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Rubber friction on smooth surfaces

The European Physical Journal E volume 21, pages 69–80 (2006)Cite this article

Abstract.

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.

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References

  1. D.F. Moore, The Friction and Lubrication of Elastomers (Pergamon, Oxford, 1972).

  2. B.N.J. Persson, Sliding Friction: Physical Principles and Application, 2nd ed. (Springer, Heidelberg, 2000).

  3. B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001).

    Article  ADS  Google Scholar 

  4. B.N.J. Persson, A.I. Volokitin, Phys. Rev. B 65, 134106 (2002).

    Article  ADS  Google Scholar 

  5. M. Klüppel, G. Heinrich, Rubber Chem. Technol. 73, 578 (2000).

    Google Scholar 

  6. A. Schallamach, Wear 6, 375 (1963).

    Article  Google Scholar 

  7. Y.B. Chernyak, A.I. Leonov, Wear 108, 105 (1986).

    Article  Google Scholar 

  8. A.E. Filippov, J. Klafter, M. Urbakh, Phys. Rev. Lett. 92, 135503 (2004).

    Article  ADS  Google Scholar 

  9. Weak absorption systems (e.g., saturated hydrocarbon molecules or noble-gas atoms on metal surfaces) exhibit extremely low (pinning) barriers for parallel motion. The barriers can be estimated from the measured frequencies of parallel adsorbate vibrations, see. e.g., B.N.J. Persson, Surf. Sci. Rep. 15, 1 (1990).

    Google Scholar 

  10. M.L. Williams, R.F. Landel, J.D. Ferry, J. Am. Chem. Soc. 77, 3701 (1955).

    Article  Google Scholar 

  11. B.N.J. Persson, Phys. Rev. B 51, 13568 (1995).

    Article  ADS  Google Scholar 

  12. B.N.J. Persson, O. Albohr, G. Heinrich, H. Ueba, J. Phys. Condens. Matter 17, R1071 (2005).

  13. B.N.J. Persson, E. Brener, Phys. Rev. E 71, 036123 (2005).

    MathSciNet  Article  ADS  Google Scholar 

  14. B.N.J. Persson, Surf. Sci. 401, 445 (1998).

    Article  Google Scholar 

  15. A. Schallamach, Wear 17, 301 (1971).

    Article  Google Scholar 

  16. A.D. Roberts, A.G. Thomas, Wear 33, 45 (1975).

    Article  Google Scholar 

  17. K. Vorvolakos, M.K. Chaudhury, Langmuir 19, 6778 (2003).

    Article  Google Scholar 

  18. U. Tartaglino, V.N. Samoilov, B.N.J. Persson, J. Phys. Condens. Matter 18, 4143 (2006).

    Article  ADS  Google Scholar 

  19. B.N.J. Persson, Surf. Sci. Rep. 61, 201 (2006).

    MathSciNet  Article  ADS  Google Scholar 

  20. B.N.J. Persson, Phys. Rev. B 63, 104101 (2001).

    Article  ADS  Google Scholar 

  21. B.N.J. Persson, J. Phys. Condens. Matter. 18, 7789 (2006).

    Article  ADS  Google Scholar 

  22. The force acting on a stress domain should depend quasi-periodically on the lateral displacement $x$ i.e., $F = F_{\ab{c}}\sin(2\pi x/a)$ giving for small $x$: $F\approx F_{\ab{c}} 2 \pi x/a$. The pinning stress $F_{\ab{c}} = \sigma_{\ab{c}}D^2$ and the elastic force $F=kx$ with $k = \alpha ED$, where $\alpha$ is of order $\sim 6$. Thus we get $ED \approx \sigma_{\ab{c}} D^2/a$.

  23. A. Le Gal, M. Klüppel, J. Chem. Phys. 123, 014704 (2005).

    Article  Google Scholar 

  24. K.A. Grosch, Proc. R. Soc. London, Ser. A 274, 21 (1963)

    Google Scholar 

  25. A. Casoli, M. Brendle, J. Schultz, A. Philippe, G. Reiter, Langmuir 17, 388 (2001).

    Article  Google Scholar 

  26. T. Baumberger, C. Caroli, Adv. Phys. 55, 279 (2006)

    Article  ADS  Google Scholar 

  27. M.R. Mofidi, E. Kassfeldt, B. Prakash, to be published in Wear.

  28. J. Molter, Elastomerreibung und Kontactmechanik, DIK fortbildungsseminar, Hannover 2003.

  29. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, London, 1975).

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Affiliations

  1. IFF, FZ-Jülich, 52425, Jülich, Germany

    B. N. J. Persson & A. I. Volokitin

  2. Samara State Technical University, 443100, Samara, Russia

    A. I. Volokitin

Authors
  1. B. N. J. Persson
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  2. A. I. Volokitin
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Correspondence to B. N. J. Persson.

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Persson, B.N.J., Volokitin, A.I. Rubber friction on smooth surfaces. Eur. Phys. J. E 21, 69–80 (2006). https://doi.org/10.1140/epje/i2006-10045-9

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  • DOI: https://doi.org/10.1140/epje/i2006-10045-9

PACS.

  • 61.41.+e Polymers, elastomers, and plastics
  • 62.20.Qp Tribology and hardness
  • 62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances