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. 2023 Sep 14;9(9):1810–1819. doi: 10.1021/acscentsci.3c00502

A Model Ensemble Approach Enables Data-Driven Property Prediction for Chemically Deconstructable Thermosets in the Low-Data Regime

Yasmeen S AlFaraj †, Somesh Mohapatra ‡, Peyton Shieh †, Keith E L Husted †, Douglass G Ivanoff §,∥, Evan M Lloyd ∥,⊥, Julian C Cooper ∥,⊥, Yutong Dai †, Avni P Singhal ‡, Jeffrey S Moore §,∥, Nancy R Sottos §,∥, Rafael Gomez-Bombarelli ‡,*, Jeremiah A Johnson †,*
PMCID: PMC10540282  PMID: 37780353

Abstract

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Thermosets present sustainability challenges that could potentially be addressed through the design of deconstructable variants with tunable properties; however, the combinatorial space of possible thermoset molecular building blocks (e.g., monomers, cross-linkers, and additives) and manufacturing conditions is vast, and predictive knowledge for how combinations of these molecular components translate to bulk thermoset properties is lacking. Data science could overcome these problems, but computational methods are difficult to apply to multicomponent, amorphous, statistical copolymer materials for which little data exist. Here, leveraging a data set with 101 examples, we introduce a closed-loop experimental, machine learning (ML), and virtual screening strategy to enable predictions of the glass transition temperature (Tg) of polydicyclopentadiene (pDCPD) thermosets containing cleavable bifunctional silyl ether (BSE) comonomers and/or cross-linkers with varied compositions and loadings. Molecular features and formulation variables are used as model inputs, and uncertainty is quantified through model ensembling, which together with heavy regularization helps to avoid overfitting and ultimately achieves predictions within <15 °C for thermosets with compositionally diverse BSEs. This work offers a path to predicting the properties of thermosets based on their molecular building blocks, which may accelerate the discovery of promising plastics, rubbers, and composites with improved functionality and controlled deconstructability.

Short abstract

A machine learning model that predicts Tg for deconstructable thermosets with varied bifunctional silyl ether comonomer loadings and structures is introduced and experimentally validated.

Introduction

Materials discovery is often cited as a bottleneck in addressing time-critical challenges in medicine, sustainable chemistry, and engineering design.1−3 Even when a class of materials is found to be promising for a given application, traditional experimental approaches for screening can be arduous, costly, and inefficient for zeroing in on a desired combination of properties. Recent computational advances in molecular representations, machine learning architectures like graph neural networks,1,4,5 and high-throughput virtual screening have enabled data-driven materials discovery in specific materials contexts (e.g., for molecular crystals, organic light-emitting diodes,6 or zeolite catalysts);7−10 however, these methods remain difficult to apply to other common classes of materials such as compositionally complex, amorphous polymers and polymer networks. For example, while curated databases like PoLyInfo,11 Polymer Genome,12 or the PI1M library13 have allowed researchers to train machine learning models to predict the glass transition temperature (Tg),14−16 thermal conductivity,17 dielectric constant,18 crystallization tendency,19 and bandgap20 for linear homopolymers (i.e., polymers of a single composition) and some copolymers,21−25 there is little curated data available for three-dimensional (co)polymers such as thermosets.26−29 Representing the chemical and topological diversity of thermosets in a way that enables extrapolation to new (co)monomers and cross-linking patterns is a challenge to ML strategies that are typically overfit to known monomer chemistries and linear architectures.

Thermosets are covalently cross-linked, three-dimensional polymer networks that irreversibly adopt a given shape upon curing. These materials make up ∼20% of manufactured polymers today, and they are often designed for high-temperature, chemically harsh, and/or mechanically extreme environments, e.g., in the aerospace industry, automotive design, renewable energy, and marine applications.30−32 Thus, by their very nature, they are difficult to chemically deconstruct; most are mechanically downcycled, incinerated, or disposed of in landfills, where they persist for decades/centuries. The strategic introduction of cleavable bonds at the time of manufacturing could enable the production of deconstructable thermosets with properties on par with existing materials yet new end-of-life options.33−40

