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Applying machine learning and quantum chemistry to predict the glass transition temperatures of polymers
Glass transition temperature (T g ) is important for understanding the physical and mechanical properties of a polymer material because it relates to the thermal energy required to transition between a hard glassy state and a soft rubbery one. Over the years, various models have been developed for predicting this thermal property from molecular structure to aid in designing novel polymers in selected classes. This work builds on those efforts by utilizing both machine learning (ML) and quantum chemistry (QC) techniques to develop models that can predict T g values from the molecular structure under different data availability scenarios and for a wide variety of polymer types. For the ML model, a graph convolutional network (GCN) was used to map topological polymer features; this model was trained against a dataset of more than 7500 T g values and resulted in a root mean square error (RMSE) of 38.1 °C. The QC-based regression model was trained on 83 T g values and produced an RMSE of 34.5 °C. In conclusion, this work demonstrated that while both model techniques produce accurate predictions and are suitable for different data availability scenarios, the QC-based regression model offered a more interpretable model framework with significantly less training data.
Glass transition temperature studies of planetary ball milled glasses: Accessing the rapidly cooled glassy state in Na 4 P 2 S 7-x O x , 0 ≤ x ≤ 7, Oxy-thio phosphate glasses
This paper details the very first in-depth study of the glass transition temperature (T g ) for planetary balled milled (PBM) Na 4 P 2 S 7-x O x (NaPSO), where 0 ≤ x ≤ 7, glasses. For 0 ≤ x ≤ 5, fully amorphous, homogeneous, and chemically reacted compositions can be prepared. For samples with 5 < x ≤ 7, partially amorphous but fully chemically reacted glass-ceramics can be produced. The reproducible, thermally cyclable onset T g and the onset crystallization temperature, T c , were investigated as a function of the composition and of the short-range order (SRO) structures of the glasses. Additionally, we examined the extreme sub-T g exothermic relaxations present due to the high energy milling processing and correspondingly high effective quenching rate. Using a differential scanning calorimeter (DSC) and scanning from well below the onset T g , the glasses are observed to relax exothermally below T g . The integrated relaxation enthalpy, ΔH rel , is ~ 0 for the x = 2 glass, but is significantly exothermic for lower and higher values of x. Once the high fictive state of these glasses has been erased by scanning to above the T g , but below the T c of the glass, the DSC scans of the glasses recover normal behavior for a normally cooled glass without any relaxation exotherm. The T g s of these glasses remain relatively constant for 0 ≤ x ≤ 3, but for glasses with 3 < x ≤ 5, T g increases sharply following the combined effects of the phosphate chain length increasing caused by the formation of bridging oxygens and the increasing concentration of more charge dense non-bridging oxygens (NBOs). For x > 5, both T g and Tc decrease sharply, becoming nearly identical at x = 7 where glass formation essentially ceases. For smaller values of x, T c increases with both chain length and the structural complexity of the composition but decreases sharply for glass-ceramics of x > 5.
Glass Transition Temperature- and Specific Volume- Composition Models for Tellurite Glasses
This report provides models for predicting composition-properties for tellurite glasses, namely specific gravity and glass transition temperature. Included are the partial specific coefficients for each model, the component validity ranges, and model fit parameters.
Machine learning prediction of glass transition temperature of conjugated polymers from chemical structure
Predicting the glass transition temperature (T g ) is of critical importance as it governs the thermomechanical performance of conjugated polymers (CPs). Here, we report a predictive modeling framework to predict T g of CPs through the integration of machine learning (ML), molecular dynamics (MD) simulations, and experiments. With 154 T g data collected, an ML model is developed by taking simplified “geometry” of six chemical building blocks as molecular features, where side-chain fraction, isolated rings, fused rings, and bridged rings features are identified as the dominant ones for T g . MD simulations further unravel the fundamental roles of those chemical building blocks in dynamical heterogeneity and local mobility of CPs at a molecular level. The developed ML model is demonstrated for its capability of predicting T g of several new high-performance solar cell materials to a good approximation. The established predictive framework facilitates the design and prediction of T g of complex CPs, paving the way for addressing device stability issues that have hampered the field from developing stable organic electronics.
Investigation of experimental signatures of spin glass transition temperature
We present a series of temperature and field-dependent magnetization studies of large single-crystal spin glass samples, focusing on both field-cooled (FC) and zero-field-cooled (ZFC) magnetization studies, as well as ac susceptibility measurements. Using the above experimental techniques we aim to understand the nature of spin glass transition in presence of a field, a key factor in understanding the properties of these systems. Building on previous studies that have explored magnetic signatures indicative of spin glass transitions, our research employs a systematic approach to refine the identification of this transition temperature. Through static and dynamic measurements, we aim to shed light on the open issues regarding the key markers of spin glass transitions, enhancing our understanding of these complex systems.
