SSasdfsdfgsdfgdfgsdfgdfgsdfgsdfgsdfgdsR.pdf

- 1 -
Submitted to International Journal of Thermal Sciences, Sep. 26, 2023
Performance evaluation and optimization of nanocomposite films incorporating
CWO and ITO nanoparticles for energy-saving window applications
Haojun Zhu1,2, Kai Lu1,2, Lechuan Hu1,2, Yan Zhou1,2, Chengchao Wang1,2**, Lanxin Ma1,2
1School of Energy and Power Engineering, Shandong University, Jinan, Shandong, 250061, China
2Optics & Thermal Radiation Research Center, Institute of Frontier and Interdisciplinary Science, Shandong
University, Qingdao, Shandong, 266237, China
Abstract
Coatings with near-infrared (NIR) shielding are attracting attention in the field of energy-saving windows
due to their ability to reduce the amount of heat that enters the room in summer. Cesium tungsten oxide
(Cs0.32WO3) and Indium tin oxide (ITO) nanoparticles are potential candidates for energy-efficient windows
due to their high transmittance in the visible light range and remarkable shielding ability in almost the whole
NIR range. However, the optical properties, performance evaluation, and optimal design of spectrally selective
coatings based on these two nanoparticles have rarely been systematically studied. In this work, the radiative
properties of spherical and cylindrical CWO and ITO nanoparticles doped in different background media
(polydimethylsiloxane (PDMS), polymethyl methacrylate) (PMMA), and silicon dioxide (SiO2)) based on the
Lorenz-Mie and T-matrix theories are investigated, and spectral responses of CWO and ITO nanocomposite
films are calculated by solving the radiative transfer equation (RTE) using the Monte Carlo method. The effects
of different geometric parameters (shape, effective radius reff, size distribution (veff), and volume fraction (fv))
of CWO and ITO nanoparticles on the spectral responses are systematically analyzed. The results show that
the cylindrical nanoparticles embedded in nanocomposite films with improved NIR shielding ability can be
better than spherical nanoparticles. Evaluated by performance metrics, the nanocomposite films doped with
cylindrical CWO nanoparticles (reff = 50 nm, fv = 0.4%) and cylindrical ITO nanoparticles (reff = 20 nm, fv =
0.6%) achieve high visible light transmittance (Tlum > 60%) and high NIR shielding ability (TNIR < 10%). This
work provides a reference basis for the design of energy-efficient windows and promotes the
commercialization of energy-efficient windows.
Keywords: Localized surface plasmon resonance, NIR light shielding, Nanocomposites, Energy-saving
windows;
* Corresponding author.
** Corresponding author.
E–mail addresses: sduwcc18@sdu.edu.cn (C. Wang), malanxin@sdu.edu.cn (L. Ma).
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4587820
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 2 -
1. Introduction
International Energy Agency (IEA) reported, in 2021, the operation of buildings will account for 30% of
global final energy consumption. However, more than half of building energy consumption is used for indoor
climate control, and cooling energy consumption accounts for more than 70% of building energy consumption
[1, 2]. Energy-saving window with selective coatings effectively reduces energy consumption in building
cooling by decreasing solar gain (absorption or reflection of near-infrared (NIR) light) [3, 4]. Many studies
have been conducted on spectral selective films, in which mixing nanoparticles with transparent resin with
thermal insulation provides selective absorption/reflection of NIR range and ensures suitable visible light
transmittance, which is well applied to energy-saving windows [5-7].
Noble metal nanoparticles, transparent conductive metal oxides (TCO), and alkali-doped tungsten oxide
(MxWO3) nanoparticles exhibit localized surface plasmon resonance (LSPR) and effectively enhance light
absorption and scattering, enabling their nanocomposite films to obtain strong NIR shielding ability and reduce
solar radiation transmittance through windows [8-11]. Silver (Ag), as the most commonly used spectral
selective metal, is doped in polymethyl methacrylate (PMMA) to form nanocomposite films, which can
achieve excellent radiative shielding performance with visible light transmittance above 50% and radiation
transmittance controlled below 20% [12, 13]. However, the application of the materials mentioned above is
limited by technical and cost constraints due to the high production requirements of their particle shape and
size. Ag nanowires (AgNWs) have the advantages of one-dimensional properties, simple fabrication, and high
visible light transmittance, which is well used for solar spectral selective coatings [14]. Spraying a mixture of
AgNWs and polyvinyl butyral (PVB) on the window has shown excellent visible light transmittance (83%)
and low emissivity with low cost (minimal use of silver) [15]. Compared with the transmittance of about 63.3%
when AgNWs are separately coated on polydimethylsiloxane (PDMS), they significantly improve the
transmittance [16, 17]. Although Ag nanocomposite films achieve good energy savings, there are limitations
in commercial applications due to their high cost and macroscopic instability of metal nano-surfaces [15, 18].
Comparatively, TCO and MxWO3 nanoparticle-based complexes can overcome the drawbacks of Ag
nanoparticles, such as higher cost, susceptibility to environmental impact, and technical difficulties in
fabrication. For MxWO3 nanoparticles, Cesium tungsten oxide (Cs0.32WO3) shows great promise as a solar
filter because it combines excellent NIR shielding ability with a high visible light transmittance, which is
required for superior solar spectral selective materials on windows [10, 19]. It is well known that CWO will
degrade in humid thermal environments limiting its commercial application [20]. However, nanocomposite
films synthesized by doping CWO nanoparticles in PMMA media will withstand high temperatures and humid
environments, while exhibiting high visible light transmittance ( > 70%) and high NIR shielding ability, which
are further considered for commercial applications [21]. The nanocomposite films are prepared by dispersing
the core-shell structured CWO@ polydopamine (PDA) nanoparticles in polyvinyl alcohol (PVA) medium to
ensure specific visible light transmittance (60%) and high NIR shielding ability (85.5%) and stability in humid
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 3 -
environments. [20]. Furthermore, although high NIR shielding ability is achieved by coating polyethylene
terephthalate (PET) surfaces with CWO films, nanocomposite films formed by embedding CWO nanoparticles
in PET can significantly reduce the photochromic effect and improve the stability of the material [10, 22]. In
addition, among numerous TCO materials, Indium tin oxide (ITO) combines high transmittance in the visible
range, high shielding ability in the NIR range, and high absorption in the ultraviolet area, making it a potential
material for energy-efficient windows [23-25]. Earlier, it has been shown that powerful NIR shielding coating
films are prepared by dispersing ITO nanoparticles (NPs) in a silica matrix and maintaining high visible light
transparency (80%) [26]. Moreover, nanocomposite films formed by doping a low volume fraction of ITO
particles in polyvinyl butyral (PVB) absorb about 100% of the Ultraviolet (UV) light while ensuring a
transmittance of more than 70%, which improves the shielding effect by 80% compared with pure PVB [27].
It can be seen from the above studies that nanoparticle films doped with nanoparticles with localized
plasmon resonance are widely studied because they can ensure high visible transmittance while effectively
shielding NIR light. Currently, most theoretical research on these nanocomposite films only analyzes one type
of CWO and ITO nanocomposite films, lacking comprehensive comparison and performance analysis of
nanocomposite films doped with different nanoparticles. In this work, the radiative properties of spherical and
cylindrical CWO and ITO nanoparticles are firstly investigated based on Lorenz-Mie theory and T-matrix
respectively, and the spectral responses of CWO and ITO nanocomposite films are studied by using the Monte
Carlo method. The effects of geometrical parameters (mainly including the shape, size, and volume fraction
of nanoparticles) on the optical properties of nanocomposite films are analyzed comprehensively. Then, the
best nanocomposite film doped with nanoparticles of different shapes is evaluated by performance metrics to
achieve high visible light transmittance and excellent NIR shielding ability, which provides a reference for the
practical application of energy-saving windows.
2. Model and Methods
The schematic diagram of the working principle of the nanocomposite film is represented in Fig. 1. As
shown in Fig. 1(a), the nanocomposite film on a transparent glass selectively transmits the visible wavelength
range of 0.38–0.78 μm and isolates the NIR wavelength range of 0.78–2.5 μm, reducing the heat energy into
the indoor environment to achieve energy saving in summer. The spectral selective coating is a thin film doped
with CWO/ITO nanoparticles, as shown in Fig. 1(b). It can be perceived that absorbing NIR light through
CWO/ITO nanoparticles can reduce the increase in indoor heat. Fig. 1(c–d) show the characteristics of the size
and shape of CWO and ITO nanoparticles purchased on the market. CWO nanoparticles are in the form of
unevenly sized sheets (similar to spheres or columns), while ITO nanoparticles are in the form of relatively
uniform rods. Therefore, the shape of nanoparticles is approximated as cylinders and spheres for subsequent
calculations. In addition, for the convenience of analysis, gamma distribution was used to analyze the effect of
different particle size distributions on nanocomposite films. Fig. 1(b) clarifies three geometric parameters of
nanoparticles: shape, size, and volume fraction (fv) as variables. In this work, we calculate the optical properties
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 4 -
of the spherical nanoparticles with different radii (r) by Lorenz-Mie theory [28, 29] and the cylindrical
nanoparticles with different aspect ratio (AR = L/D (length/diameter)) and volume-equivalent sphere radius
(reff) by the T-matrix method [29]. Then the spectral responses of the nanocomposite films are obtained by
solving the RTE using the Monte Carlo method. Finally, the excellent performance of energy-saving
nanocomposite films is demonstrated through the evaluation by performance metrics.
Fig. 1. (a) Spectral selective film on the window. (b) Schematic diagram of the principle of spectrally selective films
applied to energy-saving windows. (c) SEM images of CWO nanoparticles. (d) SEM images of ITO nanoparticles.
2.1 The theoretical model of individual nanoparticles
2.1.1 Radiative properties of a single nanoparticle
The radiative properties of individual nanoparticles are fundamental to solving the radiative transfer of
nanoparticle systems. Lorentz-Mie theory combined with the complex refractive index of individual particles
and background media is used to calculate the radiative properties of nanoparticles. The scattering and
extinction cross-sections can be obtained by using the following equations [28, 29]:
(1)
(2)
where nm is the real part of the refractive index of the background medium, and k1 = 2πnm/λ is the wave number
in the background medium. an and bn are the Lorenz-Mie coefficients. The scattering phase function presents
Energy-saving window Infrared :0.76—2.5 μm
Visible :0.36—0.76 μm
Spectral selective
transmittance film
(a)
(c) (d)
h
fv
r
Infrared
Visible
h
fv
reff
(b)
L
D
 
