Abstract

Opacified aerogels are particulate thermal insulating materials in which micrometric opacifier mineral grains are surrounded by silica aerogel nanoparticles. A geometric model was developed to characterize the spectral properties of such microsize grains surrounded by much smaller particles. The model represents the material’s microstructure with the spherical opacifier’s spectral properties calculated using the multi-sphere T-matrix (MSTM) algorithm. The results are validated by comparing the measured reflectance of an opacified aerogel slab against the value predicted using the discrete ordinate method (DOM) based on calculated optical properties. The results suggest that the large particles embedded in the nanoparticle matrices show different scattering and absorption properties from the single scattering condition and that the MSTM and DOM algorithms are both useful for calculating the spectral and radiative properties of this particulate system.

© 2014 Optical Society of America

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  1. J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
    [CrossRef]
  2. J. Zhao, Y. Duan, X. Wang, B. Wang, “Effects of solid-gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels,” J. Nanopart. Res. 14(8), 1–15 (2012).
    [CrossRef] [PubMed]
  3. J. Fricke, T. Tillotson, “Aerogels: production, characterization, and applications,” Thin Solid Films 297(1-2), 212–223 (1997).
    [CrossRef]
  4. J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
    [CrossRef]
  5. X. Wang, D. Sun, Y. Duan, Z. Hu, “Radiative characteristics of opacifier-loaded silica aerogel composites,” J. Non-Cryst. Solids 375, 31–39 (2013).
    [CrossRef]
  6. V. Napp, R. Caps, H. P. Ebert, J. Fricke, “Optimization of the thermal radiation extinction of silicon carbide in a silica powder matrix,” J. Therm. Anal. Calorim. 56(1), 77–85 (1999).
    [CrossRef]
  7. J. M. Dlugach, M. I. Mishchenko, D. W. Mackowski, “Scattering and absorption properties of polydisperse wavelength-sized particles covered with much smaller grains,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2351–2355 (2012).
    [CrossRef]
  8. C. Tien and B. L. Drolen, “Thermal Radiation in Particulate Media with Dependent and Independent Scattering,” in Annual Review of Numerical Fluid Mechanics and Heat Transfer, T. C. Chawla, ed. (Hemisphere, 1987).
  9. M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15(20), 13188–13202 (2007).
    [CrossRef] [PubMed]
  10. M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 1. Foldy-Lax equations, order-of-scattering expansion, and coherent field,” Opt. Express 16(3), 2288–2301 (2008).
    [CrossRef] [PubMed]
  11. H. Yu, D. Liu, Y. Duan, X. Wang, “Theoretical model of radiative transfer in opacified aerogel based on realistic microstructures,” Int. J. Heat Mass Tran. 70, 478–485 (2014).
    [CrossRef]
  12. D. W. Mackowski, M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
    [CrossRef]
  13. W. A. Fiveland, “Discrete ordinate methods for radiative heat transfer in isotropically and anisotropically scattering media,” J. Heat Transfer-Trans. ASME 109(3), 809–812 (1987).
    [CrossRef]
  14. T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47(19), 1400–1403 (1981).
    [CrossRef]
  15. A. Emmerling, J. Fricke, “Scaling properties and structure of aerogels,” J. Sol-Gel Sci. Techn. 8, 781–788 (1997).
  16. M. I. Mishchenko, L. Liu, G. Videen, “Conditions of applicability of the single-scattering approximation,” Opt. Express 15(12), 7522–7527 (2007).
    [CrossRef] [PubMed]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  18. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
  19. S. Lallich, F. Enguehard, D. Baillis, “Experimental determination and modeling of the radiative properties of silica nanoporous matrices,” J. Heat Transfer-Trans. ASME 131(8), 082701 (2009).
    [CrossRef]
  20. A. Tamanai, H. Mutschke, J. Blum, R. Neuhäuser, “Experimental infrared spectroscopic measurement of light extinction for agglomerate dust grains,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 373–381 (2006).
    [CrossRef]

2014 (1)

