Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective Young's moduli dependent on layer number

By Z. C. Tu, Z. Ou-Yang. 2001

342 citations recorded by the source corpus.

The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky et al. [Nature (London) 355, 333 (1992)] and is shown to be consistent with the classic shell theory by which Young's modulus, the Poisson ratio, and the effective wall thickness of SWNT's are obtained as $Y=4.70 \mathrm{TPa},$ $\ensuremath{\nu}=0.34,$ and $h=0.75 \mathrm{\AA{}},$ respectively. The elasticity of a multiwalled carbon nanotube (MWNT) is investigated as the combination of the above SWNT's of layer distance $d=3.4 \mathrm{\AA{}}$ and the effective Young's modulus of the MWNT is found to be an apparent function of the number of layers, N, varying from 4.70 to 1.04 TPa for $N=1$ to $\ensuremath{\infty}.$

Subfields: Biomedical Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/3617f904c320e3cfe1d43549205c7ef05fae403c

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In Materials Chemistry

Citations in the corpus

On the effective elastic moduli of carbon nanotubes for nanocomposite structures (2004, methodology): “Recently, Tu and Ou-yang [26] have theoretically studied the elastic properties of single and multi-walled nanotubes using the local density approximation model combined with a classical elastic shell theory.”
Finite element modeling of single-walled carbon nanotubes (2005, background): “074 Tu and Ou-Yang [24] Local density approximation model 0.”
Thermo-mechanical behavior of low-dimensional systems: The local bond average approach (2009, background): “– the Y value remains almost constant for a given number of walls without changing with the tube diameter [60], and – the Y value increases as the number of walls (k) or wall thickness is reduced [358].”
Graphene versus MoS2: A short review (2014, methodology): “17 eV using the geometric approach with interactions described by the VFFM [5, 6] and 1.”
Mechanics of deformation of single- and multi-wall carbon nanotubes (2004, neutral): “Yakobson et al.(1996) MD 59.36 2.235 5.5 0.066 Zhou et al.(2000) TB 61.71 2.922 5.1 0.074 Tu and Ou-Yang (2002) LDA 57.64 3.055 4.7 0.075 Kundin et al.(2001) ab initio 56.4 3.843 3.859 0.089 Present authors FE 59.36 2.886 4.84 0.075”
Review article: Polymer-matrix Nanocomposites, Processing, Manufacturing, and Application: An Overview (2006, background): “Recently, Lau [275] conducted an analytical study on the interfacial bonding properties of nanotube/polymer composites by using a well-developed local density approximation model [276], classical elastic shell theory and conventional fiber-pullout model.”