Tribology Letters

, Volume 45, Issue 1, pp 37–48 | Cite as

Modeling Sliding Contact of Rough Surfaces with Molecularly Thin Lubricants

  • Antonis I. Vakis
  • Andreas A. Polycarpou
Original Paper


The sliding contact between two rough surfaces in the presence of a molecularly thin lubricant layer is investigated. Under very high shear rates, the lubricant is treated as a semi-solid layer with normal and lateral shear-dependent stiffness components obtained from experimental data. The adhesive force in the presence of lubricant is also adapted from the Sub-boundary lubrication model and improved to account for variation in surface energy with penetration into the lubricant layer. A model is then proposed, based on the Improved sub-boundary lubrication model, which accounts for lubricant contact and adhesion and its validity is discussed. The model is in good agreement with published experimental measurements of friction in the presence of molecularly thin lubricant layers and suggests that a molecularly thin lubricant bearing could be successfully used to reduce solid substrate damage at the interface.


Nanotribology Magnetic data storage Sub-boundary lubrication Rough surfaces Adhesion Friction 



This study falls under the Cyprus Research Promotion Foundation’s Framework Programme for Research, Technological Development and Innovation 2009–2010 (DESMI 2009–2010), co-funded by the Republic of Cyprus and the European Regional Development Fund, and specifically under Grant PENEK/0609/03.


