Abstract

A systematic evaluation of the effects of polydispersity of chainlike aggregates in terms of primary particle number density and size on the scattering quantities and data inversion is presented. For aggregates with refractive index in the range |m-1| = 0.8–1.2, average size parameter x < 0.40, and primary particle number Np < 20, it is shown that the effects of polydispersity of primary particle size on the light-scattering quantities are much stronger than the polydispersity of the number of primary particles per aggregate. For aggregates with polydisperse primary particle size, the assumption of monodispersity tends to underestimate the real and imaginary parts of the refractive index and the number of primary particles. Specifically, for values of the distribution width σ greater than 0.10, the effect of polydispersity of the size of primary particles must be considered in the data inversion schemes. Furthermore, in the same range of values for the refractive index, particle size parameter, and primary particle number, the assumption of monodispersity for aggregates with polydisperse particle number tends to underestimate the value of the real part of the refractive index and overestimate the value of the imaginary part of the refractive index and primary particle size. However, for values of the distribution width σ less than 0.60, the effects of polydispersity of primary particle number can be neglected. In addition, the suitable pairing sets of the measured scattering quantities for data inversion are presented and discussed.

© 2002 Optical Society of America

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References

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  1. C. M. Megaridis, R. A. Dobbins, “Morphological description of flame generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
    [CrossRef]
  2. R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
    [CrossRef] [PubMed]
  3. C. M. Sorensen, N. Liu, J. Cai, “Fractal cluster size distribution measurement using static light scattering,” J. Colloid Interface Sci. 174, 456–460 (1995).
    [CrossRef]
  4. T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot,” J. Quant. Spectrosc. Radiat. Transfer 55, 357–371 (1996).
    [CrossRef]
  5. G. Shu, T. T. Charalampopoulos, “Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols,” Appl. Opt. 39, 6713–6724 (2000).
    [CrossRef]
  6. W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1994).
    [CrossRef]
  7. W. Lou, T. T. Charalampopopulos, “On the inverse scattering problem for characterization of agglomerated particulates,” J. Phys. D 28, 2585–2594 (1995).
    [CrossRef]
  8. Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996) pp. 1851–1857.
  9. D. T. Venizelos, W. Lou, T. T. Charalampopoulos, “Development of an algorithm for the calculation of the scattering properties of agglomerates,” Appl. Opt. 35, 542–548 (1996).
    [CrossRef] [PubMed]
  10. G. Shu, T. T. Charalampopoulos, “Reciprocity theorem for the calculation of average scattering properties of agglomerated particles,” Appl. Opt. 39, 5827–5833 (2000).
    [CrossRef]
  11. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  12. W. H. Press, B. P. Flanney, S. A. Teulosky, W. T. Vettering, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).
  13. T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 88–99 (1991).
    [CrossRef]
  14. C. M. Sorensen, J. Cai, N. Liu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
    [CrossRef] [PubMed]
  15. B. Vaglieco, O. Monda, F. F. Corcione, M. P. Mengüc, “Optical and radiative properties of particulates at diesel engine exhaust,” Combust. Sci. Technol. 102, 283–299 (1994).
    [CrossRef]
  16. M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smokes,” Opt. Acta 33, 577–591 (1986).
    [CrossRef]
  17. J. Nelson, “Test of a mean field theory for the optics of clusters,” J. Mod. Opt. 36, 1031–1057 (1989).
    [CrossRef]
  18. H. Y. Chen, M. F. Islander, J. E. Penner, “Light scattering and absorption by fractal agglomerates and coagulation of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
    [CrossRef]

2000

1996

D. T. Venizelos, W. Lou, T. T. Charalampopoulos, “Development of an algorithm for the calculation of the scattering properties of agglomerates,” Appl. Opt. 35, 542–548 (1996).
[CrossRef] [PubMed]

T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot,” J. Quant. Spectrosc. Radiat. Transfer 55, 357–371 (1996).
[CrossRef]

