Large-Scale, Long-Time Atomistic Simulations of Proton Transport in Polymer Electrolyte Membranes Using a Neural Network Interatomic Potential

In recent years, machine learning interatomic potentials (MLIPs) have attracted significant attention as a method that enables large-scale, long-time atomistic simulations while maintaining accuracy comparable to electronic structure calculations based on density functional theory (DFT) and ab initio wavefunction theories. However, a challenge with MLIP-based molecular dynamics (MD) simulations is their lower stability compared to those using conventional classical potentials. Analyzing highly heterogeneous systems or amorphous materials often requires large-scale and long-time simulations, necessitating the development of robust MLIPs that allow for stable MD simulations. In this study, using our neural network potential (NNP) generator, we construct an NNP model that enables large-scale, long-time MD simulations of perfluorinated ionomer membranes (Nafion) across a wide range of hydration levels. We successfully build a robust deep potential (DP) model by iteratively expanding the dataset through active-learning loops. Specifically, by combining the sampling of off-equilibrium structures via non-equilibrium DPMD simulations with the structure screening in a 3D structural feature space incorporating minimum interatomic distances, it is possible to significantly enhance the robustness of the DP model, which allows for stable MD simulations of large Nafion systems ranging from approximately 10,000 to 20,000 atoms for an extended duration of 31 ns. The MD simulations employing the developed DP model yield self-diffusion coefficients of hydrogen atoms that more closely match experimental values in a wide range of hydration levels compared to previous ab initio MD simulations of smaller systems.