Wall thickness of single-walled carbon nanotubes and its Young's modulus

Abstract

Young's modulus of single-walled carbon nanotubes (SWCNTs) was calculated by a modern pseudo-potential ab initio method. Using different models for wall thickness, we found that the Young's modulus of an SWCNT varies in a wide range from 0.94 to 5.81 TPa. Here, an SWCNT's wall thickness was obtained by electronic structure calculation. Using the wall thickness, we obtained that the Young's modulus of an SWCNT is 1.06-1.16 TPa, which is in agreement with the experimental result of 1.20-1.25 TPa.

Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites

“…Similar observations hold for an orthorhombic crystal. From the Table III data, it is observed that for Ni/CNT composites, the c ii ͑i =1-6͒, c 11 + c 22 −2c 12 , c 22 + c 33 −2c 23 , c 11 + c 33 −2c 13 , and c 11 + c 22 + c 33 +2c 12 +2c 23 +2c 13 are all positive, and thus it can be reasonably concluded that Ni/CNTs composites are mechanically stable. This is an encouraging result for the fabrication of nanocomposite materials by embedding the CNTs in metal matrices.…”

“…For the composites with the MWCNT, c 12 and c 13 decrease for both low and high CNT volume fractions. For c 23 , however, a small increase is seen for both volume fractions. The values of c 44 , c 55 , and c 66 decrease in the composites compared to pure Ni ͑125 GPa͒ and depend on the CNT concentration in the composites.…”

“…2͑d͒ shows MWCNT that fits the periodicity of fcc Ni matrix. The wall thickness of SWCNTs were assumed to be 0.32 nm based on electrondensity distribution calculations 23 and similar methods. 24,25 To simulate the Ni/CNTs nanocomposites with low CNT volume fractions, four different single-crystal Ni supercells containing a hollow cylindrical void at the center were built.…”

“…For each deformation step ͑0.0002 step size͒, we minimized system energy by relaxing positions of all atoms. Nine-independent elastic constants ͑c 11 , c 22 , c 33 , c 12 , c 23 , c 31 , c 44 , c 55 , and c 66 ͒ and three independent constants ͑c 11 , c 12 , and c 44 ͒ of Ni/CNTs and pure fcc Ni were determined in this study. The directiondependent Young's modulus ͑E͒, 26 which measures the stiffness of a material, was calculated from the slope of the strain-stress curves for pristine CNTs.…”

“…For an orthorhombic crystal, this imposes the following constraints: 47 c 11 + c 22 Ͼ 2c 12 , c 22 + c 33 Ͼ 2c 23 , c 11 + c 33 Ͼ 2c 31 , c ii Ͼ 0 ͑i =1-6͒, and c 11 + c 22 + c 33 +2c 12 +2c 23 +2c 31 Ͼ 0. These criteria simplify to c 11 Ͼ 0, c 44 Ͼ 0 c 11 +2c 12 Ͼ 0, and c 11 − c 12 Ͼ 0 for cubic crystals such as fcc Ni.…”