Anharmonic properties of Raman modes in double wall carbon nanotubes

The temperature dependence of the radial breathing modes (RBMs) and the zone-center tangential optical phonons (G-bands) of doublewalled carbon nanotubes (DWCNTs) has been investigated between 300 and 700 K using Raman scattering. As expected, with increasing temperature, the frequencies of the Raman peaks, including the RBMs and G-bands downshift simultaneously. We show here that the temperature dependence of the RBMs can be fitted by a simple linear dependence and different RBMs have different frequency shifts. We observe a noticeable nonlinearity in the temperature dependence of the G-band associated with the outer semiconducting tube G + ext (s). The deviation from the linear trend is due to the contribution of the third-order anharmonic term in the lattice potential energy with a pure temperature effect. An estimated value of 1.5 for the Gruneisen parameter of the G + ext (s) band was found.