Electrostatic deflections of cantilevered semiconducting single-walled carbon nanotubes

How do carbon nanotubes behave in an external electric field? What will be the relation between the intensity of the electric field and the tube’s deformation? What are the geometry effects on the response of carbon nanotubes to electric fields? To answer these questions, we have developed a computational technique combining a dipole interaction model with the AIREBO potential to study electrostatic-field induced deformations of carbon nanotubes. In this work, we find that the deflection angle of cantilevered semiconducting single-walled carbon nanotubes is proportional to the square of the electric-field strength, and the tubes can be most bent when the field angle ranges from 45° to 60° for a given weak field strength. Furthermore, the deflection angle is also found to be proportional to the aspect ratio $L∕R$. Our results provide a good qualitative agreement with those of a previous experimental study by Poncharal et al., (1999).

Figure 1

(Color online) Induced dipoles in a (8,0) tube (with nonoptimized structure) in an electrostatic field. Field angle $\theta =45°$. Field strength $E=0.71\mathrm{V}∕\mathrm{nm}$. Tube length $L=1.988\mathrm{nm}$. The spheres stand for atoms. The arrow with a dashed line on the left presents the electric-field vector in the $y\text{−}z$ plane. The arrows with solid lines on the tube stand for the induced dipoles.

Figure 2

(Color online) Induced deflections of a (8,0) cantilevered tube in electrostatic fields with different field intensities. The direction of the applied electric fields is parallel to the $y\text{−}z$ plane with $\theta =45°$. The original length of the tube is about $6.54\mathrm{nm}$. The arrow with a dashed line represents the electric-field vector. (a) shows a tube relaxed in vacuum without any electric field. (b)–(d) show the deflected shape of the tubes in various applied external electric fields $(E=1.0–3.0\mathrm{V}∕\mathrm{nm})$.

Figure 3

(Color online) Vectors of induced forces in a (8,0) tube bent by an electrostatic field. $\theta =45°$. $E=4.0\mathrm{V}∕\mathrm{nm}$. $L=6.54\mathrm{nm}$. The spheres represent the carbon atoms. The arrow with a dashed line represents the external electric-field vector. The arrows on the atoms stand for the induced forces, which are calculated as the negative gradients of the electrostatic energy.

Figure 4

(Color online) Sine of deformation angles, $\sin \left(\phi \right)$, versus the square of the electric-field strength $E$ for a (8,0) tube. The tube length is about $6.54\mathrm{nm}$. $\theta =45°$. The round points stand for the simulation data and the dashed line represents the fitting line.

Figure 5

(Color online) Change of potential energy $\Delta U^p$ of this (8,0) tube versus the square of $\sin \left(\phi \right)$. The tube length is about $6.54\mathrm{nm}$. $\theta =45°$. The round points stand for the simulation data and the dashed line represents the fitting line.

Figure 6

$\sin \left(\phi \right)$ versus electric-field angles $\theta$ for a (8,0) tube. The tube length is about $6.54\mathrm{nm}$. $E=3.0\mathrm{V}∕\mathrm{nm}$. The round points stand for the simulation data.

Figure 7

(Color online) $\sin \left(\phi \right)$ versus aspect ratio $(L∕R)$. $\theta =45°$. $E=3.0\mathrm{V}∕\mathrm{nm}$. The round points stand for the simulation data and the dashed line represents the fitting line.