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Comparative Study of Dimensionality and Symmetry Breaking on Nanoscale Friction in the Prandtl–Tomlinson Model with Varying Effective Stiffness

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Abstract

Friction Force Microscopy (FFM) measurements on NaCl immersed in ethanol display an increase of the effective contact stiffness with the applied load. This stiffness is estimated from the measured local contact interaction of the tip with the NaCl surface and the Prandtl–Tomlinson (PT) parameter, which reflects the relation between the corrugation stiffness and the effective contact stiffness. Different from FFM measurements in ultrahigh vacuum, for measurements in ethanol surroundings the PT parameters showed a maximum with the applied load. We incorporated this measured load-dependent effective stiffness together with the load-dependent amplitude of the corrugation energy into simulations based on the PT model, and studied its effect on the lateral friction for symmetric 1D and 2D potentials, as well as for an asymmetric 1D potentials. The simulations reproduced the experimentally observed non-monotonous behavior of the PT parameter, and enabled a glimpse on the relation of the characteristic observables (mean maximal slip forces and stiffness) with respect to their governing parameters (corrugation energy, effective stiffness). In all, apart from large deviations from symmetry in the interaction potential, the PT parameter provides a reliable estimate for nanoscale friction over periodic surfaces.

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References

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

    CAS  Google Scholar 

  2. Bhushan, B., Israelachvili, J.N., Landman, U.: Nanotribology: friction, wear and lubrication at the atomic scale. Nature 374, 607–616 (1995)

    CAS  Google Scholar 

  3. Carpick, R.W., Salmeron, M.: Scratching the Surface: fundamental investigations of tribology with atomic force microscopy. Chem. Rev. 97, 1163–1194 (1997)

    CAS  Google Scholar 

  4. Carpick, R.W., Ogletree, D.F., Salmeron, M.: A general equation for fitting contact area and friction vs load measurements. J. Colloid Interface Sci. 211, 395–400 (1999)

    CAS  Google Scholar 

  5. Mo, Y., Turner, K.T., Szlufarska, I.: Friction laws at the nanoscale. Nature 457, 1116–1119 (2009)

    CAS  Google Scholar 

  6. Müser, M.H.: Velocity dependence of kinetic friction in the Prandtl-Tomlinson model. Phys. Rev. B 84, 125419 (2011)

    Google Scholar 

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

    Google Scholar 

  8. Cihan, E., İpek, S., Durgun, E., Baykara, M.Z.: Structural lubricity under ambient conditions. Nat. Commun. 7, 12055 (2016)

    CAS  Google Scholar 

  9. Dong, Y., Li, Q., Martini, A.: Molecular dynamics simulation of atomic friction: a review and guide. J. Vac. Sci. Technol. 31, 030801 (2013)

    Google Scholar 

  10. Gnecco, E., Bennewitz, R., Gyalog, T., Loppacher, C., Bammerlin, M., Meyer, E., et al.: Velocity dependence of atomic friction. Phys. Rev. Lett. 84, 1172–1175 (2000)

    CAS  Google Scholar 

  11. Sang, Y., Dubé, M., Grant, M.: Thermal effects on atomic friction. Phys. Rev. Lett. 87, 174301 (2001)

    CAS  Google Scholar 

  12. Dudko, O.K., Filippov, A.E., Klafter, J., Urbakh, M.: Dynamic force spectroscopy: a Fokker-Planck approach. Chem. Phys. Lett. 352, 499–504 (2002)

    CAS  Google Scholar 

  13. Fusco, C., Fasolino, A.: Velocity dependence of atomic-scale friction: a comparative study of the one- and two-dimensional tomlinson model. Phys. Rev. B 71, 045413 (2005)

    Google Scholar 

  14. Evstigneev, M., Schirmeisen, A., Jansen, L., Fuchs, H., Reimann, P.: Force Dependence of Transition Rates in Atomic Friction. Phys. Rev. Lett. 97, 240601 (2006)

    Google Scholar 

  15. Apostoli, C., Giusti, G., Ciccoianni, J., Riva, G., Capozza, R., Woulache, R.L., et al.: Velocity dependence of sliding friction on a crystalline surface. Beilstein J. Nanotechnol. 8, 2186–2199 (2017)

    CAS  Google Scholar 

  16. Iglesias, M.L., Gonçalves, S.: Sliding and dry friction: prandtl-tomlinson athermal model revisited. Braz. J. Phys. 48, 585–591 (2018)

