Self-adaptive radiative cooling based on phase change materials

Masashi Ono; Kaifeng Chen; Wei Li; Shanhui Fan

doi:10.1364/OE.26.00A777

1. Introduction

The universe, at a temperature of 3 K, represents the ultimate heat sink both in terms of its temperature and its capacity. Moreover, the earth atmosphere is highly transparent in the wavelength range of 8 – 13 μm. This transparency window coincides with the peak of blackbody radiation spectrum at typical ambient temperature near 300 K. Thus, any objects on earth, given sky access, can radiate heat out to the universe and thus lower its temperature. Such a process is known as radiative cooling.

Nighttime cooling effect has been known for centuries [1–3]. Recently, there has been a significant effort in pursuing daytime radiative cooling, by constructing systems that reflect the entire solar spectrum, while generate strong thermal radiation in the wavelength range of 8 – 13 μm [4]. Raman et al have demonstrated a photonic radiative cooler made of a multi-layer photonic structure, with an equilibrium temperature that is 5 °C below the ambient air temperature, in spite of having about 900 W/m² of sunlight directly impinging upon it [5]. Subsequently, daytime radiative cooling have been considered in various material systems and structures [6–12] and has motivated further studies of radiative cooling in other scenarios [13–18]. At a hot temperature above thermal comfort, for example daytime in summer, radiative cooling technology can be used to efficiently dissipate heat of buildings, vehicles and human body, therefore significantly reduce the energy consumption and improve thermal comfort.

Despite the successes, so far, all the existing radiative cooling systems are static in the sense that the thermal emissivity of the systems is fixed once they are constructed. However, as temperature varies across days and seasons, when the environment temperature is below a critical temperature such that cooling is no longer desired, for example during nighttime in winter, radiative cooling may no longer be desirable and may even increase the energy consumption if heating is required. Therefore, for many applications, it would be highly desirable to develop a self-adaptive radiative cooling system, that can enable cooling when the environment temperature is above the critical temperature, and disable cooling when it’s below.

In this paper, we propose a self-adaptive radiative cooling system. Such a system can automatically turn on and off radiative cooling, depending on temperature, without any extra energy input for switching. Our approach is based on a planar photonic multilayer system incorporating phase change materials such as vanadium dioxide (VO₂) and a spectrally-selective filter. We numerically show that such a system can perform radiative cooling, when the system is above the transition temperature of VO₂, and automatically turn off radiative cooling when the temperature is below the transition temperature. Our results here explore new functionalities of radiative cooling applications and could be potentially used in a wide range of applications such as vehicles, buildings, textiles and smart thermal regulations.

2. Self-adaptive Radiative Cooling

We start by presenting the general concept of self-adaptive radiative cooling and design considerations. The idea is to design a system that is able to switch on and off radiative cooling, depending on the temperature of the environment. We aim to design a system that provides radiative cooling when the environment is hot, and turns off radiative cooling when the temperature is below a critical temperature [Fig. 1(a)].

Fig. 1 (a) Schematic showing the concept of self-adaptive radiative cooling: when temperature is above the critical temperature T_c, radiative cooling is turned on; when temperature is below the critical temperature T_c, radiative cooling is turned off. (b) Schematic of the ideal spectrum for self-adaptive radiative cooling. The spectrum switches between an ‘on’ and an ‘off’ state depending on the ambient temperature.

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In order to achieve such functionalities, distinct spectral features for ‘on’ and ‘off’ states are required. When the system is in the ‘on’ state, the system needs to fulfil the requirement of daytime radiative cooling, as outlined in [4]. The system needs to maximize emissivity in the atmosphere transparency window in the wavelength range of 8 – 13 μm to efficiently emit heat to the outer space [Fig. 1(b)], while minimize absorption from both the sun light and the thermal radiation from the atmosphere by suppressing the emissivity for the rest of the wavelength range. On the other hand, when the system temperature is below a critical temperature, the system needs to be in the ‘off’ state, where it should exhibit minimum thermal emissivity in the entire thermal wavelength range to turn off radiative cooling process.

