Scaling Behavior of Bipolar Nanopore Rectification with Multivalent Ions

TL;DR

This study uncovers a scaling law for bipolar nanopore rectification influenced by pore size, electrolyte concentration, and ion valences, using PNP and LEMC models to account for ion correlations especially with multivalent ions.

Contribution

It introduces a universal scaling parameter 1 that captures rectification behavior across different electrolytes and pore conditions, incorporating ion correlations via LEMC.

Findings

Rectification depends on the parameter 1, combining pore radius, electrolyte screening length, and ion valences.

Ion correlations are significant for multivalent ions and are captured by LEMC but not by mean-field models.

The scaling law applies to various electrolyte valence combinations, demonstrating its broad applicability.

Abstract

We present a scaling behavior of a rectifying bipolar nanopore as a function of the parameter $\xi=R_{\mathrm{P}}/(\lambda z_{\mathrm{if}})$, where $R_{\mathrm{P}}$ is the radius of the pore, $\lambda$ is the characteristic screening length of the electrolyte filling the pore, and $z_{\mathrm{if}}=\sqrt{z_{+}|z_{-}|}$ is a scaling factor that makes scaling work for electrolytes containing multivalent ions ($z_{+}$ and $z_{-}$ are cation and the anion valences). By scaling we mean that the rectification of the pore (defined as the ratio of currents in the forward and reversed biased states) depends on pore radius, concentration, $c$, and ion valences via the parameter $\xi$ implicitly. This feature is based on the fact that rectification depends on the voltage-sensitive appearance of depletion zones that, in turn, depend on the relation of $R_{\mathrm{P}}$ to the rescaled screening length $\lambda z_{\mathrm{if}}$. In this modeling study, we use the Poisson-Nernst-Planck (PNP) theory and a particle simulation method, the Local Equilibrium Monte Carlo (LEMC). The latter can compute ion correlations that are ignored in the mean-field treatment of PNP and that are very important for multivalent ions (we show results for 1:1, 2:1, 3:1, and 2:2 electrolytes). In addition to the $z_{\mathrm{if}}$ factor, we show that one must choose a screening length appropriate to the system, in our case the Debye length for $\lambda$ for PNP and the screening length given by the Mean Spherical Approximation for LEMC.