Empirical relationships between optical properties and equivalent diameters of fractal soot aggregates at 550 nm wavelength

Apoorva Pandey; Rajan K. Chakrabarty; Li Liu; Michael I. Mishchenko

doi:10.1364/OE.23.0A1354

Empirical relationships between optical properties and equivalent diameters of fractal soot aggregates at 550 nm wavelength

Apoorva Pandey, Rajan K. Chakrabarty, Li Liu, and Michael I. Mishchenko

Optics Express
Vol. 23,
Issue 24,
pp. A1354-A1362
(2015)
•https://doi.org/10.1364/OE.23.0A1354

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Apoorva Pandey, Rajan K. Chakrabarty, Li Liu, and Michael I. Mishchenko, "Empirical relationships between optical properties and equivalent diameters of fractal soot aggregates at 550 nm wavelength," Opt. Express 23, A1354-A1362 (2015)

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Related Topics
Table of Contents Category
- Atmospheric Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Aerosols (010.1110)
- Atmospheric optics (010.1290)
- Atmospheric scattering (010.1310)
- Backscattering (290.1350)
- Scattering, particles (290.5850)
- Scattering theory (290.5825)

About this Article
History
- Original Manuscript: July 24, 2015
- Revised Manuscript: September 3, 2015
- Manuscript Accepted: September 7, 2015
- Published: September 24, 2015
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 11, Iss. 1

Accessible

Open Access

Abstract

Soot aggregates (SAs)–fractal clusters of small, spherical carbonaceous monomers–modulate the incoming visible solar radiation and contribute significantly to climate forcing. Experimentalists and climate modelers typically assume a spherical morphology for SAs when computing their optical properties, causing significant errors. Here, we calculate the optical properties of freshly-generated (fractal dimension D_f = 1.8) and aged (D_f = 2.6) SAs at 550 nm wavelength using the numerically-exact superposition T-Matrix method. These properties were expressed as functions of equivalent aerosol diameters as measured by contemporary aerosol instruments. This work improves upon previous efforts wherein SA optical properties were computed as a function of monomer number, rendering them unusable in practical applications. Future research will address the sensitivity of variation in refractive index, fractal prefactor, and monomer overlap of SAs on the reported empirical relationships.

