In this theoretical study, a disordered metamaterial coating with randomly embedded TiO2 dielectric microspheres in a polydimethylsiloxane matrix has been designed for the purpose of daytime passive radiative cooling. While retaining the necessary optical properties of high reflectivity (≈94%) in the solar spectrum and high emissivity (≈96%) in the atmospheric transparency window, the coating exhibits the following additional desirable properties: (a) low volume fraction of TiO2 microspheres, ensuring minimal possibility of agglomeration of particles during fabrication; and (b) a cooling power of 81.8 W/m2, which is among the highest for similar coatings that have been developed. We also show how a modified form of Kubelka–Munk theory with empirical relations originally developed to analyze optical scattering in biological tissue layers can be used for designing radiative cooling structures. The predictions from this method have been validated using Monte Carlo simulations. It is expected that this study will motivate further similar designs in the rapidly expanding market for effective and easy-to-fabricate coatings for daytime passive radiative cooling applications.
Disordered media coatings are finding increasing use in applications such as day-time radiative cooling paints and solar thermal absorber plate coatings which require tailored optical properties over a broad spectrum ranging from visible to far-IR wavelengths. Both monodisperse and polydisperse configurations with thickness of coatings up to 500 µm are currently being explored for use in these applications. In such cases it becomes increasingly important to explore utility of analytical and semi-analytical methods for design of such coatings to help reduce the computational cost and time for design. While well-known analytical methods such as Kubelka-Munk and four-flux theory have previously been used for analysis of disordered coatings, analysis of their utility has so far in literature been restricted to either solar spectrum or IR but not simultaneously over the combined spectrum as required for the above applications. In this work, we have analysed the applicability of these two analytical methods for such coatings over the entire wavelength range from visible to IR, and based on observed deviation from exact numerical simulation we propose a semi-analytical technique to aid in the design of these coatings with significant computational cost savings.
Analytical techniques such as Kubelka Munk theory, four flux theory, diffusion theory, Monte Carlo simulation technique are used to calculate radiative properties of the disordered coatings for various applications. These techniques deviate significantly from exact numerical solver when particles are in dependent scattering regime and/or when matrix absorption is high. To overcome this, we have proposed a semi-analytical technique to calculate the optical properties of disordered coatings over the entire wavelength range from visible to IR. In this work, we have shown the applicability of semi-analytical technique to model the radiative properties of monodisperse and polydisperse coating for passive daytime radiative cooling. We have used TiO2/PDMS for monodisperse and TiO2/ZrO2/PDMS for polydisperse coating.
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