2 2
sca,Mie 2
1
1
2
(2 1) n n
n
C n a b
k


  


ext,Mie 2
1
1
2
(2 1)Re( )
n n
n
C n a b
k


  


P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 5 -
the spatial scattering energy distribution, which is described as follows [28, 29]:
(3)
where S11 and S22 are the amplitude scattering matrix elements.
T-matrix is one of the most powerful and widely used tools for rigorously computing electromagnetic
scattering by single and compounded particles, which can be used to calculate the radiative properties of
individual cylindrical nanoparticles. The scattering and extinction cross-sections can be obtained by using the
following equations [29]:
(4)
(5)
where T(P) is the elements of the T-matrix computed in the particle reference frame. The scattering phase
function is described as [29]:
(6)
where Ω is the solid angle.
The conventional gamma distribution is used here to represent particle size distribution for polydisperse
systems. The gamma distribution function, n(r), is as described by Hansen and Travis [30]:
(7)
(8)
(9)
where a and b correspond to the effective radius reff and the effective variance veff, when rmin = 0 and rmax = ∞.
The size distribution with veff = 0 corresponds to the monodisperse case. 〈G.〉r represents the average area of
the geometric projection of each particle.
The average-ensemble extinction and scattering coefficient factors for each particle can be calculated as
follows [29]:
(10)
2 2
p,Mie 11 22
sca
2
( ) [| ( ) | | ( ) | ]
S S
C

     
11 22
ext,T 2
1
1
2
Re [ ( ) ( )]
n
mnmn mnmn
n m n
C T P T P
k

 
  
 

' 2 2
2
sca,T ' '
2
1 ' 1 ' ' 1 1
1
2
| ( )|
n n
kl
mnm n
n m n n m n k l
C T P
k
 
     
     

p,T
d
4π
( )
d
sca
sca
C
C
 


(1 3 )
( ) constant exp , (0,0.5)
b
b
r
n r r b
ab


 
   
 
 
max
min
3
eff
1
( )

  r
r
r
r r n r dr
G

m
ma
i
x
n
2 2
eff eff
2
eff
1
( ) ( )
 
  
r
r
r
v r r r n r dr
G r

i
max
m n
ext ex ext
1
t
( ) ( ) ( )
)
(
r
N
r
i i
i
i
r
C n r C r dr u n r C r

 
   
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 6 -
(11)
where ri and ui are the division points and weights of the quadrature formula, respectively, on the interval [rmin,
rmax], and Nr is the number of quadrature division points.
This geometrical interpretation of the extinction cross-section illustrates the basic principle of introducing
an extinction dimensionless efficiency factor. The scattering factor Qsca is defined as the ratio of the scattering
cross-section 〈Csca〉 to the geometrically projected area of the scattering in the direction of incidence, and the
extinction factor Qext and the absorption factor Qabs are defined in the same way as the scattering factor Qsca as
follows [29]:
(12)
(13)
(14)
2.2 Optical properties of nanoparticle systems
For nanocomposite films composed of nanoparticles doped in different background media, the total
radiative/optical properties of the nanoparticle system can be calculated by the following equations [13, 31]:
(15)
(16)
(17)
where μsca, μext, and Φ(θ) are the scattering coefficient, extinction coefficient, and scattering phase function of
nanoparticle systems, respectively; μsca,p and μext,p is are the scattering coefficient and extinction coefficient of
nanoparticles, respectively. μext,m = 4πκ/λ is the extinction coefficient of the background medium, κ is the
imaginary part of the refractive index of the background medium; fv is the volume fraction of nanoparticles;
and 〈V〉r is the average volume per particle. The refractive index data of background media PDMS, PMMA,
and SiO2 and nanoparticles CWO, ITO are obtained from Ref. [32-36], which all are shown in Fig. 2(a–b).
i
max
m n
sca sc sca
1
a
( ) ( ) ( )
)
(
r
N
r
i i
i
i
r
C n r C r dr u n r C r

 
   
ext
ext
r
C
G
Q



 
abs
abs
r
C
G
Q



 
sca
sca
r
C
G
Q



 
max
min
sca sca,p 0 sca sca
( ) ( ) 
  
r
v
r
f
n n r C r dr C
V
 
ext ext,p ext,m ext ext,m
   
v
f
C
V
   
max
min
0
p
sca
( ) ( , ) ( )
  

r
r
n
r n r

 
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 7 -
Fig. 2. Optical constants of (a) CWO and ITO nanoparticle and (b) PDMS, PMMA, and SiO2.
2.3 Spectral responses of nanocomposite functional films
Based on the results of the radiative properties derived in the previous section, the radiative energy
transfer can be calculated by solving the radiative transfer equation (RTE) using the Monte Carlo method [31,
37, 38]:
(18)
where λ is the wavelength; Iλ(s) is the spectral radiation along the optical path s; Ibλ(s) is the black body emission
of the medium; Ω is the solid angle.
An infinite beam of light is vertically incident from the air to the upper boundary of the layer of the
nanocomposite films. Transmission at the boundary is considered using Snell's law and Fresnel's relation [31].
After interacting with the layer, the transmitted photons are collected. The hemispheric transmittance T(λ) can
be calculated as follows:
(19)
where N0 is the total number of photons incident on the layer, and Nt is the number of photons collected using
the detectors positioned in the hemispherical space outside the upper surface.
2.4 Performance metrics
To evaluate the optical performance of building windows, the luminous transmittance Tlum, the solar
energy transmittance Tsol, and the infrared transmittance TNIR are considered [39]:
(20)
0.5 1.0 1.5 2.0 2.5
0
2
4
6
8
10
n
Wavelength, λ (μm)
CWO-n
ITO-n
0
2
4
6
8
10
CWO-k
ITO-k
k
0.5 1.0 1.5 2.0 2.5
1.3
1.4
1.5
1.6
1.7
1.8
n
PDMS-n
PMMA-n
SiO2-n
0.5
1.0
1.5
2.0
2.5
0
k
PDMS-k
PMMA-k
SiO2-k
×10-3
(a) (b)
 
         
sca
ext ext sca 4
,Ω Φ Ω,Ω Ω
4
b
dI s
I s I s I s d
ds

   
 


