Understanding Carbon Nanotubes (eBook)

Preface 6
Contents 9
List of Contributors 12
1 Polymorphism and Structure of Carbons 16
1.1 Historical Introduction 16
1.1.1 A Short Story of Carbon 16
1.1.2 The Carbon Element 17
1.1.3 New Forms 19
1.1.4 Basic Concepts: Orbital Hybridizations 20
and Coordination Number 20
1.2 Polymorphism of Crystalline Phases 20
1.2.1 Thermodynamic Stability and Associated Phase Diagram 20
1.2.2 Theoretical Approaches and New Predicted Phases 23
1.2.3 Structures on Curved Surfaces 24
1.2.4 Carbon Nanotubes: Structures and Defects 26
1.3 Non-Crystalline Carbons 28
1.3.1 De.nitions 28
1.3.2 Textures Symmetries in Carbon Materials 29
1.3.3 Textures Resulting in Plastic or Liquid Phases 31
1.3.4 Textures Resulting of Process in Gaseous or Vapor Phases 35
1.3.5 Relation between Textures and Mechanical Properties 37
1.4 Transport Properties 39
1.4.1 Introduction 39
1.4.2 Electrical Resistivity and Magnetoresistance 42
Conduction and Transmission 42
Zero-Field Resistivity 43
Magnetoresistance 46
1.4.3 Thermal Conductivity 48
1.4.4 Thermoelectric Power 51
1.4.5 Relation between Structure and Transport Properties 52
1.5 Doped Carbons and Parent Materials 52
1.5.1 Doped Carbons and Solid Solutions 53
1.5.2 Parent Materials 53
1.5.3 Heterofullerenes and Heteronanotubes 56
1.6 Conclusion 57
Acknowledgements 58
References 58
2 Synthesis Methods and Growth Mechanisms 63
2.1 Introduction 63
2.2 High-Temperature Methods for the Synthesis 65
of Carbon and Boron Nitride MWNTs and SWNTs 65
2.2.1 Generalities on High Temperature Methods 65
2.2.2 The Electric Arc Discharge Technique 65
Principle and Description 65
In-Situ Diagnoses 66
Synthesis of Either SWNTs or MWNTs 67
2.2.3 Laser Ablation 69
Principle and Description 69
In-situ Diagnoses 70
2.2.4 Vaporization Induced by a Solar Beam 72
Principle and Description 73
In-situ Diagnoses and Simulation of the Synthesis 74
2.2.5 Upscaling 74
2.2.6 Synthesis of Heteroatomic Nanotubes 75
Pure BN MWNT and SWNT 75
B–C–N Nanotubes 76
2.2.7 Conclusion 76
2.3 Catalytic CVD Growth of Filamentous Carbon 77
2.3.1 Thermodynamics of Carbon CVD 78
Decomposition of Hydrocarbons 78
Disproportionation of Carbon Monoxide (2CO 79
C + CO2) 79
Thermodynamic E.ects of Carbon Polymorphism 80
Formation of Carbides as a Cause of Deviation from Equilibrium 81
2.3.2 Kinetics and Mechanisms of Filament Growth 81
The 81
Mechanism 81
Quantitative Kinetic Study of Carbon Deposition 83
from CO over a Supported Fe-Co Catalyst 83
2.3.3 In.uence of the Morphology and Physical State 86
of the Catalytic Particle 86
Structure of Filaments Grown from Solid Crystalline Particles 86
Growth of Filaments from Liquid Particles 88
Dynamics and Restructuring 90
of Catalytic Nanoparticles During Growth 90
2.4 Synthesis of MWNT and SWNT 91
via Medium-Temperature Routes 91
2.4.1 From Carbon Nano.bres to Carbon Nanotubes by CCVD 91
2.4.2 Synthesis of Carbon Multiwalled Nanotubes (MWNT) 93
by CCVD 93
Synthesis of MWNT Using Supported Catalysts 93
Synthesis of MWNT Using Catalytic Particles Formed 94
in-situ from an Organometallic Precursor 94
Synthesis of MWNT Aligned in Bundles 94
Localized Synthesis of Oriented MWNT 95
Conclusions 96
2.4.3 Synthesis of Carbon Single-Walled Nanotubes (SWNT) 97
by CCVD 97
Methods Using Catalytic Particles Formed 97
in-situ from an Organometallic Precursor 97
Methods Using Supported Catalytic Nanoparticles 99
