Ideal Polyhedral Model for Boron Nanotubes with Distinct Bond Lengths

Abstract

In this Article, we extend both the rolled-up model and the polyhedral geometric model for single-walled boron nanotubes with equal bond lengths to the corresponding models but having distinct bond lengths. The boron nanotubes considered here are assumed to be formed by sp2 hybridization and π-bonds and may have as many as three different bond lengths, and the nanotube lattice is assumed to comprise a triangular pattern. Beginning with the two postulates that all equivalent bond lengths lying on the same helix are equal and that all of the atoms are equidistant from a common axis of symmetry, we derive exact formulas for the geometric parameters such as chiral angles, bond angles, radius, and unit cell length. Results for both the rolled-up model and the prior geometric model are shown to emerge from the new geometric model in the limit of large radius and in the limit of equal bond lengths, respectively. Numerical results for the new polyhedral model are related to existing numerical results for a novel boron nanotube structure, which involves 1/9 of the atoms missing. This novel structure is believed to be more energetically favorable than the conventional model.