Abstract

Near-infrared, frequency-domain photon migration measurements of phase shift are used to derive accurate values of isotropic scattering coefficients in concentrated, interacting suspensions of aqueous polystyrene microspheres with volume concentrations ranging from 1% to 45% by solids and mean diameters ranging from 135 to 500 nm. Under conditions of high ionic strength, the isotropic scattering coefficient can be quantitatively predicted by the Percus–Yevick model for hard-sphere interactions and Mie theory. In addition, the attractive interactions between scatterers arising from the addition of soluble poly(ethylene glycol) with molecular weights of 100 and 600 K cause hindered scattering. The increases in static structure and decreases in isotropic scattering coefficient agree with that predicted by Mie theory and the depletion interaction model developed by Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)]. These results demonstrate the success of monitoring interaction between particles by use of multiple-scattered light and the necessity of incorporating models for these interactions when predicting scattering of dense, concentrated suspensions.

© 1999 Optical Society of America

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References

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  1. Allen Terence, Particle Size Measurement, 5th ed. (Chapman & Hall, London, 1997).
  2. E. M. Sevick-Muraca, “A review on coupling particle size measurements for control and monitoring of particulate processes,” (International Fine Particle Research Institute, Inc., Cheshire, UK, 1997).
  3. C. F. Riebel, F. Loffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
    [CrossRef]
  4. J. Coghill, M. J. Millen, B. D. Sowerby, “On-line particle size analysis using ultrasonic velocity spectrometry,” Part. Part. Syst. Charact. 14, 116–121 (1997).
  5. W. O’Brien, “Electro-acoustic effects in a dilute suspension of spherical particles,” J. Fluid Mech. 1990, 71–86 (1988).
    [CrossRef]
  6. W. O’Brien, “The electroacoustic equations for a colloidal suspension,” J. Fluid Mech. 212, 81–93 (1990).
    [CrossRef]
  7. S. M. Richter, R. R. Shinde, G. V. Balgi, E. M. Sevick-Muraca, “Particle sizing using frequency-domain photon migration,” Part. Part. Syst. Charact. 15, 9–16 (1998).
    [CrossRef]
  8. G. V. Balgi, E. M. Sevick-Muraca, “Characterization of particulate systems through frequency-domain measurements of photon migration,” presented at the OSA Annual Meeting, Orlando, Florida, 1998 (Optical Society of America, Washington, D.C.).
  9. G. V. Balgi, J. Pierce, J. Reynolds, R. Mayer, E. M. Sevick-Muraca, “Frequency domain photon migration,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.
  10. R. J. Hunter, Foundations of Colloidal Science (Clarendon, Oxford, 1995), Vol. II.
  11. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  12. W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
    [CrossRef]
  13. S. Asakura, F. Oosawa, “On interaction between two bodies immersed in a solution of macromolecules,” J. Chem. Phys. 22, 1255–1256 (1954).
    [CrossRef]
  14. H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
    [CrossRef]
  15. J. Fishkin, T. C. Peter So, Albert E. Cerussi, S. Fantini, M. A. Franceschini, E. Gratton, “Frequency-domain method for measuring spectral properties in multiple-scattering media: methemoglobin absorption spectrum in a tissue-like phantom,” Appl. Opt. 34, 1143–1155 (1995).
  16. J. E. Pierce, “Particle sizing in concentrated suspensions using frequency domain photon migration techniques,” M.S. thesis (Purdue University, West Lafayette, Indiana, 1997).
  17. E. J. Rohm, K. D. Horner, M. Ballauff, “Interactions in mixtures of latex particles and polymers as revealed by turbidimetry,” Colloid Polym. Sci. 274, 732–740 (1996).
    [CrossRef]
  18. S. Banerjee, R. Shinde, E. M. Sevick-Muraca, “Depletion interactions in colloid-polymer mixtures as studied by photon migration,” J. Colloid Interface Sci. (to be published).
  19. P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatter correlation effects on photon migration transport in dense random media,” Phys. Rev. B Rapid Commun. 42, 2621–2623 (1990).
    [CrossRef]
  20. S. Fraden, G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
    [CrossRef] [PubMed]
  21. P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
    [CrossRef] [PubMed]
  22. P. D. Kaplan, A. D. Dinsmore, A. G. Yodh, D. J. Pine, “Diffuse-transmission spectroscopy: a structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827–4835 (1994).
    [CrossRef]
  23. R. Garg, R. K. Prud’homme, I. A. Aksay, F. Liu, R. R. Alfano, “Optical transmission in highly concentrated dispersion,” J. Opt. Soc. Am. A 15, 932–935 (1998).
    [CrossRef]
  24. E. Dickinson, “Creaming, flocculation and rheology,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.
  25. A. Brisson, G. L.’Espèrance, M. Caron, “Use of image analysis technique to quantify pigment dispersion,” J. Coatings Tech. 63, 111–118 (1991).
  26. M. A. Brown, A. L. Smith, E. J. Staples, “A method using total internal reflection microscopy and radiation pressure to study weak interaction forces of particles near surfaces,” Langmuir 5, 1319–1324 (1989).
    [CrossRef]
  27. J. Israelachvilli, Intermolecular and Surface Forces (Academic, London, 1992).