To realize such a self-adaptive emissivity switch, we use phase change material as the switching element. Compare to other thermal emission switching techniques [19] such as electrical carrier injection [20,21] or mechanical switch [22,23], using phase change materials as switching element, where the phase change is thermally induced, does not involve any power input or feedback control, greatly reducing the system complexity [24–30]. As an illustration, we choose VO₂ as the phase change material. VO₂ has metal-insulator phase transition, exhibiting metallic or insulating state when temperature is above or below the phase transition temperature, respectively. In the infrared wavelength range, optical properties of the two states show distinct features, the insulating state is a low-loss dielectric, whereas the metallic state is a plasmonic metal with a high damping constant as shown in Fig. 2 [31,32]. Such phase transition has been previously employed in demonstrating unique thermal emission properties such as negative differential thermal emittance [24], thermal homeostasis [25] and radiative thermal runaway [26].

Fig. 2 The real part (a) and the imaginary part (b) of the dielectric constants for VO₂ used in the paper in the wavelength range from visible to mid-infrared.

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Typically, the phase transition temperature of un-doped VO₂ is around 68 °C [31,33]. However, it has been reported that co-doping of W and Sr to pure VO₂ can significantly reduce phase transition temperature, even to below room temperature [34–36]. Therefore, for self-adaptive radiative cooling purpose, it is conceivable to use VO₂ as the switching material. With proper doping engineering, one can control the phase transition temperature of VO₂ to match the critical temperature for switching on and off radiative cooling.

3. Photonic Structure Design

We now introduce the photonic structure design that can fulfil the spectral requirement of self-adaptive radiative cooling. Our system consists of two components, with a switchable radiative cooler at the bottom, and a spectrally-selective filter on the top. The switchable radiative cooler consists of VO₂/MgF₂/W with VO₂ serves as the switching component [Fig. 3(a)]. In the following calculation, the optical constants for VO₂ shown in Fig. 2, is determined from [31,32]. And the optical constants for other materials are taken from [37].

Fig. 3 Photonic structures for realizing self-adaptive radiative cooling. (a) A schematic for the bottom radiative cooler, which is made of three layer VO₂/MgF₂/W structure. (b) Solar absorptivity of the radiative cooler. (c) Infrared emissivity of the radiative cooler. (d) A schematic showing the top spectrally-selective filter, which is made of 11 layers of Ge/MgF₂. (e) Transmissivity of the filter in the solar wavelength range. (f) Transmissivity of the filter in the thermal wavelength range. (g) Schematic of the combined system. (h) Solar absorptivity of the radiative cooler in presence of the filter on top. (i) Infrared emissivity of the radiative cooler in presence of the filter on top.

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The absorptivity and emissivity of the radiative cooler in solar and thermal wavelength ranges are shown in Fig. 3(b) and Fig. 3(c), respectively. When VO₂ is at metallic state, such a structure acts as a Salisbury screen absorber [38]. The resonant wavelength can be tuned by appropriately selecting the thickness of the MgF₂ layer, according to the following equation:

λ \approx 4 d_{Μ} n_{M}

Here, d_M and n_M are the thickness and the refractive index of the MgF₂ layer, respectively. With properly designed thickness of the MgF₂ and VO₂ layers, the bottom radiative cooler can exhibit strong and broadband infrared emissivity [Fig. 3(c)], with high absorptivity and therefore high emissivity in the wavelength range of 8 to 13 μm. Here, we have taken the d_M to be 2.25 μm and the thickness of VO₂ layer, d_V, to be 10 nm.

