# C60 Filling Rate in Carbon Peapods: A Nonresonant Raman Spectra Analysis

Authors: Fatima Fergani; Sidi Abdelmajid Ait Abdelkader; Hassane Chadli; Brahim Fakrach; Abdelhai Rahmani; Patrick Hermet; Abdelali Rahmani
Journal: Journal of Nanomaterials
 (2017)

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## Abstract

We calculated the nonresonant Raman spectra ofC60 peapods to determine the concentration of C60 fullerenes inside single-walled carbon nanotubes. We focus on peapods with large diameters for which C60 molecules can adopt a double helix configuration or a two-molecule layer configuration. Our calculations are performed within the framework of the bond-polarizability model combined with the spectral moment’s method. The changes in the Raman spectra as a function of C60 filling rate and the configuration of C60 molecules inside the nanotubes are identified and discussed. Our calculations support the experimental method proposed by Kuzmany to evaluate the concentration of C60 molecules inside nanotubes.


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## Body

## 1. Introduction

Single walled carbon nanotubes (SWCNT) can encapsulate small and large molecules such as fullerenes [1–5]. A C60 peapod consists of a SWCNT in which C60 fullerene molecules are inserted. This hybrid system between C60 fullerene and SWCNT has generated a lot of interest for future electronic applications. Carbon peapods have been proposed as possible candidates for novel nanometer scale devices and many efforts are devoted to the synthesis of high-quality 1D fullerene crystals inside SWCNTs [1, 4]. Due to their original one-dimensional nanosized structure and their tunable electronic properties, peapods have several potential applications as high temperature superconductors [6], memory elements [7], and nanometer-sized containers for chemical reactions [3].The structure ofC60 fullerenes inside SWCNTs is strongly dependent on the nanotube diameter, so that even small changes in the SWCNT diameter can alter the geometry of fullerene arrays. From an experimental point of view, structural analysis of peapods can be performed using transmission electron microscopy [1, 4], electron diffraction [5, 8], X-ray scattering [9], and/or Raman spectroscopy [4, 9, 10]. From a theoretical point of view, the organization of fullerenes inside nanotubes has been studied using several models: energy calculations with a simple van der Waals potential [11, 12], Monte Carlo, and molecular dynamic based methods [13–15]. It was shown that C60 molecules inside SWCNTs with a wide range of diameters (1.25–2.71 nm) can form ten different packing arrangements [13, 14]. According to the theoretical calculations, C60 molecules can arrange in a chiral array inside the SWCNTs although such a double helical packing arrangement appears to be less prominent than the zigzag one. Nevertheless, Khlobystov et al. [16] observed the double helical array of C60 molecules inside a SWCNT and a two-molecule layer inside a double-walled carbon nanotube (DWCNT) by high-resolution TEM. The helix formation of encapsulated C60’s corresponds to a weaker binding, which was shown to lead to a reversible filling-removal process of the fullerenes [17]. C60 encapsulation was successfully used as a starting point for in-the-tube chemistry [18] and because of the experimental stimuli, the enclosed C60 peas transform into SWCNTs within the outer tubes, thus producing double-wall carbon nanotubes [19].Raman spectroscopy is one of the promising tools to characterize carbon nanotubes and related nanomaterials. Raman experiments ofC60 peapods were performed by several groups [10, 20–24]. The data are mostly analyzed on the basis of the theoretical predictions stated for individual SWCNTs. The analysis of these experimental results leads to the well-established conclusion: an upshift (downshift) of the peapod radial breathing-like mode (PRBLM) with respect to the RBM of empty SWCNTs occurs for host tube diameters close or smaller (larger) than 1.37 nm [i.e., the diameter of the (10,10) SWCNT].Kuzmany et al. [10] have reported a detailed study of the Raman spectra in C60 peapods as a function of the temperature and the line excitation. In particular, they estimated the concentration of C60 molecules inside the tubes using the measured scattering intensity from the fullerenes relative to that from the tubes. In addition, the absolute concentration of each sample can be evaluated from the Raman measurements (see Table 1 of [10]) because the filling rate of the reference sample was determined from electron energy loss spectroscopy (EELS) to be 60%.In previous works [11, 25], we studied the different possible configurations of C60 molecules inside SWCNTs with diameter lower than 2.15 nm. We predicted that C60 molecules inserted inside a SWCNT adopt a linear arrangement for a tube diameter lower than 1.45 nm (called linear peapods) whereas a zigzag configuration is preferred for larger diameters up to 2.15 nm (called zigzag peapods). Raman spectra of free C60 peapods and packed in bundles have been calculated for linear and zigzag configurations within the bond-polarizability model [11, 25–27]. Our results were in qualitative agreement with the experiments. In particular, we suggested that (i) the presence of two PRBLMs [22, 23] could be related to a low C60 filling rate and (ii) the downshift of the PRBLM in peapods with large diameters could be the fingerprint of the formation of zigzag C60 chains [11].Here, the nonresonant Raman spectra ofC60 peapods with large diameters (2.15–2.28 nm) are calculated within the framework of the bond-polarizability model combined with the spectral moment’s method [28]. This work therefore extends our previous calculations to a larger range of diameters in which C60 molecules can adopt a double helix (Figure 1(a)) or a two-molecule layer (Figure 1(b)) configuration [29]. Although the nonresonant approach cannot predict the variation of the line intensities with the excitation energies, our predictions are useful to follow their evolution as a function of different parameters such as the filling rate of C60 molecules inside SWCNT. The objectives of our work are threefold. First, we list the ground state configuration of C60 molecules inside a nanotube as a function of its diameter. Then, we report for each configuration their associated Raman responses. Finally, we evaluate, for a large range of diameters, the reliability and the transferability of the experimental method proposed by Kuzmany to estimate the relative C60 concentration in peapods.Figure 1
Schematic view of ordered phases resulting fromC60 packing in single-walled carbon nanotubes: (a) double helix and (b) two-molecule layers.
(a)
(b)


