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An interesting area of modern membrane science is the development of "smart" membranes, which can affect the transport properties of selected components via external tuning. When the target components are ions, such a tuning can be realized with the help of electric field created by the conductive pore surface. We have proposed in this work a mathematical model of ions transport in a cylindrical nanopore with the electronic charge at the conductive surface and the chemical charge, which is separated from the surface by the Stern layer. The model is based on one-dimensional equations for potential, ion concentrations, and pressure in the diffuse layer. It is applied for describing the membrane potential at zero current, which characterizes the type and strength of ionic selectivity. It is shown that the change of surface potential in the direction from negative to positive results in the continuous change of pore selectivity from cation to anion. The decrease in the Stern layer capacitance and increase in the pore radius lead to the decrease in ionic selectivity. The presence of positive (negative) chemical charge causes the shift of potential value, at which the selectivity is switched, in the direction of negative (positive) values. At this value of potential, the membrane becomes non-selective, the diffusive flux of ions reaches maximum, and the osmotic flow ceases. The suggested model provides a qualitative and quantitative description of experimental results on switchable selectivity of tracketched membranes modified by the gold coating.

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