Pumping of Confined Water in Carbon Nanotubes by Rotation-Translation Coupling

Bidirectional single file water transport in a carbon nanotube is known to occur in “bursts” in short nanotubes. Here we show that in long carbon nanotubes, when the orientation of the water molecules is maintained along one direction, a net water transport along that direction can be attained due to coupling between rotational and translational motions. The rotations of the water molecules are correlated more with the translation of the neighboring water molecule with the acceptor oxygen than the neighbor with the donor hydrogen. This mechanism can be used to pump water through nanotubes.

Figure 1

The cumulative flux of water molecules crossing the tube as a function of time for (a) $(10,0)$ and (b) $(16,0)$ CNTs for various values of $E_{\mathrm{ext}}$.

Figure 2

(a) Trajectory of water molecules in a $(10,0)$ ($E=0\mathrm{V}/\mathrm{nm}$) CNT. Each color represents a water molecule’s trajectory for 1.9 ps. The ball-stick models (various colors) denote the position of water at $t=0$. (b) Schematic of a single file water with body centered principal axes frame $xyz$ and the fixed box reference frame $XYZ$.

Figure 3

Velocity autocorrelations [$(\mathrm{nm}/\mathrm{ps}{)}^2$], angular velocity autocorrelations [$(\mathrm{rad}/\mathrm{ps}{)}^2$], and nonvanishing velocity-angular velocity cross correlations ($\mathrm{nm}/\mathrm{ps}·\mathrm{rad}/\mathrm{ps}$) for water molecules inside a $(10,0)$ tube for $E=0\mathrm{V}/\mathrm{nm}$.

Figure 4

Cross correlations of angular velocity ${\omega }_z$ with $v_x$ for $(16,0)$ tubes for $E=1\mathrm{V}/\mathrm{nm}$, $E=0\mathrm{V}/\mathrm{nm}$, and in the bath.

Figure 5

(a) Cross correlation of the axial velocity of the neighboring $(n\pm i)$th water molecule with axial velocity of the $n$th water molecule for the $(10,0)$ tube. (b) Cross correlation of the axial velocity of the neighboring $(n\pm i)$th water molecule with the out-of-plane angular velocity ${\omega }_z$ of the $n$th water molecule. Coupling with ($n+1$) and ($n+2$) are greater than that with ($n-1$) and ($n-2$) showing preferred transfer of rotational energy to translational energy along the $+ve$ $Z$ direction.