Self-Organization at the Frictional Interface

  • Michael Nosonovsky
  • Vahid Mortazavi
Part of the Green Energy and Technology book series (GREEN)


Despite the fact that self-organization during friction has received relatively little attention of the tribologists so far, it has a potential for the creation of self-healing and self-lubricating materials, which are of importance for the green or environment-friendly tribology. The principles of the thermodynamics of irreversible processes and of the nonlinear theory of dynamical systems are used to investigate the formation of spatial and temporal structures during friction. The transition to the self-organized state with low friction and wear occurs through the destabilization of the steady-state (stationary) sliding. The criterion for the destabilization is discussed and examples like formation of a protective film and slip waves are discussed. Some cases like running-in stage, elastic structures, and Turing pattern formation as evidences of self-organization are studied. A special self-healing mechanism may be embedded into material by coupling corresponding required forces. The analysis provides a structure–property relationship which can be applied for the design optimization of composite self-lubricating and self-healing materials for various ecologically friendly applications and green tribology.


Entropy Production Shannon Entropy Thermodynamic Force Entropy Production Rate Selective Transfer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors acknowledge the support of the University of Wisconsin-Milwaukee (UWM) Research Growth Initiative (RGI) and UWM Research Foundation Bradley Catalyst grants.


  1. 1.
    H. A. Abdel-Aal, Wear and irreversible entropy generation in dry sliding, Annals of University “Dunarea De Jos” Galati, Fascicle VIII, Tribology. 34–45 (2006) ISSN 1221–4590Google Scholar
  2. 2.
    G.G. Adams, Self-excited oscillations of the two elastic half-spaces sliding with a constant coefficient of friction. ASME J. Appl. Mech. 62, 867–872 (1995). doi: 10.1115/1.2896013 zbMATHCrossRefGoogle Scholar
  3. 3.
    G.G. Adams, Steady sliding of two elastic half-spaces with friction reduction due to interface stick-slip. ASME J. Tribol. 65, 470–475 (1998)Google Scholar
  4. 4.
    M. Adler, J. Ferrante, A. Schilowitz, D. Yablon, F. Zypman, Self-organized criticality in nano tribology. Mater. Res Soc. 782, 111 (2004)Google Scholar
  5. 5.
    A. Aizawa, A. Mitsuo, S. Yamamoto, T. Sumitomo, S. Muraishic, Self-lubrication mechanism via the in situ formed lubricious oxide tribofilm. Wear 259(1–6), 708–718 (2005)CrossRefGoogle Scholar
  6. 6.
    P. Bak, How Nature Works: The Science of Self-Organized Criticality (Springer, New York, 1996)zbMATHGoogle Scholar
  7. 7.
    J.R. Barber, Thermoelastic instabilities in the sliding of conforming solids. Proc. R. Soc. London A 312, 381–394 (1969)CrossRefGoogle Scholar
  8. 8.
    L.I. Bershadski, On the self-organization and concepts of wear-resistance in tribosystems. Trenie I Iznos (Russian Friction and Wear) 13, 1077–1094 (1992)Google Scholar
  9. 9.
    L.I. Bershadski, B.I. Kostetski, General concept in tribology. Trenie I Iznos (Russian Friction and Wear) 14, 6–18 (1993)Google Scholar
  10. 10.
    B. Bhushan, M. Nosonovsky, Scale effects in friction using strain gradient plasticity and dislocation-assisted sliding (microslip). Acta Mater. 51, 4331–4340 (2003). doi: 10.1016/S1359-6454(03)00261-1 CrossRefGoogle Scholar
  11. 11.
    P.J. Blau, Friction and Wear Transitions of Materials: Break-In, Run-In, Wear-In (Noyes Publications, New Jersey, 1989)Google Scholar
  12. 12.
    M.D. Bryant, M.M. Khonsari, F.F. Ling, On the thermodynamics of degradation. Proc. R. Soc. A 464, 2001–2014 (2008). doi: 10.1098/rspa.2007.0371 zbMATHCrossRefGoogle Scholar
  13. 13.
    S.V. Buldyrev, J. Ferrante, F.R. Zypman, Dry friction avalanches: experiments and theory. Phys. Rev. E 74, 066–110 (2006). doi: 10.1103/PhysRevE.74.066110 CrossRefGoogle Scholar
  14. 14.
