The spherical curvature induced by pentagons in corannulenes and hexagonal sheets is shown to be the basic constituent that controls the growth of fullerenes and single-walled carbon nanotubes (SWNTs) in soot forming and carbon vapour environments. Formation of the initial ring of five or six atoms is the essential step which with the addition of further pentagons and hexagons determines whether a spinning fullerene is to be formed or the cap that lifts up and leads to the formation of an SWNT. A continuum elastic model is developed to determine the criteria for the growth of these structures. The observed dominance of the growth of 14 A diameter armchair SWNTs in sooting and carbonaceous environments Is explained by using the nanoelastic model of C shells.
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