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References

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Publication

R. K. Chakrabarty, N. D. Beres, H. Moosmüller, S. China, C. Mazzoleni, M. K. Dubey, L. Liu, and M. I. Mishchenko, “Soot superaggregates from flaming wildfires and their direct radiative forcing,” Sci. Rep. 4, 5508 (2014).
[Crossref] [PubMed]
C. Sorensen, “Light scattering by fractal aggregates: a review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]
L. Liu, M. I. Mishchenko, and W. P. Arnott, “A study of radiative properties of fractal soot aggregates using the superposition T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 109(15), 2656–2663 (2008).
[Crossref]
C. M. Sorensen, J. Cai, and N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31(30), 6547–6557 (1992).
[Crossref] [PubMed]
M. K. Wu and S. K. Friedlander, “Note on the power law equation for fractal-like aerosol agglomerates,” J. Colloid Interface Sci. 159(1), 246–248 (1993).
[Crossref]
R. Zhang, A. F. Khalizov, J. Pagels, D. Zhang, H. Xue, and P. H. McMurry, “Variability in morphology, hygroscopicity, and optical properties of soot aerosols during atmospheric processing,” Proc. Natl. Acad. Sci. U.S.A. 105(30), 10291–10296 (2008).
[Crossref] [PubMed]
T. C. Bond, S. J. Doherty, D. Fahey, P. Forster, T. Berntsen, B. DeAngelo, M. Flanner, S. Ghan, B. Kärcher, D. Koch, S. Kinne, Y. Kondo, P. K. Quinn, M. C. Sarofim, M. G. Schultz, M. Schulz, C. Venkataraman, H. Zhang, S. Zhang, N. Bellouin, S. K. Guttikunda, P. K. Hopke, M. Z. Jacobson, J. W. Kaiser, Z. Klimont, U. Lohmann, J. P. Schwarz, D. Shindell, T. Storelvmo, S. G. Warren, and C. S. Zender, “Bounding the role of black carbon in the climate system: A scientific assessment,” J. Geophys. Res. Atmos. 118(11), 5380–5552 (2013).
[Crossref]
E. Andrews, P. Sheridan, M. Fiebig, A. McComiskey, J. Ogren, P. Arnott, D. Covert, R. Elleman, R. Gasparini, D. Collins, H. Jonsson, B. Schmid, and J. Wang, “Comparison of methods for deriving aerosol asymmetry parameter,” J. Geophys. Res. Atmos. 111(D5), D05S04 (2006).
[Crossref]
C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petäjä, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Radiative absorption enhancements due to the mixing state of atmospheric black carbon,” Science 337(6098), 1078–1081 (2012).
[Crossref] [PubMed]
H. Li, C. Liu, L. Bi, P. Yang, and G. W. Kattawar, “Numerical accuracy of “equivalent” spherical approximations for computing ensemble-averaged scattering properties of fractal soot aggregates,” J. Quant. Spectrosc. Radiat. Transf. 111(14), 2127–2132 (2010).
[Crossref]
R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, M. A. Garro, J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, and D. R. Worsnop, “Light scattering and absorption by fractal-like carbonaceous chain aggregates: comparison of theories and experiment,” Appl. Opt. 46(28), 6990–7006 (2007).
[Crossref] [PubMed]
H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: A review,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 844–878 (2009).
[Crossref]
M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: A 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 650–658 (2010).
[Crossref]
P. F. DeCarlo, J. G. Slowik, D. R. Worsnop, P. Davidovits, and J. L. Jimenez, “Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 1: Theory,” Aerosol Sci. Technol. 38(12), 1185–1205 (2004).
[Crossref]
M. Laborde, M. Schnaiter, C. Linke, H. Saathoff, K. Naumann, O. Möhler, S. Berlenz, U. Wagner, J. Taylor, D. Liu, M. Flynn, J. D. Allan, H. Coe, K. Heimerl, F. Dahlkötter, B. Weinzierl, A. G. Wollny, M. Zanatta, J. Cozic, P. Laj, R. Hitzenberger, J. P. Schwarz, and M. Gysel, “Single Particle Soot Photometer intercomparison at the AIDA chamber,” Atmos. Meas. Tech. 5(12), 3077–3097 (2012).
[Crossref]
T. Onasch, A. Trimborn, E. Fortner, J. Jayne, G. Kok, L. Williams, P. Davidovits, and D. Worsnop, “Soot particle aerosol mass spectrometer: development, validation, and initial application,” Aerosol Sci. Technol. 46(7), 804–817 (2012).
[Crossref]
M. Lindskog and E. Nordin, Ageing of Diesel Aerosols: Design and Implementation of a Teflon Simulation Chamber (Lund University, 2009).
R. K. Chakrabarty, M. A. Garro, S. Chancellor, C. M. Herald, and H. Moosmüller, “FracMAP: A user-interactive package for performing simulation and orientation-specific morphology analysis of fractal-like solid nano-agglomerates,” Comput. Phys. Commun. 180, 1376–1381 (2009).
[Crossref]
R. K. Chakrabarty, M. A. Garro, B. A. Garro, S. Chancellor, H. Moosmüller, and C. M. Herald, “Simulation of aggregates with point-contacting monomers in the cluster–dilute regime. Part 1: Determining the most reliable technique for obtaining three-dimensional fractal dimension from two-dimensional images,” Aerosol Sci. Technol. 45(1), 75–80 (2011).
[Crossref]
C. M. Sorensen and G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186(2), 447–452 (1997).
[Crossref] [PubMed]
K. Park, D. B. Kittelson, and P. H. McMurry, “Structural properties of diesel exhaust particles measured by transmission electron microscopy (TEM): Relationships to particle mass and mobility,” Aerosol Sci. Technol. 38(9), 881–889 (2004).
[Crossref]
T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]
D. W. Mackowski and M. I. Mishchenko, “Calculation of the T-matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
[Crossref]
M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).
L. Liu and M. I. Mishchenko, “Effects of aggregation on scattering and radiative properties of soot aerosols,” J. Geophys. Res. Atmos. 110(D11), D11211 (2005).
[Crossref]

2014 (1)

R. K. Chakrabarty, N. D. Beres, H. Moosmüller, S. China, C. Mazzoleni, M. K. Dubey, L. Liu, and M. I. Mishchenko, “Soot superaggregates from flaming wildfires and their direct radiative forcing,” Sci. Rep. 4, 5508 (2014).
[Crossref] [PubMed]

2013 (1)

