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I believe that the G band (~1600 cm-1) shows the stretching mode of the graphene in a carbon nanotube (e.g. chiral, zigzag, armchair) and the 2D band (~2680 cm-1) shows the number of walls in the CNT. I vaguely remember there is some information that can be gleaned from the ratio of the two. Is this the case?

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I think there might be a mistake in your question...

Around $\pu{2680 cm-1}$, there is the $S_1$ band (attributed to overtone or combination scattering). I think the $2D$ band you are referring to is the band shouldering the $G$ band (also called $D'$) which is around $\pu{1680 cm-1}$.

About the ratio, there are two ratios that are often used to characterise $\mathrm{sp^2}$ carbon based materials such as the CNT. $$\text{Intensity ratio} = R_1 = \frac{I(G)}{I(D)}$$ $$\text{Area ratio} = R_2 = \frac{A(G)}{A(G)+A(D)+A(D')}$$

Both these ratios help characterise the degree of organization of your sample.

For more information or more details, I would recommend checking out Spectrochim. Acta, Part A 2003, 59 (10), 2267–2276

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