0 400 800 1200 1600

Frequency (cm-1)

Fig. 19.55. Dependence of the infrared-active (7,4) chiral nanotube mode frequencies on tubule diameter d, [19.83,87], which is found from the (n, m) index pairs by Eq. (19.2). The value of d, for the (n, m) = (7,4) nanotube is 7.56 Â.

cies for the nanotube modes rapidly converge to their asymptotic limits for large d,.

The most significant aspects of these predicted results are the detailed differences in the spectra between tubules of similar diameters but different symmetry, thereby providing, in principle, an independent means (other than electron diffraction characterization by TEM) for yielding information on the chirality of the nanotubes. It is seen in these spectra that certain mode frequencies are strongly dependent on tubule diameter, and others are either weakly dependent or almost independent of d,. Thus, the Raman and infrared spectra will be dominated by sharp line features corresponding to Raman- or infrared-active modes with frequencies almost independent of dt, while the weakly d,-dependent mode frequencies will give rise to broad spectral features of low intensity [19.148].

As d, becomes large, the mode frequencies for armchair and zigzag tubules approach the frequencies of the 2D graphene modes at the T and M points in the 2D Brillouin zone. For chiral tubules, only the T point modes are involved. The effects of the tubule geometry on the values of the Raman and infrared frequencies should be observable only for small-diameter (< 40 Á) tubules. It is convenient to refer to the effects related to the small tubule diameters as quantum effects, since they arise from the small number of carbon atoms around the tubule diameter. The Raman and infrared line intensities, furthermore, are expected to decrease, as the diameter increases, for all the modes except for the Raman-active mode at 1590 cm-1, which is the only one which will have nonvanishing intensity in the limit of infinite diameter for single-wall nanotubes. For multiwall nano-tubes, an infrared mode near 1590 cm-1 should retain significant intensity as well as an infrared mode near 860 cm-1 for out-of-plane vibrations as n -*■ oo. For tubules with small diameters (~20 Á), a broad feature near 1350 cm-1 along with a weak peak near 860 cm-1 should be observable in the Raman spectra [19.84],

19.7.3. Experiments on Vibrational Spectra of Carbon Nanotubes

A number of experimental studies have been made of the Raman spectra of carbon nanotubes [19.149-151], No papers have yet been published on the infrared spectra. In most of these Raman studies, the diameters of the nanotubes were sufficiently large that the observed spectra are similar to those from highly disordered graphite, yielding little information of relevance to the expected quantum effects in carbon nanotubes discussed in §19.7.2. Of the various published papers, the work by Holden et al. [19.149] provides the most information about quantum effects and for this reason is discussed first.

In the work of Holden et al. [19.149], Raman scattering measurements were carried out on carbonaceous material containing nanoscale soot, carbon-coated nanoscale Co particles, and nanotubes generated from a dc arc discharge between carbon electrodes in 300 torr of He [19.149], the conditions used to synthesize single-wall carbon nanotubes [19.31] (see §19.2.2). Raman microprobe measurements were used to obtain the distribution of the various carbon microstructures in the cathode of the carbon arc [19.152],

Of particular interest are the unique features of the Raman spectra obtained from the Co-catalyzed nanotube-containing soot, as shown in Fig. 19.56(e), in comparison with Raman spectra of other carbon materials shown on an expanded scale in Fig. 19.57. The distinctive features of spectrum in Fig. 19.56(e) include two sharp first-order lines at 1566 and 1592 cm"1. Also prominent in the first-order Raman spectrum are a broad band centered at 1341 cm"1 and two second-order features at 2681 cm"1 = 2(1341 cm"1) and 3180 cm"1 = 2(1592 cm"1). The weak Raman peak near 1460 cm"1 [Fig. 19.56(d) and (e)] is identified with fullerene impurities in

1000 2000 3000 Raman shift (cm-1)

Fig. 19.56. Experimental Raman spectra (T = 300 K) of: (a) glassy carbon (phenolformaldehyde precursor); (b) nanosoot, as synthesized by laser pyrolysis; (c) nanosoot from (b) after heat treatment at 2820°C; (d) soot obtained by the dc carbon arc method; (e) same as (d) but with Co added to anode; (f) highly oriented pyrolytic graphite (HOPG); and (g) single-crystal diamond (type Ha) [19.149], the nanotube samples. In comparison, the Raman spectrum [Fig. 19.56(d)] for the dc arc-derived carbons prepared in the same way as that studied in Fig. 19.56(e), except for the absence of the cobalt catalyst, shows no evidence for the sharp 1566 and 1592 cm-1 lines, or the sharp second-order features at 2681 cm"1 and 3180 cm-1, although other broad features in both spectra are strikingly similar in shape and frequency [19.149].

To show that the sharp features in Fig. 19.56(e) are not associated with ordinary amorphous soot, glassy carbon or graphitic carbons, etc., Raman spectra are included in Fig. 19.56 for a variety of sp2 and sp3 solid forms of carbon. These include the Raman spectrum for diamond [Fig. 19.56(g)], shown with its single sharp line at 1335 cm-1, and for highly oriented pyrolytic graphite (HOPG) [Fig. 19.56(f)], showing a sharp first-order line at 1582 cm-1 and several features in the second-order Raman spectrum, including one at 3248 cm-1, which is close to 2(1582 cm"1) = 3164 cm"1, but significantly upshifted, due to 3D dispersion of the uppermost phonon branch in graphite. The most prominent feature in the graphite second-

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