Current voltage curves in synthetic conical nanopores described by a simple Poisson / Nernst Planck model

We have developed a theoretical model [1] for ionic transport through synthetic conical nanopores. The results have been compared with experiments obtained for single, gold–coated conical nanopores. The model [1] describes quantitatively the ionic transport through synthetic conical nanopores. It is based on the Poisson and Nernst-Planck (PNP) equations and allows the calculation of realistic profiles of average ionic concentration and electric potential along the pore. The only adjustable parameter is the surface charge density σ. Within this formalism, the concentration and potential profiles are computed together as self-consistent solutions of the PNP equations, in this way avoiding the assumption of a given potential distribution along the pore. We have compared the results provided by the PNP model with recent experimental data by Siwy et al. [2] obtained for two poly(ethylene terephthalate) (PET) filters containing single gold–coated conical nanopores. They were produced by chemically etching a PET foil containing a single heavy ion track (irradiated at UNILAC, GSI) and subsequently covering the pore walls with gold by electroless plating. After this procedure, the small radius of the pores was ≈ 5 nm and the wide radius ≈ 300 nm. The length of the pores was ≈ 12 μm. In the experimental setup, the membrane separated the two halves of an electrolytic cell, containing 0.1 M KF solutions. I-V curves were recorded at several pH values, for pores with differently modified surfaces. The results in Fig. 1a were obtained from a nanopore modified with 2mercaptopropionic acid, yielding a negative surface charge at pH = 6.6, and a neutral surface charge at pH = 3.5. In Fig. 1b, the nanopore surface contained mercaptoethylammonium groups and the measurements were conducted at pH = 6.6, yielding a positive surface charge. When the pore wall is uncharged, the I–V curve is linear (full circles in Fig. 1a). When the surface becomes charged, the corresponding I–V curves show rectification (open circles). For negative surface charge, the electric current is higher for V > 0 than for V < 0 (states “on” and “off”). If the charge on the pore wall becomes positive, the “on” and “off” states of the nanopore appear at V < 0 and V > 0, respectively. The theoretical results in Fig. 1 (dashed and full lines) are parametric in the surface charge density σ (e is the elementary charge). In all the calculations we used the (infinite dilution) diffusion coefficients D+ = 1.47· 10 cm/s, and D– = 2.03· 10 cm/s of the ionic species. Figure 1: Experimental (circles) [2] and theoretical (curves) results for the negatively (a) and positively (b) charged nanopore. The curves are parametric in the surface charge density σ.