Size Dependence of the Thin-Shell Model for Carbon Nanotubes

There has been much debate on the choice for the representative wall thickness for the thin-shell model, although this model has demonstrated remarkable success in capturing many types of behavior of single-walled carbon nanotubes (SWNTs), in determining the buckling strains under compression, torsion, and bending, in particular. This analysis, using the Tersoff-Brenner potential and ab initio calculations, shows that the elasticity of the model thin shell evolves from isotropic to square symmetric with the decreasing tube diameter, leading to significant diameter dependence for all the elastic moduli and the representative wall thickness. Furthermore, the elastic moduli of multiwalled carbon nanotubes of diameters up to 10 nm are also size dependent.

Figure 1

Ab initio validation for the TB-potential molecular dynamics simulations: (a) Prestrains of relaxed SWNTs. (b) Excess energies vs axial and circumferential extensions for the $(4,4)$ SWNT.

Figure 2

Diameter dependence of all the thin-shell model parameters: (a) the axial and circumferential Young’s moduli, (b) the shear modulus, (c) Poisson’s ratios, and (d) the wall thickness.

Figure 3

Size dependence of axial and bending Young’s moduli of MWNTs.