Abstract

Multiple scattering currently presents a major limitation for intensity correlation spectroscopy of quasi-elastically scattered light from concentrated colloidal systems. Theoretical treatments have been restricted to low orders of multiple scattering. Experimentally, suppression of multiple scattering by dual-beam cross-correlation setups has been restricted to a 90-deg fixed scattering angle. We propose a variable scattering angle cross-correlation scheme and present the results of a successful experiment on a highly concentrated aqueous suspension of polystyrene spheres.

© 1990 Optical Society of America

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References

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  1. E. O. Schulz-DuBois, ed., Photon Correlation Techniques in Fluid Mechanics, Vol. 38 of Springer Series on Optical Science (Springer-Verlag, Berlin1983).
    [CrossRef]
  2. R. Pecora, ed., Dynamic Light Scattering (Plenum, New York, 1985).
    [CrossRef]
  3. G. D. J. Phillies, “Suppression of multiple scattering effects in quasielastic light scattering by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
    [CrossRef]
  4. G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. 24, 1939–1943 (1981).
    [CrossRef]
  5. J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
    [CrossRef]
  6. H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
    [CrossRef]
  7. C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light double scattered from a system of Brownian particles,” Phys. Rev. A 14, 1520–1532 (1976).
    [CrossRef]
  8. J. Böheim, W. Hess, R. Klein, “Depolarized light scattering from interacting Brownian spheres,” Z. Phys. 332, 237–243 (1979).
  9. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988), and references therein.
    [CrossRef] [PubMed]
  10. C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Multiple scattering from a system of Brownian particles,” Phys. Rev. 17, 3020–2035 (1978).
  11. G. A. Schumacher, T. G. M. van de Ven, “Brownian motion of charged particles surrounded by electric double layers,” Faraday Discuss. Chem. Soc. 83, paper 19 (1987).
    [CrossRef]
  12. H. Oshima, T. W. Healy, L. R. White, “Sedimentation velocity and potential in dilute suspension of charged spherical colloidal particles,” J. Chem. Soc. Faraday Trans. 2 80, 1299–1317 (1984).
    [CrossRef]
  13. K. Schätzel, J. Merz, “Measurement of small electrophoretic mobilities by light scattering and analysis of the amplitude weighted phase structure function,” J. Chem. Phys. 81, 2482–2488 (1984).
    [CrossRef]

1988

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

1987

G. A. Schumacher, T. G. M. van de Ven, “Brownian motion of charged particles surrounded by electric double layers,” Faraday Discuss. Chem. Soc. 83, paper 19 (1987).
[CrossRef]

1986

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

1984

H. Oshima, T. W. Healy, L. R. White, “Sedimentation velocity and potential in dilute suspension of charged spherical colloidal particles,” J. Chem. Soc. Faraday Trans. 2 80, 1299–1317 (1984).
[CrossRef]

K. Schätzel, J. Merz, “Measurement of small electrophoretic mobilities by light scattering and analysis of the amplitude weighted phase structure function,” J. Chem. Phys. 81, 2482–2488 (1984).
[CrossRef]

1983

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

1981

G. D. J. Phillies, “Suppression of multiple scattering effects in quasielastic light scattering by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. 24, 1939–1943 (1981).
[CrossRef]

1979

J. Böheim, W. Hess, R. Klein, “Depolarized light scattering from interacting Brownian spheres,” Z. Phys. 332, 237–243 (1979).

1978

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Multiple scattering from a system of Brownian particles,” Phys. Rev. 17, 3020–2035 (1978).

1976

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light double scattered from a system of Brownian particles,” Phys. Rev. A 14, 1520–1532 (1976).
[CrossRef]

Böheim, J.

J. Böheim, W. Hess, R. Klein, “Depolarized light scattering from interacting Brownian spheres,” Z. Phys. 332, 237–243 (1979).

Chaikin, P. M.

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

de Kruif, C. G.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

Dhont, J. K. G.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

Healy, T. W.

H. Oshima, T. W. Healy, L. R. White, “Sedimentation velocity and potential in dilute suspension of charged spherical colloidal particles,” J. Chem. Soc. Faraday Trans. 2 80, 1299–1317 (1984).
[CrossRef]

Herbolzheimer, E.

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

Hess, W.

