$$ {\overline{\mathrm{\rho }}}_{\mathrm{solar}}$$ and $$ {\overline{\mathrm{\epsilon }}}_{\mathrm{LWIR}}$$ of the PMMA_HPA film

Fig. 1a illustrates the fabrication process of PMMA_HPA. In brief, a monolayer of a hexagonally close-packed 5 μm SiO₂ array is fabricated using a facile unidirectional rubbing assembly method^43,44, as shown in Fig. 1b, c. A dispersion of PMMA and 200 nm SiO₂ nanospheres in acetone is then infiltrated into the SiO₂ monolayer template. After the rapid evaporation of acetone in air, the obtained PMMA/SiO₂ composite displays randomly distributed SiO₂ nanospheres and regularly distributed SiO₂ microspheres, as indicated by the micrograph and EDS elemental mappings (Fig. 1d–g). After removal of the SiO₂ nanospheres and the monolayer template by etching in hydrofluoric acid aqueous solution, a hierarchically porous array PMMA (PMMA_HPA) film with ordered symmetrical micropores (~4.6 μm diameter) and randomized nanopores (~250 nm average diameter) can be obtained (Fig. 1h, i and Supplementary Figs. 1a–c). Fourier transform infrared (FTIR) spectra and thermogravimetric analysis (TGA) confirm that PMMA_HPA is entirely composed of organic polymer without residual inorganic SiO₂ (Supplementary Figs. 1d and e), while the 49.4 wt% of SiO₂ before etching indicates a high porosity of PMMA_HPA (Supplementary Fig. 1f).

Fig. 1

Fabrication and characterization of the PMMA_HPA film.

a Schematic illustration of the fabrication of PMMA_HPA with a hierarchically porous array. b, c SEM micrographs of hexagonally close-packed monolayer SiO₂ templates. d SEM micrograph of PMMA/SiO₂ composite. e–g EDS elemental mappings of Si, O, and C in d, showing the randomly distributed SiO₂ nanospheres and regularly distributed SiO₂ microspheres of the composite. h, i SEM micrographs of PMMA_HPA showing an ordered symmetrical micropores array made of hierarchical randomized nanopores.

Figure 2 demonstrates the spectral reflectance and emissivity of the PMMA_HPA film with ~160 μm effective thickness according to the normalized ASTM G173 Global solar spectrum and the LWIR atmospheric transparency window. The PMMA_HPA film with ~60% porosity presents a high average solar reflectance ($$ {\overline{\rho }}_{\mathrm{solar}}$$ = 0.95, Fig. 2a and Supplementary Fig. 2a), which ensures excellent reflection of sunlight from all incidences and minimizes the solar heat gain. Meanwhile, the film also shows a high thermal emittance over a broad bandwidth in the mid-infrared and still emits a significant part of its thermal energy even at large emission angles ($$ {\overline{\epsilon }}_{\mathrm{LWIR}}$$ = 0.98, Fig. 2b and Supplementary Fig. 2b), which can enable strong emission of heat to the cold sink of outer space through the atmospheric transparency window at different angles in relation to the sky. One remarkable feature of our structural polymer is that the periodic ordered ~4.6 μm micropores can scatter sunlight of ultraviolet-visible-near-infrared (UV-Vis-NIR) wavelengths, and the abundant, random ~250 nm nanopores greatly reduce the mean scattering path and transmission through the material, which further enhances the scattering of shorter visible wavelengths^45,46. The combination of PMMA with air voids, one of which has a high refractive index and the other has a low refractive index $$ \left(\mathrm{\Delta }n=n_{\mathrm{PMMA}}-n_{\mathrm{air}}=1.49-1=0.49\right)$$, could provide a sharp refractive index transition across polymer-air boundaries and yield the efficient solar scattering and the required strong sky window absorptance without surface obstruction³⁴.

