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Bridging the Gap Between the Atomic-Scale and Macroscopic Modeling of Friction

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Abstract

A short survey of a modern view on the problem of friction from the physical viewpoint is presented. An atomically thin lubricant film confined between two substrates in moving contact has been studied with the help of molecular dynamics (MD) based on Langevin equations with coordinate- and velocity-dependent damping coefficient. Depending on model parameters, the system may exhibit either the liquid sliding regime, when the lubricant film melts during sliding (the “melting-freezing” mechanism of stick-slip motion), the “layer-over-layer” sliding regime, when the film keeps a layered structure at sliding, or the solid sliding regime, which may provide an extremely low friction (“superlubricity”). Atomic-scale MD simulations of friction, however, lead to a “viscosity” of the thin film, as well as to the critical velocity of the transition from stick-slip to smooth sliding, which differ by many orders of magnitude from the values observed in macroscopic experiments. This contradiction can be resolved with the help of the earthquakelike (EQ) model with a continuous distribution of static thresholds. The evolution of the EQ model is reduced to a master equation which can be solved analytically. This approach describes stick-slip and smooth sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the atomic-scale studies of contact properties.

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References

  1. Persson, B.N.J.: Sliding Friction: Physical Principles and Applications. Springer-Verlag, Berlin (1998)

    Google Scholar 

  2. Dowson, D.: History of Tribology. Longman, New York (1979)

    Google Scholar 

  3. Bowden, F.P., Tabor, D.: Friction and Lubrication of Solids. Clarendon, Oxford (1950)

    Google Scholar 

  4. Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. A 295:300–319 (1966)

    Article  CAS  ADS  Google Scholar 

  5. Robbins, M.O.: Jamming, friction and unsteady rheology. In: Liu A.J., Nagel S.R. (eds) Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales. Taylor and Francis, London (2000) and cond-mat/9912337

  6. Robbins, M.O., Müser, M.H.: Computer simulation of friction, lubrication and wear. In: Bhushan B. (eds.) Handbook of Modern Tribology, chap. 20, pp. 717–765. CRC Press, Boca Raton (2000)

  7. Persson, B.N.J., Albohr, O., Mancosu, F., Peveri, V., Samoilov, V.N., Sivebaek, I.M.: On the nature of the static friction, kinetic friction and creep. Wear 254:835–851 (2003)

    Article  CAS  Google Scholar 

  8. Baumberger, T., Caroli, C.: Solid friction from stick-slip down to pinning and aging. Adv. Phys. 55, 279–348 (2006)

    Article  ADS  Google Scholar 

  9. Braun, O.M., Naumovets, A.G.: Nanotribology: microscopic mechanisms of friction. Surf. Sci. Rep. 60, 79–158 (2006)

    Article  CAS  ADS  Google Scholar 

  10. Binnig, G., Rohrer, H., Gerber, C., Weibel, E.: Surface studies by scanning tunneling microscopy. Phys. Rev. Lett. 49, 57–61 (1982)

    Article  ADS  Google Scholar 

  11. Binnig, G., Quate, C.F., Gerber, C.: Atomic force microscope. Phys. Rev. Lett. 56, 930–933 (1986)

    Article  ADS  PubMed  Google Scholar 

  12. Mate, C.M., McClelland, G.M., Erlandsson, R., Chang, S.: Atomic-scale friction of a tungsten tip on a graphite surface. Phys. Rev. Lett. 59, 1942–1945 (1987)

    Article  CAS  ADS  PubMed  Google Scholar 

  13. Tomlinson, G.A.: A molecular theory of friction. Phil. Mag. Ser. 7, 935–939 (1929)

    Google Scholar 

  14. Kontorova, T., Frenkel, Yu.I.:On the theory of plastic deformation. Zh. Exp. Teor. Fiz. 8, 1340–1344 (1938)

    Google Scholar 

  15. Braun, O.M., Kivshar, Yu.S.: The Frenkel–Kontorova Model: Concepts, Methods, and Applications. Springer-Verlag, Berlin (2004)

    MATH  Google Scholar 

  16. Persson, B.N.J.: Theory of friction: the role of elasticity in boundary lubrication. Phys. Rev. B 50, 4771–4786 (1994)