On the other hand, at insulating state, such a structure exhibits a strongly suppressed emissivity in the wavelength range of 8 to 13 μm. Therefore, the radiative cooler, by itself, exhibits the desired spectral characteristics in the thermal wavelength range. On the other hand, in the solar wavelength range, due to lossy nature of VO₂ at both metallic state and insulating state, and the presence of Fabry-Perot resonances, the structure exhibits significant absorption in both states, which are not desirable for radiative cooling purpose [Fig. 3(b)].

To further improve the performance, we place a spectrally-selective filter on top of the radiative cooler, separated with a large air gap. This spectrally-selective filter is a 11-layer stack structure consisting of Ge/MgF₂ [Fig. 3(d)]. This component has two purposes. First, in solar wavelength range, this component serves as a sunshade, preventing the solar irradiation from reaching the bottom radiative cooler, due to the strong absorption of Ge in the solar wavelength range. As is shown in Fig. 3(e), this structure has very low transmission in the solar wavelength range. Second, in the thermal wavelength range, this component serves as a band pass filter with high transmissivity from 8 to 13 μm. Both Ge and MgF₂ are low loss materials in infrared. By optimizing the thickness of each layer (the thicknesses of the layers are presented in Table 1), this structure allows highly selective transmission from 8 to 13 μm while strongly suppresses the emissivity of the bottom component for the rest of infrared wavelength range [Fig. 3(f)].

Table 1. Material composition and thicknesses for the designed spectrally-selective filter.

View Table

We now present the performance of the radiative cooler in presence of the top filter [Fig. 3(g)]. The two components are separated with a gap with a width that is much larger than the wavelength. For such a structure, we can treat the optical properties of the combined structure with incoherent calculations [39]. In this treatment, absorptivity for the bottom radiative cooler in presence of the top filter is calculated by an incoherent summation of the contributions from the multiple reflection processes between the filter and the cooler as below:

ϵ (λ, Ω) = (1 - r_{C}) (t_{F} + t_{F} r_{C} r_{F} + t_{F} {(r_{C} r_{F})}^{2} + t_{F} {(r_{C} r_{F})}^{3} + \dots) = t_{F} (1 - r_{C}) / (1 - r_{C} r_{F})

Here, t_F, r_C, and r_F are power transmission coefficient for the filter, power reflection coefficient at the top surface of the radiative cooler, and power reflection coefficient at the bottom surface of the filter, respectively. These t_F, r_C, and r_F are functions of wavelength and incident angle.

When the system is above critical temperature and VO₂ is in the metallic state, in the presence of the top filter, the radiative cooler structure has a minimum solar absorption in the solar wavelength range [Fig. 3(h)]. Meanwhile, in the infrared wavelength range, we observe a strong selective emissivity from 8 to 13 μm and minimal absorptivity/emissivity for the rest of the thermal wavelength range, approaching the ideal spectrum required for radiative cooling [Fig. 3(i)]. On the other hand, when the system is below critical temperature and VO₂ is in the insulating state, minimum emissivity is observed and radiative cooling is turned off. Furthermore, our system also shows robust emissivity against variation of incident angle as shown in Fig. 4(a). In the metallic state, the polarization-averaged emissivity remains high in the wavelength range from 8 to 13 μm even at large incident angles up to around 70 degrees, with only a slight blue shift at large incident angles. The angle and polarization averaged emissivity from 0 to 90 degrees in the wavelength range from 8 to 13 μm is 0.636 in the metallic state. On the contrary, this averaged emissivity drops to 0.054 in the insulating phase, leading to a switching ratio of 11.8 [Fig. 4(b)]. Overall, such a temperature-dependent switching property should enable a self-adaptive radiative cooling system.

Fig. 4 (a) The emissivity of the bottom radiative cooler in presence of the top filter, as a function of incident angle and wavelength. The VO₂ is in the metallic phase. (b) Angle and polarization averaged absorptivity spectrum of the bottom radiative cooler in presence of the top filter. Red and blue line shows the absorptivity in metallic and insulating VO₂ phase, respectively.

