Theoretical prediction of diffusive ionic current through nanopores under salt gradients

In charged nanopores, ionic diffusion current reflects the ionic selectivity and ionic permeability of nanopores, which determines the performance of osmotic energy conversion, i.e., the output power and efficiency. Here, theoretical predictions of the diffusive currents through cation-selective nanopores have been developed based on the investigation of diffusive ionic transport under salt gradients with simulations. The ionic diffusion current I satisfies a reciprocal relationship with the pore length I ∝ α/L (α is a constant) in long nanopores. α is determined by the cross-sectional areas of diffusion paths for anions and cations inside nanopores, which can be described with a quadratic power of the diameter, and the superposition of a quadratic power and a first power of the diameter, respectively. By using effective concentration gradients instead of nominal ones, the deviation caused by the concentration polarization can be effectively avoided in the prediction of ionic diffusion current. With developed equations of effective concentration difference and ionic diffusion current, the diffusion current across nanopores can be well predicted in cases of nanopores longer than 100 nm and without overlapping of electric double layers. Our results can provide a convenient way for the quantitative prediction of ionic diffusion currents under salt gradients.