H. Yu, D. Liu, Y. Duan, X. Wang, “Theoretical model of radiative transfer in opacified aerogel based on realistic microstructures,” Int. J. Heat Mass Tran. 70, 478–485 (2014).
[CrossRef]

2013 (2)

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

X. Wang, D. Sun, Y. Duan, Z. Hu, “Radiative characteristics of opacifier-loaded silica aerogel composites,” J. Non-Cryst. Solids 375, 31–39 (2013).
[CrossRef]

2012 (2)

J. Zhao, Y. Duan, X. Wang, B. Wang, “Effects of solid-gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels,” J. Nanopart. Res. 14(8), 1–15 (2012).
[CrossRef] [PubMed]

J. M. Dlugach, M. I. Mishchenko, D. W. Mackowski, “Scattering and absorption properties of polydisperse wavelength-sized particles covered with much smaller grains,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2351–2355 (2012).
[CrossRef]

2011 (1)

D. W. Mackowski, M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[CrossRef]

2009 (1)

S. Lallich, F. Enguehard, D. Baillis, “Experimental determination and modeling of the radiative properties of silica nanoporous matrices,” J. Heat Transfer-Trans. ASME 131(8), 082701 (2009).
[CrossRef]

2008 (1)

2007 (2)

2006 (1)

A. Tamanai, H. Mutschke, J. Blum, R. Neuhäuser, “Experimental infrared spectroscopic measurement of light extinction for agglomerate dust grains,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 373–381 (2006).
[CrossRef]

1999 (1)

V. Napp, R. Caps, H. P. Ebert, J. Fricke, “Optimization of the thermal radiation extinction of silicon carbide in a silica powder matrix,” J. Therm. Anal. Calorim. 56(1), 77–85 (1999).
[CrossRef]

1997 (2)

J. Fricke, T. Tillotson, “Aerogels: production, characterization, and applications,” Thin Solid Films 297(1-2), 212–223 (1997).
[CrossRef]

A. Emmerling, J. Fricke, “Scaling properties and structure of aerogels,” J. Sol-Gel Sci. Techn. 8, 781–788 (1997).

1995 (1)

J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
[CrossRef]

1987 (1)

W. A. Fiveland, “Discrete ordinate methods for radiative heat transfer in isotropically and anisotropically scattering media,” J. Heat Transfer-Trans. ASME 109(3), 809–812 (1987).
[CrossRef]

1981 (1)

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47(19), 1400–1403 (1981).
[CrossRef]

Arduinischuster, M. C.

J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
[CrossRef]

Baillis, D.

S. Lallich, F. Enguehard, D. Baillis, “Experimental determination and modeling of the radiative properties of silica nanoporous matrices,” J. Heat Transfer-Trans. ASME 131(8), 082701 (2009).
[CrossRef]

Blum, J.

A. Tamanai, H. Mutschke, J. Blum, R. Neuhäuser, “Experimental infrared spectroscopic measurement of light extinction for agglomerate dust grains,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 373–381 (2006).
[CrossRef]

Caps, R.

V. Napp, R. Caps, H. P. Ebert, J. Fricke, “Optimization of the thermal radiation extinction of silicon carbide in a silica powder matrix,” J. Therm. Anal. Calorim. 56(1), 77–85 (1999).
[CrossRef]

Dlugach, J. M.

J. M. Dlugach, M. I. Mishchenko, D. W. Mackowski, “Scattering and absorption properties of polydisperse wavelength-sized particles covered with much smaller grains,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2351–2355 (2012).
[CrossRef]

Duan, Y.

H. Yu, D. Liu, Y. Duan, X. Wang, “Theoretical model of radiative transfer in opacified aerogel based on realistic microstructures,” Int. J. Heat Mass Tran. 70, 478–485 (2014).
[CrossRef]

X. Wang, D. Sun, Y. Duan, Z. Hu, “Radiative characteristics of opacifier-loaded silica aerogel composites,” J. Non-Cryst. Solids 375, 31–39 (2013).
[CrossRef]

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

J. Zhao, Y. Duan, X. Wang, B. Wang, “Effects of solid-gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels,” J. Nanopart. Res. 14(8), 1–15 (2012).
[CrossRef] [PubMed]

Ebert, H. P.

