Orientation of a benzene molecule inside a carbon nanotube

Benzene molecules confined in carbon nanotubes of varying radii are employed as semiconductors in electronic nanodevices, and their orientation determines the electrical properties of the system. In this paper, we investigate the interaction energy of all the possible configurations of a benzene molecule inside various carbon nanotubes and then we determine the equilibrium configuration. We adopt the continuous approach together with the semi-empirical Lennard-Jones potential function to model van der Waals interaction between a benzene molecule and a carbon nanotube. This approach results in an analytical expression, which accurately approximates the interaction energy and can be readily used to generate numerical data. We find that horizontal, tilted and perpendicular configurations on the axis of the carbon nanotube are all possible equilibrium configurations of the benzene molecule when the radius of the carbon nanotube is less than 5.580 Å. However, when the radius of the carbon nanotube is larger than 5.580 Å an offset horizontal orientation is the only possible equilibrium configuration of the benzene molecule. In the limiting case, the orientation of a benzene molecule on a graphene sheet can be derived simply by letting the radius of the carbon nanotube tend to infinity.