Free Volume in the Melt and How It Correlates with Experimental Glass Transition Temperatures: Results for a Large Set of Polymers

Enhanced Dielectric Strength and Capacitive Energy Density of Cyclic Polystyrene Films

The maximum capacitive energy stored in polymeric dielectric capacitors, which are ubiquitous in high-power-density devices, is dictated by the dielectric breakdown strength of the dielectric polymer. The fundamental mechanisms of the dielectric breakdown, however, remain unclear. Based on a simple free-volume model of the polymer fluid state, we hypothesized that the free ends of linear polymer chains might act as “defect” sites, at which the dielectric breakdown can initiate. Thus, the dielectric breakdown strength of cyclic polymers should exhibit enhanced stability in comparison to that of their linear counterparts having the same composition and similar molar mass. This hypothesis is supported by the ∼50% enhancement in the dielectric breakdown strength and ∼80% enhancement in capacitive energy density of cyclic polystyrene melt films in comparison to corresponding linear polystyrene control films. Furthermore, we observed that cyclic polymers exhibit a denser packing density than the linear chain melts, an effect that is consistent with and could account for the observed property changes. Our work demonstrates that polymer topology can significantly influence the capacitive properties of polymer films, and correspondingly, we can expect polymer topology to influence the gas permeability, shear modulus, and other properties of thin films dependent on film density.

Defining the Macromolecules of Tomorrow through Synergistic Sustainable Polymer Research

Transforming how plastics are made, unmade, and remade through innovative research and diverse partnerships that together foster environmental stewardship is critically important to a sustainable future. Designing, preparing, and implementing polymers derived from renewable resources for a wide range of advanced applications that promote future economic development, energy efficiency, and environmental sustainability are all central to these efforts. In this Chemical Reviews contribution, we take a comprehensive, integrated approach to summarize important and impactful contributions to this broad research arena. The Review highlights signature accomplishments across a broad research portfolio and is organized into four wide-ranging research themes that address the topic in a comprehensive manner: Feedstocks, Polymerization Processes and Techniques, Intended Use, and End of Use. We emphasize those successes that benefitted from collaborative engagements across disciplinary lines.

Free Volume Element Sizes and Dynamics in Polystyrene and Poly(methyl methacrylate) Measured with Ultrafast Infrared Spectroscopy

The size, size distribution, dynamics, and electrostatic properties of free volume elements (FVEs) in polystyrene (PS) and poly(methyl methacrylate) (PMMA) were investigated using the Restricted Orientation Anisotropy Method (ROAM), an ultrafast infrared spectroscopic technique. The restricted orientational dynamics of a vibrational probe embedded in the polymer matrix provides detailed information on FVE sizes and their probability distribution. The probe's orientational dynamics vary as a function of its frequency within the inhomogeneously broadened vibrational absorption spectrum. By characterizing the degree of orientational restriction at different probe frequencies, FVE radii and their probability distribution were determined. PS has larger FVEs and a broader FVE size distribution than PMMA. The average FVE radii in PS and PMMA are 3.4 and 3.0 Å, respectively. The FVE radius probability distribution shows that the PS distribution is non-Gaussian, with a tail to larger radii, whereas in PMMA, the distribution is closer to Gaussian. FVE structural dynamics, previously unavailable through other techniques, occur on a ∼150 ps time scale in both polymers. The dynamics involve FVE shape fluctuations which, on average, conserve the FVE size. FVE radii were associated with corresponding electric field strengths through the first-order vibrational Stark effect of the CN stretch of the vibrational probe, phenyl selenocyanate (PhSeCN). PMMA displayed unique measured FVE radii for each electric field strength. By contrast, PS showed that, while larger radii correspond to unique and relatively weak electric fields, the smallest measured radii map onto a broad distribution of strong electric fields.