    N. Bushe, I.S. Gershman, Compatibility of Tribosystems, in Self-Organization During Friction. Advanced Surface-Engineered Materials and Systems Design, ed. by G.S. Fox-Rabinovich, G.E. Totten (CRC Taylor & Francis, Boca Raton, 2006), pp. 59–80CrossRefGoogle Scholar
  15. 15.
    Z. Dai, S. Yang, Q. Xue, Thermodynamic model of fretting wear. J. Nanjing Univ. Aeronaut. Astronaut. 32, 125–131 (2000)Google Scholar
  16. 16.
    S.R. De Groot, P. Mazur, Non-Equilibrium Thermodynamics (Interscience, New York, 1962)Google Scholar
  17. 17.
    K.L. Doelling, F.F. Ling, M.D. Bryant, B.P. Heilman, An experimental study of the correlation between wear and entropy flow in machinery components. J. Appl. Phys. 88, 2999–3003 (2000)CrossRefGoogle Scholar
  18. 18.
    C. Donnet, A. Erdemir, Historical developments and new trends in tribological and solid lubricant coatings. Surf. Coat. Technol. 180, 76–84 (2004)CrossRefGoogle Scholar
  19. 19.
    V. Dufiet, J. Boissonade, Conventional and nonconventional turing patterns. J. Chem. Phys. 96, 664–673 (1991)CrossRefGoogle Scholar
  20. 20.
    V. Dufiet, J. Boissonade, Numerical studies of turing patterns selection in a two-dimensional system. Physician A 188, 158–171 (1992)CrossRefGoogle Scholar
  21. 21.
    A. Erdemir, R.A. Erck, J. Robles, Relationship of hertzian contact pressure to friction behavior of selflubricating boric acid films. Surf. Coat. Technol. 49, 435–438 (1991)CrossRefGoogle Scholar
  22. 22.
    A. Erdemir, C. Bindal, C. Zuiker, E. Savrun, Tribology of naturally occurring boric acid films on boron carbides. Surf. Coat. Technol. 86–87, 507–510 (1996)CrossRefGoogle Scholar
  23. 23.
    A. Erdemir, in Modern Tribology Handbook, ed. by B. Bhushan, vol II (CRC, Boca Raton, 2001)Google Scholar
  24. 24.
    P. Fleurquin, H. Fort, M. Kornbluth, R. Sandler, M. Segall, F. Zypman, Negentropy generation and fractality in dry friction of polished surfaces. Entropy 12, 480–489 (2010)CrossRefGoogle Scholar
  25. 25.
    G.S. Fox-Rabinovich, G.E. Totten (eds.), Self-Organization during Friction (CRC Press, FL, 2006)Google Scholar
  26. 26.
    G.S. Fox-Rabinovich, S.C. Veldhuis, A.I. Kovalev, D.L. Wainstein, I.S. Gershman, S. Korshunov, L.S. Shuster, J.L. Endrino, Features of self-organization in ion modified nanocrystalline plasma vapor deposited AlTiN coatings under severe tribological conditions. J. Appl. Phys. 102, 74–305 (2007). doi: 10.1063/1.2785947 CrossRefGoogle Scholar
  27. 27.
    D.N. Garkunov, Triboengineering (Wear and Non-Deterioration) (Moscow Agricultural Academy Press, Moscow, 2000) (in Russian)Google Scholar
  28. 28.
    D.N. Garkunov, Scientific Discoveries in Tribotechnology (MSHA, Moscow, 2004) (in Russian)Google Scholar
  29. 29.
    I.S. Gershman, N. Bushe, Elements of Thermodynamics of Self-Organization during Friction, in Self-Organization during Friction. Advanced Surface-Engineered Materials and Systems Design, ed. by G.S. Fox-Rabinovich, G.E. Totten (CRC Taylor & Francis, Boca Raton, 2006), pp. 13–58Google Scholar
  30. 30.
    I.S. Gershman, Formation of Secondary Structures and Self-Organization Process of Tribosystems during Friction with the Collection of Electric Current, in Self-Organization during Friction. Advanced Surface-Engineered Materials and Systems Design, ed. by G.S. Fox-Rabinovich, G.E. Totten (CRC Taylor & Francis, Boca Raton, FL, 2006), p. 197Google Scholar
  31. 31.
