Abstract

Calibrated measurements of optical (λ = 488-nm) scattering cross sections, in the form of Rayleigh ratios, are presented for two fractal aggregate aerosols. The aggregates have radii of gyration of approximately 280 nm, fractal dimensions of approximately 1.75, and monomer sizes of approximately 20 nm with approximately 150 monomers per cluster. One aerosol was composed of vitreous SiO2 with a refractive index of 1.46, the other of anatase TiO2 with a refractive index of 2.61. We found good agreement with the Rayleigh-Debye-Gans prediction for the scattering cross section of fractal aggregates.

© 2002 Optical Society of America

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  5. J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
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  8. T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–272 (1986).
    [CrossRef]
  9. M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
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  25. S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  33. D. J. Coumou, E. L. Mackor, J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
    [CrossRef]
  34. B. J. Olivier, C. M. Sorensen, T. W. Taylor, “Scaling dynamics of aerosol coagulation,” Phys. Rev. A 45, 5614–5622 (1992).
    [CrossRef] [PubMed]
  35. C. M. Sorensen, G. M. Wang, “Size distribution effect on the power law regime of the structure factor of fractal aggregates,” Phys. Rev. E 60, 7143–7148 (1999).
    [CrossRef]
  36. J. Cai, N. Lu, C. M. Sorensen, “Analysis of fractal cluster morphology parameters: structural coefficient and density autocorrelation function cutoff,” J. Colloid Interface Sci. 171, 470–473 (1995).
    [CrossRef]
  37. C. M. Sorensen, G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186, 447–452 (1997).
    [CrossRef] [PubMed]
  38. C. Oh, C. M. Sorensen, “The effect of monomer overlap on the morphology of fractal aggregates,” J. Colloid Interface Sci. 193, 17–25 (1997).
    [CrossRef] [PubMed]

2001 (1)

C. M. Sorensen, “Light scattering by fractal aggregates. A review,” Aerosol Sci. Technol. 35, 648–687 (2001).

1999 (1)

C. M. Sorensen, G. M. Wang, “Size distribution effect on the power law regime of the structure factor of fractal aggregates,” Phys. Rev. E 60, 7143–7148 (1999).
[CrossRef]

1997 (2)

C. M. Sorensen, G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186, 447–452 (1997).
[CrossRef] [PubMed]

C. Oh, C. M. Sorensen, “The effect of monomer overlap on the morphology of fractal aggregates,” J. Colloid Interface Sci. 193, 17–25 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (3)

D. W. Mackowski, “Electrostatic analysis of radiative absorption by sphere clusters in the Rayleigh limit: application to soot clusters,” Appl. Opt. 34, 3535–3545 (1995).
[CrossRef] [PubMed]

J. Cai, N. Lu, C. M. Sorensen, “Analysis of fractal cluster morphology parameters: structural coefficient and density autocorrelation function cutoff,” J. Colloid Interface Sci. 171, 470–473 (1995).
[CrossRef]

U. O. Köylü, Y. Xing, D. E. Rosner, “Fractal morphology analysis of combustion-generated aggregates using angular light scattering and electron microscope images,” Langmuir 11, 4848–4854 (1995).
[CrossRef]

1994 (4)

D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
[CrossRef]

U. O. Köylü, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence times,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1994).
[CrossRef]

G. W. Mulholland, C. F. Bohren, K. A. Fuller, “Light scattering by agglomerates: coupled electric and magnetic dipole method,” Langmuir 10, 2533–2546 (1994).
[CrossRef]

1993 (2)

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

1992 (2)

B. J. Olivier, C. M. Sorensen, T. W. Taylor, “Scaling dynamics of aerosol coagulation,” Phys. Rev. A 45, 5614–5622 (1992).
[CrossRef] [PubMed]

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

1991 (1)

J. C. Ku, “Correction for the extinction efficiency factors given in the Jones solution for electromagnetic scattering by agglomerates of small spheres,” J. Phys. D 24, 71–75 (1991).
[CrossRef]

1990 (1)

K. Okuyama, R. Ushio, Y. Kousaka, R. C. Flagan, J. H. Seinfeld, “Particle generation in a chemical vapor deposition process and seed particles,” AIChE J. 36, 409–422 (1990).
[CrossRef]

1989 (2)

1988 (2)

