**4.1. Raman-active modes in C60 and C70 fullerene**

Because of their structural and vibrational properties, a lot of theoretical and experimental studies have been presented on C60 and C70 fullerenes, and several interesting properties have been predicted or observed. In particular, experimentalists have reported Raman scattering spectra of C60 and C70 measured by depositing fullerenes on the electrode or metal surface in order to obtain more intensive and more distinguishable spectral signals [30–32]. The free C60 and C70 cluster belongs to the Ih and D5h symmetry group, respectively. According to group theory [33, 34], the high symmetry of C60 gives rise to 10 Raman-active modes (8Hg ⊕ 2Ag), while C70 has 53 Raman-active vibrational modes decomposed (12A1' ⊕ 22E2' ⊕ 19E1").

A large variety of theoretical methods have been applied to the calculation of C60 and C70 vibration of the internal modes and to the determination of their Raman activity. These approaches can be mainly classified as force field model [35, 36], modified neglect of diatomic overlap (MNDO) [37], Quantum-mechanical Consistent Force Field Method for Pi-Electron Systems (QCFF/PI) [38], and density functional theory [39]. The experimental and calculated frequency (cm−1) of Raman-active modes in free C70 molecule with their assignments is listed in **Table 4**.

#### **4.2. Raman spectra of carbon nanotubes**

Raman spectroscopy is one of the primary methods used to yield the geometrical structure of one isolated individual SWCNT [40] and organized into bundles [11]. The experimental Raman spectra of SWCNTs are dominated by the radial breathing mode (RBM), the D-band, the G-band, and the G'-band (see **Figure 1** in [40]).

vs. diameter (d) follow the phenomological law ωRBM <sup>=</sup> (

\_\_\_ 228 <sup>d</sup> ) √

SWCNTs [65], and C ≠ 0 for SWCNT packed in bundles (see [41] and references therein). In SWCNT bundles, the origin of the C term results from van der Waals interaction. The G-band which closely related to vibrations in all sp2 carbon materials is an intrinsic feature of a carbon nanotube. The Raman line shape of this band which depends on whether the nanotube is semiconducting or metallic allows distinguishing between both types. This band shows a

**Table 4.** Experimental and calculated frequency (cm−1) of Raman-active modes in C70 fullerene with their assignments.

**Experiment Calculation Assignment**

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

Ref [53] Ref [54] Ref [55] Ref [56] Ref [57] Ref [21]

226 228 233 219 218 E2

 250 245 243 E1" 258 261 257 253 252 A1' 399 400 396 393 391 A1' 409 411 410 408 409 E1" 455 459 452 448 451 A1' 508 501 506 502 503 E2' 569 573 569 564 565 A1' 701 704 701 701 704 A1' 714 714 713 708 E1" 737 739 738 734 739 E2' 766 770 769 750 749 E2' 1062 1062 1060 1060 1067 A1' 1182 1186 1185 1186 A1'

1227 1227 1231 1227 1229 1237 A1' 1257 1257 1260 1256 1256 1253 E2' 1296 1296 1298 1296 1296 1298 E1"

 1335 1336 1333 1328 1325 E2' 1370 1370 1366 1366 1359 E1" 1469 1471 1468 1471 1473 A1' 1493 1501 1501 E2' 1515 1517 1512 1515 1512 E1" 1565 1569 1566 1574 1583 A1'

1313 1317 1311 1312 1306 E1"

\_\_\_\_\_\_ 1 + C d<sup>2</sup>

1186 1193 E2'

with C = 0 for isolated

'

79

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The fundamental two Raman-active modes are the RBM below 350 cm−1 and the tangential mode (TM) located between 1400 and 1600 cm−1. The RBM is an important mode for the characterization and identification of specific nanotubes, in particular of their chirality. Recently, experimental and theoretical Raman studies have shown that the RBM frequency



**3.3. The spectral moment's method**

78 Fullerenes and Relative Materials - Properties and Applications

**4. Raman spectroscopy of C60 and C70 peapods**

**4.1. Raman-active modes in C60 and C70 fullerene**

**4.2. Raman spectra of carbon nanotubes**

the G-band, and the G'-band (see **Figure 1** in [40]).

of freedom).

in **Table 4**.

