Abstract

Frequency domain photon migration (FDPM) measurements were employed to accurately quantify optical properties of both the suspending fluid and particles within dense polystyrene suspensions of 143- or 226-nm mean diameter at varying concentrations (5–30% by volume). The measured absorption coefficients varied linearly with particle volume fraction whereas the isotropic scattering coefficients varied nonlinearly in agreement with the prediction that utilizes the hard-sphere structure factor model. These results validate the interference approximation of light scattering to describe light propagation accurately within dense suspensions. Furthermore, owing to the accuracy of FDPM absorption measurements, the imaginary refractive indices for both particles and their suspending fluid were determined and were found to compare favorably with literature values.

© 2004 Optical Society of America

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2002 (3)

Z. Sun, Y. Huang, E. M. Sevick-Muraca, “Precise analysis of frequency domain photon migration measurement for characterization of concentrated colloidal suspensions,” Rev. Sci. Instrum. 73, 383–393 (2002).
[CrossRef]

Y. Huang, Z. G. Sun, E. M. Sevick-Muraca, “Assessment of electrostatic interactions in dense colloidal dispersions with multiply scattered light,” Langmuir 18, 2048–2053 (2002).
[CrossRef]

Y. Huang, E. M. Sevick-Muraca, “Assessment of small-angle and angle-averaged structure factor for monitoring electrostatic colloidal interactions using multiply scattered light,” J. Colloid Interface Sci. 251, 434–442 (2002).
[CrossRef]

2001 (1)

1999 (1)

1998 (2)

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

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

1995 (2)

1994 (1)

U. Afpel, R. Grunder, M. Ballauff, “A turbidity study of particle interaction in latex suspensions,” Colloid Polym. Sci. 272, 820–829 (1994).
[CrossRef]

1993 (3)

1992 (1)

R. Rajagopalan, “Probing interaction forces in colloidal fluids through static structural data: the inverse problem,” Langmuir 8, 2898–2906 (1992).
[CrossRef]

1991 (1)

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time and frequency resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

1990 (2)

M. H. G. M. Penders, A. Vrij, “A turbidity study on colloidal silica particles in concentrated suspensions using the polydisperse adhesive hard sphere model,” J. Chem. Phys. 93, 3704–3711 (1990).
[CrossRef]

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

1978 (1)

A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut, W. G. M. Agterof, “Application of modern concepts in liquid theory to concentrated particle dispersions,” Faraday Discuss. 65, 101–113 (1978).
[CrossRef]

Afpel, U.

U. Afpel, R. Grunder, M. Ballauff, “A turbidity study of particle interaction in latex suspensions,” Colloid Polym. Sci. 272, 820–829 (1994).
[CrossRef]

Agterof, W. G. M.

A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut, W. G. M. Agterof, “Application of modern concepts in liquid theory to concentrated particle dispersions,” Faraday Discuss. 65, 101–113 (1978).
[CrossRef]

Aksay, I. A.

Alfano, R. R.

Balgi, G. V.

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

Ballauff, M.

U. Afpel, R. Grunder, M. Ballauff, “A turbidity study of particle interaction in latex suspensions,” Colloid Polym. Sci. 272, 820–829 (1994).
[CrossRef]

Cerussi, A. E.

Chance, B.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time and frequency resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Chylek, P.

Dick, V. P.

Fantini, S.

Fijnaut, H. M.

A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut, W. G. M. Agterof, “Application of modern concepts in liquid theory to concentrated particle dispersions,” Faraday Discuss. 65, 101–113 (1978).
[CrossRef]

Fishkin, J. B.

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.

French, R. H.

Garg, R.

Gratton, E.

Grunder, R.

U. Afpel, R. Grunder, M. Ballauff, “A turbidity study of particle interaction in latex suspensions,” Colloid Polym. Sci. 272, 820–829 (1994).
[CrossRef]

Hansen, J. P.

J. P. Hansen, J. R. McDonald, Theory of Simple Liquids (Academic, Orlando, Fla., 1986).

Hanuska, A. R.

Haskell, R. C.

Huang, Y.

