First Principle Calculations for Carbon Nanotubes

Nanotubes form a novel structural phase of carbon. Since materials made of nanotubes possibly posses a high application potential, a very good theoretical understanding of these materials is most important for their development into practical use. In this proposal, we suggest to perform first principle density functional calculations to investigate a variety of properties of nanotubes. The calculations will utilise the Vienna ab initio program (VASP) - a plane wave program that uses ultrasoft pseudopotentials or the augmented plane wave method. This program is particularly well suited for the investigations in mind, since efficient algorithms have been implemented in the package, that allow to treat large systems containing up to 400 carbon atoms. The following properties will be investigated by means of first principle calculations: (i) Evaluation of the full vibrational spectrum of single wall carbon nanotubes. (ii) Accurate evaluation of infrared and Raman spectra. (iii) Mechanical and thermal properties of nanotubes. (iv) Interaction between tubes, and how the interaction influences vibrational and mechanical properties. (v) Functionalisation of nanotubes and properties of defects. Investigations of the vibrational and electronic changes will be emphasised. In all investigations, we will closely collaborate with experimentalists.

Carbon nanotubes are novel carbon based materials, which are formed by rolling up a honeycomb graphite sheet. The outer wall of these nanotubes can be as thin as a single carbon atom, and the diameters of the tubes approach a few nanometers. It is believed that such ultra thin nanotubes might be used either as electronic wires or as electronic switches in next generation computers. Developing a deeper theoretical understanding for such tubes was the main aim of the present research project. Due to their reduced dimensionality nanotubes posses intriguing new properties which are related to the quantum nature of the electronic states traveling in the circumferential direction, e.g. after the circumference, the phase of an electron must match with the original phase. Another quantum mechanism that has been known to exist in one dimensional wires is called Peierls instability: at low temperatures ultra thin wires are in principle unstable and should distort or twist in such a manner that they become non metallic. Despite this theoretical prediction, such an instability has not been observed experimentally for nanotubes. The present calculations shed light on this peculiarity and indicate that for carbon nanotubes such instabilities indeed exist, but are so weak that a permanent distortion does not occur. Instead, metallic carbon nanowires posses one specific vibrational mode which is significantly softer than in non metallic wires. When the carbon atoms in the nanotube swing back and forth in a manner compatible to this particular mode, a band-gap opens (they become non-metallic, but only temporarily on a fs timescale). This mode softening has been observed but was not understood before the present theoretical study. Furthermore, the project investigated how the encapsulation of Buckminster fullerenes into nanotubes changes their electronic conductivity. Experimentally profound modifications have been observed under specific conditions, and it was suggested that these modifications can be used to tune carbon wires and transistors. Unfortunately the theoretical calculations tell a different story. The Buckminster fullerenes modify the electronic structure of the tubes, but only slightly and the modifications are far too small to allow a tuning of the relevant transport properties in actual devices.