Synthesis of Carbon Double-Walled Nanotubes (DWNT) 102
Localized Synthesis of Carbon SWNT 103
2.4.4 Template Synthesis of Carbon Nanotubes 103
2.4.5 Conclusions 105
2.5 Nucleation and Growth of C-SWNT 106
2.5.1 Summary of the Synthesis Conditions of C–SWNT: 106
Similarities and Di.erences of the Di.erent Synthesis Methods 106
2.5.2 Towards a General Phenomenological Model 108
of Nucleation and Growth 108
Analysis of the Link Between Catalyst Particles and SWNTs 108
Phenomenological Model of Nucleation and Growth 109
Particle Formation and Carbon Segregation 112
Nucleation 113
Growth and End of the Growth 114
2.5.3 Microscopic Approach of the Nucleation for a Particular 115
Family of Catalyst: the Case of the Ni-RE Catalysts 115
Experimental Procedure 115
SWNTs Morphologies and Catalyst Composition 115
Particle Analyses 116
Nucleation Model: The Catalytic Role of Rare Earth Elements 117
2.5.4 Conclusion 119
2.6 Growth Mechanisms for Carbon Nanotubes: 120
Numerical Modelling 120
2.6.1 Introduction 120
2.6.2 Open- or Close-Ended Growth for Multiwalled Nanotubes 121
2.6.3 ‘Lip-lip’ Interaction Model for Multiwalled Nanotube 123
Growth 123
2.6.4 Is Uncatalyzed Growth Possible 126
for Single-walled Nanotubes ? 126
2.6.5 Catalytic Growth Mechanisms for Single-Wall Nanotubes 126
2.6.6 Root Growth Mechanism for Single-Wall Nanotubes 129
2.6.7 Conclusion 132
2.7 BxCyNz Composite Nanotubes 133
2.7.1 BxCyNz Nanotubes 133
2.7.2 B-Doped Nanotubes 134
2.7.3 BN Tubes 135
References 136
3 Structural Analysis by Elastic Scattering Techniques 145
3.1 Basic Theories 145
3.1.1 Kinematic Theory of Di.raction 145
X-rays 146
Electrons 147
Neutrons 148
3.1.2 Transmission of Fast Electrons through a Crystalline Film 149
3.1.3 HREM Imaging 154
HREM: A Phase Contrast Imaging Mode 156
Transfer Function: HREM Images of Graphene, Graphite 158
and Ni Catalyst 158
3.1.4 Scanning Tunneling Microscopy 163
3.2 Analysis of Graphene-Based Structures with HREM 166
3.2.1 Electron Di.raction 166
3.2.2 Lattice Fringe Imaging 171
3.2.3 Dark-Field Imaging 172
3.3 Analysis of Nanotube Structures 178
with Di.raction and HREM 178
3.3.1 HREM Imaging of Nanotubes 178
Single-Walled Nanotubes 178
Multiwalled Nanotubes 181
Bundles of Single-Walled Nanotubes 184
Analysis of Defects 190
3.3.2 Di.raction by Carbon Nanotubes 191
Electron Di.raction by a Single-Walled Nanotube 196
Electron Di.raction by Multi Walled Nanotubes 198
and Bundles of Single-Walled Nanotubes 198
X-ray and Neutron Di.raction by Nanotubes 200
3.4 Analysis of the Nanotube Structure with STM 204
Acknowledgments 209
References 209
4 Electronic Structure 213
4.1 Electronic Structure: Generalities 213
4.1.1 From Atoms to Crystals 213
Atoms 213
Molecules 214
The Crystal 216
4.1.2 Semi-Classical Theory of Electronic Transport 220
Electric Conductivity 220
Drude Model 222
4.1.3 222
Covalent Structures 222
and 222
Orbitals 222
Linear Chain. Leman-Friedel-Thorpe-Weaire Model 224
4.1.4 From Graphene to Nanotubes 225
The Graphene Sheet 225
Carbon Nanotubes 228
4.2 Electronic Properties of Carbon Nanotubes 231
4.2.1 Very Small Diameter Nanotubes 231
4.2.2 Real Ballistic Conductors 231
4.2.3 Nanotubes in Bundles 233
4.2.4 Nanotubes with Polygonized Cross-Section 234
4.2.5 Multi-Walled Nanotubes 235
4.2.6 Defects in Carbon Nanotubes 237
4.2.7 Connecting Nanotubes 237
4.2.8 Haeckelite Nanotubes 239
