Preferable orientation of spherical fullerene inside boron nitride nanotubes

We provide a systematic analytical method for preferable orientation calculations of spherical fullerenes in single-walled boron nitride nanotubes. Based on the reaction energy calculations, both the minimum entering radii and the energetically favorable radii for encapsulating C(60), C(80) and C(180) molecules in boron nitride nanotubes have been proposed. The van der Waals energy as a function of the various orientations of the encapsulated fullerene molecule is shown by a potential contour map, from which we find that the low-energy state appears in the symmetry axis orientation of the encapsulated fullerene molecules with a different size. We thus propose a new systematic analytical method for optimal orientation predictions of spherical fullerenes in the confinement condition, which is based on the symmetry axis but not the method proposed in previous literature, such as using pentagons, double-bonds, and hexagons to analyze the preferable orientation of confined C(60). Our results show that the C(60) molecule in boron nitride nanotubes exhibits three lowest energy states corresponding to the five-, two- and three-fold axis orientations in three radii intervals, while only two preferable orientations-the five- and three-fold axis orientations have been observed for encapsulated C(80) and C(180) molecules.