V. Napp, R. Caps, H. P. Ebert, J. Fricke, “Optimization of the thermal radiation extinction of silicon carbide in a silica powder matrix,” J. Therm. Anal. Calorim. 56(1), 77–85 (1999).
[CrossRef]

Emmerling, A.

A. Emmerling, J. Fricke, “Scaling properties and structure of aerogels,” J. Sol-Gel Sci. Techn. 8, 781–788 (1997).

Enguehard, F.

S. Lallich, F. Enguehard, D. Baillis, “Experimental determination and modeling of the radiative properties of silica nanoporous matrices,” J. Heat Transfer-Trans. ASME 131(8), 082701 (2009).
[CrossRef]

Fiveland, W. A.

W. A. Fiveland, “Discrete ordinate methods for radiative heat transfer in isotropically and anisotropically scattering media,” J. Heat Transfer-Trans. ASME 109(3), 809–812 (1987).
[CrossRef]

Fricke, J.

V. Napp, R. Caps, H. P. Ebert, J. Fricke, “Optimization of the thermal radiation extinction of silicon carbide in a silica powder matrix,” J. Therm. Anal. Calorim. 56(1), 77–85 (1999).
[CrossRef]

J. Fricke, T. Tillotson, “Aerogels: production, characterization, and applications,” Thin Solid Films 297(1-2), 212–223 (1997).
[CrossRef]

A. Emmerling, J. Fricke, “Scaling properties and structure of aerogels,” J. Sol-Gel Sci. Techn. 8, 781–788 (1997).

J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
[CrossRef]

Gao, Y.

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

Gleissner, T.

J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
[CrossRef]

Han, Y.

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

Hu, Z.

X. Wang, D. Sun, Y. Duan, Z. Hu, “Radiative characteristics of opacifier-loaded silica aerogel composites,” J. Non-Cryst. Solids 375, 31–39 (2013).
[CrossRef]

Korder, S.

J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
[CrossRef]

Kuhn, J.

J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
[CrossRef]

Lallich, S.

S. Lallich, F. Enguehard, D. Baillis, “Experimental determination and modeling of the radiative properties of silica nanoporous matrices,” J. Heat Transfer-Trans. ASME 131(8), 082701 (2009).
[CrossRef]

Liu, D.

H. Yu, D. Liu, Y. Duan, X. Wang, “Theoretical model of radiative transfer in opacified aerogel based on realistic microstructures,” Int. J. Heat Mass Tran. 70, 478–485 (2014).
[CrossRef]

Liu, L.

Lv, Z.

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

Mackowski, D. W.

J. M. Dlugach, M. I. Mishchenko, D. W. Mackowski, “Scattering and absorption properties of polydisperse wavelength-sized particles covered with much smaller grains,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2351–2355 (2012).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[CrossRef]

Mishchenko, M. I.

J. M. Dlugach, M. I. Mishchenko, D. W. Mackowski, “Scattering and absorption properties of polydisperse wavelength-sized particles covered with much smaller grains,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2351–2355 (2012).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[CrossRef]

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 1. Foldy-Lax equations, order-of-scattering expansion, and coherent field,” Opt. Express 16(3), 2288–2301 (2008).
[CrossRef] [PubMed]

M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15(20), 13188–13202 (2007).
[CrossRef] [PubMed]

M. I. Mishchenko, L. Liu, G. Videen, “Conditions of applicability of the single-scattering approximation,” Opt. Express 15(12), 7522–7527 (2007).
[CrossRef] [PubMed]

Mutschke, H.

A. Tamanai, H. Mutschke, J. Blum, R. Neuhäuser, “Experimental infrared spectroscopic measurement of light extinction for agglomerate dust grains,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 373–381 (2006).
[CrossRef]

Napp, V.

