Abstract

The evaluation of conventional light-scattering experiments in turbid media is often highly complicated because of the presence of multiple scattering contributions. The three-dimensional (3-D) cross-correlation method presented provides an effective and handy method to suppress the influence of multiply scattered light. As the time dependence of the 3-D cross-correlation function is determined solely by the singly scattered light, the evaluation of the decay constant yields reliable values for the effective diffusion coefficient and the hydrodynamic particle size of the suspended particles. Furthermore, analysis of the amplitude of the 3-D cross-correlation function permits the determination of the differential scattering cross section even for highly turbid suspensions.

© 1998 Optical Society of America

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  1. B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1986).
  2. B. Chu, Laser Light Scattering, 2nd ed. (Academic, Boston, Mass., 1991).
  3. W. Brown, ed., Dynamic Light Scattering (Clarendon, Oxford, 1993).
  4. J. G. Shanks, J. V. Sengers, “Double scattering in critically opalescent fluids,” Phys. Rev. A 38, 885–896 (1988).
    [CrossRef] [PubMed]
  5. H. M. Booth, D. Bedeaux, P. Mazur, “On the theory of multiple scattering. II,” Physica 84A, 217–255 (1976).
  6. J. K. G. Dhont, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—general theory and static light scattering,” Physica 120A, 238–262 (1983).
  7. J. K. G. Dhont, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—dynamic light scattering,” Physica 129A, 374–394 (1985).
  8. R. A. Ferrell, J. K. Bhattacharjee, “Double-scattering correction for the critical dynamics of a classical fluid,” Phys. Rev. A 19, 348–369 (1979).
    [CrossRef]
  9. L. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light doubly scattered from a system of Brownian particles,” Phys. Rev. A. 14, 1520–1532 (1976).
    [CrossRef]
  10. A. E. Bailey, D. S. Cannell, “Practical method for calculation of multiple light scattering,” Phys. Rev. E 50, 4853–4864 (1994).
    [CrossRef]
  11. Y. Garrabos, G. Zalzer, D. Beysens, “High-resolution Rayleigh–Brillouin spectroscopy in the critical mixture nitroethane–isooctane,” Phys. Rev. A 25, 1147–1160 (1982).
    [CrossRef]
  12. R. F. Chang, H. Burstyn, J. V. Sengers, “Correlation function near the critical mixing point of a binary liquid,” Phys. Rev. A 19, 866–882 (1979).
    [CrossRef]
  13. P. N. Pusey, W. C. K. Poon, S. M. Ilett, P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
    [CrossRef]
  14. H. Güttinger, D. S. Cannell, “Correlation range and Rayleigh linewidth of xenon near the critical point,” Phys. Rev. A 22, 285–286 (1980).
    [CrossRef]
  15. H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
    [CrossRef]
  16. G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
    [CrossRef]
  17. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  18. K. Schätzel, “Suppression of multiple scattering by photon cross-correlation techniques,” J. Mod. Opt. 38, 1849–1865 (1991).
    [CrossRef]
  19. W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross-correlation,” Appl. Opt. 36, 7551–7557 (1997).
    [CrossRef]
  20. W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple scattering suppression by cross-correlation,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., Nato ASI Series (Kluwer, Dordrecht, The Netherlands, 1997), to be published.
  21. G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
    [CrossRef]
  22. G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
    [CrossRef]
  23. J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 17, 1658–1663 (1983).
    [CrossRef]
  24. 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]
  25. M. Drewel, J. Ahrens, U. Podschus, “Decorrelation of multiple scattering for an arbitrary scattering angle,” J. Opt. Soc. Am. A 7, 206–210 (1990).
    [CrossRef]
  26. P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
    [CrossRef]
  27. P. N. Segré, O. P. Behrend, P. N. Pusey, “Short time Brownian motion in colloidal suspensions: experimental and simulation,” Phys. Rev. E 52, 5070–5083 (1995).
    [CrossRef]
  28. E. Overbeck, C. Sinn, T. Palberg, “Approaching the limits of multiple scattering decorrelation: 3D light scattering apparatus utilising semiconductor lasers,” Prog. Colloid Polym. Sci. 104, 117–120 (1997).
    [CrossRef]
  29. C. Urban, P. Schurtenberg, “Dynamic light scattering in turbid suspensions: an application of different cross-correlation experiments,” Prog. Colloid Polym. Sci. (to be published).
  30. L. B. Aberle, S. Wiegand, W. Schröer, W. Staude, “Suppression of multiply scattered light by photon cross-correlation in a 3D experiment,” Prog. Colloid Polym. Sci. 104, 121–125 (1997).
    [CrossRef]
  31. Reports of this study have been given at various conferences, e.g., L. B. Aberle, S. Wiegand, W. Schröer, “Bestimmung von Teilchengrössen mit dynamischer Lichtstreuung,” presented at the Jahrestagung der Deutschen Bunsengesellschaft 1997, 8–10 May 1997, Darmstadt, Germany; L. B. Aberle, W. Schröer, W. Staude, “Determination of particle size and differential scattering cross-section by 3D-cross-correlation technique,” presented at the XIth Conference of the European Colloid and Interface Society, 14–19 September 1997, Lunteren, The Netherlands.
  32. P. N. Pusey, R. J. A. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985).
    [CrossRef]
  33. R. Klein, “Interacting Brownian particles: the dynamics of colloidal suspensions,” in Proceedings of the International School of Physics “Enrico Fermi” Course CXXXIV, F. Mallamace, H. E. Stanley, eds. (IOS Press, Amsterdam, 1997).
  34. J. Ric̆ka, “Dynamic light scattering with single mode and multimode receivers,” Appl. Opt. 32, 2860–2875 (1993).
    [CrossRef]
  35. L. M. Sorensen, G. A. Larsen, “Light scattering and viscosity studies of a ternary mixture with a double critical point,” J. Chem. Phys. 83, 1835–1842 (1985).
    [CrossRef]
  36. C. F. Bohren, D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  37. L. B. Bangs, “Uniform latex particles,” (Seragen Diagnostics, Indianapolis, Ind., 1984).
  38. R. C. Weast, ed., Handbook of Chemistry and Physics, 58th ed. (CRC, Cleveland, Ohio, 1977).
  39. P. N. Pusey, W. van Megen, “Detection of small polydispersities by photon correlation spectroscopy,” J. Chem. Phys. 80, 3513–3520 (1984).
    [CrossRef]
  40. P. N. Pusey, “Colloidal suspensions,” in Liquids, Freezing and Glass Transition, J. P. Hansen, D. Levesque, J. Zinn-Justin, eds., Les Houches Session LI (1989) (Elsevier, Amsterdam, 1991).
  41. E. v. d. Zeeuw, “Scanning angle reflectometry on colloid island films,” Ph.D. dissertation (Rijksuniversiteit te Leiden, Leiden, The Netherlands, 1996).
  42. J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
    [CrossRef]
  43. R. H. Ottewill, “Emulsion polymerization,” in Emulsion Polymerization, I. Piirma, ed. (Academic, San Diego, Calif., 1982).

