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Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid

Nature Physics volume 7, pages 576–580 (2011)Cite this article

Abstract

At timescales once deemed immeasurably small by Einstein, the random movement of Brownian particles in a liquid is expected to be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. Here we report the observation of the Brownian motion of a single particle in an optical trap with 75 MHz bandwidth and sub-ångström spatial precision and the determination of the particle’s velocity autocorrelation function. Our observation is the first measurement of ballistic Brownian motion of a particle in a liquid. The data are in excellent agreement with theoretical predictions taking into account the inertia of the particle and hydrodynamic memory effects.

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Figure 1: Schematic diagram of the experiment.
Figure 2: Example MSD for silica particles 1 μm and 2.5 μm in diameter.
Figure 3: Ballistic regime.
Figure 4: Experimental VACF and theoretical description.

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References

  1. Brown, R. A brief account of microscopical observations made in the months of June, July and August, 1827 on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. Phil. Mag. 4, 161–173 (1828).

    Article  Google Scholar 

  2. Einstein, A. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 322, 549–560 (1905).

    Article  Google Scholar 

  3. Frey, E. & Kroy, K. Brownian motion: A paradigm of soft matter and biological physics. Ann. Phys. 14, 20–50 (2005).

    Article  Google Scholar 

  4. Black, F. & Scholes, M. S. The pricing of options and corporate liabilities. J. Political Econ. 81, 637–654 (1973).

    Article  MathSciNet  Google Scholar 

  5. Smoluchowski, M. Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann. Phys. 21, 756–780 (1906).

    Article  Google Scholar 

  6. Einstein, A. Zur Theorie der Brownschen Bewegung. Ann. Phys. 324, 371–381 (1906).

    Article  Google Scholar 

  7. Langevin, P. Sur la théorie du mouvement brownien. C.R. Acad. Sci. Paris 146, 530–533 (1908).

    MATH  Google Scholar 

  8. Rahman, A. Correlations in the motion of atoms in liquid argon. Phys. Rev. 136, A404–A411 (1964).

    Article  Google Scholar 

  9. Rahman, A. Liquid structure and self-diffusion. J. Chem. Phys. 45, 2585–2592 (1964).

    Article  ADS  Google Scholar 

  10. Alder, B. J. & Wainwright, T. E. Velocity autocorrelations for hard spheres. Phys. Rev. Lett. 18, 988–990 (1967).

    Article  ADS  Google Scholar 

  11. Alder, B. J. & Wainwright, T. E. Decay of the velocity autocorrelation function. Phys. Rev. A 1, 18–21 (1970).

    Article  ADS  Google Scholar 

  12. Paul, G. L. & Pusey, P. N. Observation of a long-time tail in Brownian motion. J. Phys. A. 14, 3301–3327 (1981).

    Article  ADS  Google Scholar 

  13. Weitz, D. A., Pine, D. J., Pusey, P. N. & Tough, R. J. A. Nondiffusive Brownian motion studied by diffusing-wave spectroscopy. Phys. Rev. Lett. 63, 1747–1750 (1989).

    Article  ADS  Google Scholar 

  14. Vladimirsky, V. & Terletzky, Y. A. Hydrodynamical theory of translational Brownian motion. Zh. Eksp. Teor. Fiz. 15, 258–263 (1945).

    MathSciNet  Google Scholar 

  15. Hinch, E. J. Application of the Langevin equation to fluid suspensions. J. Fluid Mech. 72, 499–511 (1975).

    Article  ADS  MathSciNet  Google Scholar 

  16. Einstein, A. Theoretische Bemerkungen über die Brownsche Bewegung. Z. Elektrochem. 13, 41–42 (1907).

    Article  Google Scholar 

  17. Blum, J. et al. Measurement of the translational and rotational Brownian motion of individual particles in a rarefied gas. Phys. Rev. Lett. 97, 230601 (2006).

    Article  ADS  Google Scholar 

  18. Li, T., Kheifets, S., Medellin, D. & Raizen, M. G. Measurement of the instantaneous velocity of a Brownian particle. Science 328, 1673–1675 (2010).

    Article  ADS  Google Scholar 

  19. Uhlenbeck, G. E. & Ornstein, L. S. On the theory of Brownian motion. Phys. Rev. 36, 823–841 (1930).

    Article  ADS  Google Scholar 

  20. Lukić, B. et al. Direct observation of nondiffusive motion of a Brownian particle. Phys. Rev. Lett. 95, 160601 (2005).

    Article  ADS  Google Scholar 

  21. Jeney, S., Lukić, B., Kraus, J. A., Franosch, T. & Forró, L. Anisotropic memory effects in colloidal diffusion. Phys. Rev. Lett. 100, 240604 (2008).