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4. Thermal Performance

We proceed to evaluate the thermal performance of the self-adaptive radiative cooling system. We simulate the temperature of the radiative cooler by solving the heat balance equation:

Q_{total} = Q_{cooler} (T) - Q_{atm} (T_{amb}) - Q_{parasitic} (T, T_{amb}) - Q_{sun} (T) - Q_{exchange} (T, T_{filter})

Here, Q_total is the net cooling power by the radiative cooler. T,

T_{amb}

, and

T_{filter}

are the temperatures of the radiative cooler, ambient, and the filter, respectively. Q_cooler stands for the emitting power from the bottom structure expressed by:

Q_{cooler} (T) = A \int d Ω \cos θ \int_{0}^{\infty} d λ I_{BB} (T, λ) ϵ (λ, Ω, T)

A is the area of the structure, and

\int^{​} d Ω = 2 π \int_{0}^{\frac{π}{2}} d θ sin θ

is the angular integral over a hemisphere with

θ

being the polar angle.

I_{BB} (T, λ) = \frac{2 h c^{2}}{λ^{5}} \frac{1}{e^{\frac{h c}{λ k_{B} T} - 1}}

is the spectral radiance of a blackbody at device temperature T, where h is the Planck’s constant, k_B is the Boltzmann constant, c is the speed of light and

λ

is the wavelength.

ϵ (λ, Ω, T)

is the temperature-dependent emissivity of the radiative cooler in presence of the top filter. To obtain such emissivity, we assume that the phase transition of VO₂ occurs at the temperature of 293K, and the dielectric function of VO₂ smoothly interpolates between the two phases in a narrow temperature range around the phase transition temperature [25]. Absorbed power due to incident thermal radiation from atmosphere, Q_atm, is

Q_{atm} (T_{amb}) = A \int d Ω \cos θ \int_{0}^{\infty} d λ I_{BB} (T_{amb}, λ) ϵ (λ, Ω, T) ϵ_{atm} (λ, Ω)

The absorptivity of the atmosphere,

ϵ_{atm} (λ, Ω)

, is calculated by

1 - t_{atm} (λ, Ω)

, where

t_{atm} (λ, Ω)

is obtained from MODTRAN5 [40]. Parasitic power loss, Q_parasitic, due to conduction and convection is

Q_{parasitic} (T, T_{amb}) = A h (T_{amb} - T)

Here, h is the heat transfer coefficient, here we consider h = 8 Wm⁻²K⁻¹ to mimic a typical natural air convection condition. Incident solar power absorbed by the structure, Q_sun, is

Q_{sun} (T) = A \int_{0}^{\infty} d λ I_{AM 1.5} (λ) ϵ (λ, θ_{sun}, T)

The radiative thermal exchange between the radiative cooler and the top filter, Q_exchange, is

\begin{array}{l} Q_{exchange} (T, T_{filter}) = \\ A \int d Ω cos θ {\int_{0}^{\infty} d λ I_{BB} (T_{filter}, λ) ϵ_{filter} (λ, Ω) ϵ_{cooler} (λ, Ω, T) - \int_{0}^{\infty} d λ I_{BB} (T, λ) ϵ_{filter} (λ, Ω) ϵ_{cooler} (λ, Ω, T)} \end{array}

Here,

ϵ_{filter} (λ, Ω)

and

ϵ_{cooler} (λ, Ω, T)

are emissivity of the filter and the radiative cooler, respectively.

Similarly, the temperature of the filter, T_filter, is obtained by calculating net cooling power for the filter, Q_total,F, as below.

