Elucidating the Mechanisms of Ion Permeation through Sub-Nanometer Graphene Pores: Uncovering Free Energy Barriers via High-Throughput Molecular Simulations

Understanding ion transport through subnanometer graphene nanopores is critical for advancing nanoscale filtration technologies and uncovering the molecular mechanisms underlying selective ion permeation. Owing to their atomic thickness and tunable pore sizes, nanoporous graphene membranes serve as a model system for probing ion selectivity and hydration behavior under spatial confinement. This work investigates the transport of Na⁺, Cl^–, K⁺, and water through graphene nanopores to elucidate their ion-sieving characteristics. Free energy barriers associated with ion and water permeation are quantified, offering insight into the energetic costs of dehydration and translocation through nanopores. Selective ion transport is further examined using the constant potential method (CPM), which more accurately reflects experimental electrochemical conditions, and allows for the selective permeation of K⁺ over Na⁺ within nanoporous graphene membranes. The role of externally applied electric fields is also explored to assess their impact on ion hydration and transport dynamics. Together, these results contribute to a deeper mechanistic understanding of ion confinement, hydration, and selective permeation in nanoporous atomically thin membranes.