J. Frey, J. J. Pinvidic, R. Botet, R. Jullien, “Light scattering by fractal aggregates: a numerical investigation,” J. Phys. (Paris) 49, 1969–1976 (1988).
[CrossRef]

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

1987 (3)

J. Mullins, A. Williams, “The optical properties of soot: a comparison between experimental and theoretical values,” Fuel 66, 277–284 (1987).
[CrossRef]

J. E. Martin, A. J. Hurd, “Scattering from fractals,” J. Appl. Crystallogr. 20, 61–78 (1987).
[CrossRef]

E. Moreels, W. De Ceuninck, R. Finsy, “Measurements of the Rayleigh ratio of some pure liquids at several laser light wavelengths,” J. Chem. Phys. 86, 618–623 (1987).
[CrossRef]

1986 (3)

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–272 (1986).
[CrossRef]

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

1984 (1)

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

1979 (2)

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
[CrossRef]

1964 (1)

D. J. Coumou, E. L. Mackor, J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[CrossRef]

Berry, M. V.

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Bohren, C. F.

G. W. Mulholland, C. F. Bohren, K. A. Fuller, “Light scattering by agglomerates: coupled electric and magnetic dipole method,” Langmuir 10, 2533–2546 (1994).
[CrossRef]

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

Botet, R.

J. Frey, J. J. Pinvidic, R. Botet, R. Jullien, “Light scattering by fractal aggregates: a numerical investigation,” J. Phys. (Paris) 49, 1969–1976 (1988).
[CrossRef]

R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).

Cai, J.

J. Cai, N. Lu, C. M. Sorensen, “Analysis of fractal cluster morphology parameters: structural coefficient and density autocorrelation function cutoff,” J. Colloid Interface Sci. 171, 470–473 (1995).
[CrossRef]

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

Cannell, D. S.

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Carvalho, M. G.

Charalampopoulos, T. T.

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1994).
[CrossRef]

Chen, H. Y.

Coumou, D. J.

D. J. Coumou, E. L. Mackor, J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[CrossRef]

De Ceuninck, W.

E. Moreels, W. De Ceuninck, R. Finsy, “Measurements of the Rayleigh ratio of some pure liquids at several laser light wavelengths,” J. Chem. Phys. 86, 618–623 (1987).
[CrossRef]

Faeth, G. M.

U. O. Köylü, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence times,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

Farias, T. L.

Finsy, R.

E. Moreels, W. De Ceuninck, R. Finsy, “Measurements of the Rayleigh ratio of some pure liquids at several laser light wavelengths,” J. Chem. Phys. 86, 618–623 (1987).
[CrossRef]

Flagan, R. C.

K. Okuyama, R. Ushio, Y. Kousaka, R. C. Flagan, J. H. Seinfeld, “Particle generation in a chemical vapor deposition process and seed particles,” AIChE J. 36, 409–422 (1990).
[CrossRef]

Forrest, S. R.

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

Freltoft, T.

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–272 (1986).
[CrossRef]

Frey, J.

J. Frey, J. J. Pinvidic, R. Botet, R. Jullien, “Light scattering by fractal aggregates: a numerical investigation,” J. Phys. (Paris) 49, 1969–1976 (1988).
[CrossRef]

Fuller, K. A.

G. W. Mulholland, C. F. Bohren, K. A. Fuller, “Light scattering by agglomerates: coupled electric and magnetic dipole method,” Langmuir 10, 2533–2546 (1994).
[CrossRef]

Hijmans, J.

D. J. Coumou, E. L. Mackor, J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[CrossRef]

Hurd, A. J.

J. E. Martin, A. J. Hurd, “Scattering from fractals,” J. Appl. Crystallogr. 20, 61–78 (1987).
[CrossRef]

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

Iskander, M. F.

Jones, A. R.

A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
[CrossRef]

Jullien, R.

J. Frey, J. J. Pinvidic, R. Botet, R. Jullien, “Light scattering by fractal aggregates: a numerical investigation,” J. Phys. (Paris) 49, 1969–1976 (1988).
[CrossRef]

R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).

Kerker, M.

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

Kjems, J. K.

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–272 (1986).
[CrossRef]

Kousaka, Y.

K. Okuyama, R. Ushio, Y. Kousaka, R. C. Flagan, J. H. Seinfeld, “Particle generation in a chemical vapor deposition process and seed particles,” AIChE J. 36, 409–422 (1990).
[CrossRef]

Koylu, U. O.

