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Atomistic Mechanism of Carbon Nanostructure Self-Assembly as Predicted by Nonequilibrium QM/MD Simulations

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Practical Aspects of Computational Chemistry II

Abstract

We review our quantum chemical molecular dynamics (QM/MD)-based studies of carbon nanostructure formation under nonequilibrium conditions that were conducted over the past 10+ years. Fullerene, carbon nanotube, and graphene formation were simulated on the nanosecond time scale, considering experimental conditions as closely as possible. An approximate density functional method was employed to compute energies and gradients on the fly in direct MD simulations, while the simulated systems were pushed away from equilibrium via carbon concentration or temperature gradients. We find that carbon nanostructure formation from feedstock particles involves a phase transition of sp to sp2 carbon phases, which begins with the formation of Y-junctions, followed by a nucleus consisting of pentagons, hexagons, and heptagons. The dominance of hexagons in the synthesized products is explained via annealing processes that occur during the cooling of the grown carbon structure, accelerated by transition-metal catalysts when present. The dimensional structures of the final synthesis products (0D~spheres – fullerenes, 1D tubes – nanotubes, 2D sheets – graphenes) are induced by the shapes of the substrates/catalysts and their interaction strength with carbon. Our work prompts a paradigm shift away from traditional anthropomorphic formation mechanisms solely based on thermodynamic stability. Instead, we conclude that nascent carbon nanostructures at high temperatures are dissipative structures described by nonequilibrium dynamics in the manner proposed by Prigogine, Whitesides, and others. As such, the fledgling carbon nanostructures consume energy while increasing the entropy of the environment and only gradually anneal to achieve their familiar, final structure, maximizing hexagon formation wherever possible.

What can be controlled is never completely real; what is real can never be completely controlled. Vladimir V. Nabokov [1]

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References

  1. Nabokov VV (1974) Look at the harlequins! McGraw-Hill, New York

    Google Scholar 

  2. Feynman R (1959) There’s plenty of room at the bottom: an invitation to enter a new world of physics. Paper presented at the annual meeting of the American Physical Society, Pasadena

    Google Scholar 

  3. Drexler KE (1986) Engines of creation. Anchor Books, New York

    Google Scholar 

  4. Drexler KE (1992) Nanosystems: molecular machinery, manufacturing, and computation. Wiley, New York

    Google Scholar 

  5. Binnig G, Rohrer H, Gerber C, Weibel E (1982) Tunneling through a controllable vacuum gap. Appl Phys Lett 40:178–180

    Article  CAS  Google Scholar 

  6. Smalley RE (2001) Of chemistry, love, and nanobots. Sci Am 285:76–77

    Article  CAS  Google Scholar 

  7. Baum R (2003) Nanotechnology. Chem Eng News 81(48):37–42

    Google Scholar 

  8. Lehn J-M (1995) Supramolecular chemistry: concepts and perspectives. Wiley-VCH, Weinheim

    Book  Google Scholar 

  9. Pawin G, Wong KL, Kwon K-Y, Bartels L (2006) A homomolecular porous network at a Cu(111) surface. Science 313:961–962

    Article  CAS  Google Scholar 

  10. Hoster HE, Roos M, Breitruck A, Meier C, Tonigold K, Waldmann T, Ziener U, Landfester K, Behm RJ (2007) Structure formation in Bis(terpyridine) derivative adlayers: molecule-substrate versus molecule-molecule interactions. Langmuir 23:11570–11579

    Article  CAS  Google Scholar 

  11. Love JC, Estroff LA, Kriebel JK, Nuzzo RG, Whitesides GM (2005) Self-assembled monolayers of thiolates on metals as a form of nanotechnology. Chem Rev 105:1103–1169

    Article  CAS  Google Scholar 

  12. Cai J, Ruffieux P, Jaafar R, Bieri M, Braun T, Blankenburg S, Muoth M, Seitsonen AP, Saleh M, Feng X, Müllen K, Fasel R (2010) Atomistically precise bottom-up fabrication of graphene nanoribbons. Nature 466:470–473

    Article  CAS  Google Scholar 

  13. Petitjean A, Khoury RG, Kyritsakas N, Lehn J-M (2004) Dynamic devices. Shape switching and substrate binding in ion-controlled nanomechanical molecular tweezers. J Am Chem Soc 126:6637–6647

    Article  CAS  Google Scholar 

  14. Seeman NC (2010) Structural DNA nanotechnology: growing along with nano letters. Nano Lett 10:1971–1978

    Article  CAS  Google Scholar 

  15. Kinbara K, Aida T (2005) Toward intelligent molecular machines: directed motions of biological and artificial molecules and assemblies. Chem Rev 105:1377–1400

    Article  CAS  Google Scholar 

  16. Kauffman S (2000) Investigations. Oxford University Press, Oxford

    Google Scholar 

  17. Seyed-Razavi A, Snook IK, Barnard AS (2010) Origin of nanomorphology: does a complete theory of nanoparticle evolution exist? J Mater Chem 20:416–421

    Article  CAS  Google Scholar 

  18. Alivisatos AP (1996) Semiconductor clusters, nanocrystals, and quantum dots. Science 271:933–937

    Article  CAS  Google Scholar 

  19. Xu X, Zhuang J, Wang X (2008) SnO2 Quantum dots and quantum wires: controllable synthesis, self-assembled 2D architectures, and gas-sensing properties. J Am Chem Soc 130:12527–12535

    Article  CAS  Google Scholar 

  20. Smolin L (1997) The life of the cosmos. Oxford University Press, Oxford

    Google Scholar 

  21. Kroto HW, Heath JR, O’Brien SC, Curl RF, Smalley RE (1985) C60: buckminsterfullerene. Nature 318:162–163

    Article  CAS  Google Scholar 

  22. Fowler PW, Manopoulous DE (1995) An atlas of fullerenes. Oxford University Press, Oxford

    Google Scholar 

  23. Fantini C, Cruz E, Jorio A, Terrones M, Terrones H, Van Lier G, Charlier J-C, Dresselhaus MS, Saito R, Kim YA, Hayashi T, Muramatsu H, Endo M, Pimenta MA (2006) Resonance Raman study of linear carbon chains formed by the heat treatment of double-wall carbon nanotubes. Phys Rev B 73:193408/193401–193404

    Article  CAS  Google Scholar 

  24. Saito R, Dresselhaus MS, Dresselhaus G (1998) Physical properties of carbon nanotubes. Imperial College Press, London

    Book  Google Scholar 

  25. Wu YH, Yu T, Shen ZX (2010) Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications. J Appl Phys Rev 108:071301/071301–071338

    Google Scholar 

  26. Krüger A (2008) The structure and reactivity of nanoscale diamond. J Mater Chem 18:1485–1492

    Article  CAS  Google Scholar 

  27. Terrones H, Terrones M, Hernandez E, Grobert N, Charlier JC, Ajayan PM (2000) New metallic allotropes of planar and tubular carbon. Phys Rev Lett 84:1716–1719

    Article  CAS  Google Scholar 

  28. Shioyama H, Akita T (2003) A new route to carbon nanotubes. Carbon 41:179–198

    Article  CAS  Google Scholar 

  29. Iijima S, Yudasaka M, Yamada R, Bandow S, Suenaga K, Kokai F, Takahashi K (1999) Nano-aggregates of single-walled graphitic carbon nano-horns. Chem Phys Lett 309:165–170

    Article  CAS  Google Scholar 

  30. Itoh S, Ihara S, Kitakami J (1993) Toroidal form of carbon C360. Phys Rev B 47:1703–1704

    Article  CAS  Google Scholar 

  31. Amelinckx S, Zhang XB, Bernaerts D, Zhang XF, Ivanov V, Nagy JB (1994) A formation mechanism for catalytically grown helix-shaped graphite nanotubes. Science 265:635–639

    Article  CAS  Google Scholar 

  32. Lee JM, Choung JW, Yi J, Lee DH, Samal M, Yi DK, Lee C-H, Yi G-C, Paik U, Rogers JA, Park WI (2010) Vertical pillar-superlattice array and graphene hybrid light emitting diodes. Nano Lett 10:2783–2788

    Article  CAS  Google Scholar 

  33. Zakhidov AA, Baughman RA, Iqbal Z, Cui C, Khayrullin I, Dantas SO, Marti J, Ralchenko VG (1998) Carbon structures with three-dimensional periodicity at optical wavelengths. Science 282:897–901

