The Dukhin number as a scaling parameter for selectivity in the infinitely long nanopore limit: extension to multivalent electrolytes

TL;DR

This paper extends the Dukhin number as a scaling parameter for ion selectivity in infinitely long nanopores to multivalent electrolytes, supported by Poisson-Boltzmann theory and Monte Carlo simulations.

Contribution

It generalizes the Dukhin number from monovalent to multivalent electrolytes using first-principles derivation and compares theoretical predictions with simulation results.

Findings

Dukhin number effectively scales selectivity in the nanotube limit.

Monte Carlo simulations align with Poisson-Boltzmann theory, with deviations due to ionic correlations.

Charge inversion phenomena occur in multivalent electrolytes, affecting the scaling behavior.

Abstract

Scaling of the behavior of a nanodevice means that the device function (selectivity, in this work) is a unique function of a scaling parameter that is an appropriate combination of the device parameters. Although nanopores facilitate the transport of ions through a membrane of finite length if the pore is long compared to the pore radius, we deal with an important limiting case, the infinitely long nanopore (nanotube). While in our previous study (Sarkadi et al., J. Chem. Phys. 154 (2021) 154704.) we showed that the Dukhin number is an appropriate scaling parameter in the nanotube limit for 1:1 electrolytes, in this work we obtain the Dukhin number from first principles on the basis of the Poisson-Boltzmann (PB) theory and generalize it to electrolytes containing multivalent ions as well. We show that grand canonical Monte Carlo simulations for charged hard spheres in an implicit solvent give results that are similar to those obtained from the PB theory with deviations that are the consequences of ionic correlations (including finite size of ions) beyond the mean-field level of the PB theory. Such a deviation occurs when charge inversion is present, in 2:2 and 3:1 electrolytes, for example.