Table 3 Critical strains of single-walled CNTs as obtained by various researchers using atomistic simulations under different simulation conditions.

From: Analyzing fine scaling quantum effects on the buckling of axially-loaded carbon nanotubes based on the density functional theory and molecular mechanics method

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

0.005 K by velocity scaling

(8, 8)

1.11

0.0581

   

(16, 16)

2.22

0.0381

   

(19, 19)

2.63

0.0312

   

(24,24)

3.33

0.0256

Wang et al.99

REBO

0.01 K by Nose–Hoover thermostat

(8, 8)

1.12

0.053

   

(11, 11)

1.54

0.042

   

(17, 17)

2.38

0.032

   

(23, 23)

3.20

0.0225

Ni et al.57

REBO

100 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

100 K by Berendsen thermostat

(10, 10)

1.36

0.0409

   

(14, 14)

1.90

0.0329

   

(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

300 K by velocity scaling

(5, 5)

0.67813

0.0753

   

(7, 7)

0.94939

0.0651

   

(7, 7)

0.94939

0.0453

   

(8, 8)

0.0639

0.0639

   

(10, 10)

1.35627

0.0429

   

(12, 12)

1.62752

0.0373

   

(14, 14)

1.89878

0.0321

   

(16, 16)

2.17003

0.0285

   

(18, 18)

2.44128

0.0250

   

(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

  

Strain rates \(\dot{\upvarepsilon }=8.3\times {10}^{-5}\frac{nm}{ps}\)

(10, 10)

1.35627

0.0544

Present authors

MM

 

(3, 3)

0.40688

0.15007

   

(4, 4)

0.54251

0.10892

   

(5, 5)

0.67813

0.08274

   

(6, 6)

0.81376

0.0669

   

(7, 7)

0.94939

0.05464

   

(8, 8)

1.08502

0.04583

   

(9, 9)

1.22064

0.0469

   

(10, 10)

1.35627

0.03786

   

(11, 11)

1.4919

0.03121

   

(12, 12)

1.62752

0.03454

   

(13, 13)

1.76315

0.02825

   

(14, 14)

1.89878

0.02328

   

(15, 15)

2.0344

0.01935

   

(16, 16)

2.17003

0.01626

   

(17, 17)

2.30566

0.01379

   

(18, 18)

2.44128

0.01157

   

(19, 19)

2.57691

0.0098

   

(20, 20)

2.71254

0.00903

   

(21, 21)

2.84817

0.00901

   

(22, 22)

2.98379

0.00946

   

(23, 23)

3.11942

0.01693

   

(24, 24)

3.25505

0.01402

   

(25, 25)

3.39067

0.01146