    Google Scholar 

  17. Szoszkiewicz, R., Riedo, E.: Nanoscopic friction as a probe of local phase transitions. Appl. Phys. Lett. 87, 033105 (2005)

    Google Scholar 

  18. Schirmeisen, A., Jansen, L., Hölscher, H., Fuchs, H.: Temperature dependence of point contact friction on silicon. Appl. Phys. Lett. 88, 123108 (2006)

    Google Scholar 

  19. Krylov, S.Y., Frenken, J.W.M.: The crucial role of temperature in atomic scale friction. J. Phys. Condens. Matter. 20, 354003 (2008)

    Google Scholar 

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

    Google Scholar 

  21. Jansen, L., Hölscher, H., Fuchs, H., Schirmeisen, A.: Temperature dependence of atomic-scale stick-slip friction. Phys. Rev. Lett. 104, 256101 (2010)

    Google Scholar 

  22. Mazo, J.J., Dietzel, D., Schirmeisen, A., Vilhena, J.G., Gnecco, E.: Time strengthening of crystal nanocontacts. Phys. Rev. Lett. 118, 246101 (2017)

    Google Scholar 

  23. Ouyang, W., Cheng, Y., Ma, M., Urbakh, M.: Load-velocity-temperature relationship in frictional response of microscopic contacts. J Mech Phys Solids 137, 103880 (2020)

    Google Scholar 

  24. Fujisawa, S., Kishi, E., Sugawara, Y., Morita, S.: Atomic-scale friction observed with a two-dimensional frictional-force microscope. Phys. Rev. B 51, 7849–7857 (1995a)

    CAS  Google Scholar 

  25. Hölscher, H., Schwarz, U.D., Wiesendanger, R.: Modelling of the scan process in lateral force microscopy. Surf. Sci. 375, 395–402 (1997)

    Google Scholar 

  26. Fujisawa, S., Yokoyama, K., Sugawara, Y., Morita, S.: Analysis of experimental load dependence of two-dimensional atomic-scale friction. Phys. Rev. B 58, 4909–4916 (1998)

    CAS  Google Scholar 

  27. Müser, M.H.: Structural lubricity: role of dimension and symmetry. Europhys. Lett. (EPL) 66, 97–103 (2004)

    Google Scholar 

  28. Gao, G., Cannara, R.J., Carpick, R.W., Harrison, J.A.: Atomic-scale friction on diamond: a comparison of different sliding directions on (001) and (111) surfaces Using MD and AFM. Langmuir 23, 5394–5405 (2007)

    CAS  Google Scholar 

  29. Karino, W., Shindo, H.: Frictional force microscopic detection of anisotropy at NaCl (100), (110) and (111) surfaces. Tribol. Int. 40, 1568–1573 (2007)

    CAS  Google Scholar 

  30. Steiner, P., Roth, R., Gnecco, E., Baratoff, A., Maier, S., Glatzel, T., et al.: Two-dimensional simulation of superlubricity on NaCl and highly oriented pyrolytic graphite. Phys. Rev. B 79, 045414 (2009)

    Google Scholar 

  31. Fajardo, O.Y., Gnecco, E., Mazo, J.J.: Anisotropy effects and friction maps in the framework of the 2d PT model. Physica B Condens. Matter. 455, 44–48 (2014)

    CAS  Google Scholar 

  32. Takoutsing, C.S., Djuidjé Kenmoé, G., Kofané, T.C.: Effects of anisotropy and substrate shape on atomic friction force in two-dimensional model. Tribol. Lett. 65, 107 (2017)

    Google Scholar 

  33. Dagdeviren, O.E.: Exploring load, velocity, and surface disorder dependence of friction with one-dimensional and two-dimensional models. Nanotechnology 29, 315704 (2018)

    Google Scholar 

  34. Fujisawa, S., Kishi, E., Sugawara, Y., Morita, S.: Load dependence of two-dimensional atomic-scale friction. Phys. Rev. B 52, 5302–5305 (1995b)

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  36. Socoliuc, A., Bennewitz, R., Gnecco, E., Meyer, E.: Transition from stick-slip to continuous sliding in atomic friction: entering a new regime of ultralow friction. Phys. Rev. Lett. 92, 134301 (2004)

    CAS  Google Scholar 

  37. Fusco, C., Fasolino, A.: Power-law load dependence of atomic friction. Appl. Phys. Lett. 84, 699–701 (2004)

    CAS  Google Scholar 

  38. Pawlak, R., Ouyang, W., Filippov, A.E., Kalikhman-Razvozov, L., Kawai, S., Glatzel, T., et al.: Single-molecule tribology: force microscopy manipulation of a porphyrin derivative on a copper surface. ACS Nano. 10, 713–722 (2016)

