Abstract
The static and kinetic friction experienced by a point mass elastically driven at different angles on surface lattices with square, hexagonal, and honeycomb symmetries are estimated by analytical and numeric calculations based on the Prandtl–Tomlinson (PT) model. Assuming a strong surface coupling, the anisotropy of static friction increases from 3.7 up to 46.3% when the density of packing of the surface atoms is reduced, but this is not the case for kinetic friction, the anisotropy of which is maximal on a square lattice. Although these results have not been supported by accurate experimental verifications so far, the PT model was successfully applied to interpret anisotropy effects in the friction force profiles measured, among other surfaces, on rectangular lattices with complex unit cells and on stepped crystal surfaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Overney, R.M., Takano, H., Fujihira, M., Paulus, W., Ringsdorf, H.: Anisotropy in friction and molecular stick-slip motion. Phys. Rev. Lett. 72, 3546–3549 (1994)
Takano, H., Fujihira, M.: Study of molecular scale friction on stearic acid crystals by friction force microscopy. J. Vac. Sci. Technol. B 14, 1272–1275 (1996)
Liley, M., Gourdon, D., Stamou, D., Meseth, U., Fischer, T.M., Lautz, C., Stahlberg, H., Vogel, H., Burnham, N.A., Duschl, C.: Friction anisotropy and asymmetry of a compliant monolayer induced by a small molecular tilte. Science 280, 273–275 (1998)
Dienwiebel, M., Verhoeven, G.S., Pradeep, N., Frenken, J.W.M., Heimber, J.A., Zandbergen, H.W.: Superlubricity of graphite. Phys. Rev. Lett. 92(1–4), 126101 (2004)
Park, J.Y., Ogletree, D.F., Salmeron, M., Ribeiro, R.A., Canfield, P.C., Jenks, C.J., Thiel, P.A.: High frictional anisotropy of periodic and aperiodic directions on a quasicrystal surface. Science 309, 1354–1356 (2005)
Kalihari, V., Haugstad, G., Frisbie, C.D.: Distinguishing elastic shear deformation from friction on the surfaces of molecular crystals. Phys. Rev. Lett. 104(1–4), 086102 (2010)
Campione, M., Fumagalli, E.: Friction anisotropy of the surface of organic crystals and its impact on scanning force microscopy. Phys. Rev. Lett. 105(1–4), 166103 (2010)
Fessler, G., Zimmermann, I., Glatzel, T., Gnecco, E., Steiner, P., Roth, R., Keene, T.D., Liu, S.X., Decurtins, S., Meyer, E.: Orientation dependent molecular friction on organic layer compound crystals. Appl. Phys. Lett. 98(1–3), 083119 (2011)
Verhoeven, G.S., Dienwiebel, M., Frenken, J.W.M.: Model calculations of superlubricity of graphite. Phys. Rev. B 70(1–10), 165418 (2004)
Filippov, A.E., Vanossi, A., Urbakh, M.: Origin of friction anisotropy on a quasicrystal surface. Phys. Rev. Lett. 104(1–4), 074302 (2010)
Müser, M.H.: Velocity dependence of kinetic friction in the Prandtl-Tomlinson model. Phys. Rev. B 84(1–13), 125419 (2011)
Fajardo, O.Y., Mazo, J.J.: Effects of surface disorder and temperature on atomic friction. Phys. Rev. B 82(1–7), 035435 (2010)
Fajardo, O.Y., Mazo, J.J.: Surface defects and temperature on atomic friction. J. Phys.: Condens. Matt. 23, 355008 (2011)
Kerssemakers, J., De Hosson, J.T.M.: Atomic-force microscopy imaging of transition-metal layered compounds—a 2-dimensional stick–slip system. Appl. Phys. Lett. 67, 347–349 (1995)
Hölscher, H., Schwarz, U.D., Wiesendanger, R.: Modelling of the scan process in lateral force microscopy. Surf. Sci. 375, 395–402 (1997)
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)
Steiner, P., Gnecco, E., Filleter, T., Gosvami, N.N., Maier, S., Meyer, E., Bennewitz, R.: Atomic friction investigations on ordered superstructures. Trib. Lett. 39, 321–327 (2010)
Steiner, P., Roth, R., Gnecco, E., Baratoff, A., Meyer, E.: Angular dependence of static and kinetic friction on alkali halide surfaces. Phys. Rev. B 82(1–9), 205417 (2010)
Gnecco, E.: Quasi-isotropy of static friction on hexagonal surface lattices. Europhys. Lett. 91(1–6), 66008 (2010)
Braun, O.M., Ferrando, R.: Role of long jumps in surface diffusion. Phys. Rev. E 65(1–11), 061107 (2002)
Pina, C.M., Miranda, R., Gnecco, E.: Anisotropic surface coupling while sliding on dolomite and calcite crystals. Phys. Rev. B 85(1–4), 073402 (2012)
Hölscher, H., Ebeling, D., Schwarz, U.D.: Friction at atomic-scale surface steps: Experiment and theory. Phys. Rev. Lett. 101(1–4), 246105 (2008)
Steiner, P., Gnecco, E., Krok, F., Budzioch, J., Walczak, L., Konior, J., Szymonski, M., Meyer, E.: Atomic-scale friction on stepped surfaces of ionic crystals. Phys. Rev. Lett. 106(1–4), 186104 (2011)
Ehrlich, G., Hudda, F.G.: Atomic view of surface self-diffusion: Tungsten on tungsten. J. Chem. Phys. 44, 1039–1049 (1966)
Schwöbel, R.L., Shipsey, E.J.: Step motion on crystal surfaces. J. Appl. Phys. 37, 3682–3686 (1966)
Campione, M., Trabattoni, S., Moret, M.: Nanoscale mapping of frictional anisotropy. Trib. Lett. 45, 219–224 (2012)
Zhao, X., Phillpot, S.R., Sawyer, W.G., Sinnott, S.B., Perry, S.S.: Transition from thermal to athermal friction under cryogenic conditions. Phys. Rev. Lett. 102(1–4), 186102 (2009)
Acknowledgments
Prof. Riccardo Ferrando from the University of Genova is gratefully acknowledged for scientific discussion. Our collaboration was promoted thanks to the EUROCORES programme ‘Friction and Adhesion in Nanomechanical Systems’ (FANAS) of the European Science Foundation. OYF and JJM acknowledge Spain MICINN under Projects No. FIS2008-01240 and FIS2011-25167 cofinanced by FEDER funds.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gnecco, E., Fajardo, O.Y., Pina, C.M. et al. Anisotropy Effects in Atomic-Scale Friction. Tribol Lett 48, 33–39 (2012). https://doi.org/10.1007/s11249-012-9923-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11249-012-9923-x