## 2. Models and Computational Method

The relaxation of the different structures is obtained from an energy minimization calculation as described in previous works [11].The dynamical matrix of SWCNT and freeC60 molecule is calculated using the force constant models parametrized by Saito et al. [30] and Jishi et al. [31], respectively. The dynamical matrices associated with the coupling between the different subsystems (tube-tube, C60-C60, or tube-C60) are described by the usual (12-6) Lennard-Jones potential, ULJ(r)=4ϵ[(σ/r)12-(σ/r)6], where r is the carbon atom-atom distance. We fixed ϵ=2.964meV and σ=0.3407nm according to [12]. This model was successfully used to calculate the generalized phonon density-of-states of C60 peapods [32]. We note that similar models were used successfully to model interactions in double-wall carbon nanotubes [24, 33, 34].The Raman intensities ofC60 peapods are calculated within the framework of the nonresonant bond-polarizability model [35]. In this model, each bond is characterized by a longitudinal polarizability, αl, and a polarizability perpendicular to the bond, αp. Thus, the polarizability contribution of a particular bond b can be written as follows:(1)αijbr=13αl+2αpδij+αl-αpri^rj^-13δij,where i and j are the Cartesian directions (x, y, z) and r^ is the unit vector along the bond b which connects the atom n and the atom m covalently bonded. The derivatives of (1) with respect to the atomic displacement of the atom n in the direction k, πij,kn, are linked to the Raman susceptibility of modes (see [36] for the detailed formalism) and are given by(2)πij,kn=∑m13αl′+2αp′δijrk^+αl′-αp′ri^rj^-13δijrk^+αl-αprδikrj^+δjkri^-2ri^rj^rk^,where α′=(∂α/∂r)r=r0 and r0 is the equilibrium bond distance. The values of these parameters (α′) are usually fitted with respect to the experiments. Here, we use the same set of parameters as the one we used in the Raman calculation of the linear and zigzag C60 peapods [11, 26].


