Analytical Expressions for Bulk Modulus of Fullerene C60 in Case of Nonlinear Volumetric Deformations

Nguyen Van Thang; Nguyen Hoang Oanh, Bui Huy Kien, Vu Duc Luong, Pham Duc Hung

Article Sidebar

PDF
Published Jun 25, 2024
DOI: https://doi.org/10.25073/2588-1124/vnumap.4889

Article Details

How to Cite
VAN THANG, Nguyen et al. Analytical Expressions for Bulk Modulus of Fullerene C60 in Case of Nonlinear Volumetric Deformations. VNU Journal of Science: Mathematics - Physics, [S.l.], v. 40, n. 2, june 2024. ISSN 2588-1124. Available at: <https://js.vnu.edu.vn/MaP/article/view/4889>. Date accessed: 22 nov. 2024. doi: https://doi.org/10.25073/2588-1124/vnumap.4889.
ABNT APA BibTeX CBE EndNote - EndNote format (Macintosh & Windows) MLA ProCite - RIS format (Macintosh & Windows) RefWorks Reference Manager - RIS format (Windows only) Turabian
Issue
Vol 40 No 2
Section
Original Articles

Main Article Content

Abstract

The aim of this work is to establish the bulk modulus expressions of fullerene C60 in both linear and nonlinear deformation cases. The Lennard-Jones potential energy is used to calculate the bonding forces between carbon atoms. The research results reveal a formula demonstrating the dependence of the bulk modulus on the volume of the fullerene in the case of significant volume deformation (nonlinear case). Consequently, the bulk modulus of fullerene C60 can be determined basing on the volume deformation ratio. A comparison between the bulk modulus in general case (large deformation - nonlinear) and specific case (small deformation - linear) has been made. The results obtained through the Finite Element Method (FEM) and Density function theory (DFT) have affirmed the accuracy of the research results.

Keywords: Fullerene C60, bulk modulus, nonlinear deformation, linear deformation, expression of the bulk modulus.

References

[1] W. G. Hoover, Molecular Dynamics, Lecture Notes in Physics, Springer-Verlag, Berlin, 1986.
[2] D. Marx, J. Hutter, Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods, Cambridge University Press, New York, 2009.
[3] C. Z. Wang, C. T. Chan, Structure and Dynamics of C60 and C70 from Tight Binding Molecular Dynamics, Phys. Rev. B, Vol. 46, No. 15, 1992, pp. 9761-9767, https://doi.org/10.1103/PhysRevB.46.9761.
[4] Y. Yamaguchi, S. A. Maruyama, Molecular Dynamics Simulation of the Fullerene Formation Process, Chem. Phys. Letters, Vol. 286, No. 4, 1998, pp. 336-342, https://doi.org/10.1016/S0009-2614(98)00102-X.
[5] A. Tapia, C. Villanueva, R. P. Escalante, R. Quintal, J. Medina, F. Peñuñuri, F. Avilés, The Bond Force Constant and Bulk Modulus of Small Fullerenes Using Density Functional Theory and Finite Element Analysis, J. Mol. Model, Vol. 21, No. 6, 2015, pp. 139, https://doi.org/10.1007/s00894-015-2649-6.
[6] R. S. Ruoff, A. L. Ruoff, The Bulk Modulus of C60 Molecules and Crystals: A Molecular Mechanics Approach, Appl. Phys. Lett., Vol. 59, 1991, pp. 1553-1555, https://doi.org/10.1063/1.106280.
[7] O. O. Kovalev, V. A. Kuzkin, Analytical Expression for Bulk Moduli and Frequencies of Volumetrical Vibrations of Fullerenes C20 and C60, Nanosyst: Phys Chem Math., Vol. 2, 2011, pp. 65-70, http://nanojournal.ifmo.ru/en/articles-2/volume1/1-1/paper6/
[8] G. I. Giannopoulos, S. K. Georgantzinos, P. A. Kakavas, N. K. Anifantis, Radial Stiffness and Natural Frequencies of Fullerenes via a Structural Mechanics Spring-based Method, Fullerenes, Nanotubes and Carbon Nanostructures, Vol. 21, 2013, pp. 248-257, https://doi.org/10.1080/1536383X.2011.613539.
[9] M. Braun, J. A. Ruiz, M. R. Millán, J. A. Loya, On the Bulk Modulus and Natural Frequency of Fullerene and Nanotube Carbon Structures Obtained With a Beam Based Method, Composite Structures, Vol. 187, 2018,
pp. 10-17, https://doi.org/10.1016/j.compstruct.2017.12.038.