Macroscopic Model for Multiwalled Nanotube Growth

A model based on simple thermodynamic arguments and using physical parameters of the arc plasma has also been considered [20], in order to explain the formation of multishell tubes and spherical nanoparticles as well. Within this model, the growth of carbon structures on a microscopic scale is governed by the attachment probabilities of carbon atoms, ions and clusters of various sizes and shapes, controlled by a set of time- and space-dependent parameters in the arc plasma formed in the inter-electrode region. In a region close to the cathode surface, the growth of carbon structures occurs due to the competitive input of two groups of carbon species having different velocity distributions. An isotropic Maxwellian velocity distribution corresponding to a temperature of 4000 K is thought to cause the formation of spherical carbon nanoparticles. A directed ion current due to singly charged carbon ions accelerated in a region of potential drop leads to the formation of elongated structures, as a consequence of the creation of an axis of symmetry. The growth rates of nanotubes in the arc plasma can be estimated from the collision probabilities; i.e., the growth time for a nanotube 5nm diameter and 1mm long is approximately 10~3-10~4 s.

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