Abstract

This study compares the optical coefficients of size-selected soot particles measured at a wavelength of 870  nm with those predicted by three theories, namely, Rayleigh–Debye–Gans (RDG) approximation, volume-equivalent Mie theory, and integral equation formulation for scattering (IEFS). Soot particles, produced by a premixed ethene flame, were size-selected using two differential mobility analyzers in series, and their scattering and absorption coefficients were measured with nephelometry and photoacoustic spectroscopy. Scanning electron microscopy and image processing techniques were used for the parameterization of the structural properties of the fractal-like soot aggregates. The aggregate structural parameters were used to evaluate the predictions of the optical coefficients based on the three light-scattering and absorption theories. Our results show that the RDG approximation agrees within 10% with the experimental results and the exact electromagnetic calculations of the IEFS theory. Volume-equivalent Mie theory overpredicts the experimental scattering coefficient by a factor of 3.2. The optical coefficients predicted by the RDG approximation showed pronounced sensitivity to changes in monomer mean diameter, the count median diameter of the aggregates, and the geometric standard deviation of the aggregate number size distribution.

© 2007 Optical Society of America

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2007 (1)

J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, J. T. Jayne, L. R. Williams, M. R. Canagaratna, D. R. Worsnop, R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, J. P. Schwarz, R.-S. Gao, D. W. Fahey, G. L. Kok, “Intercomparison of instruments measuring black carbon content and optical properties of soot particles,” Aerosol Sci. Technol. 41, 295–314 (2007).
[CrossRef]

2006 (1)

A. Abu–Rahmah, W. P. Arnott, H. Moosmüller, “Integrating nephelometer with a low truncation angle and an extended calibration scheme,” Meas. Sci. Technol. 17, 1723–1732 (2006).
[CrossRef]

2005 (1)

2004 (4)

J. G. Slowik, K. Stainken, P. Davidovits, L. R. Williams, J. T. Jayne, C. E. Kolb, D. R. Worsnop, Y. Rudich, P. F. DeCarlo, J. L. Jimenez, “Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 2. Application to combustion-generated soot aerosol as a function of fuel equivalence ratio,” Aerosol Sci. Technol. 38, 1206–1222 (2004).
[CrossRef]

K. Park, D. Kittelson, P. McMurry, “Structural properties of diesel exhaust particles measured by transmission electron microscopy (TEM): relationships to particle mass and mobility,” Aerosol Sci. Technol. 38, 881–889 (2004).
[CrossRef]

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quant. Spectrosc. Radiat. Transfer 88, 149–161 (2004).
[CrossRef]

J. Hansen, L. Nazarenko, “Soot climate forcing via snow and ice albedos,” Proc. Natl. Acad. Sci. USA 101, 423–428 (2004).
[CrossRef]

2003 (3)

M. Sato, J. Hansen, D. Koch, A. Lacis, R. Ruedy, O. Dubovik, B. Holben, M. Chin, T. Novakov, “Global atmospheric black carbon inferred from AERONET,” Proc. Nat. Acad. Sci. USA 100, 6319–6324 (2003).
[CrossRef] [PubMed]

W. P. Arnott, H. Moosmüller, P. J. Sheridan, J. A. Ogren, R. Raspet, W. V. Slaton, J. L. Hand, S. M. Kreidenweis, J. L. Collett, “Photoacoustic and filter-based ambient aerosol light absorption measurements: instrument comparison and the role of relative humidity,” J. Geophy. Res. 108, 4034–4044 (2003).
[CrossRef]

J. Widmann, J. C. Yang, T. J. Smith, S. L. Manzello, G. W. Mulholland, “Measurement of the optical extinction coefficients of postflame soot in the infrared,” Combust. Flame 134, 119–129 (2003).
[CrossRef]

2002 (4)

J. G. Watson, “2002 critical review—visibility: science and regulation,” J. Air Waste Manage. Assoc. 52, 626–713 (2002).

S. Menon, J. Hansen, L. Nazarenko, Y. Luo, “Climate effects of black carbon aerosols in China and India,” Science 297, 2250–2253 (2002).
[CrossRef] [PubMed]

