POLYHEDRAL MODELS AND GEOMETRIC STRUCTURES FOR NANOTUBES

Abstract

In this thesis, some new polyhedral models for nanotubes are examined. The conventional rolled-up model for carbon nanotubes assumes that a flat sheet of graphene is rolled into a seamless right circular cylinder and therefore in terms of the geometric parameters, the curvature inherent in the structure of nanotubes is not taken into account. The conventional rolled-up model of nanotubes completely ignores any effects due to curvature while the existing ideal polyhedral models for single-walled carbon nanotubes and boron nitride nanotubes, which are both hexagonal structures, are known to give predictions for the geometric parameters of the tube which are in excellent agreement with computational studies (molecular dynamics simulations and ab initio calculations). In this thesis the notion of an ideal polyhedral model is extended to silicon and boron nanotubes, which adopt respectively squares or skew rhombi and flat equilateral triangles as their structure. The silicon nanotubes considered here are assumed to be formed by sp hybridization and thus the nanotube lattice is assumed to comprise only squares or skew rhombi. The boron nanotubes considered here are assumed to be formed by complex bonding type and therefore the nanotube lattice is assumed to comprise a triangular pattern. From molecular dynamics simulation results for carbon nanotubes and silicon nanotubes, the bond lengths are known to vary depending upon the bond direction. Often this aspect can not be ignored and therefore in this thesis both the conventional and the ideal polyhedral models are extended to include distinct bond lengths, and specifically for carbon, silicon and boron nanotubes. These general models are shown to be in excellent agreement with computational studies. We first present the standard geometric parameters for the conventional nanotube model. Noting again that the curvature inherent in this model is completely ignored, for the ideal polyhedral model for silicon nanotubes we begin with three