Abstract

Light scattering by light absorbing carbon (LAC) aggregates encapsulated into sulfate shells is computed by use of the discrete dipole method. Computations are performed for a UV, visible, and IR wavelength, different particle sizes, and volume fractions. Reference computations are compared to three classes of simplified model particles that have been proposed for climate modeling purposes. Neither model matches the reference results sufficiently well. Remarkably, more realistic core-shell geometries fall behind homogeneous mixture models. An extended model based on a core-shell-shell geometry is proposed and tested. Good agreement is found for total optical cross sections and the asymmetry parameter.

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2011 (2)

M. Kahnert and T. Rother, “Modeling optical properties of particles with small-scale surface roughness: combination of group theory with a perturbation approach,” Opt. Express 19, 11138–11151 (2011).
[CrossRef] [PubMed]

M. Kahnert and A. Devasthale, “Black carbon fractal morphology and short-wave radiative impact: a modelling study,” Atmos. Chem. Phys. 11, 11745–11759 (2011).
[CrossRef]

2010 (4)

M. Kahnert, “Modelling the optical and radiative properties of freshly emitted light absorbing carbon within an atmospheric chemical transport model,” Atmos. Chem. Phys. 10, 1403–1416 (2010).
[CrossRef]

M. Kahnert, “On the discrepancy between modelled and measured mass absorption cross sections of light absorbing carbon aerosols,” Aerosol Sci. Technol. 44, 453–460 (2010).
[CrossRef]

M. Kahnert, “Numerically exact computation of the optical properties of light absorbing carbon aggregates for wavelength of 200 nm V 12.2 μm,” Atmos. Chem. Phys. 10, 8319–8329 (2010).
[CrossRef]

K. Adachi, S. Chung, and P. R. Buseck, “Shapes of soot aerosol particles and implications for their effects on climate,” J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

2008 (5)

A. Worringen, M. Ebert, T. Trautmann, S. Weinbruch, and G. Helas, “Optical properties of internally mixed ammonium sulfate and soot particles—a study of individual aerosol particles and ambient aerosol populations,” Appl. Opt. 47, 3835–3845 (2008).
[CrossRef] [PubMed]

M. Kocifaj and G. Videen, “Optical behavior of composite carbonaceous aerosols: DDA and EMT approaches,” J. Quant. Spectrosc. Radiat. Transfer 109, 1404–1416 (2008).
[CrossRef]

V. Ramanathan and G. Carmichael, “Global and regional climate changes due to black carbon,” Nat. Geosci. 1, 221–227 (2008).
[CrossRef]

K. Adachi and P. R. Buseck, “Internally mixed soot, sulfates, and organic matter in aerosol particles from Mexico City,” Atmos. Chem. Phys. 8, 6469–6481 (2008).
[CrossRef]

M. Kocifaj, F. Kundracík, and G. Videen, “Optical properties of single mixed-phase aerosol particles,” J. Quant. Spectrosc. Radiat. Transfer 109, 2108–2123 (2008).
[CrossRef]

2007 (4)

E. Zubko, K. Muinonen, Y. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 604–615 (2007).
[CrossRef]

S. Tsyro, D. Simpson, L. Tarrasón, Z. K. K. Kupiainen, C. Pio, and K. E. Yttri, “Modelling of elemental carbon over Europe,” J. Geophys. Res. 112, D23S19 (2007).
[CrossRef]

K. Adachi, S. H. Chung, H. Friedrich, and P. R. Buseck, “Fractal parameters of individual soot particles determined using electron tomography: Implications for optical properties,” J. Geophys. Res. 112, D14202 (2007).
[CrossRef]

L. Liu and M. I. Mishchenko, “Scattering and radiative properties of complex soot and soot-containing aggregate particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 262–273 (2007).
[CrossRef]

2006 (2)

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111, D20211 (2006).
[CrossRef]

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

2005 (5)