    CAS  Google Scholar 

  39. Ye, Z., Egberts, P., Han, G.H., Johnson, A.T.C., Carpick, R.W., Martini, A.: Load-dependent friction hysteresis on graphene. ACS Nano. 10, 5161–5168 (2016)

    CAS  Google Scholar 

  40. Sharp, T.A., Pastewka, L., Lignères, V.L., Robbins, M.O.: Scale- and load-dependent friction in commensurate sphere-on-flat contacts. Phys. Rev. B 96, 155436 (2017)

    Google Scholar 

  41. Agmon, L., Shahar, I., Birodker, B.-E., Skuratovsky, S., Jopp, J., Berkovich, R.: Application of static disorder approach to friction force microscopy of catalyst nanoparticles to estimate corrugation energy amplitudes. J. Phys. Chem. C 123, 3032–3038 (2019)

    CAS  Google Scholar 

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

    Google Scholar 

  43. Cao, X.A., Gan, X., Lang, H., Yu, K., Ding, S., Peng, Y., et al.: Anisotropic nanofriction on MoS2 with different thicknesses. Tribol. Int. 134, 308–316 (2019)

    CAS  Google Scholar 

  44. Prandtl, L.: Ein Gedankenmodell zur kinetischen Theorie der festen Körper. Z. Angew. Math. Mech. 8, 85–106 (1928)

    Google Scholar 

  45. Tomlinson, G.A.C.V.I.: A molecular theory of friction. Lond. Edinb. Dubl. Phil. Mag. 7, 905–939 (1929)

    CAS  Google Scholar 

  46. Popov, V.L., Gray, J.A.T.: Prandtl-Tomlinson model: history and applications in friction, plasticity, and nanotechnologies. Z. Angew. Math. Mech. 92, 683–708 (2012)

    Google Scholar 

  47. Hölscher, H., Raberg, W., Schwarz, U.D., Hasbach, A., Wandelt, K., Wiesendanger, R.: Imaging of sub-unit-cell structures in the contact mode of the scanning force microscope. Phys. Rev. B 59, 1661–1664 (1999)

    Google Scholar 

  48. Schirmeisen, A., Jansen, L., Fuchs, H.: Tip-jump statistics of stick-slip friction. Phys. Rev. B 71, 245403 (2005)

    Google Scholar 

  49. Hölscher, H., Ebeling, D., Schwarz, U.D.: Friction at Atomic-Scale Surface Steps: Experiment and Theory. Phys Rev Lett 101, 246105 (2008)

    Google Scholar 

  50. Vanossi, A., Manini, N., Urbakh, M., Zapperi, S., Tosatti, E.: Colloquium: modeling friction: from nanoscale to mesoscale. Rev. Mod. Phys. 85, 529–552 (2013)

    CAS  Google Scholar 

  51. Krylov, S.Y., Frenken, J.W.M.: The problem of critical damping in nanofriction. Colloid J. 74, 569–572 (2012)

    CAS  Google Scholar 

  52. Krylov, S.Y., van Baarle, D.W., Beck, M.E.S., Frenken, J.W.M.: Why do we “feel” atoms in nano-scale friction? Colloid J. 79, 81–86 (2017)

    CAS  Google Scholar 

  53. Schwarz, U.D., Hölscher, H.: Exploring and explaining friction with the Prandtl-Tomlinson model. ACS Nano. 10, 38–41 (2016)

    CAS  Google Scholar 

  54. Gnecco, E., Bennewitz, R., Gyalog, T., Meyer, E.: Friction experiments on the nanometre scale. J Phys Condens Matter 13, R619–R642 (2001)

    CAS  Google Scholar 

  55. Bennewitz, R., Gnecco, E., Gyalog, T., Meyer, E.: Atomic friction studies on well-defined surfaces. Tribol. Lett. 10, 51–56 (2001)

    CAS  Google Scholar 

  56. Roth, R., Glatzel, T., Steiner, P., Gnecco, E., Baratoff, A., Meyer, E.: Multiple slips in atomic-scale friction: an indicator for the lateral contact damping. Tribol. Lett. 39, 63–69 (2010)

    CAS  Google Scholar 

  57. Agmon, L., Shahar, I., Yosufov, D., Pimentel, C., Pina, C.M., Gnecco, E., et al.: Estimation of interaction energy and contact stiffness in atomic-scale sliding on a model sodium chloride surface in ethanol. Sci. Rep. 8, 4681 (2018)

