Ab initio study of small diameter (6,6) armchair carbon nanoropes:: orientational dependent properties

A comprehensive ab initio investigation of the effects of the relative orientation (RO) between the adjacent tubes in a rope on the stability, structural, electronic, optical and Raman-active properties has been performed for the ropes of small diameter carbon (6, 6) nanotubes. A number of new features not discussed earlier are observed in the present study. The symmetric rope with an RO of 0degrees is metallic in all directions, whereas the asymmetric ropes with a non-zero value of RO are semiconductors along the tube axis but semi-metallic normal to rope axis. The band gap increases with RO up to an angle of 15degrees and thereafter reveals oscillatory behaviour. No dips appear in the symmetric rope but they do exist in the asymmetric rope. Strong optical absorption appears along the axis in the energy range 2.4-4.2 eV in the isolated tube. On the other hand, for the ropes, the strong absorption extends up to the energy region 1.8-4.5 eV. Strong peaks also occur at 0.05 and 0.15 eV for the ropes with RO = 0degrees and 15degrees, respectively. The even-parity Raman-active radial breathing mode (RBM) frequencies calculated here for the isolated (n, n), n = 3-6 tubes are seen to deviate from the usual omega proportional to 1/d law (where d is the tube diameter). For small diameter tubes, this shows an approximate variation, omega = 1/d(1/2). The RBM frequencies for the ropes are either greater or smaller compared to the isolated tube, depending on the value of RO. A cubic anharmonicity of about 14% is seen in the potential for the radial mode vibrations. The RBM frequencies calculated here for some ropes, which are lower compared to that of the isolated tube, concur with the available Raman data.