**3. Results and Analyses**

A few key features were observed in the water transport phenomena through deformed nanotubes, including a change of single-file water chain transformation to two single-file water chains forming next to each other in the XY-distortion of 2 nanotubes, resembling a near-Fickian di ffusion; formation of discontinuous single-file chain water transport in Z-distortion of 1.2 nanotubes; and a smattering water transport through XY-distortion of 4 and 6 nanotubes. Figure 3 shows the water transport through a perfect BNNT nanotube and the XY-distortion 2 BNNT nanotube.

**Figure 3.** Visualization of water chain formed in-between two reservoirs: (**a**) perfect BNNT (**b**) BNNT with XY-distortion value 2.

#### *3.1. Free Energy of Occupancy Fluctuations and Water Occupancy*

Figure 4 shows the free energy of occupancy fluctuations as a function of the number of water molecules inside the nanotube for the CNT and BNNT with XY-distortion. The free energy of the occupancy fluctuations is calculated as follows:

$$\beta F(\mathbf{N}) = -\ln p(\mathbf{N})$$

where *p*(N) is the probability of finding exactly 'N' water molecules inside the nanotube, *F*(N) is the free energy and β = (*k*BT)−1, *k*B is the Boltzmann constant, and T is the temperature [4,23].

**Figure 4.** Free energy of occupancy fluctuation as a function of number of water molecules inside and different types of deformed nanotubes compared with perfect nanotubes: (**a**) carbon nanotube (CNT) with screw distortions; (**b**) boron nitride nanotube (BNNT) with screw distortions; (**c**) carbon nanotube (CNT) with XY-distortion; (**d**) boron nitride nanotube (BNNT) with XY-distortion; (**e**) carbon nanotube (CNT) with Z-distortion nanotube; and (**f**) boron nitride nanotube (BNNT) with Z-distortion.

The plot shows that the number of water molecules inside the perfect CNT ranges from 26 to 47. The most probable number of molecules is 42. The number of molecules inside the perfect BNNT ranges from 40 to 48. The most probable number is 44. It can be seen that the XY-distortion of 2 nanotubes accommodates the maximum number of water molecules when compared to others. The XY-distorted nanotubes of higher value show a significantly lower number of molecules in both the carbon and boron nitride nanotubes. The reason for the XY-distortion nanotubes to accommodate the maximum number of water molecules is that, when a nanotube is distorted in the XY-direction with the distortion value of 2, it has su fficient space to accommodate two water molecules side by side, as shown in Figure 3. Further increase in distortion value results in a higher energy barrier, higher friction, and decreased pore volume. This reduces water transport significantly.

Figure 5 shows the comparison of water occupancy of the CNTs and BNNTswith different deformations. For the BNNT with the XY-distortion of 4, even though it has a larger pore volume compared to the CNT of the same distortion, very few molecules enter the pore. This shows that the entrance effects play a major role in water flow through nanotubes. On the visualization of the simulation, using the VMD package, we found that, for the XY-distortion of 4 and 6 (CNT and BNNT), molecules entered the nanotube, but were unable to travel further continuously. This is due to the large friction and energy barrier inside these nanotubes. For these cases, only a handful of molecules were observed to travel through the pore from one end to the other. The screw-distorted nanotubes showed a negligible effect on the water transport phenomena. They behaved almost similarly to the perfect nanotubes. This can be observed from the water occupancy and free energy of occupancy fluctuation plots.

**Figure 5.** Water occupancy inside perfect and XY-distorted nanotubes versus time in picosecond: (**a**) carbon nanotube (CNT) and (**b**) boron nitride nanotube (BNNT).
