Abstract

We are concerned with dynamic properties of interacting Brownian particles in concentrated colloidal suspensions. An effective diffusion coefficient measured by the modulated in phase low-coherence dynamic light scattering technique is investigated as a function of the volume fraction. The experimental results are compared with the numerical ones calculated under both the Cohen–de Schepper approximation for hydrodynamic interaction and the Percus–Yevick approximations for structural effect. It is confirmed that the Brownian motion of particles in the range of volume fraction from 0.01 to 0.2 is mainly dominated by the hydrodynamic interaction rather than the structural effect, which can be described well by the Cohen–de Schepper approximation.

© 2008 Optical Society of America

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References

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  1. P. N. Segre, O. P. Behrend, and P. N. Pusey, “Short time Brownian motion in colloidal suspensions: experimental and simulation,” Phys. Rev. E 52, 5070-5083 (1995).
    [CrossRef]
  2. C. W. J. Beenakker and P. Mazur, “Self-diffusion of sphere in a concentrated suspension,” Physica A (Amsterdam) 120, 388-410 (1983).
    [CrossRef]
  3. P. N. Pusey, “The dynamics of interacting Brownian particles,” J. Phys. A 8, 1433-1439 (1975).
    [CrossRef]
  4. P. N. Pusey and W. van Megen, “Measurement of the short-time self-mobility of particles in concentrated suspension. Evidence for many-particle hydrodynamic interactions,” J. Phys. (Paris) 44, 285-291 (1983).
    [CrossRef]
  5. P. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, 1976).
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    [CrossRef] [PubMed]
  7. M. H. Kao, A. G. Yodh, and D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242-245 (1993) .
    [CrossRef] [PubMed]
  8. X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, and P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516-519 (1990).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  20. N. W. Ashcroft and J. Lekner, “Structure and resisitivity of liquid metals,” Phys. Rev. 145, 83-90 (1966).
    [CrossRef]
  21. W. Hess and R. Klein, “Generalized hydrodynamics of systems of Brownian particles,” Adv. Phys. 32, 173-283 (1983).
    [CrossRef]

2007

2005

K. Ishii, R. Yoshida, and T. Iwai, “Single-scattering spectroscopy for extremely dense colloidal suspensions by use of a low-coherence interferometer,” Opt. Lett. 30, 555-557 (2005).
[CrossRef] [PubMed]

H. Xia, K. Ishii, and T. Iwai, “Hydrodynamic radius sizing of nanoparticles in dense polydisperse media by low-coherence dynamic light scattering,” Jpn. J. Appl. Phys. 44, 6261-6264 (2005).
[CrossRef]

2002

L. F. Rojas-Ochoa, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[CrossRef]

2001

1998

1995

A. J. C. Ladd, Hu Gang, J. X. Zhu, and D. A. Weitz, “Temporal and spatial dependence of hydrodynamic correlations: simulation and experiment,” Phys. Rev. E. 52, 6550-6571 (1995).
[CrossRef]

E. G. D. Cohen and I. M. de Schepper, “Comment on 'Scaling of transient hydrodynamic interactions in concentrated suspensions',” Phys. Rev. Lett. 75, 2252 (1995).
[CrossRef] [PubMed]

P. N. Segre, O. P. Behrend, and P. N. Pusey, “Short time Brownian motion in colloidal suspensions: experimental and simulation,” Phys. Rev. E 52, 5070-5083 (1995).
[CrossRef]

1993

M. H. Kao, A. G. Yodh, and D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242-245 (1993) .
[CrossRef] [PubMed]

1992

J. Z. Xue, X. L. Wu, D. J. Pine, and P. M. Chaikin, “Hydrodynamic interactions in hard-sphere suspensions,” Phys. Rev. A. 45, 989-993 (1992).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, and D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559-2562 (1992).
[CrossRef] [PubMed]

1990

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, and P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516-519 (1990).
[CrossRef] [PubMed]

S. Fraden and G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512-515 (1990).
[CrossRef] [PubMed]

1988

D. J. Pine, D. A. Weeitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134-1137 (1988).
[CrossRef] [PubMed]

1983

P. N. Pusey and W. van Megen, “Measurement of the short-time self-mobility of particles in concentrated suspension. Evidence for many-particle hydrodynamic interactions,” J. Phys. (Paris) 44, 285-291 (1983).
[CrossRef]

C. W. J. Beenakker and P. Mazur, “Self-diffusion of sphere in a concentrated suspension,” Physica A (Amsterdam) 120, 388-410 (1983).
[CrossRef]

W. Hess and R. Klein, “Generalized hydrodynamics of systems of Brownian particles,” Adv. Phys. 32, 173-283 (1983).
[CrossRef]

1975

P. N. Pusey, “The dynamics of interacting Brownian particles,” J. Phys. A 8, 1433-1439 (1975).
[CrossRef]

1966

N. W. Ashcroft and J. Lekner, “Structure and resisitivity of liquid metals,” Phys. Rev. 145, 83-90 (1966).
[CrossRef]

Adv. Phys.