Y. Huang, Z. G. Sun, E. M. Sevick-Muraca, “Assessment of electrostatic interactions in dense colloidal dispersions with multiply scattered light,” Langmuir 18, 2048–2053 (2002).
[CrossRef]

Z. Sun, Y. Huang, E. M. Sevick-Muraca, “Precise analysis of frequency domain photon migration measurement for characterization of concentrated colloidal suspensions,” Rev. Sci. Instrum. 73, 383–393 (2002).
[CrossRef]

Y. Huang, E. M. Sevick-Muraca, “Assessment of small-angle and angle-averaged structure factor for monitoring electrostatic colloidal interactions using multiply scattered light,” J. Colloid Interface Sci. 251, 434–442 (2002).
[CrossRef]

Ivanov, A. P.

Kou, L.

Labrie, D.

Leigh, J.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time and frequency resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Liu, F.

Maret, G.

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

Maris, M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time and frequency resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

McDonald, J. R.

J. P. Hansen, J. R. McDonald, Theory of Simple Liquids (Academic, Orlando, Fla., 1986).

McNeil, L. E.

Nieuwenhuis, E. A.

A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut, W. G. M. Agterof, “Application of modern concepts in liquid theory to concentrated particle dispersions,” Faraday Discuss. 65, 101–113 (1978).
[CrossRef]

Nioka, S.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time and frequency resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Penders, M. H. G. M.

M. H. G. M. Penders, A. Vrij, “A turbidity study on colloidal silica particles in concentrated suspensions using the polydisperse adhesive hard sphere model,” J. Chem. Phys. 93, 3704–3711 (1990).
[CrossRef]

Prudhomme, R. K.

Rajagopalan, R.

P. Salgi, R. Rajagopalan, “Polydispersity in colloids: implications to static structure and scattering,” Adv. Colloid Interface Sci. 43, 169–288 (1993).
[CrossRef]

R. Rajagopalan, “Probing interaction forces in colloidal fluids through static structural data: the inverse problem,” Langmuir 8, 2898–2906 (1992).
[CrossRef]

Richer, S. M.

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

Salgi, P.

P. Salgi, R. Rajagopalan, “Polydispersity in colloids: implications to static structure and scattering,” Adv. Colloid Interface Sci. 43, 169–288 (1993).
[CrossRef]

Sevick, E. M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time and frequency resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

Y. Huang, Z. G. Sun, E. M. Sevick-Muraca, “Assessment of electrostatic interactions in dense colloidal dispersions with multiply scattered light,” Langmuir 18, 2048–2053 (2002).
[CrossRef]

Y. Huang, E. M. Sevick-Muraca, “Assessment of small-angle and angle-averaged structure factor for monitoring electrostatic colloidal interactions using multiply scattered light,” J. Colloid Interface Sci. 251, 434–442 (2002).
[CrossRef]

Z. Sun, Y. Huang, E. M. Sevick-Muraca, “Precise analysis of frequency domain photon migration measurement for characterization of concentrated colloidal suspensions,” Rev. Sci. Instrum. 73, 383–393 (2002).
[CrossRef]

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

Shinde, R. R.

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

So, P. T. C.

Sun, Z.

Z. Sun, Y. Huang, E. M. Sevick-Muraca, “Precise analysis of frequency domain photon migration measurement for characterization of concentrated colloidal suspensions,” Rev. Sci. Instrum. 73, 383–393 (2002).
[CrossRef]

Sun, Z. G.

Y. Huang, Z. G. Sun, E. M. Sevick-Muraca, “Assessment of electrostatic interactions in dense colloidal dispersions with multiply scattered light,” Langmuir 18, 2048–2053 (2002).
[CrossRef]

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vrij, A.

M. H. G. M. Penders, A. Vrij, “A turbidity study on colloidal silica particles in concentrated suspensions using the polydisperse adhesive hard sphere model,” J. Chem. Phys. 93, 3704–3711 (1990).
[CrossRef]

A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut, W. G. M. Agterof, “Application of modern concepts in liquid theory to concentrated particle dispersions,” Faraday Discuss. 65, 101–113 (1978).
[CrossRef]

Xu, Y.