B. Croft, U. Lohmann, and K. von Salzen, “Black carbon aging in the Canadian Centre for climate modelling and analysis atmospheric general circulation model,” Atmos. Chem. Phys. 5, 1383–1419 (2005).
[CrossRef]

R. J. Park, D. J. Jacob, P. I. Palmer, A. D. Clarke, R. J. Weber, M. A. Zondlo, F. L. Eisele, A. R. Bandy, D. C. Thornton, G. W. Sachse, and T. C. Bond, “Export efficiency of black carbon aerosol in continental outflow: global implications,” J. Geophys. Res. 110, D11205 (2005).
[CrossRef]

L. H. van Poppel, H. Friedrich, J. Spinsby, S. H. Chung, J. H. Seinfeld, and P. R. Buseck, “Electron tomography of nanoparticle clusters: Implications for atmospheric lifetimes and radiative forcing of soot,” Geophys. Res. Lett. 32, L24811 (2005).
[CrossRef]

M. Schnaiter, C. Linke, O. Moehler, K.-H. Naumann, H. Saathoff, R. Wagner, U. Schurath, and B. Wehner, “Absorption amplification of black carbon internally mixed with secondary organic aerosol,” J. Geophys. Res. 110, D19204 (2005).
[CrossRef]

M. Kahnert, “Irreducible representations of finite groups in the T matrix formulation of the electromagnetic scattering problem,” J. Opt. Soc. Am. A 22, 1187–1199 (2005).
[CrossRef]

2004 (1)

N. Riemer, H. Vogel, and B. Vogel, “Soot aging time scales in polluted regions during day and night,” Atmos. Chem. Phys. 4, 1885–1893 (2004).
[CrossRef]

2003 (1)

M. Schnaiter, H. Horvath, O. Möhler, K.-H. Naumann, H. Saathoff, and O. W. Schöck, “UV-VIS-NIR spectral optical properties of soot and soot-containing aerosols,” J. Aerosol Sci. 34, 1421–1444 (2003).
[CrossRef]

2001 (2)

M. Z. Jacobson, “Strong radiative heating due to the mixing state of black carbon in atmospheric aerosols,” Nature 409, 695–697 (2001).
[CrossRef] [PubMed]

J. Wilson, C. Cuvelier, and F. Raes, “A modeling study of global mixed aerosol fields,” J. Geophys. Res. 106, 34081–34108 (2001).
[CrossRef]

2000 (1)

M. Z. Jacobson, “A physically-based treatment of elemental carbon optics: Implications for global direct forcing of aerosols,” Geophys. Res. Lett 27, 217–220 (2000).
[CrossRef]

1999 (1)

K. A. Fuller, W. C. Malm, and S. M. Kreidenweis, “Effects of mixing on extinction by carbonaceous particles,” J. Geophys. Res. 104, 15941–15954 (1999).
[CrossRef]

1998 (2)

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Met. Soc. 79, 831–844 (1998).
[CrossRef]

G. Videen and P. Chýlek, “Scattering by a composite sphere with an absorbing inclusion and effective medium approximations,” Opt. Commun. 158, 1–6 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

1995 (3)

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres III. spheres containing arbitrarily located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893–904 (1995).
[CrossRef]

G. Ramachandran and P. C. Reist, “Characterization of morphological changes in agglomerates subject to condensation and evaporation using multiple fractal dimensions,” Aerosol Sci. Technol. 23, 431–442 (1995).
[CrossRef]

S. Nyeki and I. Colbeck, “Fractal dimension analysis of single, in-situ, restructured carbonaceous aggregates,” Aerosol Sci. Technol. 23, 109–120 (1995).
[CrossRef]

1994 (1)

1991 (1)

Z. S. Wu and Y. P. Wang, “Electromagnetic scattering for multilayered sphere: recursive algorithms,” Radio Sci. 26, 1393–1401 (1991).
[CrossRef]

1990 (2)

