Curvature effect of vacancies in single-walled carbon nanotubes

Defect curvature was developed based on our previous proposed direction curvature theory. Defect curvature, as a universal criterion, was used to identify reactivities of mono- and di-vacancies in single-walled carbon nanotubes. Calculated results at B3LYP/6-31G* level showed that, regardless of mono- and di-vacancies, vacancy formation energies Ef decreased with increasing defect curvature KV1 (for mono-vacancies) or KV2 (for di-vacancies). Each defect model of mono-vacancies had two types of structural products. However, each defect model of di-vacancies was only corresponding to one structural product. In mono- or di-vacancies, large included angles between new formed C-C bonds (for mono-vacancies) or the linked C-C bonds of the 5-ring and 8-ring (for di-vacancies) and the tubular axis were corresponding to short C-C bonds and small Ef. These product structures for di-vacancies were related to the magnitude of KV2.