5. Raman spectral SWNT characterization

#### 5.1. Kataura plot analysis

The discussion of Section 4 means that in Raman spectra from bundled SWNTs, which is the case in this research, the majority of the signal comes from those tubes in the sample with diameters that are resonant with the excitation wavelength [4]. Therefore, this makes Kataura plots extremely useful in identifying the possible chiral indices contained in any SWNT samples one may be working with. Displayed in Figures 6–8, and Table 1, are the theoretical Kataura plots and Raman spectral data that were used to identify the chiralities present in one of the SWCNT samples used in the present study.

#### 5.2. Thermal expansion

In this section, we discuss the effect of temperature on the Raman vibrational modes of SWNTs and subsequent use of this valuable effect in obtaining an estimate of the thermal expansion for one of the SWNT samples used in the present study [10].

Considering the phonon frequency ω(V, T) as a function of volume V, and temperature T, the derivatives of this quantity with respect to pressure and volume can be connected to each other via the equations

shows two such transitions, labeled E11 and E22, between the corresponding valence and

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]:

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 m E � E<sup>0</sup>

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

The discussion of Section 4 means that in Raman spectra from bundled SWNTs, which is the case in this research, the majority of the signal comes from those tubes in the sample with diameters that are resonant with the excitation wavelength [4]. Therefore, this makes Kataura plots extremely useful in identifying the possible chiral indices contained in any SWNT samples one may be working with. Displayed in Figures 6–8, and Table 1, are the theoretical Kataura plots and Raman spectral data that were used to identify the chiralities present in

In this section, we discuss the effect of temperature on the Raman vibrational modes of SWNTs and subsequent use of this valuable effect in obtaining an estimate of the thermal expansion for

Considering the phonon frequency ω(V, T) as a function of volume V, and temperature T, the derivatives of this quantity with respect to pressure and volume can be connected to each other

, E > E<sup>0</sup>

(6)

0, E ≤ E<sup>0</sup>

1 h

8 < : r

g Eð Þ¼

Raman spectral data in SWNT sample characterization.

5. Raman spectral SWNT characterization

one of the SWCNT samples used in the present study.

one of the SWNT samples used in the present study [10].

5.1. Kataura plot analysis

5.2. Thermal expansion

via the equations

conduction bands (adapted from [3]).

164 Raman Spectroscopy

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

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].

∂ω ∂V 

∂ω ∂V 

<sup>d</sup><sup>ω</sup> <sup>¼</sup> <sup>∂</sup><sup>ω</sup> ∂V 

where BT is the isothermal bulk modulus which equals BT ¼ �<sup>V</sup> <sup>∂</sup><sup>P</sup>

which after dividing through by dT at constant pressure yields

increases with temperature, namely thermal expansion.

purified Hipco sample requires further examination.

∂ω ∂T 

P

<sup>¼</sup> <sup>∂</sup><sup>ω</sup> ∂T 

and

25-micron slit.

T

T

<sup>¼</sup> <sup>∂</sup><sup>ω</sup> ∂P 

¼ � BT V 

between the temperature derivatives at fixed volume and pressure are obtained by writing

T dV þ

> V þ

Equation (10) gives a breakdown of the measurable temperature variation of the phonon frequency on the left in terms of two contributions. The first term on the right represents the intrinsic, purely thermal contribution to the lowering of the phonon frequency caused by the anharmonic intermixing of the various phonon modes [12]. The second term, often referred to as the "pure volume" effect, represents the induced phonon shift to lower frequency with temperature due to a reduction in the bonds' force constants brought about by typical volume

The laser excitation wavelength used to obtain the Raman data for the purified Hipco produced sample was 780 nm with a 6 mW power setting. Some other collection parameters associated with this sample were an exposure time of 10.0 s during each of the 3 exposures for each recorded Raman spectrum. Lastly, the aperture setting used for the entrance slit was a

