**4.4. Raman-active modes calculation in C60 peapods**

low- and high-frequency component associated to the vibrations along the circumferential direction (G−) and the G direction of the nanotube axis (G+), respectively. In both metallic and semiconducting nanotubes, the former component is found to be dependent on the diameter of a nanotube, while the latter does not exhibit this dependence [40]. In the Raman spectra of isolated semiconducting and metallic SWCNT, the D-band and G'-band features are both

Raman spectroscopy was employed to further characterize the peapod samples and to obtain structural information on the inserted fullerene inside tubes. Many groups have performed the Raman experiments of filling SWCNTs with C60 or C70 molecules [12, 42–46] since the first synthesized by Smith et al. [4]. **Figure 5** presents two examples of peapod experimental

Usually, experimental Raman spectra have been obtained on an ensemble of peapods organized into bundles. Nevertheless, the analysis of these experimental results for bundles of C60 peapods [8, 44] leads to the well-established conclusion: the Peapod Radial Breathing-Like Mode (PRBLM) of the peapod having a tube diameter close to 1.37 nm was split into two components, downshifted and upshifted, respectively, with respect to the position of the RBM in empty SWCNT. The upshift was possibly assigned to the stress feeling by the tubes from the inside C60. For diameters between 1.45 and 1.76 nm, a single PRBLM measured

**Figure 5.** RBM Raman spectra taken for heat-treated C70 (top) and C60 (bottom) peapods (from reference [46]).

observed.

**4.3. Raman experiments on C60 and C70 peapods**

80 Fullerenes and Relative Materials - Properties and Applications

Raman spectra, one for C60@SWCNT and the other for C70@SWCNT.

The Raman cross section was calculated assuming that scattering can be described within the framework of the bond polarizability model [52]. Recently, we calculated the Raman spectra of infinite homogeneous bundles (crystal) of C60 peapods [49]. In order to reach a 100% factor filling, 20 C60 molecules are located in a length of 19.8 nm [17.7 nm] of a (10,10) [(13,13)] nanotube and the number of carbon atoms of the tube (10,10) [(13,13)] is close of 3240 [3744] atoms. For the C60@(10,10) (C60@(13,13)) peapod, a 100% factor filling corresponds to a concentration of 37% (32%) (concentration is the ratio between carbons in C60 and carbons in the tube. In **Figure 6b** are displayed the calculated polarized ZZ Raman spectra of individual C60 peapods and crystal of C60 peapods, respectively, for linear and zigzag configuration of the C60 molecules inside the tube: (bottom) linear chain of C60 confined into a (10,10) SWCNT (tube diameter close to 1.36 nm), (top) zigzag chain of C60 confined into a (13,13) SWCNT (tube diameter close to 1.76 nm).

for the individual C60@(13,13) peapod at 133 and 125 cm−1, respectively, shifts to 140 and 127 cm−1 in the infinite bundle of C60@(13,13) peapod. A new peapod bundle breathing-like mode (PBBLM) is also calculated in the Raman spectra of an infinite bundle of C60 peapods, which arises from the BBLM in SWCNT bundle [50]. Concerning the main Raman-active modes of C60 (e.g., modes located around 270 cm−1 (Hg) and 495 cm−1 (Ag)), independently of the configuration of C60 molecules inside the tube, the van der Waals interactions between

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

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**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

More recently, Raman calculations are extended to a larger range of diameters in which C<sup>60</sup>

**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).

molecules can adopt a double helix and a layer of two molecules [22].

peapods have no significant effect on these modes.

diameters of the nanotubes [51, 53–57].

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

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 found.

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.

for the individual C60@(13,13) peapod at 133 and 125 cm−1, respectively, shifts to 140 and 127 cm−1 in the infinite bundle of C60@(13,13) peapod. A new peapod bundle breathing-like mode (PBBLM) is also calculated in the Raman spectra of an infinite bundle of C60 peapods, which arises from the BBLM in SWCNT bundle [50]. Concerning the main Raman-active modes of C60 (e.g., modes located around 270 cm−1 (Hg) and 495 cm−1 (Ag)), independently of the configuration of C60 molecules inside the tube, the van der Waals interactions between peapods have no significant effect on these modes.
