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

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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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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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.

Corresponding author

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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