W. Hess and R. Klein, “Generalized hydrodynamics of systems of Brownian particles,” Adv. Phys. 32, 173-283 (1983).
[CrossRef]

Appl. Opt.

J. Phys.

P. N. Pusey and W. van Megen, “Measurement of the short-time self-mobility of particles in concentrated suspension. Evidence for many-particle hydrodynamic interactions,” J. Phys. (Paris) 44, 285-291 (1983).
[CrossRef]

J. Phys. A

P. N. Pusey, “The dynamics of interacting Brownian particles,” J. Phys. A 8, 1433-1439 (1975).
[CrossRef]

Jpn. J. Appl. Phys.

H. Xia, K. Ishii, and T. Iwai, “Hydrodynamic radius sizing of nanoparticles in dense polydisperse media by low-coherence dynamic light scattering,” Jpn. J. Appl. Phys. 44, 6261-6264 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

N. W. Ashcroft and J. Lekner, “Structure and resisitivity of liquid metals,” Phys. Rev. 145, 83-90 (1966).
[CrossRef]

Phys. Rev. A.

J. Z. Xue, X. L. Wu, D. J. Pine, and P. M. Chaikin, “Hydrodynamic interactions in hard-sphere suspensions,” Phys. Rev. A. 45, 989-993 (1992).
[CrossRef] [PubMed]

Phys. Rev. E

L. F. Rojas-Ochoa, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[CrossRef]

P. N. Segre, O. P. Behrend, and P. N. Pusey, “Short time Brownian motion in colloidal suspensions: experimental and simulation,” Phys. Rev. E 52, 5070-5083 (1995).
[CrossRef]

Phys. Rev. E.

A. J. C. Ladd, Hu Gang, J. X. Zhu, and D. A. Weitz, “Temporal and spatial dependence of hydrodynamic correlations: simulation and experiment,” Phys. Rev. E. 52, 6550-6571 (1995).
[CrossRef]

Phys. Rev. Lett.

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, and D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559-2562 (1992).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weeitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134-1137 (1988).
[CrossRef] [PubMed]

M. H. Kao, A. G. Yodh, and D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242-245 (1993) .
[CrossRef] [PubMed]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, and P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516-519 (1990).
[CrossRef] [PubMed]

S. Fraden and G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512-515 (1990).
[CrossRef] [PubMed]

E. G. D. Cohen and I. M. de Schepper, “Comment on 'Scaling of transient hydrodynamic interactions in concentrated suspensions',” Phys. Rev. Lett. 75, 2252 (1995).
[CrossRef] [PubMed]

Physica A (Amsterdam)

C. W. J. Beenakker and P. Mazur, “Self-diffusion of sphere in a concentrated suspension,” Physica A (Amsterdam) 120, 388-410 (1983).
[CrossRef]

Other

P. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, 1976).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the low-coherence DLS experimental system. The SLD and the PZT denote the superluminescent diode and the piezoelectric transducer, respectively.

Fig. 2
Fig. 2

Illustration of the measured homodyne and heterodyne power spectra of light backscattered from polystyrene latex particles with a radius of 235 nm at different path lengths with L = 30 and 80 m . The first-order component of the amplitude power spectrum appeared at 2 kHz separately from the homodyne measurements.

Fig. 3
Fig. 3

Comparison of the coherence length of the SLD with the MFP of the colloidal suspensions of particles with the radii of 165, 235, and 403 nm as a function of the volume fraction.

Fig. 4
Fig. 4

Percus–Yevick form of the structural effects as a function of the particle radius q R for four different volume fractions of 0.01, 0.05, 0.1, and 0.2.

Fig. 5
Fig. 5

Temporal amplitude autocorrelation functions of light scattered from the colloidal suspensions of particles with the radius of 235 nm for four volume fractions of 0.01, 0.08, 0.15, and 0.2. The solid lines stand for the lines of the single exponential functions that are fitted to the experimental data.

Fig. 6
Fig. 6

Variations of the effective diffusion coefficients as a function of the volume fraction for three radii of 165, 235, and 403 nm . The solid lines stand for the theoretical predictions calculated by Eq. (2) under the Cohen–de Schepper and Percus–Yevick approximations with 165 nm (solid curve), 235 nm (dashed curve), and 403 nm (dotted curve). The error bars show the standard deviations of the nonlinear least-squares fitting for the autocorrelation function.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

γ ( τ ) = E ( 0 ) E * ( τ ) / E ( 0 ) E * ( 0 ) = exp ( q 2 D eff τ ) ,
D eff = D 0 H ( q R , ϕ ) / S ( q R , ϕ ) ,
H ( ϕ ) = ( 1 ϕ ) 3 / ( 1 ϕ / 2 ) .
S ( q R ) = 1 / [ 1 ρ C d ( q R ) ] .
C d = 32 π R 3 0 1 r 2 sin ( 2 q R r ) 2 q R r ( α + β r + γ r 3 ) d r ,
α = ( 1 + 2 ϕ ) 2 / ( 1 - ϕ ) 4 ,
β = 6 ϕ ( 1 + ϕ / 2 ) 2 / ( 1 ϕ ) 4 ,
γ = ϕ α / 2.

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