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Simple dual-layer emitter for daytime radiative cooling

Yeqing Zhu, Yonghong Ye, Dong Wang, and Yurong Cao

Open Access Open Access

Abstract

This work experimentally demonstrates a simple dual-layer emitter, which is easy to prepare and can be applied to effective daytime radiative cooling. The emitter consists of a 200-µm-thick polydimethylsiloxane film on top of a 120-nm-thick Ag film, which is coated on a fused silica wafer or a plastic substrate. Due to the high reflectivity from the visible to the near-infrared and near-black emittance in the mid-infrared, the experimental results show that both structures have similar daytime radiative cooling performance. During the testing period, the typical ambient air temperature is 14-26 °C, the local wind speed is 1.6-2.6 m/s, and the relative humidity is 45-73%. We experimentally demonstrate that the emitter can achieve an average temperature reduction of about 3.3 °C from the ambient air temperature under direct sunlight. And the potential cooling power density is about 72.7 W/m2. In the presence of non-ideal atmospheric conditions and significant non-radiative heat exchange, theoretical simulations are in good agreement with the measurements. This work indicates that the dual-layer emitter may be a key element in the realization of energy-efficient radiative cooling devices.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In recent years, manipulating thermal radiation from the surface of device by using thermal photonic design has been extensively studied [1–7]. Passive radiative cooling dissipates heat from the surface and emits infrared thermal radiation to the cold universe through the atmospheric transparency window (8-13 µm) without any external active devices. Passive radiative cooling can be grouped into two categories: nighttime radiative cooling and daytime radiative cooling. In the past few decades, efficient nighttime radiative cooling has been widely investigated [8–12]. Granqvist and Hjortsberg evaporated 1-µm-thick SiO with 99% purity onto an aluminized glass plate [8]. Due to the strong lattice absorption and the destructive interference of SiO, a temperature drop of 40 °C could be theoretically achieved without non-radiative heat exchange (assuming Ta = 21 °C). Diatezua et al. prepared and tested three silicon oxynitride multilayers onto an aluminized glass substrate [10]. A broadening of the absorption peak within the atmospheric transparency window was obtained by adjusting the chemical composition and thickness of each layer. By neglecting non-radiative heat transfer, temperature drops of 52, 48 and 56 °C had been predicted.

As cooling demands peak in the daytime, daytime radiative cooling is also useful. However, due to the solar absorbance, daytime radiative cooling is still a challenge [13–18]. Raman et al. introduced an emitter consisting of seven alternating layers of HfO2 and SiO2 on top of a silver film, resulting in 97% reflection of solar irradiation [2]. With a simple experimental apparatus, the radiative emitter could cool to 4.9 °C below the ambient air temperature under direct sunlight (860 W/m2). Subsequently, Chen Z et al. proposed a cooler consisting of layers of silicon nitride (70 nm), amorphous silicon (700 nm) and aluminium (150 nm) [13]. By using a delicate vacuum chamber, an average temperature drop of 37 °C below ambient air temperature could be achieved. Li et al. designed a comprehensive photonic cooler consisting of alternating layers of Al2O3/SiN/TiO2/SiN with aperiodic thicknesses, with an anti-reflection layer of SiO2 on top [18]. They showed that the cooler could achieve a temperature reduction of over 5.7 °C by applying it to a solar panel. Shi et al. presented an implementation of a memetic algorithm for designing multilayer thin films. They showed that the optimized structures had better performance while using fewer numbers of material layers [19]. Meanwhile, M. A. Kecebas et al. proposed and analyzed thin-film optical filters for efficient daytime radiative cooling applications [20,21].

Besides the nonpolymeric film structures, various polymeric structures are proposed for passive radiative cooling [22–26]. Polydimethylsiloxane (PDMS) is inexpensive and chemically stable. It is easy to prepare and can be used for near-black infrared emitters for cooling flexible thin-film solar cells. Kou et al. proposed a simple near-black infrared emitter for efficient daytime radiative cooling [6]. They analyzed that absorbing outside of the atmospheric transparency window could be beneficial when ambient air temperature was above 283 K. The multilayer structure based radiative emitters have been broadly investigated, and novel designs of excellent performance, low cost and simple structure for daytime radiative cooling are appealing. Zhou et al. proposed a PDMS-coated metal structure [26]. They explored that the structure could achieve efficient daytime radiative cooling performance in a complex urban environment. However, the effects of different metals and substrates have not been reported previously.