    Article  CAS  Google Scholar 

  34. Terrones H, Terrones M (2003) Curved nanostructure materials. New J Phys 5:126/121–137

    Article  Google Scholar 

  35. Terrones M, Botello-Mendez AR, Campos-Delgado J, Lopez-Urias F, Vega-Cunti YI, Rodriguez-Marcias FJ, Elias AL, Munoz-Sandoval E, Cano-Marquez AG, Charlier J-C, Terrones H (2010) Graphene and graphite nanoribbons: morphology, properties, synthesis, defects and applications. Nano Today 5:351–372

    Article  CAS  Google Scholar 

  36. Krüger A (2010) Carbon materials and nanotechnology. Wiley-VCH, Weinheim

    Book  Google Scholar 

  37. Baughman RA, Zakhidov AA, de Heer WA (2002) Carbon nanotubes – the route toward applications. Science 297:787–792

    Article  CAS  Google Scholar 

  38. Mamalis AG, Vogtländer LOG, Markopoulos A (2004) Nanotechnology and nanostructured materials: tends in carbon nanotubes. Precis Eng 28:16–30

    Article  Google Scholar 

  39. Ma JC, Dougherty DA (1997) The cation-pi interaction. Chem Rev 97:1303–1324

    Article  CAS  Google Scholar 

  40. Fukui K (1981) The path of chemical reactions – the IRC approach. Acc Chem Res 14:363–368

    Article  CAS  Google Scholar 

  41. Irle S, Zheng G, Wang Z, Morokuma K (2007) Theory-experiment relationship of the “shrinking hot giant” road of dynamic fullerene self-assembly in hot carbon vapor. Nano 2:21–30

    Article  CAS  Google Scholar 

  42. Krätschmer W, Lamb LD, Fostiropoulos K, Huffman DR (1990) Solid C60: a new form of carbon. Nature 347:354–358

    Article  Google Scholar 

  43. Whittaker AG (1978) The controversial carbon solid-liquid-vapour triple point. Nature 276:695–696

    Article  CAS  Google Scholar 

  44. Sasaki K (2011) Spectroscopic studies on laser-produced carbon vapor. In: Laszlo N, Irle S (eds) Spectroscopy, dynamics and molecular theory of carbon plasmas and vapors. World Scientific, Singapore

    Google Scholar 

  45. Ashfold MNR, May PW, Rego CA, Everitt NM (1994) Thin film diamond by chemical vapour deposition methods. Chem Soc Rev 23:21–30

    Article  CAS  Google Scholar 

  46. Cheesman A, Harvey JN, Ashfold MNR (2008) Studies of carbon incorporation on the diamond 100 surface during chemical vapor deposition using density functional theory. J Phys Chem A 112(45):11436–11438

    Article  CAS  Google Scholar 

  47. Puretzky AA, Geohegan DB, Schittenhelm H, Fan X, Guillorn MA (2002) Time-resolved diagnostics of single wall carbon nanotube synthesis by laser vaporization. Appl Surf Sci 197–198:552–562

    Article  Google Scholar 

  48. Cheng HM, Li F, Su G, Pan HY, He LL, Sun X, Dresselhaus MS (1998) Large-scale and low-cost synthesis of single-walled carbon nanotubes by the catalytic pyrolysis of hydrocarbons. Appl Phys Lett 72:3282–3284

    Article  CAS  Google Scholar 

  49. Nikolaev P, Bronikowski MJ, Bradley RK, Rohmund F, Colbert DT, Smith KA, Smalley RE (1999) Gas-phase catalytic growth of single-walled carbon nanotubes from carbon monoxide. Chem Phys Lett 313:91–97

    Article  CAS  Google Scholar 

  50. Maruyama S, Kojima R, Miyauchi Y, Chiashi S, Kohno M (2002) Low-temperature synthesis of high-purity single-walled carbon nanotubes from alcohol. Chem Phys Lett 360:229–234

    Article  CAS  Google Scholar 

  51. Nagashima A, Tejima N, Oshima C (1994) Electronic states of the pristine and alkali-metal-intercalated monolayer graphite/Ni(111) systems. Phys Rev B 50(23):17487–17495

    Article  CAS  Google Scholar 

  52. Choi W, Lahiri I, Seelaboyina R, Kang YS (2010) Synthesis of graphene and its applications: a review. Crit Rev Solid State 35(1):52–71

    Article  CAS  Google Scholar 

  53. Charlier J-C, Iijima S (2001) Growth mechanisms of carbon nanotubes, vol 80, Carbon nanotubes: synthesis, structure, properties, and application. Springer, New York

    Google Scholar 

  54. Nessim GD, Seita M, Plata DL, O’Brien KP, Hart AJ, Meshot ER, Reddy CM, Gschwend PM, Thompson CV (2011) Precursor gas chemistry determines the crystallinity of carbon nanotubes synthesized at low temperature. Carbon 49:804–810

    Article  CAS  Google Scholar 

  55. Puretzky AA, Geohegan DB, Jesse S, Ivanov IN, Eres G (2005) In situ measurements and modeling of carbon nanotube array growth kinetics during chemical vapor deposition. Appl Phys A 81(2):223

    Article  CAS  Google Scholar 

  56. Wakabayashi T, Achiba Y (1992) A model for the C60 and C70 growth mechanism. Chem Phys Lett 190(5):465–468

    Article  CAS  Google Scholar 

  57. Smalley RE (1992) Self-assembly of the fullerenes. Acc Chem Res 25:98–105

    Article  CAS  Google Scholar 

  58. Ding F, Harutyunyan AR, Yakobson BI (2009) Dislocation theory of chirality-controlled nanotube growth. Proc Natl Acad Sci 106:2506–2509

    Article  CAS  Google Scholar 

  59. Kroto HW (1987) The stability of the fullerenes Cn, with n = 24, 28, 32, 36, 50, 60 and 70. Nature 384:529–531

    Article  Google Scholar 

  60. Burton WK, Cabrera N, Frank FC (1949) Role of dislocations in crystal growth. Nature 163:398–399

    Article  CAS  Google Scholar 

  61. Eres G, Rouleau CM, Yoon M, Puretzky AA, Jackson JJ, Geohegan DB (2009) Model for self-assembly of carbon nanotubes from acetylene based on real-time studies of vertically aligned growth kinetics. J Phys Chem C 113:15484–15491

    Article  CAS  Google Scholar 

  62. Irle S, Zheng G, Wang Z, Morokuma K (2006) The C60 formation puzzle “solved”: QM/MD simulations reveal the shrinking hot giant road of the dynamic fullerene self-assembly mechanism. J Phys Chem B 110:14531–14545

    Article  CAS  Google Scholar 

  63. Irle S, Ohta Y, Okamoto Y, Page AJ, Wang Y, Morokuma K (2009) Milestones in molecular dynamics simulations of single-walled carbon nanotube formation: a brief critical review. Nano Res 2:755–767

    Article  CAS  Google Scholar 

  64. Prigogine I, Stengers I (1984) Order out of chaos: man’s new dialogue with nature. Bantam Books, Toronto

    Google Scholar 

  65. Prigogine I (1997) The end of certainty – time, chaos, and the new laws of nature. The Free Press, New York

    Google Scholar 

  66. Fialkowsy M, Bishop KJM, Klajn R, Smoukov SK, Campbell CJ, Grzybowski BA (2006) Principles and implementations of dissipative (dynamic) self-assembly. J Phys Chem B 110:2482–2496

    Article  CAS  Google Scholar 

  67. Bak P (1996) How nature works: the science of self-organised criticality. Copernicus Press, New York

    Google Scholar 

  68. Tersoff J (1988) New empirical approach for the structure and energy of covalent systems. Phys Rev B 37:6991–7000

    Article  Google Scholar 

  69. Tersoff J (1989) Modeling solid-state chemistry: Interatomic potentials for multicomponent systems. Phys Rev B 39:5566–5568

    Article  Google Scholar 

  70. Brenner DW (1990) Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys Rev B 42:9458–9471

    Article  CAS  Google Scholar 

  71. Brenner DW (1992) Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. [Erratum to document cited in CA114(6):53045x]. Phys Rev B 46:1948

    Article  CAS  Google Scholar 

  72. Brenner DW (2000) The art and science of an analytical potential. Phys Status Solidi B 217:23–40

    Article  CAS  Google Scholar 

  73. Maruyama S, Yamaguchi Y (1998) A molecular dynamics demonstration of annealing to a perfect C60 structure. Chem Phys Lett 286:343–349

    Article  CAS  Google Scholar 

  74. Yamaguchi Y, Maruyama S (1998) A molecular dynamics simulation of the fullerene formation process. Chem Phys Lett 286:336–342

