4. Raman spectra of single-walled carbon nanotubes (SWNTs)

The current section is an overview of the Raman active modes of SWNTs. The current treatment is meant only to preview the Raman bands and features relied on most heavily during the authors' characterization of SWNT samples. The first of the Raman bands featured in this section is the G-band, so called since it is common to all sp2 nanocarbons, centered at ~1580 cm�<sup>1</sup> . This high energy band is a consequence of the in-plane C-C bond stretching. Interestingly due to the induced strain from the curvature of SWNT walls the G-band for these structures is split into several peaks, with the two most prominent ones being the symmetric A1 denoted as G+ and G� at ~1590 and ~1560 cm�<sup>1</sup> , respectively. The variation of the smaller of these two peaks with diameter is given by [4]:

$$
\omega\_G = 1591 + \frac{\mathcal{C}}{d\_t^2} \tag{2}
$$

<sup>ω</sup>RBM <sup>¼</sup> <sup>227</sup> dt

value of 0.05 [4].

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> Ced<sup>2</sup> t

(5)

163

Raman Spectroscopy of Graphitic Nanomaterials http://dx.doi.org/10.5772/intechopen.72769

q

The overall environmental contribution to the RBM shift is contained in the fitted constant Ce, which is unique to SWNTs produced by any of the various available techniques. In the case of SWNTs produced by the HiPCO technique used in our studies, Ce was determined to have a

The second critical feature associated with the RBM band is its role in expressing the link between the quasi 1-dimensional electronic behavior and structure of SWNTs. The phenomenon referred to above is the resonant character of the Raman spectra of SWNTs, in which the intensity of Raman scattering from a SWNT is increased many fold when the laser excitation energy is very near that of an optical transition. Figure 5 shows the density of states for a representative metallic and semi-conducting single-walled carbon nanotube, respectively, and

Figure 5. Electronic density of states for a metallic and semi conducting SWNT shows two transitions labeled, E11 and E22,

between the corresponding valence and conduction bands.

where dt is the nanotube diameter, and the value C corresponding to the G� band for semiconducting and metallic nanotubes respectively are 47.7 and 79.5 cm�<sup>1</sup> nm. The above relation is derivable solely from a careful application of elasticity theory to SWNTs [4]. The later discussion of the use of the temperature variation of the G+ band in connection with thermal conductivity is based on a time-dependent perturbation of the G+ Raman band.

Next, the Raman band at around 1300–1350 cm�<sup>1</sup> is the D-Band, which has been shown in [9] to be associated with any defects or departures from perfect regularity in the sp<sup>2</sup> graphite lattice. Equation (3) shows the variation of typical crystallite sizes La with the Raman laser excitation energy, and ratio of the intensity of the D-band and G-band, based on a more recent version of Tuinstra and Koenig's original analysis [9]:

$$L\_4(nm) = \left(\frac{560}{E\_{laser}^4}\right) \left(\frac{I\_D}{I\_G}\right)^{-1} \tag{3}$$

The final Raman band featured in this section, the radial breathing mode is only present carbon nanotube spectra, and is therefore used as an indication of their presence in sp<sup>2</sup> Carbon samples. As implied by its name the intra-planar displacement of the C-atoms in this Raman active mode is effectively in the radial direction of the resultant SWNT, as if the entire SWNT is breathing. There are two significant features associated with this particular SWNT Raman band in connection with their structural and electronic properties. The first is the inverse relationship between the RBM frequency and SWNT diameter expressed in Eq. (4):

$$
\omega\_{\text{RBM}} = \frac{A}{d\_t} \tag{4}
$$

Similar to Eq. (1) this relation is also based on continuum elasticity theory. Since the original work done on this relationship was based on individual SWNTs of the kind typically produced via the super-growth method, further work by various groups led to Eq. (5), which is an extension of the prior equation that accounts for environmental perturbations of the RBM, especially on SWNTs in macroscopic bundled samples [4]:

Raman Spectroscopy of Graphitic Nanomaterials http://dx.doi.org/10.5772/intechopen.72769 163

$$
\omega\_{\rm RBM} = \frac{227}{d\_t} \sqrt{1 + \mathcal{C}\_\epsilon d\_t^2} \tag{5}
$$

The overall environmental contribution to the RBM shift is contained in the fitted constant Ce, which is unique to SWNTs produced by any of the various available techniques. In the case of SWNTs produced by the HiPCO technique used in our studies, Ce was determined to have a value of 0.05 [4].

