Skip to main content

Thank you for visiting nature.com. 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.

Direct measurement of critical Casimir forces

Nature volume 451, pages 172–175 (2008)Cite this article

Abstract

When fluctuating fields are confined between two surfaces, long-range forces arise. A famous example is the quantum-electrodynamical Casimir force that results from zero-point vacuum fluctuations confined between two conducting metal plates1. A thermodynamic analogue is the critical Casimir force: it acts between surfaces immersed in a binary liquid mixture close to its critical point and arises from the confinement of concentration fluctuations within the thin film of fluid separating the surfaces2. So far, all experimental evidence for the existence of this effect has been indirect3,4,5. Here we report the direct measurement of critical Casimir force between a single colloidal sphere and a flat silica surface immersed in a mixture of water and 2,6-lutidine near its critical point. We use total internal reflection microscopy to determine in situ the forces between the sphere and the surface, with femtonewton resolution6. Depending on whether the adsorption preferences of the sphere and the surface for water and 2,6-lutidine are identical or opposite, we measure attractive and repulsive forces, respectively, that agree quantitatively with theoretical predictions and exhibit exquisite dependence on the temperature of the system. We expect that these features of critical Casimir forces may result in novel uses of colloids as model systems.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Data acquisition and analysis.
Figure 2: Critical Casimir potentials between a wall and a particle in a critical water–lutidine mixture.
Figure 3: Off-critical composition.

References

  1. Casimir, H. B. G. On the attraction between two perfectly conducting plates. Proc. Koninklijke Nederlandse Akad. Wetenschappen B51, 793–795 (1948)

    MATH  Google Scholar 

  2. Fisher, M. E. & de Gennes, P. G. Phenomena at the walls in a critical binary mixture. C. R. Acad. Sci. Paris B 287, 207–209 (1978)

    Google Scholar 

  3. Ganshin, A., Scheidemantel, S., Garcia, R. & Chan, M. H. W. Critical Casimir force in 4He films: confirmation of finite-size scaling. Phys. Rev. Lett. 97, 075301 (2006)

    Article  ADS  CAS  Google Scholar 

  4. Garcia, R. & Chan, M. H. W. Critical Casimir effect near the 3He-4He tricritical point. Phys. Rev. Lett. 88, 086101 (2002)

    Article  ADS  CAS  Google Scholar 

  5. Fukuto, M., Yano, Y. F. & Pershan, P. S. Critical Casimir effect in three-dimensional Ising systems: measurements on binary wetting films. Phys. Rev. Lett. 94, 135702 (2005)

    Article  ADS  Google Scholar 

  6. Prieve, D. C. Measurement of colloidal forces with TIRM. Adv. Colloid Interf. Sci. 82, 93–125 (1999)

    Article  CAS  Google Scholar 

  7. Krech, M. Fluctuation-induced forces in critical fluids. J. Phys. Cond. Matt. 11, R391–R412 (1999)

    Article  ADS  CAS  Google Scholar 

  8. Hanke, A., Schlesener, F., Eisenriegler, E. & Dietrich, S. Critical Casimir forces between spherical particles in fluids. Phys. Rev. Lett. 81, 1885–1888 (1998)

    Article  ADS  CAS  Google Scholar 

  9. Beysens, D. & Estéve, D. Adsorption phenomena at the surface of silica spheres in a binary liquid mixture. Phys. Rev. Lett. 54, 2123–2126 (1985)

    Article  ADS  CAS  Google Scholar 

  10. Beysens, D. & Narayanan, T. Wetting-induced aggregation of colloids. J. Stat. Phys. 95, 997–1008 (1999)

    Article  ADS  Google Scholar 

  11. Schlesener, F., Hanke, A. & Dietrich, S. Critical Casimir forces in colloidal suspensions. J. Stat. Phys. 110, 981–1013 (2003)

    Article  CAS  Google Scholar 

  12. Rudhardt, D., Bechinger, C. & Leiderer, P. Repulsive depletion interactions in colloid-polymer mixtures. J. Phys. Cond. Matt. 11, 10073–10078 (1999)

    Article  ADS  CAS  Google Scholar 

  13. Gallagher, P. D., Kurnaz, M. L. & Maher, J. V. Aggregation in polystyrene-sphere suspensions in near-critical binary liquid mixtures. Phys. Rev. A. 46, 7750–7755 (1992)

    Article  CAS  Google Scholar 

  14. Gallagher, P. D. & Maher, J. V. Partitioning of polystyrene latex spheres in immiscible critical liquid mixtures. Phys. Rev. A. 46, 2012–2021 (1992)

    Article  CAS  Google Scholar 

  15. Mohideen, U. & Roy, A. Precision measurement of the Casimir force from 0.1 to 0.9 µm. Phys. Rev. Lett. 81, 4549–4552 (1998)

    Article  ADS  CAS  Google Scholar 

  16. Rafai, S. & Bonn, D. &. Meunier, J. Repulsive and attractive critical Casimir forces. Physica A 386, 31–35 (2007)

    Article  ADS  Google Scholar 

  17. Vasilyev, O., Gambassi, A., Maciolek, A. & Dietrich, S. Monte Carlo simulation results for critical Casimir forces. Europhys. Lett. 80, 60009 (2007)

    Article  ADS  Google Scholar 

  18. Gülari, E., Collings, A. F., Schmidt, R. L. & Pings, C. J. Light scattering and shear viscosity studies of the binary system 2,6-lutidine-water in the critical region. J. Chem. Phys. 56, 6169–6179 (1972)

    Article  ADS  Google Scholar 

  19. Bieker, T. & Dietrich, S. Wetting of curved surfaces. Physica A 252, 85–137 (1998)

    Article  ADS  CAS  Google Scholar 

  20. Dobbs, H. T., Darbellay, G. A. & Yeomans, J. M. Capillary condensation between spheres. Europhys. Lett. 18, 439–444 (1992)

    Article  ADS  CAS  Google Scholar 

  21. Bauer, C., Bieker, T. & Dietrich, S. Wetting-induced effective interaction potential between spherical particles. Phys. Rev. E 62, 5324–5338 (2000)

    Article  ADS  CAS  Google Scholar 

  22. Ball, P. Feel the force. Nature 447, 772–774 (2007)

    Article  ADS  CAS  Google Scholar 

  23. Helden, L. et al. Single particle evanescent light scattering simulations for total internal reflection microscopy. Appl. Opt. 45, 7299–7308 (2006)

    Article  ADS  Google Scholar 

  24. Bevan, M. A. & Prieve, D. C. Hindered diffusion of colloidal particles very near to a wall: revisited. J. Chem. Phys. 113, 1228–1236 (2000)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank A. Maciołek for inspiring discussions and F. Schlesener, R. Dullens and D. Marr for comments and C. Mayer for sample preparation. This work is financially supported by the Deutsche Forschungsgemeinschaft.

Author information

Authors and Affiliations

  1. 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany ,

    C. Hertlein, L. Helden & C. Bechinger

  2. Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, 70569 Stuttgart, Germany ,

    A. Gambassi & S. Dietrich

  3. Institut für Theoretische und Angewandte Physik, Pfaffenwaldring 57, Universität Stuttgart, 70569 Stuttgart, Germany

    A. Gambassi & S. Dietrich

Authors
  1. C. Hertlein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Helden
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Gambassi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Dietrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. Bechinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Bechinger.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hertlein, C., Helden, L., Gambassi, A. et al. Direct measurement of critical Casimir forces. Nature 451, 172–175 (2008). https://doi.org/10.1038/nature06443

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature06443

This article is cited by

Comments

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.

Search

Advanced search

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