We postulate that an equivalent continuum structure (ECS) of a single-walled carbon nanotube (SWCNT) is a hollow cylinder with mean radius and length equal to that of the SWCNT, and find the thickness of the ECS so that its mechanical response in free vibrations is the same as that of the SWCNT. That is, for mechanical deformations, the ECS is energetically equivalent to the SWCNT. We use MM3 potential to study axial, torsional, radial breathing and bending vibrations of several traction free–traction free SWCNTs of different helicities and diameters and compare them with the corresponding vibrational modes and frequencies of traction free–traction free ECSs obtained by using the three-dimensional linear elasticity theory and the finite element analysis (3D-FEA). The consideration of free ends eliminates the effects of boundary conditions and avoids resolving equivalence between boundary conditions in the analyses of SWCNTs and their ECSs. It is found that the wall thickness of the ECS (and hence of a SWCNT) is and Young’s modulus of the material of the ECS (and hence of the SWCNT) is . Both quantities are independent of the helicity and the diameter of the SWCNT. We also study radial breathing mode (RBM) vibrations with the molecular dynamics and the 3D-FEA simulations, and compare them with experimental findings. Accuracy in the assignment of spectral lines for RBMs in the Raman spectroscopy is discussed.
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e-mail: rbatra@vt.edu
e-mail: ssgupta@vt.edu
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November 2008
Research Papers
Wall Thickness and Radial Breathing Modes of Single-Walled Carbon Nanotubes
R. C. Batra,
R. C. Batra
Fellow ASME
Department of Engineering Science and Mechanics,
e-mail: rbatra@vt.edu
M/C 0219 Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061
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S. S. Gupta
S. S. Gupta
Department of Engineering Science and Mechanics,
e-mail: ssgupta@vt.edu
M/C 0219 Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061
Search for other works by this author on:
R. C. Batra
Fellow ASME
Department of Engineering Science and Mechanics,
M/C 0219 Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061e-mail: rbatra@vt.edu
S. S. Gupta
Department of Engineering Science and Mechanics,
M/C 0219 Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061e-mail: ssgupta@vt.edu
J. Appl. Mech. Nov 2008, 75(6): 061010 (6 pages)
Published Online: August 20, 2008
Article history
Received:
November 15, 2007
Revised:
March 11, 2008
Published:
August 20, 2008
Citation
Batra, R. C., and Gupta, S. S. (August 20, 2008). "Wall Thickness and Radial Breathing Modes of Single-Walled Carbon Nanotubes." ASME. J. Appl. Mech. November 2008; 75(6): 061010. https://doi.org/10.1115/1.2965370
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