1997

E. Overbeck, C. Sinn, T. Palberg, “Approaching the limits of multiple scattering decorrelation: 3D light scattering apparatus utilising semiconductor lasers,” Prog. Colloid Polym. Sci. 104, 117–120 (1997).
[CrossRef]

L. B. Aberle, S. Wiegand, W. Schröer, W. Staude, “Suppression of multiply scattered light by photon cross-correlation in a 3D experiment,” Prog. Colloid Polym. Sci. 104, 121–125 (1997).
[CrossRef]

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross-correlation,” Appl. Opt. 36, 7551–7557 (1997).
[CrossRef]

1996

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

1995

P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

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

1994

A. E. Bailey, D. S. Cannell, “Practical method for calculation of multiple light scattering,” Phys. Rev. E 50, 4853–4864 (1994).
[CrossRef]

P. N. Pusey, W. C. K. Poon, S. M. Ilett, P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

1993

1991

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

K. Schätzel, “Suppression of multiple scattering by photon cross-correlation techniques,” J. Mod. Opt. 38, 1849–1865 (1991).
[CrossRef]

1990

1988

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

J. G. Shanks, J. V. Sengers, “Double scattering in critically opalescent fluids,” Phys. Rev. A 38, 885–896 (1988).
[CrossRef] [PubMed]

1987

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (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]

1985

J. K. G. Dhont, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—dynamic light scattering,” Physica 129A, 374–394 (1985).

