Ready-to-Use Polymerization Simulations Combining Universal Machine Learning Interatomic Potential with Time-Dependent Bond Boosting for Polymer and Interface Design

TL;DR

The paper addresses the challenge of simulating polymerization and curing with accurate, transferable potentials and efficient sampling of rare reactive events. It introduces a time-dependent bond-boost (TDBB) strategy that leverages a universal machine-learning interatomic potential (uMLIP) to accelerate reactions without system-specific parametrization, using a monotonic bias that grows with time. Across radical polymerization, step-growth nylon-6,6 polycondensation, and epoxy curing at a CuO interface, the approach reproduces key kinetic trends, relative reactivities, and mechanistic features, including living-like growth, Carothers-type behavior, and interfacial covalent bonding, while providing reasonable rankings of apparent propagation rates. The framework offers a practical, transferable tool for rapid, molecular-level design insights into polymer growth and interfacial adhesion, with potential extensions to higher-fidelity potentials and broader reaction catalogs to improve quantitative predictive power.

Abstract

Although polymerization and curing reactions govern the performance of advanced materials, their simulation remains challenging owing to the need for accurate, transferable potentials and rarity of chemical events. Conventional reactive force fields such as ReaxFF require system-specific parametrization, while universal machine learning interatomic potentials (uMLIPs) exhibit limited sampling efficiency. This paper introduces a novel simulation framework integrating a uMLIP with a time-dependent bond-boost scheme. The bias potential increases monotonically with time, and the use of a unified parameter set across reaction classes enables consistent acceleration without system-specific tuning. For radical polymerization of vinyl monomers, the proposed framework reproduces characteristic trends, such as linear molecular-weight growth with conversion, initiator-concentration scaling, and relative monomer reactivity trends. For step-growth polycondensation of nylon-6,6, it captures the characteristic sharp increase in molecular weight at high conversion rates, consistent with experimental behavior. For epoxy curing at a copper substrate, it reveals interfacial ring-opening and cross-linking events, consistent with spectroscopic evidence of Cu-O-C bond formation. Overall, coupling uMLIPs with time-dependent bond boost enables practical and transferable simulations of polymerization and curing processes. The proposed framework reliably resolves mechanistic pathways and relative reactivity, offering molecular-level insights into polymer growth and interfacial adhesion.

Figures (5)

• Figure 1: Schematic of the proposed simulation workflow, including four main stages: (1) definition of reactive atomic groups, where potential reactive species are identified from chemical functionalities; (2) selection and acceleration of reaction-targeted groups, where candidate atomic combinations satisfying geometric and chemical criteria are chosen and subjected to time-dependent bias potentials; (3) reaction induction and structural relaxation, in which accelerated molecular dynamics simulations promote bond rearrangements followed by unbiased relaxation; and (4) reaction evaluation and group update, where the bonding states are analyzed and reactive groups are updated for subsequent iterations.
• Figure 2: Structural and kinetic characteristics of styrene radical polymerization in toluene solvent. (a) Snapshot after polymerization and a representative polymer chain. (b) Time--conversion curves at different initiator-to-monomer (I/M) ratios. The vertical axis $\alpha$ represents the monomer conversion, defined as $\alpha = 1 - [M]/[M]_0$, where $[M]_0$ and $[M]$ are the initial and instantaneous monomer concentrations, respectively. (c) $M_\mathrm{n}$ as a function of conversion. (d) Polymerization rate plotted against $[I][M]$. The horizontal axis represents the product of the initiator and monomer concentrations, $[I][M]$, converted from number densities to molar units (1 $\text{\AA}^{-6}$ = 2.76 × 10$^{-4}$ mol$^2$ L$^{-2}$). Here, I, M, and S denote the initiator (AIBN), monomer (styrene), and solvent (toluene), respectively.
• Figure 3: (a) Time--conversion profiles (blue) and exponential fits (red) for representative vinyl monomers, with extracted apparent propagation rate constants $k_p$. (b) Ranking of the apparent $k_p$ values compared with experimental data. Rank correlations indicate Kendall’s $\tau=0.60$, Spearman’s $\rho=0.66$, and mean absolute deviation = 1.0.
• Figure 4: Structural and kinetic characteristics of nylon-6,6 step-growth polymerization under melt conditions without water removal. (a) Representative snapshot after polymerization, showing polymer chains (tan) and generated water molecules (blue). (b) Time evolution of monomer conversion ($\alpha$), which levels off below unity owing to equilibrium limitation. (c) Number-average degree of polymerization (DP$_n$) as a function of conversion, compared with the theoretical Carothers relation. The simulations reproduce the characteristic nonlinear DP$_n$--conversion relationship and incomplete conversion observed experimentally in condensation polymerizations without continuous removal of condensate.
• Figure 5: Epoxy curing at the hydroxylated CuO interface. (a) Time evolution of relative concentrations $c(t)/c(0)$ of epoxy oxygen ($O_\mathrm{e}$), primary amine nitrogen ($N_\mathrm{p}$), secondary amine nitrogen ($N_\mathrm{s}$), and surface hydroxyl hydrogen ($H_\mathrm{CuOH}$). (b) Depth-resolved reaction density $\rho_{\mathrm{rxn}}(z)$ for epoxy--primary amine (top), epoxy--secondary amine (middle), and epoxy--surface reactions (bottom), together with atomic number density profiles $\rho(z)$ of epoxy (blue), amine (orange), and CuO substrate (red). (c) Representative snapshot of the epoxy/CuO interface, with magnified view showing covalent bond formation between epoxy and surface hydroxyl groups.