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

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.