  1. 1.
    Vakis, A.I., Eriten, M., Polycarpou, A.A.: Modeling bearing and shear forces in molecularly thin lubricants. Tribol. Lett. 41(3), 573–586 (2011)CrossRefGoogle Scholar
  2. 2.
    Fukuzawa, K., Hayakawa, K., Matsumura, N., Itoh, S., Zhang, H.: Simultaneously measuring lateral and vertical forces with accurate gap control for clarifying lubrication phenomena at nanometer gap. Tribol. Lett. 37(3), 497–505 (2009)CrossRefGoogle Scholar
  3. 3.
    Vakis, A.I., Polycarpou, A.A.: Head-disk interface nanotribology for Tbit/in2 recording densities: near-contact and contact recording. J. Phys. D Appl. Phys. 43, 22 (2010)CrossRefGoogle Scholar
  4. 4.
    Suh, A.Y., Polycarpou, A.A.: Adhesive contact modeling for sub-5-nm ultralow flying magnetic storage head-disk interfaces including roughness effects. J. Appl. Phys. 97(10), 104328–104329 (2005)CrossRefGoogle Scholar
  5. 5.
    Yeo, C.-D., Sullivan, M., Lee, S.-C., Polycarpou, A.A.: Friction force measurements and modeling in hard disk drives. IEEE. Trans. Magn. 44(1), 157–162 (2008)CrossRefGoogle Scholar
  6. 6.
    Suh, A.Y., Mate, C.M., Payne, R.N., Polycarpou, A.A.: Experimental and theoretical evaluation of friction at contacting magnetic storage slider-disk interfaces. Tribol. Lett. 23(3), 177–190 (2006)CrossRefGoogle Scholar
  7. 7.
    Demirel, A.L., Granick, S.: Transition from static to kinetic friction in a model lubricated system. J. Chem. Phys. 109(16), 6889–6897 (1998)CrossRefGoogle Scholar
  8. 8.
    Demirel, A.L., Granick, S.: Relaxations in molecularly thin liquid films. J. Phys. Condens. Mat. 8, 9537–9539 (1996)CrossRefGoogle Scholar
  9. 9.
    Itoh, S., Fukuzawa, K., Hamamoto, Y., Hedong, Z., Mitsuya, Y.: Fiber wobbling method for dynamic viscoelastic measurement of liquid lubricant confined in molecularly narrow gaps. Tribol. Lett. 30(3), 177–189 (2008)CrossRefGoogle Scholar
  10. 10.
    Fukuzawa, K., Itoh, S., Mitsuya, Y.: Fiber wobbling shear force measurement for nanotribology of confined lubricant molecules. IEEE. Trans. Magn. 39, 2453–2455 (2003)CrossRefGoogle Scholar
  11. 11.
    Suh, A.Y., Polycarpou, A.A.: Design optimization of sub-5 nm head-disk interfaces using a two-degree-of-freedom dynamic contact model with friction. Int. J. Prod. Dev. 5(3–4), 268–291 (2008)Google Scholar
  12. 12.
    Lee, S.-C., Polycarpou, A.A.: Microtribodynamics of pseudo-contacting head-disk interfaces intended for 1 Tbit/in2. IEEE. Trans. Magn. 41(2), 812–818 (2005)CrossRefGoogle Scholar
  13. 13.
    Stanley, H.M., Etsion, I., Bogy, D.B.: Adhesion of contacting rough surfaces in the presence of sub-boundary lubrication. J. Tribol. 112(1), 98–104 (1990)CrossRefGoogle Scholar
  14. 14.
    Israelachvili, J.: Intermolecular and surface forces, second edition: with applications to colloidal and biological systems (Colloid Science). Academic Press, London (1992)Google Scholar
  15. 15.
    Mate, C.M., Toney, M.F., Leach, K.A.: Roughness of thin perfluoropolyether lubricant films: influence on disk drive technology. IEEE. Trans. Magn. 37(4), 1821–1823 (2001)CrossRefGoogle Scholar
  16. 16.
    Marchon, B., Dai, Q., Nayak, V., Pit, R.: The physics of disk lubricant in the continuum picture. IEEE. Trans. Magn. 41(2), 616–620 (2005)CrossRefGoogle Scholar
  17. 17.
    Pit, R., Marchon, B.: Direct measurement of lubricant relaxation on a disk surface. IEEE. Trans. Magn. 37(4), 1830–1832 (2001)CrossRefGoogle Scholar
  18. 18.
    Suh, A.Y., Polycarpou, A.A.: Effect of molecularly thin lubricant on roughness and adhesion of magnetic disks intended for extremely high-density recording. Tribol. Lett. 15(4), 365–376 (2003)CrossRefGoogle Scholar
  19. 19.
    Greenwood, J., Williamson, J.: Contact of nominally flat surfaces. P. Roy Soc. Lond. A Mat. 295(1442), 300–319 (1966)CrossRefGoogle Scholar
  20. 20.
    Ciavarella, M., Greenwood, J.A., Paggi, M.: Inclusion of ‘‘interaction’’ in the Greenwood and Williamson contact theory. Wear 265(5–6), 729–734 (2008)CrossRefGoogle Scholar
  21. 21.
    Greenwood, J.A.: A simplified elliptic model of rough surface contact. Wear 261(2), 191–200 (2006)CrossRefGoogle Scholar
  22. 22.
    Ciavarella, M., Delfine, V., Demelio, G.: A “re-vitalized” Greenwood and Williamson model of elastic contact between fractal surfaces. J. Mech. Phys. Solids 54(12), 2569–2591 (2006)CrossRefGoogle Scholar
  23. 23.
    Yu, N., Polycarpou, A.A.: Contact of rough surfaces with asymmetric distribution of asperity heights. J. Tribol. 124(2), 367–376 (2002)CrossRefGoogle Scholar
  24. 24.
    Bush, A.W., Gibson, R.D., Thomas, T.R.: The elastic contact of a rough surface. Wear 35(1), 87–111 (1975)CrossRefGoogle Scholar
  25. 25.
    Hu, H.-W., Granick, S., Schweizer, K.S.: Static and dynamical structure of confined polymer films. J. Non Cryst. Solids 172–174, 721–728 (1994)CrossRefGoogle Scholar
  26. 26.
    Itoh, S., Takahashi, K., Fukuzawa, K., Amakawa, H., Hedong, Z.: Spreading properties of monolayer lubricant films: effect of bonded molecules. IEEE. Trans. Magn. 45(11), 5055–5060 (2009)CrossRefGoogle Scholar
  27. 27.
    Guo, Q., Chung, P.S., Jhon, M.S., Choi, H.J.: Nano-rheology of single unentangled polymeric lubricant films. Macromol. Theor. Simul. 17(9), 454–459 (2008)CrossRefGoogle Scholar
  28. 28.
    Thompson, P.A., Robbins, M.O., Grest, G.S.: Structure and shear response in nanometer-thick films. Isr. J. Chem. 35(1), 93–106 (1995)Google Scholar
  29. 29.
    Gee, M.L., McGuiggan, P.M., Israelachvili, J.N., Homola, A.M.: Liquid to solidlike transitions of molecularly thin films under shear. J. Chem. Phys. 93(3), 1895–1906 (1990)CrossRefGoogle Scholar
  30. 30.
    Brinson, H., Brinson, C.: Polymer engineering science and viscoelasticity: an introduction. Springer, New York (2007)Google Scholar
  31. 31.
    Shi, X., Polycarpou, A.A.: Investigation of contact stiffness and contact damping for magnetic storage head-disk interfaces. J. Tribol. 130, 1–9 (2008)CrossRefGoogle Scholar
  32. 32.
    Kogut, L., Etsion, I.: A static friction model for elastic-plastic contacting rough surfaces. J. Tribol. 126(1), 34–40 (2004)CrossRefGoogle Scholar
  33. 33.
    Vakis, A.I., Polycarpou, A.A.: Optimization of thermal fly-height control slider geometry for Tbit/in2 recording. Microsyst. Technol. 16(6), 1021–1034 (2010)CrossRefGoogle Scholar
  34. 34.
    Tani, H., Sakamoto, K., Tagawa, N.: Conformation of ultrathin PFPE lubricants with different structure on magnetic disks—direct observation and MD simulation. IEEE. Trans. Magn. 45(11), 5050–5054 (2009)CrossRefGoogle Scholar
  35. 35.
    Waltman, R.J., Pocker, D.J., Deng, H., Kobayashi, N., Fujii, Y., Akada, T., Hirasawa, K., Tyndall, G.W.: Investigation of a new cyclotriphosphazene-terminated perfluoropolyether lubricant. Properties and interactions with a carbon surface. Chem. Mater. 15(12), 2362–2375 (2003)CrossRefGoogle Scholar
  36. 36.
    Lei, R.Z., Gellman, A.J.: Humidity effects on PFPE lubricant bonding to a-CHx overcoats. Langmuir 16(16), 6628–6635 (2000)CrossRefGoogle Scholar
  37. 37.
    Choi, H.J., Guo, Q., Chung, P.S., Jhon, M.S.: Molecular rheology of perfluoropolyether lubricant via nonequilibrium molecular dynamics simulation. IEEE. Trans. Magn. 43(2), 903–905 (2007)CrossRefGoogle Scholar
  38. 38.
    Marchon, B., Guo, X.C., Moser, A., Spool, A., Kroeker, R., Crimi, F.: Lubricant dynamics on a slider: “the waterfall effect”. J. Appl. Phys. 105, 7 (2009)CrossRefGoogle Scholar
  39. 39.
    Mate, C.M., Dai, Q., Payne, R.N., Knigge, B.E., Baumgart, P.: Will the numbers add up for sub-7-nm magnetic spacings? Future metrology issues for disk drive lubricants, overcoats, and topographies. IEEE. Trans. Magn. 41(2), 626–631 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations