Interplay of ion availability and mobility in the loss of cation selectivity for CaCl\textsubscript{2} in negatively charged nanopores: molecular dynamics using scaled-charge models

TL;DR

This work probes how confinement and interfacial chemistry reshape ion transport in negatively charged silica nanopores for NaCl and CaCl$_2$ solutions using atomistic MD with scaled-charge ECCR2 ions and TIP4P/2005 water. By decomposing local transport into $\mathbf{j}_{i}(\mathbf{r})=\mathbf{v}_{i}(\mathbf{r})c_{i}(\mathbf{r})$, the authors connect static interfacial adsorption to dynamic perm-selectivity, revealing that Ca$^{2+}$ adsorption and charge inversion erode cation selectivity and promote interior Cl$^{-}$ conduction, while Na$^{+}$ remains the mobile counterion near the wall. The results depend sensitively on force-field choices, including ion model and water model, but the qualitative mechanism—surface immobilization of Ca$^{2+}$ and bulk-like interior conduction after charge inversion—persists across tested models. The findings highlight the need for careful force-field validation in confined electrokinetics and suggest that reduced or implicit models can still capture the essential physics of nanopore perm-selectivity.

Abstract

Ion transport through charged nanopores is commonly interpreted in terms of electrical double layer structure, leading to the expectation of cation-selective conduction in negatively charged pores. This picture can break down for multivalent electrolytes, where strong ion-urface correlations and charge inversion modify transport behavior. Here, we study NaCl and CaCl$_2$ conduction through negatively charged silica nanopores using atomistic molecular dynamics simulations with scaled-charge ion models. By separating concentration and velocity contributions to the radial particle current density, we connect static adsorption to dynamic perm-selectivity. While NaCl exhibits conventional cation selectivity, CaCl$_2$ shows nearly bulk-like or even anion-favored transport due to Ca$^{2+}$ immobilization near the surface and dominant Cl$^-$ conduction in the pore interior following charge inversion. Although this qualitative mechanism is robust, its detailed manifestation depends sensitively on the balance of ion-surface and ion-water interactions encoded in the force field.

Figures (9)

• Figure 1: From left to right: axial ($z$) components of particle current density (in 1/ps$\;$nm$^{2}$), velocity (in nm/ps), and concentration (in mol/dm$^{3}$). Red and blue curves refer to full-charge and scaled-charge silanol oxygen (O$_{\mathrm{S}}$) models, respectively. Full and open symbols refer to cations and Cl$^{-}$ ions, respectively. Top row (A) refers to simulations for a scaled-charge model for NaCl with TIP4P/2005 water model kohagen_jpcb_2015, while the bottom row (B) refers to simulations for the ECCR2 model for CaCl$_{2}$ with TIP4P/2005 water model. martinek_jcp_2018
• Figure 2: Radial distribution functions (RDF) for pairs of O$_{\mathrm{S}}$ and Ca$^{2+}$ (left panel) as well as O$_{\mathrm{S}}$ and O$_{\mathrm{w}}$ (right panel), where O$_{\mathrm{S}}$ stands for the oxygen of the deprotonated silanol group and O$_{\mathrm{w}}$ stands for the oxygen atom of the water molecule modeled by the TIP4P/2005 FF. The inset of the left panel zooms in on the depletion zone between the 1st and 2nd peaks. The figure shows results for the ECCR2 model with TIP4P/2005 water. Red and blue curves refer to full-charge and scaled-charge silanol oxygen (O$_{\mathrm{S}}$) models, respectively.
• Figure 3: From top to bottom: axial ($z$) components of particle current density (in 1/ps$\;$nm$^{2}$), velocity (in nm/ps), and concentration (in mol/dm$^{3}$). Black, blue, red, and green curves refer to pore radii $R^{\mathrm{P}}\approx 1$, $1.3$, $2$, and $3$ nm, respectively. Full and open symbols refer to Ca$^{2+}$ and Cl$^{-}$ ions, respectively. The figure refers to simulations for the scaled-charge silanol oxygen (O$_{\mathrm{S}}$) model and the ECCR2 model of ions with TIP4P/2005 water.
• Figure 4: From left to right: axial ($z$) components of particle current density (in 1/ps$\;$nm$^{2}$), velocity (in nm/ps), and concentration (in mol/dm$^{3}$). Red and blue curves refer to the FULL and ECCR2 models of Ca$^{2+}$ and Cl$^{-}$, respectively. Full and open symbols refer to Ca$^{2+}$ and Cl$^{-}$ ions, respectively. The figure refers to simulations for the scaled-charge silanol oxygen (O$_{\mathrm{S}}$) model and the TIP4P/2005 model of water.
• Figure 5: From left to right: axial ($z$) components of particle current density (in 1/ps$\;$nm$^{2}$), velocity (in nm/ps), and concentration (in mol/dm$^{3}$). Black, blue, and red curves refer to the ECC, ECCR2, and ECCR models of Ca$^{2+}$ and Cl$^{-}$, respectively. Full and open symbols refer to Ca$^{2+}$ and Cl$^{-}$ ions, respectively. The figure refers to simulations for the scaled-charge silanol oxygen (O$_{\mathrm{S}}$) model and the TIP4P/2005 model of water.