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i n t e rn a t i o n a l j o u rn a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e7
Available online at w
ScienceDirect
journal homepage: www.elsevier .com/locate/he
Property models and theoretical analysis of novelsolid oxide fuel cell with triplet nano-compositeelectrode
Meina Chen, Ce Song, Zijing Lin*
Department of Physics & Collaborative Innovation Center of Suzhou Nano Science and Technology,
University of Science and Technology of China, Hefei 230026, China
a r t i c l e i n f o
Article history:
Received 25 October 2013
Received in revised form
4 January 2014
Accepted 6 February 2014
Available online xxx
Keywords:
Electric conductivity
TPB length
Hydraulic diameter
SOFC
Multi-physics modeling
Microstructure optimization
* Corresponding author. Tel.: þ86 551 636003E-mail address: [email protected] (Z. Lin)
Please cite this article in press as: Chentriplet nano-composite electrode, Ij.ijhydene.2014.02.036
0360-3199/$ e see front matter Copyright ªhttp://dx.doi.org/10.1016/j.ijhydene.2014.02.0
a b s t r a c t
Triplet nano-composite electrodes are actively examined experimentally, but there is a
shortage of theoretical study. Theoretical models are helpful for understanding the ex-
periments and provide guidance for design optimization of the novel electrode. Here new
models for computing the electrode electronic and ionic conductivities, TPB length and
hydraulic radius are presented. The novel properties determined by the models are used in
a multi-physics numerical model that couples the intricate interdependency among elec-
tric conductions, electrochemical reaction and gas transport in SOFC. The theoretical IeV
relations and hydraulic radius are in good agreement with the experiments, vali-
datingtheproposed property models. The property models are then used to examine the
influence of microstructure and material composition. The results show that: (i) Larger
core-particle size and smaller nano-particle size are helpful for improving electrode
properties; (ii) The required nano-particle loading is determined by the desired electronic
conductivity instead of the desired TPB length.
Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
reserved.
Introduction
The concept of nano-particle composite electrode is seen as
an effective way to develop highly active and advanced elec-
trode for solid oxide fuel cells (SOFCs) and has attracted
increasing attention recently [1]. Various techniques such as
infiltration [2,3], electroless coating [4,5] and Pechini-type
polymerizable complex method [6,7] have been used to
fabricate nano-particle composite electrodes with coreeshell
structures. All of these nano-composite electrodes may yield
low polarization resistances for SOFCs operated at reduced-
temperature (<700 �C) due to the enlargement of triple-
45; fax: þ86 551 63606348.
M, et al., Property modenternational Journal
2014, Hydrogen Energy P36
phase boundaries (TPBs) [3,8e11]. However, the long-term
stability is still a potential problem especially for anode with
just one kind of metal nano-particles. The metal nano-
particles such as Ni are prone to coarsening that causes
reduced TPBs and increases polarization resistance [12] and
thereby causes the anode performance degradation.
To curb the anode degradation process and to further
improve the electrode performance, anodeswith binary nano-
particles such as nano-Cu/nano-CeO2/YSZ anode [13] and
nano-Ni/nano-YSZ/YSZ anode [6] have been developed.
Together with the backbone material such as YSZ, an elec-
trodewith binary nano-particles involves threematerial types
and is therefore named as a triplet nano-composite electrode.
.
ls and theoretical analysis of novel solid oxide fuel cell withof Hydrogen Energy (2014), http://dx.doi.org/10.1016/
ublications, LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e72
As reported [6], the typical triplet nano-composite anodes can
offer many advantages such as: (1) microstructural stability,
for example, aging of the nano-Ni/nano-YSZ/YSZ anode is
controlled by a fine YSZ skeleton and the coherence between
co-conjugatedNi and YSZ; and (2) TPB expansion by the binary
nano-conjugation. These advantages imply that the triplet
nano-composite anode has a great potential to become an
excellent and practical electrode in the future. Consequently,
the design of triplet nano-composite electrode is actively
examined experimentally [1].
Compared to the intensive experimental activities, there
are very few theoretical studies. Tanner et al. [14] proposed a
model for an electrode with single-phase nano-particles as
consisting of regularly spaced corrugations of contiguous
electrolyte region, electro-catalyst, and porosity. Thismodel is
oversimplified with significant deviation from the actual
electrode structure with single-phase nano-particles and is
clearly inapplicable to the triplet nano-composite electrode.
Recently, Chen et al. [15e17] developed a theory for the elec-
trical conductivity that properly accounts for specific struc-
ture of the nano-composite electrode with one type of nano-
particles. The model yields quantitative agreement with the
experimental result on the dependence of the electronic
conductivity on the nano-particle loading. Though the basic
feature of the model of Chen et al. is reflective of the nano-
particle infiltrated electrode, a generalization of the model to
suit the specific structure of the triplet nano-composite elec-
trode is still required.
Here new expressions of electronic and ionic conductiv-
ities applicable to the triple phase nano-composite electrode
are described. The theory for computing the effective TPB
length is also given. In addition, a new model for calculating
the effective hydraulic radius that is essential for determining
the concentration polarization in nano-composite electrode is
proposed. These effective property theories are used in a
multi-physics numerical model to describe the overall IeV
performance of SOFC with nano-composite electrode. The
req ¼ ri cos a0
��1þ jnano
ð1� jnanoÞ1� fshell
nano
���1��
cos�2a0 � 13
�þ 13
�1=2
(6)
theoretical predictions are compared with the available ex-
periments and consistent quantitative agreements are found.
The new models are then used to discuss the dependences of
electrode properties on material compositions.
Theory
The triple phase nano-composite structure affects all the
essential electrode properties, including the electronic and
ionic conductivities, the effective TPB length and the hy-
draulic radius. Here models for these properties are discussed
first, followed by a summary of a multi-physics model that
utilizes these properties. The numerical method for solving
the multi-physics model is also briefly described.
Please cite this article in press as: Chen M, et al., Property modetriplet nano-composite electrode, International Journalj.ijhydene.2014.02.036
Effective properties
Effective conductivitiesUnlike a traditionalmicron-scale composite electrode thatmay
be viewedas a randompacking of spherical particles [18,19], the
nano-particles ina tripletnano-particlecomposite electrodeare
coated on the surface of core or backbone particles, as illus-
trated inFig. 1.However, if thecomplexofa coreparticleand the
nano-particles coated on the core particle surface is viewed as
an equivalent particle, the novel electrode may be viewed as a
random packing of equivalent particles. For that reason, the
traditional percolation theory based conductivity model is
applicable. For simplicity, the discussionhere is limited to cases
that the core particles are pure ionic conducting and one type of
thenano-particles is purely electronic conducting and the other
type of the nano-particles is purely ionic conducting.
Based on the physical picture of the coreeshell structure
and the percolation theory based conductivity model, math-
ematical analysis shows that the electronic conductivity sede
and the ionic conductivity sedi of the triple nano-composite
electrode may be expressed as:
sede ¼ s0
e
�r2i � r2eq
�ln½tan ðq0=2Þ�
reqri cos a0
�jshelle � PC
1� PCð1� feqÞ
�g(1)
sedi ¼ �2
ffiffiffiffiffiffiffiAB
pln tan ðq0=2Þ
r2eq lnffiffiffiffiffiffiA=B
pþcos q0ffiffiffiffiffiffi
A=Bp
�cos q0
� ð1� feqÞg (2)
A ¼ sshelli
�r2eq � r2i
�þ s0
i r2i (3)
B ¼ s0i r
2eq (4)
sshelli ¼ s0
i
�jshelli � PC
1� PC
�g
(5)
Here s0eðiÞ is the intrinsic electronic (ionic) conductivity of
the electrode material i. is the feature radius of the backbone
particle eq. is the radius of the equivalent particle, or the sum
of i and the thickness of the nano-particle shell. jshelleðiÞ is the
volume fraction of electronic (ionic) conducting nano-
particles in the shell 4. is the equivalent electrode porosity
for the random packing of equivalent particles and may be
calculated using the overall electrode porosity and the mate-
rial composition of the coreeshell structure. fshellnano refers to the
porosity for the infiltrated nano-particles shell jnano, is the
volume fraction of nano-particles in the solid phase of the
electrode q0. is the contact angle of equivalent particles and
may be determined by the geometrical relationship of
reqcosq0 ¼ ricosa0 [15], where a0 is the contact angle between
core particles aswell as between nano-particles and a0¼ 15o is
assumed [20,21] g. is a Bruggeman factor reflecting the effect
ls and theoretical analysis of novel solid oxide fuel cell withof Hydrogen Energy (2014), http://dx.doi.org/10.1016/
Fig. 1 e Schematic of triplet nano-composite electrode.
i n t e rn a t i o n a l j o u rn a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e7 3
of tortuous conduction paths C. is the percolation threshold
which can be determined by the 2D and 3D percolation
thresholds P2C and P3
C:
PC ¼ P3C þ
P2C � P3
C
�$N�1=0:9 (7)
where N ¼ (req � ri)/2rnano is the number of nano-particle
layers coated on the core particle surface and rnano denotes
the average radius of nano-particles in the shell.
Effective triple-phase boundary lengthThe TPB length for the triplet nano-composite electrode ðlvTPBÞis the sum of the effective TPB length between the core and
nano-particles ðlvTPB;core�nanoÞ and the effective TPB length be-
tween the ionic and electronic nano-particles in the shell
ðlvTPB;nano�nanoÞ.The effective volumetric TPB lengths of the triplet nano-
composite electrode can be evaluated as:
lvTPB;core�nano ¼ 2prnanoðsin a0ÞnVcoreZcore;e�nanoPcorePe�nano (8)
lvTPB;nano�nano ¼ 2prnanoðsin a0ÞnVe�nanoZe�nano;i�nanoPe�nanoPi�nano
(9)
lvTPB ¼ lvTPB;core�nano þ lvTPB;nano�nano (10)
where nVcore ðnV
e�nanoÞ is the volumetric number density of core
particles (electronic nano-particles) in the electrode Zcor-
e,e_nano. is the coordination number between the core particle
and the electronic nano-particles in the shell Ze�nano,i�nano. is
the coordination number between the electronic nano-
particles and the ionic nano-particles Pcore. is the percolation
probability of core-particles and may be assumed to be 1 as
Please cite this article in press as: Chen M, et al., Property modetriplet nano-composite electrode, International Journalj.ijhydene.2014.02.036
the core-particles are prepared as the backbone and likely to
be fully percolated Pe(i)�nano. is the percolation probability of
the electronic (ionic) nano-particles in the shell. For low nano-
particle loading, the network of nano-particles is approxi-
mately two-dimensional and one has [22]:
PeðiÞ�nano ¼ jshelleðiÞ � PC
1� PC
!5=36
(11)
Hydraulic radiusThe hydraulic radius (or pore radius), rg, is an important
parameter for gas transport in the porous electrode structure
[23]. The traditional theory for the hydraulic radius [21] as-
sumes a random packing of spherical particles. However, the
nano-particles are not randomly distributed with the core-
particles but instead coated on the core-particle surfaces.
Therefore, it is only reasonable to apply the traditional hy-
draulic radius model to the equivalent particles as the elec-
trode may be viewed as a random packing of the equivalent
super-particles (Fig. 1):
rg ¼ 2req3ð1� feqÞ (12)
Considering the LSMnano/YSZnano/YSZcore cathode re-
ported in Ref. [7], it involves the following experimental pa-
rameters: 39 nm for the radius of core-particle, 15 nm for the
radius of nano-particle jcore ¼ 42%, for the volume fraction of
the core particles and 4 ¼ 45% for the total porosity of the
electrode. Assuming the porosity of the shell layer to be
fshellnano ¼ 26%which corresponds to a close packing of the nano-
particles in the shell, the radius for the equivalent super
particle req is calculated to be 59 nm. The porosity for the
equivalent super-particles may be determined as
feq ¼ f� ð1� fÞ � ð1� jcoreÞ � fshellnano=ð1� fshell
nanoÞ and is calcu-
lated to be 34%. According to Eq. (12), the hydraulic diameter
(pore size) of the triplet nano-composite electrode is found to
be 119 nm. The result is in very reasonable agreementwith the
experimental data of 135 nme156 nm. In the other hand, the
hydraulic diameter of the LSMnano/YSZnano/YSZcore cath-
ode is calculated to be 49 nm by the traditional hydraulic
radius model [21], which is very different from the experi-
mental result [7]. The much improved agreement with the
experiment by using Eq. (12) strongly favors our hydraulic
radius model.
Multi-physical numerical model
The above models are used to calculate the new properties of
triplet nano-composite electrodes. Parameters required for
computing the new properties are chosen to correspond to the
experimental data [6] as much as possible. When the required
parameters are not specified in the experiment, e.g., the
electrode porosity and the sizes of LSM and YSZ particles in
the cathode [6], the same data set used in Ref. [20] of a typical
standard cell is adopted here.
These property data are used in a multi-physics numerical
model for the triplet nano-composite electrodes. The multi-
physics model couples the intricate interdependency among
ionic conduction, electronic conduction, electrochemical
ls and theoretical analysis of novel solid oxide fuel cell withof Hydrogen Energy (2014), http://dx.doi.org/10.1016/
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e74
reaction and gas transport. For the brevity of this paper, the
governing equations, boundary conditions and model geom-
etry settings as well as other required technical details are
omitted here, but may be found in Refs. [24e26]. The finite
element commercial software COMSOL MULTIPHSICS�
Version 3.5a [27] is used in the present study to solve the
coupled partial differential equations of electronic, ionic and
gas transport macro-models. Structured mesh elements were
used and consisted of 6800 rectangles with 109347 degrees of
freedom. The direct solver (UMFPACK) was used to solve the
coupled partial differential equations with a relative conver-
gence tolerance of 1e�6.
Results and discussion
This section first describes the validation of the proposed
models. The validated models are then used to discuss some
effects of microstructure and material compositions on the
properties of the triplet nano-composite electrode.
Model validation
Direct comparisons of the proposed models with the experi-
mental data are generally difficult due to the lack of the
experimental measurements. Other than the above
mentioned hydraulic radius, only indirect validation of the
models is possible.
Fig. 2 shows a comparison of the theoretical and experi-
mental IeV curves. The theoretical IeV curves are obtained
using our multi-physics numerical model with the electrode
propertydata computedby the abovedescribed expressions.As
shown in Fig. 2, very good agreement is obtained between the
theoretical and experiment IeV curves at different tempera-
tures. It should be pointed out that the IeV curve is strongly
influenced by the electrochemical activation polarization that
is highly dependent on the TPB length and the temperature.
Similarly, the ionic conductivities of theYSZ electrolyte and the
triple nano-composite electrode are also strongly temperature
dependent. The temperature dependence of the ionic ohmic
Fig. 2 e Comparison of theoretical and experimental IeV
curves at different temperatures.
Please cite this article in press as: Chen M, et al., Property modetriplet nano-composite electrode, International Journalj.ijhydene.2014.02.036
polarization is very different from that of the activation polar-
ization. The IeV relation is also strongly affected by the ionic
ohmic polarization [28]. The good agreement between the
theoretical and experimental IeV curves at different tempera-
tures may be obtained only if the TPB length and the ionic
conductivity of the electrode are properly determined. In other
words, the comparison provides an indirect yet strong support
for our ionic conductivity and TPB models.
The electronic conductivity of a single phase nano-
composite electrode and its relatively weak temperature
dependence obtained based on a model similar to Eq. (1) have
been verified previously [15]. The difference between the
electronic conductivities of the single- and binary-phase
nano-composite electrodes is that the former
(w1000 S cm�1) is larger than the latter (w100 S cm�1) by one
order ofmagnitude. Consequently, the electronic conductivity
of a triplet nano-composite electrode may also substantially
influence its IeV curves. The good agreement between the
theoretical and experimental IeV curves implies that the
electronic conductivity is reasonably estimated by our model.
In fact, even if the concentration polarization that is often
relatively small is not properly determined, significant de-
viations from the experiments may be obtained, as to be
shown below. Therefore, the high quality agreement of the
theoretical and experimental IeV curves serves as a strong
support of our models.