P. H. McMurry, X. Wang, K. Park, K. Ehara, “The relationship between mass and mobility for atmospheric particles: a new technique for measuring particle density,” Aerosol. Sci. Technol. 36, 227–238 (2002).
[CrossRef]

G. Wang, C. M. Sorensen, “Experimental test of the Rayleigh–Debye–Gans theory for light scattering by fractal aggregates,” Appl. Opt. 41, 4645–4651 (2002).
[CrossRef] [PubMed]

2001 (2)

V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
[CrossRef]

C. M. Sorensen, “Light scattering by fractal aggregates: a review,” Aerosol Sci. Technol. 35, 648–687 (2001).
[CrossRef]

2000 (1)

W. P. Arnott, H. Moosmüller, J. W. Walker, “Nitrogen dioxide and kerosene-flame soot calibration of photoacoustic instruments for measurement of light absorption by aerosols,” Rev. Sci. Instrum. 71, 4545–4552 (2000).
[CrossRef]

1999 (2)

W. P. Arnott, H. Moosmüller, C. F. Rogers, T. Jin, R. Bruch, “Photoacoustic spectrometer for measuring light absorption by aerosol: instrument description,” Atmos. Environ. 33, 2845–2852 (1999).
[CrossRef]

A. M. Brasil, T. L. Farias, M. G. Carvalho, “A recipe for image characterization of fractal-like aggregates,” J. Aerosol Sci. 30, 1379–1389 (1999).
[CrossRef]

1998 (2)

J. M. Haywood, V. Ramaswamy, “Global sensitivity studies of the direct radiative forcing due to anthropogenic sulfate and black carbon aerosol,” J. Geophys. Res. 103, 6043–6058 (1998).
[CrossRef]

J. S. Reid, P. V. Hobbs, “Physical and optical properties of young smoke from individual biomass fires in Brazil,” J. Geophys. Res. 103, 32013–32030 (1998).
[CrossRef]

1997 (4)

S. Vedal, “Critical review: ambient particles and health: lines that divide,” J. Air Waste Manage. Assoc. 47, 551–581 (1997).

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

P. V. Hobbs, J. S. Reid, R. A. Kotchenruther, R. J. Ferek, R. Weiss, “Direct radiative forcing by smoke from biomass burning,” Science 275, 1776–1778 (1997).
[CrossRef] [PubMed]

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

1996 (3)

K. C. Smyth, C. R. Shaddix, “The elusive history of m = 1.57–0.56 i for the refractive index of soot,” Combust. Flame 107, 314–320 (1996).
[CrossRef]

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, T. S. Bates, “Performance characteristics of a high-sensitivity, three-wavelength, total scatter∕backscatter nephelometer,” J. Atmos. Oceanic Technol. 13, 967–986 (1996).
[CrossRef]

T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Range of validity of the Rayleigh–Debye–Gans theory for optics of fractal aggregates,” Appl. Opt. 35, 6560–6567 (1996).
[CrossRef] [PubMed]

1995 (2)

U. O. Köylü, Y. C. 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]

Ü. Ö. Köylü, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
[CrossRef]

1994 (4)

S. Leonard, G. W. Mulholland, R. Puri, R. J. Santoro, “Generation of CO and smoke during underventilated combustion,” Combust. Flame 98, 20–34 (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. J. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1994).
[CrossRef]

M. Y. Choi, A. Hamins, G. W. Mulholland, T. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174–186 (1994).
[CrossRef]

1993 (3)

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]

R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
[CrossRef]

S. N. Rogak, R. C. Flagan, H. V. Nguyen, “The mobility and structure of aerosol agglomerates,” Aerosol Sci. Technol. 18, 25–47 (1993).
[CrossRef]

1992 (3)

U. O. Köylü, G. M. Faeth, “Structure of overfire soot in buoyant turbulent-diffusion flames at long residence times,” Combust. Flame 89, 140–156 (1992).
[CrossRef]

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]

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1991 (2)

1990 (3)

C. M. Megaridis, R. A. Dobbins, “Morphological description of flame-generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
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J. A. Nelson, R. J. Crookes, S. Simons, “On obtaining the fractal dimension of a three-dimensional cluster from its projection on a plane—application to smoke agglomerates,” J. Phys. D 23, 465–468 (1990).
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H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London, Ser. A 430, 577–591 (1990).
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1989 (1)