Similarly, for the second SWNT sample, the laser power setting for the heated Raman spectra was 6 mW, but this time with 532 nm excitation. A larger entrance slit aperture, 50 microns in width was used, in addition to the exposure time and number of exposures for the Raman spectra at each temperature being 10.0 s and 6 respectively. It must be noted that there is an unexpected "kink" or change in slope in Figures 9 and 10 at approximately 350 K temperature for all of the Raman bands. This phenomenon which is more noticeable in Figure 9 for the

Figures 9 and 10 show the results of our reproduction [10] of the linear downshift of the primary first order Raman frequencies with temperature for two SWNT samples, along with each sample's corresponding Scanning Electron Microscopy (SEM) images. The linearity of

T

T

∂ω ∂T 

∂V ∂T 

P

∂ω ∂V 

T

V

∂P ∂V 

> ∂ω ∂P

T

T

∂V  (7)

167

(8)

(10)

<sup>T</sup> [11]. Next, a connection

dT (9)

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

Figure 8. Theoretical Kataura plot for type 2 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].


Table 1. Identification of metal type, type 1 semiconducting and type 2 semiconducting chiral indices in SWNT samples using Kataura plots.

Raman Spectroscopy of Graphitic Nanomaterials http://dx.doi.org/10.5772/intechopen.72769 167

$$
\left(\frac{\partial \omega}{\partial V}\right)\_T = \left(\frac{\partial \omega}{\partial P}\right)\_T \left(\frac{\partial P}{\partial V}\right)\_T \tag{7}
$$

and

Figure 8. Theoretical Kataura plot for type 2 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

Table 1. Identification of metal type, type 1 semiconducting and type 2 semiconducting chiral indices in SWNT samples

using Kataura plots.

166 Raman Spectroscopy

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

$$
\left(\frac{\partial\omega}{\partial V}\right)\_T = -\left(\frac{B\_T}{V}\right)\_T \left(\frac{\partial\omega}{\partial P}\right)\_T \tag{8}
$$

where BT is the isothermal bulk modulus which equals BT ¼ �<sup>V</sup> <sup>∂</sup><sup>P</sup> ∂V <sup>T</sup> [11]. Next, a connection between the temperature derivatives at fixed volume and pressure are obtained by writing

$$d\omega = \left(\frac{\partial \omega}{\partial V}\right)\_T dV + \left(\frac{\partial \omega}{\partial T}\right)\_V dT \tag{9}$$

which after dividing through by dT at constant pressure yields

$$
\left(\frac{\partial\omega}{\partial T}\right)\_P = \left(\frac{\partial\omega}{\partial T}\right)\_V + \left(\frac{\partial V}{\partial T}\right)\_P \left(\frac{\partial\omega}{\partial V}\right)\_T \tag{10}
$$

Equation (10) gives a breakdown of the measurable temperature variation of the phonon frequency on the left in terms of two contributions. The first term on the right represents the intrinsic, purely thermal contribution to the lowering of the phonon frequency caused by the anharmonic intermixing of the various phonon modes [12]. The second term, often referred to as the "pure volume" effect, represents the induced phonon shift to lower frequency with temperature due to a reduction in the bonds' force constants brought about by typical volume increases with temperature, namely thermal expansion.

The laser excitation wavelength used to obtain the Raman data for the purified Hipco produced sample was 780 nm with a 6 mW power setting. Some other collection parameters associated with this sample were an exposure time of 10.0 s during each of the 3 exposures for each recorded Raman spectrum. Lastly, the aperture setting used for the entrance slit was a 25-micron slit.

Similarly, for the second SWNT sample, the laser power setting for the heated Raman spectra was 6 mW, but this time with 532 nm excitation. A larger entrance slit aperture, 50 microns in width was used, in addition to the exposure time and number of exposures for the Raman spectra at each temperature being 10.0 s and 6 respectively. It must be noted that there is an unexpected "kink" or change in slope in Figures 9 and 10 at approximately 350 K temperature for all of the Raman bands. This phenomenon which is more noticeable in Figure 9 for the purified Hipco sample requires further examination.