    Article  CAS  Google Scholar 

  75. Shibuta Y, Maruyama S (2002) Molecular dynamics simulation of generation process of SWNTs. Phys B 323:187–189

    Article  CAS  Google Scholar 

  76. Shibuta Y, Maruyama S (2003) Molecular dynamics simulation of formation process of single-walled carbon nanotubes by CCVD method. Chem Phys Lett 382:381–386

    Article  CAS  Google Scholar 

  77. Shibuta Y, Maruyama S (2004) Molecular dynamics of nucleation process of single-walled carbon nanotubes. Therm Sci Eng 12(4):79–80

    CAS  Google Scholar 

  78. Ding F, Bolton K, Rosen A (2004) Nucleation and growth of single-walled carbon nanotubes: a molecular dynamics study. J Phys Chem B 108(45):17369–17377

    Article  CAS  Google Scholar 

  79. Ding F, Bolton K, Rosen A (2004) Iron-carbide cluster thermal dynamics for catalyzed carbon nanotube growth. J Vac Sci Technol A 22(4):1471–1476

    Article  CAS  Google Scholar 

  80. Ding F, Rosen A, Bolton K (2004) Molecular dynamics study of the catalyst particle size dependence on carbon nanotube growth. J Chem Phys 121(6):2775–2779

    Article  CAS  Google Scholar 

  81. Ding F, Rosen A, Bolton K (2004) The role of the catalytic particle temperature gradient for SWNT growth from small particles. Chem Phys Lett 393:309–313

    Article  CAS  Google Scholar 

  82. Ding F, Rosen A, Bolton K (2005) Dependence of SWNT growth mechanism on temperature and catalyst particle size: bulk versus surface diffusion. Carbon 43:2215–2217

    Article  CAS  Google Scholar 

  83. Ding F, Rosen A, Campbell CJ, Falk LKL, Bolton K (2006) Graphitic encapsulation of catalyst particles in carbon nanotube production. J Phys Chem B 110:7666–7670

    Article  CAS  Google Scholar 

  84. Charlier J-C, De Vita A, Blase X, Car R (1997) Microscopic growth mechanisms for carbon nanotubes. Science 275:646–649

    Article  CAS  Google Scholar 

  85. Gavillet J, Loiseau A, Journet C, Willaime F, Ducastelle F, Charlier J-C (2001) Root-growth mechanism for single-wall carbon nanotubes. Phys Rev Lett 87(27):275504–275501

    Article  CAS  Google Scholar 

  86. Raty J-Y, Gygi F, Galli G (2005) Growth of carbon nanotubes on metal nanoparticles: a microscopic mechanism from ab initio molecular dynamics simulations. Phys Rev Lett 95:096103/096101–096104

    Article  CAS  Google Scholar 

  87. Porezag D, Frauenheim T, Köhler T, Seifert G, Kaschner R (1995) Construction of tight-binding-like potentials on the basis of density-functional theory: application to carbon. Phys Rev B 51:12947–12957

    Article  CAS  Google Scholar 

  88. Seifert G, Porezag D, Frauenheim T (1996) Calculations of molecules, clusters, and solids with a simplified LCAO-DFT-LDA scheme. Int J Quantum Chem 58:185–192

    Article  CAS  Google Scholar 

  89. Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G (1998) Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys Rev B 58:7260–7268

    Article  CAS  Google Scholar 

  90. Kohler C, Seifert G, Gerstmann U, Elstner M, Overhof H, Frauenheim T (2001) Approximate density-functional calculations of spin densities in large molecular systems and complex solids. Phys Chem Chem Phys 3:5109–5114

    Article  CAS  Google Scholar 

  91. Weinert M, Davenport JW (1992) Fractional occupations and density-functional energies and forces. Phys Rev B 45(23):13709–13712

    Article  Google Scholar 

  92. Witek H, Irle S, Morokuma K (2004) Analytical second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding method. J Chem Phys 121:5163

    Article  CAS  Google Scholar 

  93. Elstner M, Hobza P, Frauenheim T, Suhai S, Kaxiras E (2001) Hydrogen bonding and stacking interactions of nucleic acid base pairs: a density-functional-theory based treatment. J Chem Phys 114:5149–5155

    Article  CAS  Google Scholar 

  94. Hourahine B, Sanna S, Aradi B, Köhler C, Niehaus T, Frauenheim T (2007) Self-interaction and strong correlation in DFTB. J Phys Chem A 111:5671–5677

    Article  CAS  Google Scholar 

  95. Rapacioli M, Spiegelman F, Scemama A, Mirtschink A (2010) Modeling charge resonance in cationic molecular clusters: combining DFT-tight binding with configuration interaction. J Chem Theory Comput 7:44–55

    Article  CAS  Google Scholar 

  96. Alder BJ, Wainwright TE (1957) Phase transition for a hard sphere system. J Chem Phys 27:1208–1209

    Article  CAS  Google Scholar 

  97. Rahman A (1964) Correlations in the motion of atoms in liquid argon. Phys Rev 136:A405–A411

    Article  Google Scholar 

  98. Swope WC, Andersen HC, Berens PH, Wilson KR (1982) A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters. J Chem Phys 76(1):637–649

    Article  CAS  Google Scholar 

  99. Andersen HC (1980) Molecular dynamics simulations at constant pressure and/or temperature. J Chem Phys 72:2384–2393

    Article  CAS  Google Scholar 

  100. Berendsen HJC, Postma JPM, van Gunsteren WF, DiNola A, Haak JR (1984) Molecular dynamics with coupling to an external bath. J Chem Phys 81:3684–3690

    Article  CAS  Google Scholar 

  101. Woodcock LV (1971) Isothermal molecular dynamics calculations for liquid salts. Chem Phys Lett 10:257–261

    Article  CAS  Google Scholar 

  102. Hoover WG (1985) Canonical dynamics: equilibrium phase-space distributions. Phys Rev A 31:1695–1697

    Article  Google Scholar 

  103. Martyna GJ, Klein ML, Tuckerman M (1992) Nose-Hoover chains: the canonical ensemble via continuous dynamics. J Chem Phys 97:2635–2643

    Article  Google Scholar 

  104. Martyna GJ, Tobias DJ, Tuckerman M, Klein ML (1996) Explicit reversible integrators for extended systems dynamics. Mol Phys 87:1117–1157

    Article  CAS  Google Scholar 

  105. Nose S (1984) A unified formulation of the constant temperature molecular dynamics methods. J Chem Phys 81:511–519

    Article  CAS  Google Scholar 

  106. Rohlfing EA, Cox DM, Kaldor A (1984) Production and characterization of supersonic carbon cluster beams. J Chem Phys 81(7):3322–3330

    Article  CAS  Google Scholar 

  107. Hoffmann R (1966) Extended Hückel theory – V: cumulenes, polyenes, polyacetylenes and Cn. Tetrahedron 22:521–538

    Article  CAS  Google Scholar 

  108. Parasuk V (2011) Electronic and molecular structures of small- and medium-sized carbon clusters. In: Nemes L, Irle S (eds) Spectroscopy, dynamics and molecular theory of carbon plasmas and vapors. World Scientific, Singapore

    Google Scholar 

  109. Kroto HW, Heath JR, O’Brien SC, Curl RF, Smalley RE (1987) Long carbon chain molecules in circumstellar shells. Astrophys J 314(1):352–355

    Article  CAS  Google Scholar 

  110. Dunlap BI, Boettger JC (1996) Local-density-functional study of the fullerenes, graphene, and graphite. J Phys B At Mol Opt Phys 29(21):4907–4913

    Article  CAS  Google Scholar 

  111. Calaminici P, Geudtner G, Koster AM (2009) First-principle calculations of large fullerenes. J Chem Theory Comput 5:29–32

    Article  CAS  Google Scholar 

  112. Curl RF, Haddon RC (1993) On the formation of the fullerenes. Philos Trans R Soc London Ser A 343:19–32

    Article  CAS  Google Scholar 

  113. Mintmire JW (1996) Fullerene formation and annealing. Science 272:45–46

    Article  CAS  Google Scholar 

  114. Howard JB, McKinnon JT, Makarovsky Y, Lafleur AL, Johnson ME (1991) Fullerenes C60 and C70 in flames. Nature 352:139–141

    Article  CAS  Google Scholar 

  115. Kroto HW (1992) C60: buckminsterfullerene, the celestial sphere that fell to earth. Angew Chem Int Ed 31(2):111–129

    Article  Google Scholar 

  116. Heath JR, Zhang Q, O’Brien SC, Curl RF, Kroto HW, Smalley RE (1987) The formation of long carbon chain molecules during laser vaporization of graphite. J Am Chem Soc 109(2):359–363

    Article  CAS  Google Scholar 

  117. van Helden G, Gotts NG, Bowers MT (1993) Experimental evidence for the formation of fullerenes by collisional heating of carbon rings in the gas phase. Nature 363:60–63

