Passive radiative cooling, radiating energy from objects to the outer space through the Earth's atmospheric window, offers promising solutions for passive building cooling and renewable energy harvesting. However, static passive radiative cooling systems with a fixed thermal emissivity cannot automatically regulate emission in response to varying ambient temperature. Here, we propose an intelligent cooling system composed of nanoporous polyethylene, which acts as a solar reflector and a nanograting radiative cooler using the phase-transition material vanadium dioxide (VO2) and polydimethylsiloxane (PDMS). The top reflector enables the cooling system to reflect solar irradiation during the daytime, and the bottom cooler plays the role of switching radiative cooling in the spectrum band (8 μm < λ < 13 μm) due to the phase transition characteristic of VO2, contributing to the temperature of radiative cooler near a critical temperature. Meanwhile, continuous stretching of the material can achieve dynamic radiative cooling via deformation of the elastic PDMS substrate to realize different desired cooling temperatures. The proposed VO2-PDMS-driven radiative cooling system can not only intelligently switch between “on” and “off” radiative cooling modes but also adjust thermal comfort in its on mode in response to changes in the ambient temperature. This work has a great potential to be applied in the intelligent temperature regulation of buildings, vehicles, and utilities.

Passive radiative cooling,1–6 a process of radiating energy from objects through the atmospheric window (wavelengths 8 μm < λ < 13 μm) to the cold outer space (∼3 K),7 is a promising technology for reducing the energy consumption utilized in recent years. To achieve efficient radiative cooling, organic and inorganic materials with near-zero solar absorptivity (wavelengths 0.3 μm < λ < 2.5 μm) and high infrared emissivity within the atmospheric window simultaneously have been extensively studied.8 Consequently, micro/nanophotonic structures,1,9,10 polymer fibers,11–13 dielectric particles mixtures,4,14 infrared aerogels,15 wood-based materials,16 and a variety of other materials17–20 have been demonstrated as efficient radiative cooling throughout the day without consuming any energy.

Although static radiative cooling systems can effectively reduce energy consumption for cooling in summer, they will also result in overcooling in winter due to the fixed thermal emissivity of systems, potentially leading to higher heating costs. To adapt to the change in ambient temperature, switchable radiative cooling based on the phase-transition material vanadium dioxide (VO2) has been studied recently.21–26 When the ambient temperature is above the critical temperature of VO2, the cooling system automatically turns on radiative cooling. Below the phase transition temperature of VO2, it turns off radiative cooling. Moreover, the phase transition temperature of VO2 can be adjusted by doping tungsten (W) and strontium (Sr) into pure VO2,27 which promotes the application of VO2 in switchable radiative cooling. Ono et al. combined a photonic multilayer system made of VO2/magnesium fluoride (MgF2)/W and a spectrally selective filter, an 11-layer stack structure consisting of germanium (Ge)/MgF2, to achieve self-adaptive radiative cooling.22 Kim et al. designed a switchable radiative cooler consisting of an emitter (VO2/silicon/silver) and a solar reflector (three stacked photonic crystals) separated by a spacer.24 Relevant works of VO2-based radiative cooling were also conducted by Zhang et al.23 and Kort-Kamp.21 There are still limitations to large-scale fabrications and applications, especially when considering the relative complexity of the aforementioned structures. In addition, these VO2-based radiative cooling systems only perform binary switchable radiative cooling, turning “on/off” radiative cooling, and cannot achieve a continuous variation of the emission spectra in the atmospheric window to further modulate the cooling temperatures during the period when the radiative cooling system is in the on mode.

In this work, we propose a VO2-PDMS-driven intelligent radiative cooling system with both automatic switching and continuous adjustment functions. The cooling system is composed of a nanoporous polyethylene (NPE)13 acting as a solar reflector and a bottom nanograting emitter made of VO2 and polydimethylsiloxane (PDMS).17,28,29 The calculation results show that our system can perform switchable radiative cooling, corresponding to the ambient temperature, without external energy consumption. Meanwhile, it can achieve dynamic radiative cooling through continuous deformation of the elastic PDMS substrate, thereby obtaining different desired cooling temperatures. Furthermore, the NPE is used as a top solar reflector, rather than multilayer reflectors22–24 such as the distributed Bragg reflector (DBR),24 rendering this system more feasible and practical for large-scale fabrication. Therefore, the combination of the phase-transition material VO2, elastic material PDMS, and NPE can pave the way for applications of radiative cooling within energy-efficient buildings and vehicles and energy-intelligent management systems.

