Minkyung Kim,Dasol Lee,Younghwan Yang and Junsuk Rho,2*

This paper presents design and simulation of a switchable radiative cooler that exploits phase transition in vanadium dioxide to turn on and off in response to temperature.The cooler consists of an emitter and a solar reflector separated by a spacer.The emitter and the reflector play a role of emitting energy in mid-infrared and blocking incoming solar energy in ultraviolet to near-infrared regime,respectively.Because of the phase transition of doped vanadium dioxide at room temperature,the emitter radiates its thermal energy only when the temperature is above the phase transition temperature.The feasibility of cooling is simulated using real outdoor conditions.We confirme that the switchable cooler can keep a desired temperature,despite change in environmental conditions.

Keywords:phase change material;photonic crystal;passive thermoregulation;switchable radiative cooling;Fabry-Pérot resonance

Introduction

Every object with finite temperature emits heat by thermal radiation.If an object radiates more energy than it absorbs from its surroundings,it loses energy and cools down.This phenomenon occurs generally at night when the object is not subject to solar irradiation,and forms a basis of nocturnal radiative cooling1-3.However,it has been recently suggested that a material that reflects solar energy but radiates in an atmospheric window (wavelengths 8 μm﹤ λ ﹤ 13 μm) can lose energy during the day4.This observation has stimulated studies on diurnal radiative cooling,in which an object can cool down even under solar illumination without consuming external energy5-9.Therefore,diurnal radiative cooling has been evaluated as an alternative cooling technology for future.

For efficient radiative cooling,two conditions should be satisfied.The absorptivity of the object should be near zero in the ultraviolet (UV) to near-infrared (NIR) range,and should radiate its energy with near-unity efficiency in the wavelengths at which electromagnetic radiation can be transmitted through the atmosphere (the“atmospheric window”).To meet those conditions,structured materials such as photonic crystals10,micro/nanoporous structures11-17,multilayer18,19,and mixtures of dielectric particles20-23have been used for their ability to manipulate optical responses.However,the spectra of such media cannot be changed after fabrication.Therefore,many efforts have been devoted to find optical materials and structures that have switchable thermal characteristics.

An interesting example is the use of vanadium dioxide (VO2).It is a phase change material that has an insulating phase at temperature T below the critical temperature Tcand metallic phase at T ﹥ Tc.The phase transition of VO2has been used to develop active emitters and absorbers24-26,switchable polarization rotators27,waveguides28and nanoantennas29.Tcof pure VO2is 68°C,but can be set to around room temperature by doping molybdenum,tungsten and/or strontium30-37and by growing VO2thin film on TiO2substrates38,39.This relatively low Tcof VO2encouraged the development of an active radiative cooler40based on the transmissive filter placed on a switchable emitter and a photonic-based thermostat41consisting of repeated layers of VO2grown on TiO2film and zinc selenide.Such active thermal devices radiate only at T ﹥ Tcand thus lose their thermal energies as temperature increases while maintaining temperature similar to ambient as temperature decreases.Here,we develop a switchable radiative cooler by combining two parts:an emitter that uses doped VO2,and a solar reflector that has optimized one-dimensional multi-stacked photonic crystals.The emitter part is designed to selectively radiate in the atmospheric window whereas the solar reflector blocks solar irradiance in UV to NIR regime.Thus,the cooler exhibits positive cooling power at T ﹥ Tcand negative cooling power at T ﹤ Tc.Therefore,it maintains a moderate temperature that is resilient to environmental changes.Simulation using a diurnal cycle of outdoor temperature and solar radiation proved that the radiative cooler is capable of switchable diurnal radiative cooling.In comparison to other static radiative cooler,the switchable radiative cooler exhibits minimal variation of temperature,and is therefore useful in various applications including air conditioning and heating.

Results and discussion

Material properties and design

The optical behavior of VO2can be described as Fig.1(a).In the infrared range,VO2responses as a metal well above Tcand as an insulator well below Tc.To avoid an unphysical result,we assume that the permittivity of VO2changes continuously and smoothly in a narrow transition range [Tc-ΔT,Tc+ΔT].Thus,the permittivity of VO2is modelled individually in three distinct regimes:insulating,transition and metallic regime (Fig.1(a)).For insulating and metallic regime,we use permittivities of doped VO2presented in ref.40.In the transition regime,we assume that permittivity changes as an arctan function(Fig.1(b)):

Fig.1|Temperature-dependent material responses of VO2. (a) Schematic of temperature-dependent phase.(b) Permittivity at 2 μm when Tc=298 K.Shaded area represents transition regime.(c) Real and (d) imaginary part of permittivity in transition regime.

where εmand εiare permittivity in the metallic and insulating phase,respectively.Throughout this paper,we set Tc=298 K and ΔT=2 K.In the transition regime,both the real and imaginary parts of εtransitionchange smoothly (Figs.1(c) and 1(d)).

To minimize the absorption of solar irradiance and maximize thermal energy radiated through the atmospheric window in a switchable way,we combine an emitter and a solar reflector separated by a spacer (Fig.2)on a SiO2substrate.The emitter part is composed of stacked layers of silver (200 nm),silicon (700 nm) and VO2(10 nm) from bottom to top.A 300 nm-thick spacer made of poly(methyl methacrylate) (PMMA) is deposited on the emitter.The top of the spacer is the solar reflector consisting of three stacked photonic crystals.Each photonic crystal (PCi) is a distributed Bragg reflector(DBR) that is designed to suppress absorption at a target wavelength λiwhere λ1=0.52 μm,λ2=0.76 μm and λ3=1.18 μm.Thickness of each layer is set as λi/4n following the design rule of DBRs42.

Optical responses

The transfer-matrix method was used to calculate the absorptivity and reflectivity spectra43.We examine absorptivity and reflectivity of the emitter part and solar reflector part individually.The emitter works as a metalinsulator-metal structure at T ﹥ Tc.The Fabry-Pérot resonance due to the cavity results in high absorptivity near the atmospheric window (Fig.3(a)).In contrast,the emitter behaves as an insulator deposited on a metal and mostly reflects at T ﹤ Tc(Fig.3(b)).Therefore,the emitter performs the switching of radiation in the atmospheric window.Meanwhile,the solar reflector reflects solar irradiance in the UV to NIR range (Fig.3(c)).The high reflectivity of the solar reflector originates from the optimization of photonic crystal structures.The average absorptivity of the solar reflector at λ ﹤ 2 μm is 5.9 %.The combined structure of emitter separated by a spacer from the solar reflector has low absorption in UV to NIR and switchable absorption in the atmospheric window simultaneously.Absorptivity in UV to NIR is low in both metallic and insulating phases;the combined structure absorbs 7.6 % in average.In contrast,absorptivity in the atmospheric window are remarkably distinct in two phases.The absorptivity is high in the metallic phase,but low in the insulating phase (Figs.3(d) and 3(e)).Average absorptivity is 78 % in the metallic phase and 18 % in the insulating phase.At oblique incidence,the absorptivity remains high in the atmospheric window (Fig.3(f)).

Fig.2|Design of the switchable radiative cooler. Emitter part consists of stacked layers of silver,silicon and VO2.Solar reflector part consists of three photonic crystals that have 4 pairs of PMMA and silicon.PCi is designed to suppress absorption at λi where λ1=0.52 μm,λ2=0.76 μm and λ3=1.18 μm.Thickness of each layer is λi/4n.

Fig.3|Absorptivity and reflectivity of the switchable radiative cooler. (a,b) Absorptivity and reflectivity of the emitter part when VO2 is in (a)metallic and (b) insulating state.(c) Absorptivity and reflectivity of the solar reflector part.Three arrows represent the target wavelengths of three photonic crystals.(d,e) Absorptivity and reflectivity of the switchable radiative cooler when VO2 is in (d) metallic and (e) insulating state.Incident angle is zero.(f) Absorptivity of the switchable radiative cooler when VO2 is metallic.

Calculation of cooling flux

To evaluate the cooling flux,we consider blackbody radiation,solar irradiance,thermal exchange with atmosphere,and two other heat exchange channels4:

where T is the temperature of the switchable radiative cooler,Tambis ambient temperature,and Prad(T) corresponds to radiation flux emitted by the cooler:

where λ is the wavelength,θ is the polar angle,andsinθdθis the angular integral over a hemisphere.E is the emissivity of the cooler and is equal to the absorptivity according to Kirchhoff's law44.Since E of VO2depends on its temperature,we use E(T,λ,θ) instead of E(λ,θ).

is the spectral radiance density of a blackbody at temperature T,where h is Planck constant,c is the speed of light in free space,and kBis the Boltzmann constant.The second term represents absorbed thermal flux due to solar irradiance:

where IAM1.5is the AM1.5 spectrum of the solar illumination.Thermal flux absorbed by the atmospheric heat exchange is

where Eatm=1-t(λ)1/cosθis the emissivity of the atmosphere where t(λ) is the transmittance of the atmosphere in the zenith direction1,45.The last term is associated with conduction and convection given as

where hccis the heat transfer coefficient due to conduction and convection.We use hcc=6.9 Wm-2K-1throughout the calculations.

The cooling flux P(T) under normal incidence of solar energy is calculated using Eq.(2) to (7).For simplification,we first treat E as a temperature-independent value.We calculate the cooling flux of the cooler by assuming that VO2is either metallic or insulating regardless of temperature (Fig.4(a)).When VO2is assumed to be metallic,it has positive cooling flux above T=297.8 K and negative cooling flux below it.As expected,the cooling flux when VO2is insulating is lower than that when it is metallic.The cooling flux is zero at T=306 K for the insulating case.

In reality,E of VO2varies with T and thus,E should be treated as a function of temperature.Cooling flux is expected to be equal to that of metallic case at T ﹥ Tc+ΔT and to that of insulating case at T ﹤ Tc-ΔT.In the vicinity of Tc,it is assumed to change continuously and smoothly.We use Eq.(1) to calculate emissivity of the radiative cooler,then obtain the cooling flux in the transition regime when Tamb=303 K (Fig.4(b)).The cooling flux varies by amount of more than 100 Wm-2across the transition regime.In the atmospheric window,the cooler radiates approximately Prad=179 Wm-2when the cooling is turned on (T=Tc+ΔT) and Prad=47 Wm-2when the cooling is turned off (T=Tc-ΔT).The switchable radiative cooler is in thermal equilibrium at T=298.3 K,which corresponds to room temperature.

Fig.4|Cooling flux of the radiative cooler under normal incidence of solar energy when Tamb=303 K. (a,b) Cooling flux when permittivity of VO2 is assumed to be (a) static and (b) dynamic.Shaded area represents the transition regime.

Numerical observation of cooling in time

To confirm the cooling visually,we calculate how temperature of the switchable radiative cooler changes over time.Temperature variation obeys the thermal balance equation:

where A is the area of the cooling surface,and t is time.C is the heat capacitance,which can be obtained by summing the heat capacitances of all layers as

where cj,ρjand tjis the specific heat,density and thickness of j-th layer,respectively.The summation applies to layers shown in Fig.2 and a substrate of 500 μm-thick silicon dioxide (SiO2).The specific heat and density(Table 1) are obtained from ref.46,47for PMMA,ref.48,49for silicon,ref.48,50for silver,ref.48,51for SiO2,and ref.52,53for VO2.Strictly,specific heat of VO2depends on its temperature,but we use the specific heat at room temperature because the variation range is small (﹤ 3 Jg-1K-1).To test the cooling ability,we additionally include C0=1.325×105JK-1as the heat capacitance of an object to be cooled;it corresponds to a block of SiO2of unit area and 0.05 m thickness.

Table 1 | Specific heat and density of materials.

We simulate temperature variation in time under Tamb=303 K by using Eq.(2) and Eq.(9).For various initial temperature ranging from 280 K to 320 K,temperature converges to 298.3 K (Fig.5(a)).It shows that the cooler is turned on at T ﹥ 298.3 K but turned off at T ﹤298.3 K.The switchable cooling is also confirmed by cooling flux which is positive at T ﹥ 298.3 K and negative at T ﹤ 298.3 K (Fig.5(b)).The thermal equilibrium temperature can be tuned by designing the solar reflector part.Therefore,the switchable radiative cooler provides a pathway to constantly control the temperature at a desired value.

Fig.5|Temperature variation in time. (a) Temperature and (b) cooling flux in time for initial temperature of 280 K to 320 K with 5 K step.Temperature indicate the initial temperature of the cooler. Tamb=303 K.(c, d) A cycle of temperature of a day.(c) Tamb and solar irradiance of July 15,2018 in Pohang,Korea.(d) Temperature of switchable radiative cooler (blue) and the static radiative cooler when radiative cooling is assumed to be turned on (orange) and off (yellow).Tamb is shown as a reference (black).Initial temperature of the cooler is set equal to the initial Tamb.

The practicality of the switchable radiative cooler is assessed by simulating a cycle of temperature during a day.To emulate the outdoor condition,we use ambient temperature and solar irradiance I measured on July 15,2018 in Pohang,Korea by the Korea Meteorological Administration54(Fig.5(c)).Initial temperature of the switchable radiative cooler is set equal to that of ambient.During the whole day,the cooler has T ﹤ Tamb,with the maximum decrement of 8.5 K (Fig.5(d)).For comparison,we also plot the temperature of the radiative cooler when the cooling is turned on and off at all temperature.In all cases,temperature gets lower before 6 am when the sun rises.When the cooling is turned off,temperature increases as time passes until it reaches the equilibrium and then decreases again after the sunset.On the other hand,when the cooling is turned on,temperature decreases by approximately 10 K as a result of high cooling power.Temperature variation during a day exceeds 10 K in both cases.In contrast,the switchable radiative cooler shows a minimal change of temperature,resilient to the surrounding environment.

Conclusions

In conclusion,we present a switchable radiative cooler made of doped vanadium dioxide.The cooler emits energy in the atmospheric window only above room temperature as a result of Fabry-Pérot resonance.Thus,the cooling is conditionally turned on and off depending on the temperature.We demonstrate the switchable radiative cooling by calculating cooling flux for various temperature ranges.The switchable cooling is further supported by simulating a cycle of temperature for a day using the measured temperature and solar irradiance data.We confirm that the cooler can maintain its temperature robustly under natural weather conditions.To further improve the cooling effect of the switchable diurnal radiative cooler,the design can be optimized to have unity(zero) reflectivity in the UV to NIR range and emissivity in the atmospheric window at T ﹥ Tc(at T ﹤ Tc) or to have the highest cooling flux by various optimization methods and machine learning55-57.The switchable radiative cooler will facilitate self-adaptive control of thermal energy and can be implemented in a variety of applications such as passive cooling in environmentally-benign buildings and vehicles.