    Article  Google Scholar 

  118. Goroff NS (1996) Mechanism of fullerene formation. Acc Chem Res 29:77–83

    Article  CAS  Google Scholar 

  119. Irle S, Zheng G, Elstner M, Morokuma K (2003) From C2 molecules to fullerenes in quantum chemical molecular dynamics. Nano Lett 3:1657–1664

    Article  CAS  Google Scholar 

  120. Zheng G, Irle S, Morokuma K (2005) Towards formation of buckminsterfullerene C60 in quantum chemical molecular dynamics. J Chem Phys 122:014708

    Article  CAS  Google Scholar 

  121. Ueno Y, Saito S (2008) Geometries, stabilities, and reactions of carbon clusters: towards a microscopic theory of fullerene formation. Phys Rev B 77:085403/085401–085411

    Article  CAS  Google Scholar 

  122. Yamaguchi Y, Colombo L, Piseri P, Ravagnan L, Milani P (2007) Growth of sp-sp2 nanostructures in a carbon plasma. Phys Rev B 76:134119/134111–134117

    Google Scholar 

  123. Wakabayashi T, Kasuya D, Shiromaru H, Suzuki S, Kikuchi K, Achiba Y (1997) Towards the selective formation of specific isomers of fullerenes: T- and p-dependence in the yield of various isomers of fullerenes C60-C84. Z Phys D Atom Mol Cl 40:414–417

    Article  CAS  Google Scholar 

  124. Xu CX, Scuseria GE (1994) Tight-binding molecular dynamics simulations of fullerene annealing and fragmentation. Phys Rev Lett 72:669–672

    Article  CAS  Google Scholar 

  125. Zheng G, Wang Z, Irle S, Morokuma K (2007) Quantum chemical molecular dynamics simulations of “shrinking” of hot giant fullerenes. J Nanosci Nanotechnol 7:1662–1669

    Article  CAS  Google Scholar 

  126. Bogana M, Ravagnan L, Casari CS, Zivelonghi A, Baserga A, Bassi AL, Bottani CE, Vinati S, Salis E, Piseri P, Barborini E, Colombo L, Milani P (2005) Leaving the fullerene road: presence and stability of sp chains in sp2 carbon clusters and cluster-assembled solids. New J Phys 7(81):1–8

    Google Scholar 

  127. Guangshi T, Hengjian Z, Chuanbao C, Rongzhi L, Hesun Z (1995) The effect of the atmosphere on the formation of fullerene. J Beijing Inst Technol 4(2):141–147

    Google Scholar 

  128. Curl RF, Lee MK, Scuseria GE (2008) C60 buckminsterfullerene high yields unraveled. J Phys Chem A 112(46):11951–11955

    Article  CAS  Google Scholar 

  129. Fowler PW (1986) How unusual is C60? Magic numbers for carbon clusters. Chem Phys Lett 131(6):444–450

    Article  CAS  Google Scholar 

  130. Osawa E, Ueno H, Yoshida M, Slanina Z, Zhao X, Nishiyama M, Saito H (1998) Combined topological and energy analysis of the annealing process in fullerene formation. Stone–Wales interconversion pathways among IPR isomers of higher fullerenes. J Chem Soc, Perkin Trans 2. 1998:943–950

    Google Scholar 

  131. Sommer T, Kruse T, Roth P (1996) Thermal stability of fullerenes: a shock tube study on the pyrolysis of C60 and C70. J Phys B At Mol Opt Phys 29:4955–4964

    Article  CAS  Google Scholar 

  132. Bettinger HF, Yakobson BI, Scuseria GE (2003) Scratching the surface of buckminsterfullerene: the barriers for Stone-Wales transformation through symmetric and asymmetric transition states. J Am Chem Soc 125:5572–5580

    Article  CAS  Google Scholar 

  133. Saito S, Oshiyama A (1991) Electronic and geometric structures of C70. Phys Rev B 44(20):11532–11535

    Article  CAS  Google Scholar 

  134. Huang JY, Ding F, Jiao K, Yakobson BI (2007) Real time microscopy, kinetics, and mechanism of giant fullerene evaporation. Phys Rev Lett 99:175503/175501–175504

    Google Scholar 

  135. Zhang QL, O’Brien SC, Heath JR, Liu Y, Kroto HW, Smalley RE (1986) Reactivity of large carbon clusters: spheroidal carbon shells and their possible relevance to the formation and morphology of soot. J Phys Chem 90(4):525–528

    Article  CAS  Google Scholar 

  136. Saha B, Shindo S, Irle S, Morokuma K (2009) Quantum chemical molecular dynamics simulations of dynamic fullerene self-assembly in benzene combustion. ACS Nano 3:2241–2257

    Article  CAS  Google Scholar 

  137. Saha B, Irle S, Morokuma K (2010) Formation mechanism of polycyclic aromatic hydrocarbons in benzene combustion: quantum chemical molecular dynamics simulations. J Chem Phys 132:224303/224301–224303/224311

    Google Scholar 

  138. Chuvilin A, Kaiser U, Bichoutskaia E, Besley NA, Khlobystov AN (2010) Direct transformation of graphene to fullerene. Nature Chem 2:450–453

    Article  CAS  Google Scholar 

  139. Koshino M, Niimi Y, Nakamura E, Kataura H, Okazaki T, Suenaga K, Iijima S (2010) Analysis of the reactivity and selectivity of fullerene dimerization reactions at the atomic level. Nature Chem 2:117–124

    Article  CAS  Google Scholar 

  140. Hansen K, Yeretzian C, Whetten RL (1994) A simple rate equation for fullerene coalescence. Chem Phys Lett 218:462–466

    Article  CAS  Google Scholar 

  141. Yi J-Y, Bernholc J (1993) Reactivity, stability, and formation of fullerenes. Phys Rev B 48(8):5724–5727

    Article  CAS  Google Scholar 

  142. Endo M, Kroto HW (1992) Formation of carbon nanofibers. J Phys Chem 96:6941–6944

    Article  CAS  Google Scholar 

  143. Yoshida M, Osawa E (1995) Formalized drawing of fullerene nets. 2. Applications to mapping of pyracylene rearrangements, C2-insertion/elimination pathways, and leapfrog/carbon cylinder operations. Bull Chem Soc Jpn 68:2083–2092

    Article  CAS  Google Scholar 

  144. Suzuki S, Yamaguichi H, Ishigaki T, Kataura H, Kratschmer W, Achiba Y (2001) Time evolution of emission by carbon nanoparticles generated with a laser furnace technique. Eur Phys J D 16:369–372

    Article  CAS  Google Scholar 

  145. Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems: from dissipative structures to order through fluctuations. Wiley, New York

    Google Scholar 

  146. Guo T, Nikolaev P, Thess A, Colbert DT, Smalley RE (1995) Catalytic growth of single-walled carbon nanotubes by laser vaporization. Chem Phys Lett 243:49–54

    Article  CAS  Google Scholar 

  147. Thess A, Lee R, Nikolaev P, Dai H, Petit P, Robert J, Xu C, Lee YH, Kim SG, Rinzler AG, Colbert DT, Scuseria GE, Tomanek D, Fischer JE, Smalley RE (1996) Crystalline ropes of metallic carbon nanotubes. Science 273:483–487

    Article  CAS  Google Scholar 

  148. Guo T, Nikolaev P, Rinzler AG, Tomanek D, Colbert DT, Smalley RE (1995) Self-assembly of tubular fullerenes. J Phys Chem 99:10694–10697

    Article  CAS  Google Scholar 

  149. Iijima S (1993) Single-shell carbon nanotubes of 1-nm diameter. Nature 363:603–605

    Article  CAS  Google Scholar 

  150. Bethune DS, Kiang CH, DeVries MS, Gorman G, Savoy R, Beyers R (1993) Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer wall. Nature 363:605–607

    Article  CAS  Google Scholar 

  151. Journet C, Maser WK, Bernier P, Loiseau A, Lamy de la Chapelle M, Lefrant S, Deniard P, Lee R, Fischer JE (1997) Large-scale production of single-walled carbon nanotubes by the electric-arc technique. Nature 388:756–758

    Article  CAS  Google Scholar 

  152. Guillard T, Cetout S, Alvarez L, Sauvajol JL, Anglaret E, Bernier P, Flamant G, Laplaze D (1999) Production of carbon nanotubes by the solar route. Eur Phys J 5:251–256

