Table 3 Critical strains of single-walled CNTs as obtained by various researchers using atomistic simulations under different simulation conditions.
Authors | Potential | Simulation conditions | Chiral indices | d (nm) | Critical strain |
|---|---|---|---|---|---|
Yakobson et al.9 | Tersoff–Brenner (TB) | Conjugate gradient | (7, 7) | 0.95 | 0.05 |
Cornwell et al.98 | TB | 0.005Â K by velocity scaling | (8, 8) | 1.11 | 0.0581 |
| Â | Â | Â | (16, 16) | 2.22 | 0.0381 |
| Â | Â | Â | (19, 19) | 2.63 | 0.0312 |
| Â | Â | Â | (24,24) | 3.33 | 0.0256 |
Wang et al.99 | REBO | 0.01 K by Nose–Hoover thermostat | (8, 8) | 1.12 | 0.053 |
| Â | Â | Â | (11, 11) | 1.54 | 0.042 |
| Â | Â | Â | (17, 17) | 2.38 | 0.032 |
| Â | Â | Â | (23, 23) | 3.20 | 0.0225 |
Ni et al.57 | REBO | 100Â K by Langevin thermostat | (10, 10) | 1.35 | 0.0414 |
Zhang et al.10 | REBO | 300 K by Nose–Hoover thermostat | (12, 12) | 1.62 | 0.041 |
Buehler et al.51 | TB |  ×  | (20, 20) | 2.71 | 0.02 |
Liew et al.100 | REBO | Conjugate gradient | (10, 10) | 1.36 | 0.067 |
Shen et al.101 | REBO | 300 K by Nose–Hoover thermostat | (8, 8) | 1.09 | 0.0564 |
Zhou et al.102 | TB | 100Â K by Berendsen thermostat | (10, 10) | 1.36 | 0.0409 |
| Â | Â | Â | (14, 14) | 1.90 | 0.0329 |
| Â | Â | Â | (18, 18) | 2.45 | 0.0273 |
Leung et al.103 | REBO | Atomic scale finite element method | (7, 7) | 0.95 | 0.0492 |
Zhang et al.104 | REBO | 300Â K by velocity scaling | (5, 5) | 0.67813 | 0.0753 |
| Â | Â | Â | (7, 7) | 0.94939 | 0.0651 |
| Â | Â | Â | (7, 7) | 0.94939 | 0.0453 |
| Â | Â | Â | (8, 8) | 0.0639 | 0.0639 |
| Â | Â | Â | (10, 10) | 1.35627 | 0.0429 |
| Â | Â | Â | (12, 12) | 1.62752 | 0.0373 |
| Â | Â | Â | (14, 14) | 1.89878 | 0.0321 |
| Â | Â | Â | (16, 16) | 2.17003 | 0.0285 |
| Â | Â | Â | (18, 18) | 2.44128 | 0.0250 |
| Â | Â | Â | (20, 20) | 0.0225 | 0.0225 |
Xin et al.105 | Morse, harmonic and periodic | Strain rates \(\dot{\upvarepsilon }=2.5\times {10}^{-3}\frac{nm}{ps}\) | (7, 7) | 0.95 | 0.0488 |
Zhang et al.106 | REBO | Strain rates \(\dot{\upvarepsilon }=8.3\times {10}^{-4}\frac{nm}{ps}\) | (10, 10) | 1.35627 | 0.0451 |
| Â | Â | Strain rates \(\dot{\upvarepsilon }=8.3\times {10}^{-5}\frac{nm}{ps}\) | (10, 10) | 1.35627 | 0.0544 |
Present authors | MM | Â | (3, 3) | 0.40688 | 0.15007 |
| Â | Â | Â | (4, 4) | 0.54251 | 0.10892 |
| Â | Â | Â | (5, 5) | 0.67813 | 0.08274 |
| Â | Â | Â | (6, 6) | 0.81376 | 0.0669 |
| Â | Â | Â | (7, 7) | 0.94939 | 0.05464 |
| Â | Â | Â | (8, 8) | 1.08502 | 0.04583 |
| Â | Â | Â | (9, 9) | 1.22064 | 0.0469 |
| Â | Â | Â | (10, 10) | 1.35627 | 0.03786 |
| Â | Â | Â | (11, 11) | 1.4919 | 0.03121 |
| Â | Â | Â | (12, 12) | 1.62752 | 0.03454 |
| Â | Â | Â | (13, 13) | 1.76315 | 0.02825 |
| Â | Â | Â | (14, 14) | 1.89878 | 0.02328 |
| Â | Â | Â | (15, 15) | 2.0344 | 0.01935 |
| Â | Â | Â | (16, 16) | 2.17003 | 0.01626 |
| Â | Â | Â | (17, 17) | 2.30566 | 0.01379 |
| Â | Â | Â | (18, 18) | 2.44128 | 0.01157 |
| Â | Â | Â | (19, 19) | 2.57691 | 0.0098 |
| Â | Â | Â | (20, 20) | 2.71254 | 0.00903 |
| Â | Â | Â | (21, 21) | 2.84817 | 0.00901 |
| Â | Â | Â | (22, 22) | 2.98379 | 0.00946 |
| Â | Â | Â | (23, 23) | 3.11942 | 0.01693 |
| Â | Â | Â | (24, 24) | 3.25505 | 0.01402 |
| Â | Â | Â | (25, 25) | 3.39067 | 0.01146 |