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

Effect of penetrant-polymer interactions and shape on the motion of molecular penetrants in dense polymer networks

The diffusion of dilute molecular penetrants within polymers plays a crucial role in the advancement of material engineering for applications such as coatings and membrane separations. The potential of highly cross-linked polymer networks in these applications stems from their capacity to adjust the size and shape selectivity through subtle changes in network structures. In this paper, we use molecular dynamics simulation to understand the role of penetrant shape (aspect ratios) and its interaction with polymer networks on its diffusivity. We characterize both local penetrant hopping and the long-time diffusive motion for penetrants and consider different aspect ratios and penetrant-network interaction strengths at a variety of cross-link densities and temperatures. The shape affects the coupling of penetrant motion to the cross-link density- and temperature-dependent structural relaxation of networks and also affects the way a penetrant experiences the confinement from the network meshes. The attractive interaction between the penetrant and network primarily affects the former since only the system of dilute limit is of present interest. These results offer fundamental insights into the intricate interplay between penetrant characteristics and polymer network properties and also suggest future directions for manipulating polymer design to enhance the separation efficiency.

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

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

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.

How Segmental Dynamics and Mesh Confinement Determine the Selective Diffusivity of Molecules in Cross-Linked Dense Polymer Networks

The diffusion of molecules ("penetrants") of variable size, shape, and chemistry through dense cross-linked polymer networks is a fundamental scientific problem broadly relevant in materials, polymer, physical, and biological chemistry. Relevant applications include separation membranes, barrier materials, drug delivery, and nanofiltration. A major open question is the relationship between transport, thermodynamic state, and penetrant and polymer chemical structure. Here we combine experiment, simulation, and theory to unravel these competing effects on penetrant transport in rubbery and supercooled polymer permanent networks over a wide range of cross-link densities, size ratios, and temperatures. The crucial importance of the coupling of local penetrant hopping to polymer structural relaxation and the secondary importance of mesh confinement effects are established. Network cross-links strongly slow down nm-scale polymer relaxation, which greatly retards the activated penetrant diffusion. The demonstrated good agreement between experiment, simulation, and theory provides strong support for the size ratio (penetrant diameter to the polymer Kuhn length) as a key variable and the usefulness of coarse-grained simulation and theoretical models that average over Angstrom scale structure. The developed theory provides an understanding of the physical processes underlying the behaviors observed in experiment and simulation and suggests new strategies for enhancing selective polymer membrane design.

End-Tethered Chains Increase the Local Glass Transition Temperature of Matrix Chains by 45 K Next to Solid Substrates Independent of Chain Length

The local glass transition temperature T_g of pyrene-labeled polystyrene (PS) chains intermixed with end-tethered PS chains grafted to a neutral silica substrate was measured by fluorescence spectroscopy. To isolate the impact of the grafted chains, the films were capped with bulk neat PS layers eliminating competing effects of the free surface. Results demonstrate that end-grafted chains strongly increase the local T_g of matrix chains by ≈45 K relative to bulk T_g, independent of grafted chain molecular weight from M_n = 8.6 to 212 kg/mol and chemical end-group, over a wide range of grafting densities σ = 0.003 to 0.33 chains/nm² spanning the mushroom-to-brush transition regime. The tens-of-degree increase in local T_g resulting from immobilization of the chain ends by covalent bonding in this athermal system suggests a mechanism that substantially increases the local activation energy required for cooperative rearrangements.

Temperature dependent perylene fluorescence as a probe of local polymer glass transition dynamics

We demonstrate how the temperature dependence of perylene's fluorescence emission spectrum doped in bulk polymer matrices is sensitive to the local glass transition dynamics of the surrounding polymer segments. Focusing on the first fluorescence peak, we show that the intensity ratio I_Ratio(T) = I_Peak(T)/I_SRR between the first peak and a self referencing region (SRR) has a temperature dependence resulting from the temperature-dependent nonradiative decay pathway of the excited perylene dye that is influenced by its intermolecular collisions with the surrounding polymers segments. For different polymer matrices, poly(methyl methacrylate) (PMMA), polystyrene (PS), poly(2-vinyl pyridine) (P2VP), and polycarbonate (PC), we demonstrate that I_Ratio(T) exhibits a transition from a non-Arrhenius behavior above the glass transition temperature T_g of the polymer to an Arrhenius temperature dependence with constant activation energy E below the T_g of the polymer matrix, indicating perylene's sensitivity to cooperative α-relaxation dynamics of the polymer matrix. This transition in temperature dependence allows us to identify a perylene defined local Tperyleneg of the surrounding polymer matrix that agrees well with the known T_g values of the polymers. We define a fluorescence intensity shift factor in analogy with the Williams-Landel-Ferry (WLF) equation and use literature WLF parameters for the polymer matrix to quantify the calibration factor c_f needed to convert the fluorescence intensity ratio to the effective time scale ratio described by the conventional WLF shift factor. This work opens up a new characterization method that could be used to map the local dynamical response of the glass transition in nanoscale polymer materials using appropriate covalent attachment of perylene to polymer chains.

