Matrix effects on the breathing modes of multiwall carbon nanotubes

The analysis in the paper is based on a multiple-elastic shell model which assumes that each of the concentric tubes of multiwall carbon nanotubes is an individual elastic shell and coupled with adjacent tubes through van der Waals interaction. The effects of the matrix on the frequencies of radial breathing modes and vibration modes of multiwall carbon nanotubes embedded in the matrix is considered by a spring coefficient defined by the Winkler model. Results carried out show that the frequencies of the first mode increase monotonically as the stiffness of the matrix increase. Matrix surrounding multiwall carbon nanotubes not only change the value of amplitude ratios between tube walls of multiwall carbon nanotubes embedded in matrix, but also change the vibration modes between tube walls of multiwall carbon nanotubes from coaxial vibration to non-coaxial vibration. In the absence of the matrix, the frequencies of radial breathing modes and vibration modes of an individual multiwall carbon nanotubes predicted by the present shell model are found to agree very well with the available experimental and molecular dynamic simulation results.