 
 

  


  

t
2
0
( ) 
N
T
N


780nm
380nm
lum 780nm
380nm
( ) ( )
( )
  
 



T V d
T
V d
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 8 -
(21)
(22)
where I(λ) is the spectral radiation at AM1.5 (corresponding to the sun standing 37° above the horizon) [40];
V(λ) is the visual luminous efficiency function.
To comprehensively evaluate the optical performance of nanocomposite films, both the light harvesting
and thermal radiation shielding effects of the nanocomposite film are considered. The ideal energy-saving
window needs to have enough transmittance in the visible range and a strong blocking ability for the UV and
NIR ranges to reduce the excess heating in the room. Therefore, the evaluation factor Z is used to evaluate the
spectral performance, which is defined as [41]:
(23)
where TUV, TVIS, and TNIR are the transmittance of UV, visible, and NIR light, respectively. For an ideal case,
windows with a Z closer to 1 represent better performance.
3. Results and discussion
3.1 Model and validation
To verify the accuracy of the computational model in this work, we use the Lorenz Marie theory, the T-
matrix method, and the discrete dipole approximation (DDA) method to calculate the extinction factors of
spherical and cylindrical CWO nanoparticles, respectively [13]. As shown in Fig. 3(a), the calculation results
of DDA are in good agreement with the Lorenz-Mie theory and the calculation results of the T-matrix.
Subsequently, the accuracy of the Monte Carlo is validated by contrasting with Huang and Ruen’s study [42].
The spectral reflectance of the coating is verified when the radii of TiO2 nanoparticles are 0.1 and 0.4 μm,
respectively. The model results are matched well with the reference results as shown in Fig. 3(b), indicating
that our computational model has high accuracy.
2500nm
300nm
sol 2500nm
300nm
( ) ( )
( )
  
 



T I d
T
I d
2500nm
780nm
NIR 2500nm
780nm
( ) ( )
( )
T I d
T
I d



  
 
380nm 780nm 2500nm
UV VIS NIR
300nm 380nm 780nm
380nm 780nm 2500nm
300nm 380nm 780nm
(1 ) ( ) ( ) (1 ) ( )
( )( )( )
( ) ( ) ( )
 

  
  