Glass transition of ion-containing polymer melts in bulk and thin films

Ion-containing polymers often are good glass formers, and the glass transition temperature is an important parameter to consider for practical applications, which prescribes the working temperature range for different mechanical and dynamic properties. In this work, we present a systematic molecular dynamics simulation study on the coupling of ionic correlations with the glass transition, based on a generic coarse-grained model of ionic polymers. The variation of the glass transition temperature is examined concerning the influence of the electrostatic interaction strength, charge fraction, and charge sequence. The interplay with the film thickness effect is also discussed. Our results reveal a few typical features about the glass transition process that are in qualitative agreement with previous studies, further highlighting the effects of counterion entropy at weak ionic correlations and physical crosslinking of ionic aggregates at strong ionic correlations. Detailed parametric dependencies are displayed, which demonstrate that introducing strong ionic correlations promotes vitrification while adopting a precise charge sequence and applying strong confinement with weak surface affinity reduce the glass transition temperature. Overall, our investigation provides an improved picture towards a comprehensive understanding of the glass transition in ion-containing polymeric systems from a molecular simulation perspective.

The influence of spacer composition on thermomechanical properties, crystallinity, and morphology in ionene segmented copolymers

A series of segmented ammonium ionenes with varying weight fractions of 2000 g mol-1 poly(ethylene glycol) (PEG) or poly(tetramethylene oxide) (PTMO) soft segments were synthesized, and a simplified coarse-grained model of these materials was implemented using molecular dynamics simulations. In addition to varying soft segment type (PTMO vs. PEG), charge density and soft segment content were varied to create a comprehensive series of segmented ammonium ionenes; thermogravimetric analysis reveals that all segmented ionenes in the series are thermally stable up to 240 °C. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) show the formation of phase separated microdomains at low soft segment content. In particular, DSC shows that the hard and soft domains have distinct glass transition temperatures. Similarly, simulations show that reduced soft segment content induces stronger microphase separation, reduces soft segment mobility, and increases ionic aggregate connectivity and size. These increased ionic associations result in elastomeric behavior, as evidenced by the higher rubbery plateau moduli observed at lower soft segment contents through DMA. Moreover, simulations show that ionic aggregation increases when switching from PEG to the less polar PTMO repeat units, which is consistent with DMA results showing higher plateau moduli for PTMO-based ionenes relative to PEG ionenes. DSC and X-ray diffraction determined that the degree of crystallinity increased with soft segment content regardless of segment type. Overall, these results suggest a semi-crystalline microphase-separated morphology strongly influenced by charge density, the degree of ionic aggregation, and the resulting level of confinement and mobility of the soft segments.

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.

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.

Uniaxial Deformation and Crazing in Glassy Polymer-Grafted Nanoparticle Ultrathin Films

The deformation behavior of neat, glassy polymer-grafted nanoparticle (PGN) monolayer films is studied using coarse-grained molecular dynamics simulations and experiments on polystyrene-grafted silica. In both the simulations and experiments, apparent crazing behavior is observed during deformation. The PGN systems show a relatively more uniform, perforated sheet craze structure and significantly higher strain at break than reference homopolymers of the same length. Short chain, unentangled PGN monolayers are also simulated for comparison; these are brittle and break apart without crazing. The entangled PGN simulations are analyzed in detail for systems at both high and moderate graft density. Stress-strain curves show three distinct regions: yielding and strain localization, craze widening, and strain hardening preceding catastrophic failure. The PGN stress-strain behavior appears more similar to that of longer chain, highly entangled homopolymer films than to the reference homopolymer films of the same length as the graft chains, suggesting that the particles effectively add additional entanglement points. The moderate graft density particles have higher strain-to-failure and maximum stress than the high graft density particles. We suggest this increased robustness for lower graft density systems is due to their increased interpenetration of graft chains between neighboring particles, which leads to increased interparticle entanglements per chain.

