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Simulation of Micro/Nanopowder Mixing Characteristics for Dry Spray Additive Manufacturing of Li-Ion Battery Electrodes

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A new dry spraying additive manufacturing method for Li-ion batteries has been developed to replace the conventional slurry-casting technique for manufacturing Li-ion battery electrodes. A dry spray manufacturing process can allow for the elimination of the time- and energy-intensive slurry drying process needed due to the use solvents to make the electrodes. Previous studies into the new manufacturing method have shown successful fabrication of electrodes which have strong electrochemical and mechanical performance. Li-ion battery electrodes typically consist of three basic materials: active material (AM), binder particle additives (BPA), and conductive particle additives (CPA). In this paper, a discrete element method (DEM) simulation was developed and used to study the mixing characteristics of dry electrode powder materials. Due to the size of the particles being in the submicron to micron size range, the mixing characteristics are heavily dependent on van der Waals adhesive forces between the particles. Therefore, the effect the Li-ion battery electrode material surface energy has on the mixing characteristics was studied. Contour plots based on the DEM simulation results where the surface energy components of selected material types are changed were used to predict the mixing characteristics of different particle systems. For the cases studied, it is found that experimental mixing results are representative of the results of the DEM simulations.
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Brandon Ludwig
Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
400 West 13th Street,
Rolla, MO 65409
Jin Liu
Mechanical Engineering,
Worchester Polytechnic Institute,
100 Institute Road,
Worchester, MA 01609
Yangtao Liu
Mechanical Engineering,
Worchester Polytechnic Institute,
100 Institute Road,
Worchester, MA 01609
Zhangfeng Zheng
Mechanical Engineering,
Worchester Polytechnic Institute,
100 Institute Road,
Worchester, MA 01609
Yan Wang
Mechanical Engineering,
Worchester Polytechnic Institute,
100 Institute Road,
Worchester, MA 01609
Heng Pan
1
Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
400 West 13th Street,
Rolla, MO 65409
e-mail: hp5c7@mst.edu
Simulation of Micro/Nanopowder
Mixing Characteristics for Dry
Spray Additive Manufacturing
of Li-Ion Battery Electrodes
A new dry spraying additive manufacturing method for Li-ion batteries has been devel-
oped to replace the conventional slurry-casting technique for manufacturing Li-ion bat-
tery electrodes. A dry spray manufacturing process can allow for the elimination of the
time- and energy-intensive slurry drying process needed due to the use solvents to make
the electrodes. Previous studies into the new manufacturing method have shown success-
ful fabrication of electrodes which have strong electrochemical and mechanical perform-
ance. Li-ion battery electrodes typically consist of three basic materials: active material
(AM), binder particle additives (BPA), and conductive particle additives (CPA). In this
paper, a discrete element method (DEM) simulation was developed and used to study the
mixing characteristics of dry electrode powder materials. Due to the size of the particles
being in the submicron to micron size range, the mixing characteristics are heavily
dependent on van der Waals adhesive forces between the particles. Therefore, the effect
the Li-ion battery electrode material surface energy has on the mixing characteristics
was studied. Contour plots based on the DEM simulation results where the surface
energy components of selected material types are changed were used to predict the mix-
ing characteristics of different particle systems. For the cases studied, it is found that
experimental mixing results are representative of the results of the DEM simulations.
[DOI: 10.1115/1.4037769]
1 Introduction
Li-ion battery electrodes consist of four basic components: two
electrodes (cathode and anode), a separator, and an electrolyte.
The electrode components are made with three essential materials:
the active material (AM), binder particle additive (BPA), and con-
ductive particle additive (CPA). The AM is needed to provide the
energy for the battery while the CPA is dispersed among the AM
to improve the electroconductivity of the electrode. Binder parti-
cle additives are needed to secure the electrode material to the
current collecting substrate (typically aluminum for the cathode
and copper for the anode). Commercial Li-ion battery electrodes
are manufactured using the slurry-casting technique. In this manu-
facturing method, the electrode materials are mixed with a solvent
to dissolve the BPA. This allows the BPA to readily coat the
remaining particles (AM and CPA). The binder, most commonly
polyvinylidene fluoride (PVDF), is matched with a suitable sol-
vent, most commonly N-methyl-2-pyrrolidone (NMP), to allow
for optimal mixing and coating.
