Catalyst volume to surface area constraints for nucleating carbon nanotubes

In this Article, we describe a carbon nanotube formation model in which sp(2) carbon hemispheres form the embryonic caps from which a nanotube can grow. This requirement leads to a single wall carbon nanotube formation window concomitant with our systematic experimental findings, which show upper and lower diameter limits. Further, the successful formation of a nucleation cap (hemisphere) is governed by catalyst particle volume to surface area considerations. Single wall carbon nanotubes are only obtained when both the nanotube formation window and the precipitating catalyst size distribution cross over. The extent to which these two windows overlap establishes the mean diameter and diameter distribution of the obtained single wall carbon nanotubes.