Calculation of Raman-active modes in linear and zigzag phases of fullerene peapods H. Chadli, A. Rahmani, and K. Sbai Département de Physique, Université MY Ismail, Faculté des Sciences, Boîte Postale 11201, Zitoune, 50000 Meknès, Morocco P. Hermet, S. Rols, and J.-L. Sauvajol Laboratoire des Colloides, Verres et Nanomatériaux (UMR CNRS 5587), CC026, Université Montpellier II, 34095 Montpellier Cedex 5, France Received 28 July 2006; revised manuscript received 19 September 2006; published 10 November 2006 We report on minimum energy calculations, using a convenient Lennard-Jones expression of the van der Waals intermolecular potential, to derive the optimum configurations of C 60 molecules inside single wall carbon nanotubes. Depending on the diameter of the nanotube, C 60 molecules were found to form linear or zigzag chains inside the nanotubes. In the following, we use the spectral moments method, together with a bond-polarizability model, to calculate the nonresonant Raman spectrum for infinitely long isolated C 60 pea- pods. We present the evolution of the Raman spectrum as a function of the diameter and chirality of the nanotube. The changes of the Raman spectrum as a function of the configuration of the C 60 molecules inside the nanotubes are identified. On the other hand, the effect of the filling factor on the Raman spectrum is analyzed. These predictions are useful to interpret the experimental Raman spectra of fullerene peapods. DOI: 10.1103/PhysRevB.74.205412 PACS numbers: 63.22.+m, 78.30.Na I. INTRODUCTION Among the tremendous amount of technological and the- oretical advances that result from the discovery of fullerene 1 are new ideas and paths of investigations. Carbon nanotubes, 2 in particular, are one of the direct results of fullerenes research and they carry many hopes for future technological advances due to their special one-dimensional 1D nanosized structure. In particular, it has been suggested that their low mass over specific surface ratio could be used as nanohost for molecular energy storage. Many recent stud- ies have shown that different atoms or molecules can be trapped inside the hollow core of a single-walled carbon nanotube SWCNT. 3,4 Fullerene peapods stand as supermolecular assemblies of C 60 molecules inside SWCNTs C 60 @SWCNTs and were first observed by Smith et al. 5 from transmission electron microscopy TEM experiments. In general, peapods are ob- served organized into bundles where they are packed to- gether through van der Waals intertubes interactions, a struc- ture that is clearly visible on TEM pictures. 6–8 Efforts led to the synthesis of high-quality 1D fullerene crystals inside SWCNT’s. 5,6 These materials represent a new class of a hy- brid system between C 60 and SWCNT where the encapsu- lated C 60 peas and the SWCNT pod are bonded through van der Waals interactions. A lot of theoretical and experimental studies have been presented on peapods and several interesting properties have been predicted or observed. In particular, theoretical calcula- tions predict that the electronic states near the Fermi level are substantially modified trough the C 60 -SWCNT interaction. 9 Due to their tunable electronic properties, the potential ap- plications of peapods range from high temperature superconductor 10 to memory element 11 and nanometer-sized container for chemical reactions. 12 Raman spectroscopy has been shown to play a major role in nanotube science. 13 The Raman spectrum of SWCNT is dominated by the so-called radial breathing modes RBM below 350 cm -1 and by the tangential modes TM in the high wave number region 1400–1600 cm -1 . At a theoreti- cal level, the nonresonant Raman spectra of SWCNTs have been calculated within the bond polarizability model. 14,15 Many experimental and theoretical Raman studies have shown that the RBM follow a straightforward dependence with the tube diameter that can be used to determine the distribution of the tube diameters in samples under study. 16 For the C 60 molecule, a large variety of theoretical methods has been applied to the calculation of the internal modes and to the determination of their Raman activity. 17–22 Total energy calculations of C 60 peapods suggest that the smallest tube diameter for encasing C 60 molecules inside SWCNT is around the diameter corresponding to 10,10 or 9,9 tubes. 23 Hodak and Girifalco have shown that the struc- ture of the C 60 molecules inside nanotubes is diameter dependent. 24,25 Therefore, it is interesting to follow the changes of the empty nanotubes properties, such as phonon modes, induced by C 60 filling and also as a function of the fullerene configuration inside the nanotube. Few years ago, Raman experiments on SWCNTs encasing C 60 molecules have been reported. 26,27 For tube diameters between 1.45 and 1.76 nm, the authors observed that the radial breathing-like mode RBLM frequencies is downshifted compared to the RBM of empty SWCNTs. For smaller diameters, close to 1.37 nm, they observed two RBLM components that are up- shifted and downshifted with regards to the position of the RBM of the empty tube, respectively. Recently, Pfeiffer et al. 28 measured all the fundamental Raman lines of the en- caged C 60 peas except the H g 8 mode. They observed that both nondegenerate and totally symmetric A g modes of C 60 peas exhibit a splitting into two components. They attributed this splitting to the presence of both moving and static fullerenes inside the tubes. In this paper, we present calculations of the nonresonant Raman spectrum of fullerene peapods by using the spectral PHYSICAL REVIEW B 74, 205412 2006 1098-0121/2006/7420/2054128 ©2006 The American Physical Society 205412-1