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Remarkable Daytime Sub-ambient Radiative Cooling in BaSO4 Nanoparticle Films and Paints

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Remarkable Daytime Sub-ambient Radiative Cooling in BaSO4 Nanoparticle Films and Paints

Abstract and Figures

Radiative cooling is a passive cooling technology that offers great promises to reduce space cooling cost, combat the urban island effect and alleviate the global warming. To achieve passive daytime radiative cooling, current state-of-the-art solutions often utilize complicated multilayer structures or a reflective metal layer, limiting their applications in many fields. Attempts have been made to achieve passive daytime radiative cooling with single-layer paints, but they often require a thick coating or show partial daytime cooling. In this work, we experimentally demonstrate remarkable full daytime sub-ambient cooling performance with both BaSO4 nanoparticle films and BaSO4 nanocomposite paints. BaSO4 has a high electron bandgap for low solar absorptance and phonon resonance at 9 um for high sky window emissivity. With an appropriate particle size and a broad particle size distribution, BaSO4 nanoparticle film reaches an ultra-high solar reflectance of 97.6% and high sky window emissivity of 0.96. During field tests, BaSO4 film stays more than 4.5C below ambient temperature or achieves average cooling power of 117 W/m2. BaSO4-acrylic paint is developed with 60% volume concentration to enhance the reliability in outdoor applications, achieving solar reflectance of 98.1% and sky window emissivity of 0.95. Field tests indicate similar cooling performance to the BaSO4 films. Overall, our BaSO4-acrylic paint shows standard figure of merit of 0.77 which is among the highest of radiative cooling solutions, while providing great reliability, the convenient paint form, ease of use and the compatibility with commercial paint fabrication process.
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Remarkable Daytime Sub-ambient Radiative
Cooling in BaSO4 Nanoparticle Films and Paints
Xiangyu Li †,‡, Joseph Peoples †,‡, Peiyan Yao †,‡ and Xiulin Ruan †,‡,*
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA
* Corresponding Author, Email: ruan@purdue.edu
ABSTRACT
Radiative cooling is a passive cooling technology that offers great promises to reduce space
cooling cost, combat the urban island effect and alleviate the global warming. To achieve passive
daytime radiative cooling, current state-of-the-art solutions often utilize complicated multilayer
structures or a reflective metal layer, limiting their applications in many fields. Attempts have been
made to achieve passive daytime radiative cooling with single-layer paints, but they often require
a thick coating or show partial daytime cooling. In this work, we experimentally demonstrate
remarkable full daytime sub-ambient cooling performance with both BaSO4 nanoparticle films and
BaSO4 nanocomposite paints. BaSO4 has a high electron bandgap for low solar absorptance and
phonon resonance at 9 µm for high sky window emissivity. With an appropriate particle size and
a broad particle size distribution, BaSO4 nanoparticle film reaches an ultra-high solar reflectance
of 97.6% and high sky window emissivity of 0.96. During field tests, BaSO4 film stays more than
4.5°C below ambient temperature or achieves average cooling power of 117 W/m2. BaSO4-acrylic
paint is developed with 60% volume concentration to enhance the reliability in outdoor
2
applications, achieving solar reflectance of 98.1% and sky window emissivity of 0.95. Field tests
indicate similar cooling performance to the BaSO4 films. Overall, our BaSO4-acrylic paint shows
standard figure of merit of 0.77 which is among the highest of radiative cooling solutions, while
providing great reliability, the convenient paint form, ease of use and the compatibility with
commercial paint fabrication process.
