We show that diffusion currents for a membrane containing a single conical nanopore with a fixed surface charge and small enough opening diameter depend on the concentration gradient direction. We interpret the results based on the effect of salt concentration on the thickness of the electrical double layer within the nanopore associated with the nanopore's surface charge and the distribution of electric fields inside the pore. The experimental observations are described by a diffusional model based on the Smoluchowski-Nernst-Planck equation.

Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties of biological ion channels [P. Yu. Apel, et al., Nucl. Instr. Meth. B 184, 337 (2001); Z. Siwy, et al., Europhys. Lett. 60, 349 (2002)]. Here, the ion current rectification is studied within a reduced 1D Poisson-Nernst-Planck (PNP) model of synthetic nanopores. A conical channel of a few nm to a few hundred of nm in diameter, and of few µm long is considered in the limit where the channel length considerably exceeds the Debye screening length. The rigid channel wall is assumed to be weakly charged. A onedimensional reduction of the three-dimensional problem in terms of corresponding entropic effects is put forward. The ion transport is described by the non-equilibrium steady-state solution of the 1D Poisson-Nernst-Planck system within a singular perturbation treatment. An analytic formula for the approximate rectification current in the lowest order perturbation theory is derived. A detailed comparison between numerical results and the singular perturbation theory is presented.The crucial importance of the asymmetry in the potential jumps at the pore ends on the rectification effect is demonstrated. This so constructed 1D theory is shown to describe well the experimental data in the regime of small-to-moderate electric currents.

Ion transport through nanopores is modelled by the Smoluchowski equation. The model, based on properties of a bulk electrolyte solution and containing no adjustable parameters, is compared with ion current data recorded for single cylindrical nanopores in polymeric films. It predicts qualitatively a possibility of constructing an ion current rectifier based on the symmetric nanopore with asymmetric charge distribution. Our experimental data, however, indicate that the bulk-type diffusion approach does not describe the surface current, which gives a significant contribution to the total ion current through nanopores.

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