We have leveraged cleavable comonomers containing bifunctional silyl ethers (BSEs) as additives to facilitate the manufacturing of deconstructable variants of the industrial thermoset polydicyclopentadiene (pDCPD) (Figure 1A).41−47 BSEs are versatile cleavable bonds for deconstructable thermosets, as they are easy to synthesize from low-cost components (e.g., diols and dichlorosilanes), they feature thermally and oxidatively stable Si–O bonds, and they have diverse mechanisms for selective Si–O bond cleavage.42−46,48 Moreover, the properties of BSEs are closely linked to their Si substituents, of which there are hundreds of possible combinations that are synthesizable from commercially available reagents (e.g., a search of the keyword “dichlorosilane” on the Gelest web-catalog returns >100 unique products). This advantage also raises key challenges: it is impractical to synthesize and experimentally test all possible BSEs and their combinations experimentally, and it is difficult to predict through intuition alone how BSE comonomer structures and loadings will impact the properties of thermosets.

Figure 1.

Figure 1

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Overview of experimental synthesis–machine learning–virtual screening loop enabling the identification of new cleavable comonomer additives for pDCPD. (A) Scheme for the experimental synthesis of bifunctional silyl ether (BSE)-based cleavable comonomers with DCPD and cleavable cross-linker DDMS. (B) Comparison between the traditional paradigm for materials discovery, which relies on a synthesis-first approach, and proposed paradigms for accelerated materials discovery, which rely on an inverse-design and “product-first” approach. Specifics of this work to the proposed discovery paradigm are further clarified in the legend. Materials concept: synthesis of deconstructable thermosets. Molecular synthesis: specifying proposed cleavable comonomers. Machine learning: specifies deep learning and model ensemble architecture and hyperparameter determination. Virtual screening: determination of cleavable comonomers resulting in desirable bulk material properties from a library of possible cleavable comonomers as determined by precursor commercial availability. Materials characterization and product testing: validation of experimentally obtained glass transition temperatures, Tg, of resulting deconstructable thermosets against predicted values and performance of deconstruction studies for these materials.

Here, we propose a closed-loop strategy to overcome the challenges associated with applying data science to thermosets in the low-data regime. In particular, we focus on mapping the choice of BSE-based comonomer and/or cross-linker to Tg, a critical property of thermosets that determines their operating temperature range. Our strategy addresses two main challenges: (i) the unavailability of structure-based representations, by representing only the chemistry of the precursors, and (ii) the scarcity of data, by training heavily regularized model ensembles that enable uncertainty quantification and less noisy predictions.

Linear homopolymers or ordered copolymers have well-defined chemical structures and hence can be represented through an ordered sequence of per-monomer chemical features, or through graph convolutional neural networks acting on the whole repeat unit.49 3D stochastic polymers, however, cannot be easily represented as the numerical vectors that ML models require as inputs. Recently, hierarchical ML models have been applied to tackle the representation of 3D networks of known structure or stochastic linear polymers, but no tools are available for polymers of complex, stochastic, and unknown topologies.50−53 Our approach relies on representing the individual chemical precursors as small molecules through low-dimensional physicochemical features, such as hydrophobicity and partial charges. Doing so captures domain-specific heuristics, lowers the dimensionality of the chemical input space, and most importantly avoids the need to represent the unknown network topology of the polymer. We also utilize model ensembling, that is, using the consensus prediction from multiple models instead of single prediction, to increase the transferability of our predictions to inputs away from the training data.47 We combine ensembling over random seeds for model initialization, over data subsets (bagging, boosting), and over hyperparameter choices, i.e., varying the overall architecture of the models themselves, combining different classes of regressors from linear models to decision trees and support vector machines (Figure 1B).54 A key advantage of model ensembles, which are widely used in the general ML literature but less so in the predictive design of three-dimensional polymer networks, is that each individual model’s prediction tends to differ when predicting far from the training data, so their variance can be used as a measure of uncertainty and their mean will provide higher accuracy and more robustness than any particular member of the ensemble.55−58

We show that our resulting model, which is trained on only 101 data points (i.e., the “low data regime”) taken from the literature and results from our combined laboratories, enables predictions of how BSE-based cleavable comonomer and cross-linker loadings and Si substituents impact the Tg of deconstructable pDCPD thermosets within ±15 °C experimental accuracy across a wide temperature range (0–220 °C). Thus, this work provides a route to predict the impacts of cleavable comonomer/cross-linker composition and loading on the Tg of deconstructable pDCPD thermosets and outlines a framework for predictive (co)polymer and polymer network design in the low-data regime.