J. Nelson, “Test of a mean field theory for the optics of fractal clusters,” J. Mod. Opt. 36, 1031–1057 (1989).
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1988 (1)

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
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1987 (2)

J. E. Martin, A. J. Hurd, “Scattering from fractals,” J. Appl. Crystallogr. 20, 61–78 (1987).
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R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987).
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1986 (3)

J. K. Kjems, T. Freltoft, D. Richter, S. K. Sinha, “Neutron scattering from fractals,” Physica B & C 136, 285–290 (1986).
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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, 269–275 (1986).
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M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
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1984 (3)

J. E. Martin, D. W. Schaefer, “Dynamics of fractal colloidal aggregates,” Phys. Rev. Lett. 53, 2457–2460 (1984).
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D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
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S. A. Twomey, M. Piépgrass, T. L. Wolfe, “An assessment of the impact of pollution on global cloud albedo,” Tellus Ser. B 36, 356–366 (1984).
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1982 (1)

1981 (2)

B. S. Haynes, H. G. Wagner, “Soot formation,” Prog. Energy Combust. Sci. 7, 229–273 (1981).
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O. I. Smith, “Fundamentals of soot formation in flames with application to diesel-engine particulate-emissions,” Prog. Energy Combust. Sci. 7, 275–291 (1981).
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1979 (2)

A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
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S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A Math. Nucl. Gen. 12, L109–L117 (1979).
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1975 (1)

E. O. Knutson, K. T. Whitby, “Aerosol classification by electric mobility: apparatus, theory, and applications,” J. Aerosol Sci. 6, 443–451 (1975).
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1973 (1)

B. E. Dahneke, “Slip correction factors for nonspherical bodies. 3. The form of the general law,” J. Aerosol Sci. 4, 163–170 (1973).
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1969 (1)

W. H. Dalzell, A. F. Sarofim, “Optical constants of soot and their application to heat-flux calculations,” J. Heat Transfer 91, 100–104 (1969).
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1967 (1)

M. E. Fisher, R. J. Burford, “Theory of critical-point scattering and correlations. I. The Ising model,” Phys. Rev. A 156, 583–622 (1967).
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1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
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A. Abu–Rahmah, W. P. Arnott, H. Moosmüller, “Integrating nephelometer with a low truncation angle and an extended calibration scheme,” Meas. Sci. Technol. 17, 1723–1732 (2006).
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T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, T. S. Bates, “Performance characteristics of a high-sensitivity, three-wavelength, total scatter∕backscatter nephelometer,” J. Atmos. Oceanic Technol. 13, 967–986 (1996).
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V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
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V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
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T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, T. S. Bates, “Performance characteristics of a high-sensitivity, three-wavelength, total scatter∕backscatter nephelometer,” J. Atmos. Oceanic Technol. 13, 967–986 (1996).
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V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
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J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, J. T. Jayne, L. R. Williams, M. R. Canagaratna, D. R. Worsnop, R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, J. P. Schwarz, R.-S. Gao, D. W. Fahey, G. L. Kok, “Intercomparison of instruments measuring black carbon content and optical properties of soot particles,” Aerosol Sci. Technol. 41, 295–314 (2007).
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A. Abu–Rahmah, W. P. Arnott, H. Moosmüller, “Integrating nephelometer with a low truncation angle and an extended calibration scheme,” Meas. Sci. Technol. 17, 1723–1732 (2006).
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W. P. Arnott, H. Moosmüller, P. J. Sheridan, J. A. Ogren, R. Raspet, W. V. Slaton, J. L. Hand, S. M. Kreidenweis, J. L. Collett, “Photoacoustic and filter-based ambient aerosol light absorption measurements: instrument comparison and the role of relative humidity,” J. Geophy. Res. 108, 4034–4044 (2003).
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W. P. Arnott, H. Moosmüller, J. W. Walker, “Nitrogen dioxide and kerosene-flame soot calibration of photoacoustic instruments for measurement of light absorption by aerosols,” Rev. Sci. Instrum. 71, 4545–4552 (2000).
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W. P. Arnott, H. Moosmüller, C. F. Rogers, T. Jin, R. Bruch, “Photoacoustic spectrometer for measuring light absorption by aerosol: instrument description,” Atmos. Environ. 33, 2845–2852 (1999).
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T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, T. S. Bates, “Performance characteristics of a high-sensitivity, three-wavelength, total scatter∕backscatter nephelometer,” J. Atmos. Oceanic Technol. 13, 967–986 (1996).
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M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
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A. M. Brasil, T. L. Farias, M. G. Carvalho, “A recipe for image characterization of fractal-like aggregates,” J. Aerosol Sci. 30, 1379–1389 (1999).
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Bruch, R.