T I d T V d T I d
Z
I d V d I d
     
     
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 9 -
Fig. 3. (a) Model validation of the method for calculating the radiative properties of a single CWO particle. (b) Model
validation of the Monte Carlo method.
3.2 Effects of different geometrics parameters on the optical properties of spherical nanoparticle systems
3.2.1 The effects of radius and background media on the radiative properties of individual nanoparticles
In this section, we focus on the effect of nanoparticle size and background media on the radiative
properties of monodisperse nanoparticles. Firstly, the extinction factor Qext, absorption factor Qabs, and
scattering factor Qsca of monodisperse spherical CWO and ITO nanoparticles in different background media
based on the theoretical model mentioned above are represented in Fig. 4. Different background media have a
slight impact on the radiative properties of nanoparticles. The main reason is that the imaginary part of the
refractive indices k of PDMS, PMMA, and SiO2 in the 0.3–2.5 μm range are all close to 0 and the real part of
the refractive index n only differs slightly. Therefore, PDMS is chosen as the background medium for the
subsequent analysis.
The Qext of both CWO and ITO nanoparticles has two main peaks as shown in Fig. 4. From Fig. 4 (a–c),
it can be seen that the extinction peak of CWO nanoparticles in the short wave range is the result of the
combined effect of absorption and scattering. The extinction peak at wavelengths around 1.25 μm is mainly
due to the absorption of CWO nanoparticles, while scattering is almost negligible. The extinction peak of ITO
nanoparticles in the short wave range is mainly caused by scattering, while the main extinction peak in the
near-infrared range is due to absorption, as seen in Fig. 4(d–f). By changing the radius of the nanoparticles,
the radiative properties of the nanoparticles are changed. The extinction peak position of CWO nanoparticles
with different radii hardly changes, but the peak intensity gradually increases as the particle radius changes
from 10 nm to 70 nm. The scattering peak in the short wave range of ITO nanoparticles significantly enhances
as the radius increases. In addition, it also can be seen from Fig. 4(e) that small absorption peaks appear in the
visible range, which will affect the visible transmittance of ITO nanocomposite films.
(a) (b)
0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Extiction
factor,
Q
ext
T-matrix
DDA
AR = 1
reff = 10 nm
Mie
DDA
r = 20 nm
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
r = 0.1 m
r = 0.4 m
Huang and Ruan [42]:
r = 0.1 m
r = 0.4 m
Reflectance
(%)
Wavelength,  (m)
Our model:
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 10 -
Fig. 4. The radiative properties of monodisperse spherical nanoparticles with different radii in PDMS, PMMA, and SiO2
background media, respectively. (a) Extinction, (b) asorption, and (c) sattering factors of CWO nanoparticles. (d)
Extinction, (e) absorption, and (f) scattering factors of ITO nanoparticles.
Fig. 5 shows the influence of particle size distributions on the radiative properties of polydisperse CWO
and ITO nanoparticles with different effective variance veff and effective radii. With the increase of veff, it can
be seen that the radiative properties of CWO nanoparticles have little change when fixing reff, as shown in Fig.
5(a–c). For example, the radiative properties are similar at different veff with reff = 40 nm. For ITO nanoparticles,
the effect of particle size distribution is mainly in the short wave range is shown in Fig. 5(d–f). At small particle
sizes (reff = 20 nm), the effect of veff on radiative properties is minimal, but as the reff increases, veff significantly
affects the radiative properties of nanoparticles in the short wave range, whereas the radiative properties of
nanoparticles have little change in the NIR range.
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4
0.0
1.5
3.0
4.5
6.0
7.5
Extinction
factor,Q
ext
CWO
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4
0.0
1.5
3.0
4.5
6.0
7.5
Absorption
factor,Q
abs
CWO
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4
0.0
1.5
3.0
4.5
6.0
7.5
Scattering
factor,Q
sca
CWO
(b) (e)
(c) (f)
(a) (d)
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4
0.0
1.5
3.0
4.5
6.0
7.5
Absorption
factor,Q
abs
10/PDMS
10/PMMA
10/SiO2
30/PDMS
30/PMMA
30/SiO2
50/PDMS
50/PMMA
50/SiO2
70/PDMS
70/PMMA
70/SiO2
ITO
Particle radius, r (nm)
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4
0.0
1.5
3.0
4.5
6.0
7.5
Extinction
factor,Q
ext
10/PDMS
10/PMMA
10/SiO2
30/PDMS
30/PMMA
30/SiO2
50/PDMS
50/PMMA
50/SiO2
70/PDMS
70/PMMA
70/SiO2
ITO
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4
0.0
1.5
3.0
4.5
6.0
7.5
Scattering
factor,Q
sca
10/PDMS
10/PMMA
10/SiO2
30/PDMS
30/PMMA
30/SiO2
50/PDMS
50/PMMA
50/SiO2
70/PDMS
70/PMMA
70/SiO2
ITO
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 11 -
Fig. 5. The effect of particle size distribution on radiative properties of polydisperse spherical nanoparticles. (a) Extinction,
(b) absorption, and (c) scattering factors of CWO nanoparticles. (d) Extinction, (e) absorption, and (f) scattering factors
of ITO nanoparticles.
3.2.2 The effects of geometrical parameters on spectral responses of nanocomposite functional films
To clarify the effects of geometrical parameters of nanoparticles on the nanocomposite films, we analyze
in detail the optical response of nanocomposite films with the thickness h = 50 μm under different volume
fractions fv, particle radius r, and particle size distribution of nanoparticles. The effect of background media
and fv are first analyzed on the spectral response of monodisperse nanocomposite films. As shown in Fig. 6,
background media have little effect on the spectral transmittance of the nanocomposite films. For
nanocomposite films of PMMA background media, the spectral transmittance has significant fluctuations after
2 μm reducing transmittance in the NIR range as shown in Fig. 6(b) and (e), mainly due to the excessive
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Aborsorption
factor,Q
abs
ITO
veff = 0.01 reff = 20 nm
Variance, veff
Effective radius, reff (nm)
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Extinction
factor,Q
ext
ITO
Variance, veff
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Scattering
factor,Q
sca
ITO
Variance, veff
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Scattering
factor,Q
sca
CWO
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Extinction
factor,Q
ext
CWO
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Aborsorption
factor,Q
abs
CWO
(b)
(a)
(c)
(e)
(d)
(f)
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 12 -
variation of PMMA optical constant k after the 2 μm range. Ignoring the influence of its fluctuations, the effect
of doped particles in different media on the spectral transmittance is not significant.
Fig. 6. The effects of background media and volume fraction on the spectral transmittance of monodisperse
nanocomposite films (h = 50 μm). (a–c) The variation of transmittance of CWO nanocomposite films with different
volume fraction (fv = 0.1%, 0.3%, 0.5%, 1%, and 2%) and r = 60 nm and (d–f) the variation of transmittance of ITO
nanocomposite films with different volume fraction (fv = 0.3%, 0.5%, 0.7%, 1%, and 2%) and r = 20 nm in different
background media.
Fig. 6(a) and (d) indicate the effect of fv on the spectral responses of CWO/PDMS films and ITO/PDMS
films, respectively. As shown, the transmittance of nanocomposite films all decreases with the increase of fv,
and the best NIR shielding effect is achieved in the range around 1.25 μm. However, fv has different degrees
of influence on the spectral response of different types of nanocomposite films. Compared with ITO
nanocomposite films, the NIR shielding ability of CWO nanocomposite films is more sensitive to fv. As fv of
CWO nanoparticles increases to 0.3%, the NIR shielding ability significantly increases.
The changes in the luminous transmittance Tlum, the solar energy transmittance Tsol, and the NIR
transmittance TNIR of CWO/PDMS and ITO/PDMS film with different fv are intuitively shown in Fig. 7(a) and
(b). With the increase of fv, Tlum, Tsol, and TNIR of monodisperse nanocomposite films show a continuous
decrease. A comparison of the optical properties of the CWO and ITO nanoparticles at the same volume
fraction (fv = 0.5%) shows that the CWO/PDMS film has excellent NIR shielding (TNIR = 2.5%) but poorly
visible light transmittance (Tlum = 52.2%), whereas the ITO/PDMS composite film has high transmittance (Tlum
= 78.5%) and limited NIR shielding ability (TNIR = 40.6%) allowing more solar energy to enter the room (Tsol
= 58.6%). Increasing the fv of ITO nanoparticles from 0.5% to 2% reduces TNIR to 8.1% but Tlum decreases to
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittace
(%)
fv = 0.3%
fv = 0.5%
fv = 0.7%
fv = 1%
fv = 2%
CWO/PDMS
r = 20 nm
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittace
(%)
ITO/PMMA
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittace
(%) Wavelength, λ (μm)
ITO/SiO2
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
CWO/PMMA
Transmittace
(%)
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittace
(%)
CWO/SiO2
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittace
(%)
fv = 0.3%
fv = 0.5%
fv = 0.7%
fv = 1%
fv = 2%
ITO/PDMS
r = 20 nm
(a) (b) (c)
(d) (e) (f)
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 13 -
45.4% and CWO nanoparticles from 0.5% to 2% reduces TNIR to 0.1% but Tlum decreases to 20.8%, showing
that increasing the fv can be an effective way to regulate the NIR shielding performance with the expense of
the visible transmittance. In order to simultaneously satisfy the demand for indoor lighting and NIR shielding