    Article  CAS  Google Scholar 

  153. Shinohara H (2011) Montreal (private communication)

    Google Scholar 

  154. Rinzler AG, Liu J, Dai H, Nikolaev P, Huffman CB, Rodriguez-Marcias FJ, Boul PJ, Lu AH, Heymann D, Colbert DT, Lee RS, Fischer JE, Rao AM, Eklund PC, Smalley RE (1998) Large-scale purification of single-wall carbon nanotubes. Process, product, and characterization. Appl Phys A-Mater 67(1):29–37

    Article  CAS  Google Scholar 

  155. Sugai T, Okazaki T, Yoshida H, Shinohara H (2004) Syntheses of single- and double-wall carbon nanotubes by the HTPAD and HFCVD methods. New J Phys 43(2):431–436

    Google Scholar 

  156. Journet C, Bernier P (1998) Production of carbon nanotubes. Appl Phys A-Mater 67(1):1–9

    Article  CAS  Google Scholar 

  157. Scott CD, Arepalli S, Nikolaev P, Smalley RE (2001) Growth mechanisms for single-wall carbon nanotubes in a laser-ablation process. Appl Phys A-Mater 72(5):573–580

    Article  CAS  Google Scholar 

  158. Nishide D, Kataura H, Suzuki S, Tsukagoshi K, Aoyagi Y, Achiba Y (2003) High-yield production of single-wall carbon nanotubes in nitrogen gas. Chem Phys Lett 372(1, 2):45–50

    Article  CAS  Google Scholar 

  159. Ramesh S, Brinson B, Johnson MP, Gu Z, Saini RK, Willis P, Marriott T, Billups WE, Margrave JL, Hauge RH, Smalley RE (2003) Identification of large fullerenes formed during the growth of single-walled carbon nanotubes in the HiPco process. J Phys Chem B 107(6):1360

    Article  CAS  Google Scholar 

  160. Sadana AK, Liang F, Brinson B, Arepalli S, Farhat S, Hauge RH, Smalley RE, Billups WE (2005) Functionalization and extraction of large fullerenes and carbon-coated metal formed during the synthesis of single wall carbon nanotubes by laser oven, direct current arc, and high-pressure carbon monoxide production methods. J Phys Chem B 109:4416

    Article  CAS  Google Scholar 

  161. Cheng HM, Li F, Sun X, Brown SDM, Pimenta MA, Marucci A, Dresselhaus G, Dresselhaus MS (1998) Bulk morphology and diameter distribution of single-walled carbon nanotubes synthesized by catalytic decomposition of hydrocarbons. Chem Phys Lett 289(5–6):602–610

    Article  CAS  Google Scholar 

  162. Zhu Z, Jiang H, Susi T, Nasibulin AG, Kauppinen EI (2011) The use of NH3 to promote the production of large-diameter single-walled carbon nanotubes with a narrow (n, m) distribution. J Am Chem Soc 133:1224–1227

    Article  CAS  Google Scholar 

  163. Jackson JJ, Puretzky AA, More KL, Rouleau CM, Eres G, Geohegan DB (2010) Pulsed growth of vertically aligned nanotube arrays with variable density. ACS Nano 4:7573–7581

    Article  CAS  Google Scholar 

  164. Shukla B, Saito T, Yumura M, Iijima S (2009) An efficient carbon precursor for gas phase growth of SWCNTs. Chem Commun 2009:3422–3424

    Article  CAS  Google Scholar 

  165. Hata K, Futaba DN, Mizuno K, Namai T, Yumura M, Iijima S (2004) Water-assisted highly-efficient synthesis of impurity-free single-walled carbon nanotubes. Science 306:1362–1364

    Article  CAS  Google Scholar 

  166. Ren WC, Li F, Cheng HM (2005) Shell control and growth mechanism of carbon nanotubes by sulfur-enhanced floating catalyst method. Paper presented at the NASA/Rice University 2nd workshop on nucleation and growth of single-wall carbon nanotubes, Boerne, 8–12 April 2005

    Google Scholar 

  167. Valles C, Perez-Mendoza M, Castell P, Martinez MT, Maser WK, Benito AM (2006) Towards helical and Y-shaped carbon nanotubes: the role of sulfur in CVD processes. Nanotechnology 17:4292–4299

    Article  CAS  Google Scholar 

  168. Scott CD, Arepalli S (2005) Second NASA/Rice University workshop on SWNT nucleation and growth mechanisms. In: 2nd NASA/Rice University workshop on SWNT nucleation and growth mechanisms, Boerne, 2005

    Google Scholar 

  169. Ago H, Uehara N, Yoshihara N, Tsuji M, Yumura M, Tomonaga N, Setoguchi T (2006) Gas analysis of the CVD process for high yield growth of carbon nanotubes over metal-supported catalysts. Carbon 44:2912–2918

    Article  CAS  Google Scholar 

  170. Zhang G, Mann D, Zhang L, Javey A, Li Y, Yenilmez E, Wang Q, McVittie JP, Nishi Y, Gibbons J, Dai H (2005) Ultra-high-yield growth of vertical single-walled carbon nanotubes: hidden roles of hydrogen and oxygen. Proc Natl Acad Sci 102(45):16141–16145

    Article  CAS  Google Scholar 

  171. Xu Y-Q, Flor E, Schmidt H, Smalley RE, Hauge RH (2006) Effects of atomic hydrogen and active carbon species in 1 mm vertically aligned single-walled carbon nanotube growth. Appl Phys Lett 89:123116/123111–123116/123113

    Google Scholar 

  172. Amama PB, Pint CL, McJilton L, Kim SM, Stach EA, Murray PT, Hauge RH, Maruyama B (2009) Role of water in super growth of single-walled carbon nanotube carpets. Nano Lett 9:44–49

    Article  CAS  Google Scholar 

  173. Alexandrescu R, Crunteanu A, Morjan R-E, Morjan F, Rohmund F, Falk LKL, Ledoux G, Huisken F (2003) Synthesis of carbon nanotubes by CO2-laser-assisted thermal CVD. Infrared Phys Techn 44:43–47

    Article  CAS  Google Scholar 

  174. Wang Y, Gao X, Eres G, Ohta Y, Qian H-J, Morokuma K, Irle S (2011) Acetylene oligomerization and oligoyne cross-linking on an iron particle: quantum chemical molecular dynamics simulations inspired by experiment. Submitted

    Google Scholar 

  175. Sugai Y, Yoshida H, Shimada T, Okazaki T, Shinohara H (2003) New synthesis of high-quality double-walled carbon nanotubes by high-temperature pulsed arc discharge. Nano Lett 3(6):769–773

    Article  CAS  Google Scholar 

  176. Dai H, Rinzler AG, Nikolaev P, Thess A, Colbert DT, Smalley RE (1996) Single-wall nanotubes produced by metal-catalyzed disproportionation of carbon monoxide. Chem Phys Lett 260(3–4):471–475

    Article  CAS  Google Scholar 

  177. Ohta Y, Okamoto Y, Page AJ, Irle S, Morokuma K (2009) Quantum chemical molecular dynamics simulation of single-walled carbon nanotube cap nucleation on an iron particle. ACS Nano 3(11):3413–3420

    Article  CAS  Google Scholar 

  178. Arepalli S, Scott CD (1999) Spectral measurements in production of single-wall carbon nanotubes by laser ablation. Chem Phys Lett 302:139–145

    Article  CAS  Google Scholar 

  179. Moodley MK, Coville NJ (2010) Experimental evidence for the early nucleation of single-walled carbon nanotubes. Chem Phys Lett 498:140–144

    Article  CAS  Google Scholar 

  180. Yudasaka M, Yamada R, Sensui N, Wilkins T, Ichihashi T, Iijima S (1999) Mechanism of the effect of NiCo, Ni and Co catalysts on the yield of single-wall carbon nanotubes formed by pulsed Nd:YAG laser ablation. J Phys Chem B 103:6224–6229

    Article  CAS  Google Scholar 

  181. Yudasaka M, Kasuya Y, Kokai F, Takahashi K, Takizawa M, Bandow S, Iijima S (2002) Causes of different catalytic activities of metals in formation of single-wall carbon nanotubes. Appl Phys A-Mater 74:377–385

    Article  CAS  Google Scholar 

  182. Cau M, Dorval N, Cao B, Attal-Tretout B, Cochon JL, Loiseau A, Farhat S, Scott CD (2006) Spatial evolutions of Co and Ni atoms during single-walled carbon nanotubes formation: measurements and modeling. J Nanosci Nanotechnol 6:1298–1299

    Article  CAS  Google Scholar 

  183. Kataura H, Kumuzawa Y, Maniwa Y, Ohtsuka Y, Sen R, Suzuki S, Achiba Y (2000) Diameter control of single-walled carbon nanotubes. Carbon 38(11–12):1691–1697

