been made in understanding the related problem of near-interface relaxation and diffusion in thick films. However, the origin of "nanoconfinement effects" on the glassy dynamics of thin films, where gradients from different interfaces interact and genuine collective finite size effects may emerge, remains a longstanding open question. Here, we combine molecular dynamics simulations, probing 5 decades of relaxation, and the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory, addressing 14 decades in timescale, to establish a microscopic and mechanistic understanding of the key features of altered dynamics in freestanding films spanning the full range from ultrathin to thick films. Simulations and theory are in qualitative and near-quantitative agreement without use of any adjustable parameters. For films of intermediate thickness, the dynamical behavior is well predicted to leading order using a simple linear superposition of thick-film exponential barrier gradients, including a remarkable suppression and flattening of various dynamical gradients in thin films. However, in sufficiently thin films the superposition approximation breaks down due to the emergence of genuine finite size confinement effects. ECNLE theory extended to treat thin films captures the phenomenology found in simulation, without invocation of any critical-like phenomena, on the basis of interface-nucleated gradients of local caging constraints, combined with interfacial and finite size-induced alterations of the collective elastic component of the structural relaxation process.

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.

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.

Design rules for glass formation from model molecules designed by a neural-network-biased genetic algorithm.

The glass transition - an apparent amorphous solidification process - is a central feature of the physical properties of soft materials such as polymers and colloids. A key element of this phenomenon is the observation of a broad spectrum of deviations from an Arrhenius temperature of dynamics in glass-forming liquids, with the extent of deviation quantified by the "fragility" of glass formation. The underlying origin of "fragile" glass formation and its dependence on molecular structure remain major open questions in condensed matter physics and soft materials science. Here we employ molecular dynamics simulations, together with a neural-network-biased genetic algorithm, to design and study model rigid molecules spanning a broad range of fragilities of glass formation. Results indicate that fragility of glass formation can be controlled by tuning molecular asphericity, with extended molecules tending to exhibit low fragilities and compact molecules tending toward higher fragilities. The glass transition temperature itself, on the other hand, correlates well with high-temperature activation behavior and with density. These results point the way towards rational design of glass-forming liquids spanning a range of dynamical behavior, both via these physical insights and via future extensions of this evolutionary design strategy to real chemistries. Finally, we show that results compare well with predictions of the nonlinear Langevin theory of liquid dynamics, which is a precursor of the more recently developed elastically collective nonlinear Langevin equation theory of Mirigian and Schweizer, identifying this framework as a promising basis for molecular design of the glass transition.

Dynamical Correlations for Statistical Copolymers from High-Throughput Broad-Band Dielectric Spectroscopy.

Broad-band dielectric spectroscopy (BDS) provides a powerful method of characterizing relaxation dynamics in diverse materials. Here we describe and employ a novel instrument for high-throughput broad-band dielectric spectroscopy (HTBDS) that accelerates this capability, enabling simultaneous measurements of 48 samples. This capability is based around a coaxial switching system for rapid scanning between multiple samples on the same sample stage, coordinated with shared environmental control. We validate the instrument by measuring dielectric response in three polymers, distributed across 48 sample sites, and comparing results to measurements via a standard BDS instrument. Results are found to be reproducible and are in agreement with relaxation times from traditional BDS. We then employ HTBDS to establish mixing rules for glass transition temperatures, kinetic fragility indices, and segmental stretching exponents in a series of acrylate copolymers, a matter of considerable technological interest in a variety of technological applications. Results are consistent with the empirical Fox rule for the glass transition temperature Tg averaging in polymer blends, while they reveal a linear mixing rule for kinetic fragility indices. Finally, we test several proposed correlations between these distinct dynamical properties. These results demonstrate that HTBDS enables measurements of polymer relaxation at a throughput approximately 10 times higher than that of standard BDS approaches, opening the door to high-throughput materials design of dynamic response across a broad range of frequencies.

Poisson ratio mismatch drives low-strain reinforcement in elastomeric nanocomposites.