Effect of Microstructure on Chain Flexibility and Glass Transition Temperature of Polybenzofulvene
Polybenzofulvene (PBF) is a polydiene with a very high glass transition temperature (T g ), which makes it a potential candidate for use as the hard block for high-temperature thermoplastic elastomer applications. The T g s of polydienes are known to be related to chain flexibility. However, no studies have been reported that correlate the chain flexibility to the microstructure of PBF. Herein, we present a study of solution properties of linear PBFs with narrow molecular weight dispersity and having 1,2-addition ranging from 23% to 99%. The materials were prepared by living anionic polymerization under different conditions. Specifically, the chain flexibility as defined by the Flory's characteristic ratio, , and dependence of chain flexibility on microstructure by combined measurements of intrinsic viscosity and molecular weight using triple-detector size exclusion chromatography (SEC) is studied. The persistence lengths (l p ) and chain diameters (d B ) were also estimated using the touched-bead wormlike chain model. To the best of our knowledge, the characteristic ratio of PBF is found to be the highest of all polydienes that have been reported so far.
Temperature Dependence of Ar{sub n}{sup +} Cluster Backscattering from Polymer Surfaces: a New Method to Determine the Surface Glass Transition Temperature
In this work, time-of-flight secondary ion mass spectrometry (ToF-SIMS) was used to study the intensity variations of the backscattered Ar{sub n}{sup +} clusters as a function of temperature for several amorphous polymer surfaces (polyolefins, polystyrene, and polymethyl methacrylate). For all these investigated polymers, our results show a transition of the ratio Ar{sub 2}{sup +}/(Ar{sub 2}{sup +} + Ar{sub 3}{sup +}) when the temperature is scanned from –120 °C to +125 °C (the exact limits depend on the studied polymer). This transition generally spans over a few tens of degrees and the temperature of the inflection point of each curve is always lower than the bulk glass transition temperature (T{sub g}) reported for the considered polymer. Due to the surface sensitivity of the cluster backscattering process (several nanometers), the presented analysis could provide a new method to specifically evaluate a surface transition temperature of polymers, with the same lateral resolution as the gas cluster beam. .
Translational diffusion in supercooled water at and near the glass transition temperature—136 K
The properties of amorphous solid water at and near the calorimetric glass transition temperature, T g , of 136 K have been debated for years. One hypothesis is that water turns into a “true” liquid at T g (i.e., it becomes ergodic) and exhibits all the characteristics of an ergodic liquid, including translational diffusion. A competing hypothesis is that only rotational motion becomes active at T g , while the “real” glass transition in water is at a considerably higher temperature. To address this dispute, we have investigated the diffusive mixing in nanoscale water films, with thicknesses up to ∼100 nm, using infrared (IR) spectroscopy. The experiments used films that were composed of at least 90% H 2 O with D 2 O making up the balance and were conducted under conditions where H/D exchange was essentially eliminated. Because the IR spectra of multilayer D 2 O films (e.g., thicknesses of ∼3–6 nm) embedded within thick H 2 O films are distinct from the spectrum of isolated D 2 O molecules within H 2 O, the diffusive mixing of (initially) isotopically layered water films could be followed as a function of annealing time and temperature. The results show that water films with total thicknesses ranging from ∼20 to 100 nm diffusively mixed prior to crystallization for temperatures between 120 and 144 K. The translational diffusion had an Arrhenius temperature dependence with an activation energy of 40.8 ± 3.5 kJ/mol, which indicates that water at and near T g is a strong liquid. The measured diffusion coefficient at 136 K is 6.25 ± 1.4 × 10 −21 m 2 /s.
A Deep Neural Network for Accurate and Robust Prediction of the Glass Transition Temperature of Polyhydroxyalkanoate Homo- and Copolymers
The purpose of this study was to develop a data-driven machine learning model to predict the performance properties of polyhydroxyalkanoates (PHAs), a group of biosourced polyesters featuring excellent performance, to guide future design and synthesis experiments. A deep neural network (DNN) machine learning model was built for predicting the glass transition temperature, Tg, of PHA homo- and copolymers. Molecular fingerprints were used to capture the structural and atomic information of PHA monomers. The other input variables included the molecular weight, the polydispersity index, and the percentage of each monomer in the homo- and copolymers. The results indicate that the DNN model achieves high accuracy in estimation of the glass transition temperature of PHAs. In addition, the symmetry of the DNN model is ensured by incorporating symmetry data in the training process. The DNN model achieved better performance than the support vector machine (SVD), a nonlinear ML model and least absolute shrinkage and selection operator (LASSO), a sparse linear regression model. The relative importance of factors affecting the DNN model prediction were analyzed. Sensitivity of the DNN model, including strategies to deal with missing data, were also investigated. Compared with commonly used machine learning models incorporating quantitative structure–property (QSPR) relationships, it does not require an explicit descriptor selection step but shows a comparable performance. The machine learning model framework can be readily extended to predict other properties.