    Article  CAS  Google Scholar 

  184. Nikolaev P, Holmes W, Sosa E, Boul P, Arepalli S (2009) Effect of the laser heating of nanotube nuclei on the nanotube type population. Nano Res 2:818–827

    Article  CAS  Google Scholar 

  185. Saito Y (1995) Nanoparticles and filled nanocapsules. Carbon 33(7):979–988

    Article  CAS  Google Scholar 

  186. Harris PJF (2007) Solid state growth mechanisms for carbon nanotubes. Carbon 45:229–239

    Article  CAS  Google Scholar 

  187. Fan X, Buczko R, Puretzky AA, Geohegan DB, Howe JY, Pantelides ST, Pennycook SJ (2003) Nucleation of single-walled carbon nanotubes. Phys Rev Lett 90(14):145501/145501–145501/145504

    Article  CAS  Google Scholar 

  188. Irle S, Zheng G, Elstner M, Morokuma K (2003) Formation of fullerene molecules from carbon nanotubes: a quantum chemical molecular dynamics study. Nano Lett 3(4):465–470

    Article  CAS  Google Scholar 

  189. Zheng G, Irle S, Elstner M, Morokuma K (2004) Quantum chemical molecular dynamics model study of fullerene formation from open-ended carbon nanotubes. J Phys Chem A 108:3182–3194

    Article  CAS  Google Scholar 

  190. Rinzler AG, Hafner JA, Nikolaev P, Lou L, Kim SG, Tomanek D, Nordlander P, Colbert DT, Smalley RE (1996) Unraveling nanotubes: field emission from an atomic wire. Science 269:1550–1553

    Article  Google Scholar 

  191. Yoshida H, Takeda S, Uchiyama T, Kohno H, Homma Y (2008) Atomic-scale in-situ observation of carbon nanotube growth from solid state iron carbide nanoparticles. Nano Lett 8(7):2082–2086

    Article  CAS  Google Scholar 

  192. Yoshida H, Shimizu T, Uchiyama T, Kohno H, Homma Y, Takeda S (2009) Atomic-scale analysis on the role of molybdenum in iron-catalyzed carbon nanotube growth. Nano Lett 9:3810–3815

    Article  CAS  Google Scholar 

  193. Hofmann S, Sharma R, Ducati C, Du G, Mattevi C, Cepek C, Cantoro M, Pisana S, Parvez A, Cervantes-Sodi F, Ferrari AC, Dunin-Borkowski R, Lizzit S, Petaccia L, Goldoni A, Robertson J (2007) In situ observations of catalyst dynamics during surface-bound carbon nanotube nucleation. Nano Lett 7(3):602–608

    Article  CAS  Google Scholar 

  194. Anisimov AS, Nasibulin AG, Jiang H, Launois P, Cambedouzou J, Shandakov SD, Kauppinen EI (2010) Mechanistic investigations of single-walled carbon nanotube synthesis by ferrocene vapor decomposition in carbon monoxide. Carbon 48:380–388

    Article  CAS  Google Scholar 

  195. Harutyunyan AR, Awasthi N, Jiang A, Setyawan W, Mora E, Tokune T, Bolton K, Curtarolo S (2008) Reduced carbon solubility in Fe nanoclusters and implications for the growth of single-walled carbon nanotubes. Phys Rev Lett 100:195502/195501–195504

    Article  CAS  Google Scholar 

  196. Page AJ, Yamane H, Ohta Y, Irle S, Morokuma K (2010) QM/MD simulation of SWCNT nucleation on transition metal carbide nanoparticles. J Am Chem Soc 132:15699–15707

    Article  CAS  Google Scholar 

  197. Page AJ, Irle S, Morokuma K (2010) Polyyne chain growth and ring collapse drives Ni-catalyzed SWNT growth: a QM/MD investigation. J Phys Chem C 114:8206–8211

    Article  CAS  Google Scholar 

  198. Amara H, Bichara C, Ducastelle F (2006) Formation of carbon nanostructures on nickel surfaces: a tight-binding grand canonical Monte Carlo study. Phys Rev B 73(11):113404

    Article  CAS  Google Scholar 

  199. Amara H, Bichara C, Ducastelle F (2008) Understanding the nucleation mechanisms of carbon nanotubes in catalytic chemical vapor deposition. Phys Rev Lett 100:056105/056101–056104

    Article  CAS  Google Scholar 

  200. Amara H, Bichara C, Ducastelle F (2008) A tight-binding grand canonical Monte Carlo study of the catalytic growth of carbon nanotubes. J Nanosci Nanotechnol 8:6099–6104

    Article  CAS  Google Scholar 

  201. Amara H, Roussel JM, Bichara C, Gaspard JP, Ducastelle F (2009) Tight-binding potential for atomistic simulations of carbon interacting with transition metals: application to the Ni-C system. Phys Rev B 79(1):014109

    Article  CAS  Google Scholar 

  202. Takagi D, Hibino H, Suzuki S, Kobayashi Y, Homma Y (2007) Carbon nanotube growth from semiconductor nanoparticles. Nano Lett 7(8):2272–2275

    Article  CAS  Google Scholar 

  203. Bachmatiuk A, Börrnert F, Grobosch M, Schäffel F, Wolff U, Scott A, Zaka M, Warner JH, Klingeler R, Knupfer M, Büchner B, Rümmeli MH (2009) Investigating the graphitization mechanism of SiO2 nanoparticles in chemical vapor deposition. ACS Nano 3(12):4098–4104

    Article  CAS  Google Scholar 

  204. Huang S, Cai Q, Chen J, Qian Y, Zhang L (2009) Metal-catalyst-free growth of single-walled carbon nanotubes on substrates. J Am Chem Soc 131(6):2094–2095

    Article  CAS  Google Scholar 

  205. Liu B, Ren W, Gao L, Li S, Pei S, Liu C, Jiang C, Cheng HM (2009) Metal-catalyst-free growth of single-walled carbon nanotubes. J Am Chem Soc 131(6):2082–2083

    Article  CAS  Google Scholar 

  206. Liu B, Ren W, Liu C, Sun C-H, Gao L, Li S, Jiang C, Cheng H-M (2009) Growth velocity and direct length-sorted growth of short single-walled carbon nanotubes by a metal-catalyst-free chemical vapor deposition process. ACS Nano 3(11):3421–3430

    Article  CAS  Google Scholar 

  207. Homma Y, Liu H, Takagi D, Kobayashi Y (2009) Single-walled carbon nanotube growth with non-iron-group “catalysts” by chemical vapor deposition. Nano Res 2(10):793–799

    Article  CAS  Google Scholar 

  208. Liu H, Takagi D, Chiashi S, Chokan T, Homma Y (2010) Investigation of catalytic properties of Al2O3 particles in the growth of single-walled carbon nanotubes. J Nanosci Nanotechnol 10:4068–4073

    Article  CAS  Google Scholar 

  209. Liu H, Takagi D, Chiashi S, Homma Y (2010) The growth of single-walled carbon nanotubes on a silica substrate without using a metal catalyst. Carbon 48:114–122

    Article  CAS  Google Scholar 

  210. Liu B, Tang D-M, Sun C, Liu C, Ren W, Li F, Yu W-J, Yin L-C, Zhang L, Jiang C, Cheng H-M (2011) Importance of oxygen in the metal-free catalytic growth of single-walled carbon nanotubes from SiOx by a vapor-solid-solid mechanism. J Am Chem Soc 133:197–199

    Article  CAS  Google Scholar 

  211. Page AJ, Chandrakumar KRS, Irle S, Morokuma K (2011) SWNT nucleation from carbon-coated SiO2 nanoparticles via a vapor−solid−solid mechanism. J Am Chem Soc 133(3):621–628

    Article  CAS  Google Scholar 

  212. Page AJ, Chandrakumar KRS, Irle S, Morokuma K (2011) Do SiO2 and carbon-doped SiO2 nanoparticles melt? Insights from QM/MD simulations and ramifications regarding carbon nanotube growth. Chem Phys Lett 508:235–241

    Article  CAS  Google Scholar 

  213. Lindemann FA (1910) Z Phys 11:609

    CAS  Google Scholar 

  214. Ding F, Rosen A, Curtarolo S, Bolton K (2006) Modeling the melting of supported clusters. Appl Phys Lett 88:133110/133111–133113

    Google Scholar 

  215. Wen Y-H, Zhang Y, Zheng J-C, Zhu Z-Z, Sun S-G (2009) Orientation-dependent structural transition and melting of Au nanowires. J Phys Chem C 113:20611–20617

