Kinetic mechanism for water in vibrating carbon nanotubes

Recent simulations revealed that, when an atom in a single-wall carbon nanotube was artificially driven to oscillate radially with the two ends of the nanotube fixed, water transport became highly unusual at some oscillation frequencies. Here we systematically investigate the underlying mechanism for such effects through a series of simulations and detailed analysis. We find that the pattern and magnitude for the vibration of the nanotube are sensitive to the driving frequency but largely independent of the presence of water. At certain resonance frequencies, some carbon atoms of the nanotube oscillate at much larger amplitudes than does the driving atom. Furthermore, a strongly vibrating nanotube tends to have a much-reduced water occupancy, which is mainly due to the heating effect rather than the induced deformation. Indeed, the water molecules inside the nanotube can be significantly heated and gain large kinetic energies due to the collisions with the vibrating carbon atoms. Consequently, the kinetic rate of water exchange through the nanotube could be enhanced even when the water occupancy is low. Our findings here may help understanding the physical mechanisms of similar nanodevices.

Figure 1

(a) Simulation system, consisting of two sheets of fixed carbon atoms serving as a membrane, an uncapped (6,6) single-wall CNT, and water molecules (depicted by spheres with oxygen in red and hydrogen in white). The indicated carbon atom of the CNT was driven to oscillate harmonically along the $y$ axis. The vibrations of some other carbon atoms (blue spheres) are analyzed and described in the text. The carbon atoms (yellow spheres) at the two ends of the CNT were fixed, and the carbon atoms shown in gray spheres were strongly restrained in all simulations. (b) Cross section of the CNT.

Figure 2

Vibration of the CNT. (a) Average vibration amplitude over the nine carbon atoms [indicated in panel (c)] in the CNT, in each simulation with a different frequency $f$. (b) Amplitudes of the individual carbon atoms under five different vibration frequencies. (c) Snapshots of the CNT at $f=4000\mathrm{GHz}$ and $f=6250\mathrm{GHz}$ with the driving atom at the two extreme positions.

Figure 3

Average input power for simulations at different vibration frequencies.

Figure 4

(a) Average number of water molecules inside the CNT in each simulation with a different vibration frequency. (b) Average translational kinetic energy of the water molecules. (c) Average number of permeation events in one direction per unit time. (d) Average contribution of each velocity component ($v_x,v_y,v_z$) to the kinetic energy.

Figure 5

Motion of a labeled water molecule (represented by its oxygen atom) inside the CNT in the simulations at vibration frequencies of 4000 and 12 500 GHz. (a), (b) Snapshots of the CNT and nearby water molecules, with the labeled water molecule shown in blue. (c), (d) Position of the labeled water molecule when it crossed the CNT. (e), (f) Instantaneous velocity of the water molecule during the same period. (g), (h) The $x$ and $y$ coordinates of the water molecule and the $y$ coordinate of a nearby carbon atom during a period of 2 ps starting at the time indicated by the dashed arrows in panels (e) and (f).