L. M. Sorensen, G. A. Larsen, “Light scattering and viscosity studies of a ternary mixture with a double critical point,” J. Chem. Phys. 83, 1835–1842 (1985).
[CrossRef]

1984

P. N. Pusey, W. van Megen, “Detection of small polydispersities by photon correlation spectroscopy,” J. Chem. Phys. 80, 3513–3520 (1984).
[CrossRef]

1983

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 17, 1658–1663 (1983).
[CrossRef]

J. K. G. Dhont, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—general theory and static light scattering,” Physica 120A, 238–262 (1983).

1982

Y. Garrabos, G. Zalzer, D. Beysens, “High-resolution Rayleigh–Brillouin spectroscopy in the critical mixture nitroethane–isooctane,” Phys. Rev. A 25, 1147–1160 (1982).
[CrossRef]

1981

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

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

1980

H. Güttinger, D. S. Cannell, “Correlation range and Rayleigh linewidth of xenon near the critical point,” Phys. Rev. A 22, 285–286 (1980).
[CrossRef]

1979

R. F. Chang, H. Burstyn, J. V. Sengers, “Correlation function near the critical mixing point of a binary liquid,” Phys. Rev. A 19, 866–882 (1979).
[CrossRef]

R. A. Ferrell, J. K. Bhattacharjee, “Double-scattering correction for the critical dynamics of a classical fluid,” Phys. Rev. A 19, 348–369 (1979).
[CrossRef]

1976

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

H. M. Booth, D. Bedeaux, P. Mazur, “On the theory of multiple scattering. II,” Physica 84A, 217–255 (1976).

Aberle, L. B.

L. B. Aberle, S. Wiegand, W. Schröer, W. Staude, “Suppression of multiply scattered light by photon cross-correlation in a 3D experiment,” Prog. Colloid Polym. Sci. 104, 121–125 (1997).
[CrossRef]

Reports of this study have been given at various conferences, e.g., L. B. Aberle, S. Wiegand, W. Schröer, “Bestimmung von Teilchengrössen mit dynamischer Lichtstreuung,” presented at the Jahrestagung der Deutschen Bunsengesellschaft 1997, 8–10 May 1997, Darmstadt, Germany; L. B. Aberle, W. Schröer, W. Staude, “Determination of particle size and differential scattering cross-section by 3D-cross-correlation technique,” presented at the XIth Conference of the European Colloid and Interface Society, 14–19 September 1997, Lunteren, The Netherlands.

Ahrens, J.

Bailey, A. E.

A. E. Bailey, D. S. Cannell, “Practical method for calculation of multiple light scattering,” Phys. Rev. E 50, 4853–4864 (1994).
[CrossRef]

Bangs, L. B.

L. B. Bangs, “Uniform latex particles,” (Seragen Diagnostics, Indianapolis, Ind., 1984).

Bartlett, P.

P. N. Pusey, W. C. K. Poon, S. M. Ilett, P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Bedeaux, D.

H. M. Booth, D. Bedeaux, P. Mazur, “On the theory of multiple scattering. II,” Physica 84A, 217–255 (1976).

Behrend, O. P.

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

Berne, B. J.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1986).

Beysens, D.

Y. Garrabos, G. Zalzer, D. Beysens, “High-resolution Rayleigh–Brillouin spectroscopy in the critical mixture nitroethane–isooctane,” Phys. Rev. A 25, 1147–1160 (1982).
[CrossRef]

Bhattacharjee, J. K.

R. A. Ferrell, J. K. Bhattacharjee, “Double-scattering correction for the critical dynamics of a classical fluid,” Phys. Rev. A 19, 348–369 (1979).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Booth, H. M.

H. M. Booth, D. Bedeaux, P. Mazur, “On the theory of multiple scattering. II,” Physica 84A, 217–255 (1976).

Burstyn, H.

R. F. Chang, H. Burstyn, J. V. Sengers, “Correlation function near the critical mixing point of a binary liquid,” Phys. Rev. A 19, 866–882 (1979).
[CrossRef]

Cannell, D. S.

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross-correlation,” Appl. Opt. 36, 7551–7557 (1997).
[CrossRef]

A. E. Bailey, D. S. Cannell, “Practical method for calculation of multiple light scattering,” Phys. Rev. E 50, 4853–4864 (1994).
[CrossRef]

H. Güttinger, D. S. Cannell, “Correlation range and Rayleigh linewidth of xenon near the critical point,” Phys. Rev. A 22, 285–286 (1980).
[CrossRef]

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple scattering suppression by cross-correlation,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., Nato ASI Series (Kluwer, Dordrecht, The Netherlands, 1997), to be published.

