Under the influence of global warming, cooling has become an extensively important issue. Compared with mechanic cooling methods, passive radiative cooling plays a significant role without artificial energy supply, and therefore it is eco-friendly and non-polluting [1,2]. To achieve passive radiative cooling, potential candidate materials require opacity in middle infrared atmospheric window (8-13 µm) and transparency in the rest spectrum [3–5]. Without external heating source, thermal energy can be radiated into the atmosphere and results in cooling. However, if act with external heating source, i.e. direct sun light, the radiative cooling becomes excessively challenging because the radiative energy is hard to exceed the heating energy. Alternatively, by adding a reflector to the bottom of the radiative cooling material, the total reflection of solar energy allows daytime cooling [6–9].

Since the pioneering work of Raman [10] demonstrates a daytime cooling temperature below ambient air very recently, much effort has been devoted to exploring natural materials [11–16] and artificial structures [2,17,18] for high-efficient passive radiative cooling. The emerging concepts, including hyperbolic metamaterial [10,17,18], photonic crystal [9,19–21], and resonant scatterers [2], consult composite structures of near-unity and broadband spectral emissivity. Among them, resonant scatterers show advantages in flexible, scalable, and low-cost fabrication by microspheres that have 8-um diameter into polymers [2]. In addition, metamaterial or photonic crystal relies on high-cost micro-/ nano- manufacturing methods to produce periodicity, i.e. thin film sputtering and lithography [10,17,18].

In this work, a flexible composite structure made of Amorphous Alumina Nanotubes (AANs) is proposed to accomplish high-efficient radiative cooling. We innovatively used the method of dissolution to obtain AANs. Compared with the hard amorphous alumina material, the AANs have no strong chemical bond with each other in the two-dimensional plane. The array formed by AANs has better flexibility, and can be used by attaching to a flexible substrate with special functional flexible material. Compared with hard passive radiation cooling materials, flexible ANNs are not only suitable for receptors with regular shapes, but also easier to fit receptors with irregular shapes, chaotic textures or uneven surfaces (such as house roofs, heat shields, and engine shells) [2,10,13,22], which will give full play to the cooling performance of ANNs. Unlike periodic lattice arrays or total randomly distributed particles, the AANs are fixed at the bottom in a hexagonal lattice to avoid large scale clustering and randomly agglomerated at the top to form a porous membrane. Multiple scattering within the membrane enhances the emissivity of alumina through the 8-13 µm atmosphere window. Under direct sunlight, the flexible AANs membrane achieves a net cooling power of 71.0 W/m² in the theoretical calculation and a maximum temperature reduction of 6.7 °C to the ambient air in experiments.

The flexible composite structure consists of four functional layers, as shown in Fig. 1(a). Top AANs layer forms the passive radiative cooling part with high-efficient emission at infrared and near-unity transparency at visible. The incoming solar irradiance and outgoing IR radiation can pass through. Note that the natural convention is minimized in experiments to maximize the radiative cooling effect. A thin silica layer (transparent in visible) prevents the underneath silver reflective surface from oxidization. In-depth penetration of the solar irradiance is stopped at the silver layer surface by a total reflection [23]. Polydimethylsiloxane (PDMS) layer at the bottom provides mechanical support to the entire structure. In Fig. 1(b), the sample was attached to an aluminum foil bent almost 180 degrees. The bending of the sample can also be clearly seen which shows that our samples have good flexibility.

 

Fig. 1. (a) Schematic diagram of the daytime passive radiative cooling effect and configuration of the flexible AANs membrane. (b) Photo of the flexible AANs membrane. The silver region marked by the white circle is the flexible AANs membrane, bending at almost 40 degree.