## 3. Results and Discussion

In the framework of the spectral moment’s method, Raman frequencies are directly obtained from the position of the Raman lines in the calculated spectra. In all our calculations, the nanotube axis is along thez-axis and a carbon atom is along the x-axis of the nanotube reference frame. The laser beam is kept along the y-axis of the reference frame. We consider that both incident and scattered polarization are along the z-axis to calculate the ZZ-polarized spectra.


### 3.1. C60 Configurations inside Nanotubes

We have previously studied the different possibleC60 configurations inside SWCNT for diameters (dt) below 2.15 nm. We found that C60 molecules adopt two configurations: linear for dt≤1.45 nm and zigzag for 1.45≤dt≤2.15 nm. When the tube diameter increases up to 2.28 nm, the energy minimizations show that two other optimal configurations of C60 molecules are possible: a double helix structure (2.15≤dt≤2.23 nm) and a two-molecule layer (2.23≤dt≤2.28 nm). Optimized structural parameters issued from the energy minimizations are listed in Table 1.Table 1
Packing parameters obtained from energy minimization of theC60 molecules inside SWCNT with several diameters and chiralities.
C
60 phases
Tube index(n,m)
Tube diameterdt (nm)
C
60-tube distance dint (nm)
C
60
-
C
60 distance dm (nm)
Double helix
(
22,9
)
2.164
0.321
1.003
(
16,16
)
2.171
0.323
1.001
(
18,14
)
2.176
0.325
0.998
(
25,5
)
2.181
0.323
1.001
(
19,13
)
2.183
0.329
0.998
(
28,0
)
2.193
0.331
1.001
(
27,2
)
2.197
0.312
1.003
(
24,7
)
2.206
0.309
1.003
(
26,4
)
2.210
0.308
1.006
(
22,10
)
2.221
0.30
1.008
Two molecule layers
(
28,1
)
2.233
0.312
1.01
(
17,16
)
2.239
0.297
1.002
(
18,15
)
2.242
0.302
1.008
(
19,14
)
2.247
0.308
1.005
(
20,13
)
2.255
0.306
1.006
(
24,8
)
2.259
0.307
1.008
(
21,12
)
2.266
0.311
1.01
(
29,0
)
2.271
0.303
1.007
(
28,2
)
2.276
0.308
1.009
(
22,11
)
2.280
0.310
1.01The optimum diameter of the helix can be obtained asdh=dt-dm-2dint, where dm is C60 diameter and dint is the interlayer C60-SWCNT distance which can vary from 0.30 to 0.33 nm. These values are consistent with a general interaction for graphitic systems for which the gap distance is 0.33 nm. The double helix can be algebraically described as a single helix [13], whereas for larger tube diameters the structure consists of two-molecule layers with 0.297<dint<0.312 nm.For both configurations (double helix and two-molecule layers), the interfullereneC60-C60 distance varies from 0.998 to 1.01 nm. This result is in good agreement with the previously reported peapod interball separation of 0.97 nm from electron-diffraction profiles [8] and 0.95 nm from high-resolution transmission electron microscopy (TEM) data [9].