In this paper, a simple dual-layer emitter with high reflectivity of solar irradiation and near-black absorptivity in mid-infrared is proposed. The emitter is deposited onto two different substrates, respectively. During the daytime testing period, all structures are directly exposed to the sky and the experimental results are considered the effects of convective, cloud cover and relative humidity, etc. The experimental results show that the emitters deposited onto two different substrates have the same potential cooling performance without any wind shields, and they are insensitive to substrates. When some parasitic mechanisms are present, the radiative cooling performance of the emitter is still obvious.

2. Design and fabrication

The proposed dual-layer emitter is shown in Fig. 1. It consists of a 200-µm-thick PDMS film on top of a 120-nm-thick Ag layer, which is deposited on a substrate. The design concept is that the emissivity is unity in the mid-infrared and zero otherwise. Due to the high reflectivity of the reflective layer, the broadband thermal emission of the structure depends on the upper layer. To achieve such a design, the impacts of the reflector, the thickness of the PDMS layer and the substrate should be carefully discussed.

 figure: Fig. 1.

Fig. 1. Schematic of the dual-layer emitter for efficient daytime radiative cooling.

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The Essential Macleod software is adopted to investigate the spectral performance of the designed emitter. It is a software uses the characteristic matrix method based on Maxwell's equations. Combined with the fundamental properties of electromagnetic fields and the optical interference principle of the thin-film system, the characteristic matrix of the monolayer film can be expressed as [27]

$$M = \left[ {\begin{array}{cc} {\textrm{cos}{\delta_1}}&{i\frac{{\sin {\delta_1}}}{{\eta {}_1}}}\\ {i\eta {}_1\sin {\delta_1}}&{\textrm{cos}{\delta_1}} \end{array}} \right].$$

In Eq. (1), the optical phase ${\delta _1}$ is given by

$${\delta _1} = \frac{{2\pi }}{\lambda }{n_1}d\cos {\theta _1}.$$

Here η1 is effective admittance of the monolayer film, λ is the wavelength, n1 is the refractive index of the film, d is the thickness of the layer, θ1 is the refractive angle. For p-polarisation, η1=n1/cosθ1, and for s-polarisation, η1=n1cosθ1. Therefore, a medium of admittance Y is expressed as

$$Y = \frac{{{\eta _2}\cos {\delta _1} + i{\eta _1}\sin {\delta _1}}}{{\cos {\delta _1} + i({\eta _2}/{\eta _1})\sin {\delta _1}}}.$$

Here η2 is the substrate of admittance, η0 is an incident medium of admittance. The reflectance of the monolayer film can be expressed as

$$R = \frac{{{{({\eta _0} - {\eta _2})}^2}{{\cos }^2}{\delta _1} + {{({\eta _0}{\eta _2}/{\eta _1} - {\eta _1})}^2}{{\sin }^2}{\delta _1}}}{{{{({\eta _0} + {\eta _2})}^2}{{\cos }^2}{\delta _1} + {{({\eta _0}{\eta _2}/{\eta _1} + {\eta _1})}^2}{{\sin }^2}{\delta _1}}}.$$

A simple extension of the above method to the case of multilayer films, the characteristic matrix of multilayer films is given as

$$\left[ {\begin{array}{c} B\\ C \end{array}} \right] = \left\{ {\prod\limits_{j = 1}^K {\left[ {\begin{array}{cc} {\textrm{cos}{\delta_j}}&{i\frac{{\sin {\delta_j}}}{{\eta {}_j}}}\\ {i\eta {}_j\sin {\delta_j}}&{\textrm{cos}{\delta_j}} \end{array}} \right]} } \right\}\left[ {\begin{array}{c} 1\\ {{\eta_{K + 1}}} \end{array}} \right].$$

The reflectance of the multilayer system can be written as

$$R = (\frac{{{\eta _0}B - C}}{{{\eta _0}B + C}}){(\frac{{{\eta _0}B - C}}{{{\eta _0}B + C}})^ \ast }.$$

Here the symbol * in Eq. (6) indicates the conjugate. Based on these theories, the spectroscopic performance of the designed multilayer structure can be obtained.