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In preparation (see Fig. 2(a)), we refer to the standard two-step anodization method [21], which was carried out in a 0.3 mol / L oxalic acid solution at 40 V and 5 °C. The first anodization time is 2 hours, and the second anodization time is contingent on needs. Then, the deposition and coating process is introduced. A SiO_s layer ∼ 100 nm thick and Ag layer ∼ 500 nm thick are deposited on one side of the aluminum plate by magnetron sputtering. The 50 µm-thick PDMS layer covers the deposited film through spin coating. To remove the aluminum plate in the middle, the sample is pretreated in 1mol/L Sodium hydroxide solution for 5 minutes and then transferred to a saturated copper chloride solution for etching, which also lasts 5 minutes. Then the sample is immersed in 5 wt.% phosphoric acid solution in 60 °C water bath. After 60 min, we obtain the non-flexible counterpart of our flexible AANs (named as hard sample hereby), the porous alumina membrane shown in Fig. 2(b) with pore diameter ∼ 60 nm, pore-to-pore spacing ∼ 100 nm, and given pore thickness at µm scale. In spite of the lack of flexibility, the prepared hard sample is known as a promising candidate for passive radiative cooling [24]. Finally, we dissolve the hard sample carefully in a mixed solution of 5 wt.% phosphoric acid and 1.8 wt.% chromic acid in 60 °C water bath. Products obtained at different processing time are shown in Figs. 2(c)–2(f).

 

Fig. 2. (a) Fabrication diagram of the flexible AANs membrane. (b-f) SEM images for the membrane samples (t = 20 µm) dissolved in acid solution after 0 min (b), 15 min (c), 25 min (d) and 30 min (e) (f). Note that image (f) is the zoom-out of the image (e).

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According to Kirchhoff's law of thermal radiation, emissivity, and absorptivity of a surface at a given temperature and wavelength are equal [25]. Here, the emissivity of the hard and flexible samples is characterized by the corresponding absorptivity measured by UV-Vis spectroscopy at 0.3 - 2.5 µm (see Fig. 3(a)) and Fourier-transform infrared spectroscopy at 3 - 15 µm (see Fig. 3(b)). In the visible, the differences between the hard samples and the flexible sample are negligible. Peaks of the emissivity ingeniously avoid the peaks of solar energy, providing the high-efficient reflection of solar energy. In the mid-infrared, we found that the flexible sample exhibits stronger absorption at 8 - 13 µm atmospheric window than the hard samples. This is due to the fact that the flexible sample formed by AAN bundles in the scale of several micrometers possesses multiple scattering of the infrared light inside the bundle [26] and behaves like a geometrical gradient absorber from the viewpoint of bundle shape [27]. Then, the enhancement of absorption is achieved by dwelling the light more effectively in the highly lossy alumina. To verify the dielectric loss in our flexible AANs membrane at the operating mid-infrared, the refractive index n and extinction coefficient k of the amorphous alumina are obtained by numerically fitting the infrared ellipsometer measurement data (for the hard sample of t = 20 µm) in COMSOL simulation to the experimental emissivity result in Fig. 3(b). In detail, raw data of n and k is employed as the initial fitting values in simulation. The simulation model numerically mimics the porous alumina membrane with pore spacing of 100 nm, pore size of 60 nm, t = 20 µm, and Ag layer at the bottom. The simulated emissivity curve and the fitted n (k) are shown in Figs. 3(b) and 3(c). One can see that the simulation results fit well with the measurement results. The relatively large value of k at the atmospheric window indicates the absorption due to light energy dissipation in lossy amorphous alumina.

 

Fig. 3. (a-b) Measured spectral absorptivity / emissivity of the hard samples and flexible sample from the visible to the mid-infrared. Solar spectrum (light yellow region) and atmospheric transmittance (light blue region) are plotted for references. The hard samples have t = 5 µm, 10 µm, and 20 µm, while the flexible sample has t = 20 µm. (c) Measured refractive index (n) and extinction coefficient (k) of the amorphous alumina in the mid-infrared. (d) Relationship between the cooling power, P_net, and the temperature difference, ΔT, in the hard samples and flexible sample. The numerical results are obtained with h_c = 0.

