ABSTRACT
Raman radial breathing-like mode (RBLM) frequencies of an infinite nanopeapods are calculated within the framework of a continuum-molecular based model. The nanotube-fullerene interaction is modeled via the Lennard-Jones interatomic potential. An analytical formulation is developed and is justified due to its good agreement with the experimental and atomistic-based results. Furthermore, we propose new relationships for the van der Waals (vdW) interaction coefficients between the atoms of this hybrid nanostructure. Numerical results are also obtained for various nanopeapods on the basis of the present formulation. The RBLM frequency upshifts are predicted for small single-walled carbon nanotubes (SWCNTs). The frequency shifts can be adequately explained by the vdW intermolecular interactions acting between the fullerene and the SWCNTs atoms. To the best of our knowledge, a simple theoretical method which can predict the Raman RBLM frequencies of the nanopeapods with high precision has not been provided hitherto. We believe that the present study is likely to fill the gap.
ABSTRACT
Radial vibration of spherical nanoparticles made of materials with anisotropic elasticity is theoretically investigated using nonlocal continuum mechanics. The anisotropic elastic model is reformulated using the nonlocal differential constitutive relations of Eringen. The nonlocal differential equation of radial motion is derived in terms of radial displacement. Cubic, hexagonal, trigonal and tetragonal symmetries of the elasticity are discussed. The suggested model is justified by a good agreement between the results given by the present model and available experimental data. Furthermore, the model is used to elucidate the effect of small scale on the vibration of several nanoparticles. Our results show that the small scale is essential for the radial vibration of the nanoparticles when the nanoparticle radius is smaller than 1.5 nm.