T. C. Bond, S. J. Doherty, D. Fahey, P. Forster, T. Berntsen, B. DeAngelo, M. Flanner, S. Ghan, B. Kärcher, D. Koch, S. Kinne, Y. Kondo, P. K. Quinn, M. C. Sarofim, M. G. Schultz, M. Schulz, C. Venkataraman, H. Zhang, S. Zhang, N. Bellouin, S. K. Guttikunda, P. K. Hopke, M. Z. Jacobson, J. W. Kaiser, Z. Klimont, U. Lohmann, J. P. Schwarz, D. Shindell, T. Storelvmo, S. G. Warren, and C. S. Zender, “Bounding the role of black carbon in the climate system: A scientific assessment,” J. Geophys. Res. Atmos. 118(11), 5380–5552 (2013).
[Crossref]

2012 (3)

C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petäjä, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Radiative absorption enhancements due to the mixing state of atmospheric black carbon,” Science 337(6098), 1078–1081 (2012).
[Crossref] [PubMed]

M. Laborde, M. Schnaiter, C. Linke, H. Saathoff, K. Naumann, O. Möhler, S. Berlenz, U. Wagner, J. Taylor, D. Liu, M. Flynn, J. D. Allan, H. Coe, K. Heimerl, F. Dahlkötter, B. Weinzierl, A. G. Wollny, M. Zanatta, J. Cozic, P. Laj, R. Hitzenberger, J. P. Schwarz, and M. Gysel, “Single Particle Soot Photometer intercomparison at the AIDA chamber,” Atmos. Meas. Tech. 5(12), 3077–3097 (2012).
[Crossref]

T. Onasch, A. Trimborn, E. Fortner, J. Jayne, G. Kok, L. Williams, P. Davidovits, and D. Worsnop, “Soot particle aerosol mass spectrometer: development, validation, and initial application,” Aerosol Sci. Technol. 46(7), 804–817 (2012).
[Crossref]

2011 (1)

R. K. Chakrabarty, M. A. Garro, B. A. Garro, S. Chancellor, H. Moosmüller, and C. M. Herald, “Simulation of aggregates with point-contacting monomers in the cluster–dilute regime. Part 1: Determining the most reliable technique for obtaining three-dimensional fractal dimension from two-dimensional images,” Aerosol Sci. Technol. 45(1), 75–80 (2011).
[Crossref]

2010 (2)

H. Li, C. Liu, L. Bi, P. Yang, and G. W. Kattawar, “Numerical accuracy of “equivalent” spherical approximations for computing ensemble-averaged scattering properties of fractal soot aggregates,” J. Quant. Spectrosc. Radiat. Transf. 111(14), 2127–2132 (2010).
[Crossref]

M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: A 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 650–658 (2010).
[Crossref]

2009 (2)

R. K. Chakrabarty, M. A. Garro, S. Chancellor, C. M. Herald, and H. Moosmüller, “FracMAP: A user-interactive package for performing simulation and orientation-specific morphology analysis of fractal-like solid nano-agglomerates,” Comput. Phys. Commun. 180, 1376–1381 (2009).
[Crossref]

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: A review,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 844–878 (2009).
[Crossref]

2008 (2)

R. Zhang, A. F. Khalizov, J. Pagels, D. Zhang, H. Xue, and P. H. McMurry, “Variability in morphology, hygroscopicity, and optical properties of soot aerosols during atmospheric processing,” Proc. Natl. Acad. Sci. U.S.A. 105(30), 10291–10296 (2008).
[Crossref] [PubMed]

L. Liu, M. I. Mishchenko, and W. P. Arnott, “A study of radiative properties of fractal soot aggregates using the superposition T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 109(15), 2656–2663 (2008).
[Crossref]

2007 (1)

R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, M. A. Garro, J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, and D. R. Worsnop, “Light scattering and absorption by fractal-like carbonaceous chain aggregates: comparison of theories and experiment,” Appl. Opt. 46(28), 6990–7006 (2007).
[Crossref] [PubMed]

2006 (2)

E. Andrews, P. Sheridan, M. Fiebig, A. McComiskey, J. Ogren, P. Arnott, D. Covert, R. Elleman, R. Gasparini, D. Collins, H. Jonsson, B. Schmid, and J. Wang, “Comparison of methods for deriving aerosol asymmetry parameter,” J. Geophys. Res. Atmos. 111(D5), D05S04 (2006).
[Crossref]

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

2005 (1)

L. Liu and M. I. Mishchenko, “Effects of aggregation on scattering and radiative properties of soot aerosols,” J. Geophys. Res. Atmos. 110(D11), D11211 (2005).
[Crossref]

2004 (2)

K. Park, D. B. Kittelson, and P. H. McMurry, “Structural properties of diesel exhaust particles measured by transmission electron microscopy (TEM): Relationships to particle mass and mobility,” Aerosol Sci. Technol. 38(9), 881–889 (2004).
[Crossref]

P. F. DeCarlo, J. G. Slowik, D. R. Worsnop, P. Davidovits, and J. L. Jimenez, “Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 1: Theory,” Aerosol Sci. Technol. 38(12), 1185–1205 (2004).
[Crossref]

2001 (1)

C. Sorensen, “Light scattering by fractal aggregates: a review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]

1997 (1)

C. M. Sorensen and G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186(2), 447–452 (1997).
[Crossref] [PubMed]

1996 (1)

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T-matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
[Crossref]

1993 (1)

M. K. Wu and S. K. Friedlander, “Note on the power law equation for fractal-like aerosol agglomerates,” J. Colloid Interface Sci. 159(1), 246–248 (1993).
[Crossref]

1992 (1)

C. M. Sorensen, J. Cai, and N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31(30), 6547–6557 (1992).
[Crossref] [PubMed]

Allan, J. D.

Andrews, E.

Arnott, P.

Arnott, W.

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: A review,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 844–878 (2009).
[Crossref]

Arnott, W. P.

Bates, T. S.

Bellouin, N.

Beres, N. D.

Bergstrom, R. W.

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

Berlenz, S.

Berntsen, T.

Bi, L.

Bond, T. C.

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

Cai, J.

Cappa, C. D.

Chakrabarty, R.

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: A review,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 844–878 (2009).
[Crossref]

Chakrabarty, R. K.

Chancellor, S.

China, S.

Coe, H.

Collins, D.

Covert, D.

Cozic, J.

Cross, E. S.

Dahlkötter, F.

Davidovits, P.

DeAngelo, B.

DeCarlo, P. F.

Doherty, S. J.

Dubey, M. K.

Elleman, R.

Fahey, D.

Fiebig, M.

Flanner, M.

Flynn, M.

Forster, P.

Fortner, E.

Friedlander, S. K.

M. K. Wu and S. K. Friedlander, “Note on the power law equation for fractal-like aerosol agglomerates,” J. Colloid Interface Sci. 159(1), 246–248 (1993).
[Crossref]

Garro, B. A.

Garro, M. A.

Gasparini, R.

Ghan, S.

Guttikunda, S. K.

Gysel, M.

Hakala, J.

Han, J.-H.

Hayden, K. L.

Heimerl, K.

Herald, C. M.

Hitzenberger, R.

Hopke, P. K.

Jacobson, M. Z.

Jayne, J.

Jimenez, J. L.

Jobson, B. T.

Jonsson, H.

Kaiser, J. W.

Kärcher, B.

Kattawar, G. W.

Khalizov, A. F.

Khlebtsov, N. G.

Kinne, S.

Kittelson, D. B.

Klimont, Z.

Koch, D.

Kok, G.

Kolesar, K. R.

Kondo, Y.

Laborde, M.

Lack, D. A.

Laj, P.

Lerner, B. M.

Li, H.

Li, S. M.

Linke, C.

Liu, C.

Liu, D.

Liu, L.

L. Liu and M. I. Mishchenko, “Effects of aggregation on scattering and radiative properties of soot aerosols,” J. Geophys. Res. Atmos. 110(D11), D11211 (2005).
[Crossref]

Lohmann, U.

Lu, N.

Mackowski, D. W.

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T-matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
[Crossref]

Massoli, P.

Mazzoleni, C.

McComiskey, A.

McMurry, P. H.

Mellon, D.

Mishchenko, M. I.

L. Liu and M. I. Mishchenko, “Effects of aggregation on scattering and radiative properties of soot aerosols,” J. Geophys. Res. Atmos. 110(D11), D11211 (2005).
[Crossref]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T-matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
[Crossref]

Möhler, O.

Moosmüller, H.

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: A review,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 844–878 (2009).
[Crossref]

Naumann, K.

Nuaaman, I.

Ogren, J.

Olfert, J. S.

Onasch, T.

Onasch, T. B.

Pagels, J.

Park, K.

Petäjä, T.

Quinn, P. K.

Roberts, G. C.

C. M. Sorensen and G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186(2), 447–452 (1997).
[Crossref] [PubMed]

Saathoff, H.

Sarofim, M. C.

Schmid, B.