### 3.2. Raman Spectra of C60 Completely Filled Nanotubes

The configuration of the guest molecules inside the nanotube and the Raman spectra of peapods are diameter dependent and do not significantly depend on the tube chirality [11, 27]. Thus, we can restrict our discussion without a loss of generality to zigzag tubes.Raman spectra of peapods have been calculated for a double helix [C60@(28,0)] and a two-molecule layer [C60@(29,0)] configurations of C60 molecules. To reach a 100% filling rate, 20 C60 molecules have been encapsulated into the (28,0) SWCNT against 32 C60 molecules in the (29,0) SWCNT. In both configurations, periodic conditions have been used along the tube axis and we considered a tube length of 12.71 nm, leading to a number of carbon atoms close to 3360 in the (28,0) SWCNT and 3480 in the (29,0) SWCNT. Thus, the ratio between the number of carbons in C60 and the one in the tube, which corresponds to C60 concentration in the tubes, is about 36% and 55% for C60@(28,0) and C60@(29,0) peapods, respectively. Results are displayed in Figure 2 for the ZZ-polarization and within the PRBLM range (Figure 2(a)), the region of the radial C60 modes (Figure 2(b)), the intermediate range (Figure 2(c)), and the range of tangential modes [Ag(2) mode for C60 and G-modes for the tubes] (Figure 2(d)). For comparison purposes, we also included in Figure 2 the Raman responses of peapods where C60 molecules adopt a linear chain [C60@(17,0)] and a zigzag chain [C60@(22,0)], together with a Raman spectrum of a free C60 molecule.Figure 2
CalculatedZZ-polarized Raman spectra of C60 peapods and free C60 molecule.
(a)
(b)
(c)
(d)For the high-frequency range above 1200 cm−1, the main lines of free C60 molecules are located at 1219 (Hg(6)), 1403 (Hg(7)), 1468 (Ag(2)), and 1582 cm−1 (Hg(8)). These lines are slightly upshifted in peapods by 1-2 cm−1 as already reported in linear and zigzag peapods (see Figure 2 in [11]). The tangential-like modes (TLM) in SWCNTs are almost not affected by the insertion of C60 molecules inside the nanotube [28].In contrast, significant changes are observed below 1200 cm−1. In the region of the radial C60 modes, Ag(1) line located at 492 cm−1 in the free C60 spectrum shows a splitting into two components at (500, 513), (499, 505), (495, 497), and (495, 498) cm−1 in C60@(17,0), C60@(22,0), C60@(28,0), and C60@(29,0), respectively. This splitting was also obtained for a model consisting of a single C60 molecule capped inside a nanotube, suggesting that it is related to the interactions between C60 molecules and the nanotube host, and not to the inter-C60 interactions. Below 200 cm−1, the radial breathing mode in (17,0), (28,0), and (29,0) SWCNTs, respectively, located at 168, 102, and 98 cm−1, is upshifted in the corresponding peapods to 174, 103, and 100 cm−1. In C60@(22,0), the PRBLM displays a double-structure. This feature is made of a low-frequency (high-frequency) component located at 126 cm−1 (135 cm−1), downshifted (upshifted) with respect to the position of the RBM located at 129 cm−1 in the (22,0) SWCNT. This shift and splitting depend on the configuration of C60 molecules inside SWCNT on one side and on the inter-C60 interactions on the other side.


### 3.3. C60 Filling Rate in Nanotubes

In the case of a peapod sample, it seems reasonable to consider that all the nanotubes may not be fully filled withC60 molecules. Here, we consider the hypothesis of a partial filling of the tubes with long (quasi-infinite) C60 chains. We also 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. This hypothesis is supported by the observations reported in [37].CalculatedZZ-polarized Raman spectra of C60@(28,0) (double helix chain of C60) and C60@(29,0) (two-molecule layer) peapods are reported in Figure 3 as a function of five filling rates (20, 40, 60, 80, and 100%). The TLM range is not reported in this figure because we observed that this range slightly depends on the degree of filling of the SWCNT.Figure 3
CalculatedZZ-polarized Raman spectra of C60@(28,0) (bottom) and C60@(29,0) (top) as a function of the filling rate. From bottom to top, the filling rate is 20, 40, 60, 80, and 100%.
(a)
(b)
(c)For bothC60 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 (28,0) and (29,0) SWCNTs, respectively. For a high level of filling, it is upshifted at 103 and 100 cm−1 in C60@(28,0) and C60@(29,0) peapods, respectively. As expected, the intensity of Hg(1) line located at 270 cm−1 in C60 increases when the filling factor increases.At this stage, we investigate the evolution on the ratio between the Raman scattering intensity fromC60 molecules and that from the tubes as a function of C60 concentration inside the tubes. To make the comparison with the experimental results easier, we proceeded into three steps described as follows. (i) We performed an average of the Raman spectra over the peapod orientations with regard to the laboratory frame. Raman spectra are calculated in the VV-polarization for unoriented peapod samples. (ii) We calculated the intensity ratio between the Raman lines of C60 molecule [Hg(2), Ag(1), Hg(3), Hg(4), Hg(7), and Ag(2)] and the PRBLM or G-mode. (iii) We normalized these calculated intensity ratio with respect to the same intensity ratio calculated for the 60% filling factor sample. This normalization was chosen to comply with Kuzmany’s choice.The relativeC60 concentrations displayed in Figure 4 have been derived according to this procedure for each Raman mode in C60@(17,0), C60@(22,0), C60@(28,0), and C60@(29,0). These peapods correspond to a configuration where C60 molecules adopt a linear, zigzag, double helix, and two-molecule layer orientations, 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. Indeed, 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.Figure 4
Relative concentration of several configurations ofC60 inside SWCNTs normalized on the 60% filling rate intensities. The configurations of C60 adopt a linear, zigzag, double helix, and two-molecule layer inside (17,0), (22,0), (28,0), and (29,0), respectively.Kuzmany et al. [10] performed a detailed Raman analysis of C60 concentration in peapod bundles and a host SWCNT of 1.36 nm diameter. In order to compare our results with theirs, we calculated the average intensity ratio, also normalized on the 60% filling rate intensities, between modes of C60 in the infinite bundle of C60@(17,0) and the PRBLM [Hg(2), Ag(1), Hg(3), Hg(4), and Hg(7) mode] or the G-mode of the (17,0) nanotube [Ag(2)]. For a ~70% concentration, the average relative concentrations are found between 0.97 and 1.04 following the different C60 phonons modes, in good agreement with the experimental value evaluated [10] ~1.13. For a ~20% concentration (corresponding to the L43 sample (EELS concentration 25±10) in [10]), the average relative concentration is calculated around 0.21±0.02, in good agreement with the experimental relative concentration evaluated around 0.19.


