OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 28 — Oct. 1, 2007
  • pp: 6990–7006

Light scattering and absorption by fractal-like carbonaceous chain aggregates: comparison of theories and experiment

Rajan K. Chakrabarty, Hans Moosmüller, W. Patrick Arnott, Mark A. Garro, Jay G. Slowik, Eben S. Cross, Jeong-Ho Han, Paul Davidovits, Timothy B. Onasch, and Douglas R. Worsnop  »View Author Affiliations

Applied Optics, Vol. 46, Issue 28, pp. 6990-7006 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (671 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(290.5850) Scattering : Scattering, particles

ToC Category:

Original Manuscript: June 4, 2007
Revised Manuscript: August 9, 2007
Manuscript Accepted: August 10, 2007
Published: September 26, 2007

Rajan K. Chakrabarty, Hans Moosmüller, W. Patrick Arnott, Mark A. Garro, Jay G. Slowik, Eben S. Cross, Jeong-Ho Han, Paul Davidovits, Timothy B. Onasch, and Douglas R. Worsnop, "Light scattering and absorption by fractal-like carbonaceous chain aggregates: comparison of theories and experiment," Appl. Opt. 46, 6990-7006 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. 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]
  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]
  3. National Research Council, A Plan for a Research Program on Aerosol Radiative Forcing and Climate Change (National Academic Press, 1996).
  4. B. J. Finlayson–Pitts, J. N. Pitts, Chemistry of the Upper and Lower Atmosphere: Theory, Experiments, and Applications (Academic, 2000).
  5. J. G. Watson, “2002 critical review—visibility: science and regulation,” J. Air Waste Manage. Assoc. 52, 626–713 (2002).
  6. National Research Council, Protecting Visibility in National Parks and Wilderness Areas (National Academic Press, 1993).
  7. S. Vedal, “Critical review: ambient particles and health: lines that divide,” J. Air Waste Manage. Assoc. 47, 551–581 (1997).
  8. National Research Council (U.S.), Committee on Research Priorities for Airborne Particulate Matter, Research Priorities for Airborne Particulate Matter (National Academy Press, 1998).
  9. J. Hansen, L. Nazarenko, “Soot climate forcing via snow and ice albedos,” Proc. Natl. Acad. Sci. USA 101, 423–428 (2004). [CrossRef]
  10. 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]
  11. 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]
  12. 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). [CrossRef]
  13. 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]
  14. 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]
  15. J. S. Levine, Global Biomass Burning: Atmospheric, Climatic, and Biospheric Implications (MIT Press, 1991).
  16. 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]
  17. B. S. Haynes, H. G. Wagner, “Soot formation,” Prog. Energy Combust. Sci. 7, 229–273 (1981). [CrossRef]
  18. O. I. Smith, “Fundamentals of soot formation in flames with application to diesel-engine particulate-emissions,” Prog. Energy Combust. Sci. 7, 275–291 (1981). [CrossRef]
  19. 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]
  20. 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]
  21. 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]
  22. J. E. Penner, R. E. Dickinson, C. A. O'Neill, “Effects of aerosol from biomass burning on the global radiation budget,” Science 256, 1432–1433 (1992). [CrossRef] [PubMed]
  23. 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]
  24. P. Chylek, V. Ramaswamy, “Lower and upper bounds on extinction cross sections of arbitrarily shaped strongly absorbing or strongly reflecting nonspherical particles,” Appl. Opt. 21, 4339–4344 (1982). [CrossRef] [PubMed]
  25. 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]
  26. 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]
  27. A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979). [CrossRef]
  28. S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A Math. Nucl. Gen. 12, L109–L117 (1979). [CrossRef]
  29. J. E. Martin, D. W. Schaefer, “Dynamics of fractal colloidal aggregates,” Phys. Rev. Lett. 53, 2457–2460 (1984). [CrossRef]
  30. D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984). [CrossRef]
  31. J. K. Kjems, T. Freltoft, D. Richter, S. K. Sinha, “Neutron scattering from fractals,” Physica B & C 136, 285–290 (1986). [CrossRef]
  32. 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). [CrossRef]
