Electrostatics of straight and bent nanotubes

TL;DR

This paper analytically investigates the electrostatic response of both straight and bent single-walled carbon nanotubes to external electric fields, revealing charge distribution patterns and threshold behaviors based on nanotube properties.

Contribution

It provides a classical electrostatic model for nanotube charge distribution, including effects of bending and semiconducting gaps, which was not previously detailed.

Findings

Charge density is approximately linear along metallic nanotubes.

Charge separation occurs in semiconducting nanotubes when field exceeds a threshold.

Bending introduces additional neutral regions depending on field direction.

Abstract

Response of a single-walled carbon nanotube to external electric field, F, is calculated analytically within the classical electrostatics. Field-induced charge density distribution is approximately linear along the axis of metallic nanotube and depends rather weakly, as ln(h/r), on the nanotube length, h, (here r is the nanotube radius). In a semiconducting nanotube with a gap, E_g, charge separation occurs as F exceeds the threshold value F_{th}=E_g/eh. For F>F_{th}, positively and negatively charged regions at the ends of nanotube are separated by a neutral strip in the middle. For bent nanotubes the number of neutral strips can be one or two depending on the direction of F.