TOC GRAPHICS
Radiative cooling has shown great promises to reduce the cost of space cooling in both
residential and commercial applications.1 Contrary to active cooling which requires electricity to
drive a refrigeration cycle, radiative cooling utilizes the atmospheric transparent window (the
“sky window”) to emit thermal radiation directly to the deep sky without consuming any
energy.2 Its passive nature has the potential to reduce the urban island effect and alleviate the
global warming. If the thermal emission through the sky window exceeds the solar absorption,
the surface can maintain cooler than ambient even under direct sunlight. Early studies of
radiative cooling paints lasted for decades, but none of the paints achieved full daytime radiative
cooling.2–11 Among these, one study showed 2°C below ambient cooling on a winter day with a
3
thin layer of TiO2 on aluminum substrate, but the high solar reflectance should primarily come
from the metal substrate rather than the paint itself.9 Many paints were based on TiO2 with low
particle concentration, and the radiative cooling performance was limited by insufficient solar
reflection due to the solar absorptance in the ultra-violet (UV) band. For this reason, wide
bandgap materials were explored as fillers 12,13 to eliminate the UV absorption, while their
smaller refractive index makes photon scattering weaker. Heat reflective paints have also been
developed, but their solar reflection is still limited below 91% and does not show full-daytime
sub-ambient cooling.11,14 Alternatively, photonic structures and multilayers have recently
demonstrated full daytime sub-ambient cooling capability, which stimulated renewed interest in
radiative cooling.15,16 Other studies explored scalable non-paint approaches such as dual layers
including a metal layer,1719 polyethylene aerogel 20 and delignified wood 21. However, these
approaches are limited in one or more aspects such as complicated structure, involvement of
metallic layer, and large thickness, preventing them from many applications. In light of this,
creating high-performance radiative cooling paints is still pertinent task. Recently, non-metal
dual-layer designs were proposed to consist of top TiO2 layer for solar reflectance and bottom
layer for thermal emission, which achieved partial daytime cooling without metallic
components.22,23 A compact film of SiO2 nanoparticles was fabricated as a single-layer coating
with partial daytime cooling capability.24 A polytetrafluoroethylene (PTFE) nanoparticle coating
with a silver layer reached a record-high solar reflectance of 99%.25 Paint-like porous polymers
were developed with full-daytime cooling.26 A strategy was proposed to further enhance the solar
reflectance in particle-matrix paint by adopting a broad particle size distribution rather than one
single size.27 Combining a broad particle size distribution and a high filler concentration, CaCO3-
acrylic paint was developed and demonstrated full daytime sub-ambient cooling.2830 Another
4
study also proposed high solar reflectance in wide bandgap nanoparticle paints with high filler
concentrations.31 Considering the existing studies, developing high-performance single-layer
coatings that are thin, low cost, easy to apply, and scalable is still a challenging and urgent task
to fully utilize radiative cooling in a wide range of applications.
In this work, we experimentally demonstrate full daytime sub-ambient cooling with BaSO4
nanoparticle film and BaSO4-acrylic paints. We choose BaSO4 due to its high electron bandgap
for low solar absorptance and phonon resonance at 9 µm for high sky window emissivity. By
adopting an appropriate particle size and a broad particle size distribution, we achieve a high
solar reflectance of 97.6% and a high sky window emissivity of 0.96 with BaSO4 nanoparticle
film. Field tests indicate surface temperature more than 4.5°C below ambient temperature or
average cooling power of 117 W/m2, among the highest cooling power reported. To enhance the
reliability of the coating, BaSO4-acrylic paint is developed with 60% volume concentration. The
high filler concentration and the broad particle size distribution are added to compensate the low
refractive index of BaSO4 compared to TiO2, leading to solar reflectance of 98.1% and sky
window emissivity of 0.95. During field tests, the BaSO4 paint yields similarly high cooling
performance. Our BaSO4-acrylic paint shows standard figure of merit of 0.77 which is among the
highest of radiative cooling solutions, while providing great reliability, the convenient paint
form, ease of use and the compatibility with commercial paint fabrication process. The results
were also included in a provisional patent filed on October 3, 2018 and a non-provisional
international patent application (PCT/US2019/054566) filed on October 3, 2019 and published
on April 9, 2020.29
Commercial white paints such as TiO2-acrylic paint failed to achieve full daytime cooling, which
is attributed to its high solar absorption in the UV band (due to the 3.2 eV electron bandgap of
5
TiO2) and near-infrared (NIR) band (due to acrylic absorption). In this work, we fabricated a
BaSO4 particle film with a thickness of 150 µm on a silicon wafer (Figure 1a) along with a
commercial white paint (DutchBoy Maxbond UltraWhite Exterior Acrylic Paint). An SEM
image of the BaSO4 film is shown in Figure 1b, where air voids were introduced in the film. The
interfaces between BaSO4 nanoparticles and air void enhance the photon scattering in the film,
thus increase the overall solar reflectance. To improve the reliability of the coating under long-
term outdoor exposure, a commercial paint form as the filler-matrix composite is often preferred.
