Curvature Effect Of Vacancies In Single-walled Carbon Nanotubes

Carbon nanotubes (CNTs) exhibit interesting electronic, mechanical, and structuralproperties. However, in the experimental synthesis of CNTs, the properties mentionedabove can be hardly tailored, due to un-avoidably introducing many kinds of structuraldefects during the growth or under electron irradiation, such as adatoms, Stone-Walestopologic defects and atomic vacancies. Among them, atomic vacancies are some of themost prolific and important point defects, the existence of which undoubtedly wouldinfluence mechanical, physical and chemical properties of CNTs. Therefore, studying theatomic vacancies in CNTs is one of the fundamental issues to deeply understand variousproperties for their potential applications.Atomic vacancies have been abundantly studied, focusing on local structures andstabilities of defects and their effect on properties of tubes. An initio calculations based onthe density functional theory (DFT) were performed for the vacancy formation energies Efof mono-vacancies to octa-vacancies of the (5,5) and (n,0)(n=1～8) tube with all possibledefect patterns. Main results were as follows:(1) Defect curvaturewas developed based on our previous proposed directioncurvature theory. Defect curvature, as a universal criterion, was used to identify reactivitiesof mono-vacancies to octa-vacancies in the (5,5) tube. The structures with removed carbonatoms along zigzag chain or the tubular axis were the most stable in every Vnof the (5,5);The structures with removed carbon atoms along chair chain or the tubular axis were themost stable in every Vnof the (n,0). In addition, local structures of products disturbed thevariation rule of the EfasK Vn.(2) The stability of the models with different number n of removed carbon atoms wasstudied, it was indicated that the odd-even oscillation existed in the Efas n., when n in Vndefect was even, the vacancy formation energies Efwere larger than those of Vn+1and Vn-1defect.(3) In order to further explore the stability of tubes with vacancies, the separation of these vacancies into the smaller vacancies was investigated, when n in Vndefect was even,the first and second dissociation energies were larger than those of Vn+1and Vn-1defect,therefore, it can be conclude that the vacancies V2, V4and V6were stable in tubes.(4) The stability of the models with different number n of removed carbon atoms fromthe (n,0) tube was studied, a total rule that Efreduced with the increase of the defectcurvature. The stability of the models with different number n of removed carbon atomsfrom the same tube was studied, it was indicated that the odd-even oscillation existed in theEfas n. However, The stability of the models with same number n of removed carbonatoms from the same tube was studied, it was indicated that the three-n oscillation existedin the Efas n, when n in Vndefect was multiple of three, was corresponding to the smallestEf, a total rule that Efincreased with the increase of the tube diameter.