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.

A simulation study on the glass transition behavior and relevant segmental dynamics in free-standing polymer nanocomposite films

In polymer/nanoparticle composite (PNC) thin films, polymer chains experience strong confinement effects not only at the free surface area but also from nanoparticles (NPs). In this work, the influence of NP-polymer interaction and NP distribution on the polymer segmental dynamics and the glass transition behavior of PNC free-standing films are investigated through molecular dynamics simulations. We demonstrate that NPs will migrate to the film surface area and form an NP-concentrated layer when NP-polymer interactions are weak, while NPs are well dispersed in the bulk region when NP-polymer interactions are strong. In both cases, we find increases in the glass transition temperature Tg compared with the pure film without NPs, although with a different degree. The weakly interacting system has the same Tg as the pure bulk system without NPs. The NP layer formed at the surface area reduces both the mobility of the surface polymer beads and the mobility gradient in the film normal direction (MGFND), therefore resulting in an increase in the Tg which highlights the vital role of the mobile surface layer. In contrast, the NPs in the bulk region enlarge the MGFND. NPs have opposite influences on the polymer bead dynamic anisotropy when they interact weakly or strongly with polymers, weakened for the former and enhanced for the latter. These findings offer a clear picture of the segmental dynamics and glass transition behavior in free-standing PNC films with different NP-polymer interaction strengths. We hope these results will be helpful for the property design of related materials.

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.

Different metrics for connecting mobility and glassiness in thin films

Data continue to accrue indicating that experimental techniques may differ in their sensitivity to mobility and glassiness. In this work the Limited Mobility (LM) kinetic model is used to show that two metrics for tracking sample mobility yield quantitatively different results for the glass transition and mobile layer thickness in systems where free surfaces are present. Both LM metrics track the fraction of material that embodies mobile free volume; in one it is relative to that portion of the sample containing any kind (mobile and dormant) of free volume, and in the other it is relative to the overall sample. Without any kind of optimization, use of the latter metric leads to semi-quantitative agreement with experimental film results, both for the mobile layer thickness and the dependence of sample glass transition temperature on film thickness. Connecting the LM predictions with experiment also produces a semi-quantitative mapping between LM model length and temperature scales, and those of real systems.

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 T_g 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.

Thermodynamic Ultrastability of a Polymer Glass Confined at the Micrometer Length Scale

We employ fast scanning calorimetry to assess the thermodynamic state attained after a given cooling rate and the molecular mobility of glassy poly(4-tert-butylstyrene) confined at the micrometer length scale. We show that, for such a large confinement length scale, thermodynamic states with a fictive temperature (T_{f}) 80 K below the polymer glass transition temperature (T_{g}) are attained, which allows to bypass the geological timescales required for bulk glasses. Access to such states is promoted by a fast mechanism of equilibration. Importantly, the tremendous T_{f} decrease takes place while the molecular mobility remains bulklike, indicating marked decoupling between vitrification kinetics and molecular mobility.

Why we need to look beyond the glass transition temperature to characterize the dynamics of thin supported polymer films

There is significant variation in the reported magnitude and even the sign of [Formula: see text] shifts in thin polymer films with nominally the same chemistry, film thickness, and supporting substrate. The implicit assumption is that methods used to estimate [Formula: see text] in bulk materials are relevant for inferring dynamic changes in thin films. To test the validity of this assumption, we perform molecular simulations of a coarse-grained polymer melt supported on an attractive substrate. As observed in many experiments, we find that [Formula: see text] based on thermodynamic criteria (temperature dependence of film height or enthalpy) decreases with decreasing film thickness, regardless of the polymer-substrate interaction strength ε. In contrast, we find that [Formula: see text] based on a dynamic criterion (relaxation of the dynamic structure factor) also decreases with decreasing thickness when ε is relatively weak, but [Formula: see text] increases when ε exceeds the polymer-polymer interaction strength. We show that these qualitatively different trends in [Formula: see text] reflect differing sensitivities to the mobility gradient across the film. Apparently, the slowly relaxing polymer segments in the substrate region make the largest contribution to the shift of [Formula: see text] in the dynamic measurement, but this part of the film contributes less to the thermodynamic estimate of [Formula: see text] Our results emphasize the limitations of using [Formula: see text] to infer changes in the dynamics of polymer thin films. However, we show that the thermodynamic and dynamic estimates of [Formula: see text] can be combined to predict local changes in [Formula: see text] near the substrate, providing a simple method to infer information about the mobility gradient.