{Modelling the effect of anode particle radius and anode reaction rate constant on capacity fading of Li-ion batteries:}
http://dx.doi.org/10.5599/jese.1147 359
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372; http://dx.doi.org/10.5599/jese.1147
Open Access : : ISSN 1847-9286
www.jESE-online.org
Original scientific paper
Modelling the effect of anode particle radius and anode
reaction rate constant on capacity fading of Li-ion batteries
Vikalp Jha and Balaji Krishnamurthy
Department of Chemical Engineering, BITS Pilani, Hyderabad 500078, India
Corresponding author: balaji@hyderabad.bits-pilani.ac.in
Received: October 21, 2021; Accepted: November 26, 2021; Published: December 6, 2021
Abstract
This paper investigates the effect of anode particle radius and anode reaction rate constant
on the capacity fading of lithium-ion batteries. It is observed through simulation results that
capacity fade will be lower when the anode particle size is smaller. Simulation results also
show that when reaction rate constant is highest, the capacity loss is the lowest of lithium-
ion battery. The potential drop across the SEI layer (solid electrolyte interphase) is studied
as a function of the anode particle radius and anode reaction rate constant. Modelling
results are compared with experimental data and found to compare well.
Keywords
SEI; potential drop; side reaction; discharge
Introduction
Side reactions can cause various adverse effects leading to capacity fading in lithium-ion batteries.
The aging of Li-ion batteries usually occurs due to various parameters and electrochemical reactions,
and capacity loss varies between all stages during a charge-discharge load cycle, depending on various
parameters such as cell voltage, electrolyte concentration, temperature, and cell current. This work
shows the model for aging and capacity loss in the anode of a Li-ion battery, where the formation of
a thin film of solid-electrolyte-interface (SEI) shows an adverse capacity loss of cyclable lithium.
Capacity fading in a lithium-ion battery has been studied under various load conditions.
Haran et al. [1] studied the effect of various temperatures during various cycles in the capacity
fading of 18650 Li-ion cells. It is observed that with an increase in temperature of Li-ion batteries,
capacity fading is increased. It is observed that at temperatures higher than 55 °C, the cell ceases to
operate after 500 cycles due to ongoing SEI film formation over the anode surface. Han et al. [2]
studied the cycle life of commercial Li-ion batteries with LTO anodes in electric vehicles. The author
also found that at 55 °C, the capacity fading in the battery is more than lower operating temperature
Lithium-ion battery. Liaw et al. [3] studied the correlation of Arrhenius behavior in power and
capacity loss with cell impedance and heat generation at different temperatures and state of charge
http://dx.doi.org/10.5599/jese.1147
http://dx.doi.org/10.5599/jese.1147
http://www.jese-online.org/
mailto:balaji@hyderabad.bits-pilani.ac.in
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372 CAPACITY FADING OF Li-ION BATTERIES
360
in 18650 cylindrical Li-ion cells. It is observed that degradation in power and capacity fade seems to
relate to impedance increase in the cell with the activation energy of cell at different temperatures.
Ramadesigan et al. [4] studied the effect of the solid-phase diffusion coefficient and side reaction
rate constant in the anode, cathode, and electrolyte as a function of cycling with various
reformulated models. Colclasure et al. [5] studied various detailed chemistries and transport for SEI
films on Li-ion batteries with various states of charge (SOC) at different cycles. The author states
that SEI film grows with time according to net production rate from heterogeneous chemistry on SEI
film surface because electric-potential and concentration profiles in the SEI layer are functions of
the intercalation fraction [5].
Pinson and Bazant [6] also studied the formation of SEI layer in rechargeable batteries with
capacity loss, aging, and lifetime prediction in Li-ion batteries. Various models are studied at
different temperatures and C-rates to study SEI layer formation and capacity fading of Li-ion
batteries. The authors postulate that capacity fading depends on time, not on the number of cycles.
The temperature dependence of the diffusivity of the limiting reacting species through SEI can be
modelled using an Arrhenius dependence. Ziv et al. [7] examined electrochemical performance and
capacity loss of half and full Li-ion batteries with several cathode materials experimentally. The
authors stated that the loss of lithium ions due to side reactions is the main reason for the capacity
fading of Li-ion batteries. Liu et al. [8] studied a thermal-electrochemical model for SEI formation in
Li-ion batteries during load cycles. The authors state that the growth of SEI film is very sensitive to
the diffusion process and side reaction rate. It is also found that SEI film grows at a higher rate during
charging than during the discharge cycle. Guo et al. [9] also studied the capacity fading of Li-ion
batteries with different experiments. The authors stated that capacity fading occurred due to
several reasons, including discharge rate, number of cycles, and battery type.
Ramesh et al. [10,11] developed a mathematical model to study capacity loss in Li-ion batteries
due to temperature, formation, and dissolution rate constants of the SEI layer. The author also
developed an empirical model to study capacity fading in Li-ion batteries under different
temperatures. Xu et al. [12] also studied electrode side reactions, capacity loss and mechanical
degradation of Li-ion batteries through experimental observations. The author states that during
load cycles for higher reaction rates, columbic efficiency is lower, but capacity fading is also lower.