1995

C. M. Sorensen, N. Liu, J. Cai, “Fractal cluster size distribution measurement using static light scattering,” J. Colloid Interface Sci. 174, 456–460 (1995).
[CrossRef]

W. Lou, T. T. Charalampopopulos, “On the inverse scattering problem for characterization of agglomerated particulates,” J. Phys. D 28, 2585–2594 (1995).
[CrossRef]

1994

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

B. Vaglieco, O. Monda, F. F. Corcione, M. P. Mengüc, “Optical and radiative properties of particulates at diesel engine exhaust,” Combust. Sci. Technol. 102, 283–299 (1994).
[CrossRef]

1992

1991

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 88–99 (1991).
[CrossRef]

R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
[CrossRef] [PubMed]

1990

C. M. Megaridis, R. A. Dobbins, “Morphological description of flame generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

H. Y. Chen, M. F. Islander, J. E. Penner, “Light scattering and absorption by fractal agglomerates and coagulation of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
[CrossRef]

1989

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

1986

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

Berry, M. V.

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

Cai, J.

C. M. Sorensen, N. Liu, J. Cai, “Fractal cluster size distribution measurement using static light scattering,” J. Colloid Interface Sci. 174, 456–460 (1995).
[CrossRef]

C. M. Sorensen, J. Cai, N. Liu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

Carvalho, M. G.

T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot,” J. Quant. Spectrosc. Radiat. Transfer 55, 357–371 (1996).
[CrossRef]

Chang, H.

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 88–99 (1991).
[CrossRef]

Charalampopopulos, T. T.

W. Lou, T. T. Charalampopopulos, “On the inverse scattering problem for characterization of agglomerated particulates,” J. Phys. D 28, 2585–2594 (1995).
[CrossRef]

Charalampopoulos, T. T.

G. Shu, T. T. Charalampopoulos, “Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols,” Appl. Opt. 39, 6713–6724 (2000).
[CrossRef]

G. Shu, T. T. Charalampopoulos, “Reciprocity theorem for the calculation of average scattering properties of agglomerated particles,” Appl. Opt. 39, 5827–5833 (2000).
[CrossRef]

D. T. Venizelos, W. Lou, T. T. Charalampopoulos, “Development of an algorithm for the calculation of the scattering properties of agglomerates,” Appl. Opt. 35, 542–548 (1996).
[CrossRef] [PubMed]

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

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 88–99 (1991).
[CrossRef]

Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996) pp. 1851–1857.

Chen, H. Y.

H. Y. Chen, M. F. Islander, J. E. Penner, “Light scattering and absorption by fractal agglomerates and coagulation of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
[CrossRef]

Corcione, F. F.

B. Vaglieco, O. Monda, F. F. Corcione, M. P. Mengüc, “Optical and radiative properties of particulates at diesel engine exhaust,” Combust. Sci. Technol. 102, 283–299 (1994).
[CrossRef]

Dobbins, R. A.

R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
[CrossRef] [PubMed]

C. M. Megaridis, R. A. Dobbins, “Morphological description of flame generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

Farias, T. L.

T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot,” J. Quant. Spectrosc. Radiat. Transfer 55, 357–371 (1996).
[CrossRef]

Flanney, B. P.

W. H. Press, B. P. Flanney, S. A. Teulosky, W. T. Vettering, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

Islander, M. F.

H. Y. Chen, M. F. Islander, J. E. Penner, “Light scattering and absorption by fractal agglomerates and coagulation of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
[CrossRef]

Kerker, M.

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

Köylü, Ü. Ö.

T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot,” J. Quant. Spectrosc. Radiat. Transfer 55, 357–371 (1996).
[CrossRef]

Liu, N.

C. M. Sorensen, N. Liu, J. Cai, “Fractal cluster size distribution measurement using static light scattering,” J. Colloid Interface Sci. 174, 456–460 (1995).
[CrossRef]

C. M. Sorensen, J. Cai, N. Liu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

Lou, W.

