Mechanical Properties of Carbon Nanotubes
The entire numerical simulations of carbon nanotubes (CNTs) were carried out using the classical molecular dynamics method in which Newtonian equations of motion are solved numerically for a set of atoms interacting via Brenner’s ‘‘second generation’’ reactive empirical many-body bond order potential energy. In this study, the buckling behavior of single-walled and multiwalled carbon nanotubes are simulated by solving the equations of motions using the Gear’s predictor-corrector algorithm. The axial compression of perfectly structured single-walled and multiwalled carbon nanotubes is achieved by applying a rate of 20 and 10 m/s, respectively, at both ends. At the same time, the atoms at both ends of the nanotube are kept transparent to the interatomic forces. The end atoms are then moved inwardly along the axis by small steps, followed by a conjugate gradient minimization method whilst keeping the end atoms fixed.
Fig. 1. Morphological changes for (8,0) single-walled nanotube showing high strains concentrated at the kinks. The (8,0) nanotube at strain=0.13 (a) spontaneously collapse into a three-fin pattern while maintaining its straight axis (b). At strain=0.15, the nanotube buckles sideways (c) before further reduction in length at strain=0.17 (d).
The movie at the bottom shows the buckling behaviour of a single-walled nanotube. (Roll your mouse over the movie and click play to start the movie.)
Molecular dynamics simulations were also carried on multi-wall CNTs. Figure 2 shows the three-dimensional and cross-sectional three-walled nanotube at different strains. It is evident from Fig. 2(a) that the outer layer starts to deform first into a ring pattern at strain=0.0484, while the middle and inner layers are undeformed and their strain energies remain low. However, further compression at strain=0.0486 causes the middle layer to deform too, resulting in a sudden increase in the strain energy per atom because of the increase in potential energy due to the atoms in the middle layer. Similarly at this time, the inner layer maintains the elasticity of the nanotube temporarily as shortly after at strain=0.0493, the inner layer also starts to buckle, therefore increasing the overall potential energy and hence further increasing the strain energy per atom further. After strain=0.052, all the layers are deformed, hence there is no further abrupt increase in potential energy due to any sudden addition of nearest neighbours.
Fig. 2. Three-dimensional and cross-sectional view of morphological changes for three-walled (5,5), (10,10), and (15,15) CNT with diameter 20.4 Å. At strain=0.0484 the outer layer deforms into a ‘‘ring’’ pattern (a). Further compression at strain=0.0486 causes the middle later to deform too (b). At strain=0.0493, the inner layer also buckles (c) and at strain=0.052, all the three layers are deformed (d).
The movie below shows the animation of a cross-sectioned four-walled CNT under compression. (Roll your mouse over the movie and click play to start the movie.)
Fig. 3 shows the formation of (5-7-7-5) defect due to a 90 degrees rotation of a bond during the plastic deformation. The initial (5-7-7-5) defect is formed at a strain of 24%. As the strain increases, more (5-7-7-5) defects are generated along the circumferential direction, as shown in Fig. 3.
Fig. 3. The formation of (5-7-7-5) defects in the outermost layer of a four-walled (5,5), (10,10), (15,15) and (20,20) CNT under axial tension during the plastic deformation.
Figure 4 shows that when the strain reaches the maximum strain at 0.256, two bonds are broken leading to two holes, as shown in Fig. 4(a). As the strain increases, more bonds are broken and the holes are becoming larger until the CNT fractures. The brittle fracture process is displayed in Fig. 4(a)–(d) for the outermost layer of the four-walled CNT. Upon reaching the maximum strain, the CNTs rupture very quickly and completely fracture within a small period of time.
Fig. 4. The brittle fracture process of the outermost layer of four-walled CNTs. (a) Formation of initial fracture. (b) Fracture propagation in circumferential direction. (c) Fracture propagation in the axial and circumferential direction. (d) The CNT is almost completely broken.
The movie below shows the fracture process of a four-walled CNT. (Roll your mouse over the movie and click play to start the movie.)
More information about this research work can be found in the following publications:
- K. M. Liew, X. Q. He, and C. H. Wong, “On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation,” Acta Materialia 52, pp. 2521, 2004.
- K. M. Liew, C. H. Wong, X. Q. He, M. J. Tan, and S. A. Meguid, “Nanomechanics of single and multiwalled carbon nanotubes,” Physical Review B 69, pp. 115429, 2004.