Due to the direct influence of CPA and BPA distribution on the
electrochemical properties, extensive mixing studies have been
performed to understand the slurry preparation process on the
electrode morphology [1,2]. The effect of multiple mixing steps
and the length of mixing (some up to 48 h) have been studied [3].
Once mixed, the slurry is cast onto the current collector and must
be dried to create a dry porous electrode for further battery fabri-
cation. The drying process can take a significant amount of time
and energy (up to 24 h at 80–120 C), which increases the manu-
facturing cost of the battery electrodes [4,5]. In commercial appli-
cations, an expensive NMP recovery system is used to recover
evaporated NMP due to the environmentally hazardous properties
of NMP [610]. More environmentally friendly solvents, such as
aqueous based slurries, can be used to eliminate the need for a
recovery system but the differences in slurry rheology need to be
accounted for [1012]. The use of aqueous based slurry necessi-
tates the change to a matching binder, such as carboxymethyl cel-
lulose [6,9,11,13], as PVDF needs nonaqueous solvent to
sufficiently dissolve [1]. The slurry mixing properties must be
accounted for as high surface tension due to strong hydrogen
bonding can cause particles to agglomerate and electrode cracking
problems can occur during the drying step [10,14,15].
Eliminating the solvent, and its associated drying process, rep-
resents an ideal manufacturing process. Working electrodes have
been successfully manufactured using pulsed laser and sputtering
deposition but are handicapped by slow deposition rates and high
annealing temperatures, making commercial feasibility difficult
[1620]. A new electrode manufacturing method using dry elec-
trostatic spraying [21,22] shows a promising alternative to the
commercial slurry-casting technique due to its strong performance
and capability of reducing costs by 15%. The new method
requires only enough time for the BPA to melt to ensure strong
1
Corresponding author.
Contributed by the Manufacturing Engineering Division of ASME for publication
in the JOURNAL OF MICRO-AND NANO-MANUFACTURING. Manuscript received June 15,
2017; final manuscript received August 21, 2017; published online September 27,
2017. Assoc. Editor: Yayue Pan.
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mechanical properties [21] as opposed to the time associated with
drying out the solvent in the conventional process. Figure 1(a)
shows a diagram of the new manufacturing process using dry elec-
trostatic spraying. Unlike slurry-cast electrodes, the BPA is not
dissolved in solvent and coated on the remaining particles, and
therefore, a uniform distribution of the BPA within the AM and
CPA is needed to ensure strong mechanical bonding. Cases of
BPA and CPA agglomeration (Fig. 1(b)) could lead to weak
points allowing for poor electroconductivity and mechanically
weak locations. Uniform mixing of the additive materials will dis-
play minimal agglomerates (Fig. 1(c)) leading to more efficient
use of the additive materials. Previous studies [21,22] show that
the electrodes fabricated using the new solvent-free process are
stronger than those of the conventional method while also display-
ing similar electrochemical performance to that of the conven-
tional process. While this new method has produced electrodes
with strong electrode performance, the mixing properties of dry
battery electrode materials is not well known.
In this paper, the mixing characteristics of dry electrode pow-
ders used in the new dry manufacturing process will be studied.
Previous studies pertaining to mixing the electrode materials used
in the slurry-cast technique are not relevant to the new manufac-
turing technique, and thus, this paper focuses on understanding
the dry powder mixing process to help predict BPA and CPA dis-
tribution within a given AM. To study the mixing behavior of Li-
ion battery electrode materials, a discrete element method (DEM)
simulation has been developed to understand the effect material
properties have on the mixing uniformity of Li-ion battery elec-
trode particles. The developed DEM simulation is based on a soft-
sphere model where it is assumed the colliding particles will form
small deformations upon impact. The resulting deformation will
cause a contact area between the two particles, which is then sub-
ject to adhesive forces. Due to the micron and submicron size of
Li-ion battery electrode materials, the particle mixing is strongly
dependent on adhesive interactions once the particles collide
[23,24]. The DEM simulation results can then be used for future
studies and Li-ion battery electrode materials to better estimate
the mixing properties.