Figures 9 and 10 show the results of our reproduction [10] of the linear downshift of the primary first order Raman frequencies with temperature for two SWNT samples, along with each sample's corresponding Scanning Electron Microscopy (SEM) images. The linearity of this trend is due to the dominance of the "purely temperature" effect's contribution over that of the contribution from thermal expansion as was noted in [13] and [14], where the latter authors were able to separate each of the two contributions' effects on graphite.

The temperature effect dominance of the phonon frequency downshift mentioned above also manifests itself in the empirical polynomials usually used to express experimental data associ-

In the reported values of the temperature redshift of Raman frequencies throughout the literature the second-order term a2 is often negligible compared to its first order counterpart a1, resulting in a primarily linear trend that was caused mainly by thermal effects not associ-

We now present our results of the use of Resonant Raman Spectroscopy to determine the volume coefficient of thermal expansion (CTE) behavior of the second SWNT sample obtained through the use of the temperature shifted radial breathing mode band. The technique used to determine the volume CTE β, is the same as that used by Espinosa-Vega et al. [15]. Figure 11 shows the variation with temperature of the fractional volume change of the resonant SWNTs associated with the sole radial breathing mode band of 166.0 cm�<sup>1</sup> that was present in our spectra. The resulting volume thermal expansion coefficient β, and the same results from [15] are also displayed in Figure 11. Based on the premise of the bundled SWNTs being arranged in the sample as circular cylinders of equal length, which was the same assumption made by Espinosa-Vega et al. [15], we obtained the volume at each temperature using the previously

Figure 11. Temperature variation of the fractional change in volume and the volume thermal expansion obtained from

the radial breathing mode Raman band (left). Corresponding data are from Espinosa-Vega et al. [15] (right).

<sup>ω</sup>ð Þ¼ <sup>T</sup> <sup>ω</sup><sup>0</sup> <sup>þ</sup> <sup>a</sup>1<sup>T</sup> <sup>þ</sup> <sup>a</sup>2T<sup>2</sup> (11)

Raman Spectroscopy of Graphitic Nanomaterials http://dx.doi.org/10.5772/intechopen.72769 169

ated with this phenomenon, such as the example in Eq. (11):

ated with volumetric changes as discussed above.

discussed relationship between ωRBM and tube diameter:

Figure 9. Top left: Scanning electron microscopy (SEM) image of HipCO produced SWNT sample; top right: Variation with temperature of the first order RBM vibration; bottom left: G Raman band and bottom right: G+ Raman band of a SWNT sample heated externally with the Ventacon heat cell. A 780-nm wavelength laser excitation was used for recording the Raman spectra on this HipCO produced sample.

Figure 10. SEM image of SWNT sample (top left); temperature variation of the first order Raman RBM (top right), G band (bottom left), and G<sup>+</sup> band (bottom right), with temperature of a SWNT sample heated externally with the Ventacon heat cell. 532 nm laser excitation was used for recording the Raman spectra.

The temperature effect dominance of the phonon frequency downshift mentioned above also manifests itself in the empirical polynomials usually used to express experimental data associated with this phenomenon, such as the example in Eq. (11):

this trend is due to the dominance of the "purely temperature" effect's contribution over that of the contribution from thermal expansion as was noted in [13] and [14], where the latter

Figure 10. SEM image of SWNT sample (top left); temperature variation of the first order Raman RBM (top right), G band (bottom left), and G<sup>+</sup> band (bottom right), with temperature of a SWNT sample heated externally with the Ventacon

Figure 9. Top left: Scanning electron microscopy (SEM) image of HipCO produced SWNT sample; top right: Variation with temperature of the first order RBM vibration; bottom left: G Raman band and bottom right: G+ Raman band of a SWNT sample heated externally with the Ventacon heat cell. A 780-nm wavelength laser excitation was used for recording

heat cell. 532 nm laser excitation was used for recording the Raman spectra.

the Raman spectra on this HipCO produced sample.

