MECHANICS OF C60 FULLERENE IN THE CENTRAL FORCE FIELD APPROXIMATION

Radkevich E.A., Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

Repchenkov V.I., Candidate of Technical Sciences, Belarusian State University, Minsk, Republic of Belarus

Chizhik S.A., Corresponding Member, Presidium of the National Academy of Sciences of Belarus, Minsk, Republic of Belarus

Mikhasev G.I., Doctor of Physical and Mathematical Sciences, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

With "Mathematica" we have developed a computer finite element model of mechanical behaviour for C60 fullerene molecule in the central force field approximation. The model has under gone virtual static tests with different loading pattern - axial compression by point force; uniform external pressure. Young modulus variation limits are determined as follows 0,29 TPa <E< 10,36 TPa, under the most realistic values of force constants in accordance with hypothetical wall "thickness" of fullerene and Poisson's ratio quantity. Evidence is given that the model shows low sensitivity to fluctuations of valence bond force constants and is much more sensitive to fluctuations of nonvalent ones. Tree times changes of force constants change the results of the calculation elastic response of structure by ~16%-41%, in the former case and by ~88%-127% in the latter.

computer finite element model, variation limits, axial compression, virtual static tests, fluctuations of valence bond force

• Kerl R.F. Istoki otkrytija fullerenov: jeksperiment i gipoteza [History of discovery of fullerenes: experiment and conjecture]. Uspehi fizich. nauk [Successes of physical sciences], 1998, vol. 168, no. 3, pp. 331-342.
• Kroto G. Simmetrija, kosmos, zvezdy [Symmetry, space, stars]. Uspehi fizich. nauk [Successes of physical sciences], 1998, vol. 168, no. 3, pp. 343-358.
• Smolli R.E. Otkryvaja fullereny [Opening fullerenes]. Uspehi fizich. nauk [Successes of physical sciences], 1998, vol. 168, no. 3, pp. 32-330.
• Ruoff R.S., Ruoff A.L. The bulk modulus of molecules and crystals: A molecular mechanics approach. Appl. Phys. Lett., 1991, vol. 59, no. 13, pp. 1553-1555.
• Haijun Shen. Mechanical properties and electronic structures of compressed, and fullerene molecules. J. Matter Sci., 2007, vol. 42, pp. 7337-7342.
• Du Jing, Zeng Pan. Molecular vibrational modes of C60 and C70 via finite element method. European Journal of Mechanics A/Solids, 2009, vol. 28, no. 5, pp. 948-954.
• Zverev V.V., Kovalenko V.I. Analiz struktury fullerena kvantovo-himicheskimi metodami [Analysis of structure of fullerene with quantum-chemical methods]. Zhurnal fizich. himii [Journal of phys. chemistry], 2006, vol. 80, no. 1, pp. 110-116.
• Eleckij A.V. Jendojedral'nye struktury [Endohedral structures]. Uspehi fizich. nauk [Successes of physical sciences], 2000, vol. 170, no. 2, pp. 113-142.
• Repchenkov V.I., Nagornyj Ju.E., Syroezhkin S.V. Primenenie MKE k modelirovaniju nanostruktur [Application of MKE to nanostructures simulation]. Minsk, Belgosuniversitet, 2005. 19 p.
• Repchenkov V.I., Nagornyj Ju.E., Repchenkova E.V. Vektornaja parametrizacija nomerov stepenej svobody i nomerov jelementov v MKE [Vector parametrization of numbers of degrees of freedom and numbers of elements in the MKE]. Minsk, Belgosuniversitet, 2003. 13 p.
• Koptev G.S., Pentin Ju.A. Raschet kolebanij molekul [Calculation of molecular vibrations]. Moscow, MGU, 1977. 212 p.
• Nagornyj Ju.E. [et al.]. Raschet mehanicheskih svojstv grafena v modeli valentno-silovogo polja [Calculation of mechanical properties of graphene in model of valence force field]. Teoretich. i prikl. mehanika [Theoretical and applied mechanics], 2007, no. 22, pp. 182-186.
• Allinger N.L. Conformational Analysis. 130. MM2. A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms. J. Am. Chem. Soc., 1977, vol. 99, pp. 8127-8134.
• Chunyu Li, Tsu-Wei Chou. A structural mechanics approach for the analysis of carbon nanotubes. International Journal of Solids and Structures, 2003, vol. 40, pp. 2487-2499.
• Tienchong Changa, Huajian Gaob. Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model. Journal of the Mechanics and Physics of Solids, 2003, vol. 51, pp. 1059-1074.
• Belytschko T. [et al.]. Atomistic simulations of nanotube fracture. Phys Rev., 2002, vol. 65. B, pp. 235430-235438.
• Brenner D.W. Empirical potential for hydrocarbons for use in simulating the chemical vapor-deposition of diamond films. Phys.Rev., 1990, vol. 42. B, pp. 9458-9471.
• Lukasevich S. Lokal'nye nagruzki v plastinah i obolochkah [Local load in plates and shells]. Moscow, Mir, 1982. 544 p.
• Landau L.D., Lifshic E.M. Teoreticheskaja fizika [Theoretical physics]. Moscow, Nauka, vol. VII, 1987, pp. 33-34.
• Eleckij A.V. / Mehanichskie svojstva uglerodnyh nanostruktur i materialov na ih osnove [Mechanical properties of carbon nanostructures and related materials]. Uspehi fizich. nauk [Successes of physical sciences], 2007, vol. 177, no. 3, pp. 113-142.