Skip to main content
Log in

On the stability of single-walled carbon nanotubes and their binding strengths

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

We have studied the relative stability of hydrogen-terminated single-walled carbon nanotubes (SWNTs) segments, and open-ended SWNT fragments of varying diameter and chirality that are present at the interface of the catalytic metal particles during growth. We have found that hydrogen-terminated SWNTs differ by <1 eV in stability among different chiralities, which presents a challenge for selective and property-controlled growth. In addition, both zigzag and armchair tubes can be the most stable chirality of hydrogen-terminated SWNTs, which is a fundamental obstacle for property-controlled growth utilizing thermodynamic stability. In contrast, the most armchair-like open-ended SWNTs segments are always the most stable ones, followed in sequence by chiral index up to the least stable zigzag segments. We explain the ordering by triple bond stabilization of the carbon dangling bonds at the open ends, which is a fragment stabilization effect that is only manifested when all bonds between two layers are broken. We show convincingly that the bond strength difference between zigzag and armchair tubes is not present when individual bonds are broken or formed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Iijima S, Ichihashi T (1993) Single-shell carbon nanotubes of 1-nm diameter. Nature 363(6430):603–605

    Article  CAS  Google Scholar 

  2. Dresselhaus M, Dresselhaus G, Avouris P (2001) Carbon nanotubes: synthesis, structure. Properties and Applications, Heidelberg

    Google Scholar 

  3. Rao CNR, Satishkumar BC, Govindaraj A, Nath M (2001) Nanotubes. ChemPhysChem 2(2):78–105. doi:10.1002/1439-7641(20010216)2:2<78:aid-cphc78>3.0.co;2-7

    Article  CAS  Google Scholar 

  4. Baughman RH, Zakhidov AA, de Heer WA (2002) Carbon nanotubes—the route toward applications. Science 297(5582):787–792. doi:10.1126/science.1060928

    Article  CAS  Google Scholar 

  5. Ebbesen TW, Lezec HJ, Hiura H, Bennett JW, Ghaemi HF, Thio T (1996) Electrical conductivity of individual carbon nanotubes. Nature 382(6586):54–56

    Article  CAS  Google Scholar 

  6. Wong SS, Woolley AT, Joselevich E, Cheung CL, Lieber CM (1998) Covalently-functionalized single-walled carbon nanotube probe tips for chemical force microscopy. J Am Chem Soc 120(33):8557–8558. doi:10.1021/ja9817803

    Article  CAS  Google Scholar 

  7. Heller I, Kong J, Heering HA, Williams KA, Lemay SG, Dekker C (2004) Individual single-walled carbon nanotubes as nanoelectrodes for electrochemistry. Nano Lett 5(1):137–142. doi:10.1021/nl048200m

    Article  Google Scholar 

  8. Breuer O, Sundararaj U (2004) Big returns from small fibers: a review of polymer/carbon nanotube composites. Polym Compos 25(6):630–645. doi:10.1002/pc.20058

    Article  CAS  Google Scholar 

  9. Schelling PK, Shi L, Goodson KE (2005) Managing heat for electronics. Mater Today 8:30

    Article  Google Scholar 

  10. Ivanov I, Puretzky A, Eres G, Wang H, Pan Z, Cui H, Jin R, Howe J, Geohegan DB (2006) Fast and highly anisotropic thermal transport through vertically aligned carbon nanotube arrays. Appl Phys Lett 89(22):223110

    Article  Google Scholar 

  11. Kim W, Wang R, Majumdar A (2007) Nanostructuring expands thermal limits. Nano Today 2(1):40–47. doi:10.1016/s1748-0132(07)70018-x

    Article  Google Scholar 

  12. Rinzler AG, Hafner JH, Nikolaev P, Lou L, Kim SG, Tomanek D, Nordlander P, Colbert DT, Smalley RE (1995) Unraveling nanotubes—field-emission from an atomic wire. Science 269(5230):1550–1553. doi:10.1126/science.269.5230.1550

    Article  CAS  Google Scholar 

  13. Deheer WA, Chatelain A, Ugarte D (1995) A carbon nanotube field-emission electron source. Science 270(5239):1179–1180. doi:10.1126/science.270.5239.1179

