Quantification of Steady-State Ion Transport through Single Conical Nanopores and a Nonuniform Distribution of Surface Charges

Electrostatic interactions of mobile charges in solution with the fixed surface charges are known to strongly affect stochastic sensing and electrochemical energy conversion processes at nanodevices or devices with nanostructured interfaces. The key parameter to describe this interaction, surface charge density (SCD), is not directly accessible at nanometer scale and often extrapolated from ensemble values. In this report, the steady-state current–voltage (<i>i–V</i>) curves measured using single conical glass nanopores in different electrolyte solutions are fitted by solving Poisson and Nernst–Planck equations through finite element approach. Both high and low conductivity state currents of the rectified <i>i–V</i> curve are quantitatively fitted in simulation at less than 5% error. The overestimation of low conductivity state current using existing models is overcome by the introduction of an exponential SCD distribution inside the conical nanopore. A maximum SCD value at the pore orifice is determined from the fitting of the high conductivity state current, while the distribution length of the exponential SCD gradient is determined by fitting the low conductivity state current. Quantitative fitting of the rectified <i>i–V</i> responses and the efficacy of the proposed model are further validated by the comparison of electrolytes with different types of cations (K⁺ and Li⁺). The gradient distribution of surface charges is proposed to be dependent on the local electric field distribution inside the conical nanopore