Results and Discussion

Data Collection for the Machine Learning Model

Robust Tg prediction for deconstructable pDCPD requires a training data set with information on the chemical compositions of cleavable comonomers and cross-linkers as well as the thermoset curing parameters. To build an appropriate training data set, we collected data from existing literature examples and in-house experiments (Figure 2A, Figures S1–S87, Tables S1–S3),59−66 providing 101 different combinations of cleavable additives (9 BSE-based and 1 acetal-based), ratios of comonomers and/or cross-linkers to the curing initiator, and the initiator type (first- or second-generation Grubbs catalyst), along with their experimentally measured Tg values obtained from either differential scanning calorimetry (DSC) or estimated by dynamic mechanical analysis (DMA) after curing. For samples that displayed multiple tan(δ) peaks, which occurred in some cases at high comonomer loading or with non-BSE-based monomers (i.e., acetal-based), we used the global maximum of tan(δ) as the Tg for training our model.43,46

Figure 2.

Figure 2

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Model ensemble predicts Tg with high fidelity and highlights key input variables for prediction of Tg. (A) Distribution of Tg for 101 data points in the training data set. (B) Parity plot for fingerprint-based model shows good agreement of predicted and experimental Tg for the held-out test data set. Predictions for the test data set are based on an ensemble of different models, and mean and standard deviation of the different predictions are reported. The inset text notes the model ensemble performance metrics. Error bars note the standard deviation of the predicted Tg values using the different models in the ensemble. The y = x line in the figure is meant to be used as the parity line to ascertain the difference between the predicted and the experimental Tg values. If the dot is on the line, then the predicted Tg is the same as the experimental Tg; if it is off the line, then it is under/overpredicted. (C) Key features identified by fingerprint- and descriptor-based models are shown. Features common to both models are colored gray, descriptors are colored red, and substructures identified for the cleavable comonomer and cross-linker have a blue label. The node of the substructure is denoted by a blue dot; bonds in the atomic neighborhood, for the respective substructure, are colored black; and remaining bonds are colored gray.

Machine Learning Model Ensemble Architecture for Low-Data Regime Prediction

Machine learning models for materials design are often trained to map synthesis parameters and affordable, high-information descriptors, which can be obtained for materials before they are synthesized, to measured experimental target properties.67,68 Because important synthetic details for polymers are missing in publicly available data sets such as PoLyInfo,11 data-driven prediction models struggle to reach high accuracy despite the availability of over 5000 data points. For example, a recent review benchmarking machine learning models to predict Tg values for homopolymers reported an accuracy of only ±39 °C.14 Ramprasad and co-workers recently reported an error of 29 °C when combining a total of 9500 homopolymer and copolymer data points, combining data ensembles and a metalearner model using only chemical formulas as inputs.21,57 Moreover, limitations in materials data accessibility often result in lower predictive accuracy as a result of overfitting to the available training data. For example, Hu et al. applied a materials genome strategy to control the mechanical properties of cross-linked epoxies. This approach requires the definition of “gene” substructures of interest (epoxides and amines in this case) and uses a graph convolution network to extrapolate information about these small molecules. Subsequently, transfer learning was employed alongside polymer descriptors including molecular weight and an estimated cross-linking density to predict the properties of the bulk material. They provided experimental validation of one prediction and molecular dynamics simulations of additional ones. The models struggled with overfitting and with extrapolation due to high performance metrics, with both ML predictions and validations being close to the mean performance of the training data.69

In this work, we instead utilize model ensembles across data splits and architectural choices to achieve robust predictions for thermoset copolymers in the low-data regime using chemical features such as physicochemical descriptors, as well as structural features based on molecular connectivity, as inputs. The model ensemble has the following independent variables: cleavable BSE comonomer and cross-linker representations and respective concentrations in mol %, monomer to initiator ratio, and initiator type. The cleavable comonomers were represented as extended connectivity fingerprints, which encode the chemical substructures in a barcode-like representation unique to each molecule.70−72 This approach captures both the common and unique attributes of the individual molecules. The cleavable comonomer mol % and monomer to initiator ratios were represented as numbers, while the initiator type was treated as a categorical variable. Another model was trained with the cleavable comonomers represented with physicochemical descriptors, such as electro-topological state indices (ESI), partial charge, number of carbocycles and saturated rings, to benchmark the fingerprint representations (see Supporting Information Figures S88 and S89, Table S1).