## 3.1. C60 Configurations inside Nanotubes

We have previously studied the different possibleC60 configurations inside SWCNT for diameters (dt) below 2.15 nm. We found that C60 molecules adopt two configurations: linear for dt≤1.45 nm and zigzag for 1.45≤dt≤2.15 nm. When the tube diameter increases up to 2.28 nm, the energy minimizations show that two other optimal configurations of C60 molecules are possible: a double helix structure (2.15≤dt≤2.23 nm) and a two-molecule layer (2.23≤dt≤2.28 nm). Optimized structural parameters issued from the energy minimizations are listed in Table 1.Table 1
Packing parameters obtained from energy minimization of theC60 molecules inside SWCNT with several diameters and chiralities.
C
60 phases
Tube index(n,m)
Tube diameterdt (nm)
C
60-tube distance dint (nm)
C
60
-
C
60 distance dm (nm)
Double helix
(
22,9
)
2.164
0.321
1.003
(
16,16
)
2.171
0.323
1.001
(
18,14
)
2.176
0.325
0.998
(
25,5
)
2.181
0.323
1.001
(
19,13
)
2.183
0.329
0.998
(
28,0
)
2.193
0.331
1.001
(
27,2
)
2.197
0.312
1.003
(
24,7
)
2.206
0.309
1.003
(
26,4
)
2.210
0.308
1.006
(
22,10
)
2.221
0.30
1.008
Two molecule layers
(
28,1
)
2.233
0.312
1.01
(
17,16
)
2.239
0.297
1.002
(
18,15
)
2.242
0.302
1.008
(
19,14
)
2.247
0.308
1.005
(
20,13
)
2.255
0.306
1.006
(
24,8
)
2.259
0.307
1.008
(
21,12
)
2.266
0.311
1.01
(
29,0
)
2.271
0.303
1.007
(
28,2
)
2.276
0.308
1.009
(
22,11
)
2.280
0.310
1.01The optimum diameter of the helix can be obtained asdh=dt-dm-2dint, where dm is C60 diameter and dint is the interlayer C60-SWCNT distance which can vary from 0.30 to 0.33 nm. These values are consistent with a general interaction for graphitic systems for which the gap distance is 0.33 nm. The double helix can be algebraically described as a single helix [13], whereas for larger tube diameters the structure consists of two-molecule layers with 0.297<dint<0.312 nm.For both configurations (double helix and two-molecule layers), the interfullereneC60-C60 distance varies from 0.998 to 1.01 nm. This result is in good agreement with the previously reported peapod interball separation of 0.97 nm from electron-diffraction profiles [8] and 0.95 nm from high-resolution transmission electron microscopy (TEM) data [9].