Fig. 2

Spectroscopic response of the PMMA_HPA film.

a, b Spectral reflectance and emissivity of the PMMA_HPA film with ~160 μm effective thickness along with the normalized ASTM G173 Global solar spectrum and the LWIR atmospheric transparency window. c, d Spectral refractive index (n) and extinction coefficient (κ) of PMMA, showing negligible absorptivity in the solar range and multiple extinction peaks in the LWIR wavelengths. e Absorbance spectrum of PMMA_HPA measured with ATR-FTIR spectroscopy. f Schematic diagram showing the periodic re-entrant structure with nano/microscale pores is conducive to enhance the total scattering efficiency by multiple reflections.

As one of the most widely used and low-cost polymers, pristine PMMA film has ideal intrinsic properties to enable high-performance PDRC applications⁴⁷. Figure 2c, d show that PMMA has negligible extinction coefficient in the solar wavelengths and multiple extinction peaks at the 8, 8.6, 10.3, 11.8, and 13.2 μm within the LWIR window, which should result from the different vibrational modes of its molecular structure. These properties keep the heat gain from sunlight to a minimum and contribute to a large amount of infrared absorption/emission in the atmospheric transparency window, which is responsible for the superior PDRC. Furthermore, the absorbance spectrum measured with attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) exhibits strong infrared absorption due to C–O–C stretching vibrations between 770 and 1250 cm⁻¹ (8–13 μm, Fig. 2e), which coincidently lie in the atmospheric transparency window. Importantly, the periodic re-entrant structure with hierarchical nano/microscale pores is conducive to enhance the total scattering efficiency and increase the probability of infrared absorption/emission through multiple diffuse reflection at various incident angles (Fig. 2f). All these features benefit the radiative heat exchange between the cooling structural polymer and the atmosphere, causing sufficiently high $$ {\overline{\rho }}_{\mathrm{solar}}$$ and $$ {\overline{\epsilon }}_{\mathrm{LWIR}}$$ of our PMMA_HPA film to achieve all-day passive radiative cooling.

Different from transparent pristine PMMA, the PMMA/SiO₂ composite film is translucent due to the absorptance in the UV and visible regions, and the corresponding PMMA_HPA film has negligible transmittance because its plenty of pores can efficiently scatter sunlight of all wavelengths (Supplementary Figs. 3a–d). The spectral transmittance of the PMMA_HPA film decreases with increasing thickness (Supplementary Fig. 4). Accordingly, the solar reflectance appears to have a more pronounced increasing trend with thickness than the thermal emittance in the range of 8–13 μm (Fig. 3a–c), which likely arises from the increased backscattering of light from the thicker, nonabsorptive, porous PMMA layer. Evidently, even the emittance of the only effectively ~2 μm thick PMMA_HPA film can reach 0.85. This suggests that the porous structure is sufficient to augment the intrinsic emittance of PMMA_HPA. Further, we experimentally and theoretically demonstrated the influence of pore sizes and porosity on the optical performance. As clearly seen in Supplementary Fig. 5a, the PMMA_HPA with ~500 nm nanopores shows a high-level $$ {\overline{\rho }}_{\mathrm{solar}}$$, but its scattering of short wavelength region is inferior to that of ~200 nm nanopores. The reflectance of PMMA_HPA with ~100 nm nanopores drops gradually in the visible and NIR-to-SWIR ranges (0.4–2.5 μm), leading to a lower $$ {\overline{\rho }}_{\mathrm{solar}}$$. Such results coincide with the finite-difference time-domain (FDTD) simulation data (Supplementary Fig. 6a), indicating nanopores ranging in diameter from 200 to 300 nm are optimum to reinforce the scattering of UV and visible wavelength region. For the optimization of micropore sizes, we established a model of ordered monolayer micropore with different sizes in the range of 1 to 10 µm. Given the simulation results, one could derive that micropores ranging from 5 to 7 µm in diameter would highly contribute to the solar reflectance (Supplementary Fig. 6b). Thus, combining the optimized nanopore size of 200–300 nm and micropore size of 5–7 µm, the maximum $$ {\overline{\rho }}_{\mathrm{solar}}$$ of our hierarchical porous PMMA film can be obtained (Supplementary Fig. 6c). Moreover, the solar reflectance of the PMMA_HPA film increases with increasing porosity, while its thermal emittance does not significantly change (Supplementary Fig. 5b). FDTD simulation results also show that the nanopore density or porosity has a positive correlation with the reflectance (Supplementary Fig. 6d). However, too high porosity may reduce the mechanical strength. Based on the trade-off of the optical and mechanical properties, ~ 60% porosity was adopted in the experiment design and radiative cooling application.

