Ion current rectification inversion in conic nanopores: Nonequilibrium ion transport biased by ion selectivity and spatial asymmetry

We show both theoretically and experimentally that the ion-selectivity of a conic nanopore, as defined by a normalized density of the surface charge, significantly affects ion current rectification across the pore. For weakly selective negatively charged pores, intra-pore ion transport controls the current and internal ion enrichment/depletion at positive/reverse biased voltage (current enters/leaves through the tip, respectively), which is responsible for current rectification. For strongly selective negatively charged pores under positive bias, the current can be reduced by external field focusing and concentration depletion at the tip at low ionic strengths and high voltages, respectively. These external phenomena produce a rectification inversion for highly selective pores at high (low) voltage (ionic strength). With an asymptotic analysis of the intra-pore and external ion transport, we derive simple scaling laws to quantitatively capture empirical and numerical data for ion current rectification and rectification inversion of conic nanopores.