Introduction of nanoparticulate additives can dramatically impact elastomer mechanical response, with large enhancements in modulus, toughness, and strength. Despite the societal importance of these effects, their mechanistic origin remains unsettled. Here, using a combination of theory and molecular dynamics simulation, we show that low-strain extensional reinforcement of elastomers is driven by a nanoparticulate-jamming-induced suppression in the composite Poisson ratio. This suppression forces an increase in rubber volume with extensional deformation, effectively converting a portion of the rubber's bulk modulus into an extensional modulus. A theory describing this effect is shown to interrelate the Poisson ratio and modulus across a matrix of simulated elastomeric nanocomposites of varying loading and nanoparticle structure. This model provides a design rule for structured nanoparticulates that maximizes elastomer mechanical response via suppression of the composite Poisson ratio. It also positions elastomeric nanocomposites as having a qualitatively different character than Poisson-ratio-matched plastic nanocomposites, where this mechanism is absent.

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.

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 Tg 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 Tg 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.

Temperature-Independent Rescaling of the Local Activation Barrier Drives Free Surface Nanoconfinement Effects on Segmental-Scale Translational Dynamics near Tg.

Near-interface alterations in dynamics and glass formation behavior have been the subject of extensive study for the past two decades, both because of their practical importance and in the hope of revealing underlying correlation lengths underpinning glass transition more generally. Here we employ molecular dynamics simulations of thick films to demonstrate that these effects emerge, for segmental-scale translational dynamics at low temperature, from a temperature-independent rescaling of the local activation barrier. This rescaling manifests as a fractional power law decoupling relationship of local dynamics relative to the bulk, with a transition from a regime of weak decoupling at high temperatures to a regime of strong decoupling at low temperatures. The range of this effect saturates at low temperatures, with 90% of the surface perturbation in the barrier lost over a range of 12 segmental diameters. These findings reduce the phenomenology of Tg nanoconfinement effects to two properties-a position-dependent, temperature independent, barrier rescaling factor and an onset time scale-while substantially constraining the predictions required from any theoretical explanation of this phenomenon.

The relationship between dynamic and pseudo-thermodynamic measures of the glass transition temperature in nanostructured materials.

Despite decades of research on the effects of nanoconfinement on the glass transition temperature Tg, apparent discrepancies between pseudothermodynamic and dynamic measurements of these effects have raised questions regarding the presence of long-ranged interfacial dynamic gradients in glass-forming liquids. Here we show that these differences can be accounted for based on disparities in these methods' weightings over local Tg's within an interfacial gradient. This finding suggests that a majority of experimental data are consistent with a broad interfacial dynamic interphase in glass-forming liquids.

Does fragility of glass formation determine the strength of Tg-nanoconfinement effects?

Nanoscale confinement has been shown to alter the glass transition and associated mechanical and transport properties of glass-forming materials. Inspired by expected interrelations between nanoconfinement effects, cooperative dynamics in supercooled liquids, and the "fragility" (or temperature-abruptness) of the glass transition, it is commonly expected that nanoconfinement effects on Tg should be more pronounced for more fragile glass formers. Here we employ molecular dynamics simulations of glass formation in the bulk and under nanoconfinement of model polymers in which we systematically tune fragility by several routes. Results indicate that a correlation between fragility and the strength of nanoconfinement effects is weak to modest at best when considering all systems but can appear to be stronger when considering a subset of systems. This outcome is consistent with a reanalysis of the Adam-Gibbs theory of glass formation indicating that fragility does not necessarily track in a universal way with the scale of cooperative motion in glass-forming liquids. Finally, we find that factors such as composition gradients or variability in measurement sensitivity to different parts of the dynamic gradient have the potential to significantly confound efforts to identify trends in Tg-nanoconfinement effects with variables such as fragility, emphasizing the importance of employing diverse data sets and multiple metrologies in the study of this problem.

Spatially Distributed Rheological Properties in Confined Polymers by Noncontact Shear.

When geometrically confined to the nanometer length scale, a condition in which a large portion of the material is in the nanoscale vicinity of interfaces, polymers can show astonishing changes in physical properties. In this investigation, we employ a unique noncontact capillary nanoshearing method to directly probe nanoresolved gradients in the rheological response of ultrathin polymer films as a function of temperature and stress. Results show that ultrathin polymer films, in response to an applied shear stress, exhibit a gradient in molecular mobility and viscosity that originates at the interfaces. We demonstrate, via molecular dynamics simulations, that these gradients in molecular mobility reflect gradients in the average segmental relaxation time and the glass-transition temperature.

Neural-Network-Biased Genetic Algorithms for Materials Design: Evolutionary Algorithms That Learn.

