Learning the Influence of the Chemical Environment on Epoxy-Amine Cure Kinetics

Abstract

Accurate modelling of polymer-network formation requires describing reaction kinetics in a continuously evolving chemical environment. Epoxy-amine networks are a challenging model system: epoxy groups react successively with primary and secondary amines, while hydroxyl groups formed during cure promote autocatalysis. Semi-empirical models are easy to use, but always formulation-specific. Detailed mechanistic models provide a physically meaningful description by accounting for reactive and non-reactive complexes, but require numerous coupled reactions and parameters, limiting their extension to new formulations. Here, we develop a supervised learning framework for mechanistic model simplification. A physics-informed, fully connected residual neural Ordinary Differential Equation (ODE) network maps the instantaneous chemical state to two effective reaction-rate coefficients, reducing a detailed 13-step epoxy-amine reaction scheme to the two major reactions describing epoxy consumption by primary and secondary amines. The reduced model retains the corresponding mass-balance equations and Arrhenius temperature dependence, while the neural network learns how the evolving chemical environment modifies reactivity. Temperature and the instantaneous concentrations of epoxy, primary, secondary and tertiary amines, and hydroxyl and ether functionalities are projected into a latent representation and processed through stacked residual blocks to predict the two rate constants. These coefficients are then used within the kinetic equations to predict complete cure trajectories. The network therefore does not directly predict conversion, but learns the unresolved influence of the chemical environment on physically interpretable kinetic parameters. Training data are generated with the detailed mechanistic model across a broad range of temperatures, stoichiometric ratios, ether concentrations and conversions. Effective rate coefficients derived from the simulated concentration trajectories are used to train the neural network. Data are split at the stoichiometric-ratio level: all complete cure trajectories associated with a given ratio are assigned exclusively to the training, validation or test set, preventing leakage between correlated conversion points and trajectories. Generalisation is evaluated on unseen stoichiometries and processing conditions using both the predicted rate coefficients and the resulting integrated cure trajectories. Network architecture and training parameters are selected through automated hyperparameter optimisation. In a subsequent experimental stage, the framework is fine-tuned and validated using heat-flow measurements from differential scanning calorimetry and microcalorimetry, complemented by near-infrared spectroscopy to track reactive-group concentrations in real time. The reduced model captures hydroxyl-induced autocatalysis, differences between primary- and secondary-amine reactivity, and variations in effective reaction rates with temperature, stoichiometry and ether concentration. It thus compresses a detailed reaction scheme into a computationally efficient model while preserving a physically interpretable kinetic mechanistic scheme. This hybrid approach provides a foundation for compact and transferable models of polymerization kinetics, combining data-driven representation of chemical-environment effects with mechanistic reaction equations.