Elucidating the Physicochemical Basis of the Glass Transition Temperature in Linear Polyurethane Elastomers with Machine Learning

The glass transition temperature (T_g) is a fundamental property of polymers that strongly influences both mechanical and flow characteristics of the material. In many important polymers, configurational entropy of side chains is a dominant factor determining it. In contrast, the thermal transition in polyurethanes is thought to be determined by a combination of steric and electronic factors from the dispersed hard segments within the soft segment medium. Here, we present a machine learning model for the T_g in linear polyurethanes and aim to uncover the underlying physicochemical parameters that determine this. The model was trained on literature data from 43 industrially relevant combinations of polyols and isocyanates using descriptors derived from quantum chemistry, cheminformatics, and solution thermodynamics forming the feature space. Random forest and regularized regression were then compared to build a sparse linear model from six descriptors. Consistent with empirical understanding of polyurethane chemistry, this study indicates the characteristics of isocyanate monomers strongly determine the increase in T_g. Accurate predictions of T_g from the model are demonstrated, and the significance of the features is discussed. The results suggest that the tools of machine learning can provide both physical insights as well as accurate predictions of complex material properties.

Comparing refractive index and density changes with decreasing film thickness in thin supported films across different polymers

Density changes in thin polymer films have long been considered as a possible explanation for shifts in the thickness-dependent glass transition temperature T_g(h) in such nanoconfined systems, given that the glass transition is fundamentally associated with packing frustration during material densification on cooling. We use ellipsometry to compare the temperature-dependent refractive index with decreasing thickness n(h) for supported films of poly(2-vinyl pyridine) (P2VP), poly(methyl methacrylate) (PMMA), and polystyrene (PS), as these polymers have different silica substrate interactions. We observe similar n(h) trends for all three polymers, with near equivalence of P2VP and PS, characterized by a large apparent increase in refractive index for h ≤ 40 nm-65 nm depending on the polymer. Possible sources of molecular dipole orientation within the film are tested by varying molecular weight, polydispersity, chain conformation, and substrate chemistry. Such film inhomogeneities associated with non-uniform polarizability would invalidate the use of homogeneous layer approximations inherent in most thin film analysis methods, which we believe likely explains recent reports of large unphysical increases in film density with decreasing thickness by a variety of different experimental techniques.

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.

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.

A free volume theory on the chain length dependence of the diffusivity of linear polymers

A free volume theory was developed to account for the crossover of the chain length dependence of the center-of-mass self-diffusion coefficient of linear polymers from unentangled to entangled regimes. Similar to the original free volume theory of Cohen and Turnbull, this theory requires information about the free volume overlapping factor (α), critical free volume per bead (v), and mean free volume per bead (〈v_f,i〉). However, one additional parameter is needed and it is the critical fraction of beads having free volume greater than or equal to αv termed as φ⁺. Here, α and v can be readily determined from the intermolecular and intramolecular radial distribution functions (i.e., g(r) and g^intra(r)) obtained from molecular dynamics (MD) simulation and they were found to be 0.5 and 0.0257 nm³, respectively, for polyethylene melts and it is not dependent on N. 〈v_f,i〉 was determined using the generic van der Waals (GvdW) equation of state and it had a value of 0.01 nm³ and the volume available to each bead can also be determined by Voronoi tessellation (VT) on the corresponding MD simulation trajectories. VT yielded exact probability of finding a certain amount of free volume and the free volume distribution was found in the form of the gamma distribution that is consistent with the positron annihilation lifetime spectroscopy observation. Finally, φ⁺ was calculated using the experimentally measured activation energies for diffusion per polyethylene molecule with different chain lengths and was found to be approximately 0.22 that was in line with what was found from MD simulations.

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.

Unraveling substituent effects on the glass transition temperatures of biorenewable polyesters

Converting biomass-based feedstocks into polymers not only reduces our reliance on fossil fuels, but also furnishes multiple opportunities to design biorenewable polymers with targeted properties and functionalities. Here we report a series of high glass transition temperature (Tg up to 184 °C) polyesters derived from sugar-based furan derivatives as well as a joint experimental and theoretical study of substituent effects on their thermal properties. Surprisingly, we find that polymers with moderate steric hindrance exhibit the highest Tg values. Through a detailed Ramachandran-type analysis of the rotational flexibility of the polymer backbone, we find that additional steric hindrance does not necessarily increase chain stiffness in these polyesters. We attribute this interesting structure-property relationship to a complex interplay between methyl-induced steric strain and the concerted rotations along the polymer backbone. We believe that our findings provide key insight into the relationship between structure and thermal properties across a range of synthetic polymers.

