Reduced Graphene Oxide-Based Spectrally Selective Absorber with an Extremely Low Thermal Emittance and High Solar Absorptance.

Abstract Carbon‐based black materials exhibit strong solar absorptance (αsolar >0.90), which play key roles in transforming solar energy into available power for solar‐thermal, thermophotovoltaic, thermoelectric, and many other systems. However, because of high thermal emittance (>95%), these carbon‐based materials always cause huge energy loss that hinders the solar‐thermal conversion efficiency tremendously. In this study, a reduced graphene oxide–based spectrally selective absorber (rGO‐SSA) is demonstrated, which possesses a recorded low thermal emittance (≈4%) and high solar absorptance (αsolar ≈ 0.92) by easily regulating the reduction level of inner 2D graphene sheets. Compared to conventional carbon‐based black materials, thermal emittance of this rGO‐SSA is largely reduced by ≈95.8% and the cutoff wavelength of rGO‐SSA is broadband‐tunable that can range from 1.1 to 3.2 µm. More importantly, this simply sol‐gel coated rGO‐SSA has high temperature tolerance at 800 °C for 96 h that is hardly achieved by other cermet‐based or photonic‐based SSAs. Based on this rGO‐SSA, ultrafast solar steam escape (0.94 mg cm−2 s−1) under concentrated solar irradiance is achieved directly. The insight from this study will provide a new strategy for constructing thermally stable carbon‐based SSAs and greatly facilitate the solar‐thermal practical significance.

Using Kirchhoff's laws, emittance is equal to the absorptance in a given wavelength, namely ε(λ)=α(λ). For an absorber at working temperature T, its thermal radiation emittance can be expressed as 1 : Where E BB (λ, T) is power density distribution of BB surface: [2] E ( , )= − 1 (S3) In which c 1 =3.7405 x 10 8 W μm 4 m -2 and c 2 =1.43879 x 10 4 μm K, which are Planck's first and second radiation constants, respectively. And E BB<T> is total thermal radiation power density:

Section 2. Long-term stability and degradation mechanism of rGO-SSA
Towards the long-term stability evaluation of low-temperature SSAs for domestic solar water heating systems, the accelerating aging method has been introduced at 1994 in the work of International Energy Agency (IEA) Task X. [3] Considering the 25 years stable performance (degradation of solar fraction less than 5 %) of absorber under working condition of water heating, this accelerating aging method introduces a performance criterion (PC) function for evaluate the suitability of SSAs for long-term domestic solar water heating application: Where Δα solar =α solar (aged)α solar (unaged) is the change of solar absorptance, and Δε 100 =ε 100 (aged)ε 100 (unaged). This criterion function is widely-used for standard evaluation of SSAs for commercial low-temperature water heating application, however, the weight of Δε 100 should be modified as 0.5 for mid-temperature (100 o C<T<400 o C) to high-temperature (T>400 o C) applications: [4] = −∆ + 0.5∆ ≤ 0.05 (S6) In this work, we use the customized accelerating aging method which is widely-used in literature [4] to evaluate the high-temperature stability of rGO-SSA, in which we select a proper annealing temperature and time under argon protection to quickly approach the failure indicating the W|rGO|ARC2 is also qualified but the working condition of 800 o C for 96 hours under argon protection is very closed the failure limitation of rGO-SSA(W|rGO|ARC2).
Certainly rGO-SSA can be used for much more long-term lifetime when decreasing the working temperature, the lifetime can be extended to even 25 years (~9125 days) under sufficient working temperature: The accelerating aging is designed based on the Arrhenius' relationship, [5] in which the aging degradation mechanism is simplified as a temperature dependent thermal diffusion process. Assuming the thermal diffusion coefficient of absorber is constant over different temperatures, then absorber annealing at higher temperature will degrade faster than annealing at lower temperature, the acceleration of failure time under high temperature is defined as: [5] Where t ref is the time for approaching the failure criterion under low temperature T ref , t n is the time for approaching the failure criterion under high temperature T n , E T is the activation energy according to Arrhenius and R is the ideal gas constant (R=8.314 J K -1 mol -1 ).
Therefore, for a verified high temperature result (T n , t n ), the long-term service time under lower temperature (likewise t ref ) can be estimated by: Therefore, using this acceleration relationship, we can predict the failure time t n of rGO-SSA under low temperature T ref =177 o C given a verified higher temperature aging result (800 o C, 4 d). According to the recommend criterion in the literature, [5] the activation energy of rGO-SSA under argon protection is estimated to be ~50 kJ mol -1 , thus, for working condition of 177 o C under argon protection, the service time is predicted as ~9375 days (25.5 years).
We further analyze the mechanism for degradation of rGO-SSA at 800 o C. Generally, the degradation of SSA at high temperature could be attributed to spontaneous thermal diffusion of molecules and atoms, surface oxidation or low coating adhesion-induced ingredients change and so on. [4] First, in this study, For the melting temperature of SiO2 (~1723 o C), C (~4527 o C) and W (~3422 o C) are considerably higher than the annealing temperature (800 o C), high temperature thermal diffusion of molecules and atoms could be negligible. Secondly, the annealing test is carried under argon protection, and the failure sample sustains the smooth planar surface which indicating the surface oxidation is not evident, so the degradation from oxidation could be small either. [6] Thus, the potential mechanism of degradation of rGO-SSA could be the relatively low coating adhesion, which could be induced by the impurities and voids in the interface [7] and the intrinsically low interfacial affinity of rGO with tungsten.
In conclusion, the high temperature stability of rGO-SSA in this early stage is at a considerable value and theoretical long-term stability at 177 o C for 25.5 years, indicating the long-term stability of rGO-SSA.

Section 3. Solar-thermal Conversion Efficiency Optimization
When absorbing solar flux, absorbers losing thermal energy to environment simultaneously (for conduction, convection and radiation), only residual part of solar thermal energy is stored in absorbers. SSAs are mostly used in vacuum systems for eliminating thermal losses from conduction and convection. Assuming an isolated SSA in vacuum (conduction and convection are negligible) under concentrated sunlight (with E AM1.5G spectrum and concentration index C opt ), solar thermal efficiency (η) can be expressed as: In which, for our preset condition, overall input energy of system E input can be estimated by: (S10) And absorb-in energy of systemE absorb merely dependents on the absorptance of SSA to the input spectrum: (S11) And energy loss of systemE loss , in this case, is only caused by thermal emission: Where ε Tw is the emittance of SSA at working temperature T w , and the ambient temperature is From Supporting Equations (S9) ~ (S12), we conclude that, in vacuum isolated systems, solar thermal efficiency η is (C opt , T w ) dependent: In which it is worthy to note that α solar and ε Tw are strongly correlated to the wavelength dependent absorptance of SSA, α(λ), seeing Supporting Equations (S1) and (S2). For an ideal SSA with specific cutoff wavelength λ cut , we describe its α(λ) as a step function: [8] ( ) = 1, < 0, ≥ As we mentioned earlier, increasing working temperature induces blue-shifting E BB (λ, T w ), so E BB (λ, T w ) will intersect with solar spectrum E AM1.5G (λ) in different wavelengths. Hence, λ cut of SSA should be chosen as this intersection wavelength. However, as shown in Figure 4d, is a discrete power distribution for atmospheric absorption band (basically from H 2 O, O 3 and CO 2 [9] ) from the earth, so getting an analytic solution of intersection wavelength is impossible unless we approximate E AM1.5G (λ) with blackbody distribution.
The sun is a blackbody radiation source with surface temperature (T s ) of ~5770 K, power density distribution on solar surface is: When arrives at the earth, solar power is largely decreased but the relative intensity remains the same. So we can simply use a scaling factor to match E BB (λ, 5770K) to AM1.5G solar spectrum E AM1.5G (λ): In which β=2ⅹ10 -5 is a scaling factor, and it turns out they match well with each other (Fig.   4d). Finally, based on Supporting Equations (S3), (S10), (S15) and (S16), we get analytical solution of λ cut as the intersection wavelength of C opt x β x E BB (λ, 5770K) and E BB (λ, T w ): Note that λ cut is fixed as 4 μm when its calculated value exceeds 4 because E AM1.5G (λ) almost entirely distributed across 0.3~4 μm after atmospheric absorption. [9] And using Supporting Equations (S4) and (S13), the corresponding solar thermal efficiency can be further simplified as:

In the basis of Equations above all, we have performed a numerical analysis on Matlab
R2017b software, and the results suggest that 1~3 μm is the practical λ cut -scale for low-to-high temperature systems.  We have measured the microscale morphology of the rGO-SSA via AFM on different regions of samples and evaluated their surface roughness over an 5ⅹ5 μm area ( Figure S2). As summarized in Figure S2e, the microscale morphology of rGO-SSA is smooth and the root mean square roughness R q of region 1, 2, 3 is about 10.4, 7.7 and 13.3 nm, respectively.

Figures and Tables
Meanwhile, the surface differences of these regions are no more than 1.5 % (1.3 %, 0.2 % and 0.6 % respectively), demonstrating the planar nature of rGO-SSA surface.
In conclusion, our characterization shows that rGO-SSA has smooth surface and uniform microscale morphology. Figure S3. Optical pictures of rGO-SSA before/after thermal reduction (300 o C). Sample size: 2 x 2 cm square. Before thermal reduction, pristine Al|GO|TEOS sandwich weakly absorbs visible light (380 ~780 nm), so the optical appearance is closed to bare Al substrate (reflective, with metallic lustre). After thermal reduction, GO layer is reduced into rGO layer and TEOS is sintered into ARC layer, strong light extinction, appropriate thickness (~100 nm) of rGO layer and anti-reflection modification of ARC jointly result in the black appearance of rGO-SSA(Al|rGO|ARC) which exhibits over 0.9 absorptance across visible spectrum (Fig. 1f in main text). spectral absorptance across 300 ~2500 nm of Al|rGO in which rGO layer is ~88 nm thick. Red line indicates the spectral absorptance of Al|rGO|ARC in which rGO layer is ~100 nm thick and ARC is ~50 nm thick. Destructive region featured with gray lines represents the insufficient absorption band resulting from in destructive interference of single layer of rGO, however, this region is amended because of the modified multilayer interference of rGO|ARC after ARC coating.

Figure S5. In-situ thermal emittance characterization. (a)
Testing setup of in-situ characterization of thermal emittance. Each sample is placed on a polished Al rear (20 x 20 cm) and heated by a hotplate. Al rear is used for blocking the IR emission from the hotplate, thus improving the measuring accuracy. An IR camera is used to capture IR photos of samples in angle of incidence ~8°. Ambient high temperature heat source is prohibited in the testing procedure. (b) Scheme of studied region and testing region. For the testing region, sample surface is made coarse for better stick and surface of polyamide tape is also sanded by an abrasive paper (P600). Optical photos of studied samples are also shown with scale bar: 1 cm.
Three typical samples, BB paint, Al substrate and rGO-SSA ( Figure S5b), are studied at heating temperature 100~300 o C. Each sample has a tiny triangular reference region covered by rough PI tape, with already-known emittance ~0.95 adjusted by an embedded thermocouple. In each heating level, apparent temperatures (global emittance ~0.95) of studied region and reference region are recorded in Figure S6 via IR camera. By manually modifying the emittance of studied region until its temperature equals to referenced region, [10] in-situ ε T of these samples are determined (Fig. 3a in main text).     Notes: 1L, 2L, and 3L means the number of coating layer on the substrate is 1, 2, and 3 respectively. ARC is a SiO2 layer in this work. The emittance is sampled at 100 o C without additional caption.

Figure S11 Temperature difference and dried out time information during contact boiling period. (a)
The temperature difference (△T) and (b) dried out time of BB paint absorber (black dotted line) and rGO-SSA (blue dotted line) for different feeding rates (from 8 to 15 μl min -1 ). The video of whole droplet escaping process is recorded via IR camera. △T is read from the reference region temperature of absorber. Dried out time of droplet is judged from the maximum and minimum values of temperature falling procedure (contact boiling period) of absorber ( Fig. 5d in main text).
Video S1. Thermal reduction process of rGO-SSA.
In this video, thermal reduction process of rGO-SSA while heating on a hotplate from 50 o C to 300 o C is recorded via digital camera and IR camera. BB paint is pasted on the same substrate of rGO-SSA for vivid comparison between spectrally selective absorption and blackbody-like absorption. The whole video is accelerated by 10 times speed.
Macroscopic appearance change (left panel and the inset on right panel) features the transparent-to-black process of rGO-SSA (drastically happened at ~220 o C), which is significantly different from BB paint and can be easily captured by human eyes, the black color derived from 300 o C reduction indicates the high solar absorptance of rGO-SSA. We have also marked the apparent temperatures of rGO-SSA and BB paint on the IR video (right panel). It shows that apparent temperature of BB paint increases from 41.8 o C to 275.5 o C, which is nearly the same to the heating temperature. While the apparent temperature of rGO-SSA increases from 27.0 o C to 61.4 o C, which is also linearly proportional to the heating temperature but remains in a rather low level, it implies the low thermal emittance nature of rGO-SSA.