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Abstract
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 (${\bar{R}_{solar}}$) and emittance of the atmospheric transmittance window (${\bar{\varepsilon }_{atw}}$), 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, ${\bar{R}_{solar}}$ 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.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Outdoor enclosures for housing electronic components have come into a wide use in many fields including telecommunication, industry and military [1–3]. Undesired heat in electronic components, either due to their own generated heat or heating by external heat sources (e.g., sun), will cause extremely high internal enclosure temperature, detrimental to their own performance and life span [4–6]. Hence, the thermal management of the outdoor electronic enclosure is necessary. Traditionally, force cooling technologies are employed to address this issue, such as fan cooling, water cooling and gas cooling [7,8]. However, these cooling technologies are energy-consuming, simultaneously producing greenhouse and ozone-depleting gases [9–11]. Moreover, the work in these cooling is ultimately lost as heat, and the dissipated heat into the terrestrial environment leads to the aggravation of greenhouse effect [12]. Compared with the force cooling technologies, daytime radiative cooling (DRC) has attracted wide attention for its energy conservation and net cooling effect [13].
From fundamental thermodynamics considerations, cooling is achieved by conducting heat to a low-temperature heat sink [14]. The universe, at a temperature of 3 K, provides an ultimate heat sink. Due to the existence of the atmospheric transmittance window (8-13 μm), surface can emit thermal radiation through it into the cold universe with zero-power [15–17]. For this reason, DRC can achieve the temperature drops below ambient temperature during daytime by reflecting sunlight and emitting thermal radiation into the universe. Since DRC initially was realized by Raman based on multilayer photonic radiator [18], many DRC materials have already been reported for their broad application prospect [19–22]. Especially, Mandal [19] reported a DRC coating based on Poly (vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) with excellent ultraviolet resistance. Due to its paint-like applicability, PVDF-HFP coating can be combined with diverse substrates, such as wood and metal. Owing to these advantages, the coating is expected to be applied in the thermal management of the outdoor electronic enclosure. However, there are the critical issue with PVDF-HFP coating, which limits their applications.
As we all know, most porous polymers have low solar absorption and high infrared emittance, such as Polymethylmethacrylate (PMMA), Polyvinylidene fluoride (PVDF) and PVDF-HFP [23]. When they are made into porous structures, the mismatched refractive index of the air and the polymer will enhance the light scattering, resulting in their high ${\bar{R}_{solar}}$ and ${\bar{\varepsilon }_{atw}}$ [24]. Hence, the parameters of porous structures, such as pore size, pore spacing and porosity, will affect light scattering, leading to difference in their DRC performance. More recently, the effect of pore size distribution and porosity, based on PVDF-HFP coating, has been studied by optical simulation [23]. However, the pressing question for PVDF-HFP coating is how to prepare the coating with corresponding pore size and porosity. Although the influence of experimental variables on porosity has been simply studied, the question cannot be solved well. Hence, it is of significance to explore directly the influence of experimental variables on the DRC performance of the coating.
To solve the previous issue, in our work, we propose a handy strategy to predict and optimize PVDF-HFP coating by artificial neural network (ANN). Three-layer back propagation (BP) neural network is selected to predict spectral reflectance of the coatings under different preparation conditions. Four experimental variables are selected as inputs, including PVDF-HFP proportion relative to acetone, water proportion relative to acetone, evaporation and thickness of PVDF-HFP coating. The prediction results are screened by their calculated net cooling power, and the optimal experimental variables are obtained after siftings, representing 1.25, 1.1, 60℃ and 400 μm, respectively. The predicted ${\bar{R}_{solar}}$ and ${\bar{\varepsilon }_{atw}}$, under the optimal preparation condition, reach 0.983 and 0.932, with a 1.865% and 0.107% error from the experimental value, correspondingly. Herein, the PVDF-HFP coating, prepared under the optimal condition, achieves about 6℃ temperature drops below ambient temperature during daytime.
