Electrostatic deflections of cantilevered metallic carbon nanotubes via charge-dipole model

We compute electrostatic field induced deformations of cantilevered finite-length metallic carbon nanotubes using an energy minimization method based on a charge-dipole moment interaction potential combined with an empirical many-body potential. The influence of field strength, field direction, and tube geometry on the electrostatic deflection is investigated for both single- and double-walled tubes. These results could apply to nanoelectromechanical devices based on cantilevered carbon nanotubes.

Figure 1

(Color online) Induced dipoles and charges on an open-ended metallic (5,5) SWCNT $(L=4.8\mathrm{nm})$ subjected to a horizontal electric field $E=1.0\mathrm{V}∕\mathrm{nm}$. The positive charges move to the right side and the negative ones move to the left (the color scaling is proportional to the density of charge). The green vectors stand for the dipoles. The maximal amplitudes of these charges and dipoles are about $0.34\text{unit}$ of $e$ and $0.11\text{Debye}$, respectively.

Figure 2

Electrostatic deflection of a (5,5) SWCNT, with tube length $L\approx 19.8\mathrm{nm}$, field angle $\theta =45°$, and field strength $E=\mid \mathit{E}\mid =0.775\mathrm{V}∕\mathrm{nm}$.

Figure 3

$\sin \left(\phi \right)$ vs $E$ for two SWCNTs: a metallic one (5,5), with $L\approx 13.16\mathrm{nm}$ and radius $R=0.34\mathrm{nm}$, and a semiconducting one (6,4) with the same $L$ and $R$. The fields are applied in both $\theta =\pi ∕4$ and $\theta =5\pi ∕4$ (in opposite directions).

Figure 4

$\sin \left(\phi \right)∕\sin \left(\theta \right)$ vs $E$ for a metallic tube (5,5) $(L\approx 13.16\mathrm{nm})$.

Figure 5

Axial strain $\epsilon =\Delta L∕L$ (%) versus $E^2$ for a metallic tube (5,5) $(L\approx 13.16\mathrm{nm})$, when the electric fields are applied parallel to the tube axis.

Figure 6

In an external electric field $E=0.775\mathrm{V}∕\mathrm{nm}$ and $\theta =45°$: (a) $\sin \left(\phi \right)$ vs the radii $R$ of six metallic tubes with the same length $L\approx 13.2\mathrm{nm}$; (b) $\sin \left(\phi \right)$ vs the length of six (5,5) CNTs ($L\approx 6.52$, 13.16, 19.8, 26.44, 33.08, and $39.72\mathrm{nm}$).

Figure 7

For two metallic DWCNTs: (4,4)@(9,9) with $L\approx 12.2\mathrm{nm}$, $R^{\mathit{\text{inner}}}\approx 0.27\mathrm{nm}$, and $R^{\mathit{\text{outer}}}\approx 0.61\mathrm{nm}$, and (6,0)@(15,0) with $L\approx 12.2\mathrm{nm}$, $R^{\mathit{\text{inner}}}\approx 0.23\mathrm{nm}$, and $R^{\mathit{\text{outer}}}\approx 0.59\mathrm{nm}$. (a) $\sin \left(\phi \right)$ vs $E$; $\theta =45°$. (b) $\sin \left(\phi \right)$ vs $\cos \left(\theta \right)$; $E=2\mathrm{V}∕\mathrm{nm}$.