Coupling of Raman radial breathing modes in double-wall carbon nanotubes and bundles of nanotubes.

Measurements of the radial breathing modes from Raman Spectroscopy have been most useful in characterizing the diameters of single-wall carbon nanotubes (SWNT), where there is a simple monotonic relationship between frequency and diameter. Similar correlations have also been used to predict sizes for double and multiple wall nanotubes and for bundles of SWNT. However this can lead to significant errors because the relationship between frequencies and diameter is much more complicated for DWNT. This is because of couplings between the vibrations of various walls. To provide guidance in such assignments we used the GraFF atomistic force field to predict the in-phase and counter-phase radial breathing modes (RBMs) of double wall carbon nanotubes (DWNTs) over a broad range of inner and outer diameters and chiralities. We then developed an analytical model to describe the RBMs of dispersed DWNTs. This enables the inner and outer shell diameters to be extracted from pairs of RBM peaks. We find that nanotubes bundles show significant dependent peak broadening and shifting compared to dispersed nanotubes. For bundles of SWNT and DWNT, the relationships are much more complicated.