Scaling for rectification of bipolar nanopores as a function of a modified Dukhin number: the case of 1:1 electrolytes

TL;DR

This study investigates how the rectification behavior of bipolar nanopores scales with various system parameters using a modified Dukhin number, providing insights into the mechanisms influencing nanopore performance.

Contribution

It introduces a modified Dukhin number as a universal scaling parameter for bipolar nanopore rectification, linking device function to system parameters.

Findings

Scaling behavior depends on pore length, voltage, and surface charge.

The modified Dukhin number effectively collapses data across different parameters.

Mechanisms of parameter influence on rectification are elucidated.

Abstract

The scaling behavior for the rectification of bipolar nanopores is studied using the Nernst-Planck equation coupled to the Local Equilibrium Monte Carlo method. The bipolar nanopore's wall carries $\sigma$ and $-\sigma$ surface charge densities in its two half regions axially. Scaling means that the device function (rectification) depends on the system parameters (pore length, $H$, pore radius, $R$, concentration, $c$, voltage, $U$, and surface charge density, $\sigma$) via a single scaling parameter that is a smooth analytical function of the system parameters. Here, we suggest using a modified Dukhin number, $\mathrm{mDu}=|\sigma|l_{\mathrm{B}}^{*}\lambda_{\mathrm{D}}HU/(RU_{0})$, where $l_{\mathrm{B}}^{*}=8\pi l_{\mathrm{B}}$, $l_{\mathrm{B}}$ is the Bjerrum length, $\lambda_{\mathrm{D}}$ is the Debye length, and $U_{0}$ is a reference voltage. We show how scaling depends on $H$, $U$, and $\sigma$ and through what mechanisms these parameters influence the pore's behavior.