Abstract
The anomalous mole fraction effect (AMFE) is widely regarded as a hallmark of calcium versus monovalent ion selectivity in negatively charged pores [1]. In this experiment, a mixture of CaCl2 and monovalent electrolytes (NaCl or KCl) are used and the total conductance versus mole fraction function is computed. We talk about AMFE if this function has a minimum, but in general, this function is nonlinear due to strong correlations of ions with each other and with the charged pore wall. While AMFE is well understood in highly cation-selective narrow ion channels [2], its microscopic origin in wide synthetic nanopores, where anions may also contribute to transport, remains less clear [3].
Here, we use a reduced Nernst-Planck + Local Equilibrium Monte Carlo framework [4,5] to study ionic transport in negatively charged nanopores. Water is implicit in this model. The adjustable parameter is the diffusion coefficient of the ions in the pore. By fitting pore diffusion coefficients to either experimental conductance points [3] or conductance values obtained from molecular dynamics (MD) simulations [6], we reproduce the conductance versus mole fraction curve. We study how the different interactions of monovalent and divalent cations with the pore charges govern the selectivity behavior and how the underlying phenomena explain the behavior observed in experiments and MD simulations.
Our results demonstrate that preferential selectivity between monovalent and divalent cations is modulated by cation versus anion selectivity in wide nanopores, where anion leakage and loss of cation selectivity are observed due to the strong adsorption of divalent cations to pore charges. This effect increases with increasing calcium mole fraction. Our study is a typical example of multiscaling, where our models span the spectrum from simple representations using implicit water to all-atom models (explicit water) used in MD, and experimental reality.
References
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[4] H. Fabian, Zs. Sarkadi, M. Valisko, D. Gillespie, and D. Boda. J. Mol. Liq., 368:120715, (2022).
[5] E. Molnárné Lakics, M. Valiskó, Z. Ható, D. Gillespie, and D. Boda. J. Chem. Phys. in press, (2026).
[6] S. Shabbir, D. Boda, and Z. Ható. J. Chem. Phys. in press, ( 2026).