  33. M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986). [CrossRef]
  34. J. Nelson, “Test of a mean field theory for the optics of fractal clusters,” J. Mod. Opt. 36, 1031–1057 (1989). [CrossRef]
  35. 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]
  36. 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]
  37. 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]
  38. 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]
  39. 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]
  40. E. O. Knutson, K. T. Whitby, “Aerosol classification by electric mobility: apparatus, theory, and applications,” J. Aerosol Sci. 6, 443–451 (1975). [CrossRef]
  41. R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991). [CrossRef] [PubMed]
  42. 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]
  43. 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]
  44. 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]
  45. 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]
  46. M. R. Stolzenberg, P. H. McMurry, “TDMAFIT user's manual,” in PTL Publication 653 (U. Minnesota, 1988).
  47. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).
  48. C. M. Sorensen, “Light scattering by fractal aggregates: a review,” Aerosol Sci. Technol. 35, 648–687 (2001). [CrossRef]
  49. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  50. R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, 1987).
  51. J. E. Martin, A. J. Hurd, “Scattering from fractals,” J. Appl. Crystallogr. 20, 61–78 (1987). [CrossRef]
  52. A. Guinier, G. Fournet, Small-Angle Scattering of X Rays (Wiley, 1955).
  53. M. E. Fisher, R. J. Burford, “Theory of critical-point scattering and correlations. I. The Ising model,” Phys. Rev. A 156, 583–622 (1967). [CrossRef]
  54. R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988). [CrossRef]
  55. S. Gangopadhyay, I. Elminyawi, C. M. Sorensen, “Optical structure factor measurements of soot particles in a premixed flame,” Appl. Opt. 30, 4859–4864 (1991). [CrossRef] [PubMed]
  56. S. K. Friedlander, Smoke, Dust, and Haze (Wiley-Interscience, 1977).
  57. 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]
  58. S. N. Rogak, R. C. Flagan, H. V. Nguyen, “The mobility and structure of aerosol agglomerates,” Aerosol Sci. Technol. 18, 25–47 (1993). [CrossRef]
  59. 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]
  60. 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]
  61. 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]
  62. R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987). [CrossRef]
  63. C. M. Megaridis, R. A. Dobbins, “Morphological description of flame-generated materials,” Combust. Sci. Technol. 71, 95–109 (1990). [CrossRef]
  64. 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]
  65. 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]
  66. 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]
  67. 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]
  68. 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). [CrossRef]
  69. W. H. Dalzell, A. F. Sarofim, “Optical constants of soot and their application to heat-flux calculations,” J. Heat Transfer 91, 100–104 (1969). [CrossRef]
  70. 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.
  71. 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]
  72. 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]
  73. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908). [CrossRef]
  74. 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]
  75. R. C. Flagan, “Electrical techniques,” in Aerosol Measurement: Principles, Techniques, and Applications, P. A. Baron and K. Willeke, eds. (Wiley, 2001), pp. 537–568.
  76. B. E. Dahneke, “Slip correction factors for nonspherical bodies. 3. The form of the general law,” J. Aerosol Sci. 4, 163–170 (1973). [CrossRef]
  77. W. C. Hinds, Aerosol Technology (Wiley-Interscience, 1999).
  78. P. Yang, H. L. Wei, H. L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005). [CrossRef] [PubMed]
  79. 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). [CrossRef]
  80. G. W. Mulholland, M. Y. Choi, “Measurement of the mass specific extinction coefficient for acetylene and ethene smoke using the large agglomerate optics facility,” in Twenty-Seventh Symposium (International) on Combustion (The Combustion Institute, 1998), Vol. 1, pp. 1515–1522. [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited