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

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.

On the bulk modulus and natural frequency of fullerene and nanotube carbon structures obtained with a beam based method

“…The Bulk modulus value obtained in the current work shows a 26.76% difference with the results of the bond force method by Ruoff and Ruoff [22], due to the fact that this model only consider axial bond forces. Differences with the current Bulk modulus calculations are 16.90% for the Tapia et al model [24] based on linear spring finite element analysis, and 109.86% for the spring-based method proposed by Giannopoulos et al [26]. The use of the second spring element to simulate the bending interaction by Giannopoulos et al explains the large difference observed.…”

“…Analyzing now the influence of fullerene size, Fig. 7 shows the Bulk modulus in function of fullerene radius obtained with different techniques: the spring-based method (SBM) [26], the spring finite element analysis (SFEA) [24], the density functional theory (DFT) [24] and the BBM implemented in this work. We can see that all the results exhibit the same tendency, where the Bulk modulus decreases as the radius increases.…”

“…Method K, TPa Present work BBM: beam based method 0.71 Tapia et al [24] SFEA: spring finite element analysis 0.83 Tapia et al [24] DFT: density functional theory 0.87 Giannopoulos et al [26] SBM: spring-based method 1.49 Kaur et al [19] TP: tersoff potential 0.67 Kaur et al [19] BP: brenner potential 0.69 Amer and Maguire [20] MD: molecular dynamics 0.35 Woo et al [21] TBM: tight binding method 0.70 Ruoff and Ruoff [22] BFM: bond force method 0.90 Ruoff and Ruoff [23] CEM: continuum elasticity method 0.84…”

“…In the specific case of spherical fullerenes, some researches study their characterization mainly focusing on the analysis of fullerene C 60 [19][20][21][22][23] and to a lesser extent on other spherical carbon-molecules [24][25][26]. Generally, their prognosticated mechanical, chemical, thermal, electric and electronic properties have broadened their potential applications of fullerenes, ranging from bio-sensors, drug delivery, modern microelectronics, and bio-film resistant surfaces, to artificial molecular motors, non-bearings, mechanical reinforcement for membranes and polymer composites [27][28][29][30].…”

Superatomic states under high pressure

“…Then, the bulk modulus (B) calculated by the he relationship between the total molecular energy (E) and the volume change (ΔV) around the equilibrium volume (V 0 ): 66 , 67 , 68 …”