Durable radiative cooling against environmental aging | Panda Anku

Raw materials

1H,1H,2H,2H-perfluorooctyltrichlorosilane (PFOTS), rutile type titanium dioxide (TiO2) nanoparticles (NPs) (Supplementary Fig. 3), manganese dioxide (MnO2) particles, carbon black, ferric oxide (Fe2O3), humic acid (HAc), sodium chloride (NaCl), sodium nitrate (NaNO3), calcium sulfate dihydrate (CaSO4 ∙ 2H2O), ethanol (95%), acetone (99%), formaldehyde (99%) and toluene (99%) were purchased from Aladdin, Co. All above chemicals were used as received. Deionized (DI) water was produced from Millipore Synergy UV-R water purification system. Borosilicate glass slides (170 µm thick) were purchased from Marienfeld Superior. Adhesives from diverse brands were used obtaining similar performances. Commercial white paint was purchased from Sherwin–Williams (extra white, product number A74W00051). Poly (vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP, Kynar Flex® 2801) was purchased from Arkema. Silver and aluminum plates, plastic slides (5 mm thick) made of poly(methylmethacrylate) (PMMA), basswood sheet (10 mm thick), soiling agents (including montmorillonite, bentonite, coal ash and sand), aluminum foils, outdoor wall tiles (40 × 80 cm), tin boxes (47 × 32 × 32 cm) and spray coating equipment were purchased from local market.

Fabrication of anti-aging cooling paint (AACP) and coatings

PFOTS and TiO2 NPs were added into ethanol, which was stirred for 5 h at ambient temperature (about 25 °C) to have an apparent uniform suspension. Weight ratio of PFOTS/TiO2/ethanol as 0.1/1.3/10 (Supplementary Fig. 12) was routinely used to fabricate AACP suspension. The prepared AACP suspension could be drop/dip-cast or sprayed/brushed onto diverse surfaces to form uniform coatings. In the present work, drop-cast method was chosen to routinely fabricate coatings from AACP. By using scanning electron microscopy to observe the cross-section image of the coating layers, we obtained the coating thickness (Supplementary Fig. 4). The averaged thickness data and corresponding standard deviation were obtained from at least 5 measurements at different positions. To enhance mechanical durability of AACP coatings, a layer of adhesive was first brushed onto the substrate before the drop-cast of AACP, enhancing cohesive strength between the substrate and AACP. Commercial white paint was used as received to brush onto the substrate as control group. Porous coatings from PVDF-HFP were obtained via phase inversion-based process according to previous report9. In short, PVDF-HFP and acetone were first mixed to form a solution mixture, then water was added into it to induce liquid-solid phase inversion to have solid coatings. The weight ratio of PVDF-HFP/acetone/water was 1/8/1. For AACP’s scalability demonstration, spray coater was employed for painting on outdoor wall tiles. To obtain uniform coating layer of about 100 µm, a series of equipment parameters were chosen for the purpose, including 0.1 bar as driving pressure, nozzle size of 2.5 mm, rendering 320 mL min−1 as flow rate, about 40 cm as spray distance, and spray time of about 1 min to paint the whole tile (40 × 80 cm).

Packing density (ϕ) calculation was based on mass conservation principle. The mass density of TiO2 NPs is about 4.26 g cm−3, measured by Ultrapyc 5000 pycnometer. As an example, for 5 × 5 cm substrate, the used solid content of TiO2 suspension is 0.48 g (weight ratio of TiO2/ethanol is 1.3/10), the measured dry coating thickness is about 100 µm, then ϕ is calculated as (frac{0.478{{{{{rm{g}}}}}}/4.26{{{{{rm{g; c}}}}}}{{{{{{rm{m}}}}}}}^{-3}}{25{{{{{rm{c}}}}}}{{{{{{rm{m}}}}}}}^{2}times 100{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}approx 0.45). In practice, TiO2 concentration in ethanol is the determining factor in controlling the magnitude of ϕ, high concentration corresponding to high ϕ and vice versa.

Optical characterization of the coatings

The solar reflectance (solar) of AACP and other coating samples was measured and averaged within wavelength (λ) range of 0.3–2.5 µm using PerkinElmer LAMBDA 950 with a polytetrafluoroethylene integrating sphere. The emittance of the coatings was measured within λ of 2.5–16 µm using PerkinElmer Spotlight 200I with a gold integrating sphere. The long-wave infrared (LWIR) emittance (({bar{varepsilon }}_{{{{{{rm{LWIR}}}}}}})) at the transparent atmospheric window was calculated by averaging the emittance data over wavelength of 8–13 µm. For each coating sample, the averaged data and corresponding standard deviation were obtained from at least 3 measurements.

Surface-wetting characterization

The apparent static water contact angle (θapp) and roll-off angle (θroll) measurements were performed on OCA 50 AF, Dataphysics. For measurement of θapp, a 6 µL droplet was placed on the coating surface and sat still. The angle between the tangent to the liquid-vapor interface and the solid surface was recorded as θapp. For measurement of θroll, a 10 µL droplet was placed on the coating surface and the substrate was tilted at a speed of 0.1° per second. θroll value was recorded at the moment of droplet-rolling. For each coating sample, the averaged data and corresponding standard deviation were obtained from at least 5 measurements at different positions.

To obtain the energy dissipation factor (EDF) of water drops while impacting on the coating surfaces, a 5 µL water droplet was released from a height of 10 mm to impact the coating surface, and the droplet rebounded after impact. The maximum height (h, unit of mm) of the droplet rebounding after the first impact was recorded using a high-speed camera (Photron, Fastcam SA5) with 10,000 fps (frames per second). Then the EDF is defined as EDF = (10 − h)/10. For each coating sample, the averaged data and corresponding standard deviation were obtained from at least five measurements at different positions.

Morphology and other properties characterization

Optical microscopy images were acquired on Nikon LV ND microscope. Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) analysis were conducted on Phenom Pro X. The morphological and elemental analysis of TiO2 NPs were performed by transmission electron microscopy (TEM) using FEI Talos F200S Super-X. Thermogravimetric analysis (TGA) of the coating samples was conducted on Q50 TGA (TA Instrument) with a heating rate of 10 °C min−1 under a flow of nitrogen gas (50 mL min−1). The functional group analysis was conducted by fourier transform infrared spectroscopy (FTIR, Thermo Fisher Nicolet Is10). The powder X-ray diffraction pattern of TiO2 NPs was acquired using X-ray diffractometer (XRD, Bruker D8 Advance). The particle size distribution of TiO2 NPs was examined by dynamic light scattering (DLS), Laser particle sizer, Zetasizer Nano ZS-90. Ultra-small angle X-ray scattering (USAXS) experiments were performed on BL10U1 beamline at the Shanghai Synchrotron Radiation Facility. An Eiger-4M detector was used to collect the two-dimensional (2D) scattering data. The x-ray wavelength was 1.24 Å (corresponding energy of 10 keV). The beam size was 400 × 450 µm. All samples were coated on circular mica substrate (almost transparent to x-ray) with 0.1 mm thickness and 30 mm diameter. The distance between the coating and detector was 27,600 mm. The data collection time was 10 s for all the measurements. Fit2D (v12.077) software was used to reduce 2D raw data to one-dimensional (1D) curves. Infrared camera (R300, Mission Technology Co.) was employed to obtain infrared images.

Finite difference time-domain (FDTD) simulations

FDTD Solutions by Lumerical 2020 R2.4 was employed to investigate the effect of TiO2 NPs packing density and nanoparticle size effect on the coating’s solar reflectance. Mesh dimension is 20 × 20 × 20 nm. Due to limited computation power, close-packing model was applied, the film thickness was set as 2 µm and simulated spectrum is 0.25 to 2.5 µm of wavelength. Thickness of 10 and 20 µm were also studied and obtained similar variation trend. Diameter of 200 nm of TiO2 NPs was used to generate the date for Fig. 1c. The results are presented in Supplementary Fig. 5.

Field test for the coatings

All field tests were performed in Chengdu, China. To mimic real operating condition of AACP, we measured the coatings’ temperature variation and cooling power without the implementation of wind and radiation shield. All samples were coated on glass substrates with black tape backing, which could absorb transmitted light, if any. J-type thermocouple was attached on the back of glass and connected to Onset HOBO 4-channel thermocouple data logger UX120-014M. Solar irradiance (Isolar) data were recorded using SP-510 thermopile pyranometer from Apogee Instrument. The thermocouple monitoring ambient temperature was shield by a thermometer shelter to prevent direct solar heating. All samples and instruments were placed on a vacuum insulation panel backing with a styrofoam to limit non-radiative heat transfer. A weather station (DC5V model, YiGu Co.) was used to monitor ambient relative humidity and wind speed (Supplementary Fig. 15). The whole setup was displayed in Supplementary Fig. 17.

The cooling power of the AACP coating was determined by inputting heat power, letting the sample reach ambient temperature. Then, this heat power could be treated as equal to the cooling power of the sample without considering the non-radiative heat transfer. Detailed discussion was in the section of Estimation of radiative cooling power. We used both step-wise and close-tracking method to determine the cooling power respectively. By using step-wise method, we chose to increase heat power in a step-wise manner at noon time, letting the temperature of the sample incrementally reaching steady state within a 5 min time interval. Then we plotted the temperature difference between the sample and ambient as a function of heat power, as shown in Supplementary Fig. 13. The cooling power was then equal to the heat power when the temperature difference reached zero. The heat power was from a customized Kapton® flexible heater controlled by a Keithley 2400 SourceMeter. Proportional-integral-derivative (PID) control via LabVIEW was used to regulate the heat power in response to desired sample temperature value. A thermocouple was attached between the back of the coated glass and the heater to monitor the temperature variation giving feedback data for control accuracy. The sample temperature, heat power and corresponding standard deviation data were obtained over the last 3 min of each time interval after the initial transient peak in heat power. By using close-tracking method, the heater was controlled by the same PID control program to let the AACP surface temperature equal to the ambient temperature in a real-time close tracking manner from 11 AM to 4 PM. Then we can obtain the cooling power variation in a period of 5 h during daytime (Supplementary Fig. 14). All coatings for field tests were on 5 × 5 cm glass substrates.

Accelerated soiling evaluation based on ASTM D7897-18 standard

We simulated 3 years of natural soiling effect on the coatings according to ASTM D7897-18 standard, which was developed for evaluating soiling effect on the solar reflectance and thermal emittance of roofing materials. According this standard, we prepared the artificial soiling mixture composed of four soiling agents, i.e. soot, dust, particulate organic matter (POM) and salts, as shown in Supplementary Fig. 16. The formulas are as follows:

  1. (1)

    Soot: 0.26 ± 0.01 g of carbon black was mixed with 1 L of distilled water to have a suspension;

  2. (2)

    Dust: A mixture of 0.3 ± 0.02 g of Fe2O3, 1.0 ± 0.05 g of montmorillonite and 1.0 ± 0.05 g of bentonite was dispensed into 1 L of distilled water to obtain a suspension with a concentration of 2.3 ± 0.1 g/L;

  3. (3)

    POM: 1.4 ± 0.05 g of HAc was mixed with 1 L of distilled water to have a suspension;

  4. (4)

    Salts: A mixture of 0.3 ± 0.03 g of NaCl, 0.3 ± 0.03 g of NaNO3 and 0.4 ± 0.03 g of CaSO4 ∙ 2H2O was dissolved into 1 L of distilled water to obtain a solution with a concentration of 1.0 ± 0.1 g/L.

Soiling procedure

The above four soiling agents were mixed to simulate natural soiling materials. The weight ratio of soot/dust/POM/salts was 5/47/28/20. This soiling mixture was poured into a spraying tank, equipped with an air pressure gauge. Then we sprayed the soiling mixture continuously and evenly onto the coatings from a distance of 30 cm above. The sprayed wet soiling agents were controlled as 8 ± 1 mg cm−2. The soiled coating was then dried under an infrared heat lamp. Weathering steps before and after soiling procedure were performed to simulate ultraviolet (UV) irradiation and natural aging effect of moisture and rain. This weathering step included 2 cycles of 8 h of UV with 0.89 W m−2 at 340 nm and 60 °C, 4 h of simulated rain at 50 °C.

Additional soiling tests

Mud soiling

Mud was formulated by mixing coal ash and water. Coal ash weight ratios of 50% and 80% were produced to simulate low and high viscous mud. We dripped the mud (1 g cm−2 for each time) on the coatings to investigate the soiling effect. The soiling process was repeated ten times. The cleaning effect was shown in Supplementary Fig. 21, Supplementary Table 1 and Supplementary Movie 1.

MnO2 soiling

MnO2 particles with diameters ranging from hundreds of nanometers to tens of microns were used to simulate dust contaminations. About 10 mg cm−2 of MnO2 particles was uniformly spread on the coatings. Water drops and wind-blowing were performed to study cleaning effect respectively. The soiling-cleaning cycle was repeated 10 times. The cleaning effect is presented in Supplementary Fig. 2, Supplementary Table 1 and Supplementary Movie 2.

Sand soiling

10 mg cm−2 of sand was uniformly spread on the coatings. Water condensation was implemented on the coatings to study the cleaning effect. The coating sample was placed on a cold stage of about 5 °C tilted at 45°. The ambient temperature was about 25 °C and the relative humidity was controlled as 99%. The cleaning effect was shown in Supplementary Fig. 22.

Accelerated UV irradiation weathering test

We placed the coatings into an UV weathering chamber (HT-UV3, Haotian Testing Equipment Co.). 1000 h (~42 days) of UV irradiance with 0.89 W m−2 at 340 nm and 60 °C were used for accelerated weathering experiments. This UV dosage is equivalent to 1 year of Florida sunshine exposure (annual UV dosage of about 275 MJ m−2). Florida sunshine exposure is an international benchmark for durability tests of materials.

Additional stability tests

Thermal stability

The AACP coating with adhesives was placed on a heating stage at about 100 °C for 1000 h. The optical and wetting properties after heating were shown in Supplementary Fig. 24.

High-speed water jet test

The average jet velocity, v, can be calculated as (v=frac{4V}{pi {d}^{2}triangle t}), where V is the volume of water ejected during the time duration of Δt and d is the needle diameter. 10 mL of water was jetted out of a 2 mm diameter needle within 400 ms, with an average speed of 8 m s−1. This speed is equivalent to the speed of raindrops in the rainstorm (v ≈ 9 m s−1). Water jet with higher speed out of a faucet (d = 5 mm, v ≈ 10 m s−1) was also used to test the integrity of the AACP coating, as shown in Supplementary Movie 3.

Tape-peel test

3 M VHB 5925 tape was applied to test the adhesion force between the coating and substrate. A 1 kg roller was rolled on the tape twice to make the tape hold fast on the coating surface. Then, the tape was peeled from it. The test process and coating properties after tape-peel were shown in Supplementary Fig. 28.

Sand falling abrasion test

Sands with diameter of 50 to 300 µm were used to fall on a 24 × 60 mm coating surface from a height of 30 cm. For each time of sand falling, a total sand mass of 20 g was used. The abrasion test was repeated 100 times. The test process and coating properties after sand falling test were shown in Supplementary Fig. 29.

Scratch test

Scratch resistance test was performed according to ASTM standard D7027-20 (Test mode A). Specifically, a scratch was applied onto the AACP coating surface under a normal load of 2 N, 20 N and 50 N respectively, over a distance of 0.1 m (±0.0001 m) at a constant scratch rate of 0.1 m s−1 (±0.0005 m s−1). The coating properties after scratch test are shown in Supplementary Fig. 30 and Supplementary Table 4.

Photocatalysis effect of AACP coating

The coating sample was on glass substrates (22 × 60 mm) with a thickness of about 100 μm. The concentrations of the feeding stream of formaldehyde and toluene were both controlled as 30 ppm in nitrogen gas flow. The gas humidity was controlled at 50%, and the total flow rate was set as 25 mL/min. A UV lamp (300 W) was vertically placed above the reactor (0.357 L). The incident light wavelength was controlled at 365 nm and the light intensity 0.29 W cm−2. The lamp was turned on after reaching the adsorption-desorption equilibrium. The concentrations of formaldehyde, toluene, water and CO2 were continuously recorded by a multi-gas analyzer (DKG-42A, Duke Technology). The pollutant conversion efficiency was calculated as η (%) = (C0 − C)/C0 × 100%, where C0 and C representing the concentration of formaldehyde or toluene in the feeding stream and the real-time concentration in the outlet stream, respectively42. The results are shown in Supplementary Fig. 31.

Outdoor long-term durability test at real-world condition

Two locations in China were selected to demonstrate AACP’s outdoor long-term durability performance. One was Chengdu (30°40’36”N, 104°6’28”E) in humid and hot climate, dating from April 25th to November 10th, 2021. The other one was Xi’an (34°17’57”N, 108°58’21”E) in dry and hot climate, from May 1st to November 30th, 2021. The coating samples (5 × 15 cm) were fixed on a display board (80 × 120 cm) tilted at 30° facing the sky. All coating slides were split into three regions: unexposed/(exposed, washed)/(exposed, unwashed). We used aluminum foil to wrap one third of the slide as “unexposed” region. The “wash” was done by tap water rinsing. When the outdoor exposure was finalized, the samples were retrieved to test the optical and wetting properties. The results of aging of the samples in Xi’an were presented in Supplementary Fig. 25.

Definitions of solar reflectance and thermal emittance

The solar reflectance (solar) is defined as the ratio of the reflected solar power in the λ of 0.3–2.5 µm to the integral of solar intensity within the same wavelength range43:

$${bar{R}}_{{{{{{rm{solar}}}}}}}=frac{{int }_{0.3,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}^{2.5,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}{I}_{{{{{{rm{solar}}}}}}}left(lambda right)Rleft(lambda right){{{{{rm{d}}}}}}lambda }{{int }_{0.3,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}^{2.5,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}{I}_{{{{{{rm{solar}}}}}}}left(lambda right){{{{{rm{d}}}}}}lambda },$$

(1)

where Isolar(λ) is the ASTM G173-03 AM 1.5 Global Tilt spectrum, R(λ) is the measured spectral reflectance of the sample.

In a similar way, the thermal emittance (({bar{varepsilon }}_{{{{{{rm{LWIR}}}}}}})) is defined as the ratio of the sample’s thermal radiation energy in the primary long-wave infrared (LWIR) atmospheric transparency window (λ of 8–13 µm) to the integral of spectral intensity emitted by a standard blackbody within the same wavelength range:

$${bar{varepsilon }}_{{{{{{rm{LWIR}}}}}}}=frac{{int }_{8,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}^{13,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}{I}_{{{{{{rm{bb}}}}}}}left(T,,lambda right)varepsilon left(T,,lambda right){{{{{rm{d}}}}}}lambda }{{int }_{8,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}^{13,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}{I}_{{{{{{rm{bb}}}}}}}left(T,,lambda right){{{{{rm{d}}}}}}lambda },$$

(2)

where (varepsilon left(T,lambda right)) is the sample’s measured spectral emittance and Ibb(T, λ) is the blackbody radiation intensity at a temperature of T calculated by Planck’s law:

$${I}_{{{{{{rm{bb}}}}}}}left(T,lambda right)=frac{2{c}^{2}{{hbar }}}{{lambda }^{5}}frac{1}{{e}^{frac{{{hbar }}c}{lambda {k}_{{{{{{rm{B}}}}}}}T}}-1},$$

(3)

where (hslash) is the Planck constant, c is the speed of light in a vacuum, kB is the Boltzmann constant. In the present work, the temperature T is set as 298 K.

Estimation of radiative cooling power

To evaluate the cooling performance of the radiative cooling materials, the subambient temperature drop is a parameter to feel the cooling ability intuitively. However, since the test conditions, like location, wind speed and humidity, etc. could vary case by case, one can hardly obtain the same temperature reduction even for the same material from different tests44. Therefore, it is more appropriate to use cooling power for objectively comparing the cooling ability of various materials.

To estimate the cooling power of a radiative cooling surface, we start from the steady state heat transfer balance analysis45. For a radiative cooling surface with temperature (T) and ambient temperature Ta, the net cooling power Pnet(T, Ta) is calculated as

$${P}_{{{{{{rm{net}}}}}}}left(T,{T}_{{{{{{rm{a}}}}}}}right)={P}_{{{{{{rm{rad}}}}}}}left(Tright)-{P}_{{{{{{rm{atm}}}}}}}left({T}_{{{{{{rm{a}}}}}}}right)-(1-{bar{R}}_{{{{{{rm{solar}}}}}}}){P}_{{{{{{rm{sun}}}}}}}-{P}_{{{{{{rm{nrad}}}}}}}left(T,{T}_{{{{{{rm{a}}}}}}}right),$$

(4)

where Prad(T) is emitted power from the surface, Patm(T) is absorbed power from atmospheric radiation, Psun is energy power from the sun and Pnrad(T, Ta) is the non-radiative heat transfer power stemming from the surrounding environmental conductive and/or convective heat exchange. For a radiative cooling surface with a unit area of 1 m2, Pnrad(T, Ta) can be further expressed as hc(Ta – T) by bringing in a non-radiative heat transfer coefficient hc (unit of W m−2 K−1). Like we mentioned before, real environmental conditions could strongly influence the hc making it vary from 2 to 20 W m−2 K−1 44. Hence, to rule out this uncontrolled factor, we can set ΔT = Ta – T= 0, thus eliminating the Pnrad(T, Ta) term. In practice, we utilized a heater to compensate the heat loss of the cooling device to make its temperature equal to the ambient one. Then, the net cooling power Pnet(T, Ta) becomes Pnet(Ta, Ta) and can be further defined as Pcool(Ta), which equals to the heat power.

Now let us consider an ideal scenario, i.e. the radiative cooling material has 100% reflectance in the solar spectrum (λ of 0.3–2.5 µm) and 100% emittance in the primary atmospheric transparency window (λ of 8–13 µm). Then, (1 − solar)Psun = 0.

$${P}_{{{{{{rm{rad}}}}}}}left({T}_{{{{{{rm{a}}}}}}}right)=2pi {int }_{0}^{frac{pi }{2}}{{{{{rm{cos }}}}}}theta {{{{{rm{sin }}}}}}theta {int }_{0}^{{{infty }}}{I}_{{{{{{rm{bb}}}}}}}left({T}_{{{{{{rm{a}}}}}}},,lambda right)varepsilon left(lambda,,theta right){{{{{rm{d}}}}}}lambda {{{{{rm{d}}}}}}theta,$$

(5)

$${P}_{{{{{{rm{atm}}}}}}}left({T}_{{{{{{rm{a}}}}}}}right)=2pi {int }_{0}^{frac{pi }{2}}{{{{{rm{cos }}}}}}theta ,{{{{{rm{sin }}}}}}theta {int }_{0}^{{{infty }}}{I}_{{{{{{rm{bb}}}}}}}left({T}_{{{{{{rm{a}}}}}}},,lambda right)varepsilon left(lambda,,theta right){varepsilon }_{{{{{{rm{a}}}}}}}left(lambda,,theta right){{{{{rm{d}}}}}}lambda {{{{{rm{d}}}}}}theta,$$

(6)

and

$${varepsilon }_{{{{{{rm{a}}}}}}}left(lambda,theta right)=1-{{t}_{{{{{{rm{a}}}}}}}left(lambda,0right)}^{1/{{{{{rm{cos }}}}}}theta },$$

(7)

where (varepsilon (lambda,theta )) and ({varepsilon }_{{{{{{rm{a}}}}}}}left(lambda,theta right)) are spectral and angular emissivity of the radiative cooling surface and ambient air, ta(λ, 0) is the atmospheric transmittance at the zero zenith angle. In our estimation, the data of ta(λ, 0) is from ATRAN modeling software. The cooling power mainly relies on the surface spectral emittance through the primary atmospheric transparency window with λ of 8 to 13 µm. Then we obtain Pcool(Ta) as

$${P}_{{{{{{rm{cool}}}}}}}left({T}_{{{{{{rm{a}}}}}}}right)=2pi {int }_{0}^{frac{pi }{2}}{{{{{rm{cos }}}}}}theta {{{{{rm{sin }}}}}}theta {int }_{8,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}^{13,{{{{{rm{mu }}}}}}{{{{{rm{m}}}}}}}{I}_{{{{{{rm{bb}}}}}}}left({T}_{{{{{{rm{a}}}}}}},,lambda right)varepsilon left(lambda,,theta right){{t}_{{{{{{rm{a}}}}}}}left(lambda,,0right)}^{1/{{{{{rm{cos }}}}}}theta }{{{{{rm{d}}}}}}lambda {{{{{rm{d}}}}}}theta .$$

(8)

As a result, Pcool as a function of ambient temperature Ta can be plotted as shown in Fig. 1a of the main text. It is worth noting that we set solar = 1 to eliminate the absorbed solar power in the above discussion. We can study the impact of imperfect solar simply by reintroducing non-zero term of (1 − solar)Psun to have the net cooling energy Pnet(Ta):

$${P}_{{{{{{rm{net}}}}}}}left({T}_{{{{{{rm{a}}}}}}}right)={P}_{{{{{{rm{cool}}}}}}}left({T}_{{{{{{rm{a}}}}}}}right)-(1-{bar{R}}_{{{{{{rm{solar}}}}}}}){P}_{{{{{{rm{sun}}}}}}}.$$

(9)

Energy saving analysis on a medium size building level

We estimate the saved electricity on a three-storey commercial office building with a 1600 m2 roof for AACP and reflective white paint for a 3-year period. The simulation procedure is similar to the previous work.5 EnergyPlus (version 22.1.0) was utilized to determine the electricity usage with a standard heating, ventilation and air conditioning (HVAC) system based on hourly weather data of Singapore city (hot climate) acquired from the International Weather for Energy Calculation (IWEC) files. The interior temperature of the building was set as 24 °C at all time and HVAC system operating continuously. The cooling power of AACP was calculated according to Eq. (9) with input of ambient temperature, solar irradiance and cloud coverage data, then subtracted from the heat load for the building. Coefficient of performance (COP) of 2.8 was used to calculate the remaining heat dissipated in the building. The reflectance and emittance of the roof of the default reference building were fixed at 0.3 and 0.9. For white painted roof, the emittance was fixed at 0.9. The reflectance was set with a declining trend as 0.87, 0.82, and 0.78 for each year in a period of 3 years. For AACP, the reflectance was set as 0.93, 0.928, and 0.926 for each year, and emittance was fixed at 0.97. The simulation results are presented in Supplementary Fig. 36. Due to environmental aging, the electricity saving for white paint decreases each year from 12.2 to 8.4 kWh m−2, while AACP renders robust energy saving performance above 50 kWh m−2. In Supplementary Table 5, we compared the cost between AACP and two other common white paint based on one square meter. We find that the cost of AACP is comparable to the prices of the commercial products (~$5 m−2 vs. $4 m−2). In this case, the electricity saving difference from AACP than white paint is ~40 kWh m−2 for 1 year. We assume the grid electricity cost is $0.1 kWh−1, then the cost difference between AACP and white paint can be compensated in the first year or maybe in even shorter period, which shows the great potential for AACP to be a cost effective solution as cool roof to mitigate energy demand for heavy cooling load.

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