Scaling Behavior of Ionic Conductance Dependent on Surface Charge Inside a Single-Digit Nanopore

The ionic conductance in a charged nanopore exhibits a power-law behavior in low salinity—as has been verified in many experiments (G0∝c0α)—which is governed by surface charges. The surface charge inside a nanopore determines the zeta potential and ion distributions, which have a significant impact on ion transport, especially in a single-digit nanopore with potential leakage. However, precisely measuring surface charge density in a single-digit nanopore remains a challenge. Here, we propose a methodology for exploring the power-law variation of ionic conductance, with potential leakage taken into account. We conducted experiments to measure the ionic current using silicon nitride nanopores and employed a continuous theory to explore the relationship between pore-bound concentration and surface charges. Considering that the influence of potential leakage on concentration follows a power-law relationship, we established a coefficient (α) to examine the controlling factors of potential leakage and modified the conductance model to obtain the ion mobility inside a nanopore.