The refractive indices and extinction coefficients used in the simulations for Al (0.3-25 µm), SiO2 (0.3-25 µm), and Ag (0.3–25 µm) are from Ref. [28]. The parameters of PDMS (2.5–25 µm) are from Ref. [29], while other values of PDMS are coming from Ref. [30]. Figure 2(a) shows the simulated results of PDMS film with various thicknesses on top of 120-nm-thick Ag layer in the 0.3-25 µm wavelength range. As can be seen from Fig. 2(a), at λ < 2.5 µm, the emissivity is invariable with the increase of thickness when the thickness of PDMS is less than 200 µm. At 2.5 µm < λ < 25 µm, the emissivity increases as the thickness increases. However, when the thickness of PDMS is more than 200 µm, the emissivity barely varies. There is little difference between the sample with 300 µm thick and the rest of the thicknesses, but the effect in cooling performance is not apparent. The reason for choosing a 120-nm-thick Ag layer is shown in Fig. 2(b). When the thickness of the Ag layer d is 120 nm, the reflectivity reaches the optimum value and the transmittance is close to 0. When d > 120 nm, the results barely vary. In general, Au, Al and Ag are chosen for reflective layer. At λ > 1.0 µm, Au has a similar reflectance as Ag, while at λ < 1.0 µm, the reflectance of Au is much lower than that of Ag [31]. So here Au is not used for the reflective layer. Figure 3(a) shows the simulations of 200-µm-thick PDMS on top of two different reflective layers, Ag (red solid line) and Al (black short dotted line), respectively. In Fig. 3(a), at λ <1.4 µm, due to the interband absorption of Al near λ ≈ 0.8 µm [32], the solar reflectance of Ag is higher than that of Al. Therefore, among all these highly reflective metallic materials, Ag is the best choice. Figure 3(b) shows the simulated results of the emitter with or without a substrate. The results indicate that the emissivity of the dual-layer emitter is independent of the substrate. It is well-known that PDMS is a silicone elastomer. As PDMS is easy to prepare and it has remarkable transmittance from 0.4 to 1.8 µm, PDMS is attractive for passive radiative cooling applications [6,33]. In general, the combination of the two materials (PDMS and Ag) leads to an emitter for efficient daytime radiative cooling. The structure is able to achieve high solar reflectance between 0.3-2.5 µm and strong thermal emissivity over infrared wavelengths longer than 4.5 µm.

 figure: Fig. 2.

Fig. 2. (a) Simulated emissivity/absorptivity of a PDMS film with various thicknesses on top of a 120-nm-thick Ag layer from 0.3 to 25 µm. (b) Simulated absorptivity and transmittance of a silver layer with different thicknesses from 0.3 to 25 µm.

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 figure: Fig. 3.

Fig. 3. (a) Simulated emissivity/absorptivity of a 200-µm-thick PDMS film on top of a 120-nm-thick Ag layer (red solid curve) and a 120-nm-thick Al layer (black shot dotted curve) from 0.3 to 25 µm. (b) Simulated emissivity of a 200-µm-thick PDMS film on top of a 120-nm-thick Ag layer (blue shot dotted curve) and with a silica wafer (red solid curve) from 0.3 to 25 µm.

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To prepare the emitter, the 120-nm-thick Ag layer was deposited onto a substrate with a diameter of 9 cm and a thickness of 500 µm by thermal evaporation under high vacuum. During the thermal evaporation, the thickness of the Ag layer was monitored by a quartz crystal monitor. Finally, a PDMS film was spin-coated onto the silver-plated substrate followed by dagassing for about 10 mins and cured by a hot plate. For real-world applications, the emitter should be able to be applied to diverse substrates. Therefore, we use two types of substrates to demonstrate the cooling performance of our structure on different surfaces. One is a fused silica wafer with a thermal conductivity coefficient of 7.6 W/m·K, and the other one is a polystyrene plastic with a thermal conductivity coefficient of 0.08 W/m·K. The substrates have the same size and thickness.

3. Results and discussion

Figure 4 shows the measured absorptivity/emissivity of the emitters onto two different substrates, a fused silica wafer (black curve) and a polystyrene plastic (red curve). The spectra emittance of the emitter from 0.3 to 2.5 µm is measured by an UV-Vis-NIR Spectrophotometer (Cary 5000, at 12° angle of incidence) and a Fourier transform infraredspectrometer from 2.5 to 25 µm (FTIR, Nicolet Nexus 670, at 30° angle of incidence). As shown in Fig. 4, emitters on the two substrates have similar emittance in the 0.3-25 µm wavelength region. Due to the high reflectivity of Ag, the emitters reflect about 97.5% of incident solar radiation from 0.3 to 2.5 µm. At λ > 7 µm, the emissivity approaches about 95% due to the absorption of PDMS [6]. Comparing with the results in Fig. 3(a), it can be seen that the simulations agree well with the measurements. Although between 5 and 7 µm there are some discrepancies due to the production process, they will have little influence on the radiative cooling performance. Figure 5 shows the measured angular (from 15° to 60°) absorptivity/emissivity of emitters on two substrates in near- and mid-infrared regions. As shown in Fig. 5, the absorptivity/emissivity of emitters are insensitive to the incident angles, which will be helpful for maximizing the radiated power. Figure 5(c) shows that the measured average absorptivity/emissivity of emitters on two substrates between 15° and 60° (from 8 to13 µm) are almost the same. The results on a fused silica wafer and a plastic substrate are 0.935 and 0.936, respectively.

 figure: Fig. 4.

Fig. 4. Measured emissivity of the dual-layer emitter on top of 500-µm-thick silica wafer (black curve) and a 500-µm-thick plastic (red curve) from 0.3 to 25 µm.

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 figure: Fig. 5.

Fig. 5. (a) Measured angular absorptivity/emissivity of emitter in the 0.3-25 µm region on a fused silica wafer. (b) Measured angular absorptivity/emissivity of emitter in the 0.3-25 µm region on a plastic substrate. (c) Measured average angular absorptivity/emissivity of emitters on different substrates in the 8-13 µm region.

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In real-world applications, weather conditions and operating strategies will affect the effectiveness of passive radiative cooling performance [14–17]. We demonstrate the daytime radiative cooling performance of the dual-layer emitter by exposing all samples to the sky without any wind shields on a building roof of a six-storey in Nanjing, on November 3, 2019. Testing is operated on a clear autumn day in daytime by comparing the stagnation temperatures of samples with the ambient air temperature. During the daytime testing period, the local wind speed is 1.6-2.6 m/s, the relative humidity is 45-73% and the typical ambient air temperature is 14-26 °C. These data are from Meteorology Bureau of Nanjing City. It is noteworthy that the relative humidity has a considerable effect on the atmospheric transmittance and in turn the passive radiative cooling performance [34]. Each sample is laid on a 5-mm-thick, low thermal conductivity aerogel blanket, which is attached to the inner side of a 120-mm-diameter Petri dish. The Petri dish is supported by three 23.5-cm-height rods to suspend the Petri dish above the rooftop. The stagnation temperatures of samples and the ambient air temperature are recorded by K-type thermocouples with ± 0.5 °C accuracy. The ambient air temperature is measured in a 1-m-height sun-shaded area with free air flow near the samples. The backside of the emitter is anchored with the thermocouple, connected to a data logger (ATEST Thermometer DT-847UD). All the temperature results are recorded every 1 second. Three samples are fabricated for comparative study. These samples are a highly absorptive black alloy (a bare module, without any additional materials on top of the black alloy, magenta curve), a dual-layer emitter on a fused silica wafer (black curve), and a dual-layer emitter on a plastic substrate (red curve), respectively. In the testing period, the peak solar irradiance is about 760 W/m2. All the measurements are shown in Fig. 6(a). Ta represents the ambient air temperature. Figure 6(a) reveals that the surface temperature of the bare module increases as the sun shines. Due to the absorption of solar irradiance, the peak temperature is about 49 °C. Figure 6(b) demonstrates the measured stagnation temperature of the dual-layer emitter on a fused silica wafer (olive curve) and temperature difference of the emitter on two different substrates (cyan curve) during the testing period. Figure 6(b) illustrates that the dual-layer emitter can achieve 3.3 °C below ambient air temperature in the daytime operation without any wind shields. The average temperature difference of the two types of substrates is about 0.3 °C, which shows that they have similar radiative cooling performance. All the measurements reveal that the dual-layer emitter can achieve a significant daytime radiative cooling performance, and the cooling performance is insensitive to substrates.

