Tribology Letters

, 68:18 | Cite as

Friction–Load Relationship in the Adhesive Regime Revealing Potential Incapability of AFM Investigations

  • Junhui Sun
  • Yangyang Lu
  • Yanqing Feng
  • Zhibin LuEmail author
  • Guang’an ZhangEmail author
  • Yanping Yuan
  • Linmao Qian
  • Qunji Xue
Original Paper


Reduced friction with increasing normal load in the adhesive regime is revealed by vdW-corrected DFT calculations of various rigid junction models such as Graphene/Graphene, h-BN/h-BN, and Graphene/h-BN. The origin of the friction–load relationship arises from the decreased sliding potential corrugation with increased normal load in the attractive regime of the interfacial separation above its equilibrium. The “negative” coefficient of friction behavior, which is mainly dominated by van der Waals attraction, is expected to appear in many interfaces without significant deformation. However, the friction behavior presented here may be inaccessible to atomic forces microscope (AFM) due to the intrinsic instability. The instruments such as interfacial forces microscope with force-feedback sensor or quartz tuning forks with large stiffness are proposed to measure friction behaviors in the entire attractive region.



This work was supported by the National Natural Science Foundation of China (Nos. 51775535 and 11972344), the Fundamental Research Funds for the Central Universities (No. 2682019CX29), Open Project of State Key Laboratory of Solid Lubrication  (No. LSL-1910) and Guangdong Natural Science Foundation Project (No. 2018A030310001).

Supporting Information

DFT-Grimme calculated separation z dependence of the binding energy, normal load, and friction force for sliding systems of Gr/Gr, h-BN/h-BN, and Gr/h-BN; DFT binding energy and friction forces for Gr/Gr; detailed DFT-TS binding energy, normal load, and friction force, and discussion about negative friction coefficient for h-BN/h-BN and Gr/h-BN sliding systems.

Compliance with Ethical Standards

Conflict of interest

The authors declare no competing financial interest.

Supplementary material

11249_2019_1263_MOESM1_ESM.docx (349 kb)
Supplementary file1 (DOCX 348 kb)