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In the following, we examine the cooling capacity of the prepared hard samples and flexible sample theoretically. The net cooling power P_net, and the temperature difference ΔT between the atmosphere temperature T_atm and the sample surface temperature T, are used to quantify the cooling capacity. Considering fully the heat exchange processes [10], the net cooling power can be defined as

The relationship between the emissivity of the atmosphere and the angle $\Omega$ is

In this work, the non-radiative heat exchange between the sample and the atmosphere is neglected by setting h_c = 0. The cooling performance of the samples is calculated and shown in Fig. 3(d). The cooling power of the flexible sample reaches 71.0 W/m² when no temperature difference is found between the sample surface and the atmosphere. When the net cooling power is zero, the surface temperature of the flexible sample is 21.3 °C below that of the atmosphere. In hard samples, when temperature difference eliminates, the 20 µm thick sample has a cooling power of 76.5 W/m², the 10 µm thick sample has 69.6 W/m² and the 5 µm thick sample has only 49.6 W/m². When the net cooling power is 0, the corresponding ΔT values are −24.8 °C for the 10 µm thick sample, −24.6 °C for the 20 µm thick sample, and −18.7 °C for the 5 µm thick sample. From the perspective of cooling capacity, the gap between the flexible sample and hard samples is very small.

The experimental setup shown in Fig. 4(a) is carefully designed to explore the cooling capacity of the flexible sample and hard samples. Polystyrene is used as the thermal insulating material. Circular grooves with diameter of 1 cm and depth of 2 mm are dug in the center region to hold the samples. After sample loading, the grooves are sealed by a 50 µm thick PE film with cyanoacrylate. By virtue of the sample holder design, our samples are exposed to a very limited volume of atmosphere and almost incapable of producing convection. The external influence on the sample temperature is well suppressed. The whole experimental setup is wrapped by aluminum foil to reduce the absorption of sunlight. Since the 50 µm thick PE film is almost transparent in the wave band studied in this paper, the influence of the PE film on the experimental results can be ignored [22,28]. Due to the windy weather in Chengdu, we design a windproof frame with PE film to reduce the impact of wind. The direct sunlight cooling measurements carried out in late July 2019 (a typical sunny day, daytime average temperature = 39 °C, nighttime average temperature = 25°C, and humidity = 80%) show moderate results in Fig. 4(b). The surface temperatures of the 10 µm and 20 µm thick hard samples are almost the same, while the 5 µm thick hard sample has a temperature slightly higher than the other two. All these hard samples show a cooling effect with ΔT fluctuating between 6°C and −3°C. In general, this is parallel with theoretical calculations. The measurement shown in Fig. 4(c) is carried out on the sunny roof in early August 2019 (a typical sunny day, daytime average temperature = 39 °C, nighttime average temperature = 25°C, and humidity = 80%). In the case of continuous direct sunlight from 10:00 to 11:30, the maximal temperature difference between the flexible sample and the atmosphere is 6.7 °C, and the average temperature difference is 4.3 °C. Compared to other materials and structures [12,24], our flexible material shows comparable cooling effect. In the case of intermittent direct sunlight from 11:30 to 18:00, the average temperature difference between the flexible sample and the atmosphere is 1.9 °C. It is indicated that our flexible materials can maintain cooling effect in a temperature-changing environment. At night, the flexible sample shows weak cooling effect and the surface temperature is slightly lower than the atmosphere temperature. It is clear that our experiments demonstrate the passive radiative cooling performance of the proposed flexible material in daytime.

 

Fig. 4. (a) Schematic diagram of the experimental setup for radiative cooling measurement. Inset: photo of the experimental setup (upper left corner). (b) Rooftop temperature measurement (solid line) and the corresponding temperature difference (dash-dot line) of the 5 µm (green),10 µm (yellow), and 20 µm (blue) thick hard samples against atmosphere temperature (red) in late July 2019, Chengdu. (c) Measured 24 h temperature for the flexible sample (blue) and atmosphere (red), and the corresponding temperature difference (black). The sun sign indicates continuous direct sunlight. The sun sign with a cloud indicates intermittent direct sunlight.

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In conclusion, a kind of flexible daytime radiative cooler is fabricated based on porous membrane in which AANs possess hexagonal lattice roots at the bottom and random agglomeration at the top. The complex structure formed by AANs bundle arrays enables the emissivity enhancement, which achieves near-unity values through the atmosphere window. In theory, the designed flexible material can provide 71.0 W/m² cooling power. In experiments, the highest temperature drop on the surface of the material reaches 6.7 °C, and the average temperature drop is 4.3 °C. Furthermore, the fabricating technology of porous alumina membranes allows our materials to be rapidly produced on large scale.