VO2 is a solid–solid phase-transition material that exists in a metallic state when the temperature is above the phase transition temperature Tc and an insulating state at T < Tc. The real and imaginary parts for the permittivity of metallic and insulating VO2 in the wavelength range (0.3 μm < λ < 15 μm) are shown in Fig. 1.22 In order to obtain calculation results (temperature change and cooling power) in accordance with actual observed trends, the permittivity of VO2 is assumed to be gradient within a narrow transition range (Tc − ΔT, Tc + ΔT). The permittivity change function is set as follows:24 

εtransition=arctan(TTcΔT×10)×εmεi2arctan10+εm+εi2,
(1)

where εm and εi are the metallic and insulating permittivities, respectively. Typically, Tc of pure VO2 is around 341 K.30–32 However, its Tc can be adjusted by doping molybdenum (Mo), tungsten (W), and/or strontium (Sr) into pure VO2.33–36 Throughout this work, for the purpose of switching on and off radiative cooling, the phase-transition temperature of doped VO2 is set to Tc = 293 K (room temperature) and ΔT = 2 °C. To avoid duplication, the details of derivations can be found within the literature.24 

FIG. 1.

The (a) real part Re(ε) and (b) the imaginary part Im(ε) of the permittivity for VO2 in the wavelength range (0.3 μm < λ < 15 μm).

FIG. 1.

The (a) real part Re(ε) and (b) the imaginary part Im(ε) of the permittivity for VO2 in the wavelength range (0.3 μm < λ < 15 μm).

Close modal

Here, we propose a composite structure design consisting of a top solar reflector made of NPE13 and a bottom dynamic radiative cooler depicted schematically in Fig. 2(a). The radiative cooler is composed of stacked nanogratings of VO2 (thickness h1), potassium bromide (KBr, thickness h2), and silver (Ag, thickness h3) from top to bottom on a polydimethylsiloxane (PDMS) substrate with a thickness of 1000 nm. The stacked nanograting period and ridge width are denoted as Λ and w, respectively. The grating filling ratio is ϕ = w/Λ. The physical mechanism behind the optical response of our proposed structure relies on a Fabry–Pérot cavity specifically for resonances at mid-infrared wavelengths.21,22 After the optimization of structure variables h1, h2, h3, Λ, and w, the optimal configuration with h1 = 10 nm, h2 = 2000 nm, h3 = 200 nm, Λ = 30 nm, w = 24 nm, and then ϕ = w/Λ = 0.8 is obtained. As for the top solar reflector, NPE is placed on the radiative cooler with a gap D much larger than the thermal wavelength. The thickness (hNPE) and average pore size (R¯pore) of NPE are 12 μm and 400 nm, respectively. The spectral transmittance of infrared and visible light for NPE can be referred to the literature.13 To simplify the calculation, its spectral reflectivity is assumed to be ρλ=1τλ. More significantly in this work, the radiative cooling of the system can be dynamically modulated by mechanical strain based on the elastomeric PDMS substrate. When the PDMS substrate is stretched or compressed with a mechanical deformation of Δx, the nanograting period Λ will increase or decrease, respectively, while the nanograting width w remains unchanged. For example, in the case of positive deformation as shown in Fig. 2(b), the period Λ elongates to Λ + Δx, and the thickness of PDMS substrate h4 decreases to be h4 − Δh, where Δh is obtained based on the Poisson's ratio of PDMS (0.5). Meanwhile, the upper nanograting remains undeformed as the PDMS layer is stretched to its strain limit (strain ϵ = 128%),37 as Ag has a much larger Young's modulus than PDMS.

FIG. 2.

(a) Schematic of the dynamic radiative cooling system. The bottom radiative cooler consists of stacked nanogratings (VO2, KBr, and Ag) and the PDMS thin film. The top solar reflector is made of NPE. (b) Schematic of the reconfigurable radiative cooler under mechanical stretching (grating period Λ + Δx, width w, and PDMS thickness h4 − Δh).

FIG. 2.

(a) Schematic of the dynamic radiative cooling system. The bottom radiative cooler consists of stacked nanogratings (VO2, KBr, and Ag) and the PDMS thin film. The top solar reflector is made of NPE. (b) Schematic of the reconfigurable radiative cooler under mechanical stretching (grating period Λ + Δx, width w, and PDMS thickness h4 − Δh).

Close modal

The absorptivity (or emissivity) of the bottom radiative cooler with a grating filling ratio of 0.8 in the spectral region (0.3 μm < λ < 15 μm) is shown in Fig. 3(a). Here, the second order approximation of effective medium theory is used to obtain the effective dielectric properties of the bottom radiative cooler given by the following expressions:38–44 

εTE,2=εTE,0[1+π23(Λλ)2ϕ2(1ϕ)2(εAεB)2εTE,0],
(2a)
εTM,2=εTM,0[1+π23(Λλ)2ϕ2(1ϕ)2(εAεB)2εTE,0(εTM,0εAεB)2],
(2b)

where εA and εB are dielectric functions of the two media (optical material and vacuum) in surface gratings.38–44 It can be observed that when VO2 is at its metallic state, there is an extremely high emissivity near the atmospheric window (8 μm < λ < 13 μm) due to the existence of the cavity. In contrast, when VO2 is at insulating state, the bottom radiative cooler exhibits a very suppressed emissivity in the same spectral region. These properties allow the bottom radiative cooler to achieve the necessary switching of its radiative properties in the atmospheric window. In the solar wavelength range (0.3 μm < λ < 2.5 μm), the bottom radiative cooler exhibits highly absorptive properties when VO2 is in both metallic and insulating states due to the existence of the Fabry–Pérot resonance and the lossy characteristics of VO2 at both states, which is not desirable for passive radiative cooling.22 To eliminate this disadvantage, the NPE,13 rather than multilayer photonic crystal,22–24 is placed on top of the bottom radiative cooler with a certain gap (Dλ). Figure 3(b) shows the spectral transmissivity of the NPE in the visible and infrared wavelength range. On the one hand, the top NPE can block most solar irradiation from reaching the bottom radiative cooler. On the other hand, the NPE has highly selective transmission for the infrared radiation of bottom cooler. Here, based on the multiple reflection processes between the top NPE and the bottom radiative cooler, we utilize incoherent calculations to obtain the absorptivity for the bottom radiative cooler as follows:45 

ε(λ,Ω)=(1rC)(tN+tNrCrN+tN(rCrN)2+tN(rCrN)3+)=tN(1rC)/(1rCrN),
(3)

where tN, rN, and rC are the transmissivity of the NPE, the reflectivity of the NPE, and the reflectivity of the bottom radiative cooler, respectively. The details of the above-mentioned derivations can be found in the literature.45 The absorptivity of the composite radiative cooling system in the spectral region (0.3 μm < λ < 15 μm) after adding the NPE atop the bottom radiative cooler is shown in Fig. 3(b). It can be observed that the NPE can significantly suppress the absorption within the solar wavelength range when VO2 is in both metallic and insulating phases. Furthermore, the emissivity from 8 to 13 μm still remains favorable for the two phases of VO2, allowing the system to achieve the necessary spectral properties of an efficient VO2-based dynamic radiative cooling system.

FIG. 3.

Absorptivity of the dynamic radiative cooling system when VO2 in metallic and insulating phases without the top NPE. (b) Spectral transmissivity of NPE and absorptivity of the combined radiative cooling system in the visible and infrared wavelength range, respectively. (c) and (d) Absorptivity of the combined radiative cooling system at different stretching states (ϵ = 0%, ϵ = 60%, and ϵ = 128%) when VO2 is in metallic and insulating states, respectively.

FIG. 3.

Absorptivity of the dynamic radiative cooling system when VO2 in metallic and insulating phases without the top NPE. (b) Spectral transmissivity of NPE and absorptivity of the combined radiative cooling system in the visible and infrared wavelength range, respectively. (c) and (d) Absorptivity of the combined radiative cooling system at different stretching states (ϵ = 0%, ϵ = 60%, and ϵ = 128%) when VO2 is in metallic and insulating states, respectively.

Close modal

To illustrate the radiative modulation in response to the deformation of the radiative cooler shown as Fig. 2(b), the emissivity spectra of the structures under different strain states are calculated and shown in Figs. 3(b) and 3(c). The stretching strain is defined as the change in the period of nanograting (Δx/Λ), with the initial filling ratio having a value of 0.8. As such, the states of grating with ϕ = 0.8, 0.5, and 0.35 are achieved via zero strain (ϵ = 0%), intermediate strain (ϵ = 60%), and extreme strain (ϵ = 128%), respectively. Increases in strain result in a reduction in the filling ratio of the bottom radiative cooler. As seen in Fig. 3(c), with a decrease in the filling ratio ϕ, the spectral emissivity over the atmospheric window region will be further suppressed when VO2 is at the metallic state because the filling ratio directly affects the dielectric characteristics of the stacked nanograting structure, thus influencing the surface waves across the interfaces. For the insulating state of VO2, the mechanical stretching has little effect on the radiative cooling system, resulting in a nearly unchanged emissivity in the atmospheric window as shown in Fig. 3(d). Figure 4 shows the emissivity of our cooling system with zero strain (ϵ = 0%) against variation of the incident angle when VO2 in the metallic and insulating states. In the metallic state, the polarization-averaged emissivity remains high near the atmospheric window (8 μm < λ < 13 μm) when the incident angle increases up to around 60°, as shown in Fig. 4(a). The angle- and polarization-averaged emissivity from 0° to 90° in the wavelength range from 8 to 13 μm is 0.75 in the metallic state. On the contrary, in the insulating state, the polarization-averaged emissivity is totally suppressed across the entire spectrum, as shown in Fig. 4(b).

FIG. 4.

The emissivity of the bottom radiative cooler with zero strain (ϵ = 0%) in the presence of the top NPE, as a function of incident angle and wavelength when VO2 is in (a) metallic and (b) insulating states, respectively.

FIG. 4.

The emissivity of the bottom radiative cooler with zero strain (ϵ = 0%) in the presence of the top NPE, as a function of incident angle and wavelength when VO2 is in (a) metallic and (b) insulating states, respectively.

Close modal

The cooling performance of the radiative cooler is analyzed by solving the thermal balance equation:22,46

Qnet=Qcooler(Tcooler)Qnr(Tamb,Tcooler)Qamb(Tamb)Qsun(Tcooler),
(4)

where Qnet is the net cooling power of the radiative cooler, Qcooler is the radiation power from the bottom radiative cooler, Qnr is the non-radiative power, Qamb represents the incident thermal radiation from atmosphere, and Qsun is the incident solar power absorbed by the cooler. Tamb and Tcooler are the temperatures of ambient and bottom radiative cooler, respectively. Qcooler is given by

Qcooler(Tcooler)=A0dλIBB(Tcooler,λ)ε(λ,θ,ϕ,Tcooler),
(5)

where A is the area of the bottom radiative cooler and IBB(Tcooler,λ)=2hc2λ5exp(hc/λkBT1)1 defines the spectral radiance of a blackbody at temperature T. The non-radiative heat transfer between the bottom radiative cooler and ambient air is determined as follows:

Qnr(Tamb,Tcooler)=Ahnr(TambTcooler),
(6)

where hnr represents the non-radiative heat transfer coefficient.22 Here, hnr = 8 W m−2 K−1 is used throughout the calculations. Qamb(Tamb) is given by

Qamb(Tamb)=A0dλIBB(Tamb,λ)ε(λ,θ,ϕ,Tcooler)ε(λ,θ,ϕ),
(7)

where ε(λ,θ,ϕ) stands for the absorptivity of the atmosphere. Furthermore, Qsun(Tcooler) corresponds to the solar irradiation absorbed by the bottom radiative cooler, described by

Qsun(Tcooler)=Acosθsun0dλIAM1.5(λ)ε(λ,θsun,Tcooler).
(8)

Here, IAM1.5(λ) is the spectral irradiance intensity of solar irradiation at AM 1.5 and θsun denotes the direction of the incoming sunlight.47 The temperature-dependent emissivity of radiative cooler is given as ε(λ,θsun,Tcooler). The time-dependent temperature of the bottom radiative cooler can be obtained by solving the differential equations:

CcoolerdTdt=Qtotal(Tcooler,Tamb).
(9)

The bottom radiative cooler is placed on a Si substrate with a thickness of 500 μm, which can support the nanograting profile when the PDMS layer is under the back-forth deformation. Since the PDMS layer slides slowly under the mechanical deformation on the substrate, considered as a quasi-static process in this study, the heat capacitance of the radiative cooler (Ccooler) will consider both contribution of composite nanograting and the Si wafer, as described in the literature.22,48

The cooling performance of the radiative cooling system is evaluated by calculating the radiative cooler temperature in response to recorded 24-h outdoor weather data. In this calculation, we use the ambient temperature49 and solar illumination data50 on July 20, 2018 in Stanford, California. Figure 5 shows the temperature change of the original radiative cooler as shown in Fig. 2(a) over a 24-h period. From 12:00 a.m. to 8:30 a.m., the radiative cooler temperature is below the critical temperature 293 K (T < TC), and the radiative cooler turns off radiative cooling and keeps its temperature near ambient temperature. As the cooler temperature rises over 293 K with the ambient temperature, the radiative cooler turns on radiative cooling due to the appearance of the phase transition of VO2. It can be clearly seen that the radiative cooler temperature is significantly lower than the ambient temperature, and the difference between cooler and ambient temperatures reaches a peak of about 9.2 K around 5:09 p.m. At 10:08 p.m., when the ambient temperature falls below 293 K, the radiative cooler stops radiative cooling once again. The temperature change of the radiative cooler over this 24-h period clearly exhibits the switchable radiative cooling according to the ambient temperature. Moreover, the temperature change of a static radiative cooling system, keeping the same state as the cooling-open state of the radiative cooler, is shown in blue dashed curve in Fig. 5. The static radiative cooling system always turns on radiative cooling for the whole day and does not change in response to the ambient temperature, which may cause the system to overcool in a cold environment. In contrast, the dynamic radiative cooling system presents a small temperature fluctuation, resilient to the surrounding environment.

FIG. 5.

Thermal performance of the dynamic radiative cooling system (black curve) and the static radiative cooling system (blue dashed curve) over a 24-h cycle with ambient temperature variation (red curve).

FIG. 5.

Thermal performance of the dynamic radiative cooling system (black curve) and the static radiative cooling system (blue dashed curve) over a 24-h cycle with ambient temperature variation (red curve).

Close modal

In addition to the automatic switching function, the dynamical modulation of radiative cooling can be achieved based on the mechanical stretching of elastomeric PDMS substrate, according to our subjective requirement for the cooling temperature. Figures 3(c) and 3(d) have demonstrated the spectral absorptivity of the radiative cooling system with different stretching states (ϵ = 0%, ϵ = 60%, and ϵ = 128%) for VO2 at metallic and insulating states, respectively. Furthermore, Figs. 6(a) and 6(b) compare the simulated radiative cooler temperature and radiative cooling power across a 24-h period for the radiative cooler under different stretching strains, respectively. As seen in Fig. 6(a), similarly, when the radiative cooling system is in the off mode during cooler hours, the radiative cooler under any strains maintains a temperature near the ambient temperature. In contrast, in the on mode, its maximum temperature drops with a decrease in the strain state of the radiative cooler. When the PDMS layer is stretched to an extreme strain (ϵ = 128%, ϕ = 0.35), the difference between cooler and ambient temperatures will be as low as 8.1 K less than that of the original-state cooler. Meanwhile, we also observe a distinctly different cooling power under different stretching strains during this period as shown in Fig. 6(b). Moreover, the stretching strain does not affect the thermal performance of radiative cooler when it is in off state. Therefore, the mechanical stretching can actively and effectively modulate the temperature change of the dynamic radiative cooler when the system is conducting radiative cooling, without affecting the switchable function of radiative cooler.

FIG. 6.

(a) Thermal performance and (b) radiative cooling power of the dynamic radiative cooling system with different stretching strains over a 24-h cycle with ambient temperature variation.

FIG. 6.

(a) Thermal performance and (b) radiative cooling power of the dynamic radiative cooling system with different stretching strains over a 24-h cycle with ambient temperature variation.

Close modal

In summary, we present an intelligent radiative cooling system driven by the phase-transition material VO2, elastic material PDMS, and infrared-transparent NPE. This system can automatically turn on/off radiative cooling based on the phase transition of VO2, depending on the ambient temperature. Meanwhile, the PDMS substrate can be stretched to modulate the radiative cooling power, according to our subjective requirement for the cooling temperature. This work also verifies that the dynamic temperature regulation of radiative cooling induced by mechanical deformation of photonic metamaterials is feasible and effective, which have great potential in the application of radiative cooling. Moreover, the introduction of NPE as the top solar reflector renders the radiative cooling system more feasible and practical. Compared with existing switchable radiative cooling with a fixed critical temperature, our proposed intelligent radiative cooling system can not only automatically switch the cooling system but also adjust thermal comfort in its on mode. This work will advance the intelligent regulation of passive radiative cooling, such green buildings, textiles, and automobiles.

This work was supported by the National Science Foundation (No. CBET-1941743).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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