**4.6. Raman spectra analysis: C60 and C70 concentration determination in peapods**

The evolution of the nonresonant Raman scattering intensity ratios between the Raman mode of fullerene peas and nanotubes as a function of the fullerene concentration inside the tubes has been investigated in the framework of the spectral moment's method [21, 50]. Although the nonresonant approach cannot predict the variation of the line intensities with the excitation energies, the obtained predictions are useful to follow their evolution as a function of the filling rate of fullerenes inside SWCNT. For this purpose, we performed an average of

**Figure 10.** ZZ-polarized Raman spectra of infinite peapods displayed in the BLM region as a function of the filling factor: F = 20, 40, 60, 80, and 100% from bottom to up.

the Raman spectra over the peapod orientations with regard to the laboratory frame. Raman spectra are calculated in the VV configuration for unoriented peapod samples for various values of the fullerene filling factor. The relative intensity ratios have been calculated as a function of the C60 and C70 fullerenes concentrations.

*4.5.2. Filling factor effects*

86 Fullerenes and Relative Materials - Properties and Applications

increases.

To investigate the effect of incomplete filling rate on Raman spectra of C70 peapod, we considered three kinds of peapods: the C70@(17,0) lying, C70@(17,3) tilted, and C70@(11,11) standing orientations. The spectra were calculated for five values of the filling factor F = 20, 40, 60, 80, and 100% corresponding to 2, 4, 8, 12, and 16 C70 molecules inside SWCNTs, respectively (see **Figure 10**). Periodic conditions were applied along the tube axis to avoid finite size effects.

As expected, the filling level of C70 molecules inside the SWCNTs has no significant effect on the Raman spectrum in the TLM range (not shown). In contrast, in the BLM range, the Raman spectra are quite sensitive to the filling factor: an upshift of approximately 2–5 cm−1 is obtained for the RBM modes in standing orientations when F increases up to 100%, whereas a splitting of these modes is observed in the lying and tilted orientations. This splitting is in agreement with experimental results of Bandow et al. [8]. For example, for lying orientation (small diameters), the increase of the filling factor from 0 to 100% leads to the appearance of two lines at frequencies close to 168 and 175 cm−1. Their intensity shifts from the one located around 168 cm−1 to that located around 175 cm−1 as the filling factor

**4.6. Raman spectra analysis: C60 and C70 concentration determination in peapods**

The evolution of the nonresonant Raman scattering intensity ratios between the Raman mode of fullerene peas and nanotubes as a function of the fullerene concentration inside the tubes has been investigated in the framework of the spectral moment's method [21, 50]. Although the nonresonant approach cannot predict the variation of the line intensities with the excitation energies, the obtained predictions are useful to follow their evolution as a function of the filling rate of fullerenes inside SWCNT. For this purpose, we performed an average of

**Figure 10.** ZZ-polarized Raman spectra of infinite peapods displayed in the BLM region as a function of the filling factor:

F = 20, 40, 60, 80, and 100% from bottom to up.

First, for C60 peapod, we calculated the intensity ratio between the Raman lines of the C60 molecule [Hg(2), Ag(1), Hg(3), Hg(4), Hg(7), and Ag(2)] and the PRBLM or G-mode. In order to make the comparison with the experimental results of Kuzmany et al. [12], the calculated intensity ratio is normalized with respect to the same intensity ratio calculated for the 60% filling factor sample. The relative C60 concentrations that are derived according to this procedure are displayed in **Figure 11** for the C60@(17,0), C60@(22,0), C60@(28,0), and C60@(29,0) which correspond to linear, zigzag, double-helix, and two molecule layers chain of C60, respectively. As expected, for all the investigated peapod diameters, the relative concentrations calculated for each C60 mode are close. The relative concentrations calculated for infinite peapods increase when its diameter increases. For instance, for a filling factor ∼20%, the relative concentration is close to 0.21, 0.26, 0.3, and 0.4 for a diameter of 1.35 [C60@(17,0)], 1.76 [C60@(22,0)], 2.19 [C60@ (28,0)], and 2.27 nm [C60@(29,0)], respectively. For a ∼ 20% concentration (corresponding to the L43 sample (EELS concentration 25 ± 10) in [12]), the average relative concentration is

**Figure 11.** Relative concentration of several configurations of C60 inside SWCNTs and C70@(10,10) normalized on the 60% filling rate intensities.

calculated around 0.21 ± 0.02, in good agreement with the experimental relative concentration evaluated around 0.19. This good agreement supports the experimental method proposed by Kuzmany et al. to evaluate C60 concentration inside SWCNTs.

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Next, we calculate the integrated intensity ratios between the Raman lines of the C70 molecule [low-frequency modes located at: A1': 252 cm−1 (A1'(1), A1': 391 cm−1 (A1'(2)), A1': 451 cm−1 (A1'(3)) and high-frequency Raman modes: A1': 1473 cm−1 (A1'(4)), E1": 1512 cm−1 (E1"(1)) and A1': 1583 cm−1 (A1'(5))] and the PRBLM or G-mode. The relative concentrations derived by this way are shown in **Figure 11**. For a filling factor 20%, the relative concentration is close to 0.21 for C70 inside (10,10). The comparison of data of the relative concentration of C60 (linear chain) with those of C70 (lying orientation) shows qualitatively the same result.