Chaikin, P. M.

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

Chang, R. F.

R. F. Chang, H. Burstyn, J. V. Sengers, “Correlation function near the critical mixing point of a binary liquid,” Phys. Rev. A 19, 866–882 (1979).
[CrossRef]

Chu, B.

B. Chu, Laser Light Scattering, 2nd ed. (Academic, Boston, Mass., 1991).

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. 17, 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, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—dynamic light scattering,” Physica 129A, 374–394 (1985).

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 17, 1658–1663 (1983).
[CrossRef]

J. K. G. Dhont, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—general theory and static light scattering,” Physica 120A, 238–262 (1983).

Drewel, M.

Ferrante, A.

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

Ferrell, R. A.

R. A. Ferrell, J. K. Bhattacharjee, “Double-scattering correction for the critical dynamics of a classical fluid,” Phys. Rev. A 19, 348–369 (1979).
[CrossRef]

Garrabos, Y.

Y. Garrabos, G. Zalzer, D. Beysens, “High-resolution Rayleigh–Brillouin spectroscopy in the critical mixture nitroethane–isooctane,” Phys. Rev. A 25, 1147–1160 (1982).
[CrossRef]

Gast, A. P.

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

Güttinger, H.

H. Güttinger, D. S. Cannell, “Correlation range and Rayleigh linewidth of xenon near the critical point,” Phys. Rev. A 22, 285–286 (1980).
[CrossRef]

Herbolzheimer, E.

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

Horn, D.

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

Huffmann, D. R.

C. F. Bohren, D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ilett, S. M.

P. N. Pusey, W. C. K. Poon, S. M. Ilett, P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Klein, R.

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

R. Klein, “Interacting Brownian particles: the dynamics of colloidal suspensions,” in Proceedings of the International School of Physics “Enrico Fermi” Course CXXXIV, F. Mallamace, H. E. Stanley, eds. (IOS Press, Amsterdam, 1997).

Larsen, G. A.

L. M. Sorensen, G. A. Larsen, “Light scattering and viscosity studies of a ternary mixture with a double critical point,” J. Chem. Phys. 83, 1835–1842 (1985).
[CrossRef]

Mandl-Steininger, B.

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

Maret, G.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Mazur, P.

H. M. Booth, D. Bedeaux, P. Mazur, “On the theory of multiple scattering. II,” Physica 84A, 217–255 (1976).

Meyer, W. V.

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross-correlation,” Appl. Opt. 36, 7551–7557 (1997).
[CrossRef]

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple scattering suppression by cross-correlation,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., Nato ASI Series (Kluwer, Dordrecht, The Netherlands, 1997), to be published.

Mockler, R. C.

L. M. Sorensen, R. C. Mockler, W. J. O’Sullivan, “Depolarized correlation function of light doubly 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]

Nägele, G.

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

O’Sullivan, W. J.

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

Ottewill, R. H.

R. H. Ottewill, “Emulsion polymerization,” in Emulsion Polymerization, I. Piirma, ed. (Academic, San Diego, Calif., 1982).

Overbeck, E.

E. Overbeck, C. Sinn, T. Palberg, “Approaching the limits of multiple scattering decorrelation: 3D light scattering apparatus utilising semiconductor lasers,” Prog. Colloid Polym. Sci. 104, 117–120 (1997).
[CrossRef]

Palberg, T.

E. Overbeck, C. Sinn, T. Palberg, “Approaching the limits of multiple scattering decorrelation: 3D light scattering apparatus utilising semiconductor lasers,” Prog. Colloid Polym. Sci. 104, 117–120 (1997).
[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]

Pecora, R.

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1986).

Peters, W.

P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

Phalakornkul, J. K.

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[CrossRef]

Phillies, G. D. J.

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

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

Podschus, U.

Poon, W. C. K.