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

I. Colbeck, L. Appleby, E. J. Hardman, and R. M. Harrison, “The optical properties and morphology of cloud-processed carbonaceous smoke,” J. Aerosol Sci. 21, 527–538 (1990).
[CrossRef]

1989 (1)

J. Hallett, J. G. Hudson, and C. F. Rogers, “Characterization of combustion aerosols for haze and cloud formation,” Aerosol Sci. Technol. 10, 70–83 (1989).
[CrossRef]

1981 (1)

1973 (1)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

1935 (1)

D. A. G. Bruggemann, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. 1. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 24, 636–664 (1935).
[CrossRef]

1904 (1)

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. Ser. A 203, 385–420 (1904).
[CrossRef]

Ackermann, T. P.

Adachi, K.

K. Adachi, S. Chung, and P. R. Buseck, “Shapes of soot aerosol particles and implications for their effects on climate,” J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

K. Adachi and P. R. Buseck, “Internally mixed soot, sulfates, and organic matter in aerosol particles from Mexico City,” Atmos. Chem. Phys. 8, 6469–6481 (2008).
[CrossRef]

K. Adachi, S. H. Chung, H. Friedrich, and P. R. Buseck, “Fractal parameters of individual soot particles determined using electron tomography: Implications for optical properties,” J. Geophys. Res. 112, D14202 (2007).
[CrossRef]

Appleby, L.

I. Colbeck, L. Appleby, E. J. Hardman, and R. M. Harrison, “The optical properties and morphology of cloud-processed carbonaceous smoke,” J. Aerosol Sci. 21, 527–538 (1990).
[CrossRef]

Artaxo, P.

P. Forster, V. Ramaswamy, P. Artaxo, T. Berntsen, R. Betts, D. W. Fahey, J. Haywood, J. Lean, D. C. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. Van Dorland, “Changes in atmospheric constituents and in radiative forcing.” in Climate Change 2007: The Physical Science Basis, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miller, eds. (Cambridge University Press, 2007), Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change.

Bandy, A. R.

R. J. Park, D. J. Jacob, P. I. Palmer, A. D. Clarke, R. J. Weber, M. A. Zondlo, F. L. Eisele, A. R. Bandy, D. C. Thornton, G. W. Sachse, and T. C. Bond, “Export efficiency of black carbon aerosol in continental outflow: global implications,” J. Geophys. Res. 110, D11205 (2005).
[CrossRef]

Bergstrom, R. W.

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

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111, D20211 (2006).
[CrossRef]

Berntsen, T.

P. Forster, V. Ramaswamy, P. Artaxo, T. Berntsen, R. Betts, D. W. Fahey, J. Haywood, J. Lean, D. C. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. Van Dorland, “Changes in atmospheric constituents and in radiative forcing.” in Climate Change 2007: The Physical Science Basis, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miller, eds. (Cambridge University Press, 2007), Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change.

Betts, R.

P. Forster, V. Ramaswamy, P. Artaxo, T. Berntsen, R. Betts, D. W. Fahey, J. Haywood, J. Lean, D. C. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. Van Dorland, “Changes in atmospheric constituents and in radiative forcing.” in Climate Change 2007: The Physical Science Basis, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miller, eds. (Cambridge University Press, 2007), Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change.

Bond, T. C.

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

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111, D20211 (2006).
[CrossRef]

R. J. Park, D. J. Jacob, P. I. Palmer, A. D. Clarke, R. J. Weber, M. A. Zondlo, F. L. Eisele, A. R. Bandy, D. C. Thornton, G. W. Sachse, and T. C. Bond, “Export efficiency of black carbon aerosol in continental outflow: global implications,” J. Geophys. Res. 110, D11205 (2005).
[CrossRef]

Bruggemann, D. A. G.

D. A. G. Bruggemann, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. 1. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 24, 636–664 (1935).
[CrossRef]

Buseck, P. R.