As noted above, many machine learning models require large data sets—often more than 1000 data points—which poses a major challenge in materials research.73,74 Cross-validation and data-ensembling are typically used to help overfitting to a singular section of the data set in the process.74 To enable the robust prediction of Tg for pDCPD thermosets in the low-data regime, we used a model ensemble consisting of multiple models with different architectures and hyperparameters, i.e., parameters that define the model architecture and cannot be estimated from the data. The model ensemble consisted of 5 hyperparameter-optimized model architectures, each trained on 10 random splits of the data set, for a total of 50 individual models. For each model, 60% of the data were used for training, 20% were used to validate the model during training, and 20% were held-out to test the model ensemble after training.75−79 The top 5 model architectures were chosen based on the least root mean squared error (RMSE) on the test data set after running a similar experiment for more than 10 model architectures, including Gaussian process regression, decision trees, linear models, and multilayer perceptrons. For the final model ensemble, the RMSE of the test set was 0.30 of the standard deviation of the training data, or 14.9 °C (Figure 2B). It is noteworthy that the model exhibited lower error and uncertainty around 150 °C, which is an expected feature, as the glass transition of deconstructable pDCPD thermosets in the training set primarily exhibit Tg values close to this value. These results suggest that the model ensemble was able to balance the bias-variance trade-off, with a mixture of underfitting high bias and low variance simpler models and overfitting low bias and high variance complex models. By focusing on one class of highly diverse compounds, our approach achieves lower error than large models trained on thousands of data points across homo- and copolymer space, which have errors closer to 30 °C or higher.14,21

In addition to the fingerprint representation for the cleavable comonomers and cross-linkers, we benchmarked the descriptor representation. The descriptor-based model ensemble performed slightly worse than fingerprint-based models, with test set RMSE of 0.35 of the standard deviation of the training data, or 17.5 °C (see Supporting Information Figure S90). The fingerprint-based models depend on the substructures and their implicit influence on the chemical properties of the molecules to map the molecules to their properties, while the descriptor-based models explicitly provide information about the different chemical properties of the molecules in the model. The fingerprint representation could be easily obtained for new molecules; however, descriptors might not be readily available and may require experiments or quantum chemical calculations. Additionally, the hand-crafted list of descriptors might not always include all possible features that affect the property of interest, while fingerprints do not have such a problem.

To understand the decision-making process of the model ensemble, we analyzed the importance of input features for prediction of Tg in both the fingerprint- and descriptor-based models through so-called attribution techniques (Figure 2C, see Supporting Information Figures S88 and S89). Cleavable comonomer mol %, initiator type, and monomer to initiator ratios were observed to be important across both models. The importance attributed to these features is in line with known experimental observations that high concentrations of BSE-based cleavable comonomers lead to decreases in Tg. The fingerprint-based models associated higher Tg with aryl substituents and norbornene-based cross-linkers. We interpret this prediction to the possibility that aryl substituents may induce stronger noncovalent interactions between cleavable comonomers, while the norbornene-based cross-linkers introduce rigid, inflexible structures that decrease the free volume. The descriptor-based models, which rely on physicochemical features rather than molecular graphs, highlighted the number of aliphatic and aryl rings as being critical for Tg. The Electrotopological State Index, a combined structure and electronic descriptor commonly used in pharmaceuticals,77 and partial charges were also noted as key features, indicating the influence of the overall molecular topology and electronic charge distribution on Tg. These observations help in elucidating design principles for cleavable comonomers in high-Tg pDCPD thermosets.

