Chemical anisotropies of carbon nanotubes and fullerenes caused by the curvature directivity

The directional-curvature theory is developed as a rational basis for the strain energy and the chemical reactivity in single-walled carbon nanotubes (SWCNTs) and fullerenes. The directional curvature KD and its mean KM, derived from this theory, cover the overall curvatures of their bonds and atoms and break through the limitations of the pyramidalized-angle thetap approach, which is only available to atomic curvature. The directional-curvature theory demonstrates that KD and KM depend directly on the strain or reactive binding energies of the bonds and atoms and that there is approximate curvature conservation in SWCNTs and fullerenes. Application of this theory to addition reactions of various SWCNTs and fullerenes shows that the slope of the straight line between the strain or binding energies and KD is close to a constant, which helps clarify the puzzle as to why some functionalizations of C70 occur at the relatively flat midsection.