    Article  CAS  ADS  Google Scholar 

  17. Braun, O.M., Peyrard, M., Bortolani, V., Franchini, A., Vanossi, A.: Transition from smooth sliding to stick-slip motion in a single frictional contact. Phys. Rev. E 72, 056116-1–056116-15 (2005)

    MathSciNet  ADS  Google Scholar 

  18. Lyuksyutov, I.F., Naumovets, A.G., Pokrovsky, V.L.: Two-Dimensional Crystals. Academic Press, Boston (1990)

    Google Scholar 

  19. Braun, O.M.: Adiabatic motion of an atomic chain in periodic potential. Surf. Sci. 230, 262–276 (1990)

    Article  CAS  ADS  Google Scholar 

  20. Ying, C.S.: Structure and dynamics of a submonolayer film adsorbed on solid surfaces. Phys. Rev. B 3, 4160–4171 (1971)

    Article  ADS  Google Scholar 

  21. Sokoloff, J.B.: Sliding charge-density waves in periodic and disordered lattices. Phys. Rev. B 16, 3367–3372 (1977)

    Article  CAS  ADS  Google Scholar 

  22. Pokrovsky, V.L., Talapov, A.L.: Phase transitions and vibrational spectra of nearly incommensurate structures. Zh. Exp. Teor. Fiz. 75, 1151–1157 (1978)

    Google Scholar 

  23. Aubry, S.: Chaotic motion of an impact oscillator. In: Bishop, A.R., Schneider, T. (eds.): Solitons and Condensed Matter Physics, Solid State Sciences 8, p. 264. Springer, Berlin (1978)

  24. Aubry, S., LeDaeron, P.Y.: The discrete Frenkel–Kontorova model and its extensions. I. Exact results for the ground-states. Physica D 8, 381–422 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  25. Hirano, M., Shinjo, K.: Atomistic locking and friction. Phys. Rev. B 41, 11837–11851 (1990)

    Article  CAS  ADS  Google Scholar 

  26. Braun, O.M., Vanossi, A., Tosatti, E.: Incommensurability of a confined system under shear. Phys. Rev. Lett. 95, 0261021–0261024 (2005)

    ADS  Google Scholar 

  27. Persson, B.N.J., Ballone, P.: Squeezing lubrication films: layering transition for curved solid surfaces with long-range elasticity. J. Chem. Phys. 112, 9524–9542 (2000)

    Article  CAS  ADS  Google Scholar 

  28. Tartaglino, U., Samoilov, V.N., Persson, B.N.J.: Role of surface roughness in superlubricity. J. Phys. Condens. Matter. 18, 4143–4160 (2006)

    Article  CAS  ADS  Google Scholar 

  29. Yang, C., Tartaglino, U., Persson, B.N.J.: A multi-scale molecular dynamics approach to contact mechanics. Eur. Phys. J. E 19, 47–58 (2006)

    Article  CAS  PubMed  Google Scholar 

  30. Luan, B.Q., Hyun, S., Molinari, J.F., Bernstein, N., Robbins, M.O.: Multiscale modeling of two-dimensional contacts. Phys. Rev. E 74, 046710-1–046710-11 (2006)

    ADS  Google Scholar 

  31. Braun, O.M., Peyrard, M.: Friction in a solid lubricant film. Phys. Rev. E 63:046110-1–046110-19 (2001)

    ADS  Google Scholar 

  32. Braun, O.M.: Energy exchange in adsorbed layers. Surf. Sci. 213, 336–358 (1989)

    Article  CAS  ADS  Google Scholar 

  33. Braun, O.M., Volokitin, A.I., Zhdanov, V.P.: Vibrational spectroscopy of adsorbates. Uspekhi. Fiz. Nauk. 158, 421–450 (1989)

    CAS  Google Scholar 

  34. Braun, O.M., Ferrando, R.: Role of long jumps in surface diffusion. Phys. Rev. E 65, 061107-1–061107-11 (2002)

    Article  ADS  Google Scholar 

  35. Braun, O.M., Peyrard, M.: Dynamics and melting of a thin confined film. Phys. Rev. E 68, 011506-1–011506-11 (2003)

    ADS  Google Scholar 

  36. Zhukov, A.V., Paliy, M.V., Braun, O.M., George, T.F.: Two-stage melting in tribological systems. Phys. Lett. A 361, 437–441 (2007)

    Article  MATH  CAS  ADS  Google Scholar 

  37. Persson, B.N.J.: Theory of friction and boundary lubrication. Phys. Rev. B 48, 18140–18158 (1993)

    Article  CAS  ADS  Google Scholar 

  38. Sokoloff , J.B.: Possible microscopic explanation of the virtually universal occurrence of static friction. Phys. Rev. B 65, 115415-1–115415-9 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  39. Thompson, P.A., Robbins, M.O.: Origin of stick-slip motion in boundary lubrication. Science 250, 792–794 (1990)

    Article  CAS  ADS  PubMed  Google Scholar 

  40. Robbins, M.O., Thompson, P.A.: Critical velocity of stick-slip motion. Science 253, 916 (1991)

    Article  CAS  ADS  PubMed  Google Scholar 

  41. Hirano, M., Shinjo, K., Kaneko, R., Murata, Y.: Observation of superlubricity by scanning tunneling microscopy. Phys. Rev. Lett. 78, 1448–1451 (1997)

    Article  CAS  ADS  Google Scholar 

  42. Dienwiebel, M., Verhoeven, G.S., Pradeep, N., Frenken, J.W.M., Heimberg, J.A., Zandbergen, H.W.: Superlubricity of graphite. Phys. Rev. Lett. 92, 126101-1–126101-4 (2004)

    Article  ADS  Google Scholar 

  43. Filippov, A.E., Dienwiebel, M., Frenken, J.W.M., Klafter, J., Urbakh, M.: Torque and twist against superlubricity. Phys. Rev. Lett. 100, 046102-1–046102-4 (2008)

    Article  ADS  Google Scholar 

  44. Braun, O.M., Paliy, M., Consta, S.: Ordering of a thin lubricant film due to sliding. Phys. Rev. Lett. 92, 256103-1–256103-4 (2004)

    Article  ADS  Google Scholar 

  45. Braun, O.M.: Phenomenological theory of kinetic friction for the solid lubricant film. Phys. Scr. 78, 015802-1–015802-13 (2008)

    Article  ADS  Google Scholar 

  46. Yoshizawa, H., McGuiggan, P., Israelachvili, J.: Identification of a second dynamic state during stick-slip motion. Science 259, 1305–1308 (1993)

    Article  CAS  ADS  PubMed  Google Scholar 

  47. Olami, Z., Feder, H.J.S., Christensen, K.: Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. Phys. Rev. Lett. 68, 1244–1247 (1992)

    Article  ADS  PubMed  Google Scholar 

  48. Persson, B.N.J.: Theory of friction: stress domains, relaxation, and creep. Phys. Rev. B 51, 13568–13585 (1995)

    Article  CAS  ADS  Google Scholar 

  49. Braun, O.M., Peyrard, M.: Modeling friction on a mesoscale: master equation for the earthquakelike model. Phys. Rev. Lett. 100, 125501-1–125501-4 (2008)

    Article  ADS  Google Scholar 

  50. Farkas, Z., Dahmen, S.R., Wolf, D.E.: Static versus dynamic friction: the role of coherence. J. Stat. Mech. Theory Exp. P06015 (2005); cond-mat/0502644

  51. Braun, O.M., Röder, J.: Transition from stick-slip to smooth sliding: an earthquakelike model. Phys. Rev. Lett. 88, 096102-1–096102-4 (2002)

    ADS  Google Scholar 

  52. Filippov, A.E., Klafter, J., Urbakh, M.: Friction through dynamical formation and rupture of molecular bonds. Phys. Rev. Lett. 92, 135503-1–135503-4 (2004)

    Article  ADS  Google Scholar 

  53. Braun, O.M., Tosatti, E.: Kinetics of stick-slip friction in boundary lubrication. Europhys. Lett. 88, 48003-1–48003-6(2009)