    Article  CAS  Google Scholar 

  216. Neyts EC, Bogaerts A (2009) Numerical study of the size-dependent melting mechanisms of nickel nanoclusters. J Phys Chem C 113:2771–2776

    Article  CAS  Google Scholar 

  217. Puri P, Yang V (2007) Effect of particle size on melting of aluminum at nano scales. J Phys Chem C 111:11776–11783

    Article  CAS  Google Scholar 

  218. Kusunoki M, Rokkaku M, Suzuki T (1997) Epitaxial carbon nanotube file self-organized by sublimation decomposition of silicon carbide. Appl Phys Lett 71(18):2620–2622

    Article  CAS  Google Scholar 

  219. Page AJ, Ohta Y, Irle S, Morokuma K (2010) Mechanisms of single-walled carbon nanotube nucleation, growth and healing determined using QM/MD methods. Acc Chem Res 43:1375–1385

    Article  CAS  Google Scholar 

  220. Ohta Y, Okamoto Y, Irle S, Morokuma K (2009) Temperature dependence of iron-catalyzed continued single-walled carbon nanotube growth rates: density functional tight-binding molecular dynamics simulations. J Phys Chem C 113(1):159–169

    Article  CAS  Google Scholar 

  221. Page AJ, Minami S, Ohta Y, Irle S, Morokuma K (2010) Comparison of single-walled carbon nanotube growth from Fe and Ni nanoparticles using QM/MD simulations. Carbon 48:3014–3026

    Article  CAS  Google Scholar 

  222. Huang ZP, Wang DZ, Wen JG, Sennett M, Gibson H, Ren ZF (2002) Effect of nickel, iron and cobalt on growth of aligned carbon nanotubes. Appl Phys A-Mater 74:387–391

    Article  CAS  Google Scholar 

  223. Mora E, Harutyunyan AR (2008) Study of single-walled carbon nanotubes growth via the catalyst lifetime. J Phys Chem C 112(13):4805–4812

    Article  CAS  Google Scholar 

  224. Futaba DN, Hata K, Yamada T, Mizuno K, Yumura M, Iijima S (2005) Kinetics of water-assisted single-walled carbon nanotube synthesis revealed by a time-evolution analysis. Phys Rev Lett 95:056104/056101–056104

    Article  CAS  Google Scholar 

  225. Sharma R, Rez P, Reacy MMJ, Stuart SJ (2005) In situ observation of the growth mechanisms of carbon nanotubes under diverse reaction conditions. J Electron Microsc 54:231–237

    Article  CAS  Google Scholar 

  226. Geohegan DB, Puretzky AA, Styers-Barnett D, Hu H, Zhao B, Cui H, Rouleau CM, Eres G, Jackson JJ, Wood RF, Pannala S, Wells JC (2007) In situ time-resolved measurements of carbon nanotube and nanohorn growth. Phys Status Solidi B 244:3944–3949

    Article  CAS  Google Scholar 

  227. Yao Y, Liu R, Zhang J, Jiao L, Liu Z (2007) Raman spectral measuring of the growth rate of individual single-walled carbon nanotubes. J Phys Chem C 111:8407–8409

    Article  CAS  Google Scholar 

  228. Xiang R, Einarsson E, Okawa J, Miyauchi Y, Maruyama S (2009) Acetylene-accelerated alcohol catalytic chemical vapor deposition growth of vertically aligned single-walled carbon nanotubes. J Phys Chem C 113:7511–7515

    Article  CAS  Google Scholar 

  229. Li X, Tu X, Zaric K, Welsher K, Seo WS, Zhao W, Dai H (2007) Selective synthesis combined with chemical separation of single-walled carbon nanotubes for chirality selection. J Am Chem Soc 129:15770–15771

    Article  CAS  Google Scholar 

  230. Zheng M, Semke ED (2007) Enrichment of single chirality carbon nanotubes. J Am Chem Soc 129:6084–6085

    Article  CAS  Google Scholar 

  231. Yakobson BI (1998) Mechanical relaxation and “intramolecular plasticity” in carbon nanotubes. Appl Phys Lett 72:918–920

    Article  CAS  Google Scholar 

  232. Ding F (2005) Theoretical study of the stability of defects in single-walled carbon nanotubes as a function of their distance from the nanotube end. Phys Rev B 72:245409/245401–245407

    Google Scholar 

  233. Page AJ, Ohta Y, Okamoto Y, Irle S, Morokuma K (2009) Defect healing during single-walled carbon nanotube growth: a density-functional tight-binding molecular dynamics investigation. J Phys Chem C 113(47):20198–20207

    Article  CAS  Google Scholar 

  234. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grivorieva LV, Firsov AA (2004) Electric field effect in atomically thin carbon films. Science 306:666–669

    Article  CAS  Google Scholar 

  235. Shelton JC, Patil HR, Blakely JM (1974) Equilibrium segregation of carbon to a nickel (111) surface: a surface phase transition. Surf Sci 43:493–520

    Article  CAS  Google Scholar 

  236. Gan Y, Chu W, Qiao L (2003) STM investigation on interaction between superstructure and grain boundary in graphite. Surf Sci 539:120–128

    Article  CAS  Google Scholar 

  237. Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK (2009) The electronic properties of graphene. Rev Mod Phys 81:136–162

    Article  CAS  Google Scholar 

  238. Forbeaux I, Themlin J-M, Debever J-M (1998) Heteroepitaxial graphite on 6H-SiC(0001): interface formation through conduction-band electronic structure. Phys Rev B 58:16396–16406

    Article  CAS  Google Scholar 

  239. Kusunoki M, Suzuki T, Hirayama M, Shibata N, Kaneko K (2000) A formation mechanism of carbon nanotube films on SiC(0001). Appl Phys Lett 77(4):531–533

    Article  CAS  Google Scholar 

  240. Land TA, Michely T, Behm RJ, Hemminger JC, Comsa G (1992) STM investigation of single layer graphite structures produced on Pt(111) by hydrocarbon decomposition. Surf Sci 264:261–270

    Article  CAS  Google Scholar 

  241. Loginova E, Bartelt NC, Feibelman PJ, McCarty KF (2008) Evidence for graphene growth by C cluster attachment. New J Phys 10:093026/1–16

    Article  CAS  Google Scholar 

  242. Chae SJ, Güneş F, Kim KK, Kim ES, Han GH, Kim SM, Shin H-J, Yoon S-M, Choi J-Y, Park MH, Yang CW, Pribat D, Lee YH (2009) Synthesis of large-area graphene layers on poly-nickel substrate by chemical vapor deposition: wrinkle formation. Adv Mater 21(22):2328–2333

    Article  CAS  Google Scholar 

  243. Grüneis A, Kummer K, Vyalikh DV (2009) Dynamics of graphene growth on a metal surface: a time-dependent photoemission study. New J Phys 11(7):073050

    Article  CAS  Google Scholar 

  244. Müller F, Sachdev H, Hüfner S, Pollard AJ, Perkins EW, Russell JC, Beton PH, Gsell S, Fischer M, Schreck M, Stritzker B (2009) How does graphene grow? Easy access to well-ordered graphene films. Small 5:2291–2296

    Article  CAS  Google Scholar 

  245. Pollard AJ, Nair RR, Sabki SN, Staddon CR, Perdigao LMA, Hsu CH, Garfitt JM, Gangopadhyay S, Gleeson HF, Geim AK, Beton PH (2009) Formation of monolayer graphene by annealing sacrificial nickel thin films. J Phys Chem C 113(38):16565–16567

    Article  CAS  Google Scholar 

  246. Sutter E, Albrecht P, Sutter P (2009) Graphene growth on polycrystalline Ru thin films. Appl Phys Lett 95:133109/133101–133103

    Article  CAS  Google Scholar 

  247. Juang Z-Y, Wu C-Y, Lo C-W, Chen W-Y, Huang C-F, Hwang J-C, Chen F-R, Leou K-C, Tsai C-H (2009) Synthesis of graphene on silicon carbide substrates at low temperature. Carbon 47:2026–2031

    Article  CAS  Google Scholar 

  248. Sanchez-Barriga J, Varykhalov A, Scholz MR, Rader O, Marchenko D, Rybkin A, Shikin AM, Vescovo E (2010) Chemical vapour deposition of graphene on Ni(111) and Co(0001) and intercalation with Au to study Dirac-cone formation and Rashba splitting. Diam Relat Mater 19:734–741

    Article  CAS  Google Scholar 

  249. Coraux J, N’Diaye AT, Engler M, Busse C, Wall D, Buckanie N, Meyer zu Heringdorf F-J, van Gastel R, Poelsema B, Michely T (2009) Growth of graphene on Ir(111). New J Phys 11:023006/023001–023022

