Scaling of selectivity in uniformly charged nanopores through a modified Dukhin number for 1:1 electrolytes

TL;DR

This paper introduces a modified Dukhin number as a universal scaling parameter for ionic selectivity in uniformly charged nanopores, capturing the transition between surface and volume conduction regimes.

Contribution

The study proposes a new modified Dukhin number that accurately scales nanopore selectivity across different conditions, improving understanding of conduction regimes.

Findings

Modified Dukhin number satisfies scaling for selectivity

Radial flux profiles reveal conduction dominance regions

Inflection point indicates transition between conduction regimes

Abstract

We show that a modified version of the Dukhin number is an appropriate scaling parameter for the ionic selectivity of uniformly charged nanopores. The modified Dukhin number is an unambiguous function of the variables $\sigma$ (surface charge), $R$ (pore radius), and $c$ (salt concentration), and defined as $\mathrm{mDu}=|\sigma|/e(R/\lambda)$, where $\lambda$ is the screening length of the electrolyte carrying the $c$ dependence ($\lambda\sim c^{-1/2}$). Scaling means that the device function (selectivity) is a smooth and (in this case) monotonic function of mDu. The original Dukhin number defined as $\mathrm{Du}=|\sigma|/eRc$ ($c^{-1}$ dependence) was introduced to indicate whether the surface or the volume conduction is dominant in the pore. The modified version satisfies scaling and characterizes selectivity in the intermediate regime, where both surface and bulk conductions are present and the pore is neither perfectly selective, nor perfectly non-selective. Our modeling study using the Local Equilibrium Monte Carlo method and the Poisson-Nernst-Planck theory provides the radial flux profiles from which the radial selectivity profile can be computed. These profiles show in which region of the nanopore the surface or the volume conduction dominates for a given combination of the variables $\sigma$, $R$, and $c$. We show that the inflection point of the scaling curve may be used to characterize the transition point between the surface and volume conductions.