Machine learning has the potential to dramatically accelerate high-throughput approaches to materials design, as demonstrated by successes in biomolecular design and hard materials design. However, in the search for new soft materials exhibiting properties and performance beyond those previously achieved, machine learning approaches are frequently limited by two shortcomings. First, because they are intrinsically interpolative, they are better suited to the optimization of properties within the known range of accessible behavior than to the discovery of new materials with extremal behavior. Second, they require large pre-existing data sets, which are frequently unavailable and prohibitively expensive to produce. Here we describe a new strategy, the neural-network-biased genetic algorithm (NBGA), for combining genetic algorithms, machine learning, and high-throughput computation or experiment to discover materials with extremal properties in the absence of pre-existing data. Within this strategy, predictions from a progressively constructed artificial neural network are employed to bias the evolution of a genetic algorithm, with fitness evaluations performed via direct simulation or experiment. In effect, this strategy gives the evolutionary algorithm the ability to "learn" and draw inferences from its experience to accelerate the evolutionary process. We test this algorithm against several standard optimization problems and polymer design problems and demonstrate that it matches and typically exceeds the efficiency and reproducibility of standard approaches including a direct-evaluation genetic algorithm and a neural-network-evaluated genetic algorithm. The success of this algorithm in a range of test problems indicates that the NBGA provides a robust strategy for employing informatics-accelerated high-throughput methods to accelerate materials design in the absence of pre-existing data.

Three-Layer Model for the Emergence of Ultrastable Glasses from the Surfaces of Supercooled Liquids.

Ultrastable glasses produced by vapor deposition exhibit properties consistent with glasses that have been aged for thousands of years or more. These materials' properties are believed to emerge from the presence of a mobile layer at the surface of supercooled liquids that allows access to lower-energy states. However, the precise mechanism by which this enhanced mobility is translated into ultrastable glass behavior remains incompletely understood. Here we show that enhanced densities and stabilities consistent with ultrastable glasses specifically can emerge as a result of a mismatch in the length scales of thermodynamic and dynamic gradients at the surfaces of equilibrium supercooled liquids. In particular, ultrastable glass properties can be understood within a three-layer model of the interface in which a "facilitated layer" intermediate between the surface and bulk exhibits bulk-like liquid-state density but suppressed Tg. This mismatch in length-scale has previously been correlated with the scale of cooperative rearrangements in the supercooled state, suggesting that ultrastable glasses may be a direct consequence of the cooperative nature of dynamics in equilibrium supercooled liquids.

Tuning Polymer Glass Formation Behavior and Mechanical Properties with Oligomeric Diluents of Varying Stiffness.

Small-molecule diluents are important tools in the control of polymers' glass formation, transport, and mechanical properties. While recent work has indicated that these diluents can impose a more diverse range of effects than previously appreciated, use of these additives to rationally control polymer properties requires a predictive understanding of their effects. Here we employ molecular dynamics simulations to show that diluent-induced changes in a polymer's glass transition temperature Tg can be predicted based on the diluent's Debye-Waller factor ⟨u2⟩, a measure of picosecond time scale rattle-space, via a functional form previously found to predict nanoconfinement-induced shifts in polymer Tg. Moreover, we show that diluent-induced alterations in polymer segmental relaxation time are related to changes in modulus and ⟨u2⟩ via the Generalized Localization Model of relaxation. These results provide new design principles for the use of oligomeric diluents in achieving independent, targeted control of structural relaxation and glassy moduli.

Combined Dependence of Nanoconfined Tg on Interfacial Energy and Softness of Confinement.

We employ molecular dynamics simulations of nanolayered polymers to systematically quantify the dependence of Tg nanoconfinement effects on interfacial energy and the "softness" of confinement. Results indicate that nanoconfined Tg depends linearly on interfacial adhesion energy, with a slope that scales exponentially with the ratio of the bulk Debye-Waller factors ⟨u2⟩ of the confined and confining materials. These trends, together with a convergence at low interfacial adhesion energy to the Tg of an equivalent freestanding film, are captured in a single functional form, with only three parameters explicitly referring to the confined state. The observed dependence on ⟨u2⟩ indicates that softness of nanoconfinement should be defined in terms of the relative high frequency shear moduli, rather than low frequency moduli or relaxation times, of the confined and confining materials.