    Article  CAS  Google Scholar 

  14. Choi WB, Chung DS, Kang JH, Kim HY, Jin YW, Han IT, Lee YH, Jung JE, Lee NS, Park GS, Kim JM (1999) Fully sealed, high-brightness carbon-nanotube field-emission display. Appl Phys Lett 75(20):3129–3131. doi:10.1063/1.125253

    Article  CAS  Google Scholar 

  15. Huang Y, Duan X, Lieber CM (2005) Semiconductor nanowire for multi-color photonics. Small 1:142–147

    Article  CAS  Google Scholar 

  16. Choi WB, Chae S, Bae E, Lee J-W, Cheong B-H, Kim J-R, Kim J–J (2003) Carbon-nanotube-based nonvolatile memory with oxide–nitride–oxide film and nanoscale channel. Appl Phys Lett 82(2):275–277

    Article  CAS  Google Scholar 

  17. Avouris P, Chen Z, Perebeinos V (2007) Carbon-based electronics. Nat NANO 2(10):605–615

    Article  CAS  Google Scholar 

  18. Close GF, Yasuda S, Paul B, Fujita S, Wong HSP (2008) A 1 GHz integrated circuit with carbon nanotube interconnects and silicon transistors. Nano Lett 8(2):706–709. doi:10.1021/nl0730965

    Article  CAS  Google Scholar 

  19. Chaste J, Lechner L, Morfin P, Feve G, Kontos T, Berroir JM, Glattli DC, Happy H, Hakonen P, Placais B (2008) Single carbon nanotube transistor at GHz frequency. Nano Lett 8(2):525–528. doi:10.1021/nl0727361

    Article  CAS  Google Scholar 

  20. Wagner RS, Ellis WC (1964) Vapor-liquid-solid mechanism of single crystal growth (new method growth catalysis from impurity whisker epitaxial + large crystals si e). Appl Phys Lett 4(5):89. doi:10.1063/1.1753975

    Google Scholar 

  21. Baker RTK, Barber MA, Harris PS, Feates FS, Waite RJ (1972) Nucleation and growth of carbon deposits from the nickel catalyzed decomposition of acetylene. J Catal 26(1):51–62. doi:10.1016/0021-9517(72)90032-2

    Article  CAS  Google Scholar 

  22. Saito Y (1995) Nanoparticles and filled nanocapsules. Carbon 33(7):979–988. doi:10.1016/0008-6223(95)00026-a

    Article  CAS  Google Scholar 

  23. Rodriguez-Manzo JA, Terrones M, Terrones H, Kroto HW, Sun LT, Banhart F (2007) In situ nucleation of carbon nanotubes by the injection of carbon atoms into metal particles. Nat Nanotechnol 2(5):307–311. doi:10.1038/nnano.2007.107

    Article  CAS  Google Scholar 

  24. Ding F, Larsson P, Larsson JA, Ahuja R, Duan HM, Rosen A, Bolton K (2008) The importance of strong carbon-metal adhesion for catalytic nucleation of single-walled carbon nanotubes. Nano Lett 8(2):463–468. doi:10.1021/nl072431m

    Article  CAS  Google Scholar 

  25. Larsson P, Larsson JA, Ahuja R, Ding F, Yakobson BI, Duan HM, Rosen A, Bolton K (2007) Calculating carbon nanotube-catalyst adhesion strengths. Phys Rev B 75(11):115419. doi:10.1103/PhysRevB.75.115419

    Google Scholar 

  26. Jung YJ, Homma Y, Ogino T, Kobayashi Y, Takagi D, Wei B, Vajtai R, Ajayan PM (2003) High-density, large-area single-walled carbon nanotube networks on nanoscale patterned substrates. J Phys Chem B 107(28):6859–6864. doi:10.1021/jp0346514

    Article  CAS  Google Scholar 

  27. Huang SM, Cai XY, Du CS, Liu J (2003) Oriented long single walled carbon nanotubes on substrates from floating catalysts. J Phys Chem B 107(48):13251–13254. doi:10.1021/jp0364708

