Interlayer interactions in graphite and carbon nanotubes

Abstract

A simple tight-binding plus dispersion model is developed to describe the stacking of graphite planes, and then applied to the study of multi-walled carbon nanotubes. According to this model, the variations in the interlayer interaction energy as two nested nanotubes are rotated and translated relative to one another will be far smaller than the variations in the interlayer energy between two sheets of graphite, and multi-walled nanotubes with inter-wall spacings greater than the typical 3.4 Å will tend to deform towards having polygonal cross sections. These predictions are discussed in the light of both earlier theoretical work and recent high-resolution transmission electron microscopy (HRTEM) images of nanotube cross sections.

References

1. S. Iijima, Nature, 1991, 354, 56.
2. S. J. Tans, M. H. Devoret, H. J. Dai, A. Thess, R. E. Smalley, L. J. Geerligs and C. Dekker, Nature, 1997, 386, 474.
3. S. Frank, P. Poncharal, Z. L. Wang and W. A. de Heer, Science, 1998, 280, 1744.
4. M. Ge and K. Sattler, Science, 1993, 260, 515.
5. M. Liu and J. M. Cowley, Carbon, 1994, 32, 393.
6. N. Hamada, S. Sawada and A. Oshiyama, Phys. Rev. Lett., 1992, 68, 1579.
7. J. W. Mintmire, B. I. Dunlap and C. T. White, Phys. Rev. Lett., 1992, 68, 631.
8. C. T. White, D. H. Robertson and J. W. Mintmire, Phys. Rev. B, 1993, 47, 5485.
9. C. T. White and T. N. Todorov, Nature, 1998, 393, 240.
10. L. G. Bartlett, Part II Thesis, Oxford University, 1998.
11. H. J. F. Jansen and A. J. Freeman, Phys. Rev. B, 1987, 35, 8207.
12. J.-C. Charlier, X. Gonze and J.-P. Michenaud, Phys. Rev. B, 1991, 43, 4579.
13. J.-C. Charlier, X. Gonze and J.-P. Michenaud, Carbon, 1994, 32, 289.
14. S. B. Trickey, F. Müller-Plathe, G. H. F. Diercksen and J. C. Boettger, Phys. Rev. B, 1992, 45, 4460.
15. M. C. Schabel and J. L. Martins, Phys. Rev. B, 1992, 46, 7185.
16. J. Furthmüller, J. Hafner and G. Kresse, Phys. Rev. B, 1994, 50, 15606.
17. R. Ahuja, S. Auluck, J. Trygg, J. M. Wills, O. Eriksson and B. Johansson, Phys. Rev. B, 1995, 51, 4813.
18. J. C. Boettger, Phys. Rev. B, 1997, 55, 11202.
19. J.-C. Charlier and J.-P. Michenaud, Phys. Rev. Lett., 1993, 70, 1858.
20. L. A. Girifalco and R. A. Lad, J. Chem. Phys., 1956, 25, 693.
21. D. Tománek, S. G. Louie, H. J. Mamin, D. W. Abraham, R. E. Thomson, E. Ganz and J. Clarke, Phys. Rev. B, 1987, 35, 7790.
22. J. D. Bernal, Proc. R. Soc. London, Ser. A, 1924, 106, 749.
23. H. Lipson and A. R. Stokes, Proc. R. Soc. London, Ser. A, 1942, 181, 101.
24. R. R. Haering, Can. J. Phys., 1958, 36, 352.
25. L. Samuelson, I. P. Batra and C. Roetti, Solid State Commun., 1980, 33, 817.
26. L. Samuelson and I. P. Batra, J. Phys. C., 1980, 13, 5105.
27. C. H. Xu, C. Z. Wang, C. T. Chan and K. M. Ho, J. Phys.: Condens. Matter, 1992, 4, 6047.
28. D. Porezag, Th. Frauenheim, Th. Köhler, G. Seifert and R. Kaschner, Phys. Rev. B, 1995, 51, 12947.
29. M. T. Yin and M. L. Cohen, Phys. Rev. B, 1984, 29, 6996.
30. G. Seifert, H. Eschrig and W. Bieger, Z. Phys. Chem., 1986, 267, 529.
31. K. T. Tang and J. P. Toennies, J. Chem. Phys., 1984, 80, 3726.