Rotations and vibrations of fullerenes in the molecular complex C$_{20}$@C$_{80}$

M. A. Bubenchikov ; A. M. Bubenchikov ; D. V. Mamontov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 71 (2021), pp. 35-48

Résumé

The aim of this work is to apply classical mechanics to a description of the dynamic state of C$_{20}$@C$_{80}$ diamond complex. Endohedral rotations of fullerenes are of great interest due to the ability of the materials created on the basis of onion complexes to accumulate energy at rotational degrees of freedom. For such systems, a concept of temperature is not specified. In this paper, a closed description of the rotation of large molecules arranged in diamond shells is obtained in the framework of the classical approach. This description is used for C20@C80 diamond complex. Two different problems of molecular dynamics, distinguished by a fixing method for an outer shell of the considered bimolecular complex, are solved. In all the cases, the fullerene rotation frequency is calculated. Since a class of possible motions for a single carbon body (molecule) consists of rotations and translational displacements, the paper presents the equations determining each of these groups of motions. Dynamic equations for rotational motions of molecules are obtained employing the moment of momentum theorem for relative motions of the system near the fullerenes' centers of mass. These equations specify the operation of the complex as a molecular pendulum. The equations of motion of the fullerenes' centers of mass determine vibrations in the system, i.e. the operation of the complex as a molecular oscillator.

Détail

Keywords: nanomaterials, mathematical modeling, molecular dynamics, fullerenes, angular vibrations.

Bibliographie

[1] Keith E., Whitener Jr., “Theoretical Studies of CH4 Inside an Open-Cage Fullerene: Translation-Rotation Coupling and Thermodynamic Effects”, Journal Physical Chemistry, 114:45 (2010), 12075–12082 | DOI

[2] Keith E., Whitener Jr., Cross R. J., Saunders M., Iwamatsu Shoichi, Murata S., Nagase S., “Methane in open-cage [60] fullene”, Journal of the American Chemical Society, 131:18 (2009), 6338–6339 | DOI

[3] Huang T., Zhao J., Feng M., Dunsch L., et al., “A multi-state single-molecule switch actuated by rotation of an encapsulated cluster within a fullerene cage”, Chemical Physics Letters, 552:12 (2012), 1–12 | DOI

[4] Lima R. F., Brandao J., Marcio M., Moraes F., “Effects of rotation in the energy spectrum of”, The Europian Physics Journal D, 2014, C60 | DOI

[5] Konarev D. V., Lyubovskaya R. N., Khasanov S. S., “Transition from free rotation of C70 molecules to static disorder in the molecular C70 complex with covalently linked porphyrin dimers: \{(FeIHTPP)2O\}xC70”, Journal of Porphyrins and Phthalocyanines, 14:4 (2010), 293–297 | DOI

[6] Warner J. H., Ito Y., Zaka M., Ge L., Akachi T., Okimoto H., Porfyrakis K., Watt A. A.R., Shinohara H., Briggs G. A.D., “Rotating Fullerene Chains in Carbon Nanopeapods”, Nano Letters, 8:8 (2008), 2328–2335 | DOI

[7] Glukhova O. E., Zhbanov A. I., Rezkov A. G., “Rotation of the inner shell in a C20@C80 nanoparticle”, Physics of the Solid State, 47:2 (2005), 390–396 | DOI

[8] Glukhova O. E., “Theoretical study of the structure of the C60@C450 nanoparticle and relative motion of the encapsulated C60 molecule”, Journal of Structural Chemistry, 48, Suppl. 1 (2007), 141–146 | DOI

[9] Dunn J. L., Hands I. D., Bates C. A., “Pseudorotation in fullerene anions”, Journal of Molecular Structure, 838:1–3 (2006), 60–65 | DOI

[10] Yang S., Wey T., Scheurell K., Kemnitz E., Troyanov S. I., “Chlorination-promoted skeletal-cage transformations of C88 fullerene by C2 losses and a C-C bond rotation”, Chemistry, 21:43 (2015), 15138–15141 | DOI

[11] MacKenzie R. C.I., Frost J. M., Nelson J., “A numerical study of mobility in thin films of fullerene derivatives”, Phys. Chem., 132:6 (2010) | DOI

[12] Herman R. M., Lewis J. C., “Vibration-rotation-translation spectrum of molecular hydrogen in fullerite lattices around 80 K”, Physica B: Condensed Matter, 404:8–11 (2009), 1581–1584 | DOI

[13] Lynden-Bell R. M., Michael K. H., “Translation-rotation coupling, phase transitions, and elastic phenomena in orientationally disordered crystals”, Reviews of Modern Physics, 66:3 (1994), 721 pp. | DOI

[14] Griadun V. I., “Vacancies in nanotubes and fullernes”, Proceeding of the 16th International Crimean Conference on Microwave and Telecommunication Technology, 2006 | DOI

[15] Jaron-Becker A., Becker A., Faisal F. H.M., “Saturated ionization of fullerenes in intense laser fields”, Phys. Rev. Letters, 96 (2006), 143006 | DOI

[16] Slanina Z., Zhao X., “Model narrow nanotubes related to C36, C32 and C20: Initial computational structural sampling”, Materials Science and Engineering B, 96:2 (2002), 164–168 | DOI

[17] Bousige C., Rols S., Cambedouzou J., Verberck B., Pekker S., Kovats E., Durko G., Jalsovsky I., Pellegrini E., Launois P., “Lattice dynamics of a rotor-stator molecular crystals: Fullerene-cubane C60 C8H8”, Phys. Rev. B., 82:19 (2010) | DOI

[18] Yang L., Chen J., Dong J., “Stability of single-wall carbon nanotube tori”, Physica Status Solidi (b), 241:6 (2004), 1269–1273 | DOI

[19] Ruiz A., Hernandez-Rojas J., Breton J., Llorente J. M., “Low-temperature dynamics and spectroscopy in exohedral rare-gas C60 fullerene complexes”, J. Phys. Chem., 114 (2001) | DOI | Zbl

[20] Bozhko S. I., Levchenko E. A., Semenov V. N., Bulatov M. F., Shvets I. V., “Rotation dynamics of C60 molecules in a monolayer fullerene film on the WO$_2$/W(110) surface near the rotational phase transition”, Journal of Experimental and Theoretical Physics, 120:5 (2015), 831–837 | DOI

[21] Bubenchikov A. M., Bubenchikov M. A., Mamontov D. V., Lun-Fu A. V., “MD-simulation of fullerene rotations in molecular crystall fullerite”, Crystals, 9:10 (2019) | DOI

[22] Hosseini-Hashemi S., Sepahi-Boroujeni A., Sepahi-Boroujeni S., “Analytical and molecular dynamics studies on the impact loading of single-layered graphene sheet by fullerene”, Applied Surface Science, 437 (2018), 366–374 | DOI