The interplay of cation/anion and monovalent/divalent selectivity in negatively charged nanopores: local charge inversion and anion leakage

Abstract: The anomalous mole fraction effect (AMFE) is widely regarded as a hallmark of calcium versus monovalent ion selectivity in negatively charged pores. While AMFE is well understood in highly cation-selective narrow ion channels, its microscopic origin in wide synthetic nanopores, where anions may also contribute to transport, remains less clear. Here, we use a reduced Nernst-Planck + Local Equilibrium Monte Carlo framework to study ionic transport in a negatively charged PET nanopore, with particular emphasis on how the modeling of surface carboxyl (COO$^{-}$) groups influences charge inversion, ionic currents, and AMFE. We systematically compare fixed point-charge models and explicit-particle representations of surface oxygens and identify two controlling parameters: the distance of closest approach (DCA) between ionic charges and pore charges and grid spacing that modulates localization (while keeping average surface charge constant). By fitting pore diffusion coefficients to three experimental conductance points, we reproduce the entire experimental AMFE curve as well as anion leakage in CaCl$_2$ seen in experiments and molecular dynamics simulations. Remarkably, vastly different microscopic models of the surface groups yield indistinguishable device-level conductance curves when the DCA is matched, despite substantial differences in local Ca$^{2+}$ concentration profiles. Our results demonstrate that AMFE in wide nanopores is governed by a delicate interplay between charge inversion, anion leakage, and ionic mobility, underlying that in wide pores monovalent vs.\ divalent cation selectivity is modulated by cations vs.\ anion selecivity.