Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Ballistic nanofriction


Sliding parts in nanosystems such as nanoelectromechanical systems and nanomotors1,2,3,4,5,6,7,8,9 increasingly involve large speeds, and rotations as well as translations of the moving surfaces; yet, the physics of high-speed nanoscale friction is so far unexplored. Here, by simulating the motion of drifting and of kicked Au clusters on graphite—a workhorse system of experimental relevance10,11,12,13—we demonstrate and characterize a new ‘ballistic’ friction regime at high speed, separate from drift at low speed. The temperature dependence of the cluster slip distance and time, measuring friction, is opposite in these two regimes, consistent with theory. Crucial to both regimes is the interplay of rotations and translations, shown to be correlated in slow drift but anticorrelated in fast sliding. Despite these differences, we find the velocity dependence of ballistic friction to be, like drift, viscous.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Simulated gold cluster on graphite substrate.
Figure 2: Thermal diffusion of deposited Au clusters on graphite.
Figure 3: (X,Y) ballistic trajectories of a kicked cluster at different temperatures.
Figure 4: Slowdown dynamics of kicked Au clusters.
Figure 5: Time decay of kinetic energies of purely sliding and of sliding/rotating ballistic Au clusters.


  1. Gimzewski, J. K. et al. Rotation of a single molecule within a supramolecular bearing. Science 281, 531–533 (1998).

    Article  CAS  Google Scholar 

  2. Urbakh, M., Klafter, J., Gourdon, D. & Israelachvili, J. The nonlinear nature of friction. Nature 430, 525–528 (2004).

    Article  CAS  Google Scholar 

  3. van Delden, R. A. et al. Unidirectional molecular motor on a gold surface. Nature 437, 1337–1340 (2005).

    Article  CAS  Google Scholar 

  4. Browne, W. R. & Feringa, B. L. Making molecular machines work. Nature Nanotech. 1, 25–35 (2006).

    CAS  Google Scholar 

  5. Kim, S. H., Asay, D. B. & Dugger, M. T. Nanotribology and MEMS. Nano Today 2, 22–29 (2007).

    Article  Google Scholar 

  6. Balzani, V., Credi, A. & Venturi, M. Molecular devices and machines. Nano Lett. 2, 18–25 (2007).

    Google Scholar 

  7. Fleishman, D., Klafter, J., Porto, M. & Urbakh, M. Mesoscale engines by nonlinear friction. Nano Lett. 7, 837–842 (2007).

    Article  CAS  Google Scholar 

  8. Ternes, M., Lutz, C. P., Hirjibehedin, C. F., Giessibl, F. J. & Heinrich, A. J. The force needed to move an atom on a surface. Science 319, 1066–1069 (2008).

    Article  CAS  Google Scholar 

  9. Filippov, A. E., Vanossi, A. & Urbakh, M. Rotary motors sliding along surfaces. Phys. Rev. E 79, 021108 (2009).

    Article  Google Scholar 

  10. Bardotti, L. et al. Diffusion and aggregation of large antimony and gold clusters deposited on graphite. Surf. Sci. 367, 276–292 (1996).

    Article  CAS  Google Scholar 

  11. Luedtke, W. D. & Landman, U. Slip diffusion and Levy flights of an adsorbed gold nanocluster. Phys. Rev. Lett. 82, 3835–3838 (1999).

    Article  CAS  Google Scholar 

  12. Lewis, L. J., Jensen, P., Combe, N. & Barrat, J-L. Diffusion of gold nanoclusters on graphite. Phys. Rev. B 61, 16084–16090 (2000).

    Article  CAS  Google Scholar 

  13. Maruyama, Y. Temperature dependence of Levy-type stick-slip diffusion of a gold nanocluster on graphite. Phys. Rev. B 69, 245408 (2004).

    Article  Google Scholar 

  14. Hedgeland, H. et al. Measurement of single-molecule frictional dissipation in a prototypical nanoscale system. Nature Phys. 5, 561–564 (2009).

    Article  CAS  Google Scholar 

  15. Risken, H. The Fokker Planck Equation (Springer, 1984).

    Book  Google Scholar 

  16. Bowden, F. P. & Tabor, D. Friction: An Introduction to Tribology (Anchor-Doubleday, 1973).

    Google Scholar 

  17. Tambe, N. S. & Bhushan, B. Friction model for the velocity dependence of nanoscale friction. Nanotechnology 16, 2309–2324 (2005).