The direct method to calculate the Raman spectrum requires, besides the polarization parameters, direct diagonalization of the dynamical matrix to obtain the eigenvalues and the eigenvectors of the system. The diagonalization fails or requires long computing time when the system contains a large number of atoms, as for a long C60 and C70 chains inside nanotubes. By contrast, the spectral moment's method allows computing directly the Raman responses of harmonic systems without any diagonalization of the dynamical matrix [28, 29]. In the case of C60 and C70 peapods, calculations of the Raman spectra of peapods showed that approximately 500 moments are sufficient to obtain good results for larger samples (~25,000 degrees

Because of their structural and vibrational properties, a lot of theoretical and experimental studies have been presented on C60 and C70 fullerenes, and several interesting properties have been predicted or observed. In particular, experimentalists have reported Raman scattering spectra of C60 and C70 measured by depositing fullerenes on the electrode or metal surface in order to obtain more intensive and more distinguishable spectral signals [30–32]. The free C60 and C70 cluster belongs to the Ih and D5h symmetry group, respectively. According to group theory [33, 34], the high symmetry of C60 gives rise to 10 Raman-active modes (8Hg ⊕ 2Ag), while C70 has 53 Raman-active vibrational modes decomposed (12A1' ⊕ 22E2' ⊕ 19E1").

A large variety of theoretical methods have been applied to the calculation of C60 and C70 vibration of the internal modes and to the determination of their Raman activity. These approaches can be mainly classified as force field model [35, 36], modified neglect of diatomic overlap (MNDO) [37], Quantum-mechanical Consistent Force Field Method for Pi-Electron Systems (QCFF/PI) [38], and density functional theory [39]. The experimental and calculated frequency (cm−1) of Raman-active modes in free C70 molecule with their assignments is listed

Raman spectroscopy is one of the primary methods used to yield the geometrical structure of one isolated individual SWCNT [40] and organized into bundles [11]. The experimental Raman spectra of SWCNTs are dominated by the radial breathing mode (RBM), the D-band,

The fundamental two Raman-active modes are the RBM below 350 cm−1 and the tangential mode (TM) located between 1400 and 1600 cm−1. The RBM is an important mode for the characterization and identification of specific nanotubes, in particular of their chirality. Recently, experimental and theoretical Raman studies have shown that the RBM frequency **Table 4.** Experimental and calculated frequency (cm−1) of Raman-active modes in C70 fullerene with their assignments.

vs. diameter (d) follow the phenomological law ωRBM <sup>=</sup> ( \_\_\_ 228 <sup>d</sup> ) √ \_\_\_\_\_\_ 1 + C d<sup>2</sup> with C = 0 for isolated SWCNTs [65], and C ≠ 0 for SWCNT packed in bundles (see [41] and references therein). In SWCNT bundles, the origin of the C term results from van der Waals interaction. The G-band which closely related to vibrations in all sp2 carbon materials is an intrinsic feature of a carbon nanotube. The Raman line shape of this band which depends on whether the nanotube is semiconducting or metallic allows distinguishing between both types. This band shows a 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 observed.

and its frequency are downshifted compared to the RBM in the empty SWCNT bundles. The observed downshift of the PRBLM [43, 44] is explained by the hybridization effect between SWCNTs and C60 molecules electronic states, leading to a decreasing of the electron density in the vicinity of the SWCNT, which induces a decreasing of the force constant of the C-C bond. Pfeiffer et al. [45] measured all the fundamental Raman lines of the encaged C60 peas. They observed that both nondegenerate and totally symmetric Ag modes of C60 peas exhibit a splitting into two components. They attributed this splitting to the presence of both moving and

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

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81

Kuzmany et al. [12] performed a detailed Raman analysis to evaluate the concentration of C60 molecules inside nanotubes. As expected, the relative concentrations derived from the measurement of normalized intensity ratio for each Raman mode of C60 are close. The C60 filling degree of a reference peapod sample was determined from electron energy loss spectroscopy experiment in order to evaluate the absolute C60 concentration of each peapod sample from

Concerning the C70 peapods, Hirahara et al. [46] characterized one-dimensional crystals of a variety of larger fullerenes C70 peapods by using high-resolution transmission electron microscopy and electron diffraction. They concluded that the C70 admit two different orientations depending on the nanotube diameter: the lying and standing orientation. The intermolecular distances of various fullerenes in SWCNTs are considerably smaller than those for bulk fullerene crystals, suggesting an effect of confinement in the one-dimensional channels inside SWCNTs. Raman experiments on SWCNTs encasing C70 molecules have been reported [19, 21, 42, 47, 48]. Ryabenko et al. [42] concluded that the PRBLM mode of C70 peapods are downshifted by ∼2–3 cm−1 compared to empty nanotubes. For different orientations of C70s in C70@SWCNT peapods organized into bundles, the measured PRBLM downshift after the C70 encapsulation is ∼2–6 cm−1 [47]. The downshift of the PRBLM suggests a structural relaxation or the tube diameter transformation is expected to occur with the assistance of such added carbon atoms. However, such experimental work should include Raman investigations on samples showing peapods having various structural characteristics: different tube diameters, different fullerene concentration, and bundles with various sizes, for example, various num-

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

static fullerenes inside the tubes.

bers of tubes.

the measurements of the Raman spectra (see **Table 1** of [12]).

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