  1. 1.
    Gao, J., Luedtke, W.D., Gourdon, D., Ruths, M., Israelachvili, J.N., Landman, U.: Frictional forces and Amontons’ law: from the molecular to the macroscopic scale. J. Phys. Chem. B 108, 3410–3425 (2004)CrossRefGoogle Scholar
  2. 2.
    Mo, Y., Turner, K.T., Szlufarska, I.: Friction laws at the nanoscale. Nature 457(7233), 1116 (2009)CrossRefGoogle Scholar
  3. 3.
    Urbakh, M., Klafter, J., Gourdon, D., et al.: The nonlinear nature of friction. Nature 430(6999), 525 (2004)CrossRefGoogle Scholar
  4. 4.
    Deng, Z., Smolyanitsky, A., Li, Q., et al.: Adhesion-dependent negative friction coefficient on chemically modified graphite at the nanoscale. Nat. Mater. 11(12), 1032 (2012)CrossRefGoogle Scholar
  5. 5.
    Smolyanitsky, A., Killgore, J.P.: Anomalous friction in suspended graphene. Phys. Rev. B 86, 125432–125436 (2012)CrossRefGoogle Scholar
  6. 6.
    Ye, Z., Martini, A.: Atomistic simulation of the load dependence of nanoscale friction on suspended and supported graphene. Langumar 30, 14707–14711 (2014)CrossRefGoogle Scholar
  7. 7.
    Thormann, E.: Negative friction coefficients. Nat. Mater. 12(6), 468 (2013)CrossRefGoogle Scholar
  8. 8.
    Deng, Z., Klimov, N.N., Solares, S.D., et al.: Nanoscale interfacial friction and adhesion on supported versus suspended monolayer and multilayer graphene. Langmuir 29(1), 235–243 (2012)CrossRefGoogle Scholar
  9. 9.
    Mandelli, D., Ouyang, W., Hod, O., et al.: Negative friction coefficients in superlubric graphite-hexagonal boron nitride heterojunctions. Phys. Rev. Lett. 122(7), 076102 (2019)CrossRefGoogle Scholar
  10. 10.
    Lee, C., Li, Q.Y., Kalb, W., Liu, X.Z., Berger, H., Carpick, R.W., Hone, J.: Frictional characteristics of atomically thin sheets. Science 328, 76–80 (2010)CrossRefGoogle Scholar
  11. 11.
    Sun, X.Y., Qi, Y.Z., Ouyang, W., et al.: Energy corrugation in atomic-scale friction on graphite revisited by molecular dynamics simulations. Acta Mech. Sin. 32(4), 604–610 (2016)CrossRefGoogle Scholar
  12. 12.
    Luan, B., Robbins, M.O.: The breakdown of continuum models for mechanical contacts. Nature 435, 929 (2005)CrossRefGoogle Scholar
  13. 13.
    Li, S., Li, Q., Carpick, R.W., et al.: The evolving quality of frictional contact with graphene. Nature 539(7630), 541 (2016)CrossRefGoogle Scholar
  14. 14.
    Jacobs, T.D.B., Martini, A.: Measuring and understanding contact area at the nanoscale: a review. Appl. Mech. Rev. 69(6), 060802 (2017)CrossRefGoogle Scholar
  15. 15.
    Houston, J.E., Kim, H.I.: Adhesion, friction, and mechanical properties of functionalized alkanethiol self-assembled monolayers. Accounts Chem. Res. 35(7), 547–553 (2002)CrossRefGoogle Scholar
  16. 16.
    Burns, A.R., Houston, J.E., Carpick, R.W., et al.: Friction and molecular deformation in the tensile regime. Phys. Rev. Lett. 82(6), 1181 (1999)CrossRefGoogle Scholar
  17. 17.
    Liu, Z.: The diversity of friction behavior between bi-layer graphenes. Nanotechnology 25(7), 075703 (2014)CrossRefGoogle Scholar
  18. 18.
    Sun, J., Zhang, Y., Lu, Z., et al.: Superlubricity enabled by pressure-induced friction collapse. J. Phys. Chem. Lett. 9, 2554–2559 (2018)CrossRefGoogle Scholar
  19. 19.
    Sun, J., Chang, K., Mei, D., et al.: Mutual identification between the pressure-induced superlubricity and the image contrast inversion of carbon nanostructures from AFM technology. J. Phys. Chem. Lett. 10, 1498–1504 (2019)CrossRefGoogle Scholar
  20. 20.
    Sun, J., Zhang, Y., Lu, Z., et al.: Attraction induced frictionless sliding of rare gas monolayer on metallic surfaces: an efficient strategy for superlubricity. Phys. Chem. Chem. Phys. 19(18), 11026–11031 (2017)CrossRefGoogle Scholar
  21. 21.
    Sun, J., Zhang, Y., Feng, Y., et al.: How vertical compression triggers lateral interlayer slide for metallic molybdenum disulfide? Tribol. Lett. 66(1), 21 (2018)CrossRefGoogle Scholar
  22. 22.
    Righi, M.C., Ferrario, M.: Pressure induced friction collapse of rare gas boundary layers sliding over metal surfaces. Phys. Rev. Lett. 99(17), 176101 (2007)CrossRefGoogle Scholar
  23. 23.
    Gao, L., Ma, Y., Liu, Y., et al.: Anomalous frictional behaviors of Ir and Au tips sliding on graphene/Ni (111) substrate: density functional theory calculations. J. Phys. Chem. C 121(39), 21397–21404 (2017)CrossRefGoogle Scholar
  24. 24.
    Chen, J., Gao, W.: Unconventional behavior of friction at the nanoscale beyond Amontons' law. ChemPhysChem 18, 2033–2039 (2017)CrossRefGoogle Scholar
  25. 25.
    McGraw, J.D., Niguès, A., Chennevière, A., et al.: Contact dependence and velocity crossover in friction between microscopic solid/solid contacts. Nano Lett. 17(10), 6335–6339 (2017)CrossRefGoogle Scholar
  26. 26.
    Giessibl, F.J.: High-speed force sensor for force microscopy and profilometry utilizing a quartz tuning fork. Appl. Phys. Lett. 73(26), 3956–3958 (1998)CrossRefGoogle Scholar
  27. 27.
    Delrio, F.W., De Boer, M.P., Knapp, J.A., Reedy, E.D., Clews, P.J., Dunn, M.L.: The role of van der Waals forces in adhesion of micromachined surfaces. Nat. Mater. 4, 629–634 (2005)CrossRefGoogle Scholar
  28. 28.
    Bunch, J.S., van der Zande, A.M., Verbridge, S.S., Frank, I.M., Tanenbaum, D.M., Parpia, J.M., Graighead, H.G., McEuen, P.L.: Electromechanical resonators from graphene sheets. Science 26, 490–493 (2007)CrossRefGoogle Scholar
