Study of the cap structure of (3,3), (4,4) and (5,5)-SWCNTs: Application of the sphere-in-contact model

We have applied the sphere-in-contact model supported by hybrid Density Functional Theory (DFT) calculations to elucidate the cap geometry of the sub-nanometer in dimension (3,3), (4,4) and (5,5) single-wall carbon-nanotubes (SWCNTs). Our approach predicts certain cap-geometries that do not comprise of the commonly known for their stability combination of pentagonal and hexagonal carbon rings but also tetragonal, trigonal and all-pentagonal structures. Based on hybrid-DFT calculations carbon atoms in these new cap geometries have similar stability to carbon found in other fullerene-like capped zig-zag and arm-chair nanotubes (i.e., (5,5), (6,6), (9,0) and (10,0)) that are known to be stable and synthetically accessible. We find that the cap structure of the (3,3)-CNTs is a pointy carbon geometry comprised of six pentagonal rings with a single carbon atom at the tip apex. In this tip geometry the carbon atom at the tip apex does not have the usual sp2 or sp3 geometry but an unusual trigonal pyramidal configuration. DFT calculations of the molecular orbitals and density-of-states of the tip show that this tip structure apart from being stable can be used in scanning probe microscopies such as STM for very high resolution imaging.