168 Raman Spectroscopy

authors were able to separate each of the two contributions' effects on graphite.

$$
\omega(T) = \omega\_0 + a\_1 T + a\_2 T^2 \tag{11}
$$

In the reported values of the temperature redshift of Raman frequencies throughout the literature the second-order term a2 is often negligible compared to its first order counterpart a1, resulting in a primarily linear trend that was caused mainly by thermal effects not associated with volumetric changes as discussed above.

We now present our results of the use of Resonant Raman Spectroscopy to determine the volume coefficient of thermal expansion (CTE) behavior of the second SWNT sample obtained through the use of the temperature shifted radial breathing mode band. The technique used to determine the volume CTE β, is the same as that used by Espinosa-Vega et al. [15]. Figure 11 shows the variation with temperature of the fractional volume change of the resonant SWNTs associated with the sole radial breathing mode band of 166.0 cm�<sup>1</sup> that was present in our spectra. The resulting volume thermal expansion coefficient β, and the same results from [15] are also displayed in Figure 11. Based on the premise of the bundled SWNTs being arranged in the sample as circular cylinders of equal length, which was the same assumption made by Espinosa-Vega et al. [15], we obtained the volume at each temperature using the previously discussed relationship between ωRBM and tube diameter:

Figure 11. Temperature variation of the fractional change in volume and the volume thermal expansion obtained from the radial breathing mode Raman band (left). Corresponding data are from Espinosa-Vega et al. [15] (right).

$$
\omega\_{RBM} = \frac{A}{d\_t} + B \tag{12}
$$

SWNT content. In other words, the slope depends on sample "purity," where samples with less purity exhibit larger/steeper slope variations in contrast with high purity samples composed almost entirely of SWNTs. Since additional analysis performed by Terekhov et al. [1] also show that the slope rate of change of the G+ band with increased laser power is inversely proportional to thermal conductivity κ, using this method allows one to estimate the thermal conductivity of a SWNT sample by simply taking the ratio of the experimentally determined slope variation and an accepted literature value of the thermal conductivity of amorphous Graphite. Figure 12 shows our reproduction of the above described effect on two SWNT samples (also pictured in the figure) of differing purity, with the less pure sample indeed exhibiting a greater

HipCO SWNT sample on the left contains ~8% residual catalyst material.

Figure 12. Variation of the G<sup>+</sup> Raman band of SWNT samples of differing purity levels. (top left) data from Terekhov, S.V., et al., AIP Conference Proceedings, (685), 2003, where the percentages indicate the estimated amount of actual carbon nanotubes present in the sample. (Top right) Our data for the two SWNT samples imaged below. The higher purity

Raman Spectroscopy of Graphitic Nanomaterials http://dx.doi.org/10.5772/intechopen.72769 171

rate of decline of the Raman G<sup>+</sup> band with increased laser power at the sample spot.

6. Temperature and gas exposure effects on graphene Raman spectra

The Raman spectra of graphene were also recorded at varying temperatures (30–200C) using the Ventacon heated cell and the 780-nm laser with the DXR Raman spectrometer. The graphene samples were all on a silicon/SiO2 substrate and subjected to consecutive heating/ cooling cycles between 30 and 200C in a sealed chamber. Figure 13 is the spectrum collected at 30C. As discussed earlier, the G-band at 1598 cm<sup>1</sup> originates from intraplanar stretching, while the peak at 2703 cm<sup>1</sup> corresponds to the 2D band. The latter band is due to a secondorder two-phonon process that is highly dispersive. It was discovered that this band can be

The respective values for A and B of 248.0 cm�<sup>1</sup> �nm and 10.0 cm�<sup>1</sup> were used by Espinosa-Vega et al. [15].

