Geometric model of silicon nanotubes

In this paper, we extend both the rolled-up and the polyhedral models for single-walled silicon nanotubes with equal bond lengths to models having distinct bond lengths. The silicon nanotubes considered here are assumed to be formed by sp³ hybridization with different bond lengths so that the nanotube lattice is assumed to comprise only skew rhombi. Beginning with the three postulates that (i) all bonds lying on the same helix are equal, (ii) all adjacent bond angles are equal, and (iii) all atoms are equidistant from a common axis of symmetry, we derive exact formulae for the polyhedral geometric parameters such as chiral angles, adjacent bond angles and radius. Finally, some molecular dynamics simulations are undertaken for comparison with the geometric model. These simulations start with equal bond lengths and then stabilize in such a way that two distinct bond lengths emerge.