  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 correlates with a/L (a is a
constant) in long nanopores. a 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.