Challenge and Solution of Characterizing Glass Transition Temperature for Conjugated Polymers by Differential Scanning Calorimetry
Thermomechanical properties of polymers greatly depend on their glass transition temperature ( T g ). Differential scanning calorimetry (DSC) is commonly used to measure T g of polymers. Yet, many conjugated polymers (CPs), especially donor–acceptor CPs (D–A CPs), do not show a clear glass transition when measured by conventional DSC using simple heat and cool scan. In this work, we discuss the origin of the difficulty for measuring T g in such type of polymers. The changes in specific heat capacity (Δ c p ) at T g were accurately probed for a series of CPs by DSC. The results showed a significant decrease in Δ c p from flexible polymer (0.28 Jg -1 K -1 for polystyrene) to rigid CPs (10 -3 Jg -1 K -1 for a naphthalene diimide-based D–A CP). When a conjugation breaker unit (flexible unit) is added to the D–A CPs, we observed restoration of the Δ c p at T g by a factor of 10, confirming that backbone rigidity reduces the Δ c p . Additionally, an increase in the crystalline fraction of the CPs further reduces Δ c p . We conclude that the difficulties of determining T g for CPs using DSC are mainly due to rigid backbone and semicrystalline nature. We also demonstrate that physical aging can be used on DSC to help locate and confirm the glass transition for D-A CPs with weak transition signals.
Consistent and reproducible computation of the glass transition temperature from molecular dynamics simulations
In many fields, from semiconductors for opto-electronic applications to ionic liquids (ILs) for separations, the glass transition temperature (Tg) of a material is a useful gauge for its potential use in practical settings. As a result, there is a great deal of interest in predicting Tg using molecular simulations. However, the uncertainty and variation in the trend shift method, a common approach in simulations to predict Tg, can be high. This is due to the need for human intervention in defining a fitting range for linear fits of density with temperature assumed for the liquid and glass phases across the simulated cooling. The definition of such fitting ranges then defines the estimate for the Tg as the intersection of linear fits. We eliminate this need for human intervention by leveraging the Shapiro–Wilk normality test and proposing an algorithm to define the fitting ranges and, consequently, Tg. Through this integration, we incorporate into our automated methodology that residuals must be normally distributed around zero for any fit, a requirement that must be met for any regression problem. Consequently, fitting ranges for realizing linear fits for each phase are statistically defined rather than visually inferred, obtaining an estimate for Tg without any human intervention. The method is also capable of finding multiple linear regimes across density vs temperature curves. We compare the predictions of our proposed method across multiple IL and semiconductor molecular dynamics simulation results from the literature and compare other proposed methods for automatically detecting Tg from density–temperature data. We believe that our proposed method would allow for more consistent predictions of Tg. We make this methodology available and open source through GitHub.
Chain flexibility and glass transition temperatures of poly(n-alkyl (meth)acrylate)s: Implications of tacticity and chain dynamics
The relationship between chain microstructure and glass transition temperature (T g ) is complicated for poly(alkyl methacrylate)s and poly(alkyl acrylate)s. Despite intensive studies, relationships between the structures of these polymers and their properties, including solution characteristics and T g , are still controversial. Solution properties, chain conformations, including Flory's characteristic ratio (C ∞ ), persistence length (l p ), and chain diameters, and T g are reported for series of poly(n-alkyl acrylate)s and poly(n-alkyl methacrylate)s having alkyl side chain lengths (n) ranging from 1 to 10 carbons in length, with uniform and well-characterized tacticities. Chain flexibilities of both series of polymers decrease as n increases, reflecting increased hindrances to rotation about backbone bonds as side chains become longer. Conversely, the T g s for both series of polymers decrease substantially as n increases, reflecting the greater side chain mobilities of long alkyl substituents. For shorter alkyl chain lengths, T g s for the poly(n-alkyl acrylate)s are much lower than for the corresponding poly(n-alkyl methacrylate)s, a difference which has been attributed in the past to the presumed reduced chain flexibility of polymethacrylates due to the presence of the α-methyl substituent. However, contrary to such expectations, C ∞ and l p values for these two series of polymers are nearly identical at a given n value, except for the longest n-alkyl substituents. Instead, the differences in T g may be attributed to the differences in tacticity of the two series – almost ideally atactic for the poly(n-alkyl acrylate)s but high in syndiotacticity for the poly(n-alkyl methacrylate)s. The T g s for the two series of polymers approach that of polyethylene at longer alkyl chain lengths. In addition, the effects of tacticity and chain dynamics on C ∞ , l p , and T g of poly(methyl methacrylate) is discussed.
