Single-wall carbon nanotube diameter distributions calculated from experimental parameters

The growth of bundles of single-wall carbon nanotubes is explained by assuming a transition state, in which precipitated graphene sheets detach from the surface of a liquid catalyst particle, forming fullerenelike caps. The energetic situation of the transition state is considered as an equilibrium of the kinetic energy: the work of adhesion of the graphene sheet toward the catalytic particle and the strain energy associated with the cap formation. The tube diameter distributions depend only on their formation temperature range, the composition of the catalytic metal and carbon-containing particles, and the type of metal used. The calculated diameter distributions for different metal catalysts agree very well with the experimental data of are and laser experiments of other groups. The observed increase of the tubes mean diameters with the formation temperature is also correctly reproduced by the simple model.