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

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). In this case, device parameters are the pore radius, the electrolyte concentration, the surface charge density on the nanopore's wall, and ionic valences. 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. (c) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

The scaling behavior of a nanodevice is determined by the appropriate combination of device parameters. In this study, we obtained the Dukhin number from first principles and generalized it to electrolytes with multivalent ions in the nanotube limit. Our results show that grand canonical Monte Carlo simulations and Poisson-Boltzmann theory produce similar results, with deviations caused by correlations between ions beyond the mean-field level of the theory. This deviation occurs in electrolytes with charge inversion, such as 2:2 and 3:1 electrolytes.