Q_{total, F} = Q_{filter} (T_{filter}) - Q_{atm, F} (T_{amb}) - Q_{parasitic, F} (T_{filter}, T_{amb}) - Q_{sun, F} + Q_{exchange} (T, T_{filter})

Here, Q_filter is the thermal radiation to the sky by the filter. Q_atm,F, Q_parasitic,F, and Q_sun,F are absorbed thermal radiation, parasitic power loss, and absorbed solar power by the filter, respectively. The formulas for Q_filter, Q_atm,F, Q_parasitic,F, and Q_sun,F are obtained by replacing the emissivity for the radiative cooler with that for the filter in the equations above for the cooler. In the calculation procedure discussed above, the equilibrium temperature for both the filter and the cooler are self-consistently determined by simultaneously solving for Eqs. (3) and (9) with both

Q_{total}

and

Q_{total, F}

set to be zero.

We can also obtain the time-dependent temperatures of the radiative cooler as well as the top filter by solving the differential equations:

C_{cooler} \frac{d T}{dt} = Q_{total} (T, T_{amb}, T_{filter})

C_{filter} \frac{d T_{filter}}{dt} = Q_{total, F} (T, T_{amb}, T_{filter})

To determine the heat capacitance of the radiative cooler, C_cooler, we assume that the radiative cooler, which consists of VO₂ (10 nm) / MgF₂ (2.25 μm) / W (5 μm) layers as mentioned in the previous section, is deposited onto a Si substrate with a thickness of 525 μm. The heat capacitance includes the contribution of the Si wafer. For the top filter, the heat capacitance C_filter is determined from the sum of the heat capacitance of each layer listed in Table 1.

We now calculate the transient temperature response of the self-adaptive radiative cooling system under various ambient temperature conditions. For each ambient temperature, we assume that at the initial time both the cooler and the filter has a temperature that is the same as the ambient temperature. We then integrate Eqs. (10) and (11) to obtain the temperature of the filter and the cooler as a function of time, as shown in Fig. 5(a).

Fig. 5 Transient thermal performance. (a) Time-dependent temperature evolution of the radiative cooler under different ambient temperature. The initial temperature is assumed to be the same as ambient temperature. The whole system is exposed to the sky at time = 0. (b) Time-dependent Q_total, Q_cooler, Q_exchange, of the radiative cooler, and the temperature of the filter $T_{filter}$ , at T_amb = 313 K. (c) Time-dependent Q_total, Q_cooler, Q_exchange, of the radiative cooler, and the temperature of the filter $T_{filter}$ , at T_amb = 298 K. (d). Time-dependent Q_total, Q_cooler, Q_exchange, of the radiative cooler, and temperature of the filter, $T_{filter}$ at T_amb = 283K.

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When the ambient temperature is significantly above the critical temperature, for example 313 K [black curve in Fig. 5(a)], the system is in the ‘on’ state. As the time evolves, the radiative cooler temperature is reduced and eventually reaches an equilibrium temperature that is about 10 K below the ambient temperature, due to the effect of radiative cooling. At the equilibrium, the net outgoing power from the cooler approaches zero. [Red line, Fig. 5(b)]. The radiative cooling power of the radiative cooler, Q_cooler, maintains over 100 W/m² in this case [blue curve in Fig. 5(b)]. Although the heat exchange between the filter and the cooler, Q_exchange, increases to ~18 W/m² as the T_filter rises to around 360 K due to solar absorption [Dashed line, Fig. 5(b)], the Q_exchange [Green line, Fig. 5(b)] is not significant in comparison with the Q_cooler in the cooling process.

When the ambient temperature is slightly above critical temperature [green curve in Fig. 5(a)], for example 298 K, the system is initially in the ‘on’ state. The cooler exhibits significant cooling power [Blue curve in Fig. 5(c)]. As time evolves, the radiative cooler temperature is reduced until it reaches the critical temperature, at which point the system is switched to the ‘off’ state, with a significant sudden reduction of the cooling power as shown by the blue curve in Fig. 5(c). After the phase transition, the radiative cooler temperature is maintained near critical temperature.

