Frictional Anisotropy of Al, Pt, and Pd Nanoparticles on a Graphene Substrate


The frictional anisotropy of metallic nanoparticles is investigated using a molecular dynamics method. Calculations of anisotropy have been performed for aluminum, palladium, and platinum nanoparticles containing 10,000 atoms. Anisotropy is studied at high sliding velocities of nanoparticles over the graphene surface. The influences of incommensurability and short-range order of nanoparticles’ contact surfaces lead to the absence of pronounced angular dependence of frictional force.

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\(\theta\) :

Angle of force application (degrees)

\(F_a\) :

Applied force (nN)

F :

Total frictional force (nN)

\(F_{x,y}\) :

Frictional force components along x and y axes (nN)

\(L_{x,y,z}\) :

Sizes of nanoparticle along x, y, and z axes (nm)

\(F_{sy}\) :

Substrate force along y axis (nN)

\(y_{\mathrm{CM}}\) :

y component of the center of mass position of nanoparticle (nm)

\(v_{y}\) :

y component of the center of mass velocity of nanoparticle (m/s)

T :

System temperature (K)

t :

Time (s)


  1. 1.

    Hill, R.: The Mathematical Theory of Plasticity. Oxford University Press, London (1950)

    Google Scholar 

  2. 2.

    Pietruszczak, S.: On inelastic behaviour of anisotropic frictional materials. Mech. Cohes. Frict. Mat. 4(3), 281–293 (1999)

    Article  Google Scholar 

  3. 3.

    Chen, L., Wang, Y., Bu, H., Chen, Y.: Simulations of the anisotropy of friction force between a silicon tip and a substrate at nanoscale. Proc. Inst. Mech. Eng. N 227(3), 130–134 (2013).

    CAS  Article  Google Scholar 

  4. 4.

    He, G., Müser, M.H., Robbins, M.O.: Adsorbed layers and the origin of static friction. Science 284(5420), 1650–1652 (1999).

    CAS  Article  Google Scholar 

  5. 5.

    Depondt, P., Ghazali, A., Levy, J.C.S.: Self-locking of a modulated single overlayer in a nanotribology simulation. Surf. Sci. 419(1), 29–37 (1998)

    CAS  Article  Google Scholar 

  6. 6.

    Almeida, C., Prioli, R., Fragneaud, B., Cancado, L., Paupitz, R., Galvao, D., De Cicco, M., Menezes, M., Achete, C., Capaz, R.: Giant and tunable anisotropy of nanoscale friction in graphene. Sci. Rep. 6, 31569 (2016).

    CAS  Article  Google Scholar 

  7. 7.

    Gnecco, E., Meyer, E. (eds.): Fundamentals of Friction and Wear on the Nanoscale, 2nd edn. Springer, Berlin (2015)

    Google Scholar 

  8. 8.

    Kumar, D., Jain, J., Gosvami, N.N.: Anisotropy in nanoscale friction and wear of precipitate containing AZ91 magnesium alloy. Tribol. Lett. 67(2), 44 (2019).

    CAS  Article  Google Scholar 

  9. 9.

    Pogrebnjak, A.D., Ponomarev, A.G., Shpak, A.P., Kunitskii, Y.A.: Application of micro- and nanoprobes to the analysis of small-sized 3d materials, nanosystems, and nanoobjects. Phys. Usp. 55(3), 270–300 (2012).

    CAS  Article  Google Scholar 

  10. 10.

    Feldmann, M., Dietzel, D., Tekiel, A., Topple, J., Grütter, P., Schirmeisen, A.: Universal aging mechanism for static and sliding friction of metallic nanoparticles. Phys. Rev. Lett. 117, 025502 (2016).

    CAS  Article  Google Scholar 

  11. 11.