2 Discrete Element Simulation Modeling
To understand the mixing of micro/nanosized powders which
represent the AM, BPA, and CPA powders, a DEM model for
adhesive fine particles has been developed. Due to the particle
sizes being in the nanometer to micrometer size range, the pro-
posed simulation model is heavily dependent on the surface adhe-
sive force interactions between the particles [23,24]. This
adhesive force is related to the interfacial energies of the Li-ion
electrode materials.
Motion of the individual particles can be described by New-
ton’s second law of motion, and the governing equation for the
translational motion of the particles can be defined by
mi
d2r
*
i
dt2¼F
*adh
iþF
*grav
i(1)
where m
i
and r
i
are the mass and position vector of a particle i,
respectively. F
adh
and F
grav
represent the adhesive contact forces
due to particle collisions and gravitational forces, respectively.
Since van der Waals adhesive forces act in a nonlinear fashion
with the other forces acting on particles, such as sliding resistance
and elastic repulsion, they cannot be simply added to them [23].
The sum of the adhesive and collision forces, F
adh
, on a particle is
given by
F
*adh
i¼Fnn
*(2)
where nis the unit normal along the line passing through the parti-
cle centroids; F
n
and F
s
are the normal force and sliding force
magnitude, respectively; and F
n
is composed of the elastic term
F
ne
and the damping term F
nd
.
For this study, only the normal force is considered. In order to
calculate normal force, contact area between two particles is mod-
eled based on a soft-sphere model where two separate particles
will experience deformation upon collision, forming a contact
area (Fig. 2(a)). Chokshi et al. [25] modified the contact theory
proposed by Johnson, Kendall, and Roberts [26] to simplify the
contact radius, a
0
,to
a0¼9pwijR2
2E

1=3
(3)
Fig. 1 Solvent-free manufacturing process: (a) schematic of
dry electrostatic spraying system, (b) representation of poorly
mixed Li-ion battery electrode powders with agglomerations of
additive particles, and (c) representation of well mixed Li-ion
battery electrode powders with uniform distribution of additive
particles
Fig. 2 Contact mechanics of colliding particles: (a) contact interface and radius represen-
tation due to the collision of iand jparticles and (b) representation of the i2jparticle over-
lap due to collision
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where Rand Eare the effective particle radius and elastic moduli,
respectively. Here, Rand Eare defined as
1
R¼1
Ri
þ1
Rj
(4)
1
E¼1v2
i
Ei
þ1v2
j
Ej
(5)
where two particles are considered with radii R
i
and R
j
, elastic
moduli E
i
and E
j
, Poisson’s ratios v
i
and v
j
. Table 1shows the
material property values needed for the DEM simulations. The
work of adhesion, w
ij
, between the two particles can be defined by
using the Fowkes equation [27]
wij ¼2ðcd
icd
jÞ0:5þ2ðcp
icp
jÞ0:5(6)
where c
i
d
and c
j
d
are the dispersive surface energy component val-
ues for material iand j, respectively, and c
i
p
and c
j
p
are the polar
surface energy component values for material iand j, respectively.
The contact area at the work of adhesion interface can be defined
as Aij ¼pa2
0.
