Unlocking enhanced thermal conductivity in polymer blends through active learning

The work addresses the challenge of improving thermal transport in polymers, which are attractive for thermal applications due to low cost, electrical resistivity, and mechanical properties but typically exhibit low thermal conductivity (about 0.1–0.5 W m−1 K−1) in the amorphous state. Traditional approaches to increase intrinsic TC focus on enhancing bonded intramolecular pathways via chain alignment (e.g., stretching, template growth), but these yield anisotropic gains and require specialized processing. Modifying non-bonded inter-chain interactions (e.g., pi–pi stacking, electrostatics, hydrogen bonding) and polymer blending offers broader tunability. While the rule of mixtures often describes blend TC, notable exceptions suggest blends can exceed constituent bounds, potentially via hydrogen-bond networks or morphology changes. Conflicting experimental and simulation reports underscore knowledge gaps: how blending alters intra- and inter-chain interactions, how these changes affect chain conformation (e.g., radius of gyration, Rg), and consequent TC. Exploring this vast chemical space experimentally or solely via MD is costly; thus, the authors propose combining high-throughput MD with active learning to efficiently discover polymer blends with TC surpassing their single-component counterparts and to elucidate structure–property relationships involving Rg and hydrogen bonding.

Prior studies indicate bonded interactions dominate heat transfer in amorphous polymers, with chain alignment achieving very high directional TC in polyethylene. However, practical processing constraints limit widespread adoption. Non-bonded interactions can also influence TC: reports exist of blends deviating from the rule of mixtures. For instance, a PAP:PAA blend was reported to achieve >1.5 W m−1 K−1 at 30:70 (attributed to inter-chain hydrogen-bond networks), though later work could not reproduce this enhancement and observed phase separation with mixture-like TC. Polymers forming intra-/inter-chain H-bonds tend to have higher TC, and introducing water verified H-bond network contributions. MD studies showed that stronger inter-chain interactions can stretch major-phase chains and increase TC; others found PAP–PAA blends phase-separated with invariant TC, but PAM–PAA improved TC via stronger H-bond contacts and short PAM bridges. In polymer informatics, most efforts target single-component polymers due to data and representation limitations. A recent ML study predicted blend compatibility from repeating units and composition, but property prediction for blends remains underexplored, motivating robust representation and data-generation strategies for blends.

