Rectification in synthetic conical nanopores: a one-dimensional Poisson-Nernst-Planck modeling

TL;DR

This paper develops a one-dimensional Poisson-Nernst-Planck model to analyze ion current rectification in synthetic conical nanopores, providing analytical formulas and demonstrating good agreement with experimental data for small to moderate currents.

Contribution

It introduces a reduced 1D PNP model with entropic effects for synthetic nanopores, deriving an analytical rectification current formula and highlighting the impact of potential asymmetry.

Findings

Analytical formula for rectification current derived

Model agrees with experimental data for small-to-moderate currents

Asymmetry in potential jumps significantly influences rectification

Abstract

Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties of biological ion channels [P. Yu. Apel, {\it et al.}, Nucl. Instr. Meth. B {\bf 184}, 337 (2001); Z. Siwy, {\it et al.}, Europhys. Lett. {\bf 60}, 349 (2002)]. Here, the ion current rectification is studied within a reduced 1D Poisson-Nernst-Planck (PNP) model of synthetic nanopores. A conical channel of a few $\mathrm{nm}$ to a few hundred of nm in diameter, and of few $\mu$m long is considered in the limit where the channel length considerably exceeds the Debye screening length. The rigid channel wall is assumed to be weakly charged. A one-dimensional reduction of the three-dimensional problem in terms of corresponding entropic effects is put forward. The ion transport is described by the non-equilibrium steady-state solution of the 1D Poisson-Nernst-Planck system within a singular perturbation treatment. An analytic formula for the approximate rectification current in the lowest order perturbation theory is derived. A detailed comparison between numerical results and the singular perturbation theory is presented. The crucial importance of the asymmetry in the potential jumps at the pore ends on the rectification effect is demonstrated. This so constructed 1D theory is shown to describe well the experimental data in the regime of small-to-moderate electric currents.