A key challenge to adopt BaSO4 as a filler material in polymer matrix is the low refractive index
of BaSO4 compared to that of TiO2. To enable strong scattering in the composite, we adopted a
particle volume concentration of 60%, which is considerably higher than those in commercial
paints. Additionally, the broad particle size distribution contributes to the solar reflectance.27 The
BaSO4-acrylic nanocomposite paint is shown in Figure 1a with an SEM image in Figure 1c. The
addition of acrylic helps bond the fillers and leads to a better reliability. Some air voids were
present in the BaSO4 paint, which also increases the solar reflectance. The particle size
distribution (398 ± 130 nm) of the BaSO4 particles was characterized with SEM images.
Figure 1. Radiative cooling coatings and SEM images. (a) BaSO4 film sample, BaSO4-acrylic paint
sample and white commercial paint. The BaSO4 film is 150 µm thick on a silicon wafer. The BaSO4 paint
and commercial paint are free-standing samples with a thickness of 400 µm. All samples are 5 cm
squares. (b) An SEM image of the BaSO4 film sample. (c) An SEM image of the BaSO4-acrylic paint
sample with 60% filler concentration. (b,c) The particle size distribution (398 ± 130 nm) was estimated
based on the SEM images. Air voids were introduced in both the BaSO4 film and the BaSO4 paint.
6
To achieve full daytime sub-ambient cooling, both high solar reflectance (contributed by
particles) and high sky window emissivity (contributed by particles and/or matrix) are essential
as illustrated in Figure 2a. Here we adopted BaSO4 with a high electron band gap ~6 eV to
reduce the absorption in UV band. Due to a phonon resonance at 9 µm which is in the sky
window, engineering the particle size can allow a single layer of BaSO4 particle film to function
both as a sky window emitter and a solar reflector. Therefore, the matrix is not needed to achieve
daytime sub-ambient cooling. The lack of acrylic matrix also reduces the NIR absorption. The
average particle size of BaSO4 was chosen as 400 nm to reflect both visible and NIR range of the
solar irradiation. A broad particle size distribution was adopted to further enhance the solar
reflectance. Detailed theoretical and experimental studies can be found in previous studies.27,28
Overall, the BaSO4 film reached a solar reflectance of 97.6% and an emissivity of 0.96 in the sky
window, as shown in Figure 2b. The solar reflectance is significantly higher than the commercial
white paint (DutchBoy Maxbond UltraWhite Exterior Acrylic Paint, 400 µm thickness),
especially in the UV and NIR range. Although the DutchBoy paint is not a heat reflective
commercial paint, the solar reflectance of the BaSO4 film is still substantially higher than those
of the commercial heat reflective paints which show solar reflectance of around 80% to 91%.11,14
The reflectance is also higher than that of the recently reported CaCO3-acrylic paint.28,32 The
silicon substrate was intended only as a supporting substrate, not to increase the solar reflectance,
nor to emit in the sky window. To avoid the substrate effect on the cooling performance, we
characterized the thickness-dependent solar reflectance with different substrates, shown in
Figure 2c. Night-time cooling performance was also characterized with different substrates in the
Supplementary Note 1 and Figure S1. For the BaSO4 paint, a standalone paint sample of 400 µm
reached similar optical properties (98.1% solar reflectance, 0.95 sky window emissivity) with a
7
high filler concentration of 60% and a broad size distribution. A Monte Carlo simulation with
modified Lorentz-Mie theory was run to help illustrate the physics behind the strong solar
reflectance of the paint, and the results are shown in Figure 2d.27,28,33 With the same filler
concentration, the simulation demonstrated a broader particle size distribution further improved
the overall solar reflectance. The simulation slightly underestimated the solar reflectance as it
cannot capture the effect of air voids. The coating thickness of the BaSO4 paint sample was
400 µm, to ensure the optical properties were substrate independent. Thinner coatings were
fabricated on transparent polyethylene terephthalate (PET) film using a film applicator to control
the wet film thickness. With low transmittance of the paint films and similar refractive index
between the paint and the PET film, the PET substrate had a negligible effect on the solar
reflectance. With a thinner coating thickness of 200 µm, 224 µm and 280 µm, the solar
reflectance reached 95.8%, 96.2% and 96.8%, respectively (Figure 2e). Monte Carlo simulation
results showed a similar trend to the experimental data, both following the diffusion behavior of
the transmission.24,34 The simulation slightly underestimated the solar reflectance, likely because
the air voids introduced in the paint were not captured by the Monte Carlo simulation. Future
studies can aim to include such effect to predict the solar reflectance more accurately.