Chokshi et al. [25] proposed that the normal force, F
ne
, could
be rearranged in terms of the contact radius to
Fne ¼FC4a
a0

3
4a
a0

3=2
"#
(7)
where F
C
is the critical force given by FC¼3pwijR=2 and a/a
0
can be found by solving
dN¼61=3dC2a
a0

2
4
3
a
a0

1=2
"#
(8)
where d
N
is the normal particle overlap defined in Eq. (9) and d
C
is the particle overlap when at the critical force F
C
. When a separa-
tion force is applied and the spheres begin to stretch, forming a neck
between the two spheres, the critical particle overlap d
C
is equal to
d
N
when separation finally occurs. In relation to the equilibrium
radius a
0
, the critical particle overlap d
c
is given by Eq. (10)
dN¼RiþRjjxixjj(9)
dC¼a2
0
26
ðÞ
1=3R
(10)
where x
i
and x
j
denote the centroid positions of the two particles.
In this case, the normal particle overlap d
N
does not actually over-
lap but represent the amount of overlap that would occur if the
spheres had not deformed and flattened (Fig. 2(b)).
A damping normal force F
nd
makes up the second part of the
normal force F
n
and is defined as
Fnd ¼gNv
*
rn
*(11)
where the g
N
is the normal dissipation coefficient (chosen to be
0.05 for this study) and v
R
is the relative particle velocity. The
normal dissipation coefficient g
N
is assumed to have the form
gN¼aðmkNÞ1=2(12)
where ais a function of the restitution coefficient (chosen to be 1)
[28]. The normal stiffness coefficient, k
n
, is estimated by F
n
/d
N.
Software used for performing the DEM simulations was devel-
oped from in-house code. The size of the mixing volume was set
such that the particles can interact with one another without being
limited by space. The boundary conditions were set to simulate a
mixing container and therefore the walls were set to be reflective.
One hour of computation time yields 12 ls of mixing time in
cases involving a larger number of particles (200) but lower par-
ticle numbers will allow for more mixing time.
3 Results
The DEM results can be used to study the surface energy
effects on mixing for any particulate system, but for this study the
effect of battery electrode materials was considered. Different
mixing cases were considered to show how AM surface energy
affects the BPA distribution and also how CPA surface energy
component values affect the distribution of CPA when mixed with
AMs with different surface energy values. The mixing behavior of
BPAs and CPAs was also considered as the mixing morphology
of these materials directly influences the electrode mechanical
strength and electroconductivity. Finally, the mixing behavior of
all three material types is characterized.
3.1 Active Material–Binder Particle Additive. Due to Li-
ion battery AM displaying various surface energy component val-
ues, the effect of the AM surface energy components on the BPA
distribution was studied. From previous studies [12,22], the dis-
persive component for cathode AM can range from 37.0 to
42.5 mN m
1
while the polar components could be from 1.35 to
177 mN m
1
. This extreme range of polar components could lead
to a vast difference in mixing uniformity of the BPA within the
AM. A DEM simulation consisting of a single 10 lm particle, act-
ing as the AM particle, and thirty 0.5 lm particles, acting as the
BPA particles, was used to characterize the AM-BPA mixing.
Surface energy components of the BPA were set according to pre-
viously measured PVDF values (dispersive and polar surface
energy components were calculated to be 24.33 mN m
1
and
6.18 mN m
1
, respectively [21]) as PVDF is a common BPA in
Li-ion battery electrodes. The PVDF surface energy values are
also consistent with previous studies [29,30] where PVDF surface
energy is measured. The BPA particles were set to be monosized
due to experimental studies using PVDF particles show a particle
standard deviation within 8% of the average. The BPA underwent
a premixing process to form an agglomerate of BPA (Fig. 3(a)).
After premixing, the BPA agglomerate is allowed to interact with
the AM particle. In the case of aggregation, it is expected that the
BPA agglomerate will experience minimal changes after interact-
ing with the AM particle (Fig. 3(b)). In the case of intermixing, it
is expected that the BPA agglomerate will begin to break apart
and attach to the AM particle, forming a layer (Fig. 3(c)). In the
DEM simulations, the output can be used to count the number of
BPA in contact with the AM particle.