Köylü, U. O.

U. O. Köylü, Y. Xing, D. E. Rosner, “Fractal morphology analysis of combustion-generated aggregates using angular light scattering and electron microscope images,” Langmuir 11, 4848–4854 (1995).
[CrossRef]

U. O. Köylü, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence times,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

Ku, J. C.

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

J. C. Ku, “Correction for the extinction efficiency factors given in the Jones solution for electromagnetic scattering by agglomerates of small spheres,” J. Phys. D 24, 71–75 (1991).
[CrossRef]

Lou, W.

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1994).
[CrossRef]

Lu, N.

J. Cai, N. Lu, C. M. Sorensen, “Analysis of fractal cluster morphology parameters: structural coefficient and density autocorrelation function cutoff,” J. Colloid Interface Sci. 171, 470–473 (1995).
[CrossRef]

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

Mackor, E. L.

D. J. Coumou, E. L. Mackor, J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[CrossRef]

Mackowski, D. W.

Martin, J. E.

J. E. Martin, A. J. Hurd, “Scattering from fractals,” J. Appl. Crystallogr. 20, 61–78 (1987).
[CrossRef]

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Moreels, E.

E. Moreels, W. De Ceuninck, R. Finsy, “Measurements of the Rayleigh ratio of some pure liquids at several laser light wavelengths,” J. Chem. Phys. 86, 618–623 (1987).
[CrossRef]

Mountain, R. D.

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

Mulholland, G. W.

G. W. Mulholland, C. F. Bohren, K. A. Fuller, “Light scattering by agglomerates: coupled electric and magnetic dipole method,” Langmuir 10, 2533–2546 (1994).
[CrossRef]

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

Mullins, J.

J. Mullins, A. Williams, “The optical properties of soot: a comparison between experimental and theoretical values,” Fuel 66, 277–284 (1987).
[CrossRef]

Nelson, J.

J. Nelson, “Test of mean field theory for the optics of fractal clusters,” J. Mod. Opt. 36, 1031–1057 (1989).
[CrossRef]

Oh, C.

C. Oh, C. M. Sorensen, “The effect of monomer overlap on the morphology of fractal aggregates,” J. Colloid Interface Sci. 193, 17–25 (1997).
[CrossRef] [PubMed]

Okuyama, K.

K. Okuyama, R. Ushio, Y. Kousaka, R. C. Flagan, J. H. Seinfeld, “Particle generation in a chemical vapor deposition process and seed particles,” AIChE J. 36, 409–422 (1990).
[CrossRef]

Olivier, B. J.

B. J. Olivier, C. M. Sorensen, T. W. Taylor, “Scaling dynamics of aerosol coagulation,” Phys. Rev. A 45, 5614–5622 (1992).
[CrossRef] [PubMed]

Penner, J. E.

Percival, I. C.

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Pinvidic, J. J.

J. Frey, J. J. Pinvidic, R. Botet, R. Jullien, “Light scattering by fractal aggregates: a numerical investigation,” J. Phys. (Paris) 49, 1969–1976 (1988).
[CrossRef]

Roberts, G. C.

C. M. Sorensen, G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186, 447–452 (1997).
[CrossRef] [PubMed]

Rosner, D. E.

U. O. Köylü, Y. Xing, D. E. Rosner, “Fractal morphology analysis of combustion-generated aggregates using angular light scattering and electron microscope images,” Langmuir 11, 4848–4854 (1995).
[CrossRef]

Schaefer, D. W.

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Seinfeld, J. H.

K. Okuyama, R. Ushio, Y. Kousaka, R. C. Flagan, J. H. Seinfeld, “Particle generation in a chemical vapor deposition process and seed particles,” AIChE J. 36, 409–422 (1990).
[CrossRef]

Shim, K.-H.

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Singham, S. B.

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

Sinha, S. K.

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–272 (1986).
[CrossRef]

Sorensen, C. M.

