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Theoretical and experimental investigation of haze in transparent aerogels

Lin Zhao, Elise Strobach, Bikram Bhatia, Sungwoo Yang, Arny Leroy, Lenan Zhang, and Evelyn N. Wang

Open Access Open Access

Abstract

Haze in optically transparent aerogels severely degrades the visual experience, which has prevented their adoption in windows despite their outstanding thermal insulation property. Previous studies have primarily relied on experiments to characterize haze in aerogels, however, a theoretical framework to systematically investigate haze in porous media is lacking. In this work, we present a radiative transfer model that can predict haze in aerogels based on their physical properties. The model is validated using optical characterization of custom-fabricated, highly-transparent monolithic silica aerogels. The fundamental relationships between the aerogel structure and haze highlighted in this study could lead to a better understanding of light-matter interaction in a wide range of transparent porous materials and assist in the development of low-haze silica aerogels for high-performance glazing units to reduce building energy consumption.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (6)
Fig. 1
Fig. 1 Diffuse transmission caused by silica nanoparticle scattering in a transparent aerogel layer. In the typical plane-parallel geometry, the light intensity within the aerogel layer depends on the distance into the layer z and the polar angle θ as shown on the right.

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Fig. 2
Fig. 2 a. Diffuse transmittance, b. Haze as a function of optical depth for isotropic, Rayleigh, and Henyey-Greenstein (g = 0.5) phase functions. The difference in diffuse transmittance and haze between isotropic and Rayleigh phase function is negligible. Results of both ω = 1 (pure scattering medium) and ω = 0.5 (partially absorbing medium) are shown.

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Fig. 3
Fig. 3 a. Schematic of the diffuse and total transmittance measurement using a spectrophotometer with an integrating sphere. b. Optical image of a piece of glass and aerogel sample C (2 cm × 2 cm) on top of printed MIT logo. c. Measured and modeled total transmittance (top), diffuse transmittance (middle), and haze (bottom) of samples A, B, and C. The diffuse transmittance of samples A and B monotonically increases towards shorter wavelength, whereas the diffuse transmittance of sample C peaks at around 252 nm. This behavior confirms the model prediction as shown by the dashed lines.

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Fig. 4
Fig. 4 a. Haze, b. Total transmittance of a 5 mm thick aerogel layer as a function of its mean particle radius and density. c. Haze and total transmittance as a function of aerogel thickness (aerogel density: 200 kg/m3, mean particle radius: 3, 6, and 9 nm).

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Fig. 5
Fig. 5 Haze and total transmittance of transparent aerogels reported in previous literature (triangles) and demonstrated in this work (stars). Solid lines are the model predictions for different scattering asymmetric factor g and single scattering albedo ω. Performance of a single-pane glass is indicated by the green shaded area.

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Fig. 6
Fig. 6 RTE model validation on a high-haze aerogel sample (thickness = 14 mm, density = 150 kg/m3, optical mean particle radius = 10.1 nm).

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Tables (1)

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Table 1 Transparent aerogel samples used in this study

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Equations (9)

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Haze= T diffuse T total = T diffuse T diffuse + T direct
μ d I d ( τ,μ ) dτ =− I d ( τ,μ )+ ω 2 ∫ −1 1 P( μ,μ' ) I d ( τ,μ' )dμ' + ω 4π P( μ, μ 0 ) F 0 e −τ
P( μ,μ' )= 1 2π ∫ 0 2π dϕ 1 2π ∫ 0 2π dϕ' P( μ,ϕ;μ',ϕ' )
P( γ )=1 ( Isotropic )
P( γ )= 3 4 ( 1+ cos 2 ( γ ) ) ( Rayleigh )
P( γ )= 1− g 2 ( 1+ g 2 −2gcos( γ ) ) 3 2 (Henyey−Greenstein)
I d ( 0,μ )=0 for 0≤μ≤1 I d ( τ 0 ,μ )=0 for -1≤μ≤0
T diffuse = 2π ∫ 0 1 I d ( τ 0 ,μ )μdμ F 0
σ abs =Nπ r 2 Q abs ( r,λ,n( λ ) ) σ sca =Nπ r 2 Q sca ( r,λ,n( λ ) )
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