Fig. 3

Variation in $$ {\overline{\mathrm{\rho }}}_{\mathrm{solar}}$$ and $$ {\overline{\mathrm{\epsilon }}}_{\mathrm{LWIR}}$$ of the PMMA_HPA films with effective thickness and polarization angle.

a Variation in $$ {\overline{\rho }}_{\mathrm{solar}}$$ and $$ {\overline{\epsilon }}_{\mathrm{LWIR}}$$ of the PMMA_HPA films with effective thickness. The error bars represent the standard deviation. b, c Measured reflectance and emissivity spectra of the PMMA_HPA films as a function of the film effective thickness. d Infrared emissivity spectra of a PMMA_HPA film at different polarization angles (θ) from 10° to 80°. e Polar distribution of the average emissivity across the atmospheric window of the PMMA_HPA film at different polarization angles (θ) from 10° to 80°. f Measured polarization-dependent infrared emissivity spectra of the PMMA_HPA films.

Figure 3d–f demonstrate the emissivity spectra of the PMMA_HPA film in the infrared range of 2.5–20 µm at different polarization angles. $$ {\overline{\epsilon }}_{\mathrm{LWIR}}$$ shows a regularly decreasing trend from 10° to 80°, mainly owing to the ordered periodic micropore array on the top surface of the PMMA_HPA film. Excitingly, the average emissivity across the atmospheric window $$ \left({\overline{\epsilon }}_{\mathrm{LWIR}}\right)$$ is greater than 0.95 over a wide polarization angle range from 10° to 80°, indicating a stable emitted heat flux through the atmospheric transparency window to the cold sink of outer space.

To investigate the influence of the hierarchical porous structure on the optical properties of the PMMA_HPA film, we further compared it with three other types of PMMA films, nanopore PMMA_NP, monolayer micropore array PMMA_MPA and pristine PMMA, as shown by the SEM images in Fig. 4a–d. Figure 4e shows that the PMMA_HPA film presents the highest average solar reflectance ($$ {\overline{\rho }}_{\mathrm{HPA}}$$ = 0.95) in UV-Vis-NIR wavelengths, while PMMA_NP drops gradually to a lower average solar reflectance ($$ {\overline{\rho }}_{\mathrm{NP}}$$ = 0.74) in the near-to-short wavelength infrared (NIR-to-SWIR) range (0.7–2.5 μm) because only these disordered nanopores are too small to effectively scatter such wavelengths. In contrast, PMMA_MPA exhibits a low value at all wavelengths ($$ {\overline{\rho }}_{\mathrm{MPA}}$$ = 0.23) because the scattering of uniform monolayer micropores is weak. Similar results can be observed for pristine PMMA ($$ {\overline{\rho }}_{\mathrm{prestine}}$$ = 0.10) due to its high transparency. The emission spectra show that all four films have strong thermal emittances in the LWIR transparency window ($$ {\overline{\epsilon }}_{\mathrm{HPA}}$$ = 0.98, $$ {\overline{\epsilon }}_{\mathrm{NP}}$$ = 0.96, $$ {\overline{\epsilon }}_{\mathrm{MPA}}$$ = 0.95 and $$ {\overline{\epsilon }}_{\mathrm{prestine}}$$ = 0.92), as shown in Fig. 4f. However, the emissivity of PMMA_MPA and pristine PMMA substantially drops in the range of mid-IR wavelengths compared to the PMMA_HPA and PMMA_NP films. This probably because that the existence of abundant hierarchically porous structure reduces the effective refractive index and leads to a more gradual refractive index transition across the polymer-air interface than PMMA_MPA and PMMA¹⁷. Thus, the impedance matching between the porous polymer and surrounding air is improved⁴⁸, which reduces the surface reflectance and results in a consistently higher emissivity for PMMA_HPA or PMMA_NP film in the mid-IR wavelengths. Besides, as we mentioned above, the porous structure with high specific surface area might increase the probability of infrared absorption through multiple diffuse reflection and enhances the emissivity.