1998 (2)

S. M. Richter, R. R. Shinde, G. V. Balgi, E. M. Sevick-Muraca, “Particle sizing using frequency-domain photon migration,” Part. Part. Syst. Charact. 15, 9–16 (1998).
[CrossRef]

R. Garg, R. K. Prud’homme, I. A. Aksay, F. Liu, R. R. Alfano, “Optical transmission in highly concentrated dispersion,” J. Opt. Soc. Am. A 15, 932–935 (1998).
[CrossRef]

1997 (1)

J. Coghill, M. J. Millen, B. D. Sowerby, “On-line particle size analysis using ultrasonic velocity spectrometry,” Part. Part. Syst. Charact. 14, 116–121 (1997).

1996 (2)

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

E. J. Rohm, K. D. Horner, M. Ballauff, “Interactions in mixtures of latex particles and polymers as revealed by turbidimetry,” Colloid Polym. Sci. 274, 732–740 (1996).
[CrossRef]

1995 (1)

1994 (1)

P. D. Kaplan, A. D. Dinsmore, A. G. Yodh, D. J. Pine, “Diffuse-transmission spectroscopy: a structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827–4835 (1994).
[CrossRef]

1992 (2)

H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

1991 (1)

A. Brisson, G. L.’Espèrance, M. Caron, “Use of image analysis technique to quantify pigment dispersion,” J. Coatings Tech. 63, 111–118 (1991).

1990 (3)

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatter correlation effects on photon migration transport in dense random media,” Phys. Rev. B Rapid Commun. 42, 2621–2623 (1990).
[CrossRef]

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

W. O’Brien, “The electroacoustic equations for a colloidal suspension,” J. Fluid Mech. 212, 81–93 (1990).
[CrossRef]

1989 (2)

C. F. Riebel, F. Loffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
[CrossRef]

M. A. Brown, A. L. Smith, E. J. Staples, “A method using total internal reflection microscopy and radiation pressure to study weak interaction forces of particles near surfaces,” Langmuir 5, 1319–1324 (1989).
[CrossRef]

1988 (1)

W. O’Brien, “Electro-acoustic effects in a dilute suspension of spherical particles,” J. Fluid Mech. 1990, 71–86 (1988).
[CrossRef]

1954 (1)

S. Asakura, F. Oosawa, “On interaction between two bodies immersed in a solution of macromolecules,” J. Chem. Phys. 22, 1255–1256 (1954).
[CrossRef]

Aksay, I. A.

Alfano, R. R.

Asakura, S.

S. Asakura, F. Oosawa, “On interaction between two bodies immersed in a solution of macromolecules,” J. Chem. Phys. 22, 1255–1256 (1954).
[CrossRef]

Balgi, G. V.

S. M. Richter, R. R. Shinde, G. V. Balgi, E. M. Sevick-Muraca, “Particle sizing using frequency-domain photon migration,” Part. Part. Syst. Charact. 15, 9–16 (1998).
[CrossRef]

G. V. Balgi, J. Pierce, J. Reynolds, R. Mayer, E. M. Sevick-Muraca, “Frequency domain photon migration,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.

