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Extended Tomlinson Model for Rheological Response

Published online by Cambridge University Press:  10 February 2011

V. Zaloj ,
M. Urbakh  and
J. Klafter
V. Zaloj
Affiliation:
Dep. of Physics, State University of Moldova, MD-2009, Chisinau, Moldova
M. Urbakh
Affiliation:
School of Chemistry, Tel Aviv University, 69978, Tel Aviv, Israel
J. Klafter
Affiliation:
School of Chemistry, Tel Aviv University, 69978, Tel Aviv, Israel
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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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 543: Symposium W – Dynamics in Small Confining Systems IV , 1998 , 69
Copyright
Copyright © Materials Research Society 1999

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References

[1] Bowden, F. P. and Tabor, D., The Friction and Lubrications of Solids (Clarenton Press, Oxford, 1985).Google Scholar
[2] Micro/Nanotribology and its Applications, edited by Bhushan, B. (Kluwer Academic Publishers, Dordrecht, 1997).Google Scholar
[3] Yoshizawa, H., McGuiggan, P., and Israelachvili, J., Science 259, 1305 (1993).Google Scholar
[4] Hu, H.-W., Carson, G. A., and Granick, S., Phys. Rev. Lett. 66, 2758 (1991).Google Scholar
[5] Klein, J. and Kumacheva, E., Science 269, 816 (1995).Google Scholar
[6] Thomson, P. A., Robbins, M. O., and Grest, G. S., Israel Journal of Chemistry 35, 93 (1995).Google Scholar
[7] Rozman, M. G., Urbakh, M., and Klafter, J., Phys. Rev. Lett. 77, 683 (1996).Google Scholar
[8] Carlson, J. M. and Batista, A. A., Phys. Rev. E 52, 4153 (1996).Google Scholar
[9] Braiman, Y., Family, F., and Hentschel, G., Phys. Rev. B 55, 5491 (1996).Google Scholar
[10] Gao, J. P., Luedtke, W. D., and Landman, U., Phys. Rev. Lett. 79, 705 (1997).Google Scholar
[11] Rozman, M. G., Urbakh, M., Klafter, J., and Elmer, F.-J., J. Phys. Chem. 102, 7924 (1998).Google Scholar
[12] Persson, B. N. J., Sliding Friction. Physical Properties and Applications (Springer-Verlag, Berlin, 1998).Google Scholar
[13] Baumberger, T. and Caroli, C., Eur. Phys. J. B 4, 13 (1998).Google Scholar
[14] Ferry, J. D., Viscoelastic Properties of Polymers (John Willey & Sons, Inc., New York, 1970).Google Scholar
[15] Peachey, J., Alsten, J. V., and Granick, S., Rev. Sci. Instrum. 62, 462 (1991).Google Scholar
[16] Cho, Y.-K. and Granick, S., Wear 200, 346 (1996).Google Scholar
[17] Luengo, G., Israelachvili, J., and Granick, S., Wear 200, 328 (1996).Google Scholar
[18] Zaloj, V., Urbakh, M., and Klafter, J., Phys. Rev. Lett. 81, 1227 (1998).Google Scholar
[19] Tomlinson, G. A., Philos. Mag. 7, 905 (1929).Google Scholar
[20] Rozman, M. G., Urbakh, M., and Klafter, J., Phys. Rev. E 54, 6485 (1996).Google Scholar
[21] Luengo, G., Schmitt, F.-J., Hill, R., and Israelachvili, J., Macromolecules 30, 2482 (1997).Google Scholar
[22] Berman, A. D., Ducker, W. A., and Israelachvili, J. N., Langmuir 12, 4559 (1996).Google Scholar
[23] Zaloj, V., Urbakh, M., and Klafter, J., J. Chem. Phys. 110, (1999), in Press.Google Scholar
[24] Klein, J. and Kumacheva, E., J. Chem. Phys. 108, 6996 (1998).Google Scholar
[25] Kumacheva, E. and Klein, J., J. Chem. Phys. 108, 7010 (1998).Google Scholar
[26] Nasuno, S., Kudrolli, A. B. A., and Golub, J. P., Phys. Rev. E 58, 2161 (1998).Google Scholar
[27] Thomson, P. A. and Grest, G. S., Phys. Rev. Lett 67, 1751 (1991).Google Scholar
[28] Demirel, A. L. and Granick, S., J. Chem. Phys. 109, 6889 (1998).Google Scholar
[29] Rozman, M. G., Urbakh, M., and Klafter, J., Phys. Rev. E 57, 7340 (1998).Google Scholar
[30] Elmer, F. J., Phys. Rev. E 57, R4903 (1998).Google Scholar
[31] Gao, J. P., Luedtke, W. D., and Landman, U., J. Phys. Chem. B 102, 5033 (1998).Google Scholar
[32] Heuberger, M., Drummond, C., and Israelachvili, J., J. Phys. Chem. B 102, 5038 (1998).Google Scholar