Schnaiter, M.

Schultz, M. G.

Schulz, M.

Schwarz, J. P.

Sheridan, P.

Shindell, D.

Slowik, J. G.

Song, C.

Sorensen, C.

C. Sorensen, “Light scattering by fractal aggregates: a review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]

Sorensen, C. M.

C. M. Sorensen and G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186(2), 447–452 (1997).
[Crossref] [PubMed]

Storelvmo, T.

Subramanian, R.

Taylor, J.

Trimborn, A.

Venkataraman, C.

Videen, G.

Wagner, U.

Wang, J.

Warren, S. G.

Weinzierl, B.

Williams, E. J.

Williams, L.

Wollny, A. G.

Worsnop, D.

Worsnop, D. R.

Wriedt, T.

Wu, M. K.

M. K. Wu and S. K. Friedlander, “Note on the power law equation for fractal-like aerosol agglomerates,” J. Colloid Interface Sci. 159(1), 246–248 (1993).
[Crossref]

Xue, H.

Yang, P.

Zakharova, N. T.

Zanatta, M.

Zaveri, R. A.

Zender, C. S.

Zhang, D.

Zhang, H.

Zhang, R.

Zhang, S.

Aerosol Sci. Technol. (6)

C. Sorensen, “Light scattering by fractal aggregates: a review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

Appl. Opt. (2)

Atmos. Meas. Tech. (1)

Comput. Phys. Commun. (1)

J. Colloid Interface Sci. (2)

C. M. Sorensen and G. C. Roberts, “The prefactor of fractal aggregates,” J. Colloid Interface Sci. 186(2), 447–452 (1997).
[Crossref] [PubMed]

M. K. Wu and S. K. Friedlander, “Note on the power law equation for fractal-like aerosol agglomerates,” J. Colloid Interface Sci. 159(1), 246–248 (1993).
[Crossref]

J. Geophys. Res. Atmos. (3)

L. Liu and M. I. Mishchenko, “Effects of aggregation on scattering and radiative properties of soot aerosols,” J. Geophys. Res. Atmos. 110(D11), D11211 (2005).
[Crossref]

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

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T-matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (4)

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: A review,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 844–878 (2009).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

Sci. Rep. (1)

Science (1)

Other (2)

M. Lindskog and E. Nordin, Ageing of Diesel Aerosols: Design and Implementation of a Teflon Simulation Chamber (Lund University, 2009).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

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Fig. 1 Example of a 3-d quasi-fractal agglomerate simulated by FracMAP and its 2-d pixelated projection image for a stable orientation.

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Fig. 2 Variation of (a) C_scat (µm²), (b) C_abs (µm²), and (c) g, with mobility diameter, d_m (µm) of soot aggregates with D_f equal to 1.8 (fresh) and 2.6 (aged).

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Fig. 3 Variation of (a) C_scat (µm²), (b) C_abs (µm²), and (c) g, with mass equivalent diameter, d_me (µm) of soot aggregates with D_f equal to 1.8 (fresh) and 2.6 (aged).

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Fig. 4 Variation of (a) C_scat (µm²), (b) C_abs (µm²), and (c) g, with vacuum aerodynamic diameter, d_Va (µm) of soot aggregates with D_f equal to 1.8 (fresh) and 2.6 (aged).

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Tables (4)

Table 1 Estimated equivalent aerosol diameters (nm) for fresh and aged soot aggregates as a function of monomer number (N).

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Table 2 Best fit empirical equations connecting the mobility diameter, d_m (in μm) and the optical properties of fresh and aged SA.

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Table 3 Best fit empirical equations connecting the mass equivalent diameter, d_me (in μm) and the optical properties of fresh and aged SA.

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Table 4 Best fit empirical equations connecting the vacuum aerodynamic diameter, d_Va (in μm) and the optical properties of fresh and aged SA.