8
Figure 2. Radiative cooling schematic, spectral characterization results and Monte Carlo simulation on the
solar reflectance. (a) To achieve a high cooling power with passive radiative cooling, both high solar
reflectance and high sky window emissivity are needed. The solar reflectance is contributed by filler
materials, while the sky window emissivity can come from fillers and/or matrix. For particle films, the
particles have to both reflect solar light and emit in the sky window. (b) The emissivities of BaSO4 film and
BaSO4 paint were characterized, compared with commercial white paint (DutchBoy Maxbond UltraWhite
Exterior Acrylic Paint, thickness of 400 µm) from 0.25 µm to 20 µm. Both the particle film and
nanocomposite paint showed significant enhancement of solar reflectance while maintaining high sky
window emissivity. (c) The solar reflectances of the BaSO4 films with different thicknesses and substrates
were measured, demonstrating that the solar reflectance of the BaSO4 film at 150 µm is substrate
independent. (d) Monte Carlo simulation of the BaSO4 paint with 400 µm thickness demonstrated that both
high filler concentration and broad particle size distribution increased the overall solar reflectance. (e) The
solar reflectances of the BaSO4-acrylic paint with 60% particle concentration and different film thicknesses
were compared with the Monte Carlo simulation results. The thin paint coatings are supported by PET films.
Onsite field tests were performed to demonstrate the full daytime sub-ambient cooling of the
BaSO4 film. In Figure 3a, the BaSO4 film achieved full daytime cooling below the ambient
temperature with a peak solar irradiation of 907 W/m2 in West Lafayette, IN on March 14-16,
2018 with 42% humidity at noon. The temperature of the sample dropped 10.5°C below the
ambient temperature during the nights, and stayed 4.5°C below ambient even at the peak solar
irradiation, whereas the commercial paint rose 6.8°C above the ambient temperature. A direct
measurement of the cooling power in Reno, NV on July 28, 2018 showed that the cooling power
reached an average of 117 W/m2 over a 24-hour period with 10% humidity at noon, shown in
Figure 3b. We observed similar daytime cooling power to nighttime without solar irradiation,
both above 110 W/m2. Thermal emission power increases with higher surface temperature in the
9
daytime, which compensates the higher solar absorption. Thus, simply reporting the cooling
power without considering the surface temperature can be a misleading measure of the cooling
performance. In this case, the thermal emissive power of the BaSO4 film reaches 106 W/m2 at
15°C. Overall, our BaSO4 film can maintain a constant high cooling power regardless of the
solar irradiation. We further demonstrated the cooling performance of BaSO4 paint with onsite
field tests, as shown in Figure 3c and Figure 3d. The BaSO4 paint remained cooler than ambient
for more than 24 hours under the peak solar irradiation of 993 W/m2 (around 50% humidity at
12:00 PM). The cooling power measurement showed an average cooling power over 80 W/m2
with the surface temperature as low as -10°C, equivalent to a cooling power of 113 W/m2 at
15°C (see more details in the Supplementary Note 2).
Figure 3. Field test results of the BaSO
4
nanoparticle film and BaSO
4
-acrylic nanocomposite paint. (a) The
temperatures of the BaSO4 nanoparticle film and commercial white paint were compared to the ambient
temperature for over 24 hours. (b) The cooling power was directly measured for the BaSO4 nanoparticle
film using a feedback heater. (c) The temperature of BaSO4 paint was compared with the ambient
temperature. (d) The cooling power of BaSO4 paint was measured in both daytime and nighttime. The
orange regions stand for the solar irradiation intensity.
The figure of merit RC was used here to fairly access the radiative cooling performance
independent of weather conditions, as 28
10
 = − (1 − )
where  is the sky window emissivity,  is the solar reflectance, and is the ratio of the
solar irradiation power over the blackbody emissive power through the sky window. With
surface temperature of 300 K and set as 10, our BaSO4 film and BaSO4 paint reach the
standard RC of 0.72 and 0.77, respectively, which are higher than state-of-the-art radiative
cooling solutions as 0.32 16, 0.53 18, 0.35 19, 0.49 28, and 0.57 35.
To demonstrate the reliability of our BaSO4 paint, we conducted abrasion test, outdoor
weathering and viscosity characterizations. The abrasion tests were performed according to
ASTM D4060 with a Taber Abraser Research Model, and the results are shown in Figure 4a.36 A
pair of abrasive wheels were placed on the sample surface with 250 g load on each wheel. Mass
loss was measured, and wheel refacing was done every 500 cycles. The wear index was defined
as the weight loss (mg) for every 1000 cycles. The BaSO4 paint reached a wear index of 150,
comparable to the commercial exterior paint with wear index of 104. The weathering test was
conducted by exposing the BaSO4 paint outdoors for 3 weeks (Figure 4b). The solar reflectance
remained the same within the experimental uncertainty. The sky window emissivity was
measured to be 0.95 both at the beginning and the end of the testing period. Additionally, a
running water test was included in the Video S1. In Figure 4c, we measured the viscosity of the
BaSO4 paint, which was similar to the commercial paints.37 The Video S1 further demonstrated
that the BaSO4 paint was able to be brushed and dried similarly to the commercial paints. A
detailed cost analysis of the BaSO4 paint is included in the Supplementary Note 3.
11
Figure 4. Reliability tests of the BaSO
4
paint. (a) Abrasion tests were conducted with BaSO
4
paint and
commercial exterior paint according to ASTM D4060.36 Our BaSO4 paint demonstrated comparable
abrasion resistance with commercial exterior paint. (b) We exposed the BaSO4 paint outdoor for a 3-week
period. (c) The viscosity of the BaSO4 paint was characterized and compared with those of the commercial
paints.37
In this work, we experimentally demonstrate full daytime radiative cooling with BaSO4
nanoparticle film and BaSO4-acrylic nanocomposite paint. By adopting an appropriate particle
size and a broad particle size distribution, we achieve a high solar reflectance of 97.6% and high
sky window emissivity of 0.96 with BaSO4 nanoparticle film. Onsite field tests indicate surface
temperature more than 4.5°C below ambient temperature or average cooling power of 117 W/m2,
among the highest cooling power reported. To enhance the reliability of the coating, BaSO4-
acrylic paint is developed with 60% volume concentration. The high filler concentration and
broad particle size distribution help reach 98.1% solar reflectance and 0.95 sky window
emissivity. During field tests, the BaSO4 paint yields similarly high cooling power while
providing great reliability, convenient paint form, ease of use and the compatibility with
commercial paints.
METHODS
BaSO4 Nanoparticle Film and BaSO4-Acrylic Paint Fabrication
A BaSO4 particle film of 150 µm thickness was fabricated on a silicon wafer. 400 nm BaSO4
particles, deionized water and ethanol were mixed with a mass ratio of 2:1:1 and coated on the
12
substrate until fully dried. The average particle size was chosen as 400 nm to reflect both visible
and near infrared range of the solar irradiation. To fabricate the BaSO4-acrylic nanocomposite
paint, Dimethylformamide and BaSO4 nanoparticles (400 nm diameter, US Research
Nanomaterials) were mixed and ultra-sonicated for 15 minutes with a Fisherbrand Model 505
Sonic Dismembrator. The mixture was degassed to remove air bubbles introduced during the
ultra-sonication process. Acrylic (Elvacite 2028 from Lucite International) was then slowly
added and mixed until fully dissolved. The mixture was poured into a mold to be left fully dried
overnight, resulting in a free-standing layer with a thickness of 400 µm to eliminate the substrate
effect on the overall coating performance. A series of thinner coatings of the BaSO4 film and
paint were also prepared with film applicators (BYK Film Applicator) to study the effect of
coating thickness. The dry film thickness was measured with a coordinate measuring machine
(Brown&Sharp MicroXcel PFX).
Spectral Emissivity Characterization
The solar reflectance from 250 nm to 2.5 µm was measured with a Perkin Elmer Lambda 950
UV-Vis-NIR spectrometer with an integrating sphere. A certified Spectralon diffuse reflectance
standard was used, and the solar reflectance was calculated based on the AM 1.5 solar
spectrum.38 The uncertainty of the solar reflectance was 0.5%, based on the measurement of five
samples. The emissivity from 2.5 µm to 20 µm was characterized with a Nicolet iS50 FTIR with
a PIKE Technology integrating sphere. The sky window emissivity was calculated based on the
atmospheric transparent window of air mass 1.5 and water column 1.0 mm (IR Transmission
Spectra, Gemini Observatory). The uncertainty of 0.02 was estimated based on the PIKE
Technologies Mid-IR diffuse reflectance standard.
