Carbon nanotubes are being extensively studied for their interesting bulk, structural, mechanical and electronic properties. They exist as single nanotubes of various kinds as well as materials of these in forms of bunches of either single wall (SWNT) or multi-wall formations (MWNT). Recent technological advances looking for their semi-conducting properties have tremendously increased our effort to understand some basic properties of carbon nanotubes, especially related to their electronic properties.

The present paper investigates structural properties of double walled nanotubes, by calculating the rotational and translational freedom during movement of one nanotube with respect to the other one. This investigation will lead us to understand the magnitude of fixation energy of such double walled nanotubes at any given temperature. It will also help in calculating properties of bunches of MWNT.

For our model study, we represent the inter-nanotube interaction potential derivable from carbon atom-atom interaction potentials in a form close to Van-der-Waals potential energy. Such atom-atom interaction potentials have been considered to be very useful to represent various carbon based molecular crystals, like fullerene solids[1] and bunches of carbon nanotubes in triangular lattices.

The basic procedure of the model calculation follows writing the total potential energy of long double wall nanotubes of different radii as dictated by (n,m) indices. It so turns out that the minimum energy configuration requires the inter-nanotube distance to be around 0.339nm, in close agreement to that measured by Ebbessen and Ajayan [2].

One of the tubes of the double wall structure is rotated along the long axis to obtain total energy of the combination as a function of rotational angle, which is measured from an initial configuration. Similarly, the outer tube is also translated along the long axis (z-axes) to obtain total energy as a function of increment of shift, Dz. The potential energy in the minimum energy configuration comes out to be 0.023 eV/atom, the number of atoms taken here being the total number of atoms on the surfaces of the two nanotubes. The barrier height in case of rotation is around 0.007 meV/atom and periodicity around 180. Similarly, for translation along z-axis, the barrier height comes out to be around 0.008meV/atom with z periodicity around 2.46 Å (equaling the lattice constant of graphite sheet). The potential used here has also been deployed to calculate interlayer separation, Young’s modulus along ‘c’ axis and energy per atom between two graphite sheets, and the results of Young’s modulus and interlayer separation compare very well with the measured values existing in literature, indicating that energy estimate should be acceptable. However, striking differences have been observed with the density functional calculation using LDA of Charlier and Michenaud [3]. This discrepancy needs to be understood.

We also estimate the potential energy/atom of a multi wall nanotubes, by increasing the number of walls and observe that the energy saturates on increasing the walls, and nearly 90% of the energy is obtained on formation of 8 wall nanotubes.

The models for such double or multi-wall nanotubes provide a platform to forms multiwall nanotubes materials in the form of bunches, like SWNT bunches. In the case of MWNT bunches, the non-rigidity of the MWNT in the form of rotational and translational motion would be useful input.

References:

V.K. Jindal, Shuchi Gupta and K. Dharamvir, Phantoms(nanotubes) 8,5,(2000)

T. W. Ebbessen and P.M. Ajayan, Nature (London) 358, 220(1992).

J.C. Charlier and J.P. Michenaud, Phys. Rev. Lett. 70, 1858(2000).

^{*}Corresponding Address:
V.K. Jindal
Department of Physics, Panjab University
Chandigarh 160014 INDIA
phone: 91-172-534458
fax: 91-172-783336
email: jindal@pu.ac.in http://www.pu.ac.in/phys/vkjindal