 figure: Fig. 6.

Fig. 6. (a) On-site measurements of the dual-layer emitter on a silica surface (black curve), a plastic surface (red curve), ambient air (blue curve), and a bare module (magenta curve) between 09:00 and 16:00 on a building roof of a six-storey in Nanjing, in November 2019. The yellow shaded regions represent solar irradiance. (b) Measured stagnation temperature of the dual-layer emitter (olive curve) on a silica wafer and temperature difference of the emitter on two substrates (cyan curve) between 09:00 and 16:00.

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The net cooling power Pcool of a radiative emitter is defined as [2]

$${P_{cool}} = {P_{rad}} - {P_{atm}} - {P_{sun}} - {P_{con}}.$$

In Eq. (7), the thermal radiation by the emitter is [2]

$${P_{rad}}({T_s}) = A\int_0^{\pi /2} {2\pi \sin \theta \cos \theta } d\theta \int_0^\infty {{I_{BB}}({T_s},\lambda )\varepsilon (\theta ,\lambda )d} \lambda .$$

The atmospheric thermal radiation is [2]

$${P_{atm}}({T_a}) = A\int_0^{\pi /2} {2\pi \sin \theta \cos \theta } d\theta \int_0^\infty {{I_{BB}}({T_a},\lambda ){\varepsilon _a}(\theta ,\lambda )d} \lambda .$$

The incident solar power absorbed by the emitter is [2]

$${P_{sun}} = A\int_0^\infty {\varepsilon (0,\lambda ){I_{AM1.5}}(\lambda )d} \lambda .$$

The nonradiative loss can be given by [2]

$${P_{con}}({T_s},{T_a}) = {h_c}A({T_a} - {T_s}).$$

In Eqs. (8) and (9), IBB is the blackbody spectral radiance according to Planck’s law [2]

$${I_{BB}} = \frac{{2h{c^2}}}{{{\lambda ^5}}}\frac{1}{{{e^{hc/(\lambda {k_B}T)}} - 1}},$$
where c is the speed of light, h is the Planck’s constant, λ represents the wavelength, and kB is the Boltzmann constant. In Eq. (8), A is the area of the emitter, Ts is the surface temperature of the emitter, and ε(θ,λ) is the spectral and angular emissivity of the emitter. In Eq. (9), εa(θ,λ) is the emissivity of the atmosphere, εa(θ,λ) = 1-t(0,λ)1/cosθ [9], where t(0,λ) is the atmospheric transmittance in the zenith direction [35]. In Eq. (10), IAM1.5(λ) is the solar irradiance, the AM1.5 spectrum. We assume that the emitter is facing the sun at a fixed angle. In Eq. (11), hc is an overall heat transfer coefficient that combing convection and conduction heat transfer.