4.2.9 Molecular Junctions Based on Nanotubes 239
4.3 Non-Carbon Nanotubes 241
4.3.1 Boron Nitride Nanotubes 241
4.3.2 BxCyNz Nanotubes 244
Ordered Forms of BC3 245
Ordered Forms of BC2N 245
Disorder and Doping in BCN Compounds 248
4.3.3 WS2, MoS2 and Other Nanotubes: from Synthesis to Predictions 249
4.4 Monitoring the Electronic Structure of SWNTs 250
by Intercalation and Charge Transfer 250
4.4.1 Introduction 250
4.4.2 Optical Absorption and Raman Spectroscopy of SWNTs 251
4.4.3 Experimental Evidences of Intercalation 253
and Charge Transfer in SWNTs 253
Evidences of Intercalation in SWNT Material 253
Evidence of Charge Transfer upon Intercalation 253
of Electron Donors or Acceptors 253
4.4.4 Tuning and Monitoring the Electronic Structure of SWNTs 255
Fermi Level of Two Phases in Contact 255
Chemical Doping Process 256
Electronic Structure and Electrical Transport of Doped SWNTs 257
Tangential Modes of Vibration of Doped SWNTs 260
4.4.5 Conclusion 262
4.5 Field Emission 262
4.5.1 Introduction 262
4.5.2 Field Emission and the Fowler-Nordheim Model 263
Electron Emission 263
The Fowler-Nordheim Model 264
The Fowler-Nordheim Equation 267
Total Energy Distribution 268
4.5.3 Field Ampli.cation 269
Field Enhancement for In.nitely Long Emitters 270
Emitters on Surfaces 270
Other E.ects In.uencing the Field Enhancement 271
Shielding and Screening E.ects 272
4.5.4 Measuring Field Emission 272
Experimental Techniques 272
What Can we Learn from Field Emission Results? 274
Do’s and Don’ts in 275
– 275
Measurements 275
4.5.5 Selective Overview of Experimental Results 276
E.ect of the Applied Field 276
Field Enhancement Factor 277
Emitter Degradation 278
Work Function 279
Emission Mechanisms 280
Field Emission as a Characterization Method 282
Applications 283
4.5.6 Conclusion 285
References 285
5 Spectroscopies on Carbon Nanotubes 291
5.1 Vibrational Spectroscopies 291
5.1.1 Phonons 292
5.1.2 Raman Scattering 296
0) 301
5.2 Electron Energy-Loss Spectroscopy 304
5.2.1 Principles of Electron Energy-Loss Spectroscopy 304
in a Transmission Scattering Geometry 304
0 306
5.2.2 Basic Tools Developed for Interpreting 309
and Using Core-Loss Signals 309
5.2.3 Spatially Resolved EELS 312
5.2.4 Elemental Mapping Using Core-Loss Signals 315
Multiple Least Square Fitting 315
5.3 Raman Spectroscopy of Carbon Nanotubes 316
5.3.1 Introduction 316
5.3.2 Charge-Transfer Compounds (Doping) of SWNT 323
5.3.3 Anisotropic Fibers of Nanotubes 326
5.3.4 Functionalization and Separation 327
5.3.5 Isolated Tubes 331
5.4 Applications of EELS to Nanotubes 336
5.4.1 A Few Examples of Elemental Mapping with EELS Core 336
Edges 336
Sensitivity, Limits of Detection in EELS Elemental Mapping 337
5.4.2 Mapping Bonding States and Electronic Structures 338
with ELNES Features 338
5.4.3 Curvature Induced E.ects on the Chemical Bonding 339
in Single Shell Carbon Nanotubes 339
5.4.4 Study of the Valence Electron Excitations in Nanotubes 340
Near Field EEL Spectroscopy Experimental Evidence 342
of Surface Plasmon Coupling in Nanotubes 342
5.4.5 Plasmon Dispersion Relations in Ropes of SWNTs 343
References 345
6 Transport Properties 349
6.1 Quantum Transport in Low-dimensional Materials 349
6.1.1 Ballistic Conduction and Quantized Conductance 349
Drude-Sommerfeld Theory of Metals 349
The Scattering Approach to Quantum Transport 351
Quantum Resistance Properties 354
6.1.2 Coulomb Interactions 358
