The study of rectifying systems like conical nanopores demands an extension of our understanding of ionic selectivity. The asymmetric conduction shown by these pores is connected to the idea of directionality: the rates of ionic transport and the charge regulation exerted by the system are nonsymmetrical. As a result, ionic selectivity is not only a property of the nanopore itself but also depends crucially on the direction of the concentration gradient. Previous studies of current-voltage curves provide an adequate description of the conductive properties of the system but give only indirect clues about how charge regulation is performed. In this sense, the study of the reversal potential offers additional and essential information. To this end, here we present a model for reversal potential in conical nanopores based on the Poisson and Nernst-Planck (PNP) equations. The theoretical results are compared with experimental data, and good agreement is found using only one fitting parameter, the surface charge density, which is determined independent of the currentvoltage characteristics.

The pH-switchable ion transport and selectivity in nanopore membranes with fixed charges is theoretically analyzed using a model based on the Nernst−Planck flux equations. The ionization state of the weak polyelectrolyte groups attached to the pore surface appears to be a crucial factor in order to understand the conductive properties of the pore. The model allows for the calculation of the fluxes of all of the ionic species involved and the membrane potential. Comparison of the theoretical results with the experimental data by Martin el al. (Science 1995, 268, 700−2; J. Phys. Chem. B 2001, 105, 1925−34; and Adv. Mater. 2001, 13, 1351−62) and Stroeve et al. (Langmuir 2000, 16, 2401−4; and Langmuir 2001, 17, 5271−5) for surface modified nanopores with fixed charges shows that the model can describe qualitatively the changes of the permeate ion flux and the membrane potential with the pH and the solute concentration of the external solutions. The effect of applying an electric potential to the nanopore walls is also studied. Some of the main characteristics that allow a simple description of pH-switchable effects on nanopore membranes with fixed charges are clearly shown.