    Vanossi, A., Dietzel, D., Schirmeisen, A., Meyer, E., Pawlak, R., Glatzel, T., Kisiel, M., Kawai, S., Manini, N.: Recent highlights in nanoscale and mesoscale friction. Beilstein J. Nanotechnol. 9, 1995–2014 (2018).

    CAS  Article  Google Scholar 

  12. 12.

    Ye, Z., Martini, A., Thiel, P., Lovelady, H.H., McLaughlin, K., Rabson, D.A.: Atomistic simulation of frictional anisotropy on quasicrystal approximant surfaces. Phys. Rev. B 93, 235438 (2016).

    CAS  Article  Google Scholar 

  13. 13.

    Castro-Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: The electronic properties of graphene. Rev. Mod. Phys. 81(1), 109–162 (2009).

    CAS  Article  Google Scholar 

  14. 14.

    Khomenko, A.V., Prodanov, N.V.: Study of friction of Ag and Ni nanoparticles: an atomistic approach. J. Phys. Chem. C 114(47), 19958–19965 (2010).

    CAS  Article  Google Scholar 

  15. 15.

    Khomenko, A.V., Prodanov, N.V., Persson, B.N.J.: Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene. Condens. Matter Phys. 16, 33401 (2013).

    CAS  Article  Google Scholar 

  16. 16.

    Khomenko, A., Zakharov, M., Boyko, D., Persson, B.N.J.: Atomistic modeling of tribological properties of Pd and Al nanoparticles on a graphene surface. Beilstein J. Nanotechnol. 9, 1239–1246 (2018).

    CAS  Article  Google Scholar 

  17. 17.

    Khomenko, A.V., Yushchenko, O.V.: Solid-liquid transition of ultrathin lubricant film. Phys. Rev. E 68, 036110 (2003)

    Article  Google Scholar 

  18. 18.

    Khomenko, A.V., Lyashenko, I.A.: Hysteresis phenomena during melting of an ultrathin lubricant film. Phys. Solid State 49(5), 936–940 (2007)

    CAS  Article  Google Scholar 

  19. 19.

    Khomenko, A., Lyashenko, I.: Melting of ultrathin lubricant film due to dissipative heating of friction surfaces. Tech. Phys. 52(9), 1239–1243 (2007).

    CAS  Article  Google Scholar 

  20. 20.

    Khomenko, A.V., Lyashenko, I.A.: Phase dynamics of a thin lubricant film between solid surfaces at the deformational defect of shear modulus. J. Phys. Stud. 11(3), 268–278 (2007). (in Ukrainian)

    Google Scholar 

  21. 21.

    Fessler, G., Sadeghi, A., Glatzel, T., Goedecker, S., Meyer, E.: Atomic friction: anisotropy and asymmetry effects. Tribol. Lett. 67(2), 59 (2019).

    Article  Google Scholar 

  22. 22.

    Khomenko, A.V., Boyko, D.V., Zakharov, M.V., Khomenko, K.P., Khyzhnya, Y.V.: Molecular dynamics of aluminum nanoparticles friction on graphene. In: Proceedings of the IEEE 7th International Conference on Nanomaterials: Application Properties (NAP’17) (IEEE, USA) 6, p. 01NNPT01-1-4. (2017)

  23. 23.

    Khomenko, A.V., Zakharov, M.V., Khomenko, K.P., Khyzhnya, Y.V., Trofimenko, P.E.: Atomistic modeling of friction force dependence on contact area of metallic nanoparticles on graphene. In: Proceedings of the IEEE 8th International Conference on Nanomaterials: Application Properties (NAP’18) (IEEE, USA) 4, p. 04NNLS15-1-4 (2018)

  24. 24.

    Sasaki, N., Kobayashi, K., Tsukada, M.: Atomic-scale friction image of graphite in atomic-force microscopy. Phys. Rev. B. 54(3), 2138–2149 (1996).

    CAS  Article  Google Scholar 

  25. 25.

