Effect of Membrane Thickness on Ion Transport in pH-Regulated Zero-Depth Interfacial Nanopores

Zero-depth interfacial nanopores, which are formed by two crossed nanoscale channels at their intersection interface, have been proposed to increase the spatial resolution of solid-state nanopores. However, research on zero-depth interfacial nanopores is still in its early stages. Although it has been shown that the current passing through an interfacial nanopore is largely independent of the membrane thickness, existing studies have not fully considered the impact of membrane thickness on other ion transport characteristics within these nanopores. In this paper, we investigate the electrokinetic ion transport phenomenon in the zero-depth interfacial nanopores, especially focusing on the influence of membrane thickness on the ion transport phenomenon. Our model incorporates the Poisson-Nernst-Planck equations and the Navier-Stokes equations, featuring a pH-regulated surface charge density. We find that when the thickness of the nanochannels is close to the interface size of the formed interfacial nanopore, the phenomenon of ion transport in the interfacial nanopore is similar to that in a conventional cylindrical nanopore. However, when the thickness of the nanochannels is much greater than the interface size of the formed interfacial nanopore, several distinct phenomena occur. The surface charge density on the inner walls of the interfacial nanopores has a small peak at the interface of the two crossing nanochannels, and the anion concentration changes greatly between the two nanochannels; that is, a much greater anion concentration forms in the nanochannel near the anode side than in the nanochannel near the cathode side. When the surface charge is nonzero, the electric field within the interfacial nanopore creates three extreme points, and the directions of the local electric fields are opposite at the ends of the membrane.