    Article  CAS  Google Scholar 

  28. Ciuparu D, Chen Y, Lim S, Haller GL, Pfefferle L (2003) Uniform-diameter single-walled carbon nanotubes catalytically grown in cobalt-incorporated MCM-41. J Phys Chem B 108(2):503–507. doi:10.1021/jp036453i

    Article  Google Scholar 

  29. Kim NS, Lee YT, Park J, Han JB, Choi YS, Choi SY, Choo J, Lee GH (2003) Vertically aligned carbon nanotubes grown by pyrolysis of iron, cobalt, and nickel phthalocyanines. J Phys Chem B 107(35):9249–9255. doi:10.1021/jp034895o

    Article  CAS  Google Scholar 

  30. Li KinlochIA, Shaffer MSP, Singh C, Geng J, Johnson BFG, Windle AH (2004) Growth of single-walled carbon nanotubes by the rapid heating of a supported catalyst. Chem Mater 16(26):5637–5643. doi:10.1021/cm0495111

    Article  CAS  Google Scholar 

  31. Li Y, Liu J, Wang Y, Wang ZL (2001) Preparation of monodispersed Fe–Mo nanoparticles as the catalyst for CVD Synthesis of carbon nanotubes. Chem Mater 13(3):1008–1014. doi:10.1021/cm000787s

    Article  CAS  Google Scholar 

  32. Wang B, Wei L, Yao L, Li L-J, Yang Y, Chen Y (2007) Pressure-induced single-walled carbon nanotube (n, m) selectivity on Co–Mo catalysts. J Phys Chem C 111(40):14612–14616. doi:10.1021/jp0762525

    Article  CAS  Google Scholar 

  33. Qingwen L, Hao Y, Yan C, Jin Z, Zhongfan L (2002) A scalable CVD synthesis of high-purity single-walled carbon nanotubes with porous MgO as support material. J Mater Chem 12(4):1179–1183

    Article  Google Scholar 

  34. Mabudafhasi ML, Bodkin R, Nicolaides CP, Liu XY, Witcomb MJ, Coville NJ (2002) The ruthenium catalysed synthesis of carbon nanostructures. Carbon 40(14):2737–2742. doi:10.1016/s0008-6223(02)00192-6

    Article  CAS  Google Scholar 

  35. Ritschel M, Leonhardt A, Elefant D, Oswald S, Buchner B (2007) Rhenium-catalyzed growth carbon nanotubes. J Phys Chem C 111(24):8414–8417. doi:10.1021/jp070467x

    Article  CAS  Google Scholar 

  36. Li Z, Larsson JA, Larsson P, Ahuja R, Tobin JM, O’Byrne J, Morris MA, Attard G, Holmes JD (2008) Copper/molybdenum nanocomposite particles as catalysts for the growth of bamboo-structured carbon nanotubes. J Phys Chem C 112(32):12201–12206. doi:10.1021/jp8023556

    Article  CAS  Google Scholar 

  37. O’Byrne JP, Li Z, Tobin JM, Larsson JA, Larsson P, Ahuja R, Holmes JD (2010) Growth of carbon nanotubes from heterometallic palladium and copper catalysts. J Phys Chem C 114(18):8115–8119. doi:10.1021/jp909309t

    Article  Google Scholar 

  38. Yazyev OV, Pasquarello A (2008) Effect of metal elements in catalytic growth of carbon nanotubes. Phys Rev Lett 100(15):156102

    Article  Google Scholar 

  39. 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

    Article  CAS  Google Scholar 

  40. Lee YH, Kim SG, Tomnek D (1997) Catalytic growth of single-wall carbon nanotubes: an ab initio study. Phys Rev Lett 78(12):2393–2396

    Article  CAS  Google Scholar 

  41. Charlier J-C, De Vita A, Blase X, Car R (1997) Microscopic growth mechanisms for carbon nanotubes. Science 275(5300):647–649. doi:10.1126/science.275.5300.647

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  43. Raty J-Y, Fo Gygi, Galli G (2005) Growth of carbon nanotubes on metal nanoparticles: a microscopic mechanism from ab initio molecular dynamics simulations. Phys Rev Lett 95(9):096103

