Systematic coarse-graining of epoxy resins with machine learning-informed energy renormalization

Designing high-performance epoxy resins computationally requires efficient methods to replace costly experiments. Molecular models are crucial for bridging the gap between molecular dynamics (MD) simulations and experimental results, accurately predicting the tunable macroscopic properties of epoxy resins and their composites. However, the chemical complexity of epoxy resins, the numerous properties to be predicted, and their strong dependence on the degree of crosslinking (DC) pose significant challenges. All-atom (AA) MD simulations are effective for predicting DC's effect on properties like glass-transition temperature, thermal expansion coefficient, and elastic response, but are computationally expensive for high-throughput design. Coarse-grained (CG) models offer significantly improved computational efficiency, but require careful calibration of force fields to maintain chemistry-specificity. Existing CG models for epoxies often focus on specific crosslinking states or properties, lacking transferability across different temperatures or curing states. The authors address these limitations by presenting a novel method that leverages machine learning to achieve DC-transferability and accurately predict multiple properties simultaneously.

Previous studies using all-atom molecular dynamics have shown success in predicting the effects of degree of crosslinking on various properties of epoxy resins. However, these simulations are computationally expensive. Coarse-grained models offer a computationally efficient alternative, but accurate calibration across different curing states and temperatures remains a challenge. Existing coarse-grained models have either matched structural features or thermomechanical properties for highly crosslinked networks, but lacked the transferability across different curing conditions. Machine learning approaches have been used in coarse-grained modeling of other systems, but applications to complex chemistries like epoxy resins have been limited. A recent study used a particle swarm optimization algorithm to calibrate a temperature-dependent force field, but only targeted the elastic modulus for three curing states. This study aimed to address this gap by developing a general coarse-grained framework for epoxy resins that can target multiple properties at different degrees of crosslinking and demonstrate its applicability to more than one cure chemistry.

The authors developed a coarse-grained model for epoxy resins using a combination of energy renormalization and machine learning. The model uses Bisphenol A diglycidyl ether (DGEBA) as the epoxy and either 4,4-Diaminodicyclohexylmethane (PACM) or polyoxypropylene diamines (Jeffamine D400) as curing agents. The model consists of seven bead types, with bonded parameters calibrated using a Boltzmann inversion (BI) approach. The non-bonded parameters were calibrated using Gaussian process models, allowing for efficient handling of high-dimensional parametrization and multi-response calibrations. Initially, a high-dimensional and flexible class of radial basis functions (RBFs) was assumed for the DC-dependent non-bonded parameters. Uncertainty quantification, calculated from the fluctuations of the Gaussian process prediction, was used to simplify the calibration functions while maintaining accuracy. The final model reduced the number of free parameters from 43 (all RBFs) to 21, demonstrating a significant improvement in efficiency.

The all-atom simulations provided target properties (density, Debye-Waller factor, Young's modulus, and yield stress) at various degrees of crosslinking for both DGEBA+PACM and DGEBA+D400 systems. Sensitivity analysis revealed a strong influence of σᵢ parameters on density and cohesive energies εᵢⱼ on dynamics and mechanical properties. The initial attempt to use sigmoid functions for DC dependence proved too restrictive, leading to the adoption of RBFs. Uncertainty quantification guided the simplification of the calibration functions, reducing the number of free parameters from 43 to 21. The optimized CG model showed excellent agreement with the AA simulations for all eight target properties, with an average root mean squared percentage error (RMSPE) of 10%. The CG model accurately predicted the mean square displacement and stress-strain response, validating the model's predictive power beyond the target properties. The CG simulations ran approximately 1000 times faster than the AA simulations.

The findings demonstrate the successful development of a highly efficient and accurate coarse-grained model for epoxy resins. This model addresses limitations of previous approaches by achieving transferability across different degrees of crosslinking and accurately predicting multiple macroscopic properties. The use of machine learning and uncertainty quantification allows for a significant reduction in the complexity of the force field without compromising accuracy. The model's improved computational efficiency enables larger-scale simulations, opening avenues for investigating complex phenomena such as heterogeneity and fracture processes at length scales inaccessible to all-atom simulations. The framework is readily adaptable to other systems and can be tailored to specific applications by adjusting the weights assigned to different target properties.

This study successfully developed a coarse-grained model for epoxy resins using a novel combination of energy renormalization and machine learning. The model achieves high accuracy and significant computational efficiency compared to all-atom simulations. The framework presented provides a valuable tool for designing and investigating epoxy resin systems, contributing to advancements in material science and engineering. Future work will focus on expanding the model to incorporate bond-breaking events to simulate fracture and impact resistance, and extending the model to systems with multiple curing agents in varying stoichiometric ratios.

The current model is validated for stoichiometric ratios of the curing agents. While preliminary results suggest robustness to variations in stoichiometry, further investigation is needed for a complete understanding. The accuracy of the model's predictions is influenced by the inherent uncertainties in both the all-atom and coarse-grained simulations, which are approximated using Gaussian process models. Extending the study to encompass a wider range of temperatures would further enhance the model’s applicability.