Proton Transport through Water-Filled Carbon Nanotubes

Proton transfer along 1D chains of water molecules inside carbon nanotubes is studied by simulations. Ab initio molecular dynamics and an empirical valence bond model yield similar structures and time scales. The proton mobility along 1D water chains exceeds that in bulk water by a factor of 40, but is reduced if orientational defects are present. Excess protons interact with hydrogen-bonding defects through long-range electrostatics, resulting in coupled motion of protons and defects.

Figure 1

Typical defect configurations as found in our MD-simulations: (a) Eigen cation, (b) $D$ defect, (c) $L$ defect.

Figure 2

Time correlation function $C(t)$ obtained from CPMD (solid line) and EVB simulation (dashed line). The inset contains the same correlation functions for short times. D instead of H atoms were used in both simulations.

Figure 3

Top: Effective interaction $F(z/L)$ between the center of charge and the $D$ defect in a periodic water chain for different numbers $N$ of water molecules (circles: $N=12$, squares: $N=24$, diamonds: $N=36$, triangles: $N=48$). Bottom: Effective interaction $F(z/L)$ between the center of charge and the tube end points of an open water chain for different numbers $N$ of water molecules (circles: $N=12$, squares: $N=24$). In both panels, the solid lines are predictions of the dipole models shown as insets.

Figure 4

Mean square displacement $⟨z^2(t)⟩$ of the excess charge along the tube axis (top) and half its time derivative (bottom) for different numbers of water molecules in a periodic tube. Dotted lines are results from Brownian dynamics simulations.

Figure 5

Top: Mean square displacement in $z$ direction for the excess proton, a $D$ defect and an $L$ defect in open carbon nanotubes containing $120$ water molecules. Bottom: Time derivative of the mean square displacement divided by two.