D. T. Venizelos, W. Lou, T. T. Charalampopoulos, “Development of an algorithm for the calculation of the scattering properties of agglomerates,” Appl. Opt. 35, 542–548 (1996).
[CrossRef] [PubMed]

W. Lou, T. T. Charalampopopulos, “On the inverse scattering problem for characterization of agglomerated particulates,” J. Phys. D 28, 2585–2594 (1995).
[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]

Megaridis, C. M.

R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
[CrossRef] [PubMed]

C. M. Megaridis, R. A. Dobbins, “Morphological description of flame generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

Mengüc, M. P.

B. Vaglieco, O. Monda, F. F. Corcione, M. P. Mengüc, “Optical and radiative properties of particulates at diesel engine exhaust,” Combust. Sci. Technol. 102, 283–299 (1994).
[CrossRef]

Monda, O.

B. Vaglieco, O. Monda, F. F. Corcione, M. P. Mengüc, “Optical and radiative properties of particulates at diesel engine exhaust,” Combust. Sci. Technol. 102, 283–299 (1994).
[CrossRef]

Nelson, J.

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

Penner, J. E.

H. Y. Chen, M. F. Islander, J. E. Penner, “Light scattering and absorption by fractal agglomerates and coagulation of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
[CrossRef]

Percival, I. C.

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

Press, W. H.

W. H. Press, B. P. Flanney, S. A. Teulosky, W. T. Vettering, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

Shu, G.

Sorensen, C. M.

C. M. Sorensen, N. Liu, J. Cai, “Fractal cluster size distribution measurement using static light scattering,” J. Colloid Interface Sci. 174, 456–460 (1995).
[CrossRef]

C. M. Sorensen, J. Cai, N. Liu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

Teulosky, S. A.

W. H. Press, B. P. Flanney, S. A. Teulosky, W. T. Vettering, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

Vaglieco, B.

B. Vaglieco, O. Monda, F. F. Corcione, M. P. Mengüc, “Optical and radiative properties of particulates at diesel engine exhaust,” Combust. Sci. Technol. 102, 283–299 (1994).
[CrossRef]

Venizelos, D. T.

Vettering, W. T.

W. H. Press, B. P. Flanney, S. A. Teulosky, W. T. Vettering, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

Zhang, Z.

Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996) pp. 1851–1857.

Appl. Opt.

Combust. Flame

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 88–99 (1991).
[CrossRef]

Combust. Sci. Technol.

C. M. Megaridis, R. A. Dobbins, “Morphological description of flame generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

B. Vaglieco, O. Monda, F. F. Corcione, M. P. Mengüc, “Optical and radiative properties of particulates at diesel engine exhaust,” Combust. Sci. Technol. 102, 283–299 (1994).
[CrossRef]

J. Colloid Interface Sci.

C. M. Sorensen, N. Liu, J. Cai, “Fractal cluster size distribution measurement using static light scattering,” J. Colloid Interface Sci. 174, 456–460 (1995).
[CrossRef]

J. Mod. Opt.

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

H. Y. Chen, M. F. Islander, J. E. Penner, “Light scattering and absorption by fractal agglomerates and coagulation of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
[CrossRef]

J. Phys. D

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

W. Lou, T. T. Charalampopopulos, “On the inverse scattering problem for characterization of agglomerated particulates,” J. Phys. D 28, 2585–2594 (1995).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot,” J. Quant. Spectrosc. Radiat. Transfer 55, 357–371 (1996).
[CrossRef]

Opt. Acta

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

Other

Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996) pp. 1851–1857.

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

W. H. Press, B. P. Flanney, S. A. Teulosky, W. T. Vettering, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

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Figures (9)

Fig. 1
Fig. 1

Schematic of monodisperse chainlike aggregates.

Fig. 2
Fig. 2

Polydisperse chainlike aggregates generated in Fe(CO)5-seeded CO/O2 diffusion flame.

Fig. 3
Fig. 3

Schematic of chainlike aggregates consisting of polysized primary particles but with the same number of primary particles.

