Table 7 Critical buckling strain of nanotubes with finite length and diameter wrapped obtained by wrapping different nanosheets.

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

 

Chirality

Armchair

Zigzag

Chirality of \((n,n/2)\)

Armchair

Zigzag

Chirality of \((n,n/2)\)

Armchair

Zigzag

Chirality of \((n,n/2)\)

Armchair

Zigzag

Chirality of \((n,n/2)\)

Diameter

0.4069

0.3915

0.4144

0.9494

1.018

1.0359

2.0344

2.0359

2.0717

2.9838

2.9756

2.9004

Variation percentage

0

 − 3.7751

1.8359

0

7.2225

9.109

0

0.0742

1.8354

0

 − 0.276

 − 2.794

2a

Critical strain

0.181

0.1795

0.1611

0.0698

0.0689

0.0518

0.0303

0.04

0.021

0.0169

0.0313

0.0124

Variation percentage

0

 − 0.8179

 − 10.997

0

 − 1.275

 − 25.73

0

32.036

 − 30.81

0

85.765

 − 26.51

3a

Critical strain

0.1723

0.1753

0.1522

0.0681

0.0699

0.0496

0.0268

0.0424

0.0197

0.0152

0.0339

0.0113

Variation percentage

0

1.7468

 − 11.682

0

2.6424

 − 27.22

0

58.038

 − 26.41

0

122.26

 − 25.67

5a

Critical strain

0.1602

0.1643

0.1382

0.062

0.0677

0.044

0.0229

0.0415

0.0156

0.0119

0.0335

0.0091

Variation percentage

0

2.5657

 − 13.74

0

9.129

 − 29.03

0

81.144

 − 31.95

0

181.38

 − 23.66

8a

Critical strain

0.162

0.1663

0.1382

0.0622

0.0695

0.0438

0.0227

0.0432

0.0155

0.0115

0.0351

0.0093

Variation percentage

0

2.6854

 − 14.661

0

11.652

 − 29.56

0

90.388

 − 31.79

0

205.31

 − 19.32

2z

Critical strain

0.1401

0.1414

0.1239

0.0533

0.0533

0.0381

0.0193

0.03

0.013

0.0122

0.0229

0.0097

Variation percentage

0

0.9854

 − 11.546

0

 − 0.019

 − 28.49

0

55.412

 − 32.78

0

88.414

 − 20.62

3z

Critical strain

0.1337

0.1371

0.1155

0.0498

0.0534

0.0343

0.016

0.0306

0.0097

0.0091

0.0237

0.0092

Variation percentage

0

2.5125

 − 13.617

0

7.3524

 − 31.04

0

90.818

 − 39.48

0

159.82

0.4391

5z

Critical strain

0.1397

0.1441

0.1193

0.0519

0.0576

0.0354

0.0166

0.034

0.01

0.0091

0.0268

0.0092

Variation percentage

0

3.1861

 − 14.57

0

10.903

 − 31.9

0

104.45

 − 40.08

0

195.48

1.1025

9z

Critical strain

0.1458

0.1502

0.1236

0.054

0.0615

0.037

0.0175

0.0372

0.0109

0.0091

0.0297

0.0094

Variation percentage

0

2.9975

 − 15.241

0

13.807

 − 31.52

0

112.03

 − 37.69

0

225.11

3.0702

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