P. N. Pusey, W. C. K. Poon, S. M. Ilett, P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Pusey, P. N.

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

P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

P. N. Pusey, W. C. K. Poon, S. M. Ilett, P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

P. N. Pusey, W. van Megen, “Detection of small polydispersities by photon correlation spectroscopy,” J. Chem. Phys. 80, 3513–3520 (1984).
[CrossRef]

P. N. Pusey, R. J. A. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985).
[CrossRef]

P. N. Pusey, “Colloidal suspensions,” in Liquids, Freezing and Glass Transition, J. P. Hansen, D. Levesque, J. Zinn-Justin, eds., Les Houches Session LI (1989) (Elsevier, Amsterdam, 1991).

Ric?ka, J.

Schätzel, K.

P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

K. Schätzel, “Suppression of multiple scattering by photon cross-correlation techniques,” J. Mod. Opt. 38, 1849–1865 (1991).
[CrossRef]

Schröer, W.

L. B. Aberle, S. Wiegand, W. Schröer, W. Staude, “Suppression of multiply scattered light by photon cross-correlation in a 3D experiment,” Prog. Colloid Polym. Sci. 104, 121–125 (1997).
[CrossRef]

Reports of this study have been given at various conferences, e.g., L. B. Aberle, S. Wiegand, W. Schröer, “Bestimmung von Teilchengrössen mit dynamischer Lichtstreuung,” presented at the Jahrestagung der Deutschen Bunsengesellschaft 1997, 8–10 May 1997, Darmstadt, Germany; L. B. Aberle, W. Schröer, W. Staude, “Determination of particle size and differential scattering cross-section by 3D-cross-correlation technique,” presented at the XIth Conference of the European Colloid and Interface Society, 14–19 September 1997, Lunteren, The Netherlands.

Schurtenberg, P.

C. Urban, P. Schurtenberg, “Dynamic light scattering in turbid suspensions: an application of different cross-correlation experiments,” Prog. Colloid Polym. Sci. (to be published).

Segré, P. N.

P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

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

Sengers, J. V.

J. G. Shanks, J. V. Sengers, “Double scattering in critically opalescent fluids,” Phys. Rev. A 38, 885–896 (1988).
[CrossRef] [PubMed]

R. F. Chang, H. Burstyn, J. V. Sengers, “Correlation function near the critical mixing point of a binary liquid,” Phys. Rev. A 19, 866–882 (1979).
[CrossRef]

Shanks, J. G.

J. G. Shanks, J. V. Sengers, “Double scattering in critically opalescent fluids,” Phys. Rev. A 38, 885–896 (1988).
[CrossRef] [PubMed]

Sinn, C.

E. Overbeck, C. Sinn, T. Palberg, “Approaching the limits of multiple scattering decorrelation: 3D light scattering apparatus utilising semiconductor lasers,” Prog. Colloid Polym. Sci. 104, 117–120 (1997).
[CrossRef]

Smart, A. E.

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross-correlation,” Appl. Opt. 36, 7551–7557 (1997).
[CrossRef]

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple scattering suppression by cross-correlation,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., Nato ASI Series (Kluwer, Dordrecht, The Netherlands, 1997), to be published.

Sorensen, L. M.

L. M. Sorensen, G. A. Larsen, “Light scattering and viscosity studies of a ternary mixture with a double critical point,” J. Chem. Phys. 83, 1835–1842 (1985).
[CrossRef]

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

Staude, W.

L. B. Aberle, S. Wiegand, W. Schröer, W. Staude, “Suppression of multiply scattered light by photon cross-correlation in a 3D experiment,” Prog. Colloid Polym. Sci. 104, 121–125 (1997).
[CrossRef]

Taylor, T. W.

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross-correlation,” Appl. Opt. 36, 7551–7557 (1997).
[CrossRef]

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple scattering suppression by cross-correlation,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., Nato ASI Series (Kluwer, Dordrecht, The Netherlands, 1997), to be published.

Tin, P.

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross-correlation,” Appl. Opt. 36, 7551–7557 (1997).
[CrossRef]

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple scattering suppression by cross-correlation,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., Nato ASI Series (Kluwer, Dordrecht, The Netherlands, 1997), to be published.

Tough, R. J. A.

P. N. Pusey, R. J. A. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985).
[CrossRef]

Urban, C.

C. Urban, P. Schurtenberg, “Dynamic light scattering in turbid suspensions: an application of different cross-correlation experiments,” Prog. Colloid Polym. Sci. (to be published).

van Megen, W.