## 3.2. Raman Spectra of C60 Completely Filled Nanotubes

The configuration of the guest molecules inside the nanotube and the Raman spectra of peapods are diameter dependent and do not significantly depend on the tube chirality [11, 27]. Thus, we can restrict our discussion without a loss of generality to zigzag tubes.Raman spectra of peapods have been calculated for a double helix [C60@(28,0)] and a two-molecule layer [C60@(29,0)] configurations of C60 molecules. To reach a 100% filling rate, 20 C60 molecules have been encapsulated into the (28,0) SWCNT against 32 C60 molecules in the (29,0) SWCNT. In both configurations, periodic conditions have been used along the tube axis and we considered a tube length of 12.71 nm, leading to a number of carbon atoms close to 3360 in the (28,0) SWCNT and 3480 in the (29,0) SWCNT. Thus, the ratio between the number of carbons in C60 and the one in the tube, which corresponds to C60 concentration in the tubes, is about 36% and 55% for C60@(28,0) and C60@(29,0) peapods, respectively. Results are displayed in Figure 2 for the ZZ-polarization and within the PRBLM range (Figure 2(a)), the region of the radial C60 modes (Figure 2(b)), the intermediate range (Figure 2(c)), and the range of tangential modes [Ag(2) mode for C60 and G-modes for the tubes] (Figure 2(d)). For comparison purposes, we also included in Figure 2 the Raman responses of peapods where C60 molecules adopt a linear chain [C60@(17,0)] and a zigzag chain [C60@(22,0)], together with a Raman spectrum of a free C60 molecule.Figure 2
CalculatedZZ-polarized Raman spectra of C60 peapods and free C60 molecule.
(a)
(b)
(c)
(d)For the high-frequency range above 1200 cm−1, the main lines of free C60 molecules are located at 1219 (Hg(6)), 1403 (Hg(7)), 1468 (Ag(2)), and 1582 cm−1 (Hg(8)). These lines are slightly upshifted in peapods by 1-2 cm−1 as already reported in linear and zigzag peapods (see Figure 2 in [11]). The tangential-like modes (TLM) in SWCNTs are almost not affected by the insertion of C60 molecules inside the nanotube [28].In contrast, significant changes are observed below 1200 cm−1. In the region of the radial C60 modes, Ag(1) line located at 492 cm−1 in the free C60 spectrum shows a splitting into two components at (500, 513), (499, 505), (495, 497), and (495, 498) cm−1 in C60@(17,0), C60@(22,0), C60@(28,0), and C60@(29,0), respectively. This splitting was also obtained for a model consisting of a single C60 molecule capped inside a nanotube, suggesting that it is related to the interactions between C60 molecules and the nanotube host, and not to the inter-C60 interactions. Below 200 cm−1, the radial breathing mode in (17,0), (28,0), and (29,0) SWCNTs, respectively, located at 168, 102, and 98 cm−1, is upshifted in the corresponding peapods to 174, 103, and 100 cm−1. In C60@(22,0), the PRBLM displays a double-structure. This feature is made of a low-frequency (high-frequency) component located at 126 cm−1 (135 cm−1), downshifted (upshifted) with respect to the position of the RBM located at 129 cm−1 in the (22,0) SWCNT. This shift and splitting depend on the configuration of C60 molecules inside SWCNT on one side and on the inter-C60 interactions on the other side.