    Article  Google Scholar 

  18. Jensen, P. Growth of nanostructures by cluster deposition: Experiments and simple models. Rev. Mod. Phys. 71, 1695–1735 (1999).

    Article  CAS  Google Scholar 

  19. Krim, J., Solina, D. H. & Chiarello, R. Nanotribology of a Kr monolayer: A quartz-crystal microbalance study of atomic-scale friction. Phys. Rev. Lett. 66, 181–184 (1991).

    Article  CAS  Google Scholar 

  20. Bruschi, L., Carlin, A. & Mistura, G. Depinning of atomically thin Kr films on gold. Phys. Rev. Lett. 88, 046105 (2002).

    Article  CAS  Google Scholar 

  21. Pisov, S., Tosatti, E., Tartaglino, U. & Vanossi, A. Gold clusters sliding on graphite: A possible quartz crystal microbalance experiment? J. Phys. Condens. Matter 19, 305015 (2007).

    Article  Google Scholar 

  22. Dietzel, D. et al. Frictional duality observed during nanoparticle sliding. Phys. Rev. Lett. 101, 125505 (2008).

    Article  Google Scholar 

  23. Paolicelli, G., Rovatti, M., Vanossi, A. & Valeri, S. Controlling single cluster dynamics at the nanoscale. Appl. Phys. Lett. 95, 143121 (2009).

    Article  Google Scholar 

  24. Dienwiebel, M. et al. Superlubricity of graphite. Phys. Rev. Lett. 92, 126101 (2004).

    Article  Google Scholar 

  25. Filippov, A. E., Dienwiebel, M., Frenken, J. W. M., Klafter, J. & Urbakh, M. Torque and twist against superlubricity. Phys. Rev. Lett. 100, 046102 (2008).

    Article  Google Scholar 

  26. Farkas, Z., Bartels, G., Unger, T. & Wolf, D. E. Frictional coupling between sliding and spinning motion. Phys. Rev. Lett. 90, 248302 (2003).

    Article  Google Scholar 

  27. Weidman, P. D. & Malhotra, C. P. Regimes of terminal motion of sliding spinning disks. Phys. Rev. Lett. 95, 264303 (2005).

    Article  CAS  Google Scholar 

  28. Johnson, R. A. Analytic nearest-neighbor model for fcc metals. Phys. Rev. B 37, 3924–3931 (1988).

    Article  CAS  Google Scholar 

  29. Tersoff, J. Empirical interatomic potential for carbon, with applications to amorphous carbon. Phys. Rev. Lett. 61, 2879–2882 (1988).

    Article  CAS  Google Scholar 

  30. Kolmogorov, A. N. & Crespi, V. H. Registry-dependent interlayer potential for graphitic systems. Phys. Rev. B 71, 235415 (2005).

    Article  Google Scholar 

Download references


Discussions with U. Landman, G. E. Santoro, N. Manini and M. Urbakh are gratefully acknowledged. This work is part of Eurocores Projects FANAS/AFRI sponsored by the Italian Research Council (CNR), and FANAS/ACOF. It is also sponsored in part by The Italian Ministry of University and Research, through PRIN/COFIN contracts 20087NX9Y7 and 2008y2p573. A.V. acknowledges partial financial support by the Regional (Emilia Romagna) Net-Lab INTERMECH.

Author information

Authors and Affiliations



All authors contributed equally to the work presented in this Letter.

Corresponding authors

Correspondence to Andrea Vanossi or Erio Tosatti.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 553 kb)

Supplementary Information

Supplementary Movie 1 (MPG 16315 kb)

Supplementary Information

Supplementary Movie 2 (AVI 37341 kb)

Supplementary Information

Supplementary Movie 3 (MPG 18890 kb)

Supplementary Information

Supplementary Movie 4 (MPG 13504 kb)

Supplementary Information

Supplementary Movie 5 (MPG 1317 kb)

Supplementary Information

Supplementary Movie 6 (MPG 20385 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Guerra, R., Tartaglino, U., Vanossi, A. et al. Ballistic nanofriction. Nature Mater 9, 634–637 (2010).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing