Thickness of graphene and single-wall carbon nanotubes

Young's modulus and the thickness of single wall carbon nanotubes (CNTs) obtained from prior atomistic studies are largely scattered. In this paper we establish an analytic approach to bypass atomistic simulations and determine the tension and bending rigidities of graphene and CNTs directly from the interatomic potential. The thickness and elastic properties of graphene and CNTs can also be obtained from the interatomic potential. But the thickness, and therefore elastic moduli, also depend on type of loading (e.g., uniaxial tension, uniaxial stretching, equibiaxial stretching), as well as the nanotube radius $R$ and chirality when $R<1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. This explains why the…