W. P. Arnott, H. Moosmüller, C. F. Rogers, T. Jin, R. Bruch, “Photoacoustic spectrometer for measuring light absorption by aerosol: instrument description,” Atmos. Environ. 33, 2845–2852 (1999).
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M. E. Fisher, R. J. Burford, “Theory of critical-point scattering and correlations. I. The Ising model,” Phys. Rev. A 156, 583–622 (1967).
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M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quant. Spectrosc. Radiat. Transfer 88, 149–161 (2004).
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Caldow, R.

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, T. S. Bates, “Performance characteristics of a high-sensitivity, three-wavelength, total scatter∕backscatter nephelometer,” J. Atmos. Oceanic Technol. 13, 967–986 (1996).
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Canagaratna, M. R.

J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, J. T. Jayne, L. R. Williams, M. R. Canagaratna, D. R. Worsnop, R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, J. P. Schwarz, R.-S. Gao, D. W. Fahey, G. L. Kok, “Intercomparison of instruments measuring black carbon content and optical properties of soot particles,” Aerosol Sci. Technol. 41, 295–314 (2007).
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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).
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Cantrell, W.

V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
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Carvalho, M. G.

A. M. Brasil, T. L. Farias, M. G. Carvalho, “A recipe for image characterization of fractal-like aggregates,” J. Aerosol Sci. 30, 1379–1389 (1999).
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T. L. Farias, Ü. Ö. Köylü, M. G. Carvalho, “Range of validity of the Rayleigh–Debye–Gans theory for optics of fractal aggregates,” Appl. Opt. 35, 6560–6567 (1996).
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Ü. Ö. Köylü, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
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Cass, G. R.

V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
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Chakrabarty, R. K.

J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, J. T. Jayne, L. R. Williams, M. R. Canagaratna, D. R. Worsnop, R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, J. P. Schwarz, R.-S. Gao, D. W. Fahey, G. L. Kok, “Intercomparison of instruments measuring black carbon content and optical properties of soot particles,” Aerosol Sci. Technol. 41, 295–314 (2007).
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Chang, H.

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London, Ser. A 430, 577–591 (1990).
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Charalampopoulos, T. T.

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H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London, Ser. A 430, 577–591 (1990).
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T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, T. S. Bates, “Performance characteristics of a high-sensitivity, three-wavelength, total scatter∕backscatter nephelometer,” J. Atmos. Oceanic Technol. 13, 967–986 (1996).
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Chin, M.

M. Sato, J. Hansen, D. Koch, A. Lacis, R. Ruedy, O. Dubovik, B. Holben, M. Chin, T. Novakov, “Global atmospheric black carbon inferred from AERONET,” Proc. Nat. Acad. Sci. USA 100, 6319–6324 (2003).
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Choi, M. Y.

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Chung, C. E.

V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
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Chylek, P.