P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

P. N. Pusey, W. van Megen, “Detection of small polydispersities by photon correlation spectroscopy,” J. Chem. Phys. 80, 3513–3520 (1984).
[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).
[CrossRef] [PubMed]

Wiegand, S.

L. B. Aberle, S. Wiegand, W. Schröer, W. Staude, “Suppression of multiply scattered light by photon cross-correlation in a 3D experiment,” Prog. Colloid Polym. Sci. 104, 121–125 (1997).
[CrossRef]

Reports of this study have been given at various conferences, e.g., L. B. Aberle, S. Wiegand, W. Schröer, “Bestimmung von Teilchengrössen mit dynamischer Lichtstreuung,” presented at the Jahrestagung der Deutschen Bunsengesellschaft 1997, 8–10 May 1997, Darmstadt, Germany; L. B. Aberle, W. Schröer, W. Staude, “Determination of particle size and differential scattering cross-section by 3D-cross-correlation technique,” presented at the XIth Conference of the European Colloid and Interface Society, 14–19 September 1997, Lunteren, The Netherlands.

Wiese, H.

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

Wolf, P. E.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Zalzer, G.

Y. Garrabos, G. Zalzer, D. Beysens, “High-resolution Rayleigh–Brillouin spectroscopy in the critical mixture nitroethane–isooctane,” Phys. Rev. A 25, 1147–1160 (1982).
[CrossRef]

Zeeuw, E. v. d.

E. v. d. Zeeuw, “Scanning angle reflectometry on colloid island films,” Ph.D. dissertation (Rijksuniversiteit te Leiden, Leiden, The Netherlands, 1996).

Appl. Opt.

J. Chem. Phys.

G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy 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. 17, 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]

L. M. Sorensen, G. A. Larsen, “Light scattering and viscosity studies of a ternary mixture with a double critical point,” J. Chem. Phys. 83, 1835–1842 (1985).
[CrossRef]

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

P. N. Pusey, W. van Megen, “Detection of small polydispersities by photon correlation spectroscopy,” J. Chem. Phys. 80, 3513–3520 (1984).
[CrossRef]

J. Mod. Opt.

K. Schätzel, “Suppression of multiple scattering by photon cross-correlation techniques,” J. Mod. Opt. 38, 1849–1865 (1991).
[CrossRef]

P. N. Segré, W. van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-colour dynamic light scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Condens. Matter

P. N. Pusey, W. C. K. Poon, S. M. Ilett, P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Phys. Rev. A

H. Güttinger, D. S. Cannell, “Correlation range and Rayleigh linewidth of xenon near the critical point,” Phys. Rev. A 22, 285–286 (1980).
[CrossRef]

Y. Garrabos, G. Zalzer, D. Beysens, “High-resolution Rayleigh–Brillouin spectroscopy in the critical mixture nitroethane–isooctane,” Phys. Rev. A 25, 1147–1160 (1982).
[CrossRef]

R. F. Chang, H. Burstyn, J. V. Sengers, “Correlation function near the critical mixing point of a binary liquid,” Phys. Rev. A 19, 866–882 (1979).
[CrossRef]

J. G. Shanks, J. V. Sengers, “Double scattering in critically opalescent fluids,” Phys. Rev. A 38, 885–896 (1988).
[CrossRef] [PubMed]

R. A. Ferrell, J. K. Bhattacharjee, “Double-scattering correction for the critical dynamics of a classical fluid,” Phys. Rev. A 19, 348–369 (1979).
[CrossRef]

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

Phys. Rev. A.

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

Phys. Rev. E

A. E. Bailey, D. S. Cannell, “Practical method for calculation of multiple light scattering,” Phys. Rev. E 50, 4853–4864 (1994).
[CrossRef]

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

J. K. Phalakornkul, A. P. Gast, R. Pecora, G. Nägele, A. Ferrante, B. Mandl-Steininger, R. Klein, “Structure and short time dynamics of polydisperse charge stabilized suspensions,” Phys. Rev. E 54, 661–675 (1996).
[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).
[CrossRef] [PubMed]

Physica

H. M. Booth, D. Bedeaux, P. Mazur, “On the theory of multiple scattering. II,” Physica 84A, 217–255 (1976).

J. K. G. Dhont, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—general theory and static light scattering,” Physica 120A, 238–262 (1983).