performance of energy-efficient windows, we further consider the particle size of nanoparticles to
comprehensively regulate the optical properties of monodisperse nanocomposite films.
Fig. 7. (a) The luminous transmittance Tlum and the solar energy transmittance Tsol of CWO/PDMS films with different
volume fractions. (b) The luminous transmittance Tlum and the solar energy transmittance Tsol of ITO/PDMS with different
volume fractions.
The particle radius r also has varying degrees of influence on the transmittance of two types monodisperse
nanoparticles, as shown in Fig. 8. Fig. 8(a) and (c) indicate the transmittance of the CWO and ITO
nanocomposite films with a radius range of 10–70 nm for nanoparticles. The transmittance of CWO/PDMS
and ITO/PDMS films in the NIR range hardly improves with increasing r, while the transmittance in the visible
range exhibits a substantial decrease, especially for the ITO/PDMS films. This behavior may be due to the
sharp increase of Qext with increasing particle size in the visible range, as shown in Fig. 4. It is clear from Fig.
8(b) and (d) that when the radius of the nanoparticles increases from 30 nm to 50 nm, the Tlum of the
CWO/PDMS film decreases by 8.9% with TNIR only decreasing by 0.3% and the Tlum of the ITO/PDMS film
decreases by 39.9% with TNIR only decreasing by 9.6%. In addition, the nanocomposite film doped with small
ITO nanoparticles (r = 10 nm) has low NIR shielding ability (TNIR = 36.9%) with excellent visible light
transmittance (Tlum = 84.4%), and it is difficult to be widely used for energy-saving windows due to the
limitation of nanoparticle fabrication technology. Overall, changing the particle size of the nanoparticles is
able to adjust the visible light transmittance of the nanocomposite films, but has little impact on its NIR
shielding ability.
37.2
27.6
22.3
17.3
9.0
72.3
61.2
52.2
41.6
20.8
12.3
4.9 2.5 1.1 0.1
0.1 0.3 0.5 1 2
0
20
40
60
80
100
CWO/PDMS
r = 20 nm
Transmittance
(%)
Volume fraction, fv (%)
Tsol
Tlum
TNIR
84.6
69.5
58.6
41.4
24.4
90.9
84.5
78.5
65.5
45.4
78.5
55.6
40.6
20.9
8.1
0.1 0.3 0.5 1 2
0
20
40
60
80
100
r = 20 nm
Transmittance
(%)
Tsol
Tlum
TNIR
ITO/PDMS
(a) (b)
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 14 -
Fig. 8. The effects of different nanoparticle radii on the spectral response of monodisperse nanocomposite films. (a) The
spectral transmittance and (b) the luminous transmittance Tlum and the solar energy transmittance Tsol of CWO/PDMS
films. (c) The spectral transmittance and (d) the luminous transmittance Tlum and the solar energy transmittance Tsol of
ITO/PDMS films.
Considering the inhomogeneous particle size of commercial nanoparticles, the gamma distribution is used
to approximate the particle size distribution of nanoparticles for computational analysis. Fig. 9(a–d) present
the effects of particle size distributions on the spectral transmittance of the nanocomposite films for veff = 0.01,
0.05, and 0.15. When veff is below 0.05, there is only a slight difference in the transmittance between
monodisperse and polydisperse nanocomposite films. However, as veff increases from 0.05 to 0.15, visible
transmittance of ITO and CWO nanocomposite films decreases slightly with Tlum loss of 6.9% and 0.7%,
respectively. It is also worth noting that the transmittance in the NIR range is almost unchanged under different
veff. Therefore, the particle size distribution has little effect on the overall optical properties of nanocomposite
film.
26.0
22.3
17.2
14.1
57.8
53.9
45.9
38.4
3.5 3.3 3.0 2.8
10 30 50 70
0
20
40
60
80
100
CWO/PDMS
fv = 0.6%
Transmittance
(%)
Tsol
Tlum
TNIR
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittance
(%)
r = 10 nm
r = 30 nm
r = 50 nm
r = 70 nm
ITO/PDMS
fv = 0.6%
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittance
(%)
r = 10 nm
r = 30 nm
r = 50 nm
r = 70 nm
CWO/PDMS
fv = 0.6%
(a)
(c)
60.8
43.4
20.7
7.4
84.4
58.8
18.9
0.4
36.9
31.8
22.2
13.0
10 30 50 70
0
20
40
60
80
100
Transmittance
(%)
Tsol
Tlum
TNIR
ITO/PDMS
fv = 0.6%
(b)
(d)
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 15 -
Fig. 9. The effects of particle size distributions on the spectral response of nanocomposite films. (a) The spectral
transmittance and (b) the luminous transmittance Tlum and the solar energy transmittance Tsol of CWO/PDMS films. (c)
The spectral transmittance and (d) the luminous transmittance Tlum and the solar energy transmittance Tsol of ITO/PDMS
films.
Based on the previous discussion, for spherical nanoparticles, it can be concluded that changing the
volume fraction and radius of the nanoparticles can effectively modulate the NIR shielding ability and visible
light transmittance of the nanocomposite films, respectively. These results indicate that by varying the volume
fraction of CWO nanoparticles with appropriate radius, CWO nanocomposite films can achieve controllable
NIR shielding ability while maintaining good visibility. The nanocomposite films doped with small spherical
ITO nanoparticles can provide high transmittance as well as lower NIR shielding ability by adjusting the
volume fraction, and it is difficult to fabricate ITO nanoparticles to satisfy such high requirements. Overall,
the NIR shielding ability of nanocomposite films doped with spherical nanoparticles can still be greatly
improved. Therefore, we further analyze the optical properties of nanocomposite films by modifying spherical
nanoparticles into cylindrical nanoparticles.
3.3 Effects of different geometrics parameters on the optical properties of cylindrical nanoparticle systems
3.3.1 The effects of aspect ratio and effective radius on the radiative properties of individual nanoparticles
The effects of nanoparticle aspect ratio AR and effective radius reff on the radiative properties of
nanoparticles are considered in this section. Fig. 10 presents the extinction factor Qext, absorption factor Qabs,
and scattering factor Qsca of cylindrical CWO and ITO nanoparticles in different AR. It is observed that the
radiative properties of CWO and ITO nanoparticles are partly determined by AR. The extinction peak which
24.6 24.5 24.3 23.5
56.5 56.2 55.9 55.2
3.4 3.4 3.4 3.4
0 0.01 0.05 0.15
0
20
40
60
80
100
Transmittance
(%)
Variance, veff
Tsol
Tlum
TNIR
CWO/PDMS
fv = 0.6%
reff = 20 nm
(a)
(c)
(b)
(d)
54.3 53.9 52.3
47.8
75.7 75.2 72.9
66.0
35.0 35.0 34.6 33.6
0 0.01 0.05 0.15
0
20
40
60
80
100
fv = 0.6%
reff = 20 nm
Transmittance
(%)
Variance, veff
Tsol
Tlum
TNIR
ITO/PDMS
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
veff = 0
ITO/PDMS
fv = 0.6%
reff = 20nm
Transmittance
(%)
veff = 0.01
veff = 0.05
veff = 0.15
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
veff = 0
veff = 0.01
veff = 0.05
veff = 0.15
CWO/PDMS
fv = 0.6%
reff = 20nm
Transmittance
(%)
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 16 -
is mainly caused by the absorption of CWO nanoparticles in the NIR range gradually decreases with an
increase in AR and the extinction peak in the short wave range remains almost invariable, as shown in Fig.
10(a–c). It can be seen that changing the shape of CWO nanoparticles can effectively increase broadband
absorption in the NIR range. On the contrary, as shown in Fig. 10(d–f), the extinction peak of ITO nanoparticles
is mainly caused by the absorption in the NIR range is constantly red-shifted and the peaks increase with the
increase of AR, which represents that better NIR shielding ability of ITO nanocomposite film can be obtained
by increasing the AR. In addition, the extinction peak which is mainly due to the scattering of ITO nanoparticles
in the short wave range higher than those of CWO nanoparticles, implies that the effect of ITO nanoparticles
on the transmittance in the short wave range of the nanocomposite film will be more obvious.
Fig. 10. The radiative properties of cylindrical nanoparticles with different aspect ratio. (a) Extinction, (b) absorption,
and (c) scattering factors of CWO nanoparticles. (d) Extinction, (e) absorption, and (f) scattering factors of ITO
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
1
2
3
4
5
Scattering
factor,Q
sca
ITO
reff = 60 nm
AR
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
1
2
3
4
5
Extinction
factor,Q
ext
ITO
reff = 60 nm
AR
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
1
2
3
4
5
Absorption
factor,Q
abs
ITO
reff = 60 nm
AR
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
1
2
3
4
5
Absorption
factor,Q
abs
CWO/PDMS
r = 60 nm
CWO
reff = 60 nm
AR
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
1
2
3
4
5
Scattering
factor,Q
sca
CWO
reff = 60 nm
AR
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
1
2
3
4
5
Extinction
factor,Q
ext
CWO
reff = 60 nm
AR
(b)
(a)
(c)
(e)
(d)
(f)
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 17 -
nanoparticles.
Fig. 11 shows the extinction factor Qext, absorption factor Qabs, and scattering factor Qsca of cylindrical
CWO and ITO nanoparticles in different reff. It is clear that the variation trend of radiative properties of
cylindrical CWO nanoparticles is similar to those of spherical nanoparticles with the increase of reff. The
position of extinction peaks of CWO nanoparticles is basically constant and the extinction peaks are gradually
increasing. As reff changes from 10 to 70 nm with an interval of 10 nm, the two extinction peaks of ITO
nanoparticles gradually increase with AR = 5 and the peak in the NIR range is accompanied by continuous red-
shifted are shown in Fig. 11(d). As seen from Fig. 11(d–f) the peak position in the NIR range of ITO
nanoparticles moves from about 1.5 μm to 2.0 μm by increasing the particle size, resulting in broadband
absorption in the NIR range.
Fig. 11. The radiative properties of cylindrical nanoparticles with different effective radii reff. (a) Extinction, (b)
absorption, and (c) scattering factors of CWO nanoparticles. (d) Extinction, (e) absorption, and (f) scattering factors of