As discussed in Section 2.1.3, our model for the hydraulic
radius of a triple nano-composite electrode provides a result
in good agreement with the available experiment. Even
though the concentration polarization is often small for
conventional electrode [28], a correct determination of the
hydraulic radius and the resulting concentration polariza-
tion is crucial for predicting the IeV relation of a cell with a
triplet nano-composite electrode. Fig. 3 shows a comparison
of the theoretical and experimental IeV curve at 700 �C. Thetheoretical model for Fig. 3 is the same as that for Fig. 2,
except that the blue theoretical curve in Fig. 3 is obtained by
Fig. 3 e Comparison of theoretical and experimental IeV
curves. Except for the hydraulic radius, all other
parameters are the same for the traditional model and our
model. (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of
this article).
ls and theoretical analysis of novel solid oxide fuel cell withof Hydrogen Energy (2014), http://dx.doi.org/10.1016/
i n t e rn a t i o n a l j o u rn a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e7 5
using the traditional theory for the hydraulic radius. Clearly,
the theory with the traditional hydraulic radius model pro-
vides a poor prediction of the IeV curve. The reason is that
the traditional model predicts a very small hydraulic radius
for the triplet nano-composite electrode, as discussed above
in Section 2.1.3. As a result, the traditional model signifi-
cantly overestimates the concentration polarization for the
triplet nano-composite. Consequently, it is important to use
the improved model for the hydraulic radius of triplet nano-
composite electrode.
Influence of microstructure and material composition onelectrode properties
There are a large number of adjustable parameters in a triplet
nano-composite electrode, e.g., the core particle radius, the
electrode porosity, the nano particle radius, the nano-particle
loading, the relative quantity of electronic and ionic nano
particles. Here we only discuss the influence of some typical
parameters on the electrode properties and leave a systematic
investigation on the parametric space for future studies.
The most commonly triplet nano-composite electrode is
manufactured by infiltrating both electronic and ionic nano-
particles onto an established porous electrode backbone
with a porosity of 60%w65% in the electrode [2]. We focus here
on discussing Ninano/YSZnano/YSZcore anodes with the
porosity of the initially porous YSZ backbone of 65%. The
volume fraction ratio of the of nano Ni and nano YSZ particles
in the shell is fixed at 6:4, a ratio that is beneficial for perco-
lation of both nano Ni and nano YSZ networks [21].
Fig. 4 shows the dependences of electronic conductivity
and TPB length on the nano Ni loading for two core-particle
radii of 150 nm and 500 nm. The radius of the nano particle
is 15 nm. As shown in Fig. 4a), the conductivity for ri ¼ 500 nm
is generally higher than that for ri ¼ 150 nm. A none-zero
conductivity is obtained for ri ¼ 500 nm at a Ni loading of a
little over 2.5%, while it requires almost 10% Ni loading for
ri ¼ 150 nm. Adequate conductivity (�100 S cm�1) is obtained
for ri ¼ 500 nm with a Ni loading of about 8%, but an almost
twice as much Ni loading is required for ri ¼ 150 nm. The re-
sults are quite understandable. For a given Ni volume fraction
in the electrode, the number of nanoNi particles coated on the
surface of a core particle is larger for a larger core particle due
Fig. 4 e Dependences of electronic conductivity and effective TP
electronic conductivity, b) TPB length.
Please cite this article in press as: Chen M, et al., Property modetriplet nano-composite electrode, International Journalj.ijhydene.2014.02.036
to the given volume ratio of the core and nano particles.
Consequently, the percolation threshold of the coated Ni
particle network is reached with a smaller Ni loading for a
larger core particle. Similarly, the conductivity for a given Ni
loading is higher for a core particle backbone of larger size due
to the presence of more layers of conducting nano Ni layers.
A larger core particle radius is also beneficial for obtaining
longer effective TPB length, as shown in Fig. 4b). However, the
difference between the TPB lengths for different core particle
radii is relatively small when the Ni loading is above the
percolation threshold for the electrode with smaller core
particle. Themost important difference occurs when the nano
Ni loading is below or near the threshold required for the
smaller core particle electrode.