J. K. G. Dhont, “Multiple Rayleigh–Gans–Debye scattering in colloidal systems—dynamic light scattering,” Physica 129A, 374–394 (1985).

Prog. Colloid Polym. Sci.

E. Overbeck, C. Sinn, T. Palberg, “Approaching the limits of multiple scattering decorrelation: 3D light scattering apparatus utilising semiconductor lasers,” Prog. Colloid Polym. Sci. 104, 117–120 (1997).
[CrossRef]

L. B. Aberle, S. Wiegand, W. Schröer, W. Staude, “Suppression of multiply scattered light by photon cross-correlation in a 3D experiment,” Prog. Colloid Polym. Sci. 104, 121–125 (1997).
[CrossRef]

Z. Phys. B

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Other

P. N. Pusey, “Colloidal suspensions,” in Liquids, Freezing and Glass Transition, J. P. Hansen, D. Levesque, J. Zinn-Justin, eds., Les Houches Session LI (1989) (Elsevier, Amsterdam, 1991).

E. v. d. Zeeuw, “Scanning angle reflectometry on colloid island films,” Ph.D. dissertation (Rijksuniversiteit te Leiden, Leiden, The Netherlands, 1996).

R. H. Ottewill, “Emulsion polymerization,” in Emulsion Polymerization, I. Piirma, ed. (Academic, San Diego, Calif., 1982).

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple scattering suppression by cross-correlation,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., Nato ASI Series (Kluwer, Dordrecht, The Netherlands, 1997), to be published.

Reports of this study have been given at various conferences, e.g., L. B. Aberle, S. Wiegand, W. Schröer, “Bestimmung von Teilchengrössen mit dynamischer Lichtstreuung,” presented at the Jahrestagung der Deutschen Bunsengesellschaft 1997, 8–10 May 1997, Darmstadt, Germany; L. B. Aberle, W. Schröer, W. Staude, “Determination of particle size and differential scattering cross-section by 3D-cross-correlation technique,” presented at the XIth Conference of the European Colloid and Interface Society, 14–19 September 1997, Lunteren, The Netherlands.

P. N. Pusey, R. J. A. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985).
[CrossRef]

R. Klein, “Interacting Brownian particles: the dynamics of colloidal suspensions,” in Proceedings of the International School of Physics “Enrico Fermi” Course CXXXIV, F. Mallamace, H. E. Stanley, eds. (IOS Press, Amsterdam, 1997).

C. F. Bohren, D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

L. B. Bangs, “Uniform latex particles,” (Seragen Diagnostics, Indianapolis, Ind., 1984).

R. C. Weast, ed., Handbook of Chemistry and Physics, 58th ed. (CRC, Cleveland, Ohio, 1977).

C. Urban, P. Schurtenberg, “Dynamic light scattering in turbid suspensions: an application of different cross-correlation experiments,” Prog. Colloid Polym. Sci. (to be published).

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1986).

B. Chu, Laser Light Scattering, 2nd ed. (Academic, Boston, Mass., 1991).

W. Brown, ed., Dynamic Light Scattering (Clarendon, Oxford, 1993).

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Figures (11)

Fig. 1
Fig. 1

Scattering geometry of the 3-D DLS-method. The directions of the illuminating laser beams are given by the wave vectors k1 and k2; while k A and k B denote the detected components of the scattered light intensity received by detectors A and B, respectively. Scattering vector q is identical for scattering geometries (k1 → k A ) and (k2 → k B ).

Fig. 2
Fig. 2

Sketch of the scattering volume. The overlapping volume of the two illuminating light beams with radius r is the double cone surrounded by the thick lines. The acceptance area of the detection optics is indicated by the gray circle.

Fig. 3
Fig. 3

Schematic drawing of the 3-D DLS setup. A description is given in the text.

Fig. 4
Fig. 4

Cross-correlation (○, □) and autocorrelation (●, ■ functions: The measurements were performed on suspensions containing spherical polystyrene particles with a diameter of 107 nm (EM). The transmission for the strongly scattering and the highly diluted sample were 0.7% (□, ■) and 97.1% (○, ●, respectively. The values refer to 1-cm path length of the light in the sample cell.

