Obtaining global equations for the Young's modulus of perfect and defective carbon nanotubes

There are limited studies which have extracted global equations for calculation of Young's modulus (E) in both pristine and defective carbon nanotubes (CNT), especially when a combination of different defects such as atom-vacancy and-misplacement exist simultaneously in the studied CNT. In this study, the finite element method was used to investigate E for a large set of perfect and defective single walled carbon nanotubes (2440 finite element models), including armchair, zigzag and chiral tubes. The obtained results were then employed as the basis for achieving accurate global equations for calculation of E in perfect and defective carbon nanotubes at various defect percentages. Despite most previous studies, which were based on the tube's diameter, the chiral indices (n, m) have been considered here as variables to predict the stiffness of carbon nanotubes. The achieved equations showed to be accurate, with maximum errors below 2% and 10% for perfect and defective tubes, respectively, compared to FE results. Based on the obtained equations, a computer execution file was developed which is capable of calculating E when different percentages of defects are introduced to the structure. The results show that unlike single defect states, the existence of any combination of atom vacancy and atom misplacement defects causes dramatic reduction in the stiffness of carbon nanotubes. Furthermore, the role of vacancy defects in the reduction of tube's elastic properties revealed to be more significant than misplacement defects. The results not only demonstrate that edge defects influence Young's modulus more noticeably, but also confirm previous works showing that armchair edged structures are less vulnerable to defects, as compared to zigzag. (paper)