Fig. 4

SEM micrographs and optical properties of different types of PMMA films.

a–d SEM micrographs of the PMMA_HPA, PMMA_NP, PMMA_MPA, and pristine PMMA films. e Reflectance spectra across the solar wavelengths of different types of PMMA films. f Infrared emissivity spectra of different types of PMMA films.

The experimental results of four types of PMMA films were also theoretically verified by FDTD simulations (Supplementary Fig. 7)⁴⁹. The numerical simulation results further reveal that hierarchical porous structure containing dual-scale nano/micro cavities would significantly improve the broadband scattering performance contrast to uniform nanoscale porous structure, especially in the range of NIR-to-SWIR, while the LWIR thermal emissivity of the two kinds of structures has negligible changes. The theoretical model of PMMA_MPA verifies that the ordered micropores monolayer does not have enough high scattering coefficient, which matches well with the experimental result. We also simulated the reflectance spectra across the solar wavelengths of the PMMA_HPA film with thickness of ~5 µm (effectively ~2 µm, Supplementary Fig. 8). Surprisingly, such thin film is sufficient to yield an efficient scattering ($$ {\overline{\rho }}_{\mathrm{HPA}-2\mathrm{\mu m}}$$ = 0.35), which further evidences the enhancement effect of hierarchical porous surface on the solar reflectance.

Besides, to verify the optical superiority of the periodic micropores array on the surface, we also investigated the optical properties of a hierarchically porous PMMA (PMMA_HP) film with loose-packed random micropores and nanopores (Supplementary Figs. 9a–c). The solar reflectance of the PMMA_HP film drops 8% in the range of NIR-to-SWIR compared to PMMA_HPA (Supplementary Fig. 9d), which contains about 5% of sunlight ($$ {\overline{\rho }}_{\mathrm{HP}}$$ = 0.90). This suggests that the close-packed periodic arrangement of the hierarchical nano/microscale pores on the surface of our PMMA_HPA can maximize both the surface area and the amount of scatters per unit and increase the overall scattering efficiency, especially in NIR-to-SWIR range, although this distribution of micropores on the surface does not influence the infrared emissivity (Supplementary Fig. 9e).

Furthermore, the PMMA_HPA film was modified by fluorosilane to become superhydrophobic with a water contact angle (WCA) of ~156° (Supplementary Fig. 10) for stable durability in various atmospheric humidity conditions. Both the solar reflectance and infrared emissivity are at high levels and vary negligibly after fluorosilane treatment (Supplementary Figs. 11a and b). Even after accelerated weathering treatment for 480 h (each cycle including the UV irradiation at 310 nm wavelength with intensity of 0.71 W/m² at 60 °C for 4 h, followed by condensation at 50 °C for 4 h with UV lamps off), the PMMA_HPA films exhibit no blistering, peeling, cracking and color changing. The porous morphology of our PMMA_HPA films basically remains the same (Supplementary Figs. 12a and b). The ATR-FTIR spectra further demonstrate that the surface-modified PMMA_HPA films before and after weathering treatment all have obvious absorption peaks of C=O at 1726 cm⁻¹, C–F at 1187 cm⁻¹, C–O–C at 1139 cm⁻¹ and C–Cl at 779, 746, 700, and 651 cm⁻¹ (Supplementary Fig. 12c), owing to the protection of fluorosilane molecules. Moreover, the constant WCAs in Supplementary Fig 12d after weathering treatment also indicate the excellent durability and potential applicability. The reflectance and emissivity spectra of the PMMA_HPA films show slight fluctuations of solar reflectance ($$ {\overline{\rho }}_{\mathrm{solar}}$$ = 0.95 ± 0.02) and negligible variations in emissivity ($$ {\overline{\epsilon }}_{\mathrm{LWIR}}$$ = 0.98 ± 0.01) with the accelerated weathering time (Supplementary Figs. 12e and f), which may be attributed to the inconspicuous yellowing effect in response to the UV irradiation. We also conducted the real outdoor exposure test for 40 days on a flat roof in Shanghai city and the results indicate the almost unchanged optical performance and WCAs (Supplementary Table S1).

All-day continuous passive radiative cooling measurements of the PMMA_HPA film

The radiative cooling performances of the structural polymers (~160 μm effective thickness and 100 mm × 100 mm in size) were measured from 20:00 on 09 Oct. to 20:00 on 10 Oct. 2019 using a 24-h uninterrupted thermal measurement on a flat roof of a five-story building under a clear sky in Shanghai, China. As shown in Fig. 5a, the strong optical scattering of sunlight gives our PMMA_HPA surface a matte and white appearance, which can be further confirmed by the CIE chromaticity coordinate analysis (Fig. 5b). Under intense solar irradiance of ~930 W/m² and relative humidity of ~40% at noon (Fig. 5c), the real-time temperature tracking of the air and four types of PMMA films are shown in Fig. 5d. Evidently, although the pristine PMMA and PMMA_MPA films can exhibit decreases in temperature by ~3.7  °C and ~4.9 °C at night, respectively, their temperatures dramatically rise to ~15.2 °C and ~14.1 °C above the ambient temperature at noon due to their transparency and translucency, respectively (Fig. 5e). The PMMA_NP film can achieve a subambient cooling of ~6.5 °C during the night but maintains almost the same temperature as the ambient environment during midday. In contrast, the PMMA_HPA film exhibits fabulous passive radiative cooling during both night and daytime. The average below-ambient temperature of the PMMA_HPA film is ~8.2 °C during the night (between 6 p.m. and 6 a.m.) and ~6.0 °C during midday (between 11 a.m. and 2 p.m.). This cooling performance is on par with those in previous reports (Supplementary Table S2).

Fig. 5

Twenty-four-hour continuous passive radiative cooling performance measurements.

a Photograph of the cooling PMMA_HPA film showing its bright white appearance (inset, water contact angle image of PMMA_HPA). b CIE chromaticity coordinates of the cooling PMMA_HPA film. c Relative humidity tracking of the air and solar irradiance at 12 PM on 10 Oct. 2019. d Temperature tracking of the air and PMMA films. e Temperature difference between the ambient and structural PMMA films.

Subambient PDRC performance in various geographical regions and climates

Radiative cooling performance in real-world applications is substantially affected by the geographical regions and climates. For instance, the net radiative cooling power of the cooler is limited by the increased solar irradiation, humidity, cloud cover, local wind speed and ambient temperature^30,50. Here, we further performed a series of experiments to evaluate and compare the effects of climates from different cities on the radiative cooling performance of our PMMA_HPA films. Three cities, Xiamen city (Southern China, Coastal), Shanghai city (Eastern China, Coastal) and Xuzhou city (Northern China, Inland), were chosen as typical test locations due to their different topographic and meteorological characteristics (Supplementary Fig. 13). The climate characteristics in Xuzhou, Shanghai and Xiamen are temperate monsoon climate, subtropical monsoon climate and subtropical marine monsoon climate, respectively, which provide a remarkable difference in humidity for our measurements. As shown in Fig. 6a–i, under clear skies with comparable solar intensity and wind speed but various humidity conditions (~38% in Xuzhou, ~47% in Shanghai, and ~54% in Xiamen), the subambient cooling of ~8.9 °C, ~7.8 °C and ~8.6 °C at noontime is observed, separately. Even in the same location (e.g., in Xiamen city), increasing solar intensity (from ~890  W/m² to ~930 W/m²), wind speed (from ~0.6 m/s to ~1.1 m/s) and humidity (from ~54% to ~64%), the PMMA_HPA film still enables cooling up to ~5.5 °C below ambient temperature (Figs. 6g–l), which has not been reported previously^40,41. Comparing Xuzhou and Xiamen city (Fig. 6a–c and j–l), we can conclude that increasing solar intensity (from ~860 W/m² to ~930 W/m²), wind speed (from ~0.5 m/s to ~1.1 m/s) and humidity (from ~38% to ~64%), the subambient cooling temperatures of PMMA_HPA film are indeed influenced (decreasing from ~8.9 °C to ~5.5 °C). The primary driver of the good performance in various geographical regions and climates should be the synergistic result of visible white (high solar reflectance) and infrared black (high infrared emissivity in both the 1st and 2nd atmospheric transparency window) that greatly minimizes the absorbing solar irradiance and the thermal radiation emitted by the atmosphere. In addition, we investigated the effect of surface modification on the daytime radiative cooling performance of the PMMA_HPA film. The results show that the PMMA_HPA films with and without surface modification can achieve subambient cooling temperatures of ~6.9 °C and ~6.5 °C, respectively (Supplementary Fig. 14). While the PMMA_HPA film without surface modification also demonstrates excellent passive radiative cooling behavior, the fluorosilane treatment enables stable performance by restricting the effect of moisture and water under different levels of humidity.

Fig. 6

Passive daytime radiative cooling performance of the PMMA_HPA film in different locations and weathers.

a–c Solar irradiance, wind speed and relative humidity, and temperatures of the air and the PMMA_HPA film in Xuzhou city. d–f Solar irradiance, wind speed and relative humidity, and temperatures of the air and the PMMA_HPA film in Shanghai city. g–i Solar irradiance, wind speed and relative humidity, and temperatures of the air and the PMMA_HPA film in Xiamen city. j–l Solar irradiance, wind speed and relative humidity, and temperatures of the air and the PMMA_HPA film in Xiamen city.

Passive radiative cooling power measurements of the PMMA_HPA film

When used in a building roof or external siding, our PMMA_HPA films can achieve all-day passive radiative cooling through reflecting sunlight and radiating heat to the cold outer space under a clear sky (Fig. 7a). Figure 7b schematically shows the direct thermal measurement system based on the net cooling equation. To further demonstrate the PDRC capability of the cooling PMMA_HPA, we adopted a feedback-controlled heating system to measure its radiative cooling power during the midday (Fig. 7c). This feedback-controlled heating system maintains the surface temperature of the PMMA_HPA film at the measured ambient temperature to minimize the impact of conductive and convective heat losses (Fig. 7d). Promisingly, the PMMA_HPA film attains an average cooling power of ~85 W/m² under solar intensity of ~900 W/m² in April in Shanghai (Fig. 7e).

Fig. 7

Net cooling power of the PMMA_HPA film during the midday.

a Schematic of the basic principles of PDRC. When used in a building roof or external siding, the PMMA_HPA film exhibits high solar reflectance and high infrared emissivity. b Two-dimensional schematic drawing of the thermal box apparatus with a feedback-controlled heater. The heater maintains the sample surface temperature at that of the ambient environment, minimizing convective and conductive heat losses. c Photo of the experimental apparatus on a rooftop in Shanghai, China. d Temperature tracking of the ambient and the PMMA_HPA film under solar intensity of ~ 900 W/m² and relative humidity of ~ 44% on April 23, 2020. e Continuous measurement of the radiative cooling power of the PMMA_HPA film during the midday.

Figure 8a, b present the net cooling power during the nighttime and daytime calculated using the radiative cooling theoretical model, respectively. More details of this model are given in the “Methods” section. The power of solar radiation is set to approximately 1000 W/m² for simplicity, and the ambient temperature T_amb is assumed to be 298.15 K in both cases. A maximum cooling power of 124.40 W/m² can be achieved for nighttime operation. For daytime operation, the calculated maximum net cooling power is 74.40 W/m² at thermal equilibrium, which is lower than the measured daytime cooling power due to the fluctuations in the ambient conditions, the uncertainty in the measurements and the theoretical model approximations.

Fig. 8

Calculated net cooling power with software MATLAB based on the theoretical simulation.

a Calculated net cooling power during the nighttime. b Calculated net cooling power during the daytime. The variable h_c is a combined nonradiative heat coefficient. Values of 0, 3, 6, 9, and 12 for h_c are used in the calculations. For daytime calculations, 5% solar power absorption is considered.

In summary, we have demonstrated and fabricated a hierarchically structured PMMA film with a dense micropore monolayer array and randomly distributed nanopores for highly efficient all-day passive subambient radiative cooling in various geographical locations and climates. Our structural polymer film exhibits sufficiently high solar reflectance and thermal emittance owing to its abundant periodic scattering micropores embedded with random nanopores and ideal intrinsic properties. Without needing any silver or aluminum reflectors, our cooling structural PMMA film realizes an average below-ambient temperature ~8.2 °C during the night and ~6.0 °C to ~8.9 °C during midday, and promisingly ~5.5 °C even under solar intensity of ~930 W/m² and relative humidity of ~64% in hot and moist subtropical marine monsoon climate, which is really an all-day and all-climate PDRC system. And the superhydrophobized PMMA_HPA film can ensure cooling performance durability by eliminating the effect of moisture and water under different levels of humidity. This study has revealed the effects of micropores, nanopores and their arrangement on optical performance, which may provide deep insight into the crucial roles of various pores and their array in solar reflectance and thermal emittance and help us design and fabricate more efficient all-day passive subambient radiative cooling materials and systems.

Fabrication of PMMA_HPA

Monodisperse 5 μm SiO₂ microspheres were placed on top of a polydimethylsiloxane (PDMS)-coated glass sheet and rubbed with another PDMS substrate with slight palm pressure along a randomly chosen direction according to our reported method^43,44. After being rubbed for 5 s, the SiO₂ microspheres had assembled into hexagonally close-packed monolayers on the PDMS surfaces. A 200 nm SiO₂ nanosphere dispersion in acetone was added to PMMA to make a dispersion of SiO₂-acetone-PMMA (1:10:1 mass ratio) under magnetic stirring at 50 °C for 2 h. This dispersion was then drop-cast onto the monolayer SiO₂ template. After the solvent was fully evaporated, a freestanding PMMA/SiO₂ composite film was obtained by peeling the coating off the smooth surface. After removal of the SiO₂ template and nanospheres with 2-5 vol% hydrofluoric acid aqueous solution, PMMA_HPA films with various effective thicknesses of 2 ± 0.5 µm to 160 ± 5 µm were obtained by casting different amounts of solution. For comparison, PMMA_NP film was fabricated by the same procedure above without using the monolayer SiO₂ template, PMMA_MPA film was obtained without SiO₂ nanospheres, and the pristine non-porous PMMA film was prepared at an acetone-PMMA (10:1 mass ratio) without using SiO₂ particles. In addition, PMMA_HP film was fabricated using random loose-packed monolayer 5 μm SiO₂ templates and 200 nm SiO₂ nanosphere. All the films above have the same effective thickness by controlling the PMMA mass and film-forming substrate size.

PMMA_HPA surface modification

To make superhydrophobic PMMA_HPA film, the sample was treated with 1H,1H,2H,2H-perfluorooctyltrichlorosilane (PFOTS) via a chemical vapor deposition (CVD) method. In detail, the PMMA_HPA film and a vial containing 1% PFOTS/ethanol solution were placed in a sealed vacuum desiccator. The desiccator was immediately pumped to vacuum for 15 min and placed at room temperature for 24 h for fluorination. The modified PMMA_HPA film was then baked in an oven at 80 °C for 1 h to remove the excessive PFOTS.

Characterization

Theoretical model of the radiative cooling performance

When the structural polymer films are exposed to a clear sky, they are influenced by the solar irradiance and atmospheric downward thermal radiation. Meanwhile, heat can be transferred from the ambient surroundings to the polymers via conduction and convection due to the temperature difference between the cooling polymers and the ambient environment. To achieve PDRC, the device must satisfy very stringent constraints as dictated by the power balance equation. The net cooling power P_cool of the structural polymers is expressed as²⁶:

where T is the surface temperature of the structural polymers and $$ T_{\mathrm{amb}}$$ is the ambient temperature. $$ P_{\mathrm{rad}}\left(T\right)$$ is the power radiated by the structural polymers, and $$ P_{\mathrm{atm}}\left(T_{\mathrm{amb}}\right)$$ is the absorbed atmospheric thermal radiation at $$ T_{\mathrm{amb}}$$. $$ P_{\mathrm{solar}}$$ is the incident solar irradiation absorbed by the structural polymers, and $$ P_{\mathrm{cond}+\mathrm{conv}}$$ is the power lost due to convection and conduction. The net cooling power defined in Eq. (1) can reach a high value by increasing the radiative power of the structural polymers and reducing either the solar absorption or parasitic heat gain³⁴. These parameters can be calculated by the following equations^26,53–55:

where A is the surface area of the radiative cooler. $$ \int d\mathrm{\Omega }=2\pi {\int }_0^{\pi /2}d\theta \sin \theta $$ is the angular integral over a hemisphere. $$ I_{\mathrm{BB}}\left(T,\lambda \right)=\frac{2h{c}^2}{{\lambda }^5}\frac{1}{e^{hc/\left(\lambda {\kappa }_{B}T\right)}-1}$$ is the spectral radiance of a blackbody at temperature T. h is Planck’s constant, κ_B is the Boltzmann constant, and c is the speed of light. $$ \mathrm{\epsilon }\left(\lambda ,\theta \right)$$ is the directional emissivity of the surface at wavelength λ. $$ {\epsilon }_{\mathrm{atm}}\left(\lambda ,\theta \right)=1-\tau {\left(\lambda \right)}^{1/\mathrm{con}\theta }$$ is the angle-dependent emissivity of the atmosphere; τ(λ) is the atmospheric transmittance in the zenith direction. $$ P_{\mathrm{rad}}\left(T\right)$$ and $$ P_{\mathrm{atm}}\left(T_{\mathrm{amb}}\right)$$ are determined by both the spectral data of the structural polymers and the emissivity spectrum of the atmosphere according MODTRAN of Mid-Latitude Summer Atmosphere Model^36,56. In Eq. (4), the solar illumination is represented by the AM1.5 spectrum $$ \left(I_{\mathrm{AM}1.5}\left(\lambda \right)\right)$$. For our PMMA_HPA film, approximately 95% of the input solar power can be reflected, and thus, the 5% absorption of the solar irradiance will reduce the net cooling power. In Eq. (5), $$ h_c=h_{\mathrm{cond}}+h_{\mathrm{conv}}$$ is a combined nonradiative heat coefficient that captures the collective effect of conductive and convective heating, which can be limited to a range between 0 and 12 W/m²/K.

The average solar reflectance ($$ {\overline{\rho }}_{\mathrm{solar}}$$) is defined as¹⁷:

where λ is the wavelength of incident light in the range of 0.3–2.5 μm, $$ I_{\mathrm{solar}}\left(\lambda \right)$$ is the normalized ASTM G173 Global solar intensity spectrum, and $$ {\rho }_{\mathrm{solar}}\left(\lambda ,\theta \right)$$ is the surface’s angular spectral reflectance. The average emittance ($$ {\overline{\epsilon }}_{\mathrm{LWIR}}$$) in the LWIR atmospheric transmittance window is defined as:

where $$ I_{\mathrm{BB}}\left(\lambda \right)$$ is the spectral intensity emitted by a blackbody and $$ {\epsilon }_{\mathrm{LWIR}}\left(\lambda ,\theta \right)$$ is the surface’s angular spectral thermal emittance in the range of 8–13 μm.