Fig. 5
Fig. 5

Intensity ratio 〈i D o (θ)〉/〈i D o (0°)〉 of the scattered light of highly diluted suspensions (transmission, ≥90%) of polystyrene spheres for various particle diameters, specified by EM (□, 107 nm; △, 236 nm; ▽, 453 nm; ◇, 481 nm). We also include the measurements of a sample of 3-methylpyridine/D2O (●), which we used to determine the angular dependence of the effective scattering volume V eff(θ). Solid curves, calculated with Mie theory,36 which yield particle diameters of 105 ± 3 nm (□), 240 ± 2 nm (△), 464 ± 19 nm (▽), and 514 ± 24 nm (◇), respectively.

Fig. 6
Fig. 6

Determination of factor A(θ) from measurements of amplitude R(θ) of the cross-correlation function of solutions containing 69-nm (EM) latex particles. The data show a variation with scattering angle θ caused by the overlap mismatch. Solid curves, fits according to Eq. (18).

Fig. 7
Fig. 7

Intensity density 〈i D o (θ)〉 of the light scattered by suspensions containing 453-nm (EM) latex particles [Eqs. (14) and (15)]. The transmissions of the samples are 1.7% (◆), 11.9% (▼), 36.0% (▲), 66.3% (■), and 89.0% (●).

Fig. 8
Fig. 8

Intensity ratio R o (θ) [Eq. (15)] of single to total scattering intensity. R o (θ) is obtained from amplitude R(θ) of the cross-correlation function corrected for the angular dependence of the overlap mismatch. The transmissions and the corresponding labels are the same as in Fig. 7.

Fig. 9
Fig. 9

The differential scattering cross section σ(θ) of 453-nm (EM) particles as obtained from the product of amplitude R o (θ) of the 3-D cross-correlation function and the scattered intensity density 〈i D o (θ)〉 according to Eqs. (14) and (15). Solid curve, Mie calculation,36 which yields a particle diameter of 464 ± 19 nm. The transmissions of the samples are 1.7% (◇), 11.9% (▽), 36.0% (△), 66.3% (□), and 89.0% (○).

Fig. 10
Fig. 10

Apparent particle sizes a cross and a auto determined from (A) cross-correlation and (B) autocorrelation functions as a function of scattering angle θ for various particle concentrations. Whereas the evaluation of the cross-correlation function yields a particle diameter of 103 ± 5 nm that is in fair agreement with the value given by the manufacturer [107 nm (EM)], the evaluation of the autocorrelation functions yields an erroneous dependence of the scattering angle and the particle concentration.

Fig. 11
Fig. 11

Hydrodynamic particle size determined from the cross-correlation functions as a function of the scattering angle for samples containing 453-nm (EM) latex particles. The transmissions of the samples are 36.0% (●) and 1.7% (▲). For clarity we inserted solid curves to guide the eye.

Tables (1)

Tables Icon

Table 1 Particle Sizesa

Equations (18)

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

I 0 I τ = I 2 + | E s 0 E s * τ + E m 0 E m * τ | 2 ,
k 1 - k A = k 2 - k B = q .
E A t = E A 1 s t + E A 2 s t + E A 1 m t + E A 2 m t .
I A 0 I B τ = I A 1 s 0 I B 2 s τ - I A 1 s I B 2 s + I A 1 + I A 2   *   I B 1 + I B 2 .
I A 1 s 0 I B 2 s τ = I A 1 s I B 2 s 1 + | A   G τ | 2 ,
G τ = E s 0 E s * τ E s t E s * t .
G τ ,   q = exp - Γ q τ ,
D eff q = D o H q S q ,
D o = k B T 3 π   η T   a = P st a ,
I A 0 I B τ I A I B = 1 + I A 1 s I B 2 s I A I B   | A   G τ | 2 .
R 2 = A 2 I A 1 s I B 2 s I A I B     A 2 I s 2 r i I D 2     A 2 1 1 + r s 2 r i 1 + r i 2 ,
I s θ = I D θ   R θ A θ r i ,
I s θ d Ω = σ θ cV eff θ exp - c σ tot l θ I L L 2 d Ω ,
σ θ d Ω = I D θ exp c σ tot l V eff θ R θ A θ r i L 2 d Ω I L c
= i D o θ R o θ L 2 d Ω I L c ,
= i o s θ   L 2 d Ω I L c ,
A θ = A D β ovl θ ,
β ovl θ     B   +   C sin θ + D sin 2 θ ,

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