The Free Energy Landscape of Li- and Na-Ion Transport in Nanoconfinement with Machine Learning Interatomic Potentials

Nanoconfined systems such as cation-exchanged zeolites provide tunable geometric and chemical environments at the nanoscale that may facilitate regulated ion transport for energy storage applications, and enable materials to extract Li from solutions. However, simulating ion transport in nanoporous materials with density functional theory (DFT) accuracy has traditionally been challenging because of system sizes comprising hundreds of atoms and simulation times of nanoseconds. In this work, we perform molecular dynamics (MD) simulations with a machine learning interatomic potential (MLIP) to study the free energy landscape of Li+ and Na+ diffusion in zeolites, with and without solvent (water in our case). Results from umbrella sampling show Li+ to encounter a free energy barrier of ∼14 kJ/mol during their transport along the pore channels, in the presence of solvent. The absence of solvent increases the free energy barrier by ∼3−4 times. We find lower free energy barriers for Na+ diffusion (∼11 kJ/mol) than Li+ and subsequently rationalize how the different coordination environments of the ions lead to the difference in the free energy landscape. A key finding in this work is that the trade-off between the ion coordination with solvent and framework atoms determines the free energy barriers of ion transport in nanoconfinement. We then perform unbiased MD simulations at a high temperature (800 K) after modifying the chemical environment inside the zeolite in terms of the Si/Al ratio. The mean-squared displacements and probability densities of Li+ and Na+ distributions in our confined system show Na+ to diffuse faster than Li+ at high temperatures. The combination of material modeling, MLIP-driven MD simulations, and free energy calculations in this work thus provides a systematic framework for studying ion transport in nanoporous materials.