Macroscopic laws of friction do not generally apply to nanoscale contacts. Although continuum mechanics models have been predicted to break down at the nanoscale1, they continue to be applied for lack of a better theory. An understanding of how friction force depends on applied load and contact area at these scales is essential for the design of miniaturized devices with optimal mechanical performance2,3. Here we use large-scale molecular dynamics simulations with realistic force fields to establish friction laws in dry nanoscale contacts. We show that friction force depends linearly on the number of atoms that chemically interact across the contact. By defining the contact area as being proportional to this number of interacting atoms, we show that the macroscopically observed linear relationship between friction force and contact area can be extended to the nanoscale. Our model predicts that as the adhesion between the contacting surfaces is reduced, a transition takes place from nonlinear to linear dependence of friction force on load. This transition is consistent with the results of several nanoscale friction experiments4,5,6,7. We demonstrate that the breakdown of continuum mechanics can be understood as a result of the rough (multi-asperity) nature of the contact, and show that roughness theories8,9,10 of friction can be applied at the nanoscale.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Luan, B. & Robbins, M. O. The breakdown of continuum models for mechanical contacts. Nature 435, 929–932 (2005)
Delrio, F. W. et al. The role of van der Waals forces in adhesion of micromachined surfaces. Nature Mater. 4, 629–634 (2005)
Zykova-Timan, T., Ceresoli, D. & Tosatti, E. Peak effect versus skating in high-temperature nanofriction. Nature Mater. 6, 230–234 (2007)
Colburn, T. J. & Leggett, G. J. Influence of solvent environment and tip chemistry on the contact mechanics of tip-sample interactions in friction force microscopy of self-assembled monolayers of mercaptoundecanoic acid and dodecanethiol. Langmuir 23, 4959–4964 (2007)
Gao, J. et al. Frictional forces and Amontons' law: from the molecular to the macroscopic scale. J. Phys. Chem. 108, 3410–3425 (2004)
Grierson, D. S. Nanotribological Properties of Nanostructured Hard Carbon Thin Films. PhD thesis, Univ. Wisconsin (2008)
Ruths, M. Boundary friction of aromatic self-assembled monolayers: Comparison of systems with one or both sliding surfaces covered with a thiol monolayer. Langmuir 19, 6788–6795 (2003)
Müser, M. H. A rigorous, field-theoretical approach to the contact mechanics of rough, elastic solids. Phys. Rev. Lett. 100, 055504 (2008)
Persson, B. N. J. Theory of rubber friction and contact mechanics. J. Chem. Phys. 115, 3840–3861 (2001)
Greenwood, J. A. & Williamson, J. B. P. Contact of nominally flat surfaces. Proc. R. Soc. Lond. A 295, 300–319 (1966)
Amontons, G. De la resistance causée dans les machines. Mem. Acad. R. A 275–282 (1699)
Bowden, F. P. & Tabor, D. The Friction and Lubrication of Solids (Clarendon, 1950)
Szlufarska, I., Chandross, M. & Carpick, R. W. Recent advances in single-asperity nanotribology. J. Phys. D 41, 123001 (2008)
Binnig, G., Quate, C. F. & Gerber, C. Atomic force microscope. Phys. Rev. Lett. 56, 930–933 (1986)
Perry, S. S. Scanning probe microscopy measurements of friction. MRS Bull. 29, 478–483 (2004)
Bush, A. W., Gibson, R. D. & Thomas, T. R. The elastic contact of a rough surface. Wear 35, 87–111 (1975)
Hertz, H. On the contact of elastic solids. J. Reine Angew. Math. 92, 156 (1881)
Maugis, D. Adhesion of spheres—the JKR-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150, 243–269 (1992)
Riedo, E., Chevrier, J., Comin, F. & Brune, H. Nanotribology of carbon based thin films: The influence of film structure and surface morphology. Surf. Sci. 477, 25–34 (2001)
Gao, G. T., 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)
Pietrement, O. & Troyon, M. Study of the interfacial shear strength pressure dependence by modulated lateral force microscopy. Langmuir 17, 6540–6546 (2001)
Socoliuc, A., Bennewitz, R., Gnecco, E. & Meyer, E. Transition from stick-slip to continuous sliding in atomic friction: Engineering a new regime of ultralow friction. Phys. Rev. Lett. 92, 134301 (2004)
Chandross, M., Lorenz, C. D., Stevens, M. & Grest, G. S. Simulations of nanotribology with realistic probe tip models. Langmuir 24, 1240–1246 (2008)
Szlufarska, I., Nakano, A. & Vashishta, P. A crossover in the mechanical response of nanocrystalline ceramics. Science 309, 911–914 (2005)
Wenning, L. & Müser, M. H. Friction laws for elastic nanoscale contacts. Europhys. Lett. 54, 693–699 (2001)
Brenner, D. et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter 14, 783–802 (2002)
Johnson, K. L. Adhesion and friction between a smooth elastic spherical asperity and a plane surface. Proc. R. Soc. Lond. Ser. A 453, 163–179 (1997)
Luan, B. & Robbins, M. O. Contact of single asperities with varying adhesion: comparing continuum mechanics to atomistic simulations. Phys. Rev. E 74, 026111 (2006)
Israelachvili, J. N. & Berman, A. D. in Handbook of Micro/Nanotribology (ed. Bhushan, B.) 2nd edn, 371–432 (CRC Press, 1999)
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)
Schwarz, U. D. A generalized analytical model for the elastic deformation of an adhesive contact between a sphere and a flat surface. J. Colloid Interface Sci. 261, 99–106 (2003)
Tabor, D. Surface forces and surface interactions. J. Colloid Interface Sci. 58, 2–13 (1977)
Horn, R. G., Israelachvili, J. N. & Pribac, F. Measurement of the deformation and adhesion of solids in contact. J. Colloid Interface Sci. 115, 480–492 (1987)
Ruths, M., Alcantar, N. A. & Israelachvili, J. N. Boundary friction of aromatic silane self-assembled monolayers measured with the surface forces apparatus and friction force microscopy. J. Phys. Chem. B 107, 11149–11157 (2003)
Putman, C. A. J., Igarashi, V. & Kaneko, R. Single-asperity friction in friction force microscopy — The composite-tip model. Appl. Phys. Lett. 66, 3221–3223 (1995)
We thank D. Morgan for helpful discussions. Financial support from the National Science Foundation grant DMR-0512228 and from the American Chemical Society PRF-47978-G5 grant is gratefully acknowledged.
Author Contributions I.S. conceived the simulations and Y.M carried them out. Y.M. and I.S. designed the data analysis and Y.M. carried it out. I.S. and Y.M. co-wrote the paper. K.T.T. provided guidance and software for finite element analysis.
About this article
Cite this article
Mo, Y., Turner, K. & Szlufarska, I. Friction laws at the nanoscale. Nature 457, 1116–1119 (2009). https://doi.org/10.1038/nature07748
Science Advances (2020)
Powder Technology (2020)
Friction properties of carbon nanoparticles (nanodiamond and nanoscroll) confined between DLC and a-SiO2 surfaces
Tribology International (2020)
Advanced Materials Interfaces (2020)
Identifying Physical and Chemical Contributions to Friction: A Comparative Study of Chemically Inert and Active Graphene Step Edges
ACS Applied Materials & Interfaces (2020)