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W. P. Arnott, H. Moosmüller, P. J. Sheridan, J. A. Ogren, R. Raspet, W. V. Slaton, J. L. Hand, S. M. Kreidenweis, J. L. Collett, “Photoacoustic and filter-based ambient aerosol light absorption measurements: instrument comparison and the role of relative humidity,” J. Geophy. Res. 108, 4034–4044 (2003).
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T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, T. S. Bates, “Performance characteristics of a high-sensitivity, three-wavelength, total scatter∕backscatter nephelometer,” J. Atmos. Oceanic Technol. 13, 967–986 (1996).
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J. A. Nelson, R. J. Crookes, S. Simons, “On obtaining the fractal dimension of a three-dimensional cluster from its projection on a plane—application to smoke agglomerates,” J. Phys. D 23, 465–468 (1990).
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J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, J. T. Jayne, L. R. Williams, M. R. Canagaratna, D. R. Worsnop, R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, J. P. Schwarz, R.-S. Gao, D. W. Fahey, G. L. Kok, “Intercomparison of instruments measuring black carbon content and optical properties of soot particles,” Aerosol Sci. Technol. 41, 295–314 (2007).
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V. Ramanathan, P. J. Crutzen, J. Lelieveld, A. P. Mitra, D. Althausen, J. Anderson, M. O. Andreae, W. Cantrell, G. R. Cass, C. E. Chung, “Indian Ocean experiment: an integrated analysis of the climate forcing and effects of the great Indo-Asian haze,” J. Geophys. Res. 106, 28371–28398 (2001).
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B. E. Dahneke, “Slip correction factors for nonspherical bodies. 3. The form of the general law,” J. Aerosol Sci. 4, 163–170 (1973).
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A. D'Alessio, A. Di Lorenzo, A. F. Sarofim, F. M. Beretta, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (The Combustion Institute, 1975), pp. 1427–1438.

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W. H. Dalzell, A. F. Sarofim, “Optical constants of soot and their application to heat-flux calculations,” J. Heat Transfer 91, 100–104 (1969).
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J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, J. T. Jayne, L. R. Williams, M. R. Canagaratna, D. R. Worsnop, R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, J. P. Schwarz, R.-S. Gao, D. W. Fahey, G. L. Kok, “Intercomparison of instruments measuring black carbon content and optical properties of soot particles,” Aerosol Sci. Technol. 41, 295–314 (2007).
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J. G. Slowik, K. Stainken, P. Davidovits, L. R. Williams, J. T. Jayne, C. E. Kolb, D. R. Worsnop, Y. Rudich, P. F. DeCarlo, J. L. Jimenez, “Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 2. Application to combustion-generated soot aerosol as a function of fuel equivalence ratio,” Aerosol Sci. Technol. 38, 1206–1222 (2004).
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J. G. Slowik, K. Stainken, P. Davidovits, L. R. Williams, J. T. Jayne, C. E. Kolb, D. R. Worsnop, Y. Rudich, P. F. DeCarlo, J. L. Jimenez, “Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 2. Application to combustion-generated soot aerosol as a function of fuel equivalence ratio,” Aerosol Sci. Technol. 38, 1206–1222 (2004).
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A. D'Alessio, A. Di Lorenzo, A. F. Sarofim, F. M. Beretta, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (The Combustion Institute, 1975), pp. 1427–1438.

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M. Sato, J. Hansen, D. Koch, A. Lacis, R. Ruedy, O. Dubovik, B. Holben, M. Chin, T. Novakov, “Global atmospheric black carbon inferred from AERONET,” Proc. Nat. Acad. Sci. USA 100, 6319–6324 (2003).
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A. M. Brasil, T. L. Farias, M. G. Carvalho, “A recipe for image characterization of fractal-like aggregates,” J. Aerosol Sci. 30, 1379–1389 (1999).
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J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, J. T. Jayne, L. R. Williams, M. R. Canagaratna, D. R. Worsnop, R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, J. P. Schwarz, R.-S. Gao, D. W. Fahey, G. L. Kok, “Intercomparison of instruments measuring black carbon content and optical properties of soot particles,” Aerosol Sci. Technol. 41, 295–314 (2007).
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W. P. Arnott, H. Moosmüller, P. J. Sheridan, J. A. Ogren, R. Raspet, W. V. Slaton, J. L. Hand, S. M. Kreidenweis, J. L. Collett, “Photoacoustic and filter-based ambient aerosol light absorption measurements: instrument comparison and the role of relative humidity,” J. Geophy. Res. 108, 4034–4044 (2003).
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Figures (9)

Fig. 1
Fig. 1

Schematic of the experimental setup used for soot generation and characterization.

Fig. 2
Fig. 2

SEM projected area equivalent diameter ( D e q ) and the SMPS mobility diameter ( D m ) number size distribution for soot particles, which were size selected at D m = 400   nm by the DMAs.

