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Accelerated ReaxFF Simulations for Describing the Reactive Cross-Linking of Polymers

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Prose below summarizes the J. Phys. Chem. A article identified by doi, title, and pdf_path.

Summary

An accelerated ReaxFF workflow (distance restraints / bond-boost-inspired energy injection to surmount epoxy–amine barriers at low temperature) cross-links bis F / DETDA epoxy compositions. The CHNO-2017_weak-derived parameter set is reoptimized on epoxide/amine coupling data; QM transition states benchmark barrier heights. Multi-step NVT polymerization builds a large atomistic network (~1872 atoms); annealing, NPT density runs, and LAMMPS tensile tests yield density, \(T_g\), and modulus compared to dogbone experiments.

Methods

  • FF reoptimization: Start from CHNO-2017_weak; refine C–O, C–N, N–H bonds/angles and N hydrogen-bond terms against epoxide–amine reactions; full tables in SI ([[2018vashisth-venue-microsoft-word]]).
  • Acceleration: Restraint energy \(E_\mathrm{rest}\) on selected atom pairs (functional form eq. 2 in paper) with tuned \(F_1,F_2,R_{12}\) to supply ≈barrier energy; systematic NVT scans calibrate barriers vs QM for noncatalyzed, water-catalyzed, and self-promoted pathways; Python post-processing removes spurious imaginary modes in TS candidates.
  • Polymer build: Stoichiometric bis F : DETDA packs at ~0.4–0.6 g/cm³; iterative doubling of system size with 500 K accelerated NVT cross-linking until a continuous network (e.g. 32 bis F + 16 DETDA molecules in the largest system reported).
  • Property evaluation: Anneal 300→600 K in 100 K steps (12.5 ps per step) alternating NVT/NPT; density from final NPT at 300 K; \(T_g\) from density vs T linear fits (300–500 K, 20 K steps, 50k steps × 0.25 fs NVT + 200k steps NPT per point); tensile modulus via LAMMPS stress/atom at 300 K, high strain rates (\(10^8\)–\(2×10^8\) s\(^{-1}\)), cubic deformation with Poisson relaxation on lateral faces, averaged over three directions.
  • Experiment: Cure protocol (121 °C / 1 h + 177 °C / 3.5 h), MDSC \(T_g\), ASTM D792 density, clip-gauge modulus—procedures cross-referenced to prior work.

MD application (LAMMPS, bis F / DETDA packs)

  • Engine / code: LAMMPS with ReaxFF as in the article’s Computational Details (issue PDF on pdf_path).
  • System size & composition: Reactive packs are built from stoichiometric bis F : DETDA stoichiometry, iteratively doubled to the continuous-network sizes reported (e.g. 32 bis F + 16 DETDA in the largest illustrative system); initial densities ~0.4–0.6 g cm⁻³ before cross-linking.
  • Boundaries / periodicity: Bulk epoxy cells use three-dimensional periodic boundary conditions in LAMMPS (standard PBC supercell for condensed-phase ReaxFF).
  • Ensemble: NVT for accelerated cross-linking windows; alternating NVT / NPT for annealing, densification, and \(T_g\) sweeps; NPT for final density points and modulus deformation cells as quoted above.
  • Timestep: 0.25 fs integration for \(T_g\) / NPT segments tied to the density-versus-temperature protocol.
  • Duration / stages: Multi-stage workflow—accelerated NVT polymerization, 300 → 600 K annealing (12.5 ps per 100 K step), long NPT / NVT blocks for \(T_g\) sampling (50k/200k-step segments per temperature), and tensile production at 300 K.
  • Thermostat / barostat: N/A — the J. Phys. Chem. A text does not spell out a named thermostat algorithm beyond specifying NVT/NPT segments; pressure for NPT portions follows the barostat usage implied by the density and modulus stages in the article.
  • Temperature: Cross-linking at 500 K (and cure-temperature-matched windows noted in the article); annealing ladder 300–600 K; \(T_g\) scans 300–500 K (20 K steps); tensile tests at 300 K.
  • Pressure: NPT segments for density / \(T_g\) / modulus as above; N/A — not applicable during pure NVT cross-linking windows.
  • Electric field: N/A — not used.
  • Replica / enhanced sampling: N/A — not used beyond the restraint-energy acceleration recipe (not umbrella / metadynamics / replica exchange).

Findings

  • QM agreement: ReaxFF barrier heights and TS geometries match QM literature data for the three epoxide–amine motif classes considered.
  • Cross-linking: Accelerated runs achieve ~82% of theoretical cross-linking extent in the large-system example discussed in the article.
  • Properties: Simulated density, \(T_g\), and Young’s modulus track experimental values within the uncertainties discussed; strain-rate scaling addressed via multi-rate simulation/experiment comparison.

Limitations

High strain-rate MD vs quasi-static experiments; accelerated MD can reject events under high local strain; restraint parameters require calibration per chemistry.

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