To evaluate the cooling performance of the dual-layer emitter, quantitatively theoretical calculations are performed. During the calculations, the atmospheric transmittance t(0,,λ) in the zenith direction shown in Fig. 7 is an significant parameter, which is derived from MODTRAN 5 [35]. The high atmospheric transmittance (black solid curve) is defined by Aerosol of urban visual range of 5 km, no clouds or rain, a clear sky transmittance in mid-latitude winter, etc. The low atmospheric transmittance (red dashed curve) is from Ref. [36] (due to the high relative humidity), which is more applicable here. As there is no convection shields during the testing period, the theoretical heat transfer coefficient hc is suggested as

$${h_c} = 8.3 + 2.5{v_{wind}},$$
where vwind is zero-incidence wind speed. The local wind speed on the testing day is 1.6-2.6 m/s, which is valid for the applicable range of the above equation 0-8 m/s. According to Eq. (13), hc is approximately 12.3-14.8 W/m2/K. For better understanding the nonradiative loss mechanisms in the measurement, heat exchange simulations are performed in COMSOL, as shown in Fig. 8. The model simulates the apparatus in two dimensions with an emitter (on the top of two different substrates), surrounding air, and the supporting aerogel blanket. The ambient air temperature is defined as 293 K. The conductive parameter of PDMS is obtained from Ref. [37], while the conductive properties of other materials are all from the system. The outside boundaries of the system are set to the ambient air temperature, as shown in Fig. 8(a). The simulation indicates the fluid mechanics in the apparatus and the conduction in the emitter and the aerogel blanket to obtain the stagnation temperature T of the emitter for different values of Pout. Pout is the heat flux leaving the emitter. With different substrates, the results are the same, which indicates that the cooling performance is insensitive to substrates. The simulations fit the measurements very well. At the steady state temperature, Pout equals to the nonradiative loss Pcon. The simulation result is shown in Fig. 8(b). Thereinto, the slope of the line represents the non-radiative heat transfer coefficient hc. It is found that the heat transfer coefficient is 12.5 W/m2/K, which is a fitting result shown in Fig. 8(b). It is much larger than the data in previous studies [2,6,13,38–40]. This is primarily due to the weather conditions of the testing day. In particular, the large relative humidity in the testing period [41,42]. When the relative humidity increases, the transparency of the atmospheric window decreases rapidly [9,39]. Figure 8(c) shows the simulated results with the emitter on three different substrates. The thermal conductivities of the three substrates are 0.08, 1.38, and 7.6 W/m·K, respectively. Cb is the thermal conductivity coefficient of the aerogel blanket and Cs is the thermal conductivity coefficient of the substrate. The simulation results reveal that when the aerogel blanket has very low thermal conductivity (Cb = 0.01 W/m·K), there is no significant difference over the temperatures of different substrates. With the increasing of the thermal conductivity coefficient of the aerogel blanket, there are slight changes among the temperature differences. The measured results are consistent with the case of Cb = 0.02 W/m·K. In addition, weather with different clouds can also affect the measurements [15]. However, our measurements demonstrate the practical potential of the dual-layer emitter in daytime radiative cooling applications.

 figure: Fig. 7.

Fig. 7. The atmospheric transmittance from MODTRAN 5 [35].

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 figure: Fig. 8.

Fig. 8. Simulations of nonradiative heat exchange. (a) The simulation of the radiative emitter (layout shown on top) and the apparatus yields a temperature distribution (Ts-Ta) (bottom) in the geometry while taking into account of the nonradiative loss in the apparatus. (b) The simulation of Pcon as a function of the temperature difference (Ts-Ta). (c) The simulated results of the temperature difference (Ts-Ta) as a function of the thickness y. (d) Zoom-in of the simulated results of the proposed emitter from -2.5 to -5.0 °C.

