najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1097Research ArticleСтатьиAnalytical expressions for bulk moduli and frequencies of volumetrical vibrations of fullerenes C20 and C60Аналитические выражения для модулей объемного сжатия и частот объемных вибраций фуллеренов C20 и C60КовалевО. О.KovalevO. O.

Saint-Petersburg

kovalevoleq@gmail.comКузькинВ. А.KuzkinV. A.

Saint-Petersburg

kuzkinva@gmail.comSaint Petersburg State Polytechnical UniversityRussian FederationInstitute for Problems in Mechanical Engineering, RASRussian Federation201117082025226570Copyright © Kovalev O.O., Kuzkin V.A., 20252025Ковалев О.О., Кузькин В.А.Kovalev O.O., Kuzkin V.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1097

In the present paper simple analytical expressions connecting bulk moduli for fullerenes 𝐶20 and 𝐶60 with stiffness of interatomic bond and geometrical characteristics of the fullerenes are derived. Ambiguities related to definition of the bulk modulus are discussed. Nonlinear volumetrical deformation of the fullerenes is considered. Pressure-volume dependence for the fullerenes under volumetrical compression are derived. Simple analytical model for volumetrical vibrations of the fullerenes is proposed. The expression connecting frequencies of volumetrical vibrations for fullerenes 𝐶20 and 𝐶60 with parameters of interatomic interactions are obtained.

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Authors are deeply grateful to Prof. A.M. Krivtsov for useful discussions and inspiration.ReferencesKroto H.W., Heath J.R., O’Brien S.C., Curl R.F., Smalley R.E. C60: Buckminsterfullerene // Nature, 1985, No. 318, P. 162–163.Kroto H.W., Heath J.R., O’Brien S.C., Curl R.F., Smalley R.E. C60: Buckminsterfullerene // Nature, 1985, No. 318, P. 162–163.Dresselhaus M.S., Dresselhaus G., Eklund P.C. Science of fullerenes and carbon nanotubes: Their Properties and Applications. — Academic Press, 1996. — 965 p.Dresselhaus M.S., Dresselhaus G., Eklund P.C. Science of fullerenes and carbon nanotubes: Their Properties and Applications. — Academic Press, 1996. — 965 p.Sokolov V.I., Stankevich I.V. Fullerenes — new allotropic carbon forms: structure, an electronic structure and chemical properties // Successes of chemistry, 1993, V. 62(5), P. 455.Sokolov V.I., Stankevich I.V. Fullerenes — new allotropic carbon forms: structure, an electronic structure and chemical properties // Successes of chemistry, 1993, V. 62(5), P. 455.Hoover W.G. Molecular dynamics // In: Lecture Notes in Physics, Vol. 258. — Springer, Berlin, 1986. — 138 p.Hoover W.G. Molecular dynamics // In: Lecture Notes in Physics, Vol. 258. — Springer, Berlin, 1986. — 138 p.Marx D., Hutter J. Ab initio molecular dynamics: basic theory and advanced methods. — Cambridge University Press, New York, 2009.Marx D., Hutter J. Ab initio molecular dynamics: basic theory and advanced methods. — Cambridge University Press, New York, 2009.Wang C.Z., Chan C.T. Structure and dynamics of C60 and C70 from tight-binding molecular dynamics // Phys. Rev. B, 1992, V. 46, No. 15, P. 9761–9762.Wang C.Z., Chan C.T. Structure and dynamics of C60 and C70 from tight-binding molecular dynamics // Phys. Rev. B, 1992, V. 46, No. 15, P. 9761–9762.Yamaguchi Y., Maruyama S. A Molecular Dynamics Simulation of the Fullerene Formation Process // Chem. Phys. Letters, 1998, V. 286/3, No. 4, P. 336–342.Yamaguchi Y., Maruyama S. A Molecular Dynamics Simulation of the Fullerene Formation Process // Chem. Phys. Letters, 1998, V. 286/3, No. 4, P. 336–342.Ruoff R.S., Ruoff A.L. The bulk modulus of C60 molecules and crystals: A molecular mechanics approach // Appl. Phys. Lett., 1991, P. 1553–1555.Ruoff R.S., Ruoff A.L. The bulk modulus of C60 molecules and crystals: A molecular mechanics approach // Appl. Phys. Lett., 1991, P. 1553–1555.Sakhaee-Pourand A., Vafai A. Natural frequencies of C60, C70, and C80 fullerenes // Appl. Phys. Lett., 2010, V. 96, P. 021903.Sakhaee-Pourand A., Vafai A. Natural frequencies of C60, C70, and C80 fullerenes // Appl. Phys. Lett., 2010, V. 96, P. 021903.Kuzmany H., Pfeiffer R., Hulman M., Kramberger C. Raman spectroscopy of fullerenes and fullerene-nanotube composites. Raman spectroscopy in carbons: from nanotubes to diamond // In: Philosophical Transactions: Mathematical, Physical and Engineering Sciences, Vol. 362, No. 1824, The Royal Society, London, 2004, P. 2375–2406.Kuzmany H., Pfeiffer R., Hulman M., Kramberger C. Raman spectroscopy of fullerenes and fullerene-nanotube composites. Raman spectroscopy in carbons: from nanotubes to diamond // In: Philosophical Transactions: Mathematical, Physical and Engineering Sciences, Vol. 362, No. 1824, The Royal Society, London, 2004, P. 2375–2406.

The authors declare that there are no conflicts of interest present.