Tg Prediction for Mixtures of BSE-Based Cleavable Comonomers and Cross-Linkers

We previously showed that treatment of iPrSi-based pDCPD thermosets with a fluoride or acid source can facilitate deconstruction of the thermoset to soluble products, while networks containing cleavable cross-linkers show a decline in cross-linking density without solubilization under similar cleavage conditions (Figure 3A).43 Here, we first assessed our model ensemble’s performance using mixtures of iPrSi8, which was present in the training set at different mol % values, and the cleavable cross-linker didicyclopentadiene methyl silyl ether (DDMS), which was assessed at a fixed loading (10 mol %) and thus comprised one data point in the training set (Figure 3A, Figures S79–81 and S91–S107, Tables S3 and S4). iPrSi8 copolymerizes with DCPD to introduce cleavable bonds within the strands of the cross-linked pDCPD network without introducing any new cross-links, thereby lowering the cross-linking density of the material and the Tg.43 By contrast, DDMS introduces new cleavable cross-links, leading to an overall increased cross-linking density that is expected to increase Tg. Here, we sought to combine iPrSi8 and DDMS to enable pDCPD deconstruction while also tuning the cross-link density. Figure 3B shows predicted Tg values from our fingerprint-based model ensemble as a function of the mol % of DDMS and iPrSi. As expected, increasing the mol % of iPrSi8 lowers Tg (x-axis, blue), while increasing DDMS incorporation raises Tg (y-axis, red) relative to virgin pDCPD (lower left corner). To test the validity of these predictions, we synthesized pDCPD thermosets bearing 0–20 mol % iPrSi8 and 10–20 mol % DDMS and estimated their Tg values as the peaks in the tan(δ) curves as measured by DMA. The predicted and experimental results were within the expected confidence interval as indicated by the standard deviation of the machine learning model, suggesting that the model captures key aspects of how the molecular features of iPrSi8 and DDMS impact the Tg of these thermosets (Figure 3C). For example, in a sample comprising 10% iPrSi8 and 20% DDMS, the measured Tg value was 152 ± 6 °C, which agrees well with the predicted Tg value of 158 ± 17 °C. Full chemical deconstructability of this sample was confirmed by exposure to tetrabutylammonium fluoride (TBAF) in tetrahydrofuran (THF) at 50 °C for 24 h. Thus, this predicted combination of iPrSi8 and DDMS provides a pDCPD thermoset that is chemically deconstructable, with a Tg that is 13 °C greater than our previously reported deconstructable pDCPD based on iPrSi8 alone and close to the value of virgin pDCPD (166 ± 5 °C).

Figure 3.

Figure 3

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Model ensemble successfully captures the variation in Tg in a titration study with a previously reported iPrSi8 comonomer and DDMS cross-linker. (A) Chemical structures of iPrSi8 comonomer and DDMS cross-linker used in the mol % sweep experiment. (B) 2D plot of predicted Tg values for different ratios of iPrSi8 (cleavable comonomer) and DDMS (cleavable cross-linker) shows the decreasing Tg with the increasing comonomer mol % and decreasing cross-linker mol %. The sharp boundaries in the plot are a consequence of limited data around the respective compositions. (C) Parity plot showing the reasonable agreement of experimental and predicted Tg values for the five selected compositions of iPrSi8 and DDMS. Vertical error bars note standard deviation of the Tg predicted using the different models in the ensemble, and horizontal error bars note the standard deviation across the experimental replicates. The y = x line in the figure is meant to be used as the parity line to ascertain the difference between the predicted and experimental Tg values. If the dot is on the line, then the predicted Tg is same as the experimental Tg; if it is off the line, then it is under/overpredicted. (D) Dynamic mechanical analysis (DMA) temperature sweeps of iPrSi8 and DDMS-containing pDCPD thermosets at variable mol % with Tg as the peak of tan(δ). Color follows the legend of panel C. The dashed line shows the Tg of virgin pDCPD.

Screening, Identifying, And Experimentally Validating Predicted Properties of New BSE-Based Cleavable Comonomers

Having shown that our model can predict the Tg values of pDCPD thermosets using various concentrations of iPrSi8 mixed with DDMS, we sought to explore how the Si substituents in BSE-based cleavable comonomers could be leveraged to tune this property further. BSE comonomers such as iPrSi8 can be readily prepared through substitution reactions of an appropriate diol (e.g., (Z)-pent-2-ene-1,5-diol or (Z)-but-2-ene-1,4-diol) and a dichlorosilane (SiCl2R2) (Figure 4A). As noted above, there are over 100 commercially available dichlorosilanes; synthesizing all possible BSE comonomers to study their effect on the Tg of pDCPD would be impractical. Thus, we used the same model described above to screen a library of BSE comonomer candidates that could, in principle, be synthesized from commercially available starting materials (Figure 4A). Our model suggested three BSEs, which were not in the training data set, with desirable predicted Tg values: the previously reported comonomer PhSi7 and two novel BSE comonomers LinF7 and PFP7, which were synthesized on the ∼2 g scale through cyclization of the corresponding dichlorosilane with (Z)-but-2-ene-1,4-diol in the presence of imidazole in dichloromethane (Figures S108–S114). 1H NMR, 13C NMR, and high-resolution mass spectrometry confirmed the structures of these comonomers. The thermal stabilities of pDCPD thermosets formed with 10% BSE comonomer loadings were assessed using thermogravimetric analysis (TGA) prior to thermomechanical characterization. Sufficient stability at the elevated temperatures required for DMA analysis was observed for materials containing PhSi7 and LinF7, but not PFP7 (Figure S127), and hence all subsequent experimental studies were carried out on samples containing LinF7 and PhSi7. Deconstructable pDCPD samples (Figure 4B) were prepared by mixing 10 mol % of each BSE comonomer into neat DCPD, followed by addition of Grubbs second-generation catalyst at a final concentration of 2 mg/mL (∼3100:1 monomer to catalyst ratio) and curing in an oven at 120 °C for 30 min. Samples with 10 mol % of each comonomer along with 10 or 20 mol % DDMS cross-linker were also prepared for comparison (Tables S4 and S5). Tg values were determined experimentally for each sample through DMA analysis (Figure 4C, Figures S116–S136) for comparison to our model predictions.