C. M. Sorensen, “Light scattering by fractal aggregates. A review,” Aerosol Sci. Technol. 35, 648–687 (2001).

C. M. Sorensen, G. M. Wang, “Size distribution effect on the power law regime of the structure factor of fractal aggregates,” Phys. Rev. E 60, 7143–7148 (1999).
[CrossRef]

C. M. Sorensen, G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186, 447–452 (1997).
[CrossRef] [PubMed]

C. Oh, C. M. Sorensen, “The effect of monomer overlap on the morphology of fractal aggregates,” J. Colloid Interface Sci. 193, 17–25 (1997).
[CrossRef] [PubMed]

J. Cai, N. Lu, C. M. Sorensen, “Analysis of fractal cluster morphology parameters: structural coefficient and density autocorrelation function cutoff,” J. Colloid Interface Sci. 171, 470–473 (1995).
[CrossRef]

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

B. J. Olivier, C. M. Sorensen, T. W. Taylor, “Scaling dynamics of aerosol coagulation,” Phys. Rev. A 45, 5614–5622 (1992).
[CrossRef] [PubMed]

C. M. Sorensen, “Scattering and absorption of light by particles and aggregates,” in Handbook of Surface and Colloid Chemistry, K. S. Birdi, ed. (CRC Press, Boca Raton, Fla., 1997), pp. 533–558.

Taylor, T. W.

B. J. Olivier, C. M. Sorensen, T. W. Taylor, “Scaling dynamics of aerosol coagulation,” Phys. Rev. A 45, 5614–5622 (1992).
[CrossRef] [PubMed]

Teixeira, J.

J. Teixeira, “Experimental methods for studying fractal aggregates,” in On Growth and Form, Fractal and Non-Fractal Patterns in Physics, H. E. Stanley, N. Ostrowski, eds. (Nijhoff, Dordrecht, The Netherlands, 1986) pp. 145–165.

Ushio, R.

K. Okuyama, R. Ushio, Y. Kousaka, R. C. Flagan, J. H. Seinfeld, “Particle generation in a chemical vapor deposition process and seed particles,” AIChE J. 36, 409–422 (1990).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wang, G. M.

C. M. Sorensen, G. M. Wang, “Size distribution effect on the power law regime of the structure factor of fractal aggregates,” Phys. Rev. E 60, 7143–7148 (1999).
[CrossRef]

Williams, A.

J. Mullins, A. Williams, “The optical properties of soot: a comparison between experimental and theoretical values,” Fuel 66, 277–284 (1987).
[CrossRef]

Wiltzius, P.

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Witten, T. A.

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

Xing, Y.

U. O. Köylü, Y. Xing, D. E. Rosner, “Fractal morphology analysis of combustion-generated aggregates using angular light scattering and electron microscope images,” Langmuir 11, 4848–4854 (1995).
[CrossRef]

Aerosol Sci. Technol. (1)

C. M. Sorensen, “Light scattering by fractal aggregates. A review,” Aerosol Sci. Technol. 35, 648–687 (2001).

AIChE J. (1)

K. Okuyama, R. Ushio, Y. Kousaka, R. C. Flagan, J. H. Seinfeld, “Particle generation in a chemical vapor deposition process and seed particles,” AIChE J. 36, 409–422 (1990).
[CrossRef]

Appl. Opt. (3)

Fuel (1)

J. Mullins, A. Williams, “The optical properties of soot: a comparison between experimental and theoretical values,” Fuel 66, 277–284 (1987).
[CrossRef]

J. Appl. Crystallogr. (1)

J. E. Martin, A. J. Hurd, “Scattering from fractals,” J. Appl. Crystallogr. 20, 61–78 (1987).
[CrossRef]

J. Chem. Phys. (1)

E. Moreels, W. De Ceuninck, R. Finsy, “Measurements of the Rayleigh ratio of some pure liquids at several laser light wavelengths,” J. Chem. Phys. 86, 618–623 (1987).
[CrossRef]

J. Colloid Interface Sci. (3)

J. Cai, N. Lu, C. M. Sorensen, “Analysis of fractal cluster morphology parameters: structural coefficient and density autocorrelation function cutoff,” J. Colloid Interface Sci. 171, 470–473 (1995).
[CrossRef]

C. M. Sorensen, G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186, 447–452 (1997).
[CrossRef] [PubMed]

C. Oh, C. M. Sorensen, “The effect of monomer overlap on the morphology of fractal aggregates,” J. Colloid Interface Sci. 193, 17–25 (1997).
[CrossRef] [PubMed]

J. Heat Transfer (1)

U. O. Köylü, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence times,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