Shirazi et al. [13] studied the effect of composite electrode’s particle size effect on electrochemical
and heat generation of Li-ion batteries. The author states that for smaller particle size, the thermal
characteristics of the battery is improved in comparison to larger particle size [13]. Singhvi et al. [14]
developed a mathematical model to observe the effect of acid attack on capacity fading in Li-ion
batteries. The author considers SEI formation due to the transport and reaction of solvent species.
Cheng et al. [15] developed a mechanism for capacity loss of 18650 cylindrical Li-ion battery cells.
The author postulates that the capacity loss of Li-ion batteries can be explained by continuous SEI
layer formation over the surface of anode and side reactions. Side reaction products deposit on a
separator and reduce its porosity, leading to capacity fading. Tomaszewska et al. [16] reviewed
various research on fast charging of Li-ion batteries. It was observed that for fast charging, rate-
limiting processes are beneficial to reduce battery degradation and increase in cycle life.
Meanwhile, Li plating, the structure of Li deposits, and temperature distribution during cycling
lead to the degradation of Li-ion batteries. Gantenbein et al. [17] studied the capacity loss of Li-ion
batteries over different SOC ranges. The author states that capacity fading originates from active
electrodes and active lithium loss. Lee et al. [18] also studied the loss of cyclable Li on the
performance degradation of Li-ion batteries. The author stated that the discharge behavior of the
Jha and Krishnamurthy J. Electrochem. Sci. Eng. 12(2) (2022) 359-372
http://dx.doi.org/10.5599/jese.1147 361
cell had a strong dependence on discharge C-rate and loss of cyclable lithium. Khaleghi Rahiman et
al. [19] developed a mathematical model to study cell life with various parameters. The author
studied capacity loss and SEI formation in Li-ion batteries at different temperatures at different
SOCs. The author postulates that cathode side reactions are accelerated at higher SOCs and
temperatures. In our model, we compare the effect of anode particle radius and anode reaction rate
constant on the capacity fading of a lithium-ion battery.
Model development
A 1D model of a Li-ion battery interface is created, as shown in Figure 1. The components of a Li-
ion battery are the negative electrode, positive electrode, and separator. Graphite electrode (LixC6)
MCMB is used for negative electrode material, NCA electrode (LiNi0.8Co0.15Al0.05O2) is used for
positive electrode material and LiPF6 (3:7 in EC: EMC) is used as a liquid electrolyte.
Figure 1. Schematic of the 1D electrochemical model of Li-ion battery
Model equations
The model equations analyze the current equilibrium in the electrolyte and electrodes, the mass
balance for the lithium and electrolyte in Li-ion batteries. The Li-ion battery physics at interface
analyses five dependent variables:
a) s - the electric potential,
b) e - the electrolyte potential,
c) ∆SEI - the potential losses due to solid-electrolyte interface (SEI),
d) cLi - the concentration of lithium in the electrode particles
e) ce - the electrolyte salt concentration.
The domain equations in the electrolyte are the conservation of current and the mass balance
for the salt according to the following [20]:
( )
e,eff
sum e e e e
e
2 ln
1 1 ln
ln
RT f
i Q t c
F c
+
+ = − + + +
(1)
( )e sume e e e e
ec i QD c R t
t F
+
+
+ − = −
(2)
where e denotes the electrolyte conductivity, f is the activity coefficient for the salt, t+ is the transport
number for Li+, isum is the sum of all electrochemical current sources, and Qe denotes an arbitrary
electrolyte current source. In the mass balance for the salt, e denotes the electrolyte volume fraction,
De is the electrolyte salt diffusivity, and Re the total Li+ source term in the electrolyte.
In the electrode, the current density, is is defined as
http://dx.doi.org/10.5599/jese.1147
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372 CAPACITY FADING OF Li-ION BATTERIES
362
is = -ss (3)
where s is electrical conductivity. The domain equation for the electrode is the conservation of
current expressed as
is = -isum + Qs (4)
where Qs is an arbitrary current source term. The electrochemical reactions in the physics interface
are assumed to be insertion reactions occurring at the surface of small solid spherical particles of
radius rp in the electrodes.
The insertion reaction is described as:
During charging, at anode
xLi+ + xe- + graphite → LixC6 (5)
at cathode
LixNi0.8Co0.15Al0.05O2 → xLi+ + xe- + Ni0.8Co0.15Al0.05O2 (6)
During discharging, at Anode
LixC6 →xLi+ + xe- + graphite (7)
at cathode
xLi+ + xe- + Ni0.8Co0.15Al0.05O2 → LixNi0.8Co0.15Al0.05O2 (8)
An important parameter for lithium insertion electrodes is the state-of-charge variable for the
solid particles, denoted SOC. This is defined as
Li
Li,max
SOC
c
c
= (9)
The equilibrium potentials E0 of lithium insertion electrode reactions are typically functions of
SOC. The electrode reaction occurs on the particle surface and lithium diffuses to and from the
surface in the particles. The mass balance of Li in the particles is described as
Li
s Li( )
c
D c
t
=
(10)
where cLi is the concentration of Li in the electrode. This equation is solved locally by this physics
interface in a 1D pseudo dimension, with the solid phase concentrations at the nodal points for the
element discretization of the particle as the independent variable. The gradient is calculated in
Cartesian, cylindrical, or spherical coordinates, depending on if the particles are assumed to be best
described as flakes, rods or spheres, respectively.