Figure 4.

Figure 4

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Model ensemble reliably predicts Tg values of deconstructable pDCPD thermosets with novel BSE-based cleavable comonomers and DDMS. (A) General scheme for BSE-based cleavable comonomer synthesis. Structures of comonomers synthesized, predicted, and experimentally verified by our model are shown in black (PhSi7 and LinF7), and that of comonomer synthesized and predicted but not verified in bulk material due to lack of stability is shown in gray (PFP7). (B) Images of pDCPD samples with 10 mol % comonomer and 20 mol %. DDMS in 0.2 M TBAF in THF shows full dissolution. Samples shown contain PhSi7 and LinF7, respectively. (C) Dynamic mechanical analysis (DMA) temperature sweeps of pDCPD thermoset samples doped with 10% comonomer, 10% comonomer, and 10% DDMS and those with 10% comonomer and 20% DDMS showing Tg from the peak of tan(δ). Dashed line shows Tg of virgin pDCPD. (D) Parity plot shows reasonable agreement of experimental and predicted Tg for the six selected compositions of PhSi7, LinF7, and DDMS. Vertical error bars note standard deviation of the Tg predicted using the different models in the ensemble, and horizontal error bars note the standard deviation across the experimental replicates. Color scheme follows the legend of panel C. The y = x line in the figure is meant to be used as the parity line to ascertain the difference between the predicted and experimental Tg values. If the dot is on the line, then the predicted Tg is same as the experimental Tg; if it is off the line, then it is under/overpredicted.

The measured Tg value for each pDCPD sample containing 10 mol % LinF7 was within the expected error as presented by the model’s standard deviation for the predicted Tg (predicted, 141 ± 19 °C; experimentally measured, 143 ± 1 °C). Agreement between the prediction and experiment was also observed for LinF7 samples containing DDMS. For example, samples with 10 mol % LinF7 and 10 mol % DDMS had a predicted Tg of 174 ± 10 °C and an experimental Tg within the predicted error at 166 ± 4 °C. This Tg value is ∼20 °C greater than that of iPrSi8 samples loaded with similar concentrations of DDMS, showing that our method not only accurately predicts Tg values in these systems but also can be used to fine-tune and explore molecular subspaces to provide deconstructable thermosets with improved thermomechanical properties. Finally, we were interested in targeting deconstructable thermosets with predicted Tg values similar to that of virgin, nondeconstructable pDCPD. Our model predicted a Tg of 180 ± 9 °C for samples containing 10% LinF7 and 20% DDMS. Experimental verification showed that these samples did match the Tg of virgin pDCPD (167 ± 5 °C), with Tg values of 170 ± 1 °C.

Predictions for samples containing PhSi7 deviated more than justified by the model variance, suggesting a model bias. Nevertheless, the predictions remained within reasonable agreement with experiment, particularly compared to existing computational methods. For example, for thermosets containing 10 mol % PhSi7, the predicted Tg was 118 ± 6 °C, while the experimental value was 127 ± 2 °C. Additionally, for thermosets containing 10% PhSi7 and 20% DDMS, the predicted Tg was 174 ± 6 °C, while the experimentally observed value was 153 ± 3 °C. (Figure 4D).