## 3.3. C60 Filling Rate in Nanotubes

In the case of a peapod sample, it seems reasonable to consider that all the nanotubes may not be fully filled withC60 molecules. Here, we consider the hypothesis of a partial filling of the tubes with long (quasi-infinite) C60 chains. We also 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. This hypothesis is supported by the observations reported in [37].CalculatedZZ-polarized Raman spectra of C60@(28,0) (double helix chain of C60) and C60@(29,0) (two-molecule layer) peapods are reported in Figure 3 as a function of five filling rates (20, 40, 60, 80, and 100%). The TLM range is not reported in this figure because we observed that this range slightly depends on the degree of filling of the SWCNT.Figure 3
CalculatedZZ-polarized Raman spectra of C60@(28,0) (bottom) and C60@(29,0) (top) as a function of the filling rate. From bottom to top, the filling rate is 20, 40, 60, 80, and 100%.
(a)
(b)
(c)For bothC60 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 (28,0) and (29,0) SWCNTs, respectively. For a high level of filling, it is upshifted at 103 and 100 cm−1 in C60@(28,0) and C60@(29,0) peapods, respectively. As expected, the intensity of Hg(1) line located at 270 cm−1 in C60 increases when the filling factor increases.At this stage, we investigate the evolution on the ratio between the Raman scattering intensity fromC60 molecules and that from the tubes as a function of C60 concentration inside the tubes. To make the comparison with the experimental results easier, we proceeded into three steps described as follows. (i) We performed an average of the Raman spectra over the peapod orientations with regard to the laboratory frame. Raman spectra are calculated in the VV-polarization for unoriented peapod samples. (ii) We calculated the intensity ratio between the Raman lines of C60 molecule [Hg(2), Ag(1), Hg(3), Hg(4), Hg(7), and Ag(2)] and the PRBLM or G-mode. (iii) We normalized these calculated intensity ratio with respect to the same intensity ratio calculated for the 60% filling factor sample. This normalization was chosen to comply with Kuzmany’s choice.The relativeC60 concentrations displayed in Figure 4 have been derived according to this procedure for each Raman mode in C60@(17,0), C60@(22,0), C60@(28,0), and C60@(29,0). These peapods correspond to a configuration where C60 molecules adopt a linear, zigzag, double helix, and two-molecule layer orientations, 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. Indeed, 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.Figure 4
Relative concentration of several configurations ofC60 inside SWCNTs normalized on the 60% filling rate intensities. The configurations of C60 adopt a linear, zigzag, double helix, and two-molecule layer inside (17,0), (22,0), (28,0), and (29,0), respectively.Kuzmany et al. [10] performed a detailed Raman analysis of C60 concentration in peapod bundles and a host SWCNT of 1.36 nm diameter. In order to compare our results with theirs, we calculated the average intensity ratio, also normalized on the 60% filling rate intensities, between modes of C60 in the infinite bundle of C60@(17,0) and the PRBLM [Hg(2), Ag(1), Hg(3), Hg(4), and Hg(7) mode] or the G-mode of the (17,0) nanotube [Ag(2)]. For a ~70% concentration, the average relative concentrations are found between 0.97 and 1.04 following the different C60 phonons modes, in good agreement with the experimental value evaluated [10] ~1.13. For a ~20% concentration (corresponding to the L43 sample (EELS concentration 25±10) in [10]), the average relative concentration is calculated around 0.21±0.02, in good agreement with the experimental relative concentration evaluated around 0.19.


## 4. Conclusions

In this paper, we investigated onC60 peapods for a large range of diameters (2.15–2.28 nm). The optimal configurations of C60 molecules are derived using a convenient Lennard-Jones potential. We found that C60 molecules adopt a double helix arrangement in SWCNTs with diameters between 2.16 and 2.23 nm, whereas a layer of two molecules is preferred for larger diameters up to 2.28 nm. For the obtained configurations, the nonresonant Raman spectra have been calculated as a function of the tube diameter and C60 filling rate using the bond-polarizability model combined with the spectral moment’s method. The variation of the average intensity ratio between C60 Raman-active modes and the nanotube ones, as a function of the concentration molecules, has been analyzed and a general good agreement is found between calculations and measurements. This good agreement supports the experimental method proposed by Kuzmany et al. to evaluate C60 concentration inside SWCNTs.Finally, to improve the comparison between our models and the experimental data, calculations of the nonresonant Raman spectra of peapods with some structural defects on its wall, as experimentally observed [19, 38], are currently in progress.



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*Source: 9248153-2017-05-18.xml*