Predicting glass transition temperature and melting point of organic compounds via machine learning and molecular embeddings
We developed tgBoost a machine learning model to predict glass transition temperature ( T g) of organic species considering their molecular structure and functionality for better predictions of the phase state of secondary organic aerosols.
Extrusion Deposition Additive Manufacturing Utilizing High Glass Transition Temperature Latent Cured Epoxy Systems
This paper investigates the formulation, chemo-rheological properties, and extrusion deposition additive manufacturing (AM) of high glass transition temperature epoxies. Currently there are two methods of using thermoset materials in extrusion deposition AM. The first approach uses a reactive material that will fully cross-link during the build process. The second approach, which is explored in this paper, uses a reactive material that requires a thermal curing cycle after deposition is completed. Yield stress fluids for successful deposition were produced by blending various ratios of rheology modifying fillers into latent curing epoxy systems. After analyzing the rheological properties of the various blends via shear, temperature, and cure rate, the preferred formulation was selected. Test specimens for flexural analysis and dynamic mechanical analysis were printed from down selected combinations. This work resulted in the identification of key parameters for printing latent cured epoxy systems that will be scaled for the first large scale 3D printed epoxy for composite tooling applications.
Stockmayer fluid simulations for viscosity and glass transition temperature of ionic liquids
We develop a Stockmayer fluid model for molecular dynamics simulations of ionic liquids that captures molecular polarization, ionic conductivity, viscosity, and glass transition temperature, using ethylammonium nitrate (EAN) as an example. The ions in EAN are treated as spheres interacting via the Lennard-Jones potential with an embedded point charge and a permanent dipole moment. We show that our simulation results for EAN are consistent with experimental data and then explore the effects of the molecular parameters on the viscosity of ionic liquids. Our results indicate that viscosity monotonically increases with ionic charge and dipole moment but non-monotonically changes with ionic diameter (or molar volume). This non-monotonic trend arises from the competition among the electrostatic interactions, molecular packing, and size asymmetry between the cation and anion. In conclusion, our model also shows that long-lived ion pairs result in higher viscosities.
Collapse of the effective response time near the spin glass transition temperature
Kenning et al. discovered the collapse of the effective response time, 𝑡$^{eff}_{𝐻}$(𝑡 w ;𝑇), independent of aging time, 𝑡 w , as one approached the spin glass transition temperature 𝑇 g from below. Nordblad and Lundgren observed the same effect by reducing the temperature from 𝑇 g (𝐻). We analyze the behavior of ln 𝑡$^{eff}_{𝐻}$(𝑡 w ;𝑇) in the temperature range near and below 𝑇 g using a scaling law that takes into account both the magnetic field 𝐻 and the time-dependent spin-glass coherence length 𝜉(𝑡,𝑡 w ;𝑇). As a result, an overdetermined predictive fit to the experimental data accounts for a quasioscillatory structure of ln 𝑡$^{eff}_{𝐻}$ (𝑡 w ;𝑇) as a function of magnetic field 𝐻 2 for reduced temperatures as large as 𝑇/𝑇 g = 0.98.
Influence of Chain Rigidity and Dielectric Constant on the Glass Transition Temperature in Polymerized Ionic Liquids
Polymerized ionic liquids (PolyILs) are promising candidates for a wide range of technological applications due to their single ion conductivity and good mechanical properties. Tuning the glass transition temperature (T g ) in these materials constitutes a major strategy to improve room temperature conductivity while controlling their mechanical properties. In this paper, we show experimental and simulation results demonstrating that in these materials T g does not follow a universal scaling behavior with the volume of the structural units V m (including monomer and counterion). Instead, T g is significantly influenced by the chain flexibility and polymer dielectric constant. We propose a simplified empirical model that includes the electrostatic interactions and chain flexibility to describe T g in PolyILs. Finally, our model enables design of new functional PolyILs with the desired T g .