G. V. Balgi, E. M. Sevick-Muraca, “Characterization of particulate systems through frequency-domain measurements of photon migration,” presented at the OSA Annual Meeting, Orlando, Florida, 1998 (Optical Society of America, Washington, D.C.).

Ballauff, M.

E. J. Rohm, K. D. Horner, M. Ballauff, “Interactions in mixtures of latex particles and polymers as revealed by turbidimetry,” Colloid Polym. Sci. 274, 732–740 (1996).
[CrossRef]

Banerjee, S.

S. Banerjee, R. Shinde, E. M. Sevick-Muraca, “Depletion interactions in colloid-polymer mixtures as studied by photon migration,” J. Colloid Interface Sci. (to be published).

Brisson, A.

A. Brisson, G. L.’Espèrance, M. Caron, “Use of image analysis technique to quantify pigment dispersion,” J. Coatings Tech. 63, 111–118 (1991).

Brown, M. A.

M. A. Brown, A. L. Smith, E. J. Staples, “A method using total internal reflection microscopy and radiation pressure to study weak interaction forces of particles near surfaces,” Langmuir 5, 1319–1324 (1989).
[CrossRef]

Caron, M.

A. Brisson, G. L.’Espèrance, M. Caron, “Use of image analysis technique to quantify pigment dispersion,” J. Coatings Tech. 63, 111–118 (1991).

Carvalho, B. L.

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

Cerussi, Albert E.

Coghill, J.

J. Coghill, M. J. Millen, B. D. Sowerby, “On-line particle size analysis using ultrasonic velocity spectrometry,” Part. Part. Syst. Charact. 14, 116–121 (1997).

Dickinson, E.

E. Dickinson, “Creaming, flocculation and rheology,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.

Dinsmore, A. D.

P. D. Kaplan, A. D. Dinsmore, A. G. Yodh, D. J. Pine, “Diffuse-transmission spectroscopy: a structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827–4835 (1994).
[CrossRef]

Fantini, S.

Fetters, L. J.

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

Fishkin, J.

Fraden, S.

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

Franceschini, M. A.

Garg, R.

Gratton, E.

Horner, K. D.

E. J. Rohm, K. D. Horner, M. Ballauff, “Interactions in mixtures of latex particles and polymers as revealed by turbidimetry,” Colloid Polym. Sci. 274, 732–740 (1996).
[CrossRef]

Huang, J. S.

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

Hunter, R. J.

R. J. Hunter, Foundations of Colloidal Science (Clarendon, Oxford, 1995), Vol. II.

Israelachvilli, J.

J. Israelachvilli, Intermolecular and Surface Forces (Academic, London, 1992).

Kaplan, P. D.

P. D. Kaplan, A. D. Dinsmore, A. G. Yodh, D. J. Pine, “Diffuse-transmission spectroscopy: a structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827–4835 (1994).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

L.’Espèrance, G.

A. Brisson, G. L.’Espèrance, M. Caron, “Use of image analysis technique to quantify pigment dispersion,” J. Coatings Tech. 63, 111–118 (1991).

Lekkerkerker, H. N. W.

H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
[CrossRef]

Lin, M. Y.

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

Liu, F.

Loffler, F.

C. F. Riebel, F. Loffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
[CrossRef]

Maret, G.

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

Mayer, R.

G. V. Balgi, J. Pierce, J. Reynolds, R. Mayer, E. M. Sevick-Muraca, “Frequency domain photon migration,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.

Millen, M. J.

J. Coghill, M. J. Millen, B. D. Sowerby, “On-line particle size analysis using ultrasonic velocity spectrometry,” Part. Part. Syst. Charact. 14, 116–121 (1997).

Narayanan, T.

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

O’Brien, W.

W. O’Brien, “The electroacoustic equations for a colloidal suspension,” J. Fluid Mech. 212, 81–93 (1990).
[CrossRef]

W. O’Brien, “Electro-acoustic effects in a dilute suspension of spherical particles,” J. Fluid Mech. 1990, 71–86 (1988).
[CrossRef]

Oosawa, F.

