Tapia A, Villanueva C, Peón-Escalante R, Quintal R, Medina J, Peñuñuri F, Avilés F
Facultad de Ingeniería, Universidad Autónoma de Yucatán, Av. Industrias no contaminantes por Periférico Norte, Cordemex, C.P. 97310, Mérida, Yucatán, Mexico,
J Mol Model. 2015 Jun;21(6):139. doi: 10.1007/s00894-015-2649-6. Epub 2015 May 10.
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.
使用密度泛函理论（DFT）计算了Cn富勒烯（n = 20、28、36、50、60）的专用键力常数和体积模量。DFT预测C20、C28、C36、C50和C60的键力常数分别为611、648、675、686和691 N/m，这表明对于更大的富勒烯，键力常数会增加。DFT预测的体积模量随着富勒烯直径的减小而增加，从C60的0.874 TPa增加到C20的1.830 TPa。然后将DFT预测的键力常数用作富勒烯有限元分析（FEA）的输入，在结构模型中富勒烯被视为空间框架，其中键刚度由DFT计算的键力常数表示。与DFT一致，FEA预测较小的富勒烯更硬，并且相对于DFT低估了体积模量。随着富勒烯尺寸的增加，FEA和DFT对体积模量预测的差异减小，从C20的20.9%差异减小到C60的仅4%差异。因此，可以得出结论，在知道适当的键力常数的情况下，FEA可以用作模拟小富勒烯弹性行为的合理近似方法。