    Article  Google Scholar 

  44. Reich S, Li L, Robertson J (2006) Control the chirality of carbon nanotubes by epitaxial growth. Chem Phys Lett 421(4–6):469–472. doi:10.1016/j.cplett.2006.01.110

    Google Scholar 

  45. Reich S, Li L, Robertson J (2005) Structure and formation energy of carbon nanotube caps. Phys Rev B 72(16):165423

    Article  Google Scholar 

  46. Helveg S, Lopez-Cartes C, Sehested J, Hansen PL, Clausen BS, Rostrup-Nielsen JR, Abild-Pedersen F, Norskov JK (2004) Atomic-scale imaging of carbon nanofibre growth. Nature 427(6973):426–429. doi:http://www.nature.com/nature/journal/v427/n6973/suppinfo/nature02278_S1.html

    Google Scholar 

  47. Shin Y-H, Hong S (2008) Carbon diffusion around the edge region of nickel nanoparticles. Appl Phys Lett 92(4):043103

    Article  Google Scholar 

  48. Liu Y, Dobrinsky A, Yakobson BI (2010) Graphene edge from armchair to zigzag: the origins of nanotube chirality? Phys Rev Lett 105(23):235502

    Article  Google Scholar 

  49. Dumlich H, Reich S (2010) Chirality-dependent growth rate of carbon nanotubes: a theoretical study. Phys Rev B 82(8):085421

    Article  Google Scholar 

  50. Borjesson A, Bolton K (2011) Modeling of ostwald ripening of metal clusters attached to carbon nanotubes. J Phys Chem C 115(50):24454–24462. doi:10.1021/jp202328w

    Article  CAS  Google Scholar 

  51. Ding F, Harutyunyan AR, Yakobson BI (2009) Dislocation theory of chirality-controlled nanotube growth. Proc Nat Acad Sci 106(8):2506–2509. doi:10.1073/pnas.0811946106

    Article  CAS  Google Scholar 

  52. Wang Y, Kim MJ, Shan H, Kittrell C, Fan H, Ericson LM, Hwang W-F, Arepalli S, Hauge RH, Smalley RE (2005) Continued growth of single-walled carbon nanotubes. Nano Lett 5(6):997–1002. doi:10.1021/nl047851f

    Article  CAS  Google Scholar 

  53. Smalley RE, Li Y, Moore VC, Price BK, Colorado R, Schmidt HK, Hauge RH, Barron AR, Tour JM (2006) Single wall carbon nanotube amplification: en route to a type-specific growth mechanism. J Am Chem Soc 128(49):15824–15829. doi:10.1021/ja065767r

    Article  CAS  Google Scholar 

  54. Iwasaki T, Robertson J, Kawarada H (2008) Mechanism analysis of interrupted growth of single-walled carbon nanotube arrays. Nano Lett 8(3):886–890. doi:10.1021/nl073119f

    Article  CAS  Google Scholar 

  55. Bolton K, Ding F, Rosén A (2011) Atomistic simulations of catalyzed carbon nanotube growth. J Nanosci Nanotechnol 6(5):1211–1224. doi:10.1166/jnn.2006.145

    Google Scholar 

  56. Ding F, Bolton K, Rosén A (2004) Nucleation and growth of single-walled carbon nanotubes: a molecular dynamics study. J Phys Chem B 108(45):17369–17377. doi:10.1021/jp046645t

    Article  CAS  Google Scholar 

  57. Duan H, Ding F, Rosén A, Harutyunyan A, Tokune T, Curtarolo S, Bolton K (2007) Initial growth of single-walled carbon nanotubes on supported iron clusters: a molecular dynamics study. Eur Phys J D Atomic Mol Opt Plasma Phys 43(1):185–189. doi:10.1140/epjd/e2007-00109-6

    CAS  Google Scholar 

  58. Maruyama S, Shibuta Y (2002) Molecular dynamics in formation process of SWNTs. Mol Cryst Liquid Cryst 387:311–316. doi:10.1080/10587250290113592