(b) (e)
(c) (f)
(a) (d)
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Absorption
factor,Q
abs
10
20
30
40
50
60
70
ITO
AR = 5
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Scattering
factor,Q
sca
10
20
30
40
50
60
70
ITO
AR = 5
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Extinction
factor,Q
ext
CWO
AR = 1
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Absorption
factor,Q
abs
CWO
AR = 1
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Scattering
factor,Q
sca
CWO
AR = 1
0.5 1.0 1.5 2.0 2.5
0.0
1.5
3.0
4.5
6.0
7.5
Extinction
factor,Q
ext
10
20
30
40
50
60
70
ITO
AR = 5
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 18 -
ITO nanoparticles.
3.3.2 The effects of geometrical parameters on spectral responses of nanocomposite functional films
The effects of aspect ratio AR, volume fraction fv, and effective radius reff on the spectral responses of
CWO/PDMS films are analyzed separately in Fig. 12. AR of the CWO nanoparticle has a small effect on the
transmittance for CWO/PDMS films, as shown in Fig. 12(a). It is evident from Fig. 12(d) that the change in
transmittance ranges ΔTlum is less than 1.5% and ΔTNIR does not exceed 1% as AR increases from 1 to 5.
However, the transmittance of the CWO/PDMS films decreases with the increasing fv, and the NIR shielding
ability is changed significantly from 0.2 to 0.4% in Fig. 12(b). As fv increases from 0.2% to 0.4%, Tlum of the
nanocomposite film decreases from 80.2% to 66.6% and TNIR of the nanocomposite film decreases from 19.2%
to 4% as shown in Fig. 12(e). Whereas, Fig. 12(c) and (f) indicate reff mainly affects the visible light
transmittance of CWO/PDMS films, which is similar to that of spherical nanoparticles. From the above results,
it is evident that fv of nanoparticles has the greatest impact on the indoor light and energy acquisition of the
CWO/PDMS films.
Fig. 12. The transmittance of CWO/PDMS films. (a–c) Variation of the spectral transmittance of CWO/PDMS films with
different aspect ratios, volume fractions, and effective radii. (d–e) Variation of the luminous transmittance Tlum and the
solar energy transmittance Tsol of CWO/PDMS films with different aspect ratios, volume fractions, and effective radii.
With the increase of aspect ratio AR, volume fraction fv, and effective radius reff, the change in
transmittance of ITO/PDMS films is similar to that of CWO/PDMS films. However, compared to CWO/PDMS
films, the influence of geometric parameters ITO/PDMS is more pronounced. As can be seen from Fig. 13(a)
and (d), the AR of ITO nanoparticles effectively improves the shielding performance of ITO/PDMS film in the
NIR range. As AR of the nanoparticles increases from 1 to 5, TNIR and Tlum of the ITO/PDMS films decrease
26.2 25.5 25.8 25.6 25.8
61.1 60.1 60.4 60.9 61.0
3.4 2.5 2.9 2.1 2.4
1 2 3 4 5
0
20
40
60
80
100
Transmittance
(%)
Aspect Ratio, AR
Tsol
Tlum
TNIR
CWO/PDMS
reff= 30 nm
fv = 0.5%
45.4
29.5
22.5
18.2
15.1
80.2
66.6
55.8
46.9
39.6
19.2
4.0
0.9 0.2 0.0
0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
Transmittance
(%)
Tsol
Tlum
TNIR
CWO/PDMS
AR = 3
reff= 30 nm
27.7 25.4
22.3 20.5
63.2 60.9
56.6
52.4
1.8 1.9 2.0 2.5
10 30 50 70
0
20
40
60
80
100
Transmittance
(%)
Effective raduis, reff (nm)
Tsol
Tlum
TNIR
CWO/PDMS
fv = 0.5%
AR = 3
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittance
(%)
AR = 1
AR = 2
AR = 3
AR = 4
AR = 5
CWO/PDMS
reff = 30 nm
fv = 0.5%
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittace
(%)
fv = 0.2%
fv = 0.4%
fv = 0.6%
fv = 0.8%
fv = 1%
CWO/PDMS
reff = 30 nm
AR = 3
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittance
(%)
reff = 10 nm
reff = 30 nm
reff = 50 nm
reff = 70 nm
CWO/PDMS
AR = 3
fv = 0.5%
(a) (b) (c)
(d) (e) (f)
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 19 -
by 25.9% and 22.9%, respectively. The influence of fv as another important variable on the transmittance of
nanocomposite films is shown in Fig.13 (b) and (e). A lower volume fraction (fv = 0.2%) provides high visible
transmittance (Tlum = 80.6%) and low NIR shielding ability (TNIR = 38.5%). ITO nanoparticles by selecting the
appropriate AR and fv can make ITO nanocomposite films to satisfy our desired needs. Overall, ITO/PDMS
film is most influenced by reff of nanoparticles, especially Tlum, indicating the importance of controlling the
appropriate particle size.
Fig. 13. The transmittance of ITO/PDMS films. (a–c) Variation of transmittance of ITO/PDMS films with different aspect
ratios, volume fractions, and effective radii. (d–e) Variation of the luminous transmittance Tlum and the solar energy
transmittance Tsol of ITO/PDMS films with different aspect ratios, volume fractions, and effective radii.
3.4 Optimal solution by the evaluation method
The optical performance of nanocomposite films is evaluated by the quality factor Z, where the
geometrical parameters of the doped nanoparticles range from 5 to 70nm in particle radius and from 0.1% to
2% in volume fraction. Changing the shape of the nanoparticles to cylindrical significantly improves the optical
properties of the nanocomposite films, as shown in Fig. 14. On the one hand, the optimal Z of spherical
nanoparticles doped nanocomposite films (ZCWO = 0.516 and ZITO = 0.413) is lower than that of cylindrical
nanoparticles doped nanocomposite films (ZCWO = 0.545 and ZITO = 0.517). On the other hand, the overall
properties of nanocomposite films doped with cylindrical nanoparticles are significantly improved with the
same nanoparticle geometry parameters. In particular, it can be seen that spherical ITO nanoparticle-doped
nanocomposite films are the worst.
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittance
(%)
AR = 1
AR = 2
AR = 3
AR = 4
AR = 5
ITO/PDMS
reff = 30 nm
fv = 0.5%
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittance
(%)
fv = 0.2%
fv = 0.4%
fv = 0.6%
fv = 0.8%
fv = 1%
ITO/PDMS
reff = 30 nm
AR=3
0.5 1.0 1.5 2.0 2.5
0
20
40
60
80
100
Transmittance
(%)
reff = 10 nm
reff = 30 nm
reff = 50 nm
reff = 70 nm
ITO/PDMS
AR = 3
fv = 0.5%
(a) (b) (c)
(d) (e) (f)
50.6
33.0
12.0
4.6
83.5
57.1
14.6
6.8
16.8
13.2
7.1
2.9
10 30 50 70
0
20
40
60
80
100
Transmittance
(%)
Effective raduis, reff (nm)
Tsol
Tlum
TNIR
ITO/PDMS
fv = 0.5%
AR = 3
49.9
41.0
33.0
28.5 26.1
71.6
64.7
57.1
51.9
48.7
32.9
22.1
13.2
8.9 7.0
1 2 3 4 5
0
20
40
60
80
100
Transmittance
(%)
Aspect Ratio, AR
Tsol
Tlum
TNIR
ITO/PDMS
reff = 30 nm
fv = 0.5%
58.1
39.2
28.2
21.0
16.0
80.6
64.4
50.6
39.6
30.8
38.5
18.2
9.8
5.7 3.5
0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
Transmittance
(%)
Tsol
Tlum
TNIR
ITO/PDMS
AR = 3
reff = 30 nm
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 20 -
Fig. 14. The quality factor Z for nanocomposite films with nanoparticle radius (effective radius) ranging from 5–70 nm
and volume fractions of 0.1–2%. The evaluated results of (a) CWO/PDMS and (b) ITO/PDMS films doped with spherical
nanoparticles. The evaluated results of (c) CWO/PDMS and (d) ITO/PDMS films doped with cylindrical nanoparticles.
Fig. 15 gives the optimal spectral properties of the further evaluated nanocomposite films doped with
different nanoparticles. Fig. 15(a) and (b) compare the spectral transmittance of nanocomposite films doped
with spherical and cylindrical nanoparticles. All transmittances in the visible range are very high and almost
unchanged. Surprisingly, the nanocomposite films are able to maintain a high visible light transmittance while
improving the NIR shielding ability by changing the shape of the nanoparticles. Compared with that before
reshaping, the transmittance of CWO/PDMS and ITO/PDMS film doped with cylindrical nanoparticles are
reduced by 40% and 68% in about 2.25 μm, respectively. To compare with other literature to demonstrate the
excellent performance of our nanocomposite films, we use this method to calculate the Figure of Merit (FOM)
of energy-saving nanocomposite films in this study:
(24)
As clarified in Fig. 15(c), the FOM of the nanocomposite films doped with cylindrical nanoparticles is
greater than 1.9 with the luminous transmittance Tlum all above 60%, which is larger than the FOM of
CWO/PMMA film (1.74 reported in Ref. [21]). The cylindrical CWO nanoparticle-doped nanocomposite film
has high visible light transmittance (Tlum = 62.6%) and can effectively shield 95.8% of NIR light. Meanwhile,
the cylindrical ITO nanoparticle-doped nanocomposite film significantly has a high NIR shielding ability (TNIR
(a) (b)
(c) (d)
10 20 30 40 50 60 70
0.4
0.8
1.2
1.6
2.0
0.1
Volume
fraction,
f
v
(%)
Particle radius, reff (nm)
0.00
0.07
0.14
0.21
0.28
0.34
0.41
0.48
0.55
Z
CWO/PDMS
AR = 2
10 20 30 40 50 60 70
0.4
0.8
1.2
1.6
2.0
0.1
Volume
fraction,
f
v
(%)
Particle radius, reff (nm)
0.00
0.07
0.14
0.21
0.28
0.34
0.41
0.48
0.55
Z
ITO/PDMS
AR = 5
10 20 30 40 50 60 70
0.4
0.8
1.2
1.6
2.0
0.1
Volume
fraction,
f
v
(%)
CWO/PDMS
0.00
0.07
0.14
0.21
0.28
0.34
0.41
0.48
0.55
Z
10 20 30 40 50 60 70
0.4
0.8
1.2
1.6
2.0
0.1
Volume
fraction,
f
v
(%)
ITO/PDMS
0.00
0.07
0.14
0.21
0.28
0.34
0.41
0.48
0.55
Z
lum
sol
FOM 
T
T
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 21 -
= 6.3%) while maintaining visible light transmittance (Tlum = 65.5%). These results clearly indicate that the
above nanocomposite films have very good optical properties.
Fig. 15. (a–b) The optimal spectra and their geometrical parameters are evaluated using the evaluation method with PDMS
as the background medium. (c) A comprehensive evaluation of evaluation criteria Z and FOM.
As discussed above, nanocomposite films doped with cylindrical nanoparticles have better optical
performance than nanocomposite films doped with spherical nanoparticles, as the former simultaneously
possess excellent NIR shielding ability and high transmittance. Compared to ITO/PDMS films, CWO/PDMS