A contour plot (Fig. 3(d)) of the contact points over a range of
surface energy components shows that low dispersive energy val-
ues (0–10 mN m
1
) and polar energy values from 0 to 35 mN m
1
of active material results in the BPA agglomerate experiencing
minimal break-up when interacting with the active material
Table 1 Material input parameters for DEM simulations
Material Radius, R(lm) Density, q(g cm
3
) Young’s modulus, E(GPa) Poisson’s ratio (v)
AM 5 4.90 38 0.18
BPA 0.25 1.78 4.3 0.34
CPA 0.125 2.20 5.0 0.23
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particle (Fig. 3(b)shows a DEM simulation result where aggrega-
tion was found). In this range, the BPA agglomerate would either
weakly attach to the AM particle surface or bounce on and off of
the AM particle due to very weak work of adhesion between the
AM-BPA surfaces. Outside of the range, the DEM simulation
results show BPA beginning to form a monolayer on the AM sur-
face (Fig. 3(c)shows a DEM simulation result where intermixing
was found). For both cases, intermixed and aggregation, the mix-
ing time and the evolution of the contact points can be compared
in Fig. 3(e). In the intermixed case, the time to achieve all BPA
contacts on the AM particle was 2.4 ms. It can be seen that the
number of contacts in the intermixed case gradually increased
while the aggregation case exhibited sporadic BPA contact with
the AM particle, further showing the weak attraction between the
two materials. Known AM surface energy components were
added to the DEM contour plot results to show how BPA is
expected to mix with the AM (Fig. 3(d)).
3.2 Active Material–Conductive Particle Additive. In this
case, the surface energy components of the CPA were allowed to
vary while the dispersive and polar surface energy components of
the AM particle were kept constant at 40 mN m
1
and 2 mN m
1
,
respectively. The surface energy component values for the AM
were selected to represent a case where negligible polar surface
energy component is experienced as is the case of the previously
measured as-received LiCoO
2
(LCO) [22]. Similar to the AM-
BPA case, the AM-CPA DEM simulations involved a single
10 lm AM particle while the CPA were represented by 0.25 lm
particles (200 in total). The particles representing CPA were set to
be monosized due to experimental measurements using Super C65
carbon showing a standard deviation of 11% of the average size.
Initially, a premixing step was incorporated into the DEM simula-
tions to form an agglomerate of CPA (Fig. 4(a)). For intermixing
to occur, the CPA should begin to assemble on the AM surface
(Fig. 4(b)) while minimal CPA assembly should happen when
aggregation occurs (Fig. 4(c)). A series of DEM simulations were
used to plot the number of CPA contacts on the AM surface (Fig.
4(d)). The DEM contour plots show that the location of peak inter-
mixing is at 20 mN m
1
dispersive component and 0 mN m
1
polar
component. Figure 4(b)shows the DEM mixing results from a sim-
ulation using 20 mN m
1
dispersive energy and 0 mN m
1
polar
energy and it can be seen that the CPA agglomerate has broken
apart and formed on the surface of the AM particle. In the contour
plot (Fig. 4(d)), the intermixing to aggregation trend is found to
radiate from the peak intermixing location. The crossover location
denoting a change between intermixing and aggregation is near the
25-50 contact point area location in the DEM contour plot. This
area in the DEM contour plot shows the location where the CPA
agglomerate attaches to the AM particle and slowly begins to form
around the AM surface. The 0-25 contact point area in the DEM
results denotes where very few CPA are in contact with the AM
particle (Fig. 4(c)). In this case, the CPA comes into contact with
the AM but does not alter its shape to conform to the AM surface.
Active material-conductive particle additive mixing behavior
was further studied by increasing the polar surface energy
Fig. 3 AM-BPA mixing. DEM simulation snapshots of AM-BPA mixing showing (a) premix-
ing, (b) aggregation, and (c) intermixing. Analytical (d) and DEM (e) contour plots showing
similar mixing behavior. (f) Comparison of mixing time found in DEM cases where intermix-
ing and aggregation occurs.
