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Reactive molecular dynamics of an oxalic acid and DGEBA vitrimer

Preprint·ChemRxiv, CC BY 4.0

Figure 9: Polymerization scheme of DGEBA and oxalic acid, built from 57 to 114, 228 and 456 atoms. 1:1 stoichiometry is maintained at every step.

Figure 9: Polymerization scheme of DGEBA and oxalic acid, built from 57 to 114, 228 and 456 atoms. 1:1 stoichiometry is maintained at every step.

Atoms in final chain
456
Density at 300 K
1.2975g/cm3
Glass transition (Tg)
about 76C
Young's modulus
4.36GPa
Poisson's ratio
0.371

Data description

Vitrimers are crosslinked polymers whose bonds can rearrange, so a strong network can still be reshaped and recycled. Designing them is hard because crosslinking is too slow to follow with ordinary molecular dynamics.

We simulate the polymerization of DGEBA and oxalic acid at 1:1 stoichiometry with reactive molecular dynamics in LAMMPS, using the ReaxFF CHNO-2017_weak force field. A COLVARS harmonic bias on three distances drives an SN2-like nucleophilic attack, then proton transfer, giving a beta-hydroxy ester. The network is built hierarchically at 57, 114, 228, 456 atoms.

The annealed polymer has a density of 1.2975 g/cm3 at 300 K and a glass transition near 76 C, both above the adipic acid vitrimer of Kamble et al. Uniaxial tension at 2e9 1/s gives a mean Young's modulus of 4.36 GPa and a Poisson's ratio of 0.371.

Simulation summary
DetailValue
ReactionDGEBA + oxalic acid, 1:1
Force fieldReaxFF CHNO-2017_weak, fix qeq/reax
Bias methodCOLVARS, harmonic bias on 3 distances
Temperature423 K
Timestep0.05 fs
EnsembleNVT, Nose-Hoover
SoftwareLAMMPS, ORCA
Final system456 atoms (8 DGEBA + 8 oxalic acid)

Intended use

Recyclable thermosets

Screen vitrimer chemistries that keep thermoset strength but can be reprocessed at end of life.

Self-healing materials

Study how rearranging bonds in the network could let a damaged part repair itself.

Property prediction before synthesis

Estimate density, glass transition and stiffness from simulation before anyone mixes a resin.

Comparable studies

The oxalic acid network is compared with the adipic acid and DGEBA vitrimer reported by Kamble et al. Reformix is shown in blue.

Density at 300 K

g/cm3
  • Oxalic acid vitrimer (this work)
    Reformix
    1.2975g/cm3
  • Adipic acid vitrimer
    Kamble et al.
    1.215g/cm3

Glass transition temperature (Tg)

C
  • Oxalic acid vitrimer (this work)
    Reformix
    76C
  • Adipic acid vitrimer
    Kamble et al.
    42.8C

Directional properties

Values from uniaxial tension along each axis at 2e9 1/s strain rate.

Young's modulus by direction

GPa
  • X axis
    4.29
  • Y axis
    2.67
  • Z axis
    6.13

Mean 4.36 +/- 1.00 GPa

Poisson's ratio by direction

  • X axis
    0.37545
  • Y axis
    0.3878
  • Z axis
    0.3487

Mean 0.371 +/- 0.012

Simulation

Structural relaxation and density behavior during polymerization and annealing.

RMSD plateau, stage 1

A

0.9

RMSD plateau, stage 2

A

2.6

RMSD during polymerization

Fig 8
Figure 8a: RMSD profile, stage 1: reaction between one DGEBA and one oxalic acid molecule.
Figure 8a: RMSD profile, stage 1: reaction between one DGEBA and one oxalic acid molecule.
Figure 8b: RMSD profile, stage 2: polymerization between two stage 1 products.
Figure 8b: RMSD profile, stage 2: polymerization between two stage 1 products.

Density during annealing

Fig 10
Figure 10: Evolution of polymer density during two annealing cycles.
Figure 10: Evolution of polymer density during two annealing cycles.

Density time series at 300 K

Fig 12
Figure 12: Density time series from the final annealing segment at 300 K. The shaded region marks equilibration.
Figure 12: Density time series from the final annealing segment at 300 K. The shaded region marks equilibration.