The linear temperature dependence of the volume coefficient of thermal expansion (CTE) β was then obtained as shown in Figure 11 with Espinosa-Vega's data on the right for comparison. According to [12], both the fractional volume data and subsequent linear trend in β led to the conclusion that the temperature dependence of the volume varied as e<sup>c</sup>þbTþaT<sup>2</sup> . The resulting values for the parameters a, b, and c from our model were �1.46 � <sup>10</sup>�<sup>6</sup> , 0.00125142, and �0.245 respectively. The linear downshift in the data for <sup>β</sup> goes from 0.2 � <sup>10</sup>�<sup>6</sup> to �0.5 � <sup>10</sup>�<sup>7</sup> <sup>K</sup>�<sup>1</sup> , with a slope of �1.6 � <sup>10</sup>�<sup>9</sup> <sup>K</sup>�<sup>2</sup> , over the experimental temperature range of ~300–473 K. Espinosa-Vega et al.'s data show <sup>β</sup> decreasing from 5.8 � <sup>10</sup>�<sup>6</sup> to 4.7 � <sup>10</sup>�<sup>6</sup> <sup>K</sup>�<sup>1</sup> over a larger temperature range of 300–875 K [15].

Espinosa-Vega et al.'s Raman spectra were obtained in a nitrogen atmosphere, whereas ours were collected under open air ambient conditions. This is why the Espinosa-Vega experiment was allowed to operate at the very high (maximum) temperature of 875 K before the onset of any irreversible changes to the Raman spectrum frequencies, such as the loss of intensity brought about by the thermal deterioration of the SWNTs. The smaller values of the temperature slope values Δω/ΔT obtained in the nitrogen atmosphere, as opposed to in open air, also meant that Espinosa-Vega et al.'s SWCNTs had a greater thermal stability [15].

Another possible reason for Espinosa-Vega et al.'s β values being much greater than ours was that their experiment was performed on SWNT samples at a much lower density, possibly even at the individual level, due to the pre-processing they performed on their samples. They initially formed a dispersion of their SWNTs with benzene, which was then annealed on a Silicon surface before any Raman spectra were done. The Raman measurements in the present study, however, were all performed on macroscopic bundled samples where van der Waals interactions among the individual tubes were a significant factor. Espinosa-Vega et al. also provided data on the linear decrease of the volume CTE for SWNTs in ambient air, which ranged from 3.3 � <sup>10</sup>�<sup>6</sup> to 2.7 � <sup>10</sup>�<sup>6</sup> <sup>K</sup>�<sup>1</sup> again over the operating temperature range of 300– 875 K. Although, their volume CTE values are still larger, the decrease from their values associated with their experiments done in a nitrogen atmosphere support our earlier suggestion of our lower values of β(T) being due in part to the lower thermal stability of the SWNTs under ambient air conditions.

#### 5.3. Thermal conductivity

We conclude this section dealing with SWNT properties of interest obtainable via Resonant Raman spectroscopy, with a discussion on obtaining an estimate of sample thermal conductivity. The method used was developed by Terekhov et al. [1], who show that there is a demonstrable correlation between the slope of the variation of the G+ Raman band with increasing laser power at the sample spot for SWNT samples containing different percentages of true

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

The linear temperature dependence of the volume coefficient of thermal expansion (CTE) β was then obtained as shown in Figure 11 with Espinosa-Vega's data on the right for comparison. According to [12], both the fractional volume data and subsequent linear trend in β led to the conclusion that the temperature dependence of the volume varied as e<sup>c</sup>þbTþaT<sup>2</sup>

and �0.245 respectively. The linear downshift in the data for <sup>β</sup> goes from 0.2 � <sup>10</sup>�<sup>6</sup> to

of ~300–473 K. Espinosa-Vega et al.'s data show <sup>β</sup> decreasing from 5.8 � <sup>10</sup>�<sup>6</sup> to 4.7 � <sup>10</sup>�<sup>6</sup> <sup>K</sup>�<sup>1</sup>