    Article  Google Scholar 

  59. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865

    Article  CAS  Google Scholar 

  60. Schafer A, Huber C, Ahlrichs R (1994) Fully optimized contracted gaussian-basis sets of triple zeta valence quality for atoms li to kr. J Chem Phys 100(8):5829–5835

    Article  Google Scholar 

  61. Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys Chem Chem Phys 7(18):3297–3305

    Article  CAS  Google Scholar 

  62. Treutler O, Ahlrichs R (1995) Efficient molecular numerical-integration schemes. J Chem Phys 102(1):346–354. doi:10.1063/1.469408

    Article  CAS  Google Scholar 

  63. Von Arnim M, Ahlrichs R (1998) Performance of parallel TURBOMOLE for density functional calculations. J Comput Chem 19(15):1746–1757. doi:10.1002/(sici)1096-987x(19981130)19:15<1746:aid-jcc7>3.3.co;2-m

    Article  Google Scholar 

  64. Eichkorn K, Treutler O, Öhm H, Häser M, Ahlrichs R (1995) Auxiliary basis sets to approximate coulomb potentials. Chem Phys Lett 242(6):652–660

    Article  CAS  Google Scholar 

  65. Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47(1):558–561

    Article  CAS  Google Scholar 

  66. Kresse G, Hafner J (1994) Ab initio molecular-dynamics simulation of the liquid-metal, amorphous-semiconductor transition in germanium. Phys Rev B 49(20):14251–14269

    Article  CAS  Google Scholar 

  67. Kresse G, Furthmuller J (1996) Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6(1):15–50. doi:10.1016/0927-0256(96)00008-0

    Article  CAS  Google Scholar 

  68. Kresse G, Furthmuller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54(16):11169–11186

    Article  CAS  Google Scholar 

  69. Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50(24):17953–17979

    Article  Google Scholar 

  70. Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758–1775

    Article  CAS  Google Scholar 

  71. Hod O, Scuseria GE (2008) Half-metallic zigzag carbon nanotube dots. ACS Nano 2(11):2243–2249. doi:10.1021/nn8004069

    Article  CAS  Google Scholar 

  72. Hod O, Peralta JE, Scuseria GE (2007) Edge effects in finite elongated graphene nanoribbons. Phys Rev B 76(23):233401

    Article  Google Scholar 

  73. Rochefort A, Salahub DR, Avouris P (1999) Effects of finite length on the electronic structure of carbon nanotubes. J Phys Chem B 103(4):641–646. doi:10.1021/jp983725m

    Article  CAS  Google Scholar 

  74. Kim Y-H, Choi J, Chang KJ, Tomnek D (2003) Defective fullerenes and nanotubes as molecular magnets: An ab initio study. Phys Rev B 68(12):125420

    Article  Google Scholar 

  75. Cremer D, Wu A, Larsson A, Kraka E (2000) Some thoughts about bond energies, bond lengths, and force constants. J Mol Model 6(4):396–412. doi:10.1007/pl00010739

    Article  CAS  Google Scholar 

  76. Larsson JA, Cremer D (1999) Theoretical verification and extension of the McKean relationship between bond lengths and stretching frequencies. J Mol Struct 485–486(0):385–407. doi:10.1016/s0022-2860(99)00093-9

    Google Scholar 

  77. 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. doi:10.1021/nl080452q

    Article  CAS  Google Scholar 

  78. 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(10):1375–1385. doi:10.1021/ar100064g

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors are grateful for funding from Intel, Enterprise Ireland, Science Foundation Ireland, and the Marie Curie early stage research training (EST)—NANOCAGE. Calculations were performed at Tyndall National Institute’s in-house clusters provided by Science Foundation, Ireland (SFI), at the SFI/HEA Irish Centre for High-End Computing (ICHEC), and at Swedish National Supercomputing facilities.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jakub D. Baran.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baran, J.D., Kołodziejczyk, W., Larsson, P. et al. On the stability of single-walled carbon nanotubes and their binding strengths. Theor Chem Acc 131, 1270 (2012). https://doi.org/10.1007/s00214-012-1270-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-012-1270-3

Keywords

Navigation