In addition, for its excellent solar reflection, strong infrared radiation, and low cost, PVDF-HFP coating is expected to be applied in extreme environments, especially in space as thermal control coating [25,26,27]. Regardless of these advantages, it is equally significant to consider its reliability in high-low temperature variations and electron irradiation, which has never been reported. In consequence, to further expand its application in space, we assessed the reliability of the PVDF-HFP coating in the simulative extreme environment. It should be pointed out that the ${\bar{R}_{solar}}$ of the coating has a degradation rate over 11% after exposing in the simulative extreme environment. Peculiarly, the internal structure of the coating is damaged by electron irradiation, resulting in breaking of the coating. The experimental results show that the PVDF-HFP coating is untrustworthy as thermal control coating, though its excellent ultraviolet resistance can ensure a long-term terrestrial application. Consequently, these simulative methods and experimental results provide direction for fabricating the high-performance DRCs.
2. Simulative and experimental section
As seen from the Fig. 1a, simulative and experimental section consists of three parts. Firstly, the database, obtained from the experiment, is imported to train the ANN. Employed by the phase inversion method, a total of 100 PVDF-HFP coatings under different preparation conditions, shown in Fig.S1b, are prepared as training samples for the ANN. Specifically, we prepare the PVDF-HFP-acetone-water with different mass ratio precursor solution firstly, PVDF-HFP coatings are obtained after acetone and water evaporate. The evaporation of acetone and water will form nanopores and micropores, respectively (Fig. 1c). The porous structure increases its solar reflectance, and the C-C, C-H and C-F chemical bonds (Fig. 1d) in PVDF-HFP increase its infrared emittance, which contributes to its DRC performance.
Fig. 1. Prediction and optimization of neural network. (a) A schematic of finding an optimal solution. (b) The network model in use is schematically depicted. The components x1, x2, x3, x4 and output (1-100) refer to PVDF-HFP proportion, water proportion, evaporation temperature, PVDF-HFP coating thickness and spectral reflectance, respectively. (c) PVDF-HFP coating prepared by phase conversion method. (d) The chemical structure of PVDF-HFP.
Secondly, three-layer BP neural network is utilized to prediction and optimization, which has been applied in solving nonlinear problems widely [28,29]. Figure1b presents that the BP neural network consists of 4 nodes of input layer, 20 nodes of hidden layer and 100 nodes of output layer. Inputs represent experimental variables, being PVDF-HFP proportion (x1), water proportion (x2), evaporation temperature (x3) and thickness of PVDF-HFP coating (x4). In the S1 and S3, experimental variables (x1, x2, x3) will influence the porosity of PVDF-HFP coating, then affecting DRC capacity of the coating. The effect of x4 has been studied over the past few years, with DRC capacity improved as x4 increasing [19]. Outputs represent spectral reflectance from 0.4 μm to 14 μm, equally divided into 100 parts. The number of hidden layer nodes is determined by the following Equation $h = \sqrt {m + n} + a$, where h is the number of hidden layer nodes, m is the number of input layer nodes, n is the number of output layer nodes, and a is a constant between 1 and 10 [30]. Herein, a is about 9.8, and the number of hidden layer nodes is selected as 20. In this paper, the neural network toolbox of MATLAB is applied to train the obtained database. The sample database, imported into BP neural network, is divided into three parts: training part, validation part and test part, accounting for 70%, 15% and 15% of the total sample database, respectively. The trained BP neural network is employed to predict the spectral reflectance under different preparation conditions. The preparation conditions to be predicted are listed as follows. Concretely, the predicted x1 whose increment is 0.05 ranges from 0.75 to 1.25, x2 whose increment is 0.05 ranges from 0.75 to 1.25, x3 whose increment is 10℃ ranges from 20℃ to 100℃, and x4 whose increment is 10 μm ranges from 100 μm to 400 μm. Subsequently, the predicted conditions are screened by the respective calculated net cooling power (Qcooling), whose calculations are shown in S2.
Lastly, the PVDF-HFP coating under the optimal preparation condition is measured for spectral reflectance, then compared with the predicted spectral reflectance. Subsequently, its surface temperature drops below ambient temperature is obtained by the self-made radiative cooler during daytime to verify its excellent DRC performance. In addition, we validate the reliability of the PVDF-HFP coating via the simulative extreme environment to explore the possibility of applying the coating in space.
Preparation: PVDF-HFP was purchased from SIGMA. The deionized water and acetone were from the laboratory in Nanjing University of Science and Technology. The PVDF-HFP was first dissolved in acetone with the stirrer, and then the deionized water was added in. After the precipitate dissolved, the PVDF-HFP-acetone-water with different mass ratio precursor solution was obtained. The precursor solution was coated on the clean base plate, PVDF-HFP coatings are obtained after evaporation of acetone and water.