    H. Haken, Synergetics. An Introduction. Non equilibrium Phase Transitions in Physics, Chemistry and Biology, 3rd edn. (Springer-Verlag, New York, 1983)Google Scholar
  32. 32.
    F. Ilie, C. Tita, Investigation of layers formed through selective transfer with atomic force microscopy. Paper presented in ROTRIB’07, 10th international conference on tribology, Bucharest, Romania, 2007Google Scholar
  33. 33.
    Q. Jun, A. Linan, P.J. Blau, Sliding friction and wear characteristics of Al2O3-Al nanocomposites. STLE/ASME international joint tribology conference, ASME, New York, 2006 (IJTC 2006, Ser. 2006)Google Scholar
  34. 34.
    E. Kagan, Turing systems, entropy, and kinetic models for self-healing surfaces. Entropy 12, 554–569 (2010)CrossRefGoogle Scholar
  35. 35.
    B.E. Klamecki, Wear—an entropy production model. Wear 58, 325–330 (1980)CrossRefGoogle Scholar
  36. 36.
    B.E. Klamecki, A thermodynamic model of friction. Wear 63, 113–120 (1980)CrossRefGoogle Scholar
  37. 37.
    B.E. Klamecki, Energy dissipation in sliding. Wear 77, 115–128 (1982)CrossRefGoogle Scholar
  38. 38.
    B.E. Klamecki, An entropy-based model of plastic deformation energy dissipation in sliding. Wear 96, 319–329 (1984)CrossRefGoogle Scholar
  39. 39.
    T Leppänen, Computational studies of pattern formation in turing systems, Dissertation for the degree of Doctor of science in technology, Helsinki University of Technology (2004)Google Scholar
  40. 40.
    J.F. Lin, H.Y. Chu, Analysis of the bénard cell-like worn surface type occurred during oil-lubricated sliding contact. Proceedings of the ASME/STLE 2009 international joint tribology conference, IJTC2009, Memphis, Tennessee (2009)Google Scholar
  41. 41.
    M.R. Lovell, M.A. Kabir, P.L. Menezes, C.F. Higgs III, Influence of boric acid additive size on green lubricant performance, Phil. Trans. R. Soc. A 368(1929), 4851–4868 (2010)CrossRefGoogle Scholar
  42. 42.
    S. Maegawa, K. Nakano, Mechanism of stick-slip associated with Schallamach waves. Wear 268, 924–930 (2010)CrossRefGoogle Scholar
  43. 43.
    P.H. Mayrhofera, C. Mitterer, J.G. Wen, J.E. Greene, I. Petrov, Self-organized nanocolumnar structure in superhard TiB2 thin films. Appl. Phys. Lett. 86, 131909 (2005)CrossRefGoogle Scholar
  44. 44.
    J.A.C. Martins, J. Guimara˜es, L.O. Faria, Dynamic surface solutions in linear elasticity and viscoelasticity with frictional boundary conditions. ASME J. Vib. Acoust. 117, 445–451 (1995)CrossRefGoogle Scholar
  45. 45.
    P.H. Mayrhofera, C. Mitterera, L. Hultmanb, H. Clemensa, Microstructural design of hard coatings. Prog. Mater. Sci. 51(8), 1032–1114 (2006)CrossRefGoogle Scholar
  46. 46.
    P.L. Menezes, Kishore, S.V. Kailas, Studies on friction and transfer layer using inclined scratch. Tribol. Int. 39(2), 175–183 (2006)CrossRefGoogle Scholar
  47. 47.
    V. Mortazavi, M. Nosonovsky, In Friction-induced pattern-Formation and Turing systems. Langmuir. 27(8), 4772–4779 (2011a)CrossRefGoogle Scholar
  48. 48.
    V. Mortazavi, M. Nosonovsky, Wear-induced microtopography evolution and wetting properties of self-cleaning, lubricating and healing surfaces. J. Adhes. Sci. Technol. 25(12), 1337–1359 (2011b)CrossRefGoogle Scholar
  49. 49.
    J.D. Murray, Mathematical Biology, 2nd edn. (Springer Verlag, Berlin, 1989)zbMATHGoogle Scholar
  50. 50.
    G. Nicolis, I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977)zbMATHGoogle Scholar
  51. 51.
    M. Nosonovsky, Self-organization at the frictional interface for green tribology. Phil. Trans. R. Soc. A 368(1929), 4755–4774 (2010a)MathSciNetCrossRefGoogle Scholar
  52. 52.