    Article  CAS  Google Scholar 

  250. Lacovig P, Pozzo M, Alfe D, Baraldi A, Lizzit S (2009) Growth of dome-shaped carbon nanoislands on Ir(111): the intermediate between carbidic clusters and quasi-free-standing graphene. Phys Rev Lett 103:166101/166101–166104

    Google Scholar 

  251. Li X, Cai W, Colombo L, Ruoff RS (2009) Evolution of graphene growth on Ni and Cu by carbon isotope labeling. Nano Lett 9:4268–4272

    Article  CAS  Google Scholar 

  252. Lahiri J, Miller T, Adamska K, Oleynik II, Batzill M (2011) Graphene growth on Ni(111) by transformation of a surface carbide. Nano Lett 11:518–522

    Article  CAS  Google Scholar 

  253. Wang B, Ma X, Caffio M, Schaub R, Li W-X (2011) Size-selective carbon nanoclusters as precursors to the growth of epitaxial graphene. Nano Lett 11(2):424–430

    Article  CAS  Google Scholar 

  254. Saadi S, Abild-Pedersen F, Helveg S, Sehested J, Hinnemann B, Appel CC, Norskov JK (2010) On the role of metal step-edges in graphene growth. J Phys Chem C 114:11211–11227

    Article  CAS  Google Scholar 

  255. Gao J, Yip J, Zhao J, Yakobson BI, Ding F (2011) Graphene nucleation on transition metal surface: structure transformation and role of the metal step edge. J Am Chem Soc 133:5009–5015

    Article  CAS  Google Scholar 

  256. Cheng D, Barcaro G, Charlier JC, Hou M, Fortunelli A (2011) Homogenous nucleation of graphitic nanostructures from carbon chains on Ni(111). J Phys Chem C 115:10537–10543

    Article  CAS  Google Scholar 

  257. Erdös P, Renyi A (1960) On the evolution of random graphs. Magyar Tud Akad Mat Kutato Int Közl 5:17–61

    Google Scholar 

  258. Bollobas B (1984) The evolution of random graphs. Trans Am Math Soc 286:257–274

    Article  Google Scholar 

  259. Luczak T (1990) The phase transition in the evolution of random graphs. J Graph Theor 14:217–223

    Article  Google Scholar 

  260. Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of 1/f noise. Phys Rev Lett 59:381–384

    Article  Google Scholar 

  261. Stone AJ, Wales DJ (1986) Theoretical studies of icosahedral C60 and some related species. Chem Phys Lett 128(5, 6):501–503

    Article  CAS  Google Scholar 

  262. Ostwald W (1897) Studien uber die Bildung und Umwandlung fester Korper. Z Phys Chem 22:289–330

    CAS  Google Scholar 

  263. Bak P, Sneppen K (1993) Punctuated equilibrium and criticality in a simple model of evolution. Phys Rev Lett 71:4083–4086

    Article  CAS  Google Scholar 

  264. Gould SJ, Eldredge N (1977) Punctuated equilibria: the temp and mode of evolution reconsidered. Paleobiology 3:115–151

    Google Scholar 

  265. Whittaker AG (1978) Carbon: a new view of its high-temperature behavior. Science 200:763–764

    Article  CAS  Google Scholar 

  266. Jin C, Lan H, Peng L, Suenaga K, Iijima S (2009) Deriving carbon atomic chains from graphene. Phys Rev Lett 102:205501/205501–205504

    Google Scholar 

  267. Wang Y, Lin Z-Z, Zhang W, Zhuang J, Ning X-J (2009) Pulling long linear atomic chains from graphene: molecular dynamics simulations. Phys Rev B 80:233403/233401–233404

    Google Scholar 

  268. Hobi EJ, Pontes RB, Fazzio A, da Silva AJR (2010) Formation of atomic carbon chains from graphene nanoribbons. Phys Rev B 81:201406R/201401–201404

    Article  CAS  Google Scholar 

  269. Ohta Y, Okamoto Y, Irle S, Morokuma K (2009) Single-walled carbon nanotube growth from a cap fragment on an iron nanoparticle: density-functional tight-binding molecular dynamics simulations. Phys Rev B 79(19):195415

    Article  CAS  Google Scholar 

  270. Wang Z, Irle S, Zheng G, Kusunoki M, Morokuma K (2007) Carbon nanotubes grow on the C face of SiC (000–1) during sublimation decomposition: quantum chemical molecular dynamics simulations. J Phys Chem C 111:12960

    Article  CAS  Google Scholar 

  271. Ohta Y, Okamoto Y, Irle S, Morokuma K (2008) Rapid growth of a single-walled carbon nanotube on an iron cluster: density-functional tight-binding moleculer dynamics simulations. ACS Nano 2:1437–1444

    Article  CAS  Google Scholar 

  272. Jakowski J, Morokuma K (2009) Liouville–von Neumann molecular dynamics. J Chem Phys 130:224106/224101–224112

    Article  CAS  Google Scholar 

  273. van Duin ACT, Dasgupta S, Lorant F, Goddard WA III (2001) Reactive force field for hydrocarbons. J Phys Chem A 105:9396–9409

    Article  CAS  Google Scholar 

  274. Nielson KD, van Duin ACT, Oxgaard J, Deng W-Q, Goddard WA III (2005) Development of the ReaxFF reactive force field for describing transition metal catalyzed reactions, with application to the initial stages of the catalytic formation of carbon nanotubes. J Phys Chem A 109:493–499

    Article  CAS  Google Scholar 

  275. Svensson M, Humbel S, Froese RDJ, Matsubara T, Sieber S, Morokuma K (1996) ONIOM: a multilayered integrated MO + MM method for geometry optimizations and single point energy predictions. A test for Diels-Alder reactions and Pt(P(t-Bu)3)2 + H2 oxidative addition. J Phys Chem 100:19357–19363

    Article  CAS  Google Scholar 

  276. Dapprich S, Komaromi I, Byun KS, Morokuma K, Frisch MJ (1999) A New ONIOM implementation in Gaussian 98: part I. The calculation of energies, gradients, vibrational frequencies and electric field derivatives. J Mol Struct (THEOCHEM) 461–462:1–21

    Article  Google Scholar 

  277. Johnson MP, Donnet JB, Wang TK, Wang CC, Locke RW, Brinson BE, Marriott T (2002) A dynamic continuum of nanostructured carbons in the combustion furnace. Carbon 40(2):189–194

    Article  Google Scholar 

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Acknowledgments

We sincerely appreciate countless, fruitful discussions with our experimental and theoretical colleagues working in this field. In particular, we would like to thank the group of Prof. Shinohara at Nagoya University, the “SWCNT nucleation and growth workshop” in Texas, organized by Prof. Rick Smalley, and later the Smalley Institute in collaboration with NASA and AFRL, which provided a harmonious atmosphere for the exchange of ideas and results. This work was in part supported by a CREST (Core Research for Evolutional Science and Technology) grant in the Area of High Performance Computing for Multiscale and Multiphysics Phenomena from the Japanese Science and Technology Agency (JST). Stephan Irle acknowledges the Program for Improvement of Research Environment for Young Researchers from Special Coordination Funds for Promoting Science and Technology (SCF) commissioned by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan for support. Alister J. Page acknowledges the Fukui Fellowship at the Fukui Institute, Kyoto University. Simulations were performed in part using the computer resources at the Research Centre for Computational Science (RCCS), Okazaki Research Facilities, National Institutes for Natural Sciences, and at the Academic Centre for Computing and Media Studies (ACCMS) at Kyoto University.

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Authors and Affiliations

  1. Institute for Advanced Research and Department of Chemistry, Nagoya University, Nagoya, 464-8602, Japan

    Stephan Irle, Ying Wang, Yoshio Nishimoto & Hu-Jun Qian

  2. Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, 606-8103, Japan

    Alister J. Page, Biswajit Saha, K. R. S. Chandrakumar & Keiji Morokuma

  3. Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, GA, 30322, USA

    Keiji Morokuma

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  1. Stephan Irle
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Correspondence to Stephan Irle or Keiji Morokuma .

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  1. Jackson State University, P.O. Box 17910, 1400 Lynch St., Jackson, 39217, Mississippi, USA

    Jerzy Leszczynski

  2. Dept. Chemistry, Jackson State University, J. R. Lynch St. 1325, Jackson, 39217, Mississippi, USA

    Manoj K. Shukla

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Irle, S. et al. (2012). Atomistic Mechanism of Carbon Nanostructure Self-Assembly as Predicted by Nonequilibrium QM/MD Simulations. In: Leszczynski, J., Shukla, M. (eds) Practical Aspects of Computational Chemistry II. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0923-2_5

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