Structural properties of carbon nanotubes derived from ${}^{13}$C NMR

We present a detailed experimental and theoretical study on how structural properties of carbon nanotubes can be derived from ${}^{13}$C 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.

Figure 1

High resolution transmission electron microscopy (HRTEM) of different MWNTs: (a) MW1, (b) MW2, (c) MW4, and (d) MW3.

Figure 2

${}^{13}$C high-resolution MAS NMR spectra on single-, double-, triple-, and MWNTs. (a) DW1, (b) SW2, (c) SW1, (d) DW2, (e) MW4, (f) MW1, (g) MW2, and (h) MW3. The structural characteristics of each sample are listed in Table . (sidebands are denoted by ${}^{*}$).

Figure 3

${}^{13}$C NMR isotropic chemical shifts for CNTs versus the inverse of their diameter (D): experiments (circles), ab initio calculation (squares) and calculation performed by Sebastiani and Kudin et al. for different tube diameters (triangles).[48] The dashed line corresponds to δ (see Eq. (1)), the best fit of the experimental data.

Figure 4

The parameter Δ versusthe number of walls. Inset shows (a) NMR spectrum of sample MW3 with (b) the corresponding tensor fit and (c) NMR spectrum of DW2 with (d) the corresponding tensor fit. The arrows indicate where in the plot the two samples can be found.