Data and problem setup: Five datasets were constructed. Dataset 1: 608 amorphous homopolymers with MD-computed TC. Dataset 2: a stratified subset of 35 homopolymers balanced for low (<0.4 W m−1 K−1) and high (≥0.4) TC. Dataset 3: 216 binary blends formed from Dataset 2 constituents at mixing ratios 1:5, 1:1, 5:1, with MD TC. Dataset 4: combined Dataset 1 and 3 (824 entries) for regression and representation evaluation. Dataset 5: ~550,000 virtual binary blends (from Dataset 1 polymers at the three ratios) for active-learning screening. Polymer representations: Two single-polymer descriptors were used: Morgan fingerprints (MF, radius 2, 1024 bits via RDKit) and polymer embeddings (PE, 300-d continuous vectors trained following mol2vec-style embedding of polymer substructures). Two blend-composition operators were devised: weighted summation (WS) and weighted concatenation (WC), where weights reflect blend ratios. Four blend representations were compared: MF-WS, MF-WC, PE-WS, PE-WC. Representation evaluation: A random forest (RF) regressor (scikit-learn) was trained on Dataset 4 (80/20 split; 5-fold CV on training set for n_estimators in [200,2000] and max_depth in [10,110]). Performance was assessed by R2 and MSE on the test set; t-SNE visualizations and Spearman rank correlations between representation-space distances and absolute TC differences further evaluated structure–property fidelity. Active learning (AL) framework: A pool-based AL loop targeted binary classification of whether a blend’s TC exceeds both constituents (label 1) or not (label 0). An RF classifier (2-fold CV to tune n_estimators in [100,1000], max_depth in [10,110]) was trained on labeled data (Dataset 4). At each iteration, high-scoring candidates (certainty-based acquisition by predicted probability) and a random batch for baseline comparison were selected from Dataset 5 for MD labeling; labeled entries were added to Dataset 4 and removed from the pool. Iterations continued until the fraction of high-performance blends in Dataset 4 reached ~5%. A virtual experiment on Dataset 4-V3 compared acquisition strategies (certainty-, uncertainty-, balanced-, and random-sampling) by the number of experiments required to cumulatively find 1–20 positives, repeating each strategy 10 times from random seeds of 10 initial labeled points and adding candidates in batches of 4 per iteration. MD simulations: Structures were generated from SMILES (PoLyInfo) via a Python pipeline (PYSIMM). Each polymer chain comprised ~600 atoms; six chains populated each system according to the blend ratio (including 0:6/6:0 for homopolymers). GAFF2 parameters were assigned; LAMMPS was used with periodic boundary conditions. Pre-annealing included stages with truncated non-bonded interactions, followed by heating (100–1000 K), pressure ramping, and annealing with electrostatics (PPPM Ewald) and LJ cutoff 0.8 nm. Systems were cooled to 300 K and relaxed at 300 K and 1 atm for 8 ns (1 fs), with SHAKE constraints; Rg was computed as the time-average over this segment (averaging chains of the same component to get component-level Rg). For TC, each system was replicated three times along one axis to form a ~9.9 x 3.3 x 3.3 nm3 box (dimensions varying with density). NEMD was run in NVE for 5 ns (0.25 fs), no SHAKE, with Langevin heat source/sink at 320/280 K in 0.5 nm slabs at the ends; fixed regions prevented drift. Heat flux was measured from energy added/removed; temperature gradients were obtained by linear fits of the profile; TC was computed by Fourier’s law, averaging 8 segments from the last 4 ns. EMD and experimental comparisons for several polymers were provided (Supplementary) to benchmark NEMD; focus remained on relative TC changes. Hydrogen-bond analysis: After the final NPT equilibration (pre-NEMD), an additional 0.08 ns NPT at 300 K and 1 atm (1 fs) was run to compute RDFs for H-bond-relevant atom pairs (Supplementary Table 3). H-bond strength was inferred from the position and magnitude of the first peak near 2 Å: smaller radius and larger intensity indicate stronger H-bonds. GAFF2 captures H-bonding implicitly via electrostatics and torsions. For larger-scale statistics, binary indicators were defined: TC improvement (blend > both constituents), Rg improvement (blend > any constituent), and H-bond improvement (either a shift to smaller-radius peak for existing H-bonds or the emergence of a new peak within 2.72 Å in the blend vs constituents). Statistical modeling: A 3-way contingency table over 387 MD-labeled blends cross-classified the three binary variables. Log-linear models with hierarchical selection were used to test dependencies/independencies among variables (likelihood ratio tests vs saturated model). Marginal and conditional odds ratios were computed; significance was assessed (details in Supplementary).

