  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 {\AA} diameter armchair SWNTs in sooting
and carbonaceous environments is explained by using the nanoelastic model of C
shells.

Mesoscale and Nanoscale Physics