The Effect of Ionic Correlations on Scaling for Multivalent Electrolytes in Finite Nanopores: Mean-Field Theory and Beyond

Abstract

By “scaling” we mean that the device function is uniquely determined by a single scaling parameter, which is an analytical combination of the system’s input parameters. In a uniformly charged nanopore, the device function is cation selectivity, while the input parameters are pore radius (R), pore length (H), surface charge density (σ), salt concentration (c), and ionic valences (zi). In the infinitely long pore limit, we previously derived the scaling parameter for multivalent electrolytes from linearized Poisson–Boltzmann (PB) theory (Sarkadi et al., J. Mol. Liq. 357, 119072, 2022) and later showed (Sarkadi et al., J. Mol. Liq. 387, 122571, 2023) that it remains valid for 1:1 electrolytes in finite nanopores. Here, we extend this analysis to finite nanopores with multivalent electrolytes and show that a generalized Dukhin number,Du1=−(z++|z−|)σ4πlBλD2/eR (lB is the Bjerrum length, and λD is the Debye length) is an appropriate scaling parameter. Electrical double layers formed at the membrane entrances overlap in a finite pore and modify the ion distributions and, consequently, the selectivity and scaling behavior. We analyze this effect using the Nernst–Planck (NP) transport equation coupled either to the PB theory (PNP) or to the Local Equilibrium Monte Carlo method (NP+LEMC). While scaling within the mean-field PNP framework is comparable to that for 1:1 electrolytes, significant deviations arise in NP+LEMC due to strong ionic correlations. In particular, multivalent cations can overcharge the negatively charged pore wall, leading to charge inversion; the resulting anion layer causes anion leakage, reducing selectivity and altering the scaling behavior.