    Zhou, X., Wadley, H., Johnson, R., Larson, D., Tabat, N., Cerezo, A., Petford-Long, A., Smith, G., Clifton, P., Martens, R., Kelly, T.: Atomic scale structure of sputtered metal multilayers. Acta Mater. 49(19), 4005–4015 (2001).

    CAS  Article  Google Scholar 

  26. 26.

    Khomenko, A.V., Prodanov, N.V.: Molecular dynamics of cleavage and flake formation during the interaction of a graphite surface with a rigid nanoasperity. Carbon 48(4), 1234–1243 (2010).

    CAS  Article  Google Scholar 

  27. 27.

    Prodanov, N.V., Khomenko, A.V.: Computational investigation of the temperature influence on the cleavage of a graphite surface. Surf. Sci. 604(7–8), 730–740 (2010).

    CAS  Article  Google Scholar 

  28. 28.

    Rapaport, D.C.: The Art of Molecular Dynamics Simulation, 2nd edn. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  29. 29.

    Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., DiNola, A., Haak, J.R.: Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81(8), 3684–3690 (1984).

    CAS  Article  Google Scholar 

  30. 30.

    Humphrey, W., Dalke, A., Schulten, K.: VMD: visual molecular dynamics. J. Mol. Graph. 14(1), 33–38 (1996).

    CAS  Article  Google Scholar 

  31. 31.

    Choi, J.S., Kim, J.-S., Byun, I.-S., Lee, D.H., Lee, M.J., Park, B.H., Lee, C., Yoon, D., Cheong, H., Lee, K.H., Son, Y.-W., Park, J.Y., Salmeron, M.: Friction anisotropy–driven domain imaging on exfoliated monolayer graphene. Science 333(6042), 607–610 (2011).

    CAS  Article  Google Scholar 

  32. 32.

    Khomenko, A.V., Prodanov, N.V., Khomenko, M.A., Krasulya, B.O.: Frictional anisotropy of metal nanoparticles adsorbed on graphene. J. Nano-Electron. Phys. 5(3), 03018 (2013). (8pp)

    Google Scholar 

  33. 33.

    He, G., Robbins, M.O.: Simulations of the static friction due to adsorbed molecules. Phys. Rev. B 64, 035413 (2001).

    CAS  Article  Google Scholar 

  34. 34.

    He, G., Robbins, M.O.: Simulations of the kinetic friction due to adsorbed surface layers. Tribol. Lett. 10(1), 7–14 (2001).

    CAS  Article  Google Scholar 

  35. 35.

    Braun, O.M., Manini, N.: Dependence of boundary lubrication on the misfit angle between the sliding surfaces. Phys. Rev. E 83, 021601 (2011).

    CAS  Article  Google Scholar 

  36. 36.

    Dietzel, D., Feldmann, M., Schwarz, U.D., Fuchs, H., Schirmeisen, A.: Scaling laws of structural lubricity. Phys. Rev. Lett. 111, 235502 (2013).

    CAS  Article  Google Scholar 

  37. 37.

    Matsushita, K., Matsukawa, H., Sasaki, N.: Atomic scale friction between clean graphite surfaces. Sol. State Commun. 136(1), 51–55 (2005).

    CAS  Article  Google Scholar 

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This study is supported by the Ministry of Education and Science of Ukraine within the framework of project “Atomistic and statistical representation of formation and friction of nanodimensional systems” (No. 0118U003584) and visitor grant of Forschungszentrum-Jülich, Germany. A. K. is thankful to Dr. Bo N. J. Persson for hospitality during his stay in Forschungszentrum-Jülich.

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Khomenko, A., Zakharov, M. & Persson, B.N.J. Frictional Anisotropy of Al, Pt, and Pd Nanoparticles on a Graphene Substrate. Tribol Lett 67, 113 (2019).

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  • Frictional force
  • Graphene
  • Nanoparticle
  • Nanotribology
  • Aluminum
  • Palladium
  • Platinum