- Representation: PE-WS yielded the best regression performance on Dataset 4 with test R2 = 0.850 and test MSE = 0.00142, outperforming PE-WC (R2 = 0.842), MF-WS (R2 = 0.816), and MF-WC (R2 = 0.818). PE-WS also had the highest Spearman rank correlation (0.546) between representation-space distances and TC differences, indicating superior structure–property capture. MF-based representations showed clustering limitations due to feature multiplicity. - Active learning outcomes: Starting from Dataset 4-V0 (23/824 = 2.79% positives), iterative AL increased the positive fraction to ~5% by V3 (50/992 = 5.04%). Certainty-based acquisition achieved ~30% success rate (e.g., 5/16 = 31.25% in the first iteration), while random sampling achieved ~7% (e.g., 6/82 = 7.32%), demonstrating a >4x enrichment over random. - Virtual acquisition comparison: In simulations on Dataset 4-V3, certainty-based and balanced strategies required fewer MD experiments to cumulatively identify 1–20 high-TC blends than uncertainty-based and random strategies. Certainty-based excelled early via exploitation; balanced maintained better performance later by mixing exploration and exploitation. - MD validation: Of the top-10 predicted candidates (each simulated with three initial structures), 8/10 were confirmed as high-performance (two false positives), supporting model precision. - Mechanistic indicators: In the 10-case set, changes in Rg and H-bond strength generally aligned with TC changes (Rg: 8/10; H-bond: 7/10; one case not captured by either), suggesting both increased chain extension and strengthened H-bonding can accompany TC gains. - Statistical analysis on 387 blends: Log-linear modeling favored a reduced model in which H-bond improvement (C) is independent of both TC improvement (A) and Rg improvement (B), while A and B are associated. The only statistically significant odds ratio was the conditional odds ratio θ_{A|BC} = 2.87, indicating that given H-bond improvement (C=1), the odds of TC improvement (A=1) are 2.87 times higher when Rg improves (B=1) vs B=0. Overall, Rg improvement shows a strong positive association with TC enhancement, and H-bond improvement can indirectly contribute to TC gains by co-occurring with Rg increases.

The study demonstrates that ML-guided active learning integrated with standardized MD simulations can efficiently navigate the vast chemical space of polymer blends to discover cases where blend TC exceeds both constituents. By establishing an effective blend representation (PE-WS) and prioritizing high-confidence candidates, the framework substantially enriches discovery rates versus random search and reduces labeling costs. Mechanistically, results indicate a strong positive association between increased Rg (chain extension) and TC enhancement in blends, consistent with enhanced heat transport along bonded backbones when chains are more extended. While the log-linear analysis suggests H-bond improvement is not directly associated with TC or Rg improvements when considered marginally, the conditional odds ratio shows that, in the presence of H-bond improvement, Rg gains are more likely to translate into TC gains. This points to a picture where inter-chain interactions, including hydrogen bonding, can indirectly facilitate chain conformations conducive to heat transport. The findings provide data-driven guidance: targeting blend designs that promote chain extension and favorable inter-chain interactions can improve TC beyond constituent limits, while AL expedites finding such combinations.

This work extends polymer informatics into the underexplored space of polymer blends by combining high-throughput MD with active learning to identify blends whose thermal conductivity surpasses that of their constituent homopolymers. A weighted-sum polymer embedding (PE-WS) best captured blend structure–property relationships and enabled accurate ML screening. The AL framework achieved a ~4x enrichment over random sampling and validated 8/10 top predictions by MD, demonstrating practical acceleration of discovery. Statistical analyses across hundreds of blends revealed a significant positive association between Rg increases and TC improvements, with hydrogen-bond improvements providing indirect support. Future work should incorporate additional physics such as blend miscibility, phase behavior, cross-linking, and interfacial thermal resistance, expand validation against experiments, and generalize the workflow to other polymer blend properties for broader materials discovery.

- MD uncertainties: TC values show sensitivity to initial structures; ensemble simulations mitigate but do not eliminate variance. NEMD vs EMD and experimental discrepancies exist but were deemed acceptable for relative comparisons. - Force field modeling: GAFF2 does not treat hydrogen bonds explicitly; H-bond effects are captured implicitly via electrostatics and torsions. RDF-based proxies infer H-bond strength/formation and may miss subtleties. - Scope restrictions: The study focuses on amorphous binary blends and relative TC changes; effects of miscibility, phase separation, morphology, cross-linking, and interfacial thermal resistance were not explicitly modeled. - Data coverage: Although AL expanded labeled data, the chemical space remains sparsely sampled relative to all possible blends; some structure–property relationships may be underrepresented. - Experimental validation: No direct experimental confirmation of predicted high-TC blends is presented; translation from MD predictions to experiments may face processing and morphology challenges.