Search

A three-dimensional finite element (FE) model for single-walled carbon nanotubes with armchair and zigzag shapes is proposed in this paper (SWCNTs). Nodes are positioned at the locations of carbon atoms to design the FE models. And three-dimensional elastic beam components are used to model the bonds between them. The effect of the diameter length/diameter ratio on the diameter length/diameter ratio, cross sectional aspect ratio and number of elements on the Young’s modulus of SWCNTs has been considered herein. From the conducted experiments it can be observed that, the larger tube diameter can lead to higher Young’s modulus for carbon nanotubes. Such that, maximum elastic modulus for the armchair and the zigzag models has been obtained to be 1.0285TPa and 1.0396TPa when the diameters for the armchair and the zigzag models were 2.034nm and 1.957nm respectively. Increasing the length/diameter ratio has led the Young’s modulus to be increased for armchair and zigzag models such that its values can reach 1.0451TPa and 1.0191TPa respectively. The cross sectional aspect ratio of SWCNTs showed an inversely proportional effect on the elastic modulus in this work. As a result of rising the cross sectional aspect ratio to be2, the Young's modulus for armchair and zigzag models has decreased to 0.7991TPa and 0.8873TPa, accordingly. The change in geometry has been observed to be a defect and it is in general can decrease the modulus of elasticity. The number of elements in the armchair model considered as prominent factor that increases the young’s modulus to be 1.0280TPa when the number of element is 10836. In zigzag model, the number of element has no effect on the elastic modulus since the number of nodes that exposed to the applied load is fixed in this case. The findings showed that the proposed FE model may be useful for studying carbon nanotube mechanical action in the future.

Density Functional Theory (DFT) method of the type (B3LYP) and a Gaussian basis set (6-311G) were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) at the equilibrium geometry of the Di and Tetra-rings layer (6, 0) zigzag single wall carbon nanotubes (SWCNTs) by using Gaussian-09 program. Both were found to have the same symmetry of D6d point group with C--C bond alternation in all tube rings (for axial bonds, which are the vertical C--Ca bonds in rings layer and for circumferential bonds C—Cc in the outer and mid rings bonds). Assignments of the modes of vibration IR active and inactive vibration frequencies (symmetric and asymmetric modes) based on the image modes applied by the Gaussian 09 display. The whole relations for the vibration modes were also done including nCH stretching, nC--C stretching, δCH, δring (δC--C--C) deformation in plane of the molecule) and gCH, gring (gC--C--C) deformation out of plane of the molecule. The assignment also included modes of puckering, breathing and clock-anticlockwise bending vibrations.