Fig. 3
Fig. 3

Monomer number size distribution of the soot aggregates.

Fig. 4
Fig. 4

Magnified micrograph of a soot aggregate from this study, highlighting its “fluffy” nature and the high degree of overlap between the monomers.

Fig. 5
Fig. 5

Relationship between the radius of gyration R g and the projected area equivalent diameter D e q for the soot aggregates.

Fig. 6
Fig. 6

Log-log plot of N versus L max / d p for the population of soot aggregates.

Fig. 7
Fig. 7

Relationship between volume-equivalent diameter ( D v e ) and mobility diameter ( D m ) of the soot aggregates with D = 1.70 and d p = 45.5   nm .

Fig. 8
Fig. 8

Ratio of volume-equivalent Mie and RDG cross sections C sca Mie / C sca RDG , calculated for D = 1.70 , d p = 47   nm , and m = 1.57 0.56 i , versus N.

Fig. 9
Fig. 9

Volume-normalized Mie and RDG cross sections versus monomer number N.

Tables (1)

Tables Icon

Table 1 Sensitivity of the Calculated Optical Coefficients a

Equations (32)

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φ = n fuel / n O 2 ( n fuel / n O 2 ) stoich ,
N = k 0 ( R g / d p ) D ,
S ( q R g ) = x 1   exp ( x 2 ( q R g ) 2 / 3 ) , Guinier   regime ,
S ( q R g ) = ( q R g ) D , power-law   regime ,
k a 1 ,
| m | k a 1 ,
C sca p = k 4 a 4 F ( m ) ,
F ( m ) = | m 2 1 m 2 + 2 | .
C diff agg ( θ ) = N 2 C sca p S ( q R g ) .
C sca agg = N 2 8 3 π k 4 a 6 F ( m ) g ( k R g , D ) ,
g ( k R g , D ) = ( 1 + 4 3 D k 2 R g 2 ) D / 2 .
g ( k R g , D ) = ( 1 2 3 k 2 R g 2 ) , ( k R g ) 2 3 D / 8 ,
g ( k R g , D ) = β 2 ( 3 3 β + 2 β 2 ) ( k R g β ) 2 3 × ( 3 4 β + 3 β 2 ) + ( 2 k R g ) D [ 3 2 D 12 ( 6 D ) ( 4 D ) 3 β 1 D / 2 × ( 1 2 D 2 β 4 D + 2 β 2 6 D ) ] ,
( k R g ) 2 3 D / 8 ,
C abs agg = N C abs p ,
C abs p = 4 π k a 3 E ( m ) ,
E ( m ) = Im ( m 2 1 m 2 + 2 ) .
B diff agg = 8 3 π k 4 a 6 F ( m ) ( D r = 1 D r = D c n ( D r ) N 2 ( D r ) exp ( q 2 R g 2 / 3 ) d D r + D r = D c D r = n ( D r ) N 2 ( D r ) ( q R g ) D d D r ) ,
B sca agg = 8 3 π k 4 a 6 F ( m ) D m = 1 D m = n ( D m ) N 2 ( D m ) × g ( k R g ( D m ) , D ) d D m .
B abs agg = 4 π k a 3 E ( m ) D m = 1 D m = n ( D m ) N ( D m ) d D m .
D e q = D m 1.01 .
N = k a ( A agg / A p ) α ,
N ( D m ) = 4 × 10 14 ( D m ) 5 2 × 10 10 ( D m ) 4 + 4 × 10 7 ( D m ) 3 2.3 × 10 2 ( D m ) + 0.8559.
D 2 = x , y D 2 ( x , y ) .
R g , 2 2 = D 2 1 x , y D 2 ( x , y ) ( r ( x , y ) r c m ) 2 .
r c m = D 2 1 x , y D 2 ( x , y ) r ( x , y ) .
R g = k r D e q α r = 0.19 D e q 1.17 ,
R g = k r D m 0.99 α r = 0.19 D m 1.16 .
D = D f L = ln ( N k L ) ln ( L max d p ) ,
k 0 = k L ( L max R g ) D ,
k 0 = k L ( 3.0 ) D .
D v e = ( N 1 / 3 ) d p .

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