Abstract

Nanopores are nanoscale channels embedded in a membrane that enable the controlled transport of ions between the bulk phases located on the two sides of the membrane. Depending on the charge pattern created on the pore wall, the nanopore produces different output functions in response to various input parameters, from which a response function can be constructed. For uniformly charged nanopores, one such response function is selectivity. If the electrolyte concentrations differ on the two sides of the membrane, then, in addition to the electrical potential difference (voltage), the concentration gradient also acts as a driving force for ion transport.

The aim of this research is to investigate the selectivity of nanopores in this asymmetric case. If a parameter can be found that, on the one hand, can be uniquely expressed from the input system parameters through an analytical equation, and, on the other hand, for which selectivity is a unique (though not necessarily analytical) function, then the selectivity of the nanopore can be predicted easily. This phenomenon is referred to as scaling. In the case of nanopores, the input parameters include the pore radius, pore length, applied voltage, surface charge density, concentration, and ionic charges. In a previous publication of our research group [1], a scaling parameter was developed on the basis of linearized Poisson–Boltzmann theory for infinite pores. This parameter is related to the Dukhin number commonly used in the literature, and it works well as a scaling parameter for finite pores in the symmetric case, when the concentration is the same on both sides of the membrane [2,3].

The goal of this work is to extend this scaling theory to the case where the electrolyte concentrations in the bulk phases on the two sides of the membrane are different. Our derivation showed that the scaling parameter of the asymmetric system can be expressed as the harmonic mean of the scaling parameters corresponding to the left and right sides (where the left- and right-side concentrations are used separately). Using the Poisson–Nernst–Planck theory, we performed calculations for different combinations of the input system parameters and demonstrated that the scaling works as well as in the symmetric case; that is, the method has essentially the same limitations. Local Equilibrium Monte Carlo simulations have also been performed to assess the effect of ionic correlations for multivalent electrolytes.

References

[1] Zs. Sarkadi, D. Fertig, M. Valiskó, and D. Boda. J. Mol. Liq., 357:119072 (2022).

[2] Zs. Sarkadi, Z. Ható, M. Valiskó, D. Boda. J. Mol. Liq. 387:122571, 2023.

[3] Zs. Sarkadi, Z. Ható, M. Valiskó, D. Boda. submitted 2026