films doped with larger particle sizes (reff = 50 nm) and lower volume fractions (fv = 0.4%) of cylindrical
nanoparticles can achieve better optical performance (Z = 0.545), which are more beneficial for commercial
applications. The optimal geometrical parameters and the calculated results of all nanocomposite films
evaluated with different background media (PDMS, PMMA, and SiO2) are given in Table 1 as the appropriate
reference. The type of nanocomposite film can be selected for different needs.
Table 1. Optimal geometric parameters and evaluation results (both Z and FOM) of all types of nanocomposite films are
evaluated with different background media.
Composite materials
Volume fraction,
fv (%)
Aspect Ratio,
AR
Radius, (nm) Z FOM
CWO/PDMS 0.3 - 50 0.516 2.064
CWO/PMMA 0.3 - 60 0.521 2.115
CWO/SiO2 0.3 - 60 0.517 2.089
ITO/PDMS 0.9 - 20 0.413 1.540
ITO/PMMA 0.9 - 20 0.426 1.648
ITO/SiO2 0.9 - 20 0.420 1.615
CWO/PDMS 0.4 2 50 0.545 2.358
CWO/PMMA 0.4 2 50 0.540 2.347
CWO/SiO2 0.4 2 50 0.542 2.348
ITO/PDMS 0.6 5 20 0.517 1.930
ITO/PMMA 0.7 4 20 0.512 1.970
ITO/SiO2 0.7 4 20 0.513 1.962
0.5 1.0 1.5 2.0 2.5
0.3
0
20
40
60
80
100
ITO/PDMS
Transmittance
(%)
Spherical
Cylindrical
(b)
0.5 1.0 1.5 2.0 2.5
0.3
0
20
40
60
80
100
CWO/PDMS
Transmittance
(%)
Spherical
Cylindrical
(a)
r (reff)
(nm)
fv
(%)
AR
50 0.3 -
50 0.4 2
r (reff)
(nm)
fv
(%)
AR
20 0.9 -
20 0.6 5
40%
68%
CWO/PDMS ITO/PDMS
31.7
26.5
44.1
33.9
65.4 62.6
67.9 65.5
11.8
4.2
23.5
6.3
sphere cylinder sphere cylinder
0
20
40
60
80
100
Trasmittance
(%)
(c)
0.0
0.4
0.8
1.2
1.6
2.0
2.4
FOM
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 22 -
4. Conclusion
In this study, the radiative properties, performance evaluation, and optimized design of spectrally
selective films doped with CWO and ITO nanoparticles are systematically investigated. First, we analyze the
radiative properties of spherical and cylindrical nanoparticles using Lorenz-Mie theory and T-matrix methods,
respectively. Then, the spectral responses of CWO and ITO nanocomposite films are calculated using the
Monte Carlo method. The effects of geometric parameters of nanoparticles on spectral responses of
nanocomposite films are investigated by using PDMS background media as an example. Finally, the optical
properties of different nanocomposite films are analyzed and compared.
These results show that CWO and ITO nanocomposite films can be used as novel building materials for
energy-saving windows. The geometrical parameters of nanoparticles have a significant impact on the optical
properties of nanocomposite films with different background media. The nanocomposite film doped with
CWO or ITO spherical nanoparticles has good visible light transmittance (Tlum-CWO = 65.4% and Tlum-ITO =
67.9%) and certain NIR shielding ability (TNIR-CWO = 11.8% and TNIR-ITO = 23.5%), but the transmittance is
higher in the range of 1.5–2.5 μm. Fortunately, by changing the shape of spherical nanoparticles to cylindrical
nanoparticles, the nanocomposite film significantly improves NIR shielding ability (TNIR-CWO = 4.2% and TNIR-
ITO = 6.3%) while ensuring high visible light transmittance (Tlum-CWO = 62.6% and Tlum-ITO = 65.5%). Compared
with the nanocomposite films doped with spherical nanoparticles, nanocomposite films doped with cylindrical
nanoparticles have better optical properties and will be a better choice. The comprehensively evaluated
nanocomposite films with appropriate geometrical parameters achieve excellent radiation shielding
performance and high visible light transmittance. In conclusion, this work provides a theoretical reference for
the nanocomposite films applied to energy-saving windows, which further promotes the commercialization of
energy-saving windows.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that
could have appeared to influence the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
Financial support from the National Natural Science Foundation of China Grant [Nos. 51806124 and
51906127], Postdoctoral Science Foundation of China Grant [Nos. 2020T130365 and 2019M662354] and
Young Scholars Program of Shandong University is gratefully acknowledged.
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 23 -
References
[1] H. Liu, F. Wang, S. Lei, J. Ou, W. Li, Large-area fabrication of colorful superhydrophobic coatings with
high solar reflectivity, Constr. Build. Mater. 304 (2021) 124602.
[2] Y. Yang, Z. Chen, T. Vogt Wu, A. Sempey, J.-C. Batsale, In situ methodology for thermal performance
evaluation of building wall: A review, Int. J. Therm. Sci. 181 (2022) 107687.
[3] S.C. Kim, J.H. Yoon, H.M. Lee, Comparative experimental study on heating and cooling energy
performance of spectrally selective glazing, Sol. Energy 145 (2017) 78-89.
[4] S. Amirkhani, A. Bahadori-Jahromi, A. Mylona, P. Godfrey, D. Cook, Impact of low-E window films on
energy consumption and CO2 Emissions of an existing UK hotel building, Sustainability 11 (2019) 4265.
[5] J. Pu, C. Shen, J. Wang, Y. Zhang, C. Zhang, S.A. Kalogirou, Near-infrared absorbing glazing for energy-
efficient windows: A critical review and performance assessments from the building requirements, Nano
Energy 110 (2023) 108334.
[6] J. Wang, D. Shi, Spectral selective and photothermal nano structured thin films for energy efficient
windows, Appl. Energy 208 (2017) 83-96.
[7] N. Luamsri, J. Wootthikanokkhan, E. Wimolmala, P. Rakkwamsuk, W. Sangkhun, Spectral selectivity and
stability of energy-saving window films based on poly(vinyl chloride) reinforced with ATO nanoparticles,
Polym. Test. 80 (2019) 106157.
[8] R. Hong, W. Sun, Q. Liu, Z. Li, C. Tao, D. Zhang, D. Zhang, Al-induced tunable surface plasmon resonance
of Ag thin film by laser irradiation, Appl. Phys. Express 12 (2019) 085503.
[9] P. Guo, R.D. Schaller, J.B. Ketterson, R.P.H. Chang, Ultrafast switching of tunable infrared plasmons in
indium tin oxide nanorod arrays with large absolute amplitude, Nat. Photonics 10 (2016) 267-273.
[10] Y. Zhou, N. Li, Y. Xin, X. Cao, S. Ji, P. Jin, CsxWO3 nanoparticle-based organic polymer transparent
foils: low haze, high near infrared-shielding ability and excellent photochromic stability, J. Mater. Chem. C 5
(2017) 6251-6258.
[11] Q. Yang, C. Qin, Y. Zou, H. Liu, B. Zhang, X. Wu, The optical properties of nanorods with curved slots
for solar photothermal conversion, Int. J. Therm. Sci. 191 (2023) 108387.
[12] B. Shen, Y. Wang, L. Lu, H. Yang, Spraying fabrication of spectrally selective coating with improved
near-infrared shielding performance for energy-efficient glazing, Ceram. Int. 47 (2021) 18991-18997.
[13] J. Pu, C. Shen, S. Yang, C. Zhang, D. Chwieduk, S.A. Kalogirou, Feasibility investigation on using silver
nanorods in energy saving windows for light/heat decoupling, Energy 245 (2022) 123289.
[14] Z. Yu, H. Ma, Y. Shao, X. Yu, J. Chen, C. Dong, Z. Mao, D. Wang, Regulating monolayer aligned silver
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 24 -
nanowire coatings for energy-saving windows, Coatings 12 (2022) 1552.
[15] S. Lin, H. Wang, X. Zhang, D. Wang, D. Zu, J. Song, Z. Liu, Y. Huang, K. Huang, N. Tao, Z. Li, X. Bai,
B. Li, M. Lei, Z. Yu, H. Wu, Direct spray-coating of highly robust and transparent Ag nanowires for energy
saving windows, Nano Energy 62 (2019) 111-116.
[16] H. Hu, S. Wang, Y. Meng, G. Liu, M. Li, T.D. Vu, Y. Long, Layer-by-layer alignment of silver nanowires
for transparent and flexible energy-saving windows, Adv. Mater. Technol. 7 (2021) 2100824.
[17] F. Zhang, B. Cheng, J. Liu, Y. Yue, Z. Huang, Y. Zhang, D. Zang, Facile synthesis of Ag nanowires
enhanced PVB for transparent conductive film, J. Mater. Res. Technol. 9 (2020) 14509-14516.
[18] N. Abundiz-Cisneros, R. Sanginés, R. Rodríguez-López, M. Peralta-Arriola, J. Cruz, R. Machorro, Novel
Low-E filter for architectural glass pane, Energy Build. 206 (2020) 109558.
[19] Y. Chen, X. Zeng, Y. Zhou, R. Li, H. Yao, X. Cao, P. Jin, Core-shell structured CsxWO3@ZnO with
excellent stability and high performance on near-infrared shielding, Ceram. Int. 44 (2018) 2738-2744.
[20] Y. Wang, Z. Yan, M. Zhang, Z. Zhang, T. Li, M. Chen, W. Dong, Flexible core-shell CsxWO3-based films
with high UV/NIR filtration efficiency and stability, Nanoscale Adv. 3 (2021) 3177-3183.
[21] Y. Yao, Z. Chen, W. Wei, P. Zhang, Y. Zhu, Q. Zhao, K. Lv, X. Liu, Y. Gao, Cs0.32WO3/PMMA
nanocomposite via in-situ polymerization for energy saving windows, Sol. Energy Mater. Sol. Cells 215 (2020)
110656.
[22] Y. Zhou, A. Huang, H. Zhou, S. Ji, P. Jin, Organic-inorganic hybrid optical foils with strong visible
reflection, excellent near infrared-shielding ability and high transparency, Nanotechnology 29 (2018) 095705.
[23] A. Bouzidi, K. Omri, L. El Mir, H. Guermazi, Preparation, structural and optical investigations of ITO
nanopowder and ITO/epoxy nanocomposites, Mater. Sci. Semicond. Process. 39 (2015) 536-543.
[24] C. Zhang, Y. Ge, X. Huo, J. Xue, K. Li, Y. Zhang, Z. Miao, Studies on electro-optical properties of
polymer matrix/LC/ITO nanoparticles composites, Polym. Adv. Technol. 31 (2019) 544-552.
[25] Y. Bao, Y. Huang, W. Li, K. Zhu, Combination of the Monte Carlo method and DDA to evaluate the
radiative properties of ITO-pigmented and TiO2-pigmented coatings, Int. J. Therm. Sci. 146 (2019) 106076.
[26] K. Katagiri, R. Takabatake, K. Inumaru, Robust infrared-shielding coating films prepared using
perhydropolysilazane and hydrophobized indium tin oxide nanoparticles with tuned surface plasmon
resonance, ACS Appl. Mater. Interfaces 5 (2013) 10240-10245.
[27] W. Yan, H. Xiao, T. Jiang, W. Li, G. Zhang, Fabrication and thermal insulating properties of ITO/PVB
nanocomposites for energy saving glass, J. Wuhan Univ. Technol. Mater. Sci. Ed. 32 (2017) 63-66.
[28] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley: New York,
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

