Anomalous Ion Confinement Penalties and Giant Ion-Screening Effects in One-Dimensional Nanopores

Abstract

Nanoconfinement reduces the favorable hydration free energies of single ions, which is correlated with ion rejection and modified chemical reactivity in water-filled nanopores. Many factors contribute to the magnitude of the observed confinement effect. Here we use simple classical force fields and non-polarizable carbon nanotubes filled with water as minimal, "hydrogen atom"-like models to evaluate the single-ion intrinsic confinement hydration free energy penalty (Delta Delta G(hyd)). In tubes of radius R=7.5 Angstrom, we predict Delta Delta G(hyd)'s that are up to 7.8 kcal/mol, are much larger for Cl- than the smaller Na+ ion, and contradict the canonical Born Equation for ion solvation. Adding a 1.0~M background electrolyte reduces Delta Delta G(hyd) for the Na+/Cl- pair by an amount exceeding the Debye-Huckel estimate in unconfined media by almost an order of magnitude. We identify concentration-dependent ion-screening of confinement effects as a major, unheralded consequence of electrolytes in cylindrical nanopores.

Figures (5)

• Figure 0: TOC Graphic.
• Figure 1: Different contributions to $\Delta \Delta G_{hyd}$ in CNT's. (a) Intrinsic confinement effects, the focus of this work. (b) Reservoir interface potential (red); screening from reservoir (blue); and finite size effects ($L_1$, $L_2$, $L_z$, green) which are eliminated by the choice of our models. The numbers correspond to the text. (c) Reference system with infinite tube curvature. (d) Ion screening effect. Blue, white, gray, red, green, cyan, and pink represent O, H, C, Na, Cl, K, and Br atoms, respectively. Water is omitted from panel (d).
• Figure 2: (a)-(b) $\Delta \Delta G_{\rm hyd}$ for Na$^+$ (red) and Cl$^-$ (green) at different $R$, respectively, highlighting the anomalously large $\Delta \Delta G_{\rm hyd}$ for Cl$^-$ at $R$=7.5 Å. Dashed line: electrostatic contribution only; solid: total; dotted: total minus LJ-interaction with CNT. (c)-(d) Extrapolation of $\Delta G_{\rm hyd}$ to infinite pore length for Na$^+$ and Cl$^-$, respectively. $R$=7.5 Å and $R$=12.5 Å are in blue and orange.
• Figure 3: (a)-(b) Radial distribution of Na$^+$/Cl$^-$ for $R$=7.5 Å and $R$=12.5 Å, respectively. Each cell contains either a Na$^+$ (red) or a Cl$^-$ (green). $L_z$=118 Å. Water density profiles (blue) are scaled by 1/200 and 1/500 in the two panels, respectively. (c)-(d) Madelung potential at $R$=7.5 Å and $R$=12.5 Å, respectively, delimited by molecular cut-offs ($r$). Red/blue denote values for confined Na$^+$/Cl$^-$. Dashed lines are $\phi_M(r)$ with $r$$\rightarrow$$\infty$. The $g(r)$'s of bulk water with the ions are also depicted as guides.
• Figure 4: (a)-(b): $\Delta G_{\rm hyd}$ for isolated Na$^+$ and Cl$^-$, respectively, in the $R$=7.5 Å CNT. Blue/crosses: in water. Solid red or green with circles: in 1.0 M KBr with equal number of cations and anions. Dotted red or green with stars: in 1.0 M KBr with one less cation or anion. $L_z$=118 Å. These panels show that single-ion calculations are ambiguous at finite ion concentrations. (c) $\Delta \Delta G_{\rm pair}(z)$ for Na$^+$+Cl$^-$ ion pair in contact ($z$=$z_c$) or half a box length away ($z$=$z_f$=$L_z$/2) in 1.0 M KBr (orange), and sum of $\Delta G_{\rm hyd}$ for isolated Na$^+$ plus Cl$^-$ in water (blue, from Fig. \ref{['fig2']}c-d). Solid/cross, dot-dashed/plus, and dashed/circle are for $L_z$=472 Å, $L_z$=236 Å, and $L_z$=118 Å. The diamond is for $L_z$=472 Å, $z$=28 Å. Inset: ion segregation in one MD snapshot. Red, green, brown, and cyan are Na$^+$, Cl$^-$, K$^+$, and Br$^-$.