An exact polyhedral model for boron nanotubes

Abstract

An exact idealized polyhedral model is formulated to describe the geometry of single-walled boron nanotubes. The boron nanotubes considered here are assumed to be formed by sp2 hybridization and adopt a flat equilateral triangle pattern. Beginning from the two fundamental postulates that all bond lengths are equal and all atoms are equidistant from a common cylindrical axis, we derive exact formulae for the geometric parameters of the nanotube radius, bond angle and unit cell length, and we present asymptotic expansions for these quantities to the first two orders of magnitude. Good agreement is demonstrated for the predictions of the polyhedral model, compared with the results obtained from first-principles simulations. The polyhedral model allows the possible identification of an inner radius, so that the notion of nanotube wall thickness can be introduced. Finally, we examine the geometric structure of some ultra-small boron nanotubes.