Effective Wall Thickness of Single-Walled Carbon Nanotubes for Multi-Scale Analysis: The Problem and a Possible Solution
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, D torsion, 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≈ 0.1 nmandE≈3.5TPa.
KeywordsCarbon Nanotubes Atomistic Simulation Effective Thickness Plane Curf Radial Breathing Mode
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