Revisiting the access conductance of a nanopore in a charged membrane

TL;DR

This paper develops an analytical and semi-analytical theory for electric-field-driven ionic conductance in charged nanopores, extending existing models and explaining fractional conductance scaling observed experimentally.

Contribution

It introduces a generalized theory for nanopore conductance that accounts for arbitrary surface potentials and membrane thickness, validated by numerical simulations.

Findings

The theory accurately predicts ionic conductance across a wide parameter range.

Fractional scaling of conductance with electrolyte concentration is intrinsic to ultrathin membranes.

The model explains experimental observations of conductance behavior in charged nanopores.

Abstract

Electric-field-driven electrolyte transport through nanoporous membranes is important for applications including osmotic power generation, sensing and iontronics. We derive an analytical equation in the Debye--H\"uckel regime and a semi-analytical equation for arbitrary surface potentials for the electric-field-driven electric current through a pore in an ultrathin membrane, which predict scaling with fractional powers of the pore size and Debye length. We show that our theory for arbitrary electric potentials accurately quantifies the ionic conductance through an ultrathin membrane in finite-element method numerical simulations for a wide range of parameters, and generalizes a widely used theory for the access electrical conductance of a membrane nanopore to a broader range of conditions. Our theory predicts that fractional scaling of the ionic conductance with electrolyte concentration at low concentrations is an intrinsic property of charged ultrathin membranes and also occurs for thicker membranes for which the access contribution to the conductance dominates, which could help to explain experimental observations of this widely debated phenomenon.