Characterizations and Testing: The SEM (S-4800, Hitachi Co, Japan) was used to observe the microstructure of the PVDF-HFP coatings. Spectral reflectance of the coating was mainly divided into the visible-near infrared (vis-NIR, 0.4–2.5 μm) and near infrared-midinfrared (NIR-MIR, 2.5–14 μm) wave range. In the vis-NIR wave range, measurement was taken by Cary-5000 apparatus. In the NIR-MIR wave range, measurement was taken by the Vertex 80v FI-IR spectrometer. ${\bar{R}_{solar}}$ and ${\bar{\varepsilon }_{atw}}$, in the paper, were calculated by the following Eq. (2) and (3):
3. Results and discussion
From the above preparation and measurement methods, the spectral reflectance is obtained, and saved in the database, which is later imported into the BP neural network for training. After neural network training, the regression coefficients of BP neural network are shown in the Fig. 2. The regression coefficients of the training part, validation part and test part are 0.997, 0.988, and 0.988, severally. It can be known that the regression coefficient of the whole part is 0.995 (Fig. 2 d). In the figure, Y = T represents the curve when the regression coefficient is 1. In general, the closer the regression coefficients of three parts are to 1, the better the data fitting effect is, and the higher the accuracy of the BP neural network is. As a result, the trained BP neural network has a good fitting degree and accurate prediction.
Fig. 2. The regression coefficients of BP neural network. Regression coefficient of (a) the training part, (b) the validation part, (c) the test part and (d) the whole part.
The effect of PVDF-HFP coating thickness on its reflectance (0.4 μm-14 μm) is shown in Figure3. Here, only thickness(x4) is changed, and the rest of the input variables are remained as x1=1, x2=1, and x3 = 20. As shown in Fig.3a, the predicted spectral reflectance is compared with the experimental one under different thickness. The experimental and predicted optical property exhibits a good agreement for the coating with different thickness, though there is a small mismatch in total solar reflectance for sample with 73 μm thick (Fig.3b). It can be found that the ${\bar{R}_{solar}}$ increases in some extent and the ${\bar{\varepsilon }_{atw}}$ almost unchanged as the thickness increases. Overall, with x4 increasing, the reflective property in solar band enhances and that in atmospheric transmittance window band changes slightly (Fig.3c), indicating that the increase of the thickness only affects the solar reflectance and has little effect on the infrared reflectance. The increase of thickness is conducive to enhance the radiative cooling performance of PVDF-HFP coating [19].
Here, the infrared transmittance is assumed as zero. After measurement, ${\tau _{atw}}(\lambda )$ with different thickness, whose calculation is in the S4, is shown in Fig.3d. Through calculation, it can be obtained that ${\bar{\tau }_{atw}}$ is 15.14%, 5.16%, 1.89%, 0.38%, when the thickness is 73 μm, 102 μm, 180 μm, and 276 μm. When thickness is less than 100 μm, ${\bar{\tau }_{atw}}$ is more than 10%, which cannot be ignored. However, ${\bar{\tau }_{atw}}$ is less than 6% when thickness is more than 100 μm. Motived by the experimental results, ${\bar{\tau }_{atw}}$ for thickness to be predicted ranging from 100 μm to 400 μm can be ignored.
The effect of experimental variables x1, x2 and x3 on its optical property(0.4μm-14μm) is shown in the Fig. 4, orderly. As for the effect of x1 (Fig.4a), the rest of the input variables are remained as x2=1, x3=20, and x4 = 300. The solar reflectance will increase and the infrared emittance (emittance=1-reflectance) will decrease slightly whenever x1 increases or decreases. Notably, the total infrared transmittance is less than 0.38%, when thickness is 300 μm (Fig. 3(d)). Therefore, in this part of the study, ${\tau _{atw}}(\lambda )$ is assumed as zero. When the effect of x2(Fig.4b) is discussed, the rest of the input variables are remained as x1=1, x3=20, and x4 = 300. The increase or decrease of x2 will lead to the increase in the solar reflectance and slight decrease in the infrared emittance. With regard to the effect of x3(Fig.4c), the rest of the input variables are remained as x1=1, x2=1, and x4 = 300. With the increase of x3, the solar spectrum reflectance will increase first and then decrease, while the infrared emittance will change little. To further explore the effect of x1, x2 and x3 on its optical property, the effect of x1(Fig.4d), x2(Fig.4e), and x3(Fig.4f) on its porosity is studied. Specifically, increase of x1 will lead to the increase of its porosity, bringing higher solar reflectance due to more pores to scatter sunlight [24]. Increase of x2 will lead to the decrease of its porosity, while the total solar reflectance exhibits a certain upward trend. The reason for above change is that increase of x2 changes the pore size of the coating. And then, with the increase of x3, the porosity also increases firstly and decreases subsequently. The porosity of the coating reaches the maximum with x3=60. Therefore, x1, x2, and x3 will affect the porosity and pore size of the coating, further changing in its ability to scatter sunlight [19].
Fig. 3. The effect of PVDF-HFP coating thickness on its radiative cooling performance. Comparisons of (a) experimental and predicted spectral reflectance, (b) experimental and predicted ${\bar{R}_{solar}}$ and ${\bar{\varepsilon }_{atw}}$, (c) predicted spectral reflectance, and (d) experimental infrared transmittance under different thickness conditions.
Fig. 4. The effect of experimental variables x1, x2 and x3 on radiative cooling performance of coating. The effect of (a) x1, (b) x2, and (c) x3 on spectral reflectance. The effect of (d) x1, (e) x2, and (f) x3 on porosity, ${\bar{R}_{solar}}$ and ${\bar{\varepsilon }_{atw}}$.
Utilizing the BP neural network, the spectral reflectance under different preparation conditions is obtained. The Qcooling is selected as standard for evaluating DRC performance of PVDF-HFP coating. Subsequently, the simulative and experimental spectral reflectance under the predicted optimal preparation condition is shown in the Fig.5a, from which it can be seen that simulative spectral reflectance is consistent with the experimental result. After calculation, simulative PVDF-HFP coating under the predicted optimal preparation condition possesses the ${\bar{R}_{solar}}$ of 0.983 and the ${\bar{\varepsilon }_{atw}}$ of 0.932. The experimental PVDF-HFP coating under the optimal preparation condition has the ${\bar{R}_{solar}}$ of 0.965, the ${\bar{\varepsilon }_{atw}}$ of 0.931, with a 1.865% and 0.107% error from the previous predicted value. In the Fig.5b, the parameters for different cases are listed in the Table 1. Thickness(x4) has the most obvious effect on spectral reflectance, indicating that the increase in thickness significantly increases the ${\bar{R}_{solar}}$. Employing a self-made radiative cooler shown in the Fig.5c, the radiative cooling performance was assessed to verify the predicted optimal condition. The PVDF-HFP coating was placed in the adiabator, and the PE film was covered on the top of the sample. A thermocouple was placed under the sample to collect surface temperature of the coating, another one was placed in the air to obtain the ambient temperature. And the Lux meter was employed to measure solar intensity. The test was conducted at the 31° north-latitude and 112° east-longitude, where the local time was on the February 16, 2021. As shown in the Fig.5d, it can be found via experiment that the PVDF-HFP coating under the optimal preparation condition achieves about 6℃ temperature drops below ambient temperature during daytime, which verifies the high DRC performance of the optimal coating. Figure 5(e) exhibits its net cooling power (Qcooling) with different convective heat transfer coefficients, where ambient temperature is selected as 298.15 K. When temperature difference (△T) between its surface and environment is zero, its Pnet is the net cooling power of coating, indicating that the optimal coating has a net cooling power of 84.3 W·m-2. In addition, to state the optimization gains, the best and worst coating are compared. During the optimization, the worst case is obtained when x1=0.75, x2=1.25, x3=60 and x4=100. The best case is gained when x1=1.25, x2=1.1, x3=60, and x4=400. Form Fig.5f, the best scenario coating has a theoretical temperature difference with 36.5℃, compared with the worst one, has a cooling power improvement of 307.2 W·m-2. Noticeably, net cooling power of the worst one is -222.9 W·m-2, indicating that the coating will be heated. In conclusion, the prediction method in this paper is feasible and reliable.