J. Böheim, W. Hess, R. Klein, “Depolarized light scattering from interacting Brownian spheres,” Z. Phys. 332, 237–243 (1979).

Klein, R.

J. Böheim, W. Hess, R. Klein, “Depolarized light scattering from interacting Brownian spheres,” Z. Phys. 332, 237–243 (1979).

Merz, J.

K. Schätzel, J. Merz, “Measurement of small electrophoretic mobilities by light scattering and analysis of the amplitude weighted phase structure function,” J. Chem. Phys. 81, 2482–2488 (1984).
[CrossRef]

Mockler, R. C.

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Multiple scattering from a system of Brownian particles,” Phys. Rev. 17, 3020–2035 (1978).

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light double scattered from a system of Brownian particles,” Phys. Rev. A 14, 1520–1532 (1976).
[CrossRef]

Mos, H. J.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

O’Sullivan, W. J.

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Multiple scattering from a system of Brownian particles,” Phys. Rev. 17, 3020–2035 (1978).

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light double scattered from a system of Brownian particles,” Phys. Rev. A 14, 1520–1532 (1976).
[CrossRef]

Oshima, H.

H. Oshima, T. W. Healy, L. R. White, “Sedimentation velocity and potential in dilute suspension of charged spherical colloidal particles,” J. Chem. Soc. Faraday Trans. 2 80, 1299–1317 (1984).
[CrossRef]

Pathmamanoharan, C.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

Phillies, G. D. J.

G. D. J. Phillies, “Suppression of multiple scattering effects in quasielastic light scattering by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. 24, 1939–1943 (1981).
[CrossRef]

Pine, D. J.

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

Schätzel, K.

K. Schätzel, J. Merz, “Measurement of small electrophoretic mobilities by light scattering and analysis of the amplitude weighted phase structure function,” J. Chem. Phys. 81, 2482–2488 (1984).
[CrossRef]

Schumacher, G. A.

G. A. Schumacher, T. G. M. van de Ven, “Brownian motion of charged particles surrounded by electric double layers,” Faraday Discuss. Chem. Soc. 83, paper 19 (1987).
[CrossRef]

Sorensen, C. M.

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Multiple scattering from a system of Brownian particles,” Phys. Rev. 17, 3020–2035 (1978).

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light double scattered from a system of Brownian particles,” Phys. Rev. A 14, 1520–1532 (1976).
[CrossRef]

van de Ven, T. G. M.

G. A. Schumacher, T. G. M. van de Ven, “Brownian motion of charged particles surrounded by electric double layers,” Faraday Discuss. Chem. Soc. 83, paper 19 (1987).
[CrossRef]

Weitz, D. A.

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

White, L. R.

H. Oshima, T. W. Healy, L. R. White, “Sedimentation velocity and potential in dilute suspension of charged spherical colloidal particles,” J. Chem. Soc. Faraday Trans. 2 80, 1299–1317 (1984).
[CrossRef]

Faraday Discuss. Chem. Soc.

G. A. Schumacher, T. G. M. van de Ven, “Brownian motion of charged particles surrounded by electric double layers,” Faraday Discuss. Chem. Soc. 83, paper 19 (1987).
[CrossRef]

J. Chem. Phys.

K. Schätzel, J. Merz, “Measurement of small electrophoretic mobilities by light scattering and analysis of the amplitude weighted phase structure function,” J. Chem. Phys. 81, 2482–2488 (1984).
[CrossRef]

G. D. J. Phillies, “Suppression of multiple scattering effects in quasielastic light scattering by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

J. Chem. Soc. Faraday Trans. 2

H. Oshima, T. W. Healy, L. R. White, “Sedimentation velocity and potential in dilute suspension of charged spherical colloidal particles,” J. Chem. Soc. Faraday Trans. 2 80, 1299–1317 (1984).
[CrossRef]

Phys. Rev.

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Multiple scattering from a system of Brownian particles,” Phys. Rev. 17, 3020–2035 (1978).

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. 24, 1939–1943 (1981).
[CrossRef]

Phys. Rev. A

C. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light double scattered from a system of Brownian particles,” Phys. Rev. A 14, 1520–1532 (1976).
[CrossRef]

Phys. Rev. Lett.