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component of the AM particle to 100 mN m
1
while keeping the
dispersive component to the same as before. This case was used to
represent an AM material with a high polar surface energy com-
ponent as shown in previous studies [12,22]. It is expected that
DEM results will show higher CPA contact points as compared to
Fig. 4(d)due to the higher interfacial energy between the AM and
CPA surface. This expectation was confirmed by the plotting the
CPA contact points (Fig. 4(e)) from the resulting DEM simula-
tions where the AM had higher polar surface energy. The contour
plot using a low polar component displayed a large 0-25 contact
point area denoting aggregate formation; in the new contour plot
using a larger polar component, this area is mostly replaced by
25-50 contact point areas. While these areas denote relatively few
contact points when compared to the number of contacts associ-
ated with peak intermixing, it does signify the CPA agglomerate
is attached to the AM and slowly conforming to the surface
(Fig. 4(f)). The same CPA agglomerate from the 0-10 contact
point area when the AM particle has a small polar surface energy
component shows a lower degree of conformation (Fig. 4(f)).
The dots located on the DEM simulation contour plots (Figs.
4(d)and 4(f)) denote previously measured [21,3136] surface
energy values of carbon materials. They are used to show the
expected mixing behavior of common carbon-based CPA materi-
als. Surface energy measurements of graphite powders had a mini-
mal polar component (0.54 mN m
1
) while the dispersive
component was around 56.27 mN m
1
[21,31]. Graphite surface
energy measurements can be used to gain insight into the surface
energy characteristics of carbon, but it may not be representative
of the more commonly used CPA material (Carbon Black) due to
its significantly larger size (10 lm). Previous studies [3234]
measuring Carbon Black surface energy show a similar low polar
component when compared to graphite, but the dispersive compo-
nent is typically measured at smaller values in the range of
18–35 mN m
1
. An increase in the Carbon Black polar surface
energy component can be achieved through surface modification
by way of acid–base treatments as detailed by Park et al. [35]
where the treatments can be used to obtain a polar surface energy
component up to 33.1 mN m
1
[36].
The rate of mixing between an intermixed and aggregated case
can be studied from the resulting DEM outputs to gain insight into
how the CPA agglomerate begins to change shape when interact-
ing with the AM particle. Figure 4(g)shows that an intermixed
case (where the dispersive and polar components were set to
20 mN m
1
and 10 mN m
1
, respectively) quickly achieves 90
CPA contacts (of the 200 total) within 0.2 ms and then the num-
ber of contacts steadily increased. An aggregated case (where the
polar and dispersive components were set to 100 mN m
1
) shows
very few CPA contact points on the AM surface. This is due to
the work of adhesion between the AM and CPA being large
enough that some of the exposed CPA will stay in contact with
the AM surface, but not large enough such that it overcomes the
very high work of cohesion between the particles in the CPA
agglomerate.
3.3 Binder Additive–Conductive Additive. The two previ-
ous cases dealt with the mixing behaviors of different additives
among active material particles, but intermixing within the addi-
tives is also needed to ensure more efficient usage of the materi-
als. Minimal intermixing within the additives will give way to
lower bonding strength as the BPA will not create enough contacts
with the CPA material. DEM simulations for the BPA-CPA mix-
ing case were carried out with the surface energy components of
the BPA set according to the measured PVDF surface energy val-
ues [21] while the surface energy components of the CPA were
changed. According to a previous study [22] where analytical
models are presented for predicting material mixing behavior
Fig. 4 AM-CPA mixing. DEM simulation snapshots of AM-CPA mixing showing (a) premixing, (b) intermixing, and (c) aggre-
gation. (d) DEM contour plot showing the number of CPA in contact with the AM surface when the AM polar component is
2mNm
21
.(e) DEM contour plot showing the number of CPA in contact with the AM surface when the AM polar component is
100 mN m
21
.(f) CPAs showing increased contact with higher polar surface energy AM as compared to low polar surface
energy. (g) Comparison of mixing time found in DEM cases where intermixing and aggregation occurs.
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based on surface adhesion, the BPA and CPA are expected to
intermix with each other when the dispersive and polar surface
energy components are between 10 and 40 mN m
1
and 0 and
20 mN m
1
, respectively. Outside of this region, it is more likely
that the CPAs and BPAs will exhibit minimal interaction with
each other.
