Improved model of ionic transport in 2-D MoS ₂ membranes with sub-5 nm pores

Solid-state nanopores made of two-dimensional materials such as molybdenum disulfide are of great interest thanks in part to promising applications such as ion filtration and biomolecule translocation. Controlled fabrication and tunability of nanoporous membranes require a better understanding of their ionic conductivity capabilities at the nanoscale. Here, we developed a model of ionic conductivity for a KCl electrolyte through sub 5-nm single-layer MoS ₂ nanopores using equilibrium all-atom molecular dynamics simulations. We investigate the dynamics of K ⁺ and Cl ^- ions inside the pores in terms of concentration and mobility. We report that, for pore dimensions below 2.0 nm, which are of particular interest for biomolecule translocation applications, the behaviors of the concentration and mobility of ions strongly deviate from bulk properties. Specifically, we show that the free-energy difference for insertion of an ion within the pore is proportional to the inverse surface area of the pore and that the inverse mobility scales linearly as the inverse diameter. Finally, we provide an improved analytical model taking into account the deviation of ion dynamics from bulk properties, suitable for direct comparison with experiments.