S. Asakura, F. Oosawa, “On interaction between two bodies immersed in a solution of macromolecules,” J. Chem. Phys. 22, 1255–1256 (1954).
[CrossRef]

Peter So, T. C.

Pierce, J.

G. V. Balgi, J. Pierce, J. Reynolds, R. Mayer, E. M. Sevick-Muraca, “Frequency domain photon migration,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.

Pierce, J. E.

J. E. Pierce, “Particle sizing in concentrated suspensions using frequency domain photon migration techniques,” M.S. thesis (Purdue University, West Lafayette, Indiana, 1997).

Pine, D. J.

P. D. Kaplan, A. D. Dinsmore, A. G. Yodh, D. J. Pine, “Diffuse-transmission spectroscopy: a structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827–4835 (1994).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Poon, W. C. K.

H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
[CrossRef]

Prud’homme, R. K.

Pusey, P. N.

H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
[CrossRef]

Reynolds, J.

G. V. Balgi, J. Pierce, J. Reynolds, R. Mayer, E. M. Sevick-Muraca, “Frequency domain photon migration,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.

Richter, S. M.

S. M. Richter, R. R. Shinde, G. V. Balgi, E. M. Sevick-Muraca, “Particle sizing using frequency-domain photon migration,” Part. Part. Syst. Charact. 15, 9–16 (1998).
[CrossRef]

Riebel, C. F.

C. F. Riebel, F. Loffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
[CrossRef]

Rohm, E. J.

E. J. Rohm, K. D. Horner, M. Ballauff, “Interactions in mixtures of latex particles and polymers as revealed by turbidimetry,” Colloid Polym. Sci. 274, 732–740 (1996).
[CrossRef]

Saulnier, P. M.

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatter correlation effects on photon migration transport in dense random media,” Phys. Rev. B Rapid Commun. 42, 2621–2623 (1990).
[CrossRef]

Sevick-Muraca, E. M.

S. M. Richter, R. R. Shinde, G. V. Balgi, E. M. Sevick-Muraca, “Particle sizing using frequency-domain photon migration,” Part. Part. Syst. Charact. 15, 9–16 (1998).
[CrossRef]

E. M. Sevick-Muraca, “A review on coupling particle size measurements for control and monitoring of particulate processes,” (International Fine Particle Research Institute, Inc., Cheshire, UK, 1997).

G. V. Balgi, J. Pierce, J. Reynolds, R. Mayer, E. M. Sevick-Muraca, “Frequency domain photon migration,” presented at the American Institute of Chemical Engineers 1997 Annual Meeting, Los Angeles, Calif., 16–21 November 1997.

G. V. Balgi, E. M. Sevick-Muraca, “Characterization of particulate systems through frequency-domain measurements of photon migration,” presented at the OSA Annual Meeting, Orlando, Florida, 1998 (Optical Society of America, Washington, D.C.).

S. Banerjee, R. Shinde, E. M. Sevick-Muraca, “Depletion interactions in colloid-polymer mixtures as studied by photon migration,” J. Colloid Interface Sci. (to be published).

Shinde, R.

S. Banerjee, R. Shinde, E. M. Sevick-Muraca, “Depletion interactions in colloid-polymer mixtures as studied by photon migration,” J. Colloid Interface Sci. (to be published).

Shinde, R. R.

S. M. Richter, R. R. Shinde, G. V. Balgi, E. M. Sevick-Muraca, “Particle sizing using frequency-domain photon migration,” Part. Part. Syst. Charact. 15, 9–16 (1998).
[CrossRef]

Smith, A. L.

M. A. Brown, A. L. Smith, E. J. Staples, “A method using total internal reflection microscopy and radiation pressure to study weak interaction forces of particles near surfaces,” Langmuir 5, 1319–1324 (1989).
[CrossRef]

Sowerby, B. D.

J. Coghill, M. J. Millen, B. D. Sowerby, “On-line particle size analysis using ultrasonic velocity spectrometry,” Part. Part. Syst. Charact. 14, 116–121 (1997).

Staples, E. J.