Fermi Liquid 358
Tunnel Junctions and Coulomb Blockade 361
Interactions in One-dimensional Systems 365
6.2 Quantum Transport in Disordered Conductors 371
6.2.1 Introduction: Phase Coherence, Mesoscopic Regime, 371
Physical Length Scales 371
Length Scales 371
Classical Transport 372
Quantum Transport: Outline 373
6.2.2 Di.usive Electronic Transport, Transmission Coe.cient 373
and Conductance 373
Classical Probability 373
r, r 374
r 374
r). 374
Conductance 375
6.2.3 Deviations From Classical Transport: Quantum Interferences 376
6.2.4 Weak Localization 378
6.2.5 Di.usion Equation 380
Classical Di.usion and Quantum Correction 380
Solutions of the Di.usion Equation 381
6.2.6 Back to Weak-Localization 383
Dependence on the Dimensionality 383
Magnetoresistance 383
Altshuler-Aronov-Spivak Oscillations on a Cylinder 384
6.2.7 Universal Conductance Fluctuations 385
Universal Conductance Fluctuations in a Quasi-1D Wire 388
6.3 An Interaction E.ect: the Density-of-States Anomaly 389
6.3.1 Some Useful Formulas 390
6.4 Theory of Quantum Transport in Nanotubes 391
6.4.1 Ballistic Conduction in Single-walled 391
and Multiwalled Carbon Nanotubes 391
Bandstructure and Conducting Channels 391
6.4.2 E.ects of Disorder and Doping 393
Conduction Regimes 393
6.4.3 Absence of Backscattering in Undoped Nanotubes 394
6.4.4 Nature of Disorder and Defects 397
6.4.5 Elastic Mean Free Path 398
Derivation Within the Fermi Golden Rule 398
6.4.6 Quantum Interference E.ects and Magnetotransport 400
6.4.7 Contribution of Intershell Coupling 402
Commensurate Multiwalled Nanotubes 404
Incommensurate Multiwalled Nanotubes 405
6.4.8 Role of Electrode-Nanotube Contacts 406
6.4.9 Inelastic Mean Free Path 407
6.4.10 Electron-Electron Interactions 409
K- 410
6.5 Measurement Techniques 410
6.5.1 Classical (Macroscopic) Approach 411
Two-Probe Measurement 411
Four-Probe Measurement 411
Importance of the Contact Size 412
6.5.2 Experimental Problems on Mesoscopic Samples 413
Choice of the Contact Type and Realization 413
Sample on Top Versus Electrode on Top 415
Measurement of the Voltage and Current 416
Reproducibility of the Measurements 418
Calculation of the Resistivity 420
6.6 The Case of Carbon Nanotube 420
6.6.1 Study of Some Experimental Measurements 420
Measuring the Voltage Drop Using EFM Techniques 420
Extracting the Intrinsic Resistivity by Reducing 421
the Inter-Electrode Gap 421
6.7 Experimental Studies of Transport in Nanotubes 422
and Electronic Devices 422
6.7.1 Introduction 422
6.7.2 Electrical Transport in Metallic Carbon Nanotubes 422
1 423
2 423
4 423
2 424
5 424
Experimental Evidences of Electron-phonon Scattering 424
Current Saturation and Breakdown 427
6.7.3 Nanotube-Based Transistors 428
Top-Gate Nanotube-Based Transistors 428
Nanotube-Metal Schottky Barrier 429
1) 429
2). 429
3 429
6.7.4 Ambipolar Carbon Nanotube Transistors 430
Schottky Nanotube Transistor: Operating Mode 431
6.8 Transport in Nanotube Based Composites 433
6.8.1 Introduction 433
6.8.2 Transport in a Heterogeneous Medium 433
Basic Percolation Theory and E.ective Medium Approach 433
Application to Nanotube-Based Composites 434
6.8.3 Transport Mechanism 434
6.8.4 Localization and Hopping 434
6.8.5 Coulomb Interactions and Coulomb Gap 435
6.8.6 Percolation Network 435
6.8.7 High-Electric-Field E.ects 436
6.8.8 Magnetoresistance 436
6.9 Thermal Transport in Carbon Nanotubes 437
6.9.1 Introduction 437
