Ion transport through single-cation selective nanopores in thin polymer foils is examined experimentally and described by a diffusional model based on the reduction of the three-dimensional Smoluchowski equation into a one-dimensional equation of Fick–Jacobs type. The model enables semi-quantitative predictions of the transport properties of nanopores of various shapes and surface charge properties even when bulk electrolyte values of various parameters are used. The experimental conductivity data clearly indicate the presence of a surface current component not described by the bulk-type diffusion. The values of the measured surface conductivities depend, among others, on the properties of the channel's internal surface. These surface currents play a substantial role in the rectification processes and are partially responsible for the high-cation selectivity of nanopores.

Both theory and electrolytic conductivity measurements show that asymmetric nanopores partially rectify the current with a preferential direction of cation flow from a pore of high surface charge density towards a pore of low surface charge density and/or from the narrow towards the wide opening of the pore.