- 25 -
NY, USA, 1983.
[29] M.I. Mishchenko, L. Travis, A.A.A. Lacis, Scattering, Absorption, and Emission of Light by Small
Particles, Cambridge University Press: Cambridge, 2002.
[30] J.E. Hansen, L.D. Travis, Light scattering in planetary atmospheres, Space Sci. Rev. 16 (1974) 527-610.
[31] M.F. Modest, Radiative Heat Transfer, Academic Press: San Diego, CA, USA, 2013.
[32] X. Zhang, J. Qiu, J. Zhao, X. Li, L. Liu, Complex refractive indices measurements of polymers in infrared
bands, J. Quant. Spectrosc. Radiat. Transfer 252 (2020) 107063.
[33] X. Zhang, J. Qiu, X. Li, J. Zhao, L. Liu, Complex refractive indices measurements of polymers in visible
and near-infrared bands, Appl. Opt. 59 (2020) 2337-2344.
[34] X. Zhang, X. Li, F. Wang, W. Yuan, Z. Cheng, H. Liang, Y. Yan, Low-cost and large-scale producible
biomimetic radiative cooling glass with multiband radiative regulation performance, Adv. Opt. Mater. 10
(2022) 2202031.
[35] E.D. Palik, Handbook of Optical Constants of Solids, Academic Ppress, San Diego, 1998.
[36] Y. Sato, M. Terauchi, K. Adachi, High energy-resolution electron energy-loss spectroscopy study on the
near-infrared scattering mechanism of Cs0.33WO3crystals and nanoparticles, J. Appl. Phys. 112 (2012) 074308.
[37] L. Ma, F. Wang, C. Wang, C. Wang, J. Tan, Monte Carlo simulation of spectral reflectance and BRDF of
the bubble layer in the upper ocean, Opt. Express 23 (2015) 24274-24289.
[38] L.X. Ma, C.C. Wang, J.Y. Tan, Light scattering by densely packed optically soft particle systems, with
consideration of the particle agglomeration and dependent scattering, Appl. Opt. 58 (2019) 7336-7345.
[39] J. Wu, Z. Wang, B. Li, B. Liu, X. Zhao, G. Tang, D. Zeng, S. Tian, Facile synthesis of island-like ZrO2-
VO2 composite films with enhanced thermochromic performance for smart windows, Materials 16 (2022) 273.
[40] A. Mass, 1.5 Spectra, American Society for Testing and Materials (ASTM), 2014.
[41] S.M.A. Durrani, E.E. Khawaja, A.M. Al-Shukri, M.F. Al-Kuhaili, Dielectric/Ag/dielectric coated energy-
efficient glass windows for warm climates, Energy Build. 36 (2004) 891-898.
[42] Z. Huang, X. Ruan, Nanoparticle embedded double-layer coating for daytime radiative cooling, Int. J.
Heat Mass Transfer 104 (2017) 890-896.
P
r
e
p
r
i
n
t
n
o
t
p
e
e
r
r
e
v
i
e
w
e
d

SSasdfsdfgsdfgdfgsdfgdfgsdfgsdfgsdfgdsR.pdf

Recommended

Recommended

More Related Content

Similar to SSasdfsdfgsdfgdfgsdfgdfgsdfgsdfgsdfgdsR.pdf

Similar to SSasdfsdfgsdfgdfgsdfgdfgsdfgsdfgsdfgdsR.pdf (20)

Recently uploaded

Recently uploaded (20)

SSasdfsdfgsdfgdfgsdfgdfgsdfgsdfgsdfgdsR.pdf