Thermomechanical analysis

Density vs temperature

Fig 13
Figure 13: Temperature dependence of polymer density from NPT molecular dynamics. Error bars show the standard deviation.
Figure 13: Temperature dependence of polymer density from NPT molecular dynamics. Error bars show the standard deviation.

Tg inflection

Fig 14
Figure 14: Glass transition temperature from the density-temperature curve by spline inflection analysis. The red line marks Tg (about 76 C).
Figure 14: Glass transition temperature from the density-temperature curve by spline inflection analysis. The red line marks Tg (about 76 C).

Stress-strain, X direction

Fig 16
Figure 16: Stress-strain curve of the annealed polymer network at 2e9 1/s strain rate along the X direction.
Figure 16: Stress-strain curve of the annealed polymer network at 2e9 1/s strain rate along the X direction.

Poisson's ratio fit

Fig 17
Figure 17: Transverse strain in Y and Z versus axial strain along X under uniaxial tension, with linear regressions used to determine Poisson's ratio.
Figure 17: Transverse strain in Y and Z versus axial strain along X under uniaxial tension, with linear regressions used to determine Poisson's ratio.

Validation

Key bond lengths along the reaction path from the biased trajectory.

Bond lengths
BondLength (A)
TS epoxide C-O2.10
Forming C-O1.77
Product ester C-O1.31
Beta-hydroxy C-O1.42
O-H1.01

Transition state and product geometries

Fig 7
Figure 7a: Transition state showing partial C-O bond formation and proton transfer.
Figure 7a: Transition state showing partial C-O bond formation and proton transfer.
Figure 7b: Product geometry immediately after the transition state.
Figure 7b: Product geometry immediately after the transition state.
Figure 7c: Final product geometry.
Figure 7c: Final product geometry.

Method

Distance-based crosslinking compared with COLVARS-biased reactive MD.

Reaction mechanism

Fig 2
Figure 2: Reaction mechanism between an epoxy group and a carboxylic acid. The nucleophilic oxygen of the COOH group attacks the electrophilic carbon of the epoxide ring, leading to ring opening and formation of a beta-hydroxy ester.
Figure 2: Reaction mechanism between an epoxy group and a carboxylic acid. The nucleophilic oxygen of the COOH group attacks the electrophilic carbon of the epoxide ring, leading to ring opening and formation of a beta-hydroxy ester.
Distance-based crosslinking vs COLVARS-biased MD
Distance-based crosslinkingCOLVARS-biased MD
MechanismA bond is added once two atoms come within a cutoffA harmonic bias drives attack, then proton transfer
Steric effectsLargely ignoredCaptured by the reactive force field along the path
TemperatureReaction step is separate from the dynamicsRuns in the dynamics at 423 K, NVT
Atomistic detailTopology changes without a reaction pathBond breaking and forming with charge equilibration

Metadata

COLVARS parameters
Table 1. COLVARS parameters, stage 1k in kcal/mol/A^2, distances in Acv               pair                    init_A  target_A  k      lo_wall  lo_k  hi_wall  hi_kdist_CO_epoxide  O(epoxide)-C(epoxide)   1.399   2.4       80     1        5     4.5      5dist_CO_acid     C(epoxide)-O(acid)      5.459   1.43      800    1        5     6.5      5d_H_diff         H(acid)-O(epoxide)      5.761   1.1       500    -8       2     8        2Harmonic bias on each collective variable xi:  V_bias(xi) = 1/2 * k * (xi - xi_target)^2Harmonic walls keep xi inside its bounds:  V_lower(xi) = 1/2 * k_lower * (xi - lower_wall)^2   for xi < lower_wall  V_upper(xi) = 1/2 * k_upper * (xi - upper_wall)^2   for xi > upper_wall

Citation

Published work using these results should cite the preprint as below.

Reference

Reformix AI. COLVARS-Driven Reactive Molecular Dynamics of Vitrimer Polymerization and Thermomechanical Property Analysis. ChemRxiv, 2026. https://doi.org/10.26434/chemrxiv-2026-k6fn6

BibTeX
@misc{reformix2026colvars,  title     = {COLVARS-Driven Reactive Molecular Dynamics of Vitrimer Polymerization and Thermomechanical Property Analysis},  author    = {Reformix AI},  year      = {2026},  publisher = {ChemRxiv},  doi       = {10.26434/chemrxiv-2026-k6fn6},  note      = {Preprint},}

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Preprint. Posted 2026-01-03 on ChemRxiv under CC BY 4.0.

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