6.9.2 Thermal Conductivity 439
6.9.3 Thermoelectric Power 442
6.9.4 Measurement Techniques 445
References 446
7 Mechanical Properties of Individual Nanotubes and Composites 452
7.1 Mechanical Properties of Materials, Basic Notions 452
7.1.1 Elasticity of Solids 452
Uniaxial Tensile Measurement 453
Simple Shearing 453
Hydrostatic Compression 454
Microscopic Origin of Elasticity 454
7.1.2 Viscoelasticity 455
Stress Relaxation Test 456
Creep Test 456
Dynamic Test 457
7.1.3 Non-Linear Behavior and Rupture 459
7.2 Mechanical Properties of a Single Nanotube 462
7.2.1 Theory and Simulations 462
Elasticity of Carbon Nanotubes 462
Deformation and Rupture of Carbon Nanotubes 467
7.2.2 Experiments 469
Vibration Analysis 470
Nanomechanics with an AFM 471
7.3 Reinforcing Composite Materials with Nanotubes 472
7.3.1 Composite Materials and Nanocomposites 472
Mechanical Behavior of Filled Polymers. Case 472
of Micron Sized Rigid Fillers 472
Mechanical Coupling Models 473
Nanocomposites Materials 475
7.3.2 Nanotube-Based Composite Materials 482
Mechanical Coupling in the Cox Model 482
Puri.cation, Individualization and Functionalization 484
of Nanotubes 484
Nanotube-Polymer Matrix Nanocomposites 484
Nanotube Alignment 488
Nanocomposite Fibers 488
Nanotube-Metallic Matrix Nanocomposites 489
Nanotube-Ceramic Matrix Nanocomposites 490
Carbon Fiber Composites with Nanotubes 491
7.3.3 A New Material: The Nanotube Fibers 492
Nanotube Alignment Characterization 493
Approaches for Making Fibers of Aligned Nanotubes 494
Acknowledgments 501
References 501
8 Surface Properties, Porosity, Chemical and Electrochemical Applications 507
8.1 Surface Area, Porosity and Reactivity 507
of Porous Carbons 507
8.1.1 Physical Adsorption of Gases as a Tool 508
to Characterize Porous Carbons 508
Gas-Solid Interactions 508
Adsorption-Desorption Isotherms 509
Adsorption-Isotherm Equations 511
Peculiarities of Adsorption in Microporous Carbons 514
Adsorptives Other Than N2: The Usefulness of CO2 Adsorption at 273K 518
8.1.2 Reactivity of Carbons 521
The Hydroxide-Carbon Reactions 521
Nanotube Activation 523
8.2 Surface Functionality, Chemical 525
and Electrochemical Reactivity of Carbons 525
8.2.1 Surface Functionality of Carbons 525
8.2.2 Oxygen Surface Groups of Carbons 526
8.2.3 Electrochemical Grafting of Carbon Surfaces 527
The Di.erent Methods for the Modi.cation of Carbon Surfaces 527
Characterization of the Attached Organic Groups 530
The Reaction Mechanisms and the Structure 530
of the Organic Layers 530
Applications of the Modi.ed Carbon Surfaces 532
8.2.4 Functionalization of Carbon Nanotubes 533
Functionalization of Oxidized Carbon Nanotubes 534
Sidewall Functionalization of Carbon Nanotubes 534
: 535
8.3 Filling of CNTs and In-Situ Chemistry 536
8.3.1 Filling Requirements: the Role of Surface Tension 536
8.3.2 How to Fill Carbon Nanotubes? 537
Filling During the Synthesis of CNTs 537
Post-Synthesis Filling of CNTs 538
8.3.3 Structural Modi.cations of Con.ned Matter 540
8.3.4 In-situ Chemistry Inside Carbon Nanotubes 541
8.4 Electrochemical Energy Storage 542
using Carbon Nanotubes 542
8.4.1 Lithium Insertion in Carbon Nanotubes 543
8.4.2 Use of Nanotubes in Electrochemical Capacitors 548
Capacitance Properties of Nanotubes 550
Capacitance Properties of Activated Nanotubes 551
Composites with a Nanotube Backbone 552
8.4.3 Conclusion 554
References 555
Index 562