M. A. Brown, A. L. Smith, E. J. Staples, “A method using total internal reflection microscopy and radiation pressure to study weak interaction forces of particles near surfaces,” Langmuir 5, 1319–1324 (1989).
[CrossRef]

Stroobants, A.

H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
[CrossRef]

Terence, Allen

Allen Terence, Particle Size Measurement, 5th ed. (Chapman & Hall, London, 1997).

Tong, P.

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

Warren, P. B.

H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
[CrossRef]

Watson, G. H.

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatter correlation effects on photon migration transport in dense random media,” Phys. Rev. B Rapid Commun. 42, 2621–2623 (1990).
[CrossRef]

Ye, W.

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

Yodh, A. G.

P. D. Kaplan, A. D. Dinsmore, A. G. Yodh, D. J. Pine, “Diffuse-transmission spectroscopy: a structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827–4835 (1994).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Zinkin, M. P.

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatter correlation effects on photon migration transport in dense random media,” Phys. Rev. B Rapid Commun. 42, 2621–2623 (1990).
[CrossRef]

Appl. Opt. (1)

Colloid Polym. Sci. (1)

E. J. Rohm, K. D. Horner, M. Ballauff, “Interactions in mixtures of latex particles and polymers as revealed by turbidimetry,” Colloid Polym. Sci. 274, 732–740 (1996).
[CrossRef]

Europhys. Lett. (1)

H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, “Phase behavior of colloid + polymer mixtures,” Europhys. Lett. 20, 559–564 (1992).
[CrossRef]

J. Chem. Phys. (1)

S. Asakura, F. Oosawa, “On interaction between two bodies immersed in a solution of macromolecules,” J. Chem. Phys. 22, 1255–1256 (1954).
[CrossRef]

J. Coatings Tech. (1)

A. Brisson, G. L.’Espèrance, M. Caron, “Use of image analysis technique to quantify pigment dispersion,” J. Coatings Tech. 63, 111–118 (1991).

J. Fluid Mech. (2)

W. O’Brien, “Electro-acoustic effects in a dilute suspension of spherical particles,” J. Fluid Mech. 1990, 71–86 (1988).
[CrossRef]

W. O’Brien, “The electroacoustic equations for a colloidal suspension,” J. Fluid Mech. 212, 81–93 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

Langmuir (1)

M. A. Brown, A. L. Smith, E. J. Staples, “A method using total internal reflection microscopy and radiation pressure to study weak interaction forces of particles near surfaces,” Langmuir 5, 1319–1324 (1989).
[CrossRef]

Part. Part. Syst. Charact. (3)

S. M. Richter, R. R. Shinde, G. V. Balgi, E. M. Sevick-Muraca, “Particle sizing using frequency-domain photon migration,” Part. Part. Syst. Charact. 15, 9–16 (1998).
[CrossRef]

C. F. Riebel, F. Loffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
[CrossRef]

J. Coghill, M. J. Millen, B. D. Sowerby, “On-line particle size analysis using ultrasonic velocity spectrometry,” Part. Part. Syst. Charact. 14, 116–121 (1997).

Phys. Rev. B Rapid Commun. (1)

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatter correlation effects on photon migration transport in dense random media,” Phys. Rev. B Rapid Commun. 42, 2621–2623 (1990).
[CrossRef]

Phys. Rev. E (2)

W. Ye, T. Narayanan, P. Tong, J. S. Huang, M. Y. Lin, B. L. Carvalho, L. J. Fetters, “Depletion interactions in colloid-polymer mixtures,” Phys. Rev. E 54, 6500–6510 (1996).
[CrossRef]

P. D. Kaplan, A. D. Dinsmore, A. G. Yodh, D. J. Pine, “Diffuse-transmission spectroscopy: a structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827–4835 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

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

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Other (10)

S. Banerjee, R. Shinde, E. M. Sevick-Muraca, “Depletion interactions in colloid-polymer mixtures as studied by photon migration,” J. Colloid Interface Sci. (to be published).

J. E. Pierce, “Particle sizing in concentrated suspensions using frequency domain photon migration techniques,” M.S. thesis (Purdue University, West Lafayette, Indiana, 1997).

Allen Terence, Particle Size Measurement, 5th ed. (Chapman & Hall, London, 1997).

