Cation/anion and monovalent/divalent selectivity in negatively charged nanopores: The effect of modeling the charged surface groups

The anomalous mole fraction effect (AMFE) is widely regarded as a hallmark of calcium vs 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 polyethylene terephthalate 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 CaCl2 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 and grid spacing are matched, despite substantial differences in local Ca2+ concentration profiles. Our results demonstrate that AMFE in wide nanopores is governed by the strong adsorption of divalent cations to pore charges compared to monovalent cations, the resulting changes in ionic mobilities, and increased anion leakage with increasing calcium mole fraction. In wide pores, therefore, selectivity between monovalent and divalent cations is modulated by cation vs anion selectivity.