Glass transition of polymers in bulk, confined geometries, and near interfaces

When cooled or pressurized, polymer melts exhibit a tremendous reduction in molecular mobility. If the process is performed at a constant rate, the structural relaxation time of the liquid eventually exceeds the time allowed for equilibration. This brings the system out of equilibrium, and the liquid is operationally defined as a glass-a solid lacking long-range order. Despite almost 100 years of research on the (liquid/)glass transition, it is not yet clear which molecular mechanisms are responsible for the unique slow-down in molecular dynamics. In this review, we first introduce the reader to experimental methodologies, theories, and simulations of glassy polymer dynamics and vitrification. We then analyse the impact of connectivity, structure, and chain environment on molecular motion at the length scale of a few monomers, as well as how macromolecular architecture affects the glass transition of non-linear polymers. We then discuss a revised picture of nanoconfinement, going beyond a simple picture based on interfacial interactions and surface/volume ratio. Analysis of a large body of experimental evidence, results from molecular simulations, and predictions from theory supports, instead, a more complex framework where other parameters are relevant. We focus discussion specifically on local order, free volume, irreversible chain adsorption, the Debye-Waller factor of confined and confining media, chain rigidity, and the absolute value of the vitrification temperature. We end by highlighting the molecular origin of distributions in relaxation times and glass transition temperatures which exceed, by far, the size of a chain. Fast relaxation modes, almost universally present at the free surface between polymer and air, are also remarked upon. These modes relax at rates far larger than those characteristic of glassy dynamics in bulk. We speculate on how these may be a signature of unique relaxation processes occurring in confined or heterogeneous polymeric systems.

Changes in the temperature-dependent specific volume of supported polystyrene films with film thickness

Recent studies have measured or predicted thickness-dependent shifts in density or specific volume of polymer films as a possible means of understanding changes in the glass transition temperature Tg(h) with decreasing film thickness with some experimental works claiming unrealistically large (25%-30%) increases in film density with decreasing thickness. Here we use ellipsometry to measure the temperature-dependent index of refraction of polystyrene (PS) films supported on silicon and investigate the validity of the commonly used Lorentz-Lorenz equation for inferring changes in density or specific volume from very thin films. We find that the density (specific volume) of these supported PS films does not vary by more than ±0.4% of the bulk value for film thicknesses above 30 nm, and that the small variations we do observe are uncorrelated with any free volume explanation for the Tg(h) decrease exhibited by these films. We conclude that the derivation of the Lorentz-Lorenz equation becomes invalid for very thin films as the film thickness approaches ∼20 nm, and that reports of large density changes greater than ±1% of bulk for films thinner than this likely suffer from breakdown in the validity of this equation or in the difficulties associated with accurately measuring the index of refraction of such thin films. For larger film thicknesses, we do observed small variations in the effective specific volume of the films of 0.4 ± 0.2%, outside of our experimental error. These shifts occur simultaneously in both the liquid and glassy regimes uniformly together starting at film thicknesses less than ∼120 nm but appear to be uncorrelated with Tg(h) decreases; possible causes for these variations are discussed.

Enhanced diffusion and mobile fronts in a simple lattice model of glass-forming liquids

The diffusion of mobility in bulk and thin film fluids near their glass transition is examined with a kinetic lattice model, and compared to recent experiments on bulk liquids and vapor-deposited thin film glasses. The "limited mobility" (LM) lattice model exhibits dynamic heterogeneity of mobility when the fluid is near its kinetic arrest transition; a finite-parameter second-order critical point in the LM model bearing strong resemblance to the glass transition in real fluids. The spatial heterogeneity of mobility near kinetic arrest leads to dynamics that violate the Stokes-Einstein relation. To make connections with experiment, LM model simulations of self-diffusion constants in fluids near kinetic arrest are compared to those in two organic glass-formers. In addition, simulations of mobility in films that have been temperature-jumped above kinetic arrest (starting from an arrested state) are carried out. The films develop a "front" of mobility at their free surface that progresses into the film interior at a constant rate, thereby mobilising the entire film to fluidity. The velocity of the front scales with the self-diffusion constant for analogous bulk systems-an observation consistent with experiments on vapor-deposited molecular thin films.