Theoretical calculations of coefficients of friction between weakly interacting surfaces

Journal of Physical Chemistry A

Volumn 101, Issue 51, 1997, Pages 10045-10052

  Matsuzawa, Nobuyuki N ^a   Kishii, Noriyuki ^a  

^a SONY CORPORATION   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC FORCE MICROSCOPY; ATOMS; CALCULATIONS; FORCE MEASUREMENT; GRAPHITE; HYDROGEN; NAPHTHALENE; SURFACES; VAN DER WAALS FORCES;

COEFFICIENTS OF FRICTION; PYRENE;

FRICTION;

EID: 0031358012     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp9717204     Document Type: Article

References (70)

1. Amontons, G. Hist. Acad. R. Soc., Paris 1699, 12, 206.
2. Coulomb, E. Mem. Math. Phys., Paris 1785, 10, 161.
3. Hailing, J. Principles of Tribology; The Macmillan Press: U. K., 1975.
4. Friction, Wear and Lubrication; Kragelsky, I. V., Alisin. V. V., Eds.; Mir Publishers: Moscow, 1978.
5. Czichos, H. Tribology; Elsevier: Amsterdam, 1978.
6. Iliuc, I. Tribology of Thin Layers; Elsevier: Amsterdam, 1980.
7. Tribology and Mechanics of Magnetic Storage Devices; Bhushan, B., Ed.; Springer-Verlag: New York, 1990.
8. Surface Diagnostics in Tribology; Miyoshi, K., Chung, Y. W., Eds.; World Scientific: Singapore, 1993.
9. Singer, I. L. J. Vac. Sci. Technol. A 1994, 12, 2605.
10. Binnig, G.; Quate, C. F.; Gerber, Ch. Phys. Rev. Lett. 1986, 56, 930.
11. Binnig, G.; Gerber, Ch.; Stoll, E.; Albrecht, T. R.; Quate, C. F. Europhys. Lett. 1987, 3, 1281.
12. Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Phys. Rev. Lett. 1987, 59, 1942.
13. Erlandsson, R.; Hadziioannou, G.; Mate, C. M.; McClelland, G. M.; Chiang, S. J. Chem. Phys. 1988, 89, 5190.
14. Meyer, G.; Amer, N. M. Appl. Phys. Lett. 1990, 57, 2089.
15. Mikhin, N. M. In Friction, Wear and Lubrication Vol. 1; Kragelsky, I. V., Alisin, V. V., Eds.; Mir Publishers: Moscow, 1978; p 54.
16. Tomlinson, G. A. Philos. Magn. S 1929, 7, 905.
17. Frenkel, Y. I.; Kontorova, T. Zh. Eksp. Teor. Fiz. 1938, 8, 1340.
18. McClelland, G. M. In Adhesion and Friction, Springer Series of Surface Sciences, Vol. 17; Grunze, M., Kreuzer, H. J., Eds.; Springer-Verlag: Berlin, 1989; p 1.
19. Zhong, W.; Tománek, D. Phys. Rev. Lett. 1990, 64, 3054.
20. Overney, G.; Zhong, W.; Tománek, D. J. Vac. Sci. Technol. B 1991, 9, 479.
21. Tománek, D.; Zhong, W.; Thomas, H. Europhys. Lett. 1991, 15, 887.
22. Overney, R. M.; Meyer, E.; Frommer, J.; Brodbeck, D.; Lüthi, R.; Howald, L.; Güntherodt, H.-J.; Fujihira, M.; Takano, H.; Gotoh, Y. Nature 1992, 359, 133.
23. Meyer, E.; Overney, R. M.; Brodbeck, D.; Howald, L.; Lüthi, R.; Frommer, J.; Güntherodt, H.-J. Phys. Rev. Lett. 1992, 69, 1777.
24. O'Shea, S. J.; Welland, M. E.; Rayment, T. Appl. Phys. Lett. 1992, 61, 2240.
25. Hipp, M.; Bielefeldt, H.; Colchero, J.; Marti, O.; Mlynek, J. Ultramicroscopy 1992, 42-44, 1498.
26. O'Shea, S. J.; Weiland, M. E.; Wong, T. M. H. Ultramicroscopy 1993, 52, 55.
27. O'Shea, S. J.; Welland, M. E.; Rayment, T. Langmuir 1993, 9, 1826.
28. Haugstad, G.; Gladfelter, W. L.; Weberg, E. B. Langmuir 1993, 9, 3717.
29. Mate, C. M. Wear 1993, 168, 17.
30. Gaussian 94, Revision B.3; Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A.; Gaussian, Inc., Pittsburgh PA, 1995.
31. Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724.
32. Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257.
33. Hariharan, P. C.; Pople, J. A. Mol. Phys. 1974, 27, 209.
34. Gordon, M. S. Chem. Phys. Lett. 1980, 76, 163.
35. Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213.
