First-Principles Atomistic Structure and Dynamics of Polyethylene During High-Pressure Radical Polymerization via Machine Learning Force Fields

Bharatha K. Gunawardana; Teresa Shah; Bicha Azizova; Deepa Ranabhat; Yizhi Song; Akshath Shastri; Srinjoy Ghose; Thomas E. Gartner

cond-mat.mtrl-sciAug 22, 2026

First-Principles Atomistic Structure and Dynamics of Polyethylene During High-Pressure Radical Polymerization via Machine Learning Force Fields

Authors: Bharatha K. Gunawardana, Teresa Shah, Bicha Azizova, Deepa Ranabhat, Yizhi Song, Akshath Shastri, Srinjoy Ghose, Thomas E. Gartner,

Organizations: Department of Chemistry, University of North Texas, Denton, TX 76203, USA · Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA 18015, USA

Abstract

Polyethylene (PE) is one of the most commonly used synthetic polymers. While the synthesis and processing protocols for PE are well established, precise experimental assignment of microscopic structures at atomistic resolution (i.e., the position of each atom) remains largely limited to highly crystalline systems. This gap is often addressed via computer simulations using empirical interatomic potentials, which use approximate but efficient descriptions of interatomic interactions to reach the length and time scales needed to describe macromolecules. These empirical potentials typically perform well for bulk and/or collective properties but face challenges with chemical realism for complex systems, e.g., during reactive processes. In this work, we address this challenge by combining the computational efficiency of a deep potential (DP) machine-learning force field and the chemical realism of first-principles van der Waals (vdW) corrected hybrid density functional theory (DFT) enabled by a SeA high-throughput framework. Using this approach, we study the structure and dynamics of PE oligomers and polymers in an ethylene solvent under common high-pressure (supercritical) radical polymerization conditions. We found that the local solvation environment of radical-containing PE oligomers converges for chain lengths greater than (n~6), suggesting extensibility of our oligomer-trained MLFF to significantly longer polymers. We then confirmed the extensibility of these models to long PE chains by characterizing the molecular weight scaling of single-chain structure and dynamics, which showed classic good solvent behavior. Our PE MLFF retained a consistent level of fidelity and stability across a wide range of thermodynamic state points and chain lengths, at full atomistic resolution, therefore paving the way towards first-principles-based polymer structure and property prediction.

Figures & tables

Figure 1: Schematic illustration of our workflow for training the machine-learning force field (MLFF) at the hybrid DFT+vdW level by integrating SeA and the DP ecosystem.

Figure 2: Assessment of finite-size effects on the solvated ethyl radical (1-mer). Panel (a) shows the isobars of $\text{(}\text{C}{\vphantom{\text{X}}}_{\smash[t]{\text{2}}}\text{H}{\vphantom{\text{X}}}_{\smash[t]{\text{5}}}\,{\cdot}\,\text{)}\text{(}\text{C}{\vphantom{\text{X}}}_{\smash[t]{\text{2}}}\text{H}{\vphantom{\text{X}}}_{\smash[t]{\text{4}}}\text{)}\text{}{\vphantom{\text{X}}}_{\smash[t]{\text{31}}}$ in a periodic unit cell (color-shaded contour lines labeled with isovalues in kbar) plotted against corresponding isobars initiated with a 2x2x2 supercell (white dashed lines). Panel (b) provides a graphical representation of the condensed-phase system with C ( H ) atoms in cyan (white) and the radical highlighted in yellow. Panels (c-f) shows the C – C , C – H , H – H , and $\text{C}\,{\cdot}\,$ – C radial distribution functions (RDFs) of three select thermodynamic conditions labeled as color-coded open squares in (a); the marker shapes denote the initial condition—thus also the system size—used in the DPMD simulations: crosses (dots) indicate a $1\times 1\times 1$ unit cell ( $2\times 2\times 2$ supercell) as the starting configuration.

Figure 3: Three representative solvation structures (panels a–c) around an ethyl radical under a high-pressure polymerization of ethylene at $T=500$ K and $\rho=0.57$ g/cm 3 . Graphical representation of the condensed-phase systems include: (1) ball-and-stick models for the nuclei with C ( H ) atoms in brown (white) spheres; (2) localized orbital isosurfaces for the radical electrons at isovalues of $\pm 0.8$ Bohr -3/2 with positive (negative) lobes in yellow (cyan); and (3) bounding boxes with black edges for periodic unit cell used in the simulations.

Figure 4: Chain-length-dependent radial distribution functions for (a) C – C , (b) C – H , (c) H – H , and (d) $\text{C}\,{\cdot}\,$ – C pairs sampled using the 32-molecule unit cell at $T=600$ K and $\rho=0.43$ g/cm 3 .

Figure 5: Representative solvation structures of PE oligomer radicals of lengths (a) $n=2$ , (b) $n=4$ , and (c) $n=6$ under a high-pressure polymerization of ethylene at $T=500$ K and $\rho=0.57$ g/cm 3 with the consistent graphical representation used in Fig. 3 .

Figure 6: Stability of oligomer-trained MLFF for different PE chain lengths from $n=5$ (left column), $n=33$ (middle), and $n=257$ (right) within a $512$ -molecule unit cell at $T=500$ K and $p=4$ kbar (pressure consistent with the initial liquid density as shown in Fig. 2 a). For each column, the inset contains a representative snapshot of the DPMD simulation containing: (1) ball-and-stick models for the nuclei with C ( H ) atoms in translucent cyan (white) spheres; (2) blue bounding boxes for the periodic unit cells; and (3) red cylinders for polymer backbones. Beneath each inset is a model-deviation distribution plot to assess the precision of the DP MLFF, with the active-learning accuracy threshold labeled as a purple dashed line.

Figure 7: Single-chain statistics. Panel (a) shows a representative simulation snapshot of the DPMD simulation for the $n=65$ carbon chain. Panel (b) shows the scaling of chain end-to-end distance, $\braket{R_{e}}$ , as a function of degree of polymerization $n$ , panel (c) shows the ratio $\braket{R_{e}^{2}}/\braket{R_{g}^{2}}$ , where $R_{g}$ is the radius of gyration. Panel (d) describes chain dynamics via the relaxation time in $R_{e}$ , $\tau_{R_{e}}$ . In all panels, black lines denote the L-OPLS force field, blue lines denote DPMD results, and error bars denote $95\%$ confidence intervals.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Stage	$T$ (K)	New Data Size	$\%\text{acc}$
AIMD	[200,400,600]	32,400	–
1	200	0 7,253	99%
2	400	0 6,217	99%
3	600	31,390	88%–98%
4	600	15,545	96%
5	600	0 6,269	98%

Appendix

Table 1: Summary of active-learning protocol for PE oligomers from

n=1\mathrm{-}6

. The first column shows the coarse-grained active learning stages, starting from (1) the initial data generation with AIMD, (2) the first round of active learning (Stages 1–3) in which we explore each oligomer with a gradually increasing temperatures, and then (3) the second round of active learning cycles (Stages 4–5) in which we combine data from all oligomers and used refined training settings. The second, third, and fourth columns show the temperatures, new data size, and accuracy ratio

\%\text{acc}

, which is defined based on the fraction of configurations with model deviation below

0.20

eV/Å. Based on this protocol, we obtained an ensemble of four DP MLFFs with

\%\text{acc}\geq 98\%

across our target thermodynamic range. For each step, we consistently explore system densities of

\rho\in\{0.43,0.49,0.57,0.66\}

g/cm 3 .

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