Discrete element method simulations were used to check this
expectation with 0.5 lm spheres representing BPA (20 total) and
0.25 lm spheres representing CPA (400 total). The surface energy
components of CPA were set to 20 mN m
1
and 10 mN m
1
,
respectively. These values were selected as they are the values
associated with peak intermixing based on the previously pre-
sented analytical model [22]. If the model is correct, then the
DEM simulation should show a high degree of BPA and CPA
intermixing. In the simulation, it was found that individual BPA
were embedded within an agglomerate of CPA (Fig. 5(a)). An
enhanced view more readily shows this behavior where a mono-
layer of CPA is formed around BPA. Another simulation was
used to confirm the opposite case where BPA and CPA should not
intermix as well, forming an aggregate. For this simulation, both
the dispersive and polar surface energy components for CPA were
set to 100 mN m
1
. The results of this case confirm the predicted
mixing behavior where CPA form a large agglomerate (Fig. 5(b))
with BPA only attached to the surface of the CPA agglomerate.
Unlike the intermixed case where individual BPA are surrounded
by CPA, the CPA in this case have a work of cohesion too large to
enable the BPA to break apart the attached CPA surfaces. Note
that BPA only attach to the surface of CPA agglomerate with
embedding into CPA, which is clearly different from the intermix-
ing case.
3.4 Active Material–Binder Additive–Conductive Additive.
The previous DEM mixing cases considered only mixing two
materials, but in the actual case all three materials will need to be
mixed together. Two DEM simulations were considered to repre-
sent cases of Li-ion battery electrode material mixing. A single
AM particle 10 lm particle was mixed among 0.5 lm particles
representing the BPA (20 total) and 0.25 lm particles representing
the CPA (400 total). For both DEM simulations, the surface
energy for the BPA was based on the previously discussed PVDF
results and the surface energy for the CPA was set with the same
values as the intermixed case from Sec. 3.3 (dispersive and polar
surface energy components were 20 mN m
1
and 10 mN m
1
,
respectively). The surface energy values of CPA are also repre-
sentative of previous measurements of Carbon Black [32]. The
first DEM simulation had the AM surface energy measurements
based on low polar AM, representative of as-received LCO from a
previous study [22]. Figure 6(a)shows the outcome of the DEM
simulation where the BPA and CPA were dispersed on the AM
surface. BPA is shown to be intermixed among the CPA particles
with minimal agglomerations of BPA. For the other case, the
polar surface energy component was increased to 100 mN m
1
to
represent higher polar AM measurements from previous studies
[12,22]. The resulting DEM simulation shows similar results
(Fig. 6(b)) to the previous case. BPA and CPA are dispersed on
the AM surface while the BPA particles show no signs of aggrega-
tion. The behavior of the BPA on the two AM surfaces is expected
based on the DEM simulation results when only AM and BPA are
mixed as the two AM surface energies in this case lie within the
area related to intermixing (Fig. 3(d)). For CPA, the DEM simula-
tion results with only the AM and CPA are mixed largely predict
that CPA will have more contact with the higher polarity AM sur-
face than the low polar AM. In the case where all three material
types are mixed, the CPA has a similar degree of contact regard-
less of the polarity of the AM material. However, it should be
noted that the set CPA surface energy for these two cases show
similar CPA contact with the AM surfaces when only the CPA
and AM are mixed (the CPA surface energy used in this case lie
within the 80-100 contact point area associated with high AM-
CPA contact in both Figs. 4(d)and 4(e)). Using different CPA sur-
face energy values could lead to different distributions of CPA on
AM surfaces.