13
Field Test
There are two field testing setups made for cooling performance characterization on a building
roof, as shown in Figure 5. Similar characterization setups were used in previous studies.2830
The setups were created from a block of white Styrofoam for thermal insulation and enclosed by
silver mylar to reflect solar irradiation. A pyranometer (Apogee SP-510) was adopted to measure
solar irradiation. The temperature measurement setup (Figure 5a) monitored the sample and
ambient temperatures with T-type thermocouples. A thin layer of low-density polyethylene
(LDPE) film functioned as a transparent cover against forced convection. The cooling power
characterization setup (Figure 5b) included a feedback heater to characterize the cooling power
by heating the samples to the ambient temperature, which minimized heat conduction and
convection. Transparent side cover was added to reduce forced convection. Photo of both setups
are shown in Figure 5c. They were placed on a high-rise table to eliminate heating from the
ground.
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Figure 5. Field test setups for cooling performance characterization. (a) The samples were suspended in
the Styrofoam cavity to minimize thermal conduction and forced convection. The sample and ambient
temperatures were monitored during the temperature measurement. (b) To directly measure the cooling
power of the sample, a feedback heater was included to heat the sample to the ambient temperature. The
measured power consumption of the heater was the cooling power of the sample. (c) Photos of the field
test setups. Both setups were located on a high-rise table to avoid ground heating effect.
Monte Carlo Simulation
The Monte Carlo simulations were performed according to the modified Lorentz-Mie theory 27
and a correction 33 of dependent scattering effect due to high concentrations. Photon packet is
released at the top of the nanocomposite. The photon starts with a weight of unity and a normal
direction to the air-composite interface. If the photon propagates to the bottom interface and
makes it through, we consider that weight as transmitted. If the photon travels to the top surface
and goes back to the air space above the medium, it is considered reflected. A total of 500,000
photons were used in each simulation, covering 226 wavelengths from 250 nm to 20 µm.
ASSOCIATED CONTENT
The supporting information includes Supplementary Note 1, 2, 3, Figure S1, S2 and Video S1.
Supplementary Note 1: Substrate-dependence of the BaSO4 film samples
15
Supplementary Note 2: Energy balance model for the cooling power characterization
Supplementary Note 3: Cost analysis of the cooling paint
Figure S1. The effect of substrate on the sub-ambient sample temperature of the BaSO4 film
Figure S2. The theoretical cooling power compared with experimental measurements of the BaSO4
film and BaSO4 paint
Video S1. Brushing, drying and water running test of the BaSO4 paint
AUTHOR INFORMATION
Corresponding Author
Xiulin Ruan, Email: ruan@purdue.edu
URL: https://engineering.purdue.edu/NANOENERGY/
Author Contributions
Conceptualization, X.R.; Methodology, X.R., X.L. and J.P.; Investigation, X.L., J.P. and P.Y.;
Writing - Original Draft, X.R. and X.L.; Writing - Review & Editing, X.R., X.L., J.P. and P.Y.;
Funding Acquisition, X.R.; Resources, X.R.; Supervision, X.R. The manuscript was written
through contributions of all authors. All authors have given approval to the final version of the
manuscript.
Notes
The authors declare the following financial interests/personal relationships which may be
considered as potential competing interests: X.R., X.L. and J.P. are the inventors of an
international patent (PCT/US2019/054566) on the basis of the work described here.
16
ACKNOWLEDGMENT
The authors thank Dr. Mian Wang, Jacob Faulkner, Xuan Li, Nathan Fruehe, Daniel Gallagher
and Professor Zhi Zhou at Purdue University for their help on sample fabrication and
characterization. This research was supported by the Cooling Technologies Research Center at
Purdue University and the Air Force Office of Scientific Research through the Defense
University Research Instrumentation Program (Grant No. FA9550-17-1-0368).
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1
Supplementary Note 1: Substrate-dependence of the BaSO4 film samples
The 150 µm BaSO4 film was coated on a silicon substrate, which only functioned as a
supporting substrate, not to enhance the solar reflectance, nor to emit in the sky window. The
substrate effect on the sub-ambient sample temperature is shown in Figure S1, where the
different substrates had a negligible effect on the nighttime cooling performance of the 150 µm
BaSO4 film.
