*4.4.1. Diameter dependence of the Raman spectrum of C60 peapods*

C60 confined into a (10,10) SWCNT (tube diameter close to 1.36 nm), (top) zigzag chain of

In the intermediate and high-frequency regions, the calculated Raman spectra of individual peapods organized into infinite bundles do not show significant differences. It can be emphasized that a splitting of the Ag(1) and Ag(2) totally symmetric C60 modes was observed experimentally [45]. This splitting was considered as signature of the mobility of some encapsulated C60 molecules inside nanotubes [45]. In our calculations, the C60 molecules are kept at fixed positions in the considered peapods, and no splitting of the totally symmetric C60 modes is

Next, we show in **Figure 6b** the low-frequency range of Raman spectra of C60@(10,10) and C60@(13,13) peapods where the main changes are identified. We found that the PRBLM of individual C60@(10,10) linear peapod on one hand and the PRBLM(1) and PRBLM(2) of individual C60@(13,13) zigzag peapod on the other hand are slightly upshifted in bundles of C60@ (10,10) peapods and C60@(13,13) peapods, respectively. We calculated a shift of the RBLM from 170 cm−1 in the individual C60@(10,10) peapod to 186 cm−1 in the infinite bundle of C60@ (10,10) peapods. In the case of C60@(13,13), the PRBLM(1) and PRBLM(2) doublet calculated

**Figure 6.** The ZZ calculated Raman spectra of individual (curve (a)) and homogeneous bundles (curve (b)) of C60@(13,13) (top) and C60@(10,10) (bottom) (filling factor 100%). The stars give the positions of the RBM and RBLM in individual SWCNT and crystal of SWCNT, respectively. Cross indicates the frequency of Bundle Breathing Like-Mode (BBLM) in crystal of SWCNT. (left) Breathing modes range, (middle) region of the radial C60 modes, (right) range of tangential

modes: Ag(2) mode of C60 and G-modes of the nanotubes.

C60 confined into a (13,13) SWCNT (tube diameter close to 1.76 nm).

82 Fullerenes and Relative Materials - Properties and Applications

found.

**Figure 7** shows the PRBLM and PBBLM frequency dependencies as a function of the tube diameter. These dependencies are first compared with those of the RBLM and BBLM in unfilled bundles of tubes. The behavior of the PRBLM in linear peapods is qualitatively the same as those of RBLM in SWCNT bundle. However, the PRBLM frequency versus diameter relation deviates from the scaling law stated for the RBLM frequency in SWCNT bundle, especially for small diameters. For zigzag peapod, the PRBM(1) dependence as a function of the diameter is close to that of the RBLM in bundle of SWCNT. The PRBLM(1) downshifts when the tube diameter increases. Concerning the PBBLM frequency, it decreases with increasing the tube diameter and close to the frequency of BBLM, except at small diameters where a more significant increase of the PBBLM frequency is calculated. Our calculations based on DFT have clarified that the shift in the RBM frequencies of nanotubes containing fullerenes strongly depends on the diameters of the nanotubes. DFT calculations have also clarified that the shift in the RBM frequencies of nanotubes containing fullerenes strongly depends on the diameters of the nanotubes [51, 53–57].

More recently, Raman calculations are extended to a larger range of diameters in which C<sup>60</sup> molecules can adopt a double helix and a layer of two molecules [22].

**Figure 7.** Diameter dependence of the frequencies of PRBLM (for d < Dc = 1.45 nm) and PRBLM(1) (for d > Dc) (stars), and PRBLM(2) (cross). Diameter dependence of the frequency of RBLM (open circles) and BBLM (open diamonds) in bundles of SWCNTs. The critical diameter Dc between linear (tube diameters lower than Dc) and zigzag (tube diameters greater than Dc) peapods is identified by the vertical-dashed line. (b) Schematic representation of homogeneous filling mode of the different tubes within a bundle. The filling factor is related to the ratio *h* ⁄ *H* (see text).

#### *4.4.2. Filling rate effect*

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 range is not shown.

evidence on the C70 orientations as a function of the SWCNT diameters, and they address

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

http://dx.doi.org/10.5772/intechopen.71246

85

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

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

**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.

new questions as to the influence of the nanotube chirality and the C70 filling rate.

*4.5.1. Diameter effects*

orientations.

tangential-like modes (TLM) are located (panel C).

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 increases when the filling factor increases.
