Radial breathing vibration of multiwall carbon nanotubes based on a rigorous van der Waals interaction

Abstract

This paper reports the results of an investigation on radial breathing vibrations of multiwall carbon nanotubes (MWNTs) embedded in an elastic matrix, based on a rigorous van der Waals (vdW) interaction which is dependent on the change of interlayer spacing and the radii of tubes. Each of the concentric tubes of MWNTs is considered an individual elastic shell and coupled with any two tubes through a rigorous vdW interaction force. The matrix surrounding MWNTs is considered a spring in which the spring coefficient is defined by the Winkler model. The results obtained show that the radial breathing frequencies of the first vibration mode increase monotonically as the stiffness of the matrix increases. The matrix surrounding MWNTs not only changes the value of amplitude ratios between any two tube walls of the MWNTs embedded in an elastic matrix, but also changes the vibration modes between the tube walls of the MWNTs from the coaxial vibration to the non-coaxial vibration. The new features and the meaningful numerical results in the present work on radial breathing vibrations of MWNTs embedded in an elastic matrix may be used as a useful reference for Raman scattering of light that can indirectly provide structural data on nanotubes.