Quantized acoustic vibrations of single-wall carbon nanotube

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Abstract
Acoustic vibrational modes are derived for both zigzag and armchair nanotubes of finite length using the continuum theory and a variational solution of Donnell’s equation. Calculations of both even and odd modes of the displacement are performed. The dispersion relations are shown to vary with the length of the tube and the displacement field of the nanotube is used to calculate the deformation potential interaction Hamiltonian.