Abstract
We investigate the response of a confined harmonic chain to an external harmonic driving force. A model is introduced which extends the one-dimensional Tomlinson model to include motion in the normal direction. This model with lateral-normal coupling mimics recent measurements on friction, using surface forces apparatus (SFA). The model predicts a critical driving amplitude below which the response is linear. For higher amplitudes the system exhibits a nonlinear behavior and an apparent shear thinning. We discuss the effects of shear induced dilatancy, which results from the lateral-normal coupling, on the energy dissipation, and therefore on the frictional properties. It is demonstrated that measurements of response in the normal direction provide additional information on the mechanisms of friction.
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References
F. P. Bowden and D. Tabor, The Friction and Lubrications of Solids (Clarenton Press, Oxford, 1985).
Micro/Nanotribology and its Applications, edited by B. Bhushan (Kluwer Academic Publishers, Dordrecht, 1997).
H. Yoshizawa, P. McGuiggan, and J. Israelachvili, Science 259, 1305 (1993).
H.-W. Hu, G. A. Carson, and S. Granick, Phys. Rev. Lett. 66, 2758 (1991).
J. Klein and E. Kumacheva, Science 269, 816 (1995).
P. A. Thomson, M. O. Robbins, and G. S. Grest, Israel Journal of Chemistry 35, 93 (1995).
M. G. Rozman, M. Urbakh, and J. Klafter, Phys. Rev. Lett. 77, 683 (1996).
J. M. Carlson and A. A. Batista, Phys. Rev. E 52, 4153 (1996).
Y. Braiman, F. Family, and G. Hentschel, Phys. Rev. B 55, 5491 (1996).
J. P. Gao, W. D. Luedtke, and U. Landman, Phys. Rev. Lett. 79, 705 (1997).
M. G. Rozman, M. Urbakh, J. Klafter, and F.-J. Elmer, J. Phys. Chem. 102, 7924 (1998).
B. N. J. Persson, Sliding Friction. Physical Properties and Applications (Springer-Verlag, Berlin, 1998).
T. Baumberger and C. Caroli, Eur. Phys. J. B 4, 13 (1998).
J. D. Ferry, Viscoelastic Properties of Polymers (John Willey & Sons, Inc., New York, 1970).
J. Peachey, J. V. Alsten, and S. Granick, Rev. Sci. Instrum. 62, 462 (1991).
Y.-K. Cho and S. Granick, Wear 200, 346 (1996).
G. Luengo, J. Israelachvili, and S. Granick, Wear 200, 328 (1996).
V. Zaloj, M. Urbakh, and J. Klafter, Phys. Rev. Lett. 81, 1227 (1998).
G. A. Tomlinson, Philos. Mag. 7, 905 (1929).
M. G. Rozman, M. Urbakh, and J. Klafter, Phys. Rev. E 54, 6485 (1996).
G. Luengo, F.-J. Schmitt, R. Hill, and J. Israelachvili, Macromolecules 30, 2482 (1997).
A. D. Berman, W. A. Ducker, and J. N. Israelachvili, Langmuir 12, 4559 (1996).
V. Zaloj, M. Urbakh, and J. Klafter, J. Chem. Phys. 110, (1999), in Press.
E. Kumacheva and J. Klein, J. Chem. Phys. 108, 7010 (1998).
S. Nasuno, A. B. A. Kudrolli, and J. P. Golub, Phys. Rev. E 58, 2161 (1998).
P. A. Thomson and G. S. Grest, Phys. Rev. Lett 67, 1751 (1991).
A. L. Demirel and S. Granick, J. Chem. Phys. 109, 6889 (1998).
M. G. Rozman, M. Urbakh, and J. Klafter, Phys. Rev. E 57, 7340 (1998).
F. J. Elmer, Phys. Rev. E 57, R4903 (1998).
J. P. Gao, W. D. Luedtke, and U. Landman, J. Phys. Chem. B 102, 5033 (1998).
M. Heuberger, C. Drummond, and J. Israelachvili, J. Phys. Chem. B 102, 5038 (1998).
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Zaloj, V., Urbakh, M. & Klafter, J. Extended Tomlinson Model for Rheological Response. MRS Online Proceedings Library 543, 69–78 (1998). https://doi.org/10.1557/PROC-543-69
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DOI: https://doi.org/10.1557/PROC-543-69