Large-Scale Atomistic Simulations of Proton Transport in Perfluorinated Ionomer Membranes Using a Neural Network Interatomic Potential

The rapid advancement of machine learning technology in recent years has led to the development of materials discovery and materials simulation techniques utilizing machine learning in the field of materials science. Specifically, machine learning interatomic potentials (MLIPs) constructed using density functional theory (DFT) calculation results as training data have attracted significant attention because they enable molecular dynamics (MD) simulations at time and spatial scales that are not possible with ab initio simulations while maintaining accuracy comparable to DFT calculations. The construction of MLIPs requires a series of steps, including the generation of labeled data (energy and/or forces) using DFT calculations, the training of MLIP models, and the accuracy evaluation of MLIP models. We are developing a software called Generator of Neural Network Interatomic Potential for Molecular Dynamics (GeNNIP4MD) to automate this MLIP construction workflow. In GeNNIP4MD, by just providing the initial structure(s) for DFT calculations, it is possible to automatically perform data generation using active learning, training of neural network potential (NNP) models, and accuracy evaluation of NNP models. In each cycle of active learning, structure sampling is performed using MD simulations with the NNP model constructed in the previous cycle, and a two-stage screening based on the uncertainty of the force prediction and structural features is performed to efficiently sample structural data that is not present in the dataset. This two-stage screening allows for the construction of highly accurate NNP models while reducing the number of computationally expensive DFT calculations required. In this study, we employ GeNNIP4MD to create an NNP model capable of analyzing the proton transport in Nafion (perfluorinated ionomer) membranes, which are widely used as polymer electrolyte membranes. As initial structures, we prepare multiple systems consisting of Nafion monomers and water molecules with different water contents (<300 atoms) and use them as inputs to GeNNIP4MD. We employ Deep Potential (DP) as the NNP model and construct the DP model using GeNNIP4MD. At the end of all active learning cycles, the root mean squared error (RMSE) of energy is approximately 1 meV/atom and the force RMSE is below 80 meV/Å on the validation set, indicating successful construction of a highly accurate DP model. Using the constructed DP model, we perform MD simulations of large systems (>10000 atoms) composed of Nafion polymers and water molecules and find that the water-content dependence of densities and proton diffusion coefficients is successfully reproduced.