4. Raman spectra of single-walled carbon nanotubes (SWNTs)

A1 denoted as G+ and G� at ~1590 and ~1560 cm�<sup>1</sup>

version of Tuinstra and Koenig's original analysis [9]:

especially on SWNTs in macroscopic bundled samples [4]:

these two peaks with diameter is given by [4]:

~1580 cm�<sup>1</sup>

162 Raman Spectroscopy

The current section is an overview of the Raman active modes of SWNTs. The current treatment is meant only to preview the Raman bands and features relied on most heavily during the authors' characterization of SWNT samples. The first of the Raman bands featured in this section is the G-band, so called since it is common to all sp2 nanocarbons, centered at

Interestingly due to the induced strain from the curvature of SWNT walls the G-band for these structures is split into several peaks, with the two most prominent ones being the symmetric

ω<sup>G</sup> ¼ 1591 þ

where dt is the nanotube diameter, and the value C corresponding to the G� band for semiconducting and metallic nanotubes respectively are 47.7 and 79.5 cm�<sup>1</sup> nm. The above relation is derivable solely from a careful application of elasticity theory to SWNTs [4]. The later discussion of the use of the temperature variation of the G+ band in connection with thermal

Next, the Raman band at around 1300–1350 cm�<sup>1</sup> is the D-Band, which has been shown in [9] to be associated with any defects or departures from perfect regularity in the sp<sup>2</sup> graphite lattice. Equation (3) shows the variation of typical crystallite sizes La with the Raman laser excitation energy, and ratio of the intensity of the D-band and G-band, based on a more recent

> 560 E4 laser

The final Raman band featured in this section, the radial breathing mode is only present carbon nanotube spectra, and is therefore used as an indication of their presence in sp<sup>2</sup> Carbon samples. As implied by its name the intra-planar displacement of the C-atoms in this Raman active mode is effectively in the radial direction of the resultant SWNT, as if the entire SWNT is breathing. There are two significant features associated with this particular SWNT Raman band in connection with their structural and electronic properties. The first is the inverse

> <sup>ω</sup>RBM <sup>¼</sup> <sup>A</sup> dt

Similar to Eq. (1) this relation is also based on continuum elasticity theory. Since the original work done on this relationship was based on individual SWNTs of the kind typically produced via the super-growth method, further work by various groups led to Eq. (5), which is an extension of the prior equation that accounts for environmental perturbations of the RBM,

ID IG � ��<sup>1</sup>

!

conductivity is based on a time-dependent perturbation of the G+ Raman band.

Lað Þ¼ nm

relationship between the RBM frequency and SWNT diameter expressed in Eq. (4):

. This high energy band is a consequence of the in-plane C-C bond stretching.

C d2 t

, respectively. The variation of the smaller of

(2)

(3)

(4)

The second critical feature associated with the RBM band is its role in expressing the link between the quasi 1-dimensional electronic behavior and structure of SWNTs. The phenomenon referred to above is the resonant character of the Raman spectra of SWNTs, in which the intensity of Raman scattering from a SWNT is increased many fold when the laser excitation energy is very near that of an optical transition. Figure 5 shows the density of states for a representative metallic and semi-conducting single-walled carbon nanotube, respectively, and

Figure 5. Electronic density of states for a metallic and semi conducting SWNT shows two transitions labeled, E11 and E22, between the corresponding valence and conduction bands.

shows two such transitions, labeled E11 and E22, between the corresponding valence and conduction bands (adapted from [3]).

These sharp divergences between the optical transitions are known as van Hove singularities. Such singularities arise from the form of the density of states expression for a 1-dimensional sample as indicated in Eq. (6), which is derived for the simple free electron gas model [3]:

$$\log(E) = \begin{cases} \frac{1}{H} \sqrt{\frac{2 \cdot m}{E - E\_0}} & E > E\_0 \\ 0, & E \le E\_0 \end{cases} \tag{6}$$

Figure 6. Theoretical Kataura plot for metallic SWNTs. The three horizontal lines from top to bottom represent respectively, the 455, 532, and 780 nm laser excitation wavelengths used on the SWNT sample. The intersection of the horizontal lines with the Kataura plot at any of the diameters obtained from the radial breathing modes help to identify possible

Raman Spectroscopy of Graphitic Nanomaterials http://dx.doi.org/10.5772/intechopen.72769 165

Figure 7. Theoretical Kataura plot for type 1 semi conducting SWNTs. The three horizontal lines from top to bottom represent respectively, the 455, 532, and 780 nm laser excitation wavelengths used on the SWNT sample. The intersection of the horizontal lines with the Kataura plot at any of the diameters obtained from the radial breathing modes help to

identify possible chiralities in the sample. The Kataura plot data was obtained from Saito et al. [5].

chiralities in the sample. The Kataura plot data was obtained from K. Saito, et al. [5].

The density of states of the electrons and holes in SWNTs shows the two most significant characteristics of Eq. (6), namely the inverse square root variation with energy, and the van Hove divergences at energies close to the Fermi level E0. Kataura [4] made arguably one of the most significant contributions to both the theoretical description and practical use of these resonance Raman effects with the introduction of the so-called Kataura Plot in 1999. These plots of nanotube diameter or RBM frequency vs. optical transition energy Eii, which are now in common use for the identification of the chiralities present in a SWNT sample, are possible due to the Eii values' inverse dependence to SWNT diameter. The use of a theoretically derived Kataura plot for (n, m) identification begins the following section discussing our actual use of Raman spectral data in SWNT sample characterization.
