Ideal tensile strength and band gap of single-walled carbon nanotubes

The ideal tensile (compressive) strength, Young’s modulus, and band-gap changes of single-walled carbon nanotubes (SWNT’s) with zigzag types of (8,0), (9,0), and (10,0) and armchair of (8,8) under an uniaxial deformation are analyzed using a tight binding (TB) method parametrized by Tang et al. In addition, the first principle density functional theory based on the local density approximation (DFT) is employed as a cross-check. It is well known that the band gap of a SWNT changes according to the uniaxial strain. Most of the previous studies have represented the deformed atomic structure by an empirical potential and then applied band analysis to estimate the band gaps. However, this step-by-step process may allow errors due to the lack of transferability of the empirical potentials in the highly deformed state. In this study, in order to estimate the electronic structure change more accurately and examine the transferability of the TB potential, we used the TB and also the DFT method to find equilibrium atomic structures of the SWNT’s deformed by applied strain. At the same time, the band gaps of the equilibrium structure are estimated. We find that the TB results for ideal strengths, Young’s modulus, and band gaps are basically in good agreement with the DFT results. The band-gap changes are in qualitative agreement with Yang’s theory in which a uniform deformation is assumed. However, even though the theory predicts a zero gap for the armchair SWNT’s, we see a finite band gap of the (8,8) SWNT at the 20% tensile strain level, which is the extreme strain sustained immediately succeeding failure.