    Article  ADS  Google Scholar 

  22. Zhu, J. X., Durian, D. J., Muller, J., Weitz, D. A. & Pine, D. J. Scaling of transient hydrodynamic interactions in concentrated suspensions. Phys. Rev. Lett. 68, 2559–2562 (1992).

    Article  ADS  Google Scholar 

  23. Kao, M. H., Yodh, A. G. & Pine, D. J. Observation of Brownian-motion on the timescale of hydrodynamic interactions. Phys. Rev. Lett. 70, 242–245 (1993).

    Article  ADS  Google Scholar 

  24. Henderson, S., Mitchell, S. & Bartlett, P. Propagation of hydrodynamic interactions in colloidal suspensions. Phys. Rev. Lett. 88, 088302 (2002).

    Article  ADS  Google Scholar 

  25. Liverpool, T. B. & MacKintosh, F. C. Inertial effects in the response of viscous and viscoelastic fluids. Phys. Rev. Lett. 95, 208303 (2005).

    Article  ADS  Google Scholar 

  26. Atakhorrami, M., Koenderink, G. H., Schmidt, C. F. & MacKintosh, F. C. Short-time inertial response of viscoelastic fluids: Observation of vortex propagation. Phys. Rev. Lett. 95, 208302 (2005).

    Article  ADS  Google Scholar 

  27. Neuman, K. C. & Block, S. M. Optical trapping. Rev. Sci. Instrum. 75, 2787–2809 (2004).

    Article  ADS  Google Scholar 

  28. Chavez, I., Huang, R. X., Henderson, K., Florin, E-L. & Raizen, M. G. Development of a fast position-sensitive laser beam detector. Rev. Sci. Instrum 79, 105104 (2008).

    Article  ADS  Google Scholar 

  29. Gittes, F. & Schmidt, C. F. Interference model for back-focal-plane displacement detection in optical tweezers. Opt. Lett. 23, 7–9 (1998).

    Article  ADS  Google Scholar 

  30. Pralle, A., Prummer, M., Florin, E.L., Stelzer, E. H. K. & Horber, J. K. H. Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light. Microsc. Res. Tech. 44, 378–386 (1999).

    Article  Google Scholar 

  31. Clercx, H. J. H. & Schram, P. P. J. M. Brownian particles in shear flow and harmonic potentials: A study of long-time tails. Phys. Rev. A 46, 1942–1950 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  32. Giterman, M. Sh. & Gertsenshtein, M. E. Theory of the Brownian motion and the possibilities of using it for the study of the critical state of a pure substance. Sov. Phys. JETP 23 (4), 722–728 (1966).

    ADS  Google Scholar 

  33. Zwanzig, R. & Bixon, M. Compressibility effects in the hydrodynamic theory of Brownian motion. J. Fluid. Mech. 69, 21–25 (1975).

    Article  ADS  Google Scholar 

  34. Flyvbjerg, H. & Petersen, H. G. Error estimates on average of correlated data. J. Chem. Phys. 91, 461–466 (1989).

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This research was supported by NSF grants PHY-0647144 and DBI-0552094. S.J. and B.L. acknowledge support from the NCCR Nanoscale Science. M.G.R. acknowledges support from the Sid W. Richardson Foundation and the R. A. Welch Foundation, grant number F-1258. We thank V. Zyuzin for translating ref. 14.

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Authors and Affiliations

  1. Center for Nonlinear Dynamics, The University of Texas at Austin, Austin, Texas 78712, USA

    Rongxin Huang, Isaac Chavez, Katja M. Taute, Mark G. Raizen & Ernst-Ludwig Florin

  2. Institut de Physique de la Matière Complexe, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

    Branimir Lukić & Sylvia Jeney

Authors
  1. Rongxin Huang
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  2. Isaac Chavez
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  4. Branimir Lukić
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  7. Ernst-Ludwig Florin
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Contributions

R.H. and E-L.F. conceived the experiment. B.L. and S.J. contributed to the planning of the early experiments and provided an early version of the VACF analysis software. I.C., R.H., E-L.F. and M.G.R. developed, built and characterized the fast position detector, and incorporated it into the set-up. R.H. carried out the experiments in part assisted by I.C. R.H. analysed the data. R.H., K.M.T. and E-L.F. interpreted the data and wrote the manuscript. All authors discussed and commented on the final version of the manuscript.

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Correspondence to Ernst-Ludwig Florin.

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The authors declare no competing financial interests.

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Huang, R., Chavez, I., Taute, K. et al. Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid. Nature Phys 7, 576–580 (2011). https://doi.org/10.1038/nphys1953

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