As the percolation threshold is linked to both the electronic
conductivity and the effective TPB length, overall it may be
simply said that a larger radius of core-particle is beneficial for
obtaining a desirable electronic conductivity at a low nano Ni
loading. However, it is worthy pointing out that there is a
theoretical upper-limit for the core-particle size to make the
model conclusion valid. That is, the thickness of the electrode,
H, should be larger than the correlation length x, of the
percolated packing of equivalent particles [29]:
H > x ¼ ri ji � pc
�0:9. Here ji is the volume fraction of the core-
particles in the electrode and pc ¼ 0.294 is the percolation
threshold of the electrode with a random packing of spherical
particles [21,30]. In other word, the above analysis is valid only
when the core-particle radius is smaller than its upper-limit,
rmaxi ¼ H
ji � pc 0:9.
Fig. 5 shows the dependences of electronic conductivity
and effective TPB length on the radius and loading of nano Ni.
The discussion here tries to correlate with the experiments in
Refs. [2,6,31]. Hence, the volume fraction of core particles in
the electrode is set at 58.33% as used experimentally. The
radius of nano Ni particle in the experiments may vary from
10 nm to 15 nm. Considering the agglomeration of Ni particles
that is often limited to an increase of Ni particle size of 50%
[32e35], larger radii of nano Ni particles up to 25 nm are also
included.
As shown in Fig. 5, at a given Ni volume fraction, both the
electronic conductivity and the effective TPB length decrease
with the increase of the Ni particle size. The trend is opposite
to the trend for the core particle radius, but the underlying
B length on the core-particle radius and nano Ni loading: a)
ls and theoretical analysis of novel solid oxide fuel cell withof Hydrogen Energy (2014), http://dx.doi.org/10.1016/
Fig. 5 e Dependences of electronic conductivity and effective TPB length on the radius and loading of nano Ni: a) electronic
conductivity, b) TPB length.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e76
mechanism is quite similar. That is, due to the fixed volume
ratio of the core and nano particles for a given Ni volume
fraction, the number of nano Ni particles coated on the sur-
face of a core particle is smaller for larger Ni particles. As a
result, the conductivity as well as the TPB length for a given Ni
loading are lower for larger Ni particles.
As may be seen in Fig. 5, a sufficiently high TPB length
(�1013 m$m�3) may be obtained with a nano Ni loading
smaller than that required for obtaining an adequate elec-
tronic conductivity (�100 S cm�1). In other words, the required
Ni loading is determined by the desired electronic conduc-
tivity. Even though an adequate conductivity may be obtained
at a Ni loading of 9% for rnano¼ 10e15 nm, a nano Ni loading of
11% or more is required for long term operation that involves
Ni agglomeration. The extra nano-particle loading should be
considered when manufacturing practical cells.
Summary
A triplet nano-composite electrode may be viewed as a
random packing of equivalent particles with the equivalent
particle consists of a core particle and a wrapping shell of
nano-particles coated on the core particle surface. Based on
this physical picture, new theoretical expressions for
computing the electrode electronic and ionic conductivities,
effective TPB length and hydraulic radius are proposed. These
new models are used in a multi-physics numerical model to
predict the performance of SOFC with triplet nano-composite
electrode. The multi-physics model couples the intricate
interdependency among ionic conduction, electronic con-
duction, electrochemical reaction and gas transport. Numer-
ical simulation based on the proposed propertymodels shows
good agreement with the available experimental data,
demonstrating the validity of the models.
The verified models are further used to discuss the influ-
ence of microstructure and material composition on the
electrode properties. The analysis shows that: (i) The larger
the core-particle size or the smaller the nano-particle size is,
the higher the electronic conductivity and TPB length will be,
when all other factors being equal; (ii) An adequate electronic
conductivity requires a higher nano-particle loading than that
Please cite this article in press as: Chen M, et al., Property modetriplet nano-composite electrode, International Journalj.ijhydene.2014.02.036
required for obtaining a sufficiently high TPB length. The
requiredNi nano-particle loading is determined by the desired
electronic conductivity.
Acknowledgments
The financial support of the National Basic Research Program
of China (973 Program Grant No. 2012CB215405), the National
Natural Science Foundation of China (Grant Nos. 11074233 &
11374272) and the Specialized Research Fund for the Doctoral
Program of Higher Education (Grant Nos. 20113402110038 &
20123402110064) are gratefully acknowledged.
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