Fig. 4
Fig. 4

Schematic of chainlike aggregates consisting of monosized primary particles but with a different number of primary particles per aggregate.

Fig. 5
Fig. 5

Generation of primary particle sizes according to the PDF.

Fig. 6
Fig. 6

Comparison of the generated primary particle size distribution and the given ZOLD function with dm = 47.2 nm and σ = 0.4.

Fig. 7
Fig. 7

Effect of polydispersity of primary particle size on (a) Kvve, (b) Rhv, (c) Rvv, and (d) Rhh for aggregates with Np = 2, m = 1.7 + i0.7.

Fig. 8
Fig. 8

Effect of polydispersity of primary particle size on (a) Kvve, (b) Rhv, (c) Rvv, and (d) Rhh for aggregates with Np = 10, d¯ p = 60 nm, m = 1.7 + i0.7.

Fig. 9
Fig. 9

Effect of polydispersity of primary particle number on (a) Kvve, (b) Rhv, (c) Rvv, and (d) Rhh for aggregates with N¯ p = 8, xp = 0.3, m = 1.7 + i0.7.

Tables (3)

Tables Icon

Table 1 Data Inversion Errors Resulting from the Assumption of Monodispersity for Agglomerates Consisting of a Polydisperse Size of Primary Particlesa

Tables Icon

Table 2 Data Inversion Errors Resulting from the Assumption of Monodispersity for Agglomerates Consisting of a Polydisperse Number of Primary Particlessa

Tables Icon

Table 3 Example of Data Inversion for Agglomerates Consisting of Polysized Primary Particles

Equations (33)

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

1+ωC0Ei-ωj=1jiNp C2TijEj=Einc,i; i=1, 2, 3, Np,
ω=ε-1=n+ik2-1,
C0=133-2ixi2h11xi,
C2=i3 xj2j1xj,
Cvpθ=|ε-1|2|V|2,
Chpθ=|ε-1|2|H|2,
V=i=1Np Rixij1xiexp-ikri cos βiEx,i,
H=i=1Np Rixij1xiexp-ikri cos βi×cos θEy,i-sin θEz,i,
cos βi=cos θi cos θ+sin θi sin θ cosϕi-π2,
Cext=4π Imε-1i=1Np Ri2j1xiEi·Einc,i*,
C¯pp=18π202πdω 02πdψ 0π Cpp sin χdχ,
C¯pp=14π02πdψ 0π Cpp sin χdχ.
Pdp=exp-σ22dmσ2πexp-lndpdm22σ2,
lnd¯p=ln dm+1.5σ2.
Kvveθ=j=1NC¯vvjθj=1NC¯extj,
Rhvθ=j=1NC¯hvjθj=1NC¯vvjθ,
Rvvθ=j=1NC¯vvjθj=1NC¯vvjπ-θ,
Rhhθ=j=1NC¯hhjθj=1NC¯hhjπ-θ,
Kppθ=Npi=1 niCppNpi,
Kpp=N Npi=1niN CppNpi,
Pni=exp-σ22Nmσ2πexp-lnniNm22σ2,
Kppθ=NC¯ppθ,
C¯ppθ=ni=1 PniCppNpi.
Kext=NC¯ext,
C¯ext=ni=1 PniCextNpi.
Kvveθ=C¯vvθC¯ext,
Rhvθ=C¯hvθC¯vvθ,
Rvvθ=C¯vvθC¯vvπ-θ,
Rhhθ=C¯hhθC¯hhπ-θ.
C¯vvθ, Npdm=[C¯vvθ, dm+Δdm/2-C¯vvθ, dm-Δdm/2]/Δdm,
C¯vvθ, Npσd=[C¯vvθ, σd+Δσd/2-C¯vvθ, σd-Δσd/2]/Δσd,
C¯vvθ, NpNp=12 [C¯vvθ, Np+1-C¯vvθ, Np-1],
Kvveθn=1j=1NC¯extjj=1NC¯vvjθn-Kvveθj=1NC¯extjn.

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