    Google Scholar 

  58. Vilhena, J.G., Pimentel, C., Pedraz, P., Luo, F., Serena, P.A., Pina, C.M., et al.: Atomic-scale sliding friction on graphene in water. ACS Nano. 10, 4288–4293 (2016)

    CAS  Google Scholar 

  59. Verdaguer, A., Sacha, G.M., Luna, M., Ogletree, D.F., Salmeron, M.: Initial stages of water adsorption on NaCl (100) studied by scanning polarization force microscopy. J. Chem. Phys. 123, 124703 (2005)

    Google Scholar 

  60. Shimizu, T.K., Maier, S., Verdaguer, A., Velasco-Velez, J.-J., Salmeron, M.: Water at surfaces and interfaces: from molecules to ice and bulk liquid. Prog. Surf. Sci. 93, 87–107 (2018)

    CAS  Google Scholar 

  61. Ogletree, D.F., Carpick, R.W., Salmeron, M.: Calibration of frictional forces in atomic force microscopy. Rev. Sci. Instrum. 67, 3298–3306 (1996)

    CAS  Google Scholar 

  62. Varenberg, M., Etsion, I., Halperin, G.: An improved wedge calibration method for lateral force in atomic force microscopy. Rev. Sci. Instrum. 74, 3362–3367 (2003)

    CAS  Google Scholar 

  63. Carpick, R.W., Ogletree, D.F., Salmeron, M.: Lateral stiffness: A new nanomechanical measurement for the determination of shear strengths with friction force microscopy. Appl Phys Lett 70, 1548–1550 (1997)

    CAS  Google Scholar 

  64. Zhong, W., Tománek, D.: First-principles theory of atomic-scale friction. Phys. Rev. Lett. 64, 3054–3057 (1990)

    CAS  Google Scholar 

  65. Riedo, E., Gnecco, E., Bennewitz, R., Meyer, E., Brune, H.: Interaction potential and hopping dynamics governing sliding friction. Phys. Rev. Lett. 91, 084502 (2003)

    CAS  Google Scholar 

  66. Garg, A.: Escape-field distribution for escape from a metastable potential well subject to a steadily increasing bias field. Phys. Rev. B 51, 15592–15595 (1995)

    CAS  Google Scholar 

  67. Pesz, K., Gabryś, B.J., Bartkiewicz, S.J.: Analytical solution for the Feynman ratchet. Phys. Rev. E 66, 061103 (2002)

    Google Scholar 

  68. Berkovich, R., Klafter, J., Urbakh, M.: Analyzing friction forces with the Jarzynski equality. J. Phys. Condens. Matter. 20, 354008 (2008)

    Google Scholar 

  69. Gnecco, E., Roth, R., Baratoff, A.: Analytical expressions for the kinetic friction in the Prandtl-Tomlinson model. Phys. Rev. B 86, 035443 (2012)

    Google Scholar 

  70. Medyanik, S.N., Liu, W.K., Sung, I.-H., Carpick, R.W.: Predictions and observations of multiple slip modes in atomic-scale friction. Phys. Rev. Lett. 97, 136106 (2006)

    Google Scholar 

  71. Gyalog, T., Bammerlin, M., Lüthi, R., Meyer, E., Thomas, H.: Mechanism of atomic friction. EPL 31, 269–274 (1995)

    CAS  Google Scholar 

  72. Lim, Y., Park, H., Caron, A.: Investigation on the role of interfacial water on the tribology between graphite and metals. RSC Adv. 9, 7285–7291 (2019)

    CAS  Google Scholar 

  73. Cammarata, A., Nicolini, P., Simonovic, K., Ukraintsev, E., Polcar, T.: Atomic-scale design of friction and energy dissipation. Phys. Rev. B 99, 094309 (2019)

    CAS  Google Scholar 

  74. van Baarle, D.W., Krylov, S.Y., Beck, M.E.S., Frenken, J.W.M.: On the non-trivial origin of atomic-scale patterns in friction force microscopy. Tribol. Lett. 67, 15 (2018)

    Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the support from the I-CORE Program of the Planning and Budgeting Committee and The Israel Science Foundatisson (Grant No. 152/11).

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Skuratovsky, S., Agmon, L. & Berkovich, R. Comparative Study of Dimensionality and Symmetry Breaking on Nanoscale Friction in the Prandtl–Tomlinson Model with Varying Effective Stiffness. Tribol Lett 68, 113 (2020). https://doi.org/10.1007/s11249-020-01355-0

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