Finally, deconstruction of the samples containing the newly identified BSE-based cleavable comonomers into soluble fragments was confirmed upon treatment with TBAF for 24 h (Supporting Information Figures S137 and S138). For both materials, >97% of the mass of the puck fully dissolved to yield soluble fragments (Figure 4B). NMR spectroscopic analysis of the soluble fragments isolated from the deconstructed materials confirmed their composition (Figures S139–S142). We note that while LinF7 was identified by the model to be a promising CCA based on Tg, its use could result in the release of perfluoroalkylated substance (PFAS) waste. This fact highlights that our model is designed to predict a specific property (Tg); the potential environmental ramifications of any predicted additives should also be considered in parallel with the property prediction before translation to real-world applications. With more data, models like ours could incorporate these considerations and others like cost in the future.

Retrospective Prediction for Strand-Cleaving Cross-Linkers (SCCs)

In an effort to further assess our model’s performance, we conducted a retrospective analysis to predict the Tg values of a different class of previously reported cleavable additives for pDCPD that we refer to as “strand-cleaving crosslinkers” (SCCs, Figure 5), which were not in the training data.46 The model, despite having never seen any of these hybrid molecules, predicts Tg values comparable to the experimental values for all but one composition: a 100% v/v % NbMeSi thermoset that lacks DCPD. Given that this material is not a pDCPD thermoset, it is perhaps not surprising that our model inaccurately predicts its properties. Additionally, the prediction uncertainty for this sample, as quantified from the ensemble variance, was much higher than all other cases, demonstrating that the model exhibited a very low confidence in the predicted Tg.

Figure 5.

Figure 5

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Parity plot of the retrospective analysis study shows reasonable agreement between experimental and predicted Tg values for reported comonomer/cross-linker combinations, including structures the model has not been trained on such as strand-cleaving cross-linkers (SCCs) (NbMeSi and NbEtMeSi), SCC control molecules (H2NbMeSi, NbEtMeSiH2, CyEtMeSi, and CyMeSi), and CCAs (LinF7 and PhSi7) for comparison. A shape legend for the different molecules is noted in the top-left corner, and the concentrations are noted in the bottom-right corner. For a single number, the concentration is only for the comonomer, and for two numbers, separated by a comma, the first number is the comonomer concentration and the second preceded by CL (cross-linker) is the cross-linker concentration. Vertical error bars note the standard deviation of the Tg predicted using the different models in the ensemble, and horizontal error bars note the standard deviation across the experimental replicates. The values for the held-out data set are in gray. Structures from retrospective analysis shown below. The y = x line in the figure is meant to be used as the parity line to ascertain the difference between the predicted and experimental Tg values. If the dot is on the line, then the predicted Tg is same as the experimental Tg; if it is off the line, then it is under/overpredicted.

Conclusions

Herein, we have demonstrated the use of data-driven strategies to streamline the discovery of BSE-based cleavable comonomers and cross-linkers to manufacture deconstructable pDCPD thermosets with targetable Tg values. Experimental validation showed good agreement with model predictions of Tg values for cleavable comonomer and cross-linker structures that were not in the model’s training set. Importantly, this process allows for the deconstruction of pDCPD variants with predictable, tailorable properties. Moreover, when combined with recycling and upcycling schemes that leverage the rich functionality of pDCPD deconstruction fragments,41,80 this approach could enhance the end-of-life options for pDCPD. Additionally, extension of these concepts to pDCPD composites may offer a powerful way to reuse the components of composites (e.g., fillers).41,80

This research also provides a framework to leverage closed-loop data-driven design and optimization in other areas where access to larger data sets may be limited, potentially allowing for the discovery of related deconstructable materials, including thermoplastics, other thermosets, and composites. Finally, extensions of this approach could enable predictions of additional thermomechanical properties for polymeric materials, such as elastic modulus, yield stress, and cross-link density, which could accelerate strategies for improving the functionality and sustainability of these materials.

Acknowledgments

This work was supported as part of the Center for Regenerative Energy-Efficient Manufacturing of Thermoset Polymeric Materials (REMAT), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0023457.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acscentsci.3c00502.

  • Synthetic methods, characterization data, and machine learning model training and featurization data (PDF)

Author Contributions

○ Indicates equal contributions to the manuscript.

The authors declare no competing financial interest.

Supplementary Material

oc3c00502_si_001.pdf (5.8MB, pdf)

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