    Article  ADS  Google Scholar 

  54. Klein, J.: Frictional dissipation in stick-slip sliding. Phys. Rev. Lett. 98, 056101-1–056101-4 (2007)

    Article  ADS  Google Scholar 

  55. Israelachvili, J.N., McGuiggan, P.M., Homola, A.M.: Dynamic properties of molecularly thin liquid films. Science 240, 189–191 (1988)

    Article  CAS  ADS  PubMed  Google Scholar 

  56. Klein, J., Kumacheva, E.: Simple liquids confined to molecularly thin layers. I. Confinement-induced liquid-to-solid phase transitions. J. Chem. Phys. 108, 6996–7009 (1998)

    Article  CAS  ADS  Google Scholar 

  57. Srinivasan, M., Walcott, S.: Binding site models of friction due to the formation and rupture of bonds: state-function formalism, force-velocity relations, response to slip velocity transients, and slip stability. Phys. Rev. E 80, 046124-1–046124-15 (2009)

    Article  ADS  Google Scholar 

  58. Barel, I., Urbakh, M., Jansen, L., Schirmeisen, A.: Multibond dynamics of nanoscale friction: the role of temperature. Phys. Rev. Lett. 104, 066104-1–066104-4 (2010)

    Article  ADS  Google Scholar 

  59. Braun, O.M., Barel, I., Urbakh, M.: Dynamics of transition from static to kinetic friction. Phys. Rev. Lett. 103, 194301-1–194301-4 (2009)

    ADS  Google Scholar 

  60. Krim, J., Solina, D.H., Chiarello, R.: Nanotribology of a Kr monolayer: a quartz crystal microbalance study of atomic-scale friction. Phys. Rev. Lett. 66, 181-184 (1991)

    Article  CAS  ADS  PubMed  Google Scholar 

  61. Budakian, R., Putterman, S.J.: Correlation between charge transfer and stick-slip friction at a metal-insulator interface. Phys. Rev. Lett. 85, 1000–1003 (2000)

    Article  CAS  ADS  PubMed  Google Scholar 

  62. Mukhopadhyay, A., Zhao, J., Bae, S.C., Granick, S.: Contrasting friction and diffusion in molecularly thin confined films. Phys. Rev. Lett. 89, 136103-1–136103-4 (2002)

    ADS  Google Scholar 

  63. Rubinstein, S.M., Cohen, G., Fineberg, J.: Detachment fronts and the onset of dynamic friction. Nature 430, 1005–1008 (2004)

    Article  CAS  ADS  PubMed  Google Scholar 

  64. Le Bot, A., Bou Chakra, E.: Measurement of friction noise versus contact area of rough surfaces weakly loaded. Tribol. Lett. 37, 273–281 (2010)

    Article  Google Scholar 

  65. Ben Abdelouni, H., Le Bot, A., Perret-Liaudet, J., Zahouani, H.: An experimental study on roughness noise of dry rough flat surfaces. Wear 268, 335–345 (2010)

    Article  Google Scholar 

  66. Ferrer, C., Salas, F., Pascual, M., Orozco, J.: Discrete acoustic emission waves during stick-slip friction between steel samples. Tribol. Int. 43, 1–6 (2010)

    Article  CAS  Google Scholar 

  67. Kulik, V.S., Marchenko, A.A., Naumovets, A.G., Cousty, J.: Chain length dependence of the frictional properties of n-alkane monolayers self-assembled on gold (111). In: Borisenko, V.E., Gaponenko, S.V., Gurin, V.S. (eds.) Physics, Chemistry and Application of Nanostructures, pp. 74–77. World Scientific, Singapore (2005)

  68. Mosey, N.J., Müser, M.H., Woo, T.K.: Molecular mechanisms for the functionality of lubricant additives. Science 307, 1612–1615 (2005)

    Article  CAS  ADS  PubMed  Google Scholar 

  69. Gang, O., Alvine, K.J., Fukuto, M., Pershan, P.S., Black, C.T., Ocko, B.M.: Liquids on topologically nanopatterned surfaces. Phys. Rev. Lett. 95, 217801-1–217801-4 (2005)

    Article  ADS  Google Scholar 

  70. Dinelli, F., Biswas, S.K., Briggs, G.A.D., Kolosov, O.V.: Ultrasound induced lubricity in microscopic contact. Appl. Phys. Lett. 71, 1177–1179 (1997)