V. Napp, R. Caps, H. P. Ebert, J. Fricke, “Optimization of the thermal radiation extinction of silicon carbide in a silica powder matrix,” J. Therm. Anal. Calorim. 56(1), 77–85 (1999).
[CrossRef]

Neuhäuser, R.

A. Tamanai, H. Mutschke, J. Blum, R. Neuhäuser, “Experimental infrared spectroscopic measurement of light extinction for agglomerate dust grains,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 373–381 (2006).
[CrossRef]

Sander, L. M.

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47(19), 1400–1403 (1981).
[CrossRef]

Sun, D.

X. Wang, D. Sun, Y. Duan, Z. Hu, “Radiative characteristics of opacifier-loaded silica aerogel composites,” J. Non-Cryst. Solids 375, 31–39 (2013).
[CrossRef]

Tamanai, A.

A. Tamanai, H. Mutschke, J. Blum, R. Neuhäuser, “Experimental infrared spectroscopic measurement of light extinction for agglomerate dust grains,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 373–381 (2006).
[CrossRef]

Tillotson, T.

J. Fricke, T. Tillotson, “Aerogels: production, characterization, and applications,” Thin Solid Films 297(1-2), 212–223 (1997).
[CrossRef]

Videen, G.

Wang, B.

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

J. Zhao, Y. Duan, X. Wang, B. Wang, “Effects of solid-gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels,” J. Nanopart. Res. 14(8), 1–15 (2012).
[CrossRef] [PubMed]

Wang, X.

H. Yu, D. Liu, Y. Duan, X. Wang, “Theoretical model of radiative transfer in opacified aerogel based on realistic microstructures,” Int. J. Heat Mass Tran. 70, 478–485 (2014).
[CrossRef]

X. Wang, D. Sun, Y. Duan, Z. Hu, “Radiative characteristics of opacifier-loaded silica aerogel composites,” J. Non-Cryst. Solids 375, 31–39 (2013).
[CrossRef]

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

J. Zhao, Y. Duan, X. Wang, B. Wang, “Effects of solid-gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels,” J. Nanopart. Res. 14(8), 1–15 (2012).
[CrossRef] [PubMed]

Witten, T. A.

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47(19), 1400–1403 (1981).
[CrossRef]

Yu, H.

H. Yu, D. Liu, Y. Duan, X. Wang, “Theoretical model of radiative transfer in opacified aerogel based on realistic microstructures,” Int. J. Heat Mass Tran. 70, 478–485 (2014).
[CrossRef]

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

Zhang, X.

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

Zhao, J.

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

J. Zhao, Y. Duan, X. Wang, B. Wang, “Effects of solid-gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels,” J. Nanopart. Res. 14(8), 1–15 (2012).
[CrossRef] [PubMed]

Int. J. Heat Mass Tran. (1)

H. Yu, D. Liu, Y. Duan, X. Wang, “Theoretical model of radiative transfer in opacified aerogel based on realistic microstructures,” Int. J. Heat Mass Tran. 70, 478–485 (2014).
[CrossRef]

Int. J. Therm. Sci. (1)

J. Zhao, Y. Duan, X. Wang, X. Zhang, Y. Han, Y. Gao, Z. Lv, H. Yu, B. Wang, “Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation,” Int. J. Therm. Sci. 70, 54–64 (2013).
[CrossRef]

J. Heat Transfer-Trans. ASME (2)

W. A. Fiveland, “Discrete ordinate methods for radiative heat transfer in isotropically and anisotropically scattering media,” J. Heat Transfer-Trans. ASME 109(3), 809–812 (1987).
[CrossRef]

S. Lallich, F. Enguehard, D. Baillis, “Experimental determination and modeling of the radiative properties of silica nanoporous matrices,” J. Heat Transfer-Trans. ASME 131(8), 082701 (2009).
[CrossRef]

J. Nanopart. Res. (1)

J. Zhao, Y. Duan, X. Wang, B. Wang, “Effects of solid-gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels,” J. Nanopart. Res. 14(8), 1–15 (2012).
[CrossRef] [PubMed]

