Length effect of (15,15) single-walled carbon nanotube on its energy and Young´s modulus studied using linear scaling quantum mechanical method

By using a linear scaling self-consistent-charge density functional tight binding (SCC-DFTB) method, the energy and the Young´s modulus as a function of tube length for (15, 15) single-walled carbon nanotubes (SWCNTs) are investigated. It was found that with increasing the length of SWCNTs the Young´s modulus increases rapidly, then, remains a slow increase, and ultimately approaches a constant value after the length is increased to 15 nm. While a reversed variation tendency was found for the average energy of atoms in SWCNTs with change of the tube length. These characters of the length-dependent energy and Young´s modulus can be quantitatively explained by a simple formula involving the surface energy and bulk energy.