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.

Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets


The brownian motion of mesoscopic particles is ubiquitous and usually random. But in systems with periodic asymmetric barriers to movement, directed or ‘rectified’ motion can arise and may even modulate some biological processes1. In man-made devices, brownian ratchets and variants based on optical or quantum effects have been exploited to induce directed motion2,3,4,5,6,7,8,9,10,11,12,13,14, and the dependence of the amplitude of motion on particle size has led to the size-dependent separation of biomolecules6,8,15. Here we demonstrate that the one-dimensional pores of a macroporous silicon membrane16, etched to exhibit a periodic asymmetric variation in pore diameter, can act as massively parallel and multiply stacked brownian ratchets that are potentially suitable for large-scale particle separations. We show that applying a periodic pressure profile with a mean value of zero to a basin separated by such a membrane induces a periodic flow of water and suspended particles through the pores, resulting in a net motion of the particles from one side of the membrane to the other without moving the liquid itself. We find that the experimentally observed pressure dependence of the particle transport, including an inversion of the transport direction, agrees with calculations17,18 of the transport properties in the type of ratchet devices used here.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Experimental set-up.
Figure 2: Photoluminescence intensity as a function of time.
Figure 3: Simulated profile of particle concentration as a function of position for different instants in time.
Figure 4: Drift current jdrift calculated from experimental results on particle transport as a function of applied pressure amplitudes.


  1. Huxley, A. F. Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255–318 (1957)

    CAS  Article  Google Scholar 

  2. von Smoluchowski, M. Experimentell nachweisbare, der üblichen Thermodynamik widersprechende Molekularphänomene. Phys. Zeitsch. 13, 1069–1080 (1912)

    CAS  MATH  Google Scholar 

  3. Feynman, R. P., Leighton, R. B. & Sands, M. The Feynman Lectures On Physics Ch. 46 Vol. 1 (Addison-Wesley, Reading, Massachusetts, 1966)

    MATH  Google Scholar 

  4. Faucheux, L. P., Bourdieu, L. S., Kaplan, P. D. & Libchaber, A. J. Optical thermal ratchet. Phys. Rev. Lett. 74, 1504–1507 (1995)

    ADS  CAS  Article  Google Scholar 

  5. Marquet, C., Buguin, A., Talini, L. & Silberzan, P. Rectified motion of colloids in asymmetrically structured channels. Phys. Rev. Lett. 88, 168301 (2002)

    ADS  CAS  Article  Google Scholar 

  6. Derényi, I. & Astumian, R. D. AC separation of particles by biased Brownian motion in a two-dimensional sieve. Phys. Rev. E 58, 7781–7784 (1998)

    ADS  Article  Google Scholar 

  7. Rousselet, J., Salome, L., Ajdari, A. & Prost, J. Directional motion of brownian particles induced by a periodic asymmetric potential. Nature 370, 446–448 (1994)

    ADS  CAS  Article  Google Scholar 

  8. van Oudenaarden, A. & Boxer, S. G. Brownian ratchet: molecular separations in liquid bilayers supported on patterned arrays. Science 285, 1046–1048 (1999)

    CAS  Article  Google Scholar 

  9. Linke, H. et al. Experimental tunneling ratchets. Science 286, 2314–2317 (1999)

    CAS  Article  Google Scholar 

  10. Switkes, M., Marcus, C. M., Campman, K. & Gossard, A. C. An adiabatic quantum electron pump. Science 283, 1905–1908 (1999)

    ADS  CAS  Article  Google Scholar 

  11. Hänggi, P. & Bartussek, R. Lecture Notes in Physics Vol. 476 (eds Parisi, J., Müller, S. C. & Zimmermann, W.) 294–308 (Springer, Berlin, 1996)

    Google Scholar 

  12. Astumian, R. D. Thermodynamics and kinetics of a brownian motor. Science 276, 917–922 (1997)

    CAS  Article  Google Scholar 

  13. Astumian, R. D. & Hänggi, P. Brownian motors. Phys. Today 55(11), 33–39 (2002)

    ADS  Article  Google Scholar 

  14. Linke, H. (ed.) Ratchets and Brownian motors: basics, experiments and applications. Appl. Phys. A (Special Issue) 75(2), (2002)

  15. Cabodi, M., Chen, Y.-F., Turner, S. W. P., Craighead, H. G. & Austin, R. H. Continuous separation of biomolecules by the laterally asymmetric diffusion array with out-of-plane sample injection. Electrophoresis 23, 3496–3503 (2002)

    CAS  Article  Google Scholar 

  16. Müller, F. et al. Membranes for micropumps from macroporous silicon. Phys. Stat. Sol. A 182, 585–590 (2000)

    ADS  Article  Google Scholar 

  17. Kettner, C., Reimann, P., Hänggi, P. & Müller, F. Drift ratchet. Phys. Rev. E 61, 312–323 (2000)

    ADS  CAS  Article  Google Scholar 

  18. Kettner, C., Hänggi, P. & Müller, F. Verfahren und Vorrichtung zur größenabhängigen Sortierung mikroskopisch kleiner Teilchen auf der Basis von rauschinduziertem Transport. German patent pending (DE 199 07 564 A 1), submitted 22 Feb. 1999.

  19. Lehmann, V. & Föll, H. Formation mechanism and properties of electrochemically etched trenches in n-type silicon. J. Electrochem. Soc. 137, 653–659 (1990)

    CAS  Article  Google Scholar 

  20. Lehmann, V. The physics of macropore formation in low doped n-type silicon. J. Electrochem. Soc. 140, 2836–2843 (1993)

    CAS  Article  Google Scholar 

  21. Schilling, J. et al. 3D photonic crystals made out of macroporous silicon by modulation of pore diameter. Appl. Phys. Lett. 78, 1180–1182 (2001)

    ADS  CAS  Article  Google Scholar 

  22. Lehmann, V. & Grüning, U. The limits of macropore array fabrication. Thin Solid Films 297, 13–17 (1997)

    ADS  CAS  Article  Google Scholar 

  23. Tong, Q. Y. & Gösele, U. Semiconductor Wafer Bonding 53–54 (Wiley and Sons, New York, 1999)

    Google Scholar 

Download references


We thank U. Gösele for backing the ratchet project over many years. We also gratefully acknowledge discussions on the theory of the ratchet-effect with P. Hänggi, Ch. Kettner, P. Reimann and R. Eichhorn as well as critical reading of the manuscript by K. Scheerschmidt and R. B. Wehrspohn.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Frank Müller.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Matthias, S., Müller, F. Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets. Nature 424, 53–57 (2003).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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