When the ambient temperature is below the critical temperature, for example at 283 K [pink curve in Fig. 5(a)], the system is in the ‘off’ state without radiative cooling. The radiative cooler has a temperature that is almost unchanged as a function of time. In this case, the cooling power Q_cooler remains low around 12 W/m² during the entire time period considered [blue curve in Fig. 5(d)], due to the lower emissivity for the radiative cooler, as compared to the case considered above when the ambient temperature is higher than the phase transition temperature. Q_exchange also shows lower value. Therefore, the total outgoing power, Q_total, is less than 7 W/m² at the initial time and is further reduced to zero as time evolves. Such a small total outgoing power is consistent with the near complete absence of temperature variation as a function of time for the radiative cooler.

Finally, we simulate the radiative cooler temperature as a function of time under an outdoor condition. We solve Eqs. (3) and (9), using as inputs the ambient temperature [41] and solar illumination data [42] of July 19, 2017, representing typical summer climate conditions at Stanford, California. Figure 6 shows simulated radiative cooler temperature and radiative cooling power across a 24-hour period. Starting from 12:00 AM, the radiative cooler temperature is below critical temperature of 293 K. In this case, no cooling is required. The system is in the ‘off’ state with minimum cooling power and maintain its temperature near ambient temperature. As ambient temperature and device temperature increase in the morning, starting from around 9:00 AM, the radiative cooler temperature goes above the critical temperature and the system is switched to ‘on’ state, radiative cooling effect is clearly observed as the radiative cooler temperature deviates below the ambient temperature and reach a maximum difference of about 9 K around 3:00 PM when the ambient temperature is about 304 K. We also observe significant cooling power during this period when the radiative cooling is turned on. At 9:00 PM, when ambient temperature falls below the phase transition temperature, radiative cooling is again turned off. Such results clearly show the self-adaptive radiative cooling performance of our system. As a comparison, we also simulate the temperature performance of a static radiative cooler, assume its emissivity is the same as the ‘on’ state of the self-adaptive radiative cooler case shown in Fig. 3(i), but without the switching ability. As is shown in black dashed curve in Fig. 6, this static radiative cooler performs radiative cooling for the entire 24 hours, even when it’s cold at night and cooling is less desired.

Fig. 6 Thermal performance of the self-adaptive radiative cooler (black curve) over a 24h cycle with ambient temperature variation (red curve). Radiative cooling power of the radiative cooler is also plotted (blue curve). As a comparison, the thermal performance of a static radiative cooler with the same emissivity as the ‘on’ state of the self-adaptive radiative cooler is also plotted (black dashed curve).

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5. Concluding Remarks

We have presented a self-adaptive radiative cooling system based on a photonic design incorporating phase change material VO₂. This system can automatically turn on radiative cooling when the ambient temperature is above critical temperature and turn off radiative cooling when the ambient temperature is below. As a proof of concept demonstration, here we use simple planar stack structures. The concept here can be applied with other materials and structure systems for large scale implementations and can be generalized towards other radiative cooling applications, for example thermal textiles. Our results here explore new functionalities of radiative cooling applications and could be potentially used in a wide range of applications such as vehicles, buildings and textiles for energy consumption reduction and improved thermal comfort.

Funding, acknowledgments, and disclosures

This work is supported in part by the National Science Foundation (Grant No. CMMI-1562204), and by the Global Climate and Energy Project (GCEP) at Stanford University.

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Layer #	Material	Thckness (µm)
1	Ge	0.2787
2	MgF2	0.3566
3	Ge	0.5374
4	MgF2	0.2382
5	Ge	0.1838
6	MgF2	1.3190
7	Ge	0.1625
8	MgF2	1.0192
9	Ge	0.6151
10	MgF₂	0.4489
11	Ge	0.2756

Self-adaptive radiative cooling based on phase change materials

Abstract

1. Introduction

2. Self-adaptive Radiative Cooling

3. Photonic Structure Design

4. Thermal Performance

5. Concluding Remarks

Funding, acknowledgments, and disclosures

References and links

Cited By

Figures (6)

Tables (1)

Equations (11)

Optics Express