Evolution of Nonlinear Ion Transport in Nanopore Arrays: Ionic Conductance, Current Rectification, and Osmotic Power

Abstract

Understanding the ionic transport and scaling behaviors in nanopore arrays is essential for bridging fundamental ion physics and blue energy applications. By fabricating sub-3 nm and sub-20 nm diameter nanopore arrays (NPAs) spanning from few pores to N ~ 10000, we systematically investigate ionic conductance, ion current rectification, and osmotic energy conversion. We report the ionic conductance scaling laws and nonlinearity with nanopore number, with stronger deviations from linearity at lower salt concentrations. Experimental evidence reveals that surface-charge-governed conductance and ion current rectification progressively weaken with increasing N and even vanish as the NPA scales up to N ~ 10000, resulting in an underestimation of surface charge density. In a sub-3 nm densely packed array (separation ~ 25 nm), the conductance exhibits an anomalous power-law dependence on concentration, deviating markedly from the single nanopore characteristics, attributed to the strong pore interactions. Furthermore, osmotic power harvesting measurements reveal a substantial reduction in power density upon scaling, with decreases of up to three orders of magnitude over the same range. To elucidate the underlying mechanism, we developed rigorous 3D modeling showing that the nonlinear behavior originates from concentration polarization at pore entrances and suppressed electric field across NPAs, collectively hindering ion transport. Our work provides insight into nonlinear ion-transport scaling and reveals fundamental differences between transport phenomena in single nanopores and nanopore arrays.