Curvature, vacancy size and chirality effects of mono- to octa-vacancies in zigzag single-walled carbon nanotubes

Abstract

Defect curvature K_Vs (s = 1–8) was developed based on our previously proposed direction curvature theory. As a universal criterion, it could predict reactivities of mono-vacancies (V₁) to octa-vacancies (V₈) in the (n,0) tube. Calculated results showed that vacancy formation energies E_f decreased with increasing K_Vs and vacancy modes with removed carbon atoms along the armchair chain of the carbon tubes were more (for V₂ and V₃) or the most stable (for V₄–V₈) in each kind of V_s, because their corresponding K_Vs values were larger or the largest. Local product structures were inclined to have small rings including pentagon, heptagon, octagon and nonagon. Vacancy formation energies E_f obviously increased upon increasing the n value of (n,0) tubes as the vacancy size s ≤ 3 and s = 5, and for the other larger s there was a little increase for E_f as n, and they were minimal as n was 6 and 9, owing to the same oscillation rule of the energy gaps. An odd–even oscillation rule for the smallest E_f among each kind of V_s as the vacancy size s existed. For two dissociation processes, namely V_s → V_s−1 + V₁ and 2V_s → V_s−1 + V_s+1, the calculated results for two corresponding dissociation energies confirmed that the vacancies V_s were more stable when s was even.