A theoretical feasibility study of pigments for thickness-sensitive spectrally selective paints

We present a model for thickness-sensitive spectrally selective paints and use it to optimize their optical properties with respect to the particle size of the pigment. Pigments were chosen from different classes of materials such as metals, low band gap insulators and semiconductors and carbon. Silicone was chosen as the binder and the paint thickness was varied from 1 to 4 µm. Scattering and absorption cross sections were derived from Mie theory for spherical particles, and the particle radii ranged between 10 and 500 nm. The reflectance was derived from a radiative transfer formulation of a four-flux model, assuming a mono-disperse particle ensemble. The integrated values for near-normal solar absorptance and thermal emittance at 100°C were calculated from the total near-normal spectral reflectance in the wavelength range 0.3–30 µm. It was found that all the pigments investigated have an optimal particle radius of about 100 nm in the case of a 1.0 µm thick paint layer and a particle volume fraction of 0.20. The optimal particle size increases slightly for thicker films. It was also found that direct, low band gap semiconductors give the best spectral selectivity. A solar absorptance of 0.91 and a thermal emittance of 0.13 were computed for PbS particles of volume fraction 0.20 in a 2.0 µm thick paint layer on aluminium.