Structural properties of carbon nanotubes derived from 13C NMR

We present a detailed experimental and theoretical study on how structural properties of carbon nanotubes
can be derived from 13C NMR investigations. Magic angle spinning solid state NMR experiments have been
performed on single- and multiwalled carbon nanotubes with diameters in the range from 0.7 to 100 nm and
with number of walls from 1 to 90. We provide models on how diameter and the number of nanotube walls
influence NMR linewidth and line position. Both models are supported by theoretical calculations. Increasing
the diameter D, from the smallest investigated nanotube, which in our study corresponds to the inner nanotube
of a double-walled tube to the largest studied diameter, corresponding to large multiwalled nanotubes, leads
to a 23.5 ppm diamagnetic shift of the isotropic NMR line position δ. We show that the isotropic line follows
the relation δ = 18.3/D + 102.5 ppm, where D is the diameter of the tube and NMR line position δ is
relative to tetramethylsilane. The relation asymptotically tends to approach the line position expected in graphene.
A characteristic broadening of the line shape is observed with the increasing number of walls. This feature
can be rationalized by an isotropic shift distribution originating from different diamagnetic shielding of the
encapsulated nanotubes together with a heterogeneity of the samples. Based on our results, NMR is shown to be a
nondestructive spectroscopic method that can be used as a complementary method to, for example, transmission
electron microscopy to obtain structural information for carbon nanotubes, especially bulk samples.