Dynamics of a Bunch of Carbon Nano-tubes

Nano-diameter tubules made of folded graphitic sheets have drawn the attention of physicists ever since the advent of fullerene research. These are interesting because of their conductivity (depends upon chirality) as well as their mechanical properties. Bunches of such tubes, single-walled and each of same diameter (~14A), have been produced in the laboratory. In this work we explore the mechanical properties of the bunch (hexagonal packing), having assumed, for simplicity, uniform continuous distribution of carbon atoms on each tube. The atom-atom potential (6-exp) is of Kitaigorodsky type where only inter-tube interactions are considered. Intra-tube interactions are not considered (implying a rigid tube model). This approximation works very well for pure C60 solid. We find that the range of external modes is not well separated from the radial mode frequency of the single tube as indicated by measured data. Therefore interpretation of experimentally observed frequencies needs to be done in terms of total modes of the bunch, including internal as well as external modes. We have also studied pressure dependent deformations of such a bunch which is found to be very interesting and is likely to provide information about their mechanical strength.