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

Mixed equilibrium/nonequilibrium effects govern surface mobility in polymer glasses

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

Thickness-Dependent Segmental Dynamics in Supported Thin Films: Insights from a Dynamically Correlated Network Model

A large body of experimental studies shows that the local dynamics in supercooled liquids are significantly altered by spatial nanoconfinement. In a previous study, we proposed a concept of a dynamically correlated network (DCN) model, which assumes that segments in a supercooled liquid undergo cooperative rearrangements within a network-like cluster. We further demonstrated that a model modified for freestanding thin films can predict for the glass transition dynamics in atactic polystyrene (PS) films consistent with experimental results. In this study, we adapted the model to apply it to supported thin films by introducing a layer of virtual vacant segments at the free surface and virtual anchoring segments at the liquid/substrate interface. The latter segments, carrying a finite number of virtual segments, reduce mobility at the interface. We evaluated the cooperative cluster size and distribution with respect to temperature and film thickness, along with the average relaxation time and glass transition temperature Tg for supported thin films of PS. The model predicted that the thickness dependence of Tg for PS becomes stronger with increasing time scale, and this result agreed well with experimental data across different timescales from pseudothermodynamic and dynamic measurements. The results provide insights into the origin of the dynamical decoupling between pseudothermodynamic and dynamic glass transition behaviors.

Role of additive size in the segmental dynamics and mechanical properties of cross-linked polymers

Thermoset materials often involve the addition of molecular and nanoparticle additives to alter various chemo-physical properties of importance in their ultimate applications. The resulting compositional heterogeneities can lead to either enhancement or degradation of thermoset properties, depending on the additive chemical structure and concentration. We tentatively explore this complex physical phenomenon through the consideration of a model polymeric additive to our coarse-grained (CG) thermoset investigated in previous works by simply varying the size of additive segments compared to those of polymer melt. We find that the additive modified thermoset material becomes chemically heterogeneous from additive aggregation when the additive segments become much smaller than those of the thermoset molecules, and a clear evidence is observed in the spatial distribution of local molecular stiffness estimated from Debye-Waller factor 〈u2〉. Despite the non-monotonic variation trends observed in dynamical and mechanical properties with decreasing additive segmental size, both the structural relaxation time and moduli (i.e., shear modulus and bulk modulus) exhibit scaling laws with 〈u2〉. The present work highlights the complex role of additive size played in the dynamical and mechanical properties of thermoset polymers, which should provide a better understanding for the glass formation process of cross-linked polymer composites.

Dynamics of polylactic acid under ultrafine nanoconfinement: The collective interface effect and the spatial gradient

Polymers under nanoconfinement can exhibit large alterations in dynamics from their bulk values due to an interface effect. However, understanding the interface effect remains a challenge, especially in the ultrafine nanoconfinement region. In this work, we prepare new geometries with ultrafine nanoconfinement ∼10nm through controlled distributions of the crystalline phases and the amorphous phases of a model semi-crystalline polymer, i.e., the polylactic acid. The broadband dielectric spectroscopy measurements show that ultrafine nanoconfinement leads to a large elevation in the glass transition temperature and a strong increment in the polymer fragility index. Moreover, new relaxation time profile analyses demonstrate a spatial gradient that can be well described by either a single-exponential decay or a double-exponential decay functional form near the middle of the film with a collective interface effect. However, the dynamics at the 1-2 nm vicinity of the interface exhibit a power-law decay that is different from the single-exponential decay or double-exponential decay functional forms as predicted by theories. Thus, these results call for further investigations of the interface effect on polymer dynamics, especially for interfaces with perturbed chain packing.

Development of broad modulus profile upon polymer-polymer interface formation between immiscible glassy-rubbery domains

Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ([Formula: see text]) where previous work has demonstrated a long-range (∼200 nm) profile in local [Formula: see text] is established between immiscible glassy and rubbery polymer domains when the polymer-polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus [Formula: see text] is established when the polymer-polymer interface ([Formula: see text]5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad [Formula: see text] profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus [Formula: see text] spanning [Formula: see text]180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in [Formula: see text] and [Formula: see text] arise from a coupling of the spectrum of vibrational modes across the polymer-polymer interface as a result of acoustic impedance matching of sound waves with [Formula: see text] nm during interface broadening that can then trigger density fluctuations in the neighboring domain.

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.

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

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

Thickness Dependence of Segmental Dynamics in Free-Standing Thin Films Predicted by a Dynamically Correlated Network Model

The anomalous dynamics and glass transition behaviors of supercooled liquids under nanoconfinement, such as ultrathin polymer films, have attracted much attention in recent decades. However, a complete elucidation of this mechanism has not yet been achieved. For the dynamics of bulk materials without confinement, we previously proposed a dynamically correlated network (DCN) model, which was found to agree well with the experimental data. The model assumes that segments with thermal fluctuations are dynamically correlated to their neighbors to form string-like clusters, which eventually grow into networks as temperature decreases. In this study, we applied the DCN model to nanoconfined free-standing films by using a simple cubic lattice sandwiched between two free surface layers consisting of virtual "uncorrelated" segments. The average size of DCNs at lower temperatures decreased with decreasing thickness because of confinement. This trend was associated with a decrease in the percolation temperature at which the size of DCN diverges. It was also revealed that the fractal dimension of the generated DCNs exhibits a peak with respect to temperature. The segmental relaxation time for free-standing polystyrene films was evaluated, and the predicted thickness dependence of the glass transition temperature qualitatively agreed with the experimental data. The results suggest that the concept of DCN is compatible with the dynamics of free-standing thin films.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (T_g). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with T_g, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τ_α becomes almost a universal function of reduced temperature, (T - T_g)/T_g, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - T_g)/T_g. Evidently, T_g dominates both τ_α and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Thermodynamics of Point Defects in Solids and Relation with the Bulk Properties: Recent Results

For several decades, the crucial question has arisen as to whether there exists any direct interconnection between the thermodynamic parameters of point defects in solids with the bulk properties of the solid under investigation. To answer this important question, an interrelation of the defect Gibbs energy gi in solids with bulk properties has been proposed almost half a century ago. Considering that gi corresponds to an isobaric and isothermal process, this interrelation states that, for different processes (defect formation, self-diffusion activation, and heterodiffusion), gi is proportional to the isothermal bulk modulus B and the mean volume per atom Ω, termed cBΩ model. Here, we review several challenging applications of this interrelation that appeared during the last decade (2011–2021), including high pressure diamond anvil measurements, high Tc superconductors, nuclear fuels, and materials for micro-electronics devices, applications of usefulness in Geophysics and Seismology, a problem of major technological interest, search for compositions of better target properties in Cu-Co-Si alloys via machine learning as well as two independent studies on the physical origin of this interrelation that has been further strengthened during the last few years.