    M. Nosonovsky, Entropy in tribology: in search of applications. Entropy 12(6), 1345–1390 (2010b), doi:  10.3390/e12061345 CrossRefGoogle Scholar
  53. 53.
    M. Nosonovsky, G.G. Adams, Dilatational and shear waves induced by the frictional sliding of two elastic half-spaces. Int. J. Eng. Sci. 39, 1257–1269 (2001). doi: 10.1016/S0020-7225(00)00085-9 CrossRefGoogle Scholar
  54. 54.
    M. Nosonovsky, G.G. Adams, Vibration and stability of frictional sliding of two elastic bodies with a wavy contact interface. ASME J. Appl. Mech. 71, 154–300 (2004). doi: 10.1115/1.1653684 zbMATHCrossRefGoogle Scholar
  55. 55.
    M. Nosonovsky, B. Bhushan, Thermodynamics of surface degradation, self-organization and self-healing for biomimetic surfaces. Phil. Trans. R. Soc. A 367, 1607–1627 (2009)CrossRefGoogle Scholar
  56. 56.
    M. Nosonovsky, B. Bhushan, Surface self-organization: from wear to self-healing in biological and technical surfaces. Appl. Surf. Sci. 256, 3982–3987 (2010)CrossRefGoogle Scholar
  57. 57.
    M. Nosonovsky, R. Amano, J.M. Lucci, P.K. Rohatgi, Physical chemistry of self-organization and self-healing in metals. Phys. Chem. Chem. Phys. 11, 9530–9536 (2009)CrossRefGoogle Scholar
  58. 58.
    I. Prigogine, Thermodynamics of Irreversible Processes (Willey, New York, 1968)Google Scholar
  59. 59.
    I. Prigogine, From Being to Becoming (WH Freeman and Company, San Francisco, CA, 1980)Google Scholar
  60. 60.
    I. Prigogine, I. Stengers, Order Out of Chaos (Bantam, New York, 1984)Google Scholar
  61. 61.
    K. Ranjith, J.R. Rice, Slip dynamics at a dissimilar material interface. J. Mech. Phys. Solids 49, 341–361 (2001)zbMATHCrossRefGoogle Scholar
  62. 62.
    L. Rapoport, N. Fleischer, R. Tenne, Fullerene-like WS2 nanoparticles: superior lubricants for harsh conditions. Adv. Mater. 15, 651–655 (2003)CrossRefGoogle Scholar
  63. 63.
    I.L. Singer, S.D. Dvorak, K.J. Wahl, T.W. Scharf, Role of third bodies in friction and wear of protective coatings. J. Vac. Sci. Technol. A 21, 232–240 (2003)CrossRefGoogle Scholar
  64. 64.
    L.A. Sosnovskiy, S.S. Sherbakov, Surprizes of Tribo-Fatigue (Magic Book, Minsk, 2009)Google Scholar
  65. 65.
    A.M. Turing, The chemical basis of morphogenesis. Phil. Trans. R. Soc. B 237, 37–72 (1952)CrossRefGoogle Scholar
  66. 66.
    G. Wu, F. Gao, M. Kaltchev, J. Gutow, J.K. Mowlem, W.C. Schramm, P.V. Kotvis, W.T. Tysoe, An investigation of the tribological properties of thin KCl films on iron in ultrahigh vacuum: modeling the extreme-pressure lubricating interface. Wear 252, 595–606 (2002)CrossRefGoogle Scholar
  67. 67.
    A. Zmitrowicz, A thermodynamical model of contact, friction, and wear. Wear 114, 135–221 (1987)CrossRefGoogle Scholar
  68. 68.
    S. Zwaag, van der, Self-healing behaviour in man-made engineering materials: bioinspired but taking into account their intrinsic character. Phil. Trans. R. Soc. A 367, 1689–1704 (2009)CrossRefGoogle Scholar
  69. 69.
    F. Zypman, J. Ferrante, M. Jansen, K. Scanlon, P. Abel, Evidence of self-organized criticality in dry sliding friction. J. Phys. Condens. Matter. 15, L191–L196 (2003). doi: 10.1088/0953-8984/15/12/101 CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.College of Engineering and Applied ScienceUniversity of WisconsinMilwaukeeUSA

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