Pressure effect on radial breathing modes of multiwall carbon nanotubes

This paper studies the pressure effect on radial breathing modes (RBMs) of multiwall carbon nanotubes (MWNTs). The analysis is based on a multiple-elastic shell model which assumes that each of the concentric tubes of a MWNT is an individual elastic shell and coupled with adjacent tubes through van der Waals interaction. The pressure effect on RBMs of MWNTs is mainly attributed to the pressure-induced reduction of interlayer spacing and the increase of the interlayer vdW interaction coefficient defined by the second derivative of the energy-interlayer spacing relation of MWNTs. In the absence of external pressure, the RBM frequencies and vibration modes predicted by the present shell model are found to agree very well with the available experimental and molecular-dynamics simulation results. In the presence of an external pressure, our results show that high external pressure considerably raises the vdW interaction coefficients especially between the outermost few layers of MWNTs. As a result, some of the RBM frequencies of MWNTs increase significantly with increasing external pressure. The most significant pressure effect occurs for the highest-frequency mode of large-diameter MWNTs (with the innermost diameter greater than 2nm) or an intermediate-frequency mode of small-diameter MWNTs (with the innermost diameter less than 2nm), and is always associated with those RBMs in which adjacent outermost layers vibrate in opposite directions with significant change in interlayer spacing.