Figure S1. The effect of substrate on the sub-ambient sample temperature of the BaSO4 film.
The nighttime cooling performance of 150 µm BaSO4 film on different substrates was
measured and compared to a carbon black sample. All samples showed similar cooling
performance, indicating the sky window emissivity was not affected by the substrate of the
BaSO4 film.
Supplementary Note 2: Energy balance model for the cooling power characterization
Using the temperature profiles in the direct cooling power characterization, we can analyze the
cooling power and compare to the measured cooling power for validation. The net cooling
power
𝑞!""#$%&
'
according to the energy balance model is
𝑞!""#$%&
'=()!
*
+,
+- 𝛼𝐺 + 𝑞./+$/-$"%
'(𝑇)
where
𝐴
is the surface area of the sample,
()!
*
+,
+-
accounts for the transient heat transfer due to
the thermal mass of the sample and the heater,
𝛼
stands for the solar absorption of the sample,
𝐺
represents the solar irradiation,
𝑞./+$/-$"%
'(𝑇)
is the emissive power through the sky window,
and
𝑞!""#$%&
'
is the net cooling power.
𝑞./+$/-$"%
'(𝑇)
term is mostly contributed by the thermal
2
emission through the sky window, while the radiative exchange between the sample and the
ambient is negligible. Because the sky window emission is highly dependent on the weather
condition,
𝑞./+$/-$"%
'(𝑇)
is first calibrated with the nighttime cooling power measurement,
which were 106 W/m2 and 113 W/m2 at 15˚C during the field tests for BaSO4 film and BaSO4
paint, respectively. Using the experimentally measured
𝛼
,
𝐺
,
𝑇
, the theoretical net cooling
power was modeled and compared with measured results in Figure S2. The model results agree
reasonably well with the experimental measured cooling power, validating our field test results.
Figure S2. The theoretical cooling power compared with experimental measurements of the
(a) BaSO4 film and (b) BaSO4 paint. The sky window emissive power was calibrated based on
nighttime cooling power first, and the net cooling power was then estimated based on the
experimental measured temperature profiles, solar irradiation and solar reflectance.
Supplementary Note 3: Cost analysis of the cooling paint
BaSO4 is available in the natural mineral barite, and widely used in different industrial fields as
radiocontrast agent, paper brightener and main components in cosmetic products [3]. BaSO4
powders cost only $0.44 per kilogram [4], which is about half the price of TiO2 powders ($1 per
kilogram) [5]. Assuming a 30˚ roof angle and 300 µm paint thickness, the cost of the BaSO4
fillers reaches around $100 for a 150 m2 house. With a similar fabrication process to the
commercial paints, the BaSO4 paint will reach a comparable price as the commercial white
paint.
In the literature, a comprehensive test was performed with commercial white roofing materials
(85% solar reflectance) during one-month period in the summer, and concluded the energy
saving was 40 to 75 Wh/m2/day [6]. The BaSO4 cooling paint achieved a higher solar
3
reflectance of 96.8% to 98.1%, leading to a total energy saving over 80 Wh/m2/day, assuming
daily solar energy as 5000 Wh/m2/day and the AC stock average efficiency as 15. With the
electricity cost about $0.1 per kWh, the monthly cooling cost saving can be $36 for a moderate
150 m2 house.
References
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S.E. Han, Effective Radiative Cooling by Paint-Format Microsphere-Based Photonic
Random Media, ACS Photonics. 5 (2018) 1181–1187.
https://doi.org/10.1021/acsphotonics.7b01492.
[3] E. Wiberg, Inorganic chemistry, 1st English ed. /, Academic Press ;;De Gruyter, San
Diego  ;Berlin ;;New York, 2001.
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supplier-white-powder-grinding-
98_62409878694.html?spm=a2700.7724857.normalList.2.1d8b5d04CARDNj&s=p&f
ullFirstScreen=true (accessed August 30, 2020).
[5] Titanium Dioxide Price, (n.d.). https://www.alibaba.com/product-detail/High-Quality-
R-258-Titanium-Dioxide_62086879229.html (accessed August 15, 2020).
[6] H. Akbari, R. Levinson, L. Rainer, Monitoring the energy-use effects of cool roofs on
California commercial buildings, Energy Build. 37 (2005) 1007–1016.
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ResearchGate has not been able to resolve any citations for this publication.
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