K. Adachi, S. Chung, and P. R. Buseck, “Shapes of soot aerosol particles and implications for their effects on climate,” J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

K. Adachi and P. R. Buseck, “Internally mixed soot, sulfates, and organic matter in aerosol particles from Mexico City,” Atmos. Chem. Phys. 8, 6469–6481 (2008).
[CrossRef]

K. Adachi, S. H. Chung, H. Friedrich, and P. R. Buseck, “Fractal parameters of individual soot particles determined using electron tomography: Implications for optical properties,” J. Geophys. Res. 112, D14202 (2007).
[CrossRef]

L. H. van Poppel, H. Friedrich, J. Spinsby, S. H. Chung, J. H. Seinfeld, and P. R. Buseck, “Electron tomography of nanoparticle clusters: Implications for atmospheric lifetimes and radiative forcing of soot,” Geophys. Res. Lett. 32, L24811 (2005).
[CrossRef]

Carmichael, G.

V. Ramanathan and G. Carmichael, “Global and regional climate changes due to black carbon,” Nat. Geosci. 1, 221–227 (2008).
[CrossRef]

Chang, H.

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

Charalampopoulos, T. T.

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

Chung, S.

K. Adachi, S. Chung, and P. R. Buseck, “Shapes of soot aerosol particles and implications for their effects on climate,” J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

Chung, S. H.

K. Adachi, S. H. Chung, H. Friedrich, and P. R. Buseck, “Fractal parameters of individual soot particles determined using electron tomography: Implications for optical properties,” J. Geophys. Res. 112, D14202 (2007).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Electron micrograph of LAC aggregate encapsulated in sulfate shell. (Note that most of the aggregate is inside the sulfate shell, while only a small part is sticking out.) Examples of encapsulated aggregate models considered in this study with the following parameters: (b) f = 0.07, R = 500 nm, Ns=560, and (c) f = 0.20, R = 500 nm, Ns=1600.

Fig. 2
Fig. 2

(a) External mixture, (b) homogeneous internal mixture, (c) core-shell, and (d) core-shell-shell model.

Fig. 3
Fig. 3

Optical properties for λ = 304.2 nm and f =7%, computed for 5 stochastic realizations of encapsulated aggregates (symbols), externally mixed LAC and sulfate spheres (green line), homogeneous spheres with an effective refractive index based on Maxwell-Garnett EMT (red line), LAC cores with sulfate shell (blue line), and sulfate cores with LAC inner shell and sulfate outer shell (black line).

Fig. 4
Fig. 4

As Fig. 3, but for λ = 304.0 nm and f =20%.

Fig. 5
Fig. 5

As Fig. 3, but for λ = 533.2 nm and f =7%.

Fig. 6
Fig. 6

As Fig. 3, but for λ = 533.2 nm and f =20%.

Fig. 7
Fig. 7

As Fig. 3, but for λ = 1010.1 nm and f =7%.

Fig. 8
Fig. 8

As Fig. 3, but for λ = 1010.1 nm and f =20%.

Tables (2)

Tables Icon

Table 1 Number of monomers Ns in the LAC aggregates and corresponding volume-equivalent radii R of the internally mixed aerosols (where the volume of both the LAC and the soluble material has been accounted for).

Tables Icon

Table 2 Refractive indices m of LAC and sulfate at three wavelengths λ.

Equations (9)

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

N s = k 0 ( R g a ) D f ,
R g = 1 N s i = 1 N s r i 2 ,
R LAC = f 1 / 3 R
R SO 4 = ( 1 f ) 1 / 3 R
f 1 ε 1 ε 2 ε 1 + 2 ε 2 = ε eff ε 2 ε eff + 2 ε 2 .
f 1 ε 1 ε eff ε 1 + 2 ε eff + f 2 ε 2 ε eff ε 2 + 2 ε eff = 0 ,
ε eff = f 1 ε 1 + f 2 ε 2 ,
ε eff = f 1 ε 1 + f 2 ε 2 .
r 1 = ( f R 3 + r 0 3 ) 1 / 3 .

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