Effective Wall Thickness of Single-Walled Carbon Nanotubes for Multi-Scale Analysis: The Problem and a Possible Solution

摘要

Continuum mechanics models have been used to characterize the mechanical behaviour of carbon nanotubes, but their validity down to the nanometer scale has not been fully verified. A typical example is the effective wall thickness of single-walled carbon nanotubes (SWCNTs), which has not been well defined after years of effort. This paper proposes a sufficient condition for determining the effective wall thickness h and Young's modulus E of an SWCNT using in-plane stiffness, K_(in-plane), torsion stiffness, Aorsion, bending stiffness, D_(bending), and off-plane torsion stiffness, K_(torsion), as the independent elastic constants of a continuum model. The paper concludes that when the Vodenitcharova-Zhang's necessary condition and D_(bending)/K_(in-plane) = D_(torsion)/K_(torsion) are satisfied, the intersect of D_(bending) and K_(in-plane)curves in the E-h plane will determine a unique h, and in turn, leads to a defined E. For SWCNT (10, 10), h approx = 0.1 nm and E approx = 3.5 TPa.