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

Z. Phys.

J. Böheim, W. Hess, R. Klein, “Depolarized light scattering from interacting Brownian spheres,” Z. Phys. 332, 237–243 (1979).

Other

E. O. Schulz-DuBois, ed., Photon Correlation Techniques in Fluid Mechanics, Vol. 38 of Springer Series on Optical Science (Springer-Verlag, Berlin1983).
[CrossRef]

R. Pecora, ed., Dynamic Light Scattering (Plenum, New York, 1985).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Double-scattering geometry for the dual-beam–dual-detector cross-correlation setup. k01, k02, incident light wave vectors; kf2, kf2, scattered light final wave vectors; kjl1kjl2, intermediate wave vectors; ̂, incident polarization; q, scattering vectors; rD1, rD2, detector positions; ϑ1, ϑ2, scattering angles.

Fig. 2
Fig. 2

Experimental setup. M, Mirror; K, double Koesters prism; L1, L2, L3, lenses; ϑ1, ϑ2, scattering angles; δ = (ϑ1ϑ2)/2; ϑ = (ϑ1 + ϑ2)/2; λ, wavelengths; D, diaphragm; D1, D2, fiber apertures; PM1, PM2, photomultipliers.

Fig. 3
Fig. 3

Apparent hydrodynamic radii RH versus scattering angles ϑ1 and ϑ2 and detection optics angle ϑ: ▲, sample A and Δ, sample B at ϑ2 from autocorrelation at wavelength λ2; ●, sample A and ○, sample B at ϑ1 from autocorrelation at wavelength λ1; ▪, sample A, □, sample B, and +, sample C at ϑ from cross correlation.

Fig. 4
Fig. 4

Natural logarithms of experimental first-order correlation functions at sample B volume fraction. From autocorrelation at (a) λ1 = 514.5 nm and (b) λ2 = 488 nm and (c) from cross correlation.

Fig. 5
Fig. 5

Natural logarithms of experimental first-order correlation functions at stock volume fraction, from autocorrelations at (a) λ1 = 514.5 nm and (b) λ2 = 488 nm and (c) from cross correlation.

Equations (7)

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E α ( 2 ) ( r D α , t ) = j = 1 N l = 1 l j N 1 r j l × [ r ̂ D α × ( ̂ j l α ( 2 ) × r ̂ D α ) ] exp [ i ( k 0 α k j l α ) r j ] × exp [ i ( k j l α k f α ) r 1 ] exp ( ω α t ) .
E α ( r D α , 0 ) E α * ( r D α , τ ) = i = 1 k = 1 E α ( i ) ( r D α , 0 ) E α ( k ) * ( r D α , τ ) ,
E 1 ( r D 1 , 0 ) E 2 * ( r D 2 , τ ) = i = 1 k = 1 E 1 ( i ) ( r D 1 , 0 ) E 2 ( k ) * ( r D 2 , τ ) ,
E α ( 2 ) ( r D α , 0 ) E α ( 2 ) * ( r D α , τ ) = N ( N 1 ) × 1 r j l 2 [ r ̂ D α × ( ̂ j l α ( 2 ) × r ̂ d α ) ] 2 exp [ i ( k 0 α k j l α ) ( r j r j ) ] × exp [ i ( k j l α k f α ) ( r l r l ) ] exp ( i ω α τ ) ,
E 1 ( 2 ) ( r D 1 , 0 ) E 2 ( 2 ) * ( r D 2 , τ ) = N 1 ) × 1 r j l 2 [ r ̂ D 1 × ( ̂ j l 1 ( 2 ) × r ̂ D 1 ) ] [ r ̂ D 2 × ( ̂ j l 2 ( 2 ) × r ̂ D 2 ) ] × exp [ i ( k 01 k j l 1 ) ( r j r j ) ] exp [ i ( k j l 1 k f 1 ) ( r 1 r l ) ] × exp [ i ( Δ k 0 Δ k j l 1 ) r j l ] exp [ i ( ω 2 ω 1 ) t ] exp ( i ω 2 τ )
P = exp [ i ( Δ k 0 Δ k j l ) r j l ]
I 1 ( 0 ) I 2 ( τ ) / I 1 I 2 = 1 + β 2 | C ( 1 ) ( τ ) | 2 .

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