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The bond force constant and bulk modulus of small fullerenes using density functional theory and finite element analysis

  • A. TapiaEmail author
  • C. Villanueva
  • R. Peón-Escalante
  • R. Quintal
  • J. Medina
  • F. Peñuñuri
  • F. Avilés
Original Paper

Abstract

Dedicated bond force constant and bulk modulus of C n fullerenes (n = 20, 28, 36, 50, 60) are computed using density functional theory (DFT). DFT predicts bond force constants of 611, 648, 675, 686, and 691 N/m, for C20, C28, C36, C50, and C60, respectively, indicating that the bond force constant increases for larger fullerenes. The bulk modulus predicted by DFT increases with decreased fullerene diameter, from 0.874 TPa for C60 to 1.830 TPa for C20. The bond force constants predicted by DFT are then used as an input for finite element analysis (FEA) of the fullerenes, considered as spatial frames in structural models where the bond stiffness is represented by the DFT-computed bond force constant. In agreement with DFT, FEA predicts that smaller fullerenes are stiffer, and underestimates the bulk modulus with respect to DFT. The difference between the FEA and DFT predictions of the bulk modulus decreases as the size of the fullerene increases, from 20.9 % difference for C20 to only 4 % difference for C60. Thus, it is concluded that knowing the appropriate bond force constant, FEA can be used as a plausible approximation to model the elastic behavior of small fullerenes.

Keywords

Bond force constant Density functional theory Elastic properties Finite element analysis Fullerenes 

Notes

Acknowledgments

This research was supported by FOMIX-CONACYT under grant No. 170297 directed by Dr. J. A. Tapia (UADY).

Supplementary material

894_2015_2649_MOESM1_ESM.docx (38 kb)
ESM 1 (DOCX 38 kb)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • A. Tapia
    • 1
    Email author
  • C. Villanueva
    • 1
  • R. Peón-Escalante
    • 1
  • R. Quintal
    • 1
  • J. Medina
    • 1
    • 2
  • F. Peñuñuri
    • 1
  • F. Avilés
    • 1
    • 2
  1. 1.Facultad de IngenieríaUniversidad Autónoma de YucatánMéridaMexico
  2. 2.Centro de Investigación Científica de Yucatán, A.CUnidad de MaterialesMéridaMexico

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