J. Non-Cryst. Solids (2)

X. Wang, D. Sun, Y. Duan, Z. Hu, “Radiative characteristics of opacifier-loaded silica aerogel composites,” J. Non-Cryst. Solids 375, 31–39 (2013).
[CrossRef]

J. Kuhn, T. Gleissner, M. C. Arduinischuster, S. Korder, J. Fricke, “Integration of mineral powders into SiO2 aerogels,” J. Non-Cryst. Solids 186, 291–295 (1995).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (3)

A. Tamanai, H. Mutschke, J. Blum, R. Neuhäuser, “Experimental infrared spectroscopic measurement of light extinction for agglomerate dust grains,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 373–381 (2006).
[CrossRef]

J. M. Dlugach, M. I. Mishchenko, D. W. Mackowski, “Scattering and absorption properties of polydisperse wavelength-sized particles covered with much smaller grains,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2351–2355 (2012).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[CrossRef]

J. Sol-Gel Sci. Techn. (1)

A. Emmerling, J. Fricke, “Scaling properties and structure of aerogels,” J. Sol-Gel Sci. Techn. 8, 781–788 (1997).

J. Therm. Anal. Calorim. (1)

V. Napp, R. Caps, H. P. Ebert, J. Fricke, “Optimization of the thermal radiation extinction of silicon carbide in a silica powder matrix,” J. Therm. Anal. Calorim. 56(1), 77–85 (1999).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (1)

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47(19), 1400–1403 (1981).
[CrossRef]

Thin Solid Films (1)

J. Fricke, T. Tillotson, “Aerogels: production, characterization, and applications,” Thin Solid Films 297(1-2), 212–223 (1997).
[CrossRef]

Other (3)

C. Tien and B. L. Drolen, “Thermal Radiation in Particulate Media with Dependent and Independent Scattering,” in Annual Review of Numerical Fluid Mechanics and Heat Transfer, T. C. Chawla, ed. (Hemisphere, 1987).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (4)

Fig. 1
Fig. 1

TiO2 opacified aerogels: (a) monolithic slab sample; (b) SEM picture of an opacifier grain surrounded by the aerogel; (c) geometric model used in the MSTM calculations.

Fig. 2
Fig. 2

Calculated TiO2 opacifiers optical properties: (a) extinction efficiency, Qext, absorption efficiency, Qabs, and scattering albedo, ωλ, and (b) phase functions, Φλ, at 2 μm, 4 μm and 8 μm.

Fig. 3
Fig. 3

DOM results from Mie and T-matrix calculations compared with the measured reflectance.

Fig. 4
Fig. 4

Size parameters’ influence on the Mie results: (a) varied σ with given d0; (b) varied d0 with given σ.

Equations (8)

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

μ d I λ (z,μ) β λ dz = I λ (z,μ)+ ω λ 2 1 1 Φ λ (μ,μ')I (z,μ')dμ'
I λ (z=0,μ)={ I 0 (| μ μ 0 |<ε) 0(μ>0,μ μ 0 ) , I λ (z=h,μ)=0forμ0
R λ = 1 0 I λ (z=0,μ) μdμ/ 0 1 I λ (z=0,μ) μdμ
1 1 μΦ(μ)dμ k=1 N w k μ k Φ( μ k )
{ w k =2/N(k=1,2,...,N) 0 1 μ i dμ= k=1 N/2 w k μ i (i=0,1,...,N/2)
μ d I λ (z, μ k ) β λ dz = I λ (z, μ k )+ ω λ 2 k'=1 N Φ λ ( μ k , μ k' ) I λ (z, μ k' ) w k'
p(d)d(lnd)= 1 2π σ exp[ (lndln d 0 ) 2 2 σ 2 ]d(lnd)
X ¯ λ ( d 0 ,σ)= 0 X ¯ λ (d)p(d)d(lnd) i=1 N X ¯ λ (d)p(d) Δ lnd

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