  29. 29.
    Geim, A.K., Grigorieva, I.V.: Van der Waals heterostructures. Nature 499, 419–425 (2013)CrossRefGoogle Scholar
  30. 30.
    Leven, I., Krepel, D., Shemesh, O., Hod, O.: Robust superlubricity in graphene/h-BN heterojunctions. J. Phys. Chem. Lett. 4, 115–120 (2013)CrossRefGoogle Scholar
  31. 31.
    Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996)CrossRefGoogle Scholar
  32. 32.
    Tkatchenko, A., Scheffler, M.: Accurate molecular Van Der Waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett. 102, 073005 (2009)CrossRefGoogle Scholar
  33. 33.
    Marom, N., Bernstein, J., Garel, J., Tkatchenko, A., Joselevich, E., Kronik, L., Hod, O.: Stacking and registry effects in layered materials: the case of hexagonal boron nitride. Phys. Rev. Lett. 105, 046801–046804 (2010)CrossRefGoogle Scholar
  34. 34.
    Clark, S.J., Segall, M.D., Pickard, C.J., Hasnip, P.J., Probert, M.I.J., Refson, K., Payne, M.C.: First principles methods using CASTEP. Z. für Kristallogr.-Cryst. Mater. 220, 567–570 (2005)Google Scholar
  35. 35.
    Grimme, S.: Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006)CrossRefGoogle Scholar
  36. 36.
    Zhong, W., Tománek, D.: First-principles theory of atomic-scale friction. Phys. Rev. Lett. 64, 3054 (1990)CrossRefGoogle Scholar
  37. 37.
    Wang, L.F., Ma, T.B., Hu, Y.Z., et al.: Ab initio study of the friction mechanism of fluorographene and graphane. J. Phys. Chem. C 117(24), 12520–12525 (2013)CrossRefGoogle Scholar
  38. 38.
    Spanu, L., Sorella, S., Galli, G.: Nature and strength of interlayer binding in graphite. Phys. Rev. Lett. 103, 196401–196404 (2009)CrossRefGoogle Scholar
  39. 39.
    Carpick, R.W., Agrait, N., Ogletree, D.F., et al.: Measurement of interfacial shear (friction) with an ultrahigh vacuum atomic force microscope. J. Vacuum Sci. Technol. B 14(2), 1289–1295 (1996)CrossRefGoogle Scholar
  40. 40.
    Levita, G., Molinari, E., Polcar, T., Righi, M.C.: First-principles comparative study on the interlayer adhesion and shear strength of transition-metal dichalcogenides and graphene. Phys. Rev. B 92, 085434–085441 (2015)CrossRefGoogle Scholar
  41. 41.
    Zacharia, R., Ulbricht, H., Hertel, T.: Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons. Phys. Rev. B 69, 155406 (2004)CrossRefGoogle Scholar
  42. 42.
    Hod, O.: Graphite and hexagonal boron-nitride have the same interlayer distance. Why? J. Chem. Theory Comput. 8, 1360–1369 (2012)CrossRefGoogle Scholar
  43. 43.
    Binnig, G., Quate, C.F., Gerber, C.: Atomic force micro-scope. Phys. Rev. Lett. 56, 930–933 (1986)CrossRefGoogle Scholar
  44. 44.
    Vahdat, V., Grierson, D.S., Turner, K.T., Carpick, R.W.: Mechanics of interaction and atomic-scale wear of amplitude modulation atomic force microscopy probes. ACS Nano 7, 3221–3235 (2013)CrossRefGoogle Scholar
  45. 45.
    Marszalek, P.E., Dufrêne, Y.F.: Stretching single polysaccharides and proteins using atomic force microscopy. Chem. Soc. Rev. 41, 3523–3534 (2012)CrossRefGoogle Scholar
  46. 46.
    Cappella, B., Dietler, G.: Force-distance curves by atomic force microscopy. Surf. Sci. Rep. 34, 1–104 (1999)CrossRefGoogle Scholar
  47. 47.
    Joyce, S.A., Houston, J.E.: A new force sensor incorporating force-feedback control for interfacial force microscopy. Rev. Sci. Instrum. 62, 710–715 (1991)CrossRefGoogle Scholar
  48. 48.
    Carpick, R.W., Agrait, N., Ogletree, D.F., et al.: Variation of the interfacial shear strength and adhesion of a nanometer-sized contact. Langmuir 12(13), 3334–3340 (1996)CrossRefGoogle Scholar
  49. 49.
    Smolyanitsky, A.: Effects of thermal rippling on the frictional properties of free-standing graphene. RSC Adv. 5(37), 29179–29184 (2015)CrossRefGoogle Scholar
  50. 50.
    Zhang, Y., Dong, M., Gueye, B., et al.: Temperature effects on the friction characteristics of graphene. Appl. Phys. Lett. 107(1), 011601 (2015)CrossRefGoogle Scholar
  51. 51.
    Reguzzoni, M., Fasolino, A., Molinari, E., Righi, M.C.: Potential energy surface for graphene on graphene: Ab initio derivation, analytical description, and microscopic interpretation. Phys. Rev. B 86, 245434–245440 (2012)CrossRefGoogle Scholar
  52. 52.
    Pease, R.S.: Crystal structure of boron nitride. Nature 165, 722 (1950)CrossRefGoogle Scholar
  53. 53.
    Haigh, S.J., Gholinia, A., Jalil, R., Romani, S., Britnell, L., Elias, D.C., Novoselov, K.S., Ponomarenko, L.A., Geim, A.K., Gorbachev, R.: Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices. Nat. Mater. 11, 764 (2012)CrossRefGoogle Scholar
  54. 54.
    Zhong, X., Yap, Y.K., Pandey, R.: First-principles study of strain-induced modulation of energy gaps of graphene/BN and BN bilayers. Phys. Rev. B 83, 193403 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.School of Mechanical Engineering, State Key Laboratory of Traction PowerSouthwest Jiaotong UniversityChengduChina
  2. 2.State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical PhysicsChinese Academy of SciencesLanzhouChina
  3. 3.School of Applied Science and Civil EngineeringBeijing Institute of TechnologyZhuhaiChina

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