Local equilibrium configurations and minimum energy path of carbon nanotubes with Stone-Wales defects and their related pentagon-heptagon lattice defects

Abstract

The energy landscape over configurational change of defects in carbon nanotube (CNT) is clarified for a variety of distributions of Stone–Wales defects and pentagon–heptagon (5–7) defects using the Peierls–Nabarro dislocation model. Based on the theoretical model, the configurational energy is estimated by relative displacement without fatal loss of accuracy, but the calculation of energy during the configurational change of defect is simplified with reduced degrees of freedom in the displacement field. The equilibrium configurations are obtained using the conjugate-gradient method, and the saddle point on the minimum-energy path between two equilibrium configurations for evolution of defects, such as the nucleation/annihilation and movement of defects, is estimated using the nudged elastic-band method. Many equilibrium configurations stably exist because of the lattice trapping of the 5–7 defects due to the relatively large Peierls–Nabarro barrier. The total energy does not only depend on the mean value of the relative displacement, but also on the complexity of the configurations of the defects, and we draw a directed graph which shows the possible paths of the configuration change of the defects. The results provide fundamental information related to the stability of the thermal activation of defects in CNT.