**4.5. Calculation of Raman-active modes in C70 peapods**

In this section, we review the theoretical Raman spectra of the C70 peapods calculated as a function of diameter and C70 filling rate. These calculations support the experimental

**Figure 8.** Calculated ZZ-polarized Raman spectra of C60@(28,0) (bottom) and C60@(29,0) (top) as a function of the filling rate and displayed in the BLM region. From bottom to top, the filling rate is: 20, 40, 60, 80, and 100%.

evidence on the C70 orientations as a function of the SWCNT diameters, and they address new questions as to the influence of the nanotube chirality and the C70 filling rate.

#### *4.5.1. Diameter effects*

*4.4.2. Filling rate effect*

84 Fullerenes and Relative Materials - Properties and Applications

range is not shown.

increases when the filling factor increases.

**4.5. Calculation of Raman-active modes in C70 peapods**

In real carbon peapod samples, it is reasonable to consider that all the nanotubes are not completely filled with fullerenes. The degree of filling ranges from a certain percent to almost 100% [6]. In the following paragraphs, we discuss the main features of the filling rate effect on both configurations of C60 inside SWCNT, double helix, and two-molecule layer. We assume that the molecules tend to cluster inside nanotubes. Indeed, this should correspond to a low energy configuration of the system as the energy is lowered by the attractive C60-C60 interactions. The filling factor is defined as the number of carbon atoms of C60 molecules contained in the h length with regard to the number of carbon atoms contained in the H length of the host tube normalized with the concentration related to the filling factor of 100% (see **Figure 7b**). The calculated ZZ-polarized Raman spectra of the C60@(28,0) (double helix chain of C60) and C60@(29,0) (two-molecule layer) peapods are reported in **Figure 8** as a function of five filling rates (20, 40, 60, 80, and 100%). Where the RBLM range is very sensitive to filling rate and the TLM range slightly depends on the degree of filling of the SWCNT, the TLM

For both configurations, a single PRBLM is predicted whatever the tube filling. For the empty tubes, the RBM is located at 102 and 98 cm−1 for the (28,0) and (29,0) SWCNTs, respectively. For a high filling level, it is upshifted at 103 and 100 cm−1 in the C60@(28,0) and C60@(29,0) peapods, respectively. As expected, the intensity of the Hg(1) line located at 270 cm−1 in C60

In this section, we review the theoretical Raman spectra of the C70 peapods calculated as a function of diameter and C70 filling rate. These calculations support the experimental

**Figure 8.** Calculated ZZ-polarized Raman spectra of C60@(28,0) (bottom) and C60@(29,0) (top) as a function of the filling

rate and displayed in the BLM region. From bottom to top, the filling rate is: 20, 40, 60, 80, and 100%.

In order to investigate how the frequency of the Raman-active mode in C70@SWCNT changes when the C70 molecule adopts various orientations, and three zigzag SWCNTs have been considered with a diameter of 1.330 [(17,0)], 1.409 [(18,0)], and 1.487 nm [(19,0)] where C70 molecules adopt lying, tilted, and standing orientation, respectively. The calculated ZZ-polarized Raman spectra of C70 peapods are shown in **Figure 9** along with their corresponding unfilled nanotubes and the unoriented C70 molecule. Raman lines can be divided into three frequency ranges: (1) below 500 cm−1 where the breathing-like modes (BLM) dominate (panel A), (2) an intermediate range between 500 and 1500 cm−1 (panel B), and (3) above 1500 cm−1 where the tangential-like modes (TLM) are located (panel C).

In the TLM range, the main modes of SWCNT are almost not significantly sensitive to the orientation of C70 molecules inside the nanotube. In the intermediate range, the C70 spectrum is dominated by two strong lines at 1192 and 1253 cm−1, while no Raman line is expected for SWCNTs. Thus, Raman spectra of peapods show several weak lines which originate from the splitting of the C70 degenerate modes due to van der Waals interactions. In this range, Raman spectra of peapods are dominated by two lines around 740 and 1272 cm−1. A third line can also be identified at 1391 cm−1 for the standing orientation and at 1490 cm−1 for lying and tilted orientations.

**Figure 9.** ZZ-calculated Raman spectra of C70 peapods along with their corresponding unfilled nanotubes and unoriented free C70 molecule. Spectra are displayed in the BLM (A), intermediate (B), and TLM (C) ranges.

#### *4.5.2. Filling factor effects*

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.

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

Structural and Vibrational Properties of C60 and C70 Fullerenes Encapsulating Carbon Nanotubes

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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.

function of the C60 and C70 fullerenes concentrations.

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 increases.