36. McLean, A. D.; Chandler, G. S. J. Chem. Phvs. 1980, 72, 650.
37. Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650.
38. Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618.
39. ζ, respectively.
40. δ, respectively.
41. This intermolecular potential was calculated as E(x, z) = E(naphthalene or pyrene/hydrogen molecule) - E(naphthalene or pyrene) - E(hydrogen molecule). Calculated energy for naphthalene was -384.61465476981 Ha and -384.73786470882 Ha at the MP-2/6-31G* and MP-2/6-311G* level, respectively. For pyrene, the energy was -613.78733125643 Ha at the MP-2/6-31G* level, and for the hydrogen molecule, the value was -1.1441408483251 Ha at MP-2/6-31G*, and -1.1458815873186 Ha at MP-2/6-311G*.
42. We note that a similar basis set dependence has been calculated in many reports for various molecular systems. See, for example, refs 43-49.
43. Chem. Rev. (Washington, D.C.) 1994, 94, 4, No. 7.
44. Amos, R. D.; Handy, N. C.; Knowles, P. J.; Rice, J. E.; Stone, A. J. J. Phys. Chem. 1985, 89, 2186.
45. Matías, M.; Tel, L. M.; Novoa, J. J. J. Comput. Chem. 1987, 8, 51.
46. Bone, R. G. A.; Handy, N. C. Theor. Chim. Acta 1990, 78, 133.
47. Brupbacher, Th.; Lüthi, H. P.; Bauder, A. Chem. Phys. Lett. 1992, 195, 482.
48. Antonio, J.; Romero, M.; Sanz, J. F. J. Mol. Struct. 1993, 287, 149.
49. Yin, D.; MacKarell, A. D., Jr. J. Phys. Chem. 1996, 100, 2588.
50. Hobza, P.; Selzle, H. L.; Schlag, E. W. J. Chem. Phys. 1991, 95, 391.
51. Hobza, P.; Bludsky, O.; Selzle, H. L.; Schlag, E. W. J. Chem. Phys. 1992, 97, 335.
52. Hobza, P.; Bludsky, O.; Selzle, H. L.; Schlag, E. W. J. Chem. Phys. 1993, 98, 6223.
53. Hobza, P.; Selzle, H. L.; Schlag, E. W. J. Chem. Phys. 1990, 93, 5893.
54. Labardi, M.; Allegrini, M.; Salerno, M.; Frediani, C.; Ascoli, C. Appl. Phys. A 1994, 59, 5.
55. Ruan, J.-A.; Bhushan, B. J. Appl. Phys. 1994, 76, 5022.
56. Ruan, J.-A.; Bhushan, B. J. Tribol. 1994, 116, 378.
57. Tománek, D.; Ovemey, G.; Miyazaki, H.; Mahanti, S. D.; Güntherodt, H. J. Phys. Rev. Lett. 1989, 63, 876.
58. Mamin, H. J.; Ganz, E.; Abraham, D. W.; Thomson, R. E.; Clarke, J. Phys. Rev. B 1986, 34, 9015.
59. Here, we assume the area corresponding to one atom to be 2.4 Å × 2.4 Å (Note that the van der Waals' radius of hydrogen atom is 1.2 Å (CRC Handbook of Chemistry and Physics, 64th ed.; Weast, R. C., Astle, M. J., Beyer, W. H., Eds.; CRC Press: Boca Raton, FL, 1984; p D-191).
60. Whitehouse, G. D.; Nandan, D.; Whitehurst, C. A. ASLE Trans. 1970, 13, 159.
61. Sugishita, J.; Fujiyoshi, S. Wear 1981, 68, 7.
62. Miyake, S.; Takahashi, S.; Watanabe, I.; Yoshihara, H. ASLE Trans. 1987, 30, 121.
63. Zaïdi, H.; Paulmier, D.; Lepage, J. Appl. Surface Sci. 1990, 44, 221.
64. Zaïdi, H.; Paulmier, D.; Jeanmaire, A.; Néry, H. Surface Sci. 1991, 251/252, 778.
65. Zaïdi, H.; Robert, F.; Paulmier, D.; Néry, H. Appl. Surface Sci. 1993, 70/71, 103.
66. For example, American Institute of Physics Handbook; Gray, E. E., Ed., McGraw-Hill Book Co.: New York, 1963; pp 4-160.
67. P5 = -0.037207, if the units of load, energy, and length are in eV/Å, eV, and Å, respectively.
68. m = 6.11, if the units of load, energy, and length are in eV/Å, eV, and Å, respectively.
69. In the numerical calculations where the load is less than ∼0.1 nN, the distance between naphthalene and hydrogen is in the range of 2.30-2.94 Å located in the region around the minimum of the interbody potentials (the minimum is at ∼2.9 Å, see Figure 3).
70. N = 4.8 nN.