Espinosa-Vega et al.'s Raman spectra were obtained in a nitrogen atmosphere, whereas ours were collected under open air ambient conditions. This is why the Espinosa-Vega experiment was allowed to operate at the very high (maximum) temperature of 875 K before the onset of any irreversible changes to the Raman spectrum frequencies, such as the loss of intensity brought about by the thermal deterioration of the SWNTs. The smaller values of the temperature slope values Δω/ΔT obtained in the nitrogen atmosphere, as opposed to in open air, also

Another possible reason for Espinosa-Vega et al.'s β values being much greater than ours was that their experiment was performed on SWNT samples at a much lower density, possibly even at the individual level, due to the pre-processing they performed on their samples. They initially formed a dispersion of their SWNTs with benzene, which was then annealed on a Silicon surface before any Raman spectra were done. The Raman measurements in the present study, however, were all performed on macroscopic bundled samples where van der Waals interactions among the individual tubes were a significant factor. Espinosa-Vega et al. also provided data on the linear decrease of the volume CTE for SWNTs in ambient air, which ranged from 3.3 � <sup>10</sup>�<sup>6</sup> to 2.7 � <sup>10</sup>�<sup>6</sup> <sup>K</sup>�<sup>1</sup> again over the operating temperature range of 300– 875 K. Although, their volume CTE values are still larger, the decrease from their values associated with their experiments done in a nitrogen atmosphere support our earlier suggestion of our lower values of β(T) being due in part to the lower thermal stability of the SWNTs

We conclude this section dealing with SWNT properties of interest obtainable via Resonant Raman spectroscopy, with a discussion on obtaining an estimate of sample thermal conductivity. The method used was developed by Terekhov et al. [1], who show that there is a demonstrable correlation between the slope of the variation of the G+ Raman band with increasing laser power at the sample spot for SWNT samples containing different percentages of true

resulting values for the parameters a, b, and c from our model were �1.46 � <sup>10</sup>�<sup>6</sup>

meant that Espinosa-Vega et al.'s SWCNTs had a greater thermal stability [15].

, with a slope of �1.6 � <sup>10</sup>�<sup>9</sup> <sup>K</sup>�<sup>2</sup>

The respective values for A and B of 248.0 cm�<sup>1</sup>

over a larger temperature range of 300–875 K [15].

Vega et al. [15].

170 Raman Spectroscopy

�0.5 � <sup>10</sup>�<sup>7</sup> <sup>K</sup>�<sup>1</sup>

under ambient air conditions.

5.3. Thermal conductivity

þ B (12)

�nm and 10.0 cm�<sup>1</sup> were used by Espinosa-

, over the experimental temperature range

. The

, 0.00125142,

Figure 12. Variation of the G<sup>+</sup> Raman band of SWNT samples of differing purity levels. (top left) data from Terekhov, S.V., et al., AIP Conference Proceedings, (685), 2003, where the percentages indicate the estimated amount of actual carbon nanotubes present in the sample. (Top right) Our data for the two SWNT samples imaged below. The higher purity HipCO SWNT sample on the left contains ~8% residual catalyst material.

SWNT content. In other words, the slope depends on sample "purity," where samples with less purity exhibit larger/steeper slope variations in contrast with high purity samples composed almost entirely of SWNTs. Since additional analysis performed by Terekhov et al. [1] also show that the slope rate of change of the G+ band with increased laser power is inversely proportional to thermal conductivity κ, using this method allows one to estimate the thermal conductivity of a SWNT sample by simply taking the ratio of the experimentally determined slope variation and an accepted literature value of the thermal conductivity of amorphous Graphite. Figure 12 shows our reproduction of the above described effect on two SWNT samples (also pictured in the figure) of differing purity, with the less pure sample indeed exhibiting a greater rate of decline of the Raman G<sup>+</sup> band with increased laser power at the sample spot.