4 Experimental Verification
To verify the DEM results, Li-ion battery electrode materials
were mixed and SEM micrographs were taken. For the case of
AM-BPA mixing, as-received LCO powder was mixed with
PVDF powder in a high-energy mixer. The contour plot developed
from the DEM simulations point to intermixing occurring
(Fig. 3(d)). An SEM micrograph of the mixed materials shows the
expected intermixing behavior (Fig. 7(a)). A view of the DEM
simulation using the same parameters shows (Fig. 7(b)) similar
Fig. 5 BPA-CPA mixing: confirmation of analytical modeling
results where a predicted intermixed case is confirmed by a
DEM simulation (a) and where a predicted aggregation case is
confirmed by another DEM simulation (b)
Fig. 6 AM-BPA-CPA mixing: (a) DEM simulation showing mix-
ing behavior of all three materials when the AM polar surface
energy is 2 mN m
21
and (b) DEM simulation showing the mixing
behavior of all three materials when the AM polar surface
energy is increased to 100 mN m
21
040902-6 / Vol. 5, DECEMBER 2017 Transactions of the ASME
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results where the BPA (PVDF) is attached to the AM (LCO).
According to previous studies [22] where LCO was annealed to
obtain a larger polar surface energy component, the mixing of
annealed LCO with PVDF showed the BPA forming on the sur-
face of the AM and intermixing. The DEM simulations in this
study show similar behavior when the same surface energy com-
ponents are used as the material properties.
For the case of AM-CPA mixing, a previous study [22] mixed
LCO and Super C65 carbon with differing surface properties. It
was found that annealed LCO, where the dispersive and polar sur-
face energy components were 42.5 mN m
1
and >35.0 mN m
1
,
respectively, contained more Super 65 carbon particles on the
LCO surface when compared to as-received LCO where the dis-
persive and polar surface energy components were measured as
37.0 mN m
1
and 1.35 mN m
1
, respectively. This behavior was
confirmed by the DEM simulations (Fig. 4). It can be seen a large
range of CPA surface energies has a higher degree of contact with
the high polar AM surface (Fig. 4(e)) than with the low polar AM
surface (Fig. 4(d)).
For BPA-CPA DEM comparisons, PVDF and Super C65 car-
bon were mixed in a high-energy mixer. SEM micrographs of the
mixed powder (Fig. 7(c)) show individual PVDF particles embed-
ded within the Super C65 particles.
A DEM simulation using similar surface energy properties of
the materials shows similar intermixing behavior (Fig. 7(d)). The
BPA particles exhibit minimal contact with one another as the
BPA particles are individually embedded with the CPA particles.
5 Conclusion
In this paper, the effect particle surface energy had on the mix-
ing characteristics of micro/nanosized Li-ion battery electrodes
powders was studied. A DEM model based on the adhesive inter-
actions of the Li-ion battery electrode particles was developed to
simulate various mixing cases. DEM simulations were carried out
using surface energy measurements assembled from previous
studies and then compared with experimental mixing results. AM-
BPA results show that only a small range of AM surface energy
values will result in aggregation while AM-CPA mixing will be
affected by different AM polar surface energy component values.
BPA-CPA results show that BPA will be intermixed among CPA
particles when the CPA surface energy values represent common
values found in literature. For cases where all three material types
are mixed (as is the case in production), the DEM simulations
could accurately predict the mixing behavior of the accompanying
experimental studies. This study shows that mixing behavior of
other Li-ion battery electrode materials can be estimated when the
surface energy component values are known.
Funding Data
Division of Civil, Mechanical and Manufacturing Innovation
(Grant No. 1462321).
National Science Foundation (Grant Nos. CMMI-1462343
and CMMI-1462321).
Intelligent System Center (ISC).
Material Research Center (MRC) at Missouri University of
Science and Technology.
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... During the mixing process the carbon black agglomerates need to be de-agglomerated into nano-sized powders and evenly dispersed within the electrode. Ludwig et al. [173] applied DEM method to investigate the mixing uniformity of electrode particles, and studied the effect of adhesive forces, demonstrating the usefulness of DEM as a tool to investigate mixing behaviour of electrode materials using known Fig. 15. Reduced performance at high C rate can be due to decreased electronic conductivity resulting from sub-optimal conductive network [163]. ...
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