Diffusive to Barrier-Limited Transition in the Aqueous Ion Transport through Nanoporous 2D Materials

The interplay of interactions between aqueous ions and the confinement of subnanoscale pores in solid 2D membranes causes a range of barrier-limited phenomena, including selective ion trapping and permeation, mechanosensitive transport, and memristive effects. A clear understanding of the transition from diffusive to barrier-limited transport regime is lacking, however. Moreover, the limits of applicability for the analytical formalism widely used to relate measured transport data to the effective pore size are unclear. Here, with the goal of identifying the transition between regimes and determining the pore sizes below which the diffusive formalism fails, we present a computational study of water-dissociated alkali salt transport through 2D membranes featuring pores of various sizes. Triangular nitrogen-terminated multivacancies in hexagonal boron nitride are used as a simple yet illustrative example of uncharged locally dipolar pores with various degrees of cation selectivity. We find that <i>cation-cation</i> selectivity and high mechanosensitivity are the clearest indicators of the barrier-limited regime onset. We also show that for triangular pore geometries, the diffusion-based analytical formalism is expected to fail when the side of the triangle is below order ≈2 nm. For circular geometries, similar failure is expected for pore diameters below ≈1.2 nm. Because an extensive theoretical description of barrier-limited transport is a major challenge, detailed computer models currently remain the most accurate nonexperimental methods for investigating ion transport in the barrier-limited regime. Given how sensitively the permeation regime depends on the pore size, our results suggest that in addition to advances in fabrication, accurate theoretical interpretation of measured transport data is vital to harnessing the unique features of barrier-limited ionic and molecular transport in nanofluidic systems using nanoporous 2D materials.