J. Mod. Opt. (1)

J. Nelson, “Test of mean field theory for the optics of fractal clusters,” J. Mod. Opt. 36, 1031–1057 (1989).
[CrossRef]

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

J. Phys. (Paris) (1)

J. Frey, J. J. Pinvidic, R. Botet, R. Jullien, “Light scattering by fractal aggregates: a numerical investigation,” J. Phys. (Paris) 49, 1969–1976 (1988).
[CrossRef]

J. Phys. A (1)

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

J. Phys. D (2)

J. C. Ku, “Correction for the extinction efficiency factors given in the Jones solution for electromagnetic scattering by agglomerates of small spheres,” J. Phys. D 24, 71–75 (1991).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1994).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Langmuir (5)

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

G. W. Mulholland, C. F. Bohren, K. A. Fuller, “Light scattering by agglomerates: coupled electric and magnetic dipole method,” Langmuir 10, 2533–2546 (1994).
[CrossRef]

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

U. O. Köylü, Y. Xing, D. E. Rosner, “Fractal morphology analysis of combustion-generated aggregates using angular light scattering and electron microscope images,” Langmuir 11, 4848–4854 (1995).
[CrossRef]

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

Opt. Acta (1)

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Phys. Rev. A (2)

B. J. Olivier, C. M. Sorensen, T. W. Taylor, “Scaling dynamics of aerosol coagulation,” Phys. Rev. A 45, 5614–5622 (1992).
[CrossRef] [PubMed]

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

Phys. Rev. B (1)

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–272 (1986).
[CrossRef]

Phys. Rev. E (1)

C. M. Sorensen, G. M. Wang, “Size distribution effect on the power law regime of the structure factor of fractal aggregates,” Phys. Rev. E 60, 7143–7148 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
[CrossRef]

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[CrossRef]

Other (6)

R. C. Weast, ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, Ohio, 1976), Vol. 51.

C. M. Sorensen, “Scattering and absorption of light by particles and aggregates,” in Handbook of Surface and Colloid Chemistry, K. S. Birdi, ed. (CRC Press, Boca Raton, Fla., 1997), pp. 533–558.

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

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).

J. Teixeira, “Experimental methods for studying fractal aggregates,” in On Growth and Form, Fractal and Non-Fractal Patterns in Physics, H. E. Stanley, N. Ostrowski, eds. (Nijhoff, Dordrecht, The Netherlands, 1986) pp. 145–165.

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Figures (2)

Fig. 1
Fig. 1

Static structure factors S(q) for SiO2 (circles) and TiO2 (squares) aerosols. S(q) for TiO2 was multiplied by 5/3.

Fig. 2
Fig. 2

Scattered intensities, normalized to the value obtained from CCl 4 versus the Rayleigh ratio divided by the medium refractive index. Open circles are the four liquids listed in Table 2; filled circles are the two aerosols listed in Table 3. Errors for the liquid scattered intensities are represented by the symbol size.

Tables (3)

Tables Icon

Table 1 Aerosol Physical Parameters

Tables Icon

Table 2 Rayleigh Ratios at λ = 488 nm and a Scattering Angle of 90° (R v ) and Index of Refraction for the Liquids Used

Tables Icon

Table 3 Comparison of Theoretically Expected Measured Rayleigh Ratios (10-6 cm-1 sr-1) for the Two Aerosols

Equations (23)

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

N=koRg/aD,
ρ=2kR|m-1|<1,
ρagg=2kRg|m-1|3,
dσaggdΩ=N2dσmdΩ SqRg.
σagg=Nσm.
q=4πλ-1 sinθ/2,
dσmdΩ=k4a6m2-1m2+22.
Rv=2Ru/1+ρu.
Rvλ-4.6±0.15.
I=clI0vRv,
I=cI0vl0Rv/m.
Rv=n dσdΩ.
Rv=k4m2-1m2+22  panNa6N2SqRgdadN,
SqRg=CqRg-D
=Caq-Dk0N-1,
Rv=k0Cq-Dk4m2-1m2+22  paa6-Dda  nNNdN.
pa=p0 exp-ln2a/a0/2ln2σ,
Mi= aipada
Mi=p0 exp0.5i+12ln2σ,
ρaero=ρp4π/3  paa3da  nNNdN.
Rv=k0Cq-D3/4πρaero/ρpa03-Dk4m2-1m2+22×exp0.533-14D+D2ln2σ.
k0=1.3±0.1
C=1.0±0.1.

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