E. M. Sevick-Muraca, “A review on coupling particle size measurements for control and monitoring of particulate processes,” (International Fine Particle Research Institute, Inc., Cheshire, UK, 1997).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the FDPM instrument used to measure isotopic scattering coefficients of concentrated, interacting colloidal suspensions.

Fig. 2
Fig. 2

Typical experimental results of the relative phase shift Δθrel′ (in degrees) versus modulation frequency (in megahertz) for three data sets in which relative detector separations (r d1 - r d2) were 3 and 6 mm. The two separate data sets with r d1 - r d2 at 3 mm are identical and overlay one another. Symbols represent experimental data, whereas solid curves denote the least-squares fit of Eq. (3).

Fig. 3
Fig. 3

Isotropic scattering coefficient μ s ′ (in inverse centimeters) measured at 780 nm for a 500-nm mean-diameter polystyrene latex suspension as a function of solids volume fraction (percent). The symbols denote values derived from FDPM measurement, the dashed curve denotes the value of the isotropic scattering coefficient predicted from Eq. (3) for noninteracting scatterers [i.e., S(q) = 1], and the solid curve denotes the predicted value of the isotropic scattering coefficient predicted from Eq. (3) and the Percus–Yevick prediction of S(q) for a 500-nm polystyrene suspension.

Fig. 4
Fig. 4

Isotropic scattering coefficient μ s ′ (in inverse centimeters) measured at 670 nm for a 240-nm mean-diameter polystyrene latex suspension as a function of solids volume fraction (percent). The symbols denote values derived from FDPM measurements, the dashed curve denotes the value of the isotropic scattering coefficient predicted from Eq. (3) for noninteracting scatterers [S(q) = 1], and the solid curve denotes the predicted value of the isotropic scattering coefficient predicted from Eq. (3) and the Percus–Yevick prediction of S(q) for a 240-nm polystyrene suspension.

Fig. 5
Fig. 5

Isotropic scattering coefficient μ s ′ (in inverse centimeters) measured at 670 nm for a 135-nm mean-diameter polystyrene latex suspension as a function of solids volume fraction (percent). The symbols denote values derived from FDPM measurement, the dashed curve denotes the value of the isotropic scattering coefficient predicted from Eq. (3) for noninteracting scatterers [i.e., S(q) = 1], and the solid curve denotes the predicted value of the isotropic scattering coefficient predicted from Eq. (3) and the Percus–Yevick prediction of S(q) for a 135-nm polystyrene suspension.

Fig. 6
Fig. 6

Isotropic scattering coefficient μ s ′ (in inverse centimeters) measured at 670 nm for a 253-nm mean-diameter polystyrene latex suspension as a function of solids volume fraction (percent) with 0% (circles), 0.15% (squares), 0.25% (triangles), and 0.41% (diamonds) PEG of 100-K molecular weight. The symbols denote values derived from FDPM measurement, and the curve is a spline fit through the data.

Fig. 7
Fig. 7

Isotropic scattering coefficient μ s ′ (in inverse centimeters) predicted by Eq. (3) and the Asakura–Oosawa depletion model for colloids at 670 nm for a 253-nm mean-diameter polystyrene latex suspension as a function of solids volume fraction (percent) with 0% (solid curve), 0.2% (dashed curve), and 0.4% (dashed–dotted curve) polymer of 100-K molecular weight.

Fig. 8
Fig. 8

Isotropic scattering coefficient μ s ′ (in inverse centimeters) measured at 670 nm for 253-nm mean-diameter polystyrene latex suspensions as a function of solids volume fraction (percent) with 0% (circles), 0.25% PEG of 100-K molecular weight (squares), and 0.23% PEG of 600-K molecular weight (triangles). The symbols denote values derived from FDPM measurement, and the curves are spline fits from the data.

Equations (3)

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μs=6πϕx302πdφ 0π Ir2Sqsin θ1-cos θdθ,
μs=06πϕx302πdφ 0π Ir2Sq×sin θ1-cos θfxdθdx.
Δθrelλ=-|rd1-rd2|×3μsλ+μaλμaλc2+ω21/2c1/2×sin12arctanωμaλc,

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