Inverse design, fabrication, and tolerance to extreme environments of radiative cooling coating: supplement

Alternative to the traditional force cooling technologies, daytime radiative cooling (DRC) has drawn widespread attention for its zero-power. A porous polymer coating based on poly (vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) has been reported as it has excellent DRC capacity. However, performance of the PVDF-HFP coating is affected substantially by its preparation conditions, restricting its application. To resolve the issue, we utilize an artificial neural network (ANN) to predict its DRC capacity and obtain the best preparation condition by siftings. In this work, the predicted solar reflectance (R¯
s
o
l
a
r
) and emittance of the atmospheric transmittance window (e¯
a
t
w
), under the optimal preparation condition, reach 0.983 and 0.932, with a 1.865% and 0.107% error from the experimental value, correspondingly. Noticeably, the optimal PVDF-HFP coating achieves about 6℃ temperature drops below ambient temperature during daytime. In addition, to extend its applications in space, we conduct the extreme environmental experiment on the PVDF-HFP coating. After exposing in the extreme environment, R¯
s
o
l
a
r
of the coating has degradation rate over 11%. Consequently, these simulative methods and experimental results provide a positive direction for fabricating the high-performance DRCs.


Obtaining sample data
The prepared PVDF-HFP coating.
In this paper, the PVDF-HFP coatings were prepared by phase inversion method, shown in the Fig.S1a. From the Fig.S1a, it could be found that the ratio of PVDF-HFPacetone-water would affect the DRC performance of the PVDF-HFP coating. In addition, the evaporation temperature in the coating forming process would affect the surface morphology, further affecting the DRC performance of the PVDF-HFP coating.
Mandal [1] had prepared the PVDF-HFP-acetone-water with a 1:8:1 mass ratio DRCC, possessing the high radiative cooling performance, and pointed out the effect of thickness(x 4 ) in the meantime. Based on the preparation, the ratio of acetone was fixed at 8 in the paper. For this reason, four experimental variables were identified, which were PVDF-HFP proportion(x 1 ), water proportion(x 2 ) and evaporation temperature(

Calculation of net cooling power
As for the discriminant condition of sifting, net radiative cooling power (∆ ) was chose to sift the optimal preparation preparation condition. Net radiative cooling power of PVDF-HFP coatings is calculated by the following Equations (1-8) [2,3]: where ( ) is the blackbody radiation of the coating surface at T(K), is the emittance of the coating surface. Especially, for the convenience of calculation, T is equal to the ambient air temperature , assumed as 298K.
The absorbed fraction by atmospheric radiation is: where is the sky emittance, is the temperature of atmosphere, is the view factor of the coating surface to the atmosphere layer, equal to 1, σ is the Stefan- For the at daytime and night, the Berdahl and Martin relation is used: where (℃) is dew-point temperature, defined as: is related to T a and their relationship is described as: The absorbed sun radiation is: where the solar radiation density is assumed as 1000 Wm -2 in the calculation.
The non-radiative power is: In this part, the effect of (a) x 1 , (b) x 2 and (c) x 3 on the its porosity was discussed.

Influence of experimental variables on porosity
An SEM (S-4800, Hitachi Co., Japan) was used to observe the microstructure of the coatings, shown in the Fig.S3. With x1 increasing, the porosity and pore diameter of the coating would gradually increase, shown in the Fig.S3a. Moreover, the increase of the x 1 would make it more easily to form the larger and more uniform micropores. In the meantime, the increase of the x 1 was beneficial to the formation of micropores. As shown in the Fig.S3b, the porosity would gradually decrease with the increase of x 2 .
Significantly, high or low x 2 will hinder the formation of pores. From the Fig.S3c, it could be found that the porosity increased first and then decreased with the increase of x 3 , indicating that appropriate evaporation temperature was more conducive to the formation of micropores. It was worth noting that excessive evaporation temperatures could cause the destruction of coating surface morphology.

Calculation of transmittance
Where λ is the wavelength, , ( ) is the blackbody spectral radiative intensity at 25℃, and ( ) is the spectral transmittance at 8-13 μm. The ideal emitter in terrestrial and space is different. Terrestrial emitter has to ensure that the emittance is maximized across the atmospheric transparence (8-13 μm), space one does not have above limitations, requiring high emittance in infrared domain (2.5-25 μm).

Net cooling power in space
Net cooling power with different temperature in terrestrial and space is calculated.
For space net cooling power, the atmospheric transparence is not considered. The net cooling power in space is calculated by the following Equation