Adv. Colloid Interface Sci. (1)

P. Salgi, R. Rajagopalan, “Polydispersity in colloids: implications to static structure and scattering,” Adv. Colloid Interface Sci. 43, 169–288 (1993).
[CrossRef]

Anal. Biochem. (1)

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time and frequency resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Appl. Opt. (5)

Colloid Polym. Sci. (1)

U. Afpel, R. Grunder, M. Ballauff, “A turbidity study of particle interaction in latex suspensions,” Colloid Polym. Sci. 272, 820–829 (1994).
[CrossRef]

Faraday Discuss. (1)

A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut, W. G. M. Agterof, “Application of modern concepts in liquid theory to concentrated particle dispersions,” Faraday Discuss. 65, 101–113 (1978).
[CrossRef]

J. Chem. Phys. (1)

M. H. G. M. Penders, A. Vrij, “A turbidity study on colloidal silica particles in concentrated suspensions using the polydisperse adhesive hard sphere model,” J. Chem. Phys. 93, 3704–3711 (1990).
[CrossRef]

J. Colloid Interface Sci. (1)

Y. Huang, E. M. Sevick-Muraca, “Assessment of small-angle and angle-averaged structure factor for monitoring electrostatic colloidal interactions using multiply scattered light,” J. Colloid Interface Sci. 251, 434–442 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Langmuir (2)

Y. Huang, Z. G. Sun, E. M. Sevick-Muraca, “Assessment of electrostatic interactions in dense colloidal dispersions with multiply scattered light,” Langmuir 18, 2048–2053 (2002).
[CrossRef]

R. Rajagopalan, “Probing interaction forces in colloidal fluids through static structural data: the inverse problem,” Langmuir 8, 2898–2906 (1992).
[CrossRef]

Part. Part. Syst. Charact. (1)

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

Phys. Rev. Lett. (1)

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

Rev. Sci. Instrum. (1)

Z. Sun, Y. Huang, E. M. Sevick-Muraca, “Precise analysis of frequency domain photon migration measurement for characterization of concentrated colloidal suspensions,” Rev. Sci. Instrum. 73, 383–393 (2002).
[CrossRef]

Other (3)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

R. H. Boundy, R. R. Boxer, eds., Styrene, Its Polymers, Copolymers, and Derivatives (Reinhold, New York, 1952).

J. P. Hansen, J. R. McDonald, Theory of Simple Liquids (Academic, Orlando, Fla., 1986).

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Figures (5)

Fig. 1
Fig. 1

FDPM measurements of (a) AC, (b) PS as expressed by the left-hand side of Eq. (5), and (c) logarithmic ratio of AC as expressed by the left-hand side of Eq. (4) for latex A (at a volume fraction of 0.16 and ionic strength of 120-mM NaCl equivalent) as a function of source–detector fiber separation distance at six modulation frequencies.

Fig. 2
Fig. 2

Isotropic scattering coefficients (cm-1) versus volume fraction for latex A at wavelengths of 687, 785, and 828 nm and at ionic strengths of 120-, 25-, and 5-mM NaCl equivalent.

Fig. 3
Fig. 3

Isotropic scattering coefficients (cm-1) versus volume fraction for latex B at wavelengths of 687 and 828 nm and at ionic strengths of 120-, 25-, and 5-mM NaCl equivalent.

Fig. 4
Fig. 4

Absorption coefficients (cm-1) versus volume fraction for latex A at wavelengths of 687 and 828 nm and at ionic strengths of 120-, 25-, and 5-mM NaCl equivalent.

Fig. 5
Fig. 5

Absorption coefficients (cm-1) versus volume fraction for latex B at wavelengths of 687, 785, and 828 nm and at ionic strengths of 120-, 25-, and 5-mM NaCl equivalent.

Tables (2)

Tables Icon

Table 1 Absorption Efficiencies of Water α (cm-1)a as Well as from FDPM Measurements of Absorption Coefficients for Dense Suspensions of Lattices A and Bb

Tables Icon

Table 2 Volume-Based Particle Absorption Efficiency and Imaginary Refractive Indices Determined from FDPM Measurements of Absorption Coefficients for Lattices A and B

Equations (5)

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

μs=NCsca1-g,
μsλ=6ϕ2πnl/λ2d30π FqSqsin θ1-cos θdθ,
μa=ϕμa,p+1-ϕα.
lnrACrr0ACr0=-r-r032 μaμa+μs1/2×1+ωcμa21/2+11/2,
PSr-PSr0=r-r032 μaμa+μs1/2×1+ωcμa21/2-11/2,

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