3D Molecular Geometry and Band Structure Modelling of Graphene and Carbon Nanotubes

Graphene, carbon nanoribbons and carbon nanotubes are allotropes of carbon that are widely used in nanotechnology research due to their remarkable properties. Electrical and mechanical properties of those allotropes vary with their molecular geometry. Theoretically, an infinite number of such geometries do exist, and it is impossible to physically prepare samples of all of them in the real world. This paper is based on developing mathematical models to describe molecular geometries of graphene and carbon nanotubes, examining their geometry dependent electronic band structures and visually representing those relations in a 3D modelling and simulation software. Paper describes equations to derive the coordinates of the atoms, algorithms to derive the orientation of the bonds of the molecular structures, implementation of those algorithms in java3D and derivation of electronic band structures. Successful results were obtained after the implementation of the algorithms which are illustrated with few screenshots at the end.