The boundary conditions are as follows:
Li
= 0
0
r
c
r
=
(11)
Li
s LiR
p
p
r r
r r
c
D
r =
=
− = −
(12)
where RLi denotes the molar flux of lithium at the particle surface caused by the electrochemical
insertion reactions. In the porous electrodes, isum denotes the sum of all charge transfers current
density contributions according to:
isum = ΣAviloc (13)
where, Av denotes the specific surface area at any node of the lithium-ion battery interface. Active
specific surface area (m2/m3) defines the area of an electrode-electrolyte interface that is
catalytically active for porous electrode reactions. Equation 13 describing the total current source
Jha and Krishnamurthy J. Electrochem. Sci. Eng. 12(2) (2022) 359-372
http://dx.doi.org/10.5599/jese.1147 363
in the domain is a function of active specific surface area and local current in the electrode. The
source term in the mass balance is calculated from:
Li loc
l v l,src
i
R A R
nF
= − + (14)
where Rl.src is an additional reaction source that contributes to the total species source.
At the surface of the solid particles, the following equation is applied:
Li locv
Li
shape s
p
iA
R
S nF
r
= − (15)
where n is the number of electrons and Sshape (normally equal to 1) is a scaling factor accounting for
differences between the surface area (Av) used to calculate the volumetric current density and the
surface area of the particles in the solid lithium diffusion model. Sshape is 1 for Cartesian, 2 for
cylindrical, 3 for spherical coordinates and 𝜐Li is the stoichiometric coefficient.
A resistive film (also called solid-electrolyte interface, SEI) might form on the solid particles
resulting in additional potential losses in the electrodes. To model a film resistance, an extra solution
variable for the potential variation over the film is introduced in the physics interface. The governing
equation is then according to
SEI = RSEIisum (16)
where RSEI denotes generalized film resistance, which can be expressed by:
0
SEI
SEI
R
+
= (17)
where, 0 is initial film thickness, ∆ is film thickness change and SEI is film conductivity. The
activation overpotentials, for all electrode reactions in the electrode then receives an extra
potential contribution, which yields
= s - e - SEI - Eeq (18)
where, Eeq is the equilibrium potential of a cell. The battery cell capacity, Qcell,0 is equal to the sum
of the charge of cyclable species in the positive and negative electrodes and additional porous
electrode material if present in the model [20].
Qcell,0 = Qcycle,pos + Qcycle,neg + Qcycl,addm (19)
Butler-Volmer equation is used to calculate the local current density in the electrode.
a c
loc 0 exp exp
F F
i i
RT RT
−
= −
(20)
a c a e
0 c a Li,max Li Li
e,eff
( ) c
c
i Fk k c c c
c
= −
(21)
where a and c are the anode and cathode transfer coefficient and ka and kc are reaction rate
constant for anode and cathode.
Numerical methods
1D model of Li-ion battery consists of 3 geometric regions for analysis: negative electrode,
separator and a positive electrode. For numerical analysis of the computational domain, 1D meshing
is done for 49,59 and 95 mesh elements. The 1D mathematical model is developed for transient
analysis of our computational domain in Comsol 5.3a on viable concerns of Li-ion battery,
electrochemical parameters, species transport and current distribution, consisting of the principal
http://dx.doi.org/10.5599/jese.1147
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372 CAPACITY FADING OF Li-ION BATTERIES
364
model assumptions and equations with different initial conditions, boundary conditions and
numerical solver strategies for solution.
Results and discussion
Capacity fading of Li ion battery is studied with the effect of various parameters. A summary of
the list of parameters used for simulation is shown in Table 1.
Table 1. List of parameters
Description Value
Particle radius, µm 0.5, 1, 2, 2.5
Reaction rate coefficient, pmol m-3 s-1 200 , 20 , 2
Initial capacity, C m-2 55761
1C discharge current, A 15.767
Thickness of negative electrode, µm 55
Thickness of separator, µm 30
Thickness of positive electrode, µm 55
Cell temperature, ℃ 45
Maximum cell voltage, V 4.1
Minimum cell voltage, V 2.5
Initial electrolyte salt concentration, mol m-3 1200
Constant current (charge and discharge), A 15.767, -15.767
SEI Layer conductivity, S m-1 5×10-6
Initial SEI layer thickness, nm 1
Number of cycles 2000
The battery cycling consists of 3 various stages of charging and discharging, as shown in Figure 2:
Figure 2. Charge-discharge load cycle
• charging at a constant current rate of 1 C until the cell potential reaches 4.1 V.
• Charging at a constant voltage of 4.1 V.
• Discharging at constant current discharge rate at 1 C until the cell potential reaches the
minimum voltage of 2.5 V.
Jha and Krishnamurthy J. Electrochem. Sci. Eng. 12(2) (2022) 359-372
http://dx.doi.org/10.5599/jese.1147 365
Effect of particle