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Based on Eqs. (7)–(13), we use the Fortran language to write the codes to calculate the theoretical cooling performance, which are shown in Fig. 9. Figure 9(a) depicts calculated results of the dual-layer emitter at various ambient air temperatures [the measurements in Fig. 6(a)] under the AM1.5 solar irradiation of 760 W/m2, with hc=12.5 W/m2/K. As the olive curve shown in Fig. 9(a), the average stagnation temperature of the dual-layer emitter is about 4.3 °C. The net cooling powers of the emitter per unit area Pcool [43] given Ta = 293 K for heat transfer coefficient hc of 0 and 12.5 W/m2/K during daytime operation are shown in Fig. 9(b). The emissivity are the measured results in Fig. 4, and values of the two different atmospheric transmittance are from Fig. 7. It is obvious that both samples can achieve similar stagnation temperatures and net cooling power. This is primarily due to the similar spectral emittance of the emitters onto the two substrates in Fig. 4. It can be seen in Fig. 9(b), the stagnation temperature can achieve 25 and 6 °C below the ambient air temperature in high atmospheric transmittance with hc values of 0 and 12.5 W/m2/K, respectively, and yield the net cooling power of 100.4 W/m2. Meanwhile, in low atmospheric transmittance, the emitter can cool down 17.5 and 4.3 °C below the ambient air temperature with hc values of 0 and 12.5 W/m2/K, respectively. And the potential cooling power density is about 72.7 W/m2. The results show that atmospheric transmittance is a significant factor in passive radiative cooling. The measured results in Fig. 6 are consistent with the simulated results of hc=12.5 W/m2/K in low atmospheric transmittance. In general, the measurements are a little lower which is mainly due to the influence of the relative humidity, the wind speed, the atmospheric transmittance and the cloud cover during the testing period.

 figure: Fig. 9.

Fig. 9. (a) Measured temperature of the dual-layer emitter (black curve) on a silica wafer, calculated temperature of the dual-layer emitter (orange curve) [the same ambient air temperatures as in Fig. 6(a)], calculated stagnation temperature of the dual-layer emitter on a fused silica wafer (olive curve) between 09:00 and 16:00. (b) Calculated cooling power of the dual-layer emitter on a silica substrate (solid curves) and a plastic substrate (shot dashed curves) for heat transfer coefficient hc of 0 and 12.5 W/m2/K during daytime operation in two different atmospheric transmittance. The Ta is assumed to be 293 K.

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4. Conclusions

In conclusion, we both theoretically and experimentally demonstrate a dual-layer emitter. Even in the case of highly relative humidity and strongly non-radiative heat transfer, the emitter can achieve efficient daytime radiative cooling performance. The emitter can reflect about 97.5% of incident solar radiation and emit about 95% in mid-infrared wavelengths. The cooling performances of the emitter on two different thermal conductivity substrates are discussed, and it is found that the emitter is insensitive to substrates. For hc=12.5 W/m2/K, the surface temperature of the emitter can be cooled to 4.3 °C below the ambient air temperature under 760 W/m2 average solar irradiation, when ambient air temperature is assumed to be 293 K. And the potential cooling power density is about 72.7 W/m2. The theoretical results agree well with the measurements. Our results show that the novel dual-layer emitter proposed here can achieve a technically efficient production, and will has significant potential for large-scale applications in the future.

Funding

National Natural Science Foundation of China (61475073); Social Development Program of Taizhou (TS202020).

Disclosures

The authors declare no conflicts of interest.

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Figures (9)
Fig. 1.
Fig. 1. Schematic of the dual-layer emitter for efficient daytime radiative cooling.

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Fig. 2.
Fig. 2. (a) Simulated emissivity/absorptivity of a PDMS film with various thicknesses on top of a 120-nm-thick Ag layer from 0.3 to 25 µm. (b) Simulated absorptivity and transmittance of a silver layer with different thicknesses from 0.3 to 25 µm.

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Fig. 3.
Fig. 3. (a) Simulated emissivity/absorptivity of a 200-µm-thick PDMS film on top of a 120-nm-thick Ag layer (red solid curve) and a 120-nm-thick Al layer (black shot dotted curve) from 0.3 to 25 µm. (b) Simulated emissivity of a 200-µm-thick PDMS film on top of a 120-nm-thick Ag layer (blue shot dotted curve) and with a silica wafer (red solid curve) from 0.3 to 25 µm.

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Fig. 4.
Fig. 4. Measured emissivity of the dual-layer emitter on top of 500-µm-thick silica wafer (black curve) and a 500-µm-thick plastic (red curve) from 0.3 to 25 µm.

