Flow of polar and nonpolar liquids through nanotubes: A computational study

We perform ab initio density functional calculations to study the flow of water, methanol, and dimethyl ether through nanotubes of carbon and boron nitride with different diameters and chiralities. The liquids we choose are important solvents, with water and methanol being polar and dimethyl ether being nonpolar. In terms of activation barriers for liquid transport, we find the molecular-level drag to decrease with decreasing nanotube diameter but to be rather independent of the chiral index. We also find molecules with higher polarity to generally experience higher drag during flow. Counterintuitively, we find the drag for water in boron nitride nanotubes not to exceed that in carbon nanotubes due to frustration in competing long-range Coulomb interactions.

Figure 1

A (12,6) chiral nanotube of (a) carbon and (b) boron nitride (BN), containing one water molecule.

Figure 2

Interaction energy $E\left(z\right)$ between an isolated ${\mathrm{H}}_2\mathrm{O}$ molecule and a surrounding (a) armchair (8,8) and (b) zigzag (14,0) CNT obtained using the siesta code. The range of $E\left(z\right)$ values is the same in (a) and (b). We distinguish the ${\mathrm{H}}_2\mathrm{O}$-H/CNT configuration, where the H end of ${\mathrm{H}}_2\mathrm{O}$ faces the wall, from ${\mathrm{H}}_2\mathrm{O}$-O/CNT, where the O end faces the wall. Negative values of $E$ indicate energetic preference for ${\mathrm{H}}_2\mathrm{O}$ entering the nanotube. The lower panels give a schematic view of the respective nanotubes. The size of the unit cell considered is outlined by the blue box. (c) Comparison between energy changes $\mathrm{\Delta }E\left(z\right)=E\left(z\right)-E_{\min }$ along the trajectory in (a) obtained using the DFT-PBE and the vdW-optB86b energy functionals in the vasp code. Nanotube diameters $d$ are indicated in the individual panels. The $z$ coordinate represents the water position along the $z$ axis of the CNT.

Figure 3

Interaction energy $E\left(z\right)$ between an isolated ${\mathrm{H}}_2\mathrm{O}$ molecule and a surrounding (a) (8,8), (b) (14,0), (c) (6,6), (d) (10,0), and (e) (5,5) CNT. The $z$ coordinate represents the water position along the $z$ axis of the CNT. Only the stable water orientation with the hydrogens facing the wall is considered. The range of $E\left(z\right)$ values is 40 meV in all panels. Schematic geometry is shown for (f) the (8,8) and (g) the (14,0) CNT, with the size of the unit cell considered being outlined by the blue box. Nanotube diameters $d$ are indicated in the individual panels.

Figure 4

Interaction energy $E\left(z\right)$ between an isolated ${\mathrm{H}}_2\mathrm{O}$ molecule and a surrounding (a) (10,6), (b) (11,5), and (c) (12,3) CNT. The range of $E\left(z\right)$ values is 40 meV in all panels. Nanotube diameters $d$ are indicated in the individual panels. The $z$ coordinate represents the water position along the $z$ axis of the CNT. Only the stable water orientation with the hydrogens facing the wall is considered. Schematic geometries including the unit cells considered are shown below the respective $E\left(z\right)$ plots.

Figure 5

Interaction energy $E\left(z\right)$ between an isolated water molecule contained in an (a) (8,8) and (b) (14,0) BNNT, obtained using the siesta code. Nanotube diameters $d$ are indicated in the individual panels. The range of $E\left(z\right)$ values is the same in (a) and (b). (c) Comparison between energy changes $\mathrm{\Delta }E\left(z\right)=E\left(z\right)-E_{\min }$ along the trajectory in (a) obtained using the DFT-PBE and the vdW-optB86b energy functionals in the vasp code. The $z$ coordinate represents the position of the molecule along the $z$ axis of the BNNT.

Figure 6

Interaction energy $E\left(z\right)$ between an isolated (a) water (${\mathrm{H}}_2\mathrm{O}$), (b) methanol (${\mathrm{CH}}_3$-OH, MeOH), and (c) dimethyl ether (${\mathrm{CH}}_3$-O-${\mathrm{CH}}_3$, MeOMe) molecule and a surrounding (8,8) CNT. The range of $E\left(z\right)$ values is 40 meV, and nanotube diameters $d$ are indicated in all panels. The $z$ coordinate represents the position of the molecule along the $z$ axis of the CNT.