    Article  CAS  ADS  Google Scholar 

  71. Heuberger, M., Drummond, C., Israelachvili, J.: Coupling of normal and transverse motions during frictional sliding. J. Phys. Chem. B 102, 5038–5041 (1998)

    Article  CAS  Google Scholar 

  72. Gao, J., Luedtke, W.D., Landman, U.: Friction control in thin-film lubrication. J. Phys. Chem. B 102, 5033–5037 (1998)

    Article  CAS  Google Scholar 

  73. Zaloj, V., Urbakh, M., Klafter, J.: Modifying friction by manipulating normal response to lateral motion. Phys. Rev. Lett. 82, 4823–4826 (1999)

    Article  CAS  ADS  Google Scholar 

  74. Tshiprut, Z., Filippov, A.E., Urbakh, M.: Tuning diffusion and friction in microscopic contacts by mechanical excitations. Phys. Rev. Lett. 95, 016101-1–016101-4 (2005)

    Article  ADS  Google Scholar 

  75. Socoliuc, A., Gnecco, E., Maier, S., Pfeiffer, O., Baratoff, A., Bennewitz, R., Meyer, E.: Atomic-scale control of friction by actuation of nanometer-sized contacts. Science 313, 207–210 (2006)

    Article  CAS  ADS  PubMed  Google Scholar 

  76. Guerra, R., Vanossi, A., Urbakh, M.: Controlling microscopic friction through mechanical oscillations. Phys. Rev. E 78, 036110-1–036110-5 (2008)

    Article  ADS  Google Scholar 

  77. Capozza, R., Vanossi, A., Vezzani, A., Zapperi, S.: Suppression of friction by mechanical vibration. Phys. Rev. Lett. 103, 085502-1–085502-4 (2009)

    Article  ADS  Google Scholar 

  78. Raviv, U., Laurat, P., Klein, J.: Fluidity of water confined to subnanometre films. Nature 413, 51–54 (2001)

    Article  CAS  ADS  PubMed  Google Scholar 

  79. Paliy, M., Braun, O.M., Consta, S.: The friction properties of an ultrathin confined water film. Tribol. Lett. 23, 7–14 (2006)

    Article  CAS  Google Scholar 

  80. Raviv, U., Klein, J.: Fluidity of bound hydration layers. Science 297, 1540–1543 (2002)

    Article  CAS  ADS  PubMed  Google Scholar 

  81. Sivebaek, I.M., Samoilov, V.N., Persson, B.N.J.: Squeezing molecular thin alkane lubrication films between curved solid surfaces with long-range elasticity: layering transitions and wear. J. Chem. Phys. 119, 2314–2321 (2003)

    Article  CAS  ADS  Google Scholar 

  82. Braun, O.M., Manini, N., Tosatti, E.: Role of lubricant molecular shape in microscopic friction. Phys. Rev. B 78, 195402-1–195402-10 (2008)

    Article  ADS  Google Scholar 

  83. Braun, O.M.: Simple model of microscopic rolling friction. Phys. Rev. Lett. 95, 126104-1–126104-4 (2005)

    ADS  Google Scholar 

  84. Braun, O.M., Tosatti, E.: Rack-and-pinion effects in molecular rolling friction. Phil. Mag. Lett. 88, 509–515 (2008)

    Article  CAS  ADS  Google Scholar 

  85. Braun, O.M., Tosatti, E.: Molecular rolling friction: the cogwheel model. J. Phys. Condens. Matter. 20, 354007-1–354007-7 (2008)

    Article  Google Scholar 

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Acknowledgments

We wish to express our gratitude to M. Evstigneev, M. Peyrard, P. Reimann, E. Tosatti, and M. Urbakh for useful discussions. This research was supported in part by a grant from the Cariplo Foundation managed by the Landau Network—Centro Volta, whose contribution is gratefully acknowledged.

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  1. Institute of Physics, National Academy of Sciences of Ukraine, 46 Science Avenue, 03028, Kiev, Ukraine

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Braun, O.M. Bridging the Gap Between the Atomic-Scale and Macroscopic Modeling of Friction. Tribol Lett 39, 283–293 (2010). https://doi.org/10.1007/s11249-010-9648-7

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