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Fig. 5.
Fig. 5. (a) Measured angular absorptivity/emissivity of emitter in the 0.3-25 µm region on a fused silica wafer. (b) Measured angular absorptivity/emissivity of emitter in the 0.3-25 µm region on a plastic substrate. (c) Measured average angular absorptivity/emissivity of emitters on different substrates in the 8-13 µm region.

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Fig. 6.
Fig. 6. (a) On-site measurements of the dual-layer emitter on a silica surface (black curve), a plastic surface (red curve), ambient air (blue curve), and a bare module (magenta curve) between 09:00 and 16:00 on a building roof of a six-storey in Nanjing, in November 2019. The yellow shaded regions represent solar irradiance. (b) Measured stagnation temperature of the dual-layer emitter (olive curve) on a silica wafer and temperature difference of the emitter on two substrates (cyan curve) between 09:00 and 16:00.

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Fig. 7.
Fig. 7. The atmospheric transmittance from MODTRAN 5 [35].

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Fig. 8.
Fig. 8. Simulations of nonradiative heat exchange. (a) The simulation of the radiative emitter (layout shown on top) and the apparatus yields a temperature distribution (Ts-Ta) (bottom) in the geometry while taking into account of the nonradiative loss in the apparatus. (b) The simulation of Pcon as a function of the temperature difference (Ts-Ta). (c) The simulated results of the temperature difference (Ts-Ta) as a function of the thickness y. (d) Zoom-in of the simulated results of the proposed emitter from -2.5 to -5.0 °C.

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Fig. 9.
Fig. 9. (a) Measured temperature of the dual-layer emitter (black curve) on a silica wafer, calculated temperature of the dual-layer emitter (orange curve) [the same ambient air temperatures as in Fig. 6(a)], calculated stagnation temperature of the dual-layer emitter on a fused silica wafer (olive curve) between 09:00 and 16:00. (b) Calculated cooling power of the dual-layer emitter on a silica substrate (solid curves) and a plastic substrate (shot dashed curves) for heat transfer coefficient hc of 0 and 12.5 W/m2/K during daytime operation in two different atmospheric transmittance. The Ta is assumed to be 293 K.

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Equations (13)

Equations on this page are rendered with MathJax. Learn more.

M = [ cos δ 1 i sin ⁡ δ 1 η 1 i η 1 sin ⁡ δ 1 cos δ 1 ] .
δ 1 = 2 π λ n 1 d cos ⁡ θ 1 .
Y = η 2 cos ⁡ δ 1 + i η 1 sin ⁡ δ 1 cos ⁡ δ 1 + i ( η 2 / η 1 ) sin ⁡ δ 1 .
R = ( η 0 − η 2 ) 2 cos 2 δ 1 + ( η 0 η 2 / η 1 − η 1 ) 2 sin 2 δ 1 ( η 0 + η 2 ) 2 cos 2 δ 1 + ( η 0 η 2 / η 1 + η 1 ) 2 sin 2 δ 1 .
[ B C ] = { ∏ j = 1 K [ cos δ j i sin ⁡ δ j η j i η j sin ⁡ δ j cos δ j ] } [ 1 η K + 1 ] .
R = ( η 0 B − C η 0 B + C ) ( η 0 B − C η 0 B + C ) ∗ .
P c o o l = P r a d − P a t m − P s u n − P c o n .
P r a d ( T s ) = A ∫ 0 π / 2 2 π sin ⁡ θ cos ⁡ θ d θ ∫ 0 ∞ I B B ( T s , λ ) ε ( θ , λ ) d λ .
P a t m ( T a ) = A ∫ 0 π / 2 2 π sin ⁡ θ cos ⁡ θ d θ ∫ 0 ∞ I B B ( T a , λ ) ε a ( θ , λ ) d λ .
P s u n = A ∫ 0 ∞ ε ( 0 , λ ) I A M 1.5 ( λ ) d λ .
P c o n ( T s , T a ) = h c A ( T a − T s ) .
I B B = 2 h c 2 λ 5 1 e h c / ( λ k B T ) − 1 ,
h c = 8.3 + 2.5 v w i n d ,
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