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# Experimental Determination and Modeling of the Radiative Properties of Silica Nanoporous Matrices

[+] Author and Article Information
Sylvain Lallich

Centre de Thermique de Lyon, UMR CNRS 5008, Institut National des Sciences Appliquées, 20 Avenue Albert Einstein, F-69621 Villeurbanne Cedex, Francesylvainlallich@yahoo.fr

Franck Enguehard1

CEA/Le Ripault, BP 16, F-37260 Monts, Francefranck.enguehard@cea.fr

Dominique Baillis

Centre de Thermique de Lyon, UMR CNRS 5008, Institut National des Sciences Appliquées, 20 Avenue Albert Einstein, F-69621 Villeurbanne Cedex, Francedominique.baillis@insa-lyon.fr

1

Corresponding author.

J. Heat Transfer 131(8), 082701 (Jun 01, 2009) (12 pages) doi:10.1115/1.3109999 History: Received June 25, 2008; Revised February 09, 2009; Published June 01, 2009

## Abstract

Superinsulating materials are currently of interest because the heating and cooling of houses and offices are responsible for an important part of $CO2$ emissions. In this study, we aim at modeling the radiative transfer in nanoporous silica matrices that are the principal components of nanoporous superinsulating materials. We first elaborate samples from different pyrogenic amorphous silica powders that slightly differ one from another in terms of specific surface, nanoparticle diameter, and composition. The various samples are optically characterized using two spectrometers operating on the wavelength range (250 nm; $20μm$). Once the hemispherical transmittance and reflectance spectra are measured, we deduce the radiative properties using a parameter identification technique. Then, as the considered media are made of packed quasispherical nanoparticles, we try to model their radiative properties using the original Mie theory. To obtain a good agreement between experiment and theory on a large part of the wavelength range, we have to consider scatterers that are up to five times larger than the primary nanoparticles; this is attributed to the fact that the scatterers are not the nanoparticles but aggregates of nanoparticles that are constituted during the fabrication process of the powders. Nevertheless, in the small wavelength range ($λ$ smaller than $1μm$), we can never get a satisfactory agreement using the Mie theory. This disagreement is attributed to the fact that the original Mie theory does not take into account the nanostructure of the aggregates. So we have developed a code based on the discrete dipole approximation that improves the modeling results in the small wavelength range, basing our computations on aggregates generated using the diffusion-limited cluster-cluster aggregation algorithm in order to ensure a fractal dimension close to what is usually found with aggregates of silica nanoparticles.

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## Figures

Figure 3

Hemispherical transmittance spectra obtained for two samples (S1 and S2) of different thicknesses t made of the same HDK-T30 powder

Figure 4

Hemispherical reflectance spectra obtained for two samples (S1 and S2) of different thicknesses t made of the same HDK-T30 powder

Figure 5

Extinction coefficient spectra obtained by parameter identification for two samples of different thicknesses t made of the same HDK-T30 powder

Figure 6

Albedo spectra computed by parameter identification for two samples of different thicknesses t made of the same HDK-T30 powder

Figure 7

Comparison of the HDK-T30 powder of an experimental extinction coefficient spectrum (S1) with those obtained using the Mie theory for 9 nm diameter scatterers. Various correlations are applied to the Mie theory in order to account for dependent scattering effects.

Figure 8

Same as Fig. 1, but for albedo spectra

Figure 1

Figure stemmed from Ref. 43: Electron micrograph of the Cab-O-Sil fumed silica, which has been shadowed with vaporized gold to highlight the three dimensional random branching of the aggregates. Final magnification 50,000×.

Figure 2

TEM micrograph of the Wacker HDK-T30 powder

Figure 10

Same as Fig. 9, but for albedo spectra

Figure 11

Comparison of the HDK-T30 powder of two experimental extinction coefficient spectra with those obtained using the Mie theory for three different scatterer diameters. The model we use to include the contribution of water is the coated sphere model.

Figure 12

Comparison of the HDK-T30 powder of two experimental albedo spectra with those obtained using the Mie theory with the same parameters as in Fig. 1

Figure 13

Example of aggregate generated using the DLCCA algorithm and made of 87 nanoparticles of 9 nm diameter; this aggregate is representative of our HDK-T30 powder samples

Figure 14

Comparison of the HDK-T30 powder of an experimental extinction coefficient spectrum to the spectra obtained using the Mie theory on the one hand and using the DDA on the aggregate of Fig. 1 on the other hand. Concerning the DDA results, we present the minimum, the arithmetic mean, and the maximum values yielded by the computations over 100 target orientations.

Figure 15

Comparison of the HDK-T30 powder of an experimental albedo spectrum to the spectra obtained using the Mie theory on the one hand and using the DDA on the aggregate of Fig. 1 on the other hand. Concerning the DDA results, we present the minimum, the arithmetic mean, and the maximum values yielded by the computations over 100 target orientations.

Figure 16

Comparison of the EH5 powder of an experimental extinction coefficient spectrum to the spectra obtained using the Mie theory on the one hand and using the DDA on a DLCCA representative aggregate on the other hand. For the results obtained with the DDA, we present the minimum, the arithmetic mean, and the maximum values of the computations over 100 target orientations.

Figure 17

Comparison of the EH5 powder of an experimental albedo spectrum to the spectra obtained using the Mie theory on the one hand and using the DDA on a DLCCA representative aggregate on the other hand. For the results obtained with the DDA, we present the minimum, the arithmetic mean, and the maximum values of the computations over 100 target orientations.

Figure 18

Comparison of the COK84 powder of an experimental extinction coefficient spectrum to the spectra obtained using the Mie theory on the one hand and using the DDA on a DLCCA representative aggregate on the other hand. For the results obtained with the DDA, we present the minimum, the arithmetic mean, and the maximum values of the computations over 100 target orientations.

Figure 19

Comparison of the COK84 powder of an experimental albedo spectrum to the spectra obtained using the Mie theory on the one hand and using the DDA on a DLCCA representative aggregate on the other hand. For the results obtained with the DDA, we present the minimum, the arithmetic mean, and the maximum values of the computations over 100 target orientations.

Figure 20

Comparison of the HDK-T30 powder of two experimental albedo spectra with those obtained using the Mie theory for uniform distributions of scatterer diameters equal to 36 nm, 38 nm, 40 nm, 42 nm, and 44 nm

Figure 21

Evolution of the DDA extinction coefficient spectrum in relation to the diameter of the nanoparticles constituting the DLCCA representative aggregate

Figure 22

Same as Fig. 1, but here the DDA computations are performed on an aggregate generated using the DLA algorithm

Figure 9

Comparison of the HDK-T30 powder of an experimental extinction coefficient spectrum with those obtained using the Mie theory for 9 nm diameter scatterers. The results obtained using the correlations developed in Ref. 23 are presented to appreciate the impact of multiple and dependent scattering.

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