Fig. 5. Radiative cooling performance of PDVF-HFP coating under the optimal preparation condition. Comparisons of (a) experimental and predicted spectral reflectance and (b) different predicted spectral reflectance. (c) The self-made radiative cooler. (d) Temperature difference between the coating surface and environment. (e) Net cooling power under the optimal preparation condition. (f) Gains after optimization.
Table 1. The parameters for different cases in the Fig. 5(b).
For its excellent solar reflection, strong infrared radiation, and low cost, PVDF-HFP coating is expected to be applied in extreme environments, particularly in space. From S5 and S6, it is revealed that the PVDF-HFP coating has higher net cooling power in space. For these superiorities, we also assessed the space stability of the PVDF-HFP coating by simulating extreme environmental experiment. The experimental conditions and the test results are illustrated in Fig. 6. In the high-low temperature cycle experiment, the coating was fixed on the sample holder, where the temperature range was set from -100℃ to 130℃, the heating rate was 10℃/min, and the number of cycles was 9.5 times. In the electron irradiation experiment, the irradiation energy was 1 MeV with dose rate of 5×1010 e/cm2s and the accumulated dose of 1×1015 e/cm2. After the high-low temperature cycle, the ${\bar{R}_{solar}}$ decreases from 0.96 to 0.85 with a degradation rate of 11% ($\phi = ({{R_{before}} - {R_{after}}} )/{R_{before}}$), while the ${\bar{\varepsilon }_{atw}}$ changes little. The results of the electron irradiation indicate that the ${\bar{R}_{solar}}$ decreases from 0.96 to 0.79 with a degradation rate of 18%. Specifically, after high-low temperature cycle, high temperature destroys the porous structure of the coating. From the Fig.S3c, at 100℃, the porous structure of the coating surface is destroyed, which will reduce the scattering efficiency of the coating. For this reason, ${\bar{R}_{solar}}$ is degraded after suffering from high-low temperature cycle. Seriously, the coating was broken after electron irradiation due to the breaking of chemical bonds, introducing polarized chemical groups which can cause the coating surface to polarize [28]. In detail, its C-F bonds are cracked, and highly reactive F- radicals are generated, which can cleave C-C bonds after electron irradiation [31]. For the reason, the molecular weight of the component molecules in the PVDF-HFP coating decreases, leading to the degradation of the mechanical property of the coating, even fragmentation. Consequently, PVDF-HFP coating has poor reliability in the extreme environment.
Fig. 6. Results of the extreme environment experiment. Comparison of (a) the solar spectra and (b) the infrared spectra before and after high-low temperature cycle experiment. (c) solar spectra before and after electron irradiation.
4. Conclusion
In conclusion, we propose the method to find out the preparation conditions with the optimal radiative cooling performance of the PVDF-HFP coating, enhancing the radiative cooling performance of the original coating. The predicted ${\bar{R}_{solar}}$ and ${\bar{\varepsilon }_{aw}}$ under the optimal condition were 0.983, 0.932, with a 1.865% and 0.107% error from the respective experimental value correspondingly, verifying the reliability of the prediction method at the same time. Furthermore, the PVDF-HFP coating under the optimal condition obtained 6℃ temperature drops below ambient temperature during daytime. Herein, the method proposed provides a reliable solution to improve the performance of the radiative cooler. In addition, the ${\bar{R}_{solar}}$ of the PVDF-HFP coating has a degradation rate over 11% in undergoing the experiment of extreme environment (e.g., high-low temperature and particles irradiation cases), indicating a poor reliability. Therefore, for wider applications, it is extremely urgent to improve the reliability of coatings in extreme environments. All in all, these simulative and experimental results provide a positive direction for fabricating the high-performance DRCs.
Funding
Natural Science Foundation of Jiangsu Province (No. BK20180070); National Natural Science Foundation of China (No. 51876091).
Acknowledgements
H. Zhang and J. Huang contributed equally to this work. This work was supported by the National Natural Science Foundation of China (Grant No. 51876091), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20180070).
Disclosures
D.F. conceived the ideal and designed the experiments. H. Z and J.H. performed the experiment and numerical simulation. P. T provided the experimental devices. All authors contributed to the writing of the manuscript. The authors declare no competing financial interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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