The D+G band is a defect activated process as the D-band is. There you notice a correlation between the D-band intensity and the D+G intensity as it requires a defect for an elastic scattering event to provide momentum conservation in the Raman-process. The 2D-band however is a fully allowed process in graphene as it utilizes the same phonon twice (forward/backward scattering) to provide momentum conservation and hence will not require a defect for its activation. I am not an expert in multiwalled CNTs but I would assume that similar effects as we known them from graphite/few layer graphene are in place. Here the amount of interacting walles will have a great influence on the possible transitions and hence will dampen the signal intensity the "thicker" your MWCNTs get. This picture is a little simplified though as for CNTs due to their curvature you will have a lot more possible bands for electrons to scatter to from the beginning.
Another aspect that will reduce 2D-band intensity is destruction of the bandstructure by introduction of defects and hence amorphization. This is well studied in the breakdown of the 2nd order spectrum of graphene upon ion-bombardment, covalent functionalization or just oxidation. The more sp3-centers you incorporate, the more defects you have, the higher the D-band - up to a certain point (approx. 3 nm mean free path between 2 defects). Beyond this critical density the whole spectrum breaks down, signals broaden, 2nd order spectrum vanishes and the spectrum you will obtain mimics that of amorphous charcoal.
The G band is due to graphitic carbon, i.e. that in the walls of CNTs. The D band is due to disorder. The 2G band is not perfectly understood but it often said to be more intense with fewer walls and dampened out as the number of walls increases. These three bands should be present in your samples. It seems normal to me. The lower the D band the better for defect free CNTs of course.
The G- band (graphene out-phase) about ~1570cm-1 of transverse graphene vibration and D-band of ~1350cm-1 of longitudinal vibration (disorder carbon). the other D2 and G2 are refer to "overtone" of D and G peaks resonance.
The D+G band is a defect activated process as the D-band is. There you notice a correlation between the D-band intensity and the D+G intensity as it requires a defect for an elastic scattering event to provide momentum conservation in the Raman-process. The 2D-band however is a fully allowed process in graphene as it utilizes the same phonon twice (forward/backward scattering) to provide momentum conservation and hence will not require a defect for its activation. I am not an expert in multiwalled CNTs but I would assume that similar effects as we known them from graphite/few layer graphene are in place. Here the amount of interacting walles will have a great influence on the possible transitions and hence will dampen the signal intensity the "thicker" your MWCNTs get. This picture is a little simplified though as for CNTs due to their curvature you will have a lot more possible bands for electrons to scatter to from the beginning.
Another aspect that will reduce 2D-band intensity is destruction of the bandstructure by introduction of defects and hence amorphization. This is well studied in the breakdown of the 2nd order spectrum of graphene upon ion-bombardment, covalent functionalization or just oxidation. The more sp3-centers you incorporate, the more defects you have, the higher the D-band - up to a certain point (approx. 3 nm mean free path between 2 defects). Beyond this critical density the whole spectrum breaks down, signals broaden, 2nd order spectrum vanishes and the spectrum you will obtain mimics that of amorphous charcoal.
its all depends on the wavelength your using, normally if you got D+G bands its should overtone in 2700 + 2900 cm-1 in less intensity, but if you got disorder carbon means the ( ID/IG is high) much then the appearance of G2 will be eliminated.