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Equations (6)

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N = k_{0} \times {(\frac{R_{g}}{r_{0}})}^{D_{f}}

ω = \frac{C_{s c a t}}{C_{s c a t} + C_{a b s}}

g = - 7.14 f^{3} + 7.46 f^{2} - 3.96 f + 0.9893

d_{m e} = d_{m o n o} \times N^{\frac{1}{3}}

d_{V a} = \frac{ρ_{p}}{ρ_{o}} \times \frac{d_{v e}}{χ}

χ = \frac{d_{m}}{d_{v e}} \times \frac{C (K n_{v e})}{C (K n_{m})}

N	Mobility diameter¹(nm)		Mass equivalent diameter² (nm)	Vacuum aerodynamic diameter¹ (nm)
N	Fresh soot (D_f = 1.8)	Aged soot (D_f = 2.6)	Fresh and aged soot	Fresh soot (D_f = 1.8)	Aged soot (D_f = 2.6)
5	114 ± 0.6	105 ± 4.2	85	86 ± 0.7	101 ± 5.7
10	151 ± 4.8	135 ± 6.2	107	98 ± 4.4	123 ± 8.0
25	227 ± 8.4	198 ± 10	146	109 ± 5.7	143 ± 10.2
50	317 ± 10.5	260 ± 7.5	184	112 ± 5.3	166 ± 6.0
100	427 ± 7.0	341 ± 12	232	123 ± 0.6	193 ± 9.7
150	531 ± 15	402 ± 5.0	265	119 ± 4.8	209 ± 4.3
200	605 ± 18.6	455 ± 28	292	123 ± 5.3	217 ± 18.9
250	663 ± 15.4	489 ± 20	315	128 ± 4.2	234 ± 14.7
300	703 ± 44	530 ± 12	333	136 ± 12.1	240 ± 8.1

Optical property	Fresh SA (D_f = 1.8)		Aged SA (D_f = 2.6)
Optical property	Equation	Adjusted R²	Equation	Adjusted R²
C_scat	$0.24 \times (d_{m}^{2.8})$	0.998	$0.93 \times (d_{m}^{3})$	0.998
C_abs	$0.4 \times (d_{m}^{2.1})$	0.998	$0.8 \times (d_{m}^{2.3})$	0.998
g	$- 1.94 \times d_{m}^{2} + 2.51 \times d_{m} - 0.13$	0.993	$- 3.7 \times d_{m}^{2} + 4.14 \times d_{m} - 0.36$	0.991

Optical property	Fresh SA (D_f = 1.8)		Aged SA (D_f = 2.6)
Optical property	Equation	Adjusted R²	Equation	Adjusted R²
C_scat	$5.83 \times (d_{m e}^{3.76})$	0.999	$6.75 \times (d_{m e}^{3.55})$	0.999
C_abs	$5.14 \times (d_{m e}^{2.91})$	1	$3.64 \times (d_{m e}^{2.70})$	0.999
g	$- 9.77 \times d_{m e}^{2} + 6.32 \times d_{m e} - 0.35$	0.995	$- 8.32 \times d_{m e}^{2} + 6.55 \times d_{m e} - 0.45$	0.988

Optical property	Fresh SA (D_f = 1.8)		Aged SA (D_f = 2.6)
Optical property	Equation	Adjusted R²	Equation	Adjusted R²
C_scat	$2.9 \times 10^{6} \times (d_{V a}^{8.61})$	0.863	$595 \times (d_{V a}^{5.88})$	0.994
C_abs	$4.43 \times 10^{5} \times (d_{V a}^{7.26})$	0.863	$96.28 \times (d_{V a}^{4.38})$	0.996
g	$- 112.7 \times d_{V a}^{2} + 38.12 \times d_{V a} - 2.38$	0.922	$- 14.92 \times d_{V a}^{2} + 10.84 \times d_{V a} - 0.92$	0.972

N	Mobility diameter¹(nm)		Mass equivalent diameter² (nm)	Vacuum aerodynamic diameter¹ (nm)
N	Fresh soot (D_f = 1.8)	Aged soot (D_f = 2.6)	Fresh and aged soot	Fresh soot (D_f = 1.8)	Aged soot (D_f = 2.6)
5	114 ± 0.6	105 ± 4.2	85	86 ± 0.7	101 ± 5.7
10	151 ± 4.8	135 ± 6.2	107	98 ± 4.4	123 ± 8.0
25	227 ± 8.4	198 ± 10	146	109 ± 5.7	143 ± 10.2
50	317 ± 10.5	260 ± 7.5	184	112 ± 5.3	166 ± 6.0
100	427 ± 7.0	341 ± 12	232	123 ± 0.6	193 ± 9.7
150	531 ± 15	402 ± 5.0	265	119 ± 4.8	209 ± 4.3
200	605 ± 18.6	455 ± 28	292	123 ± 5.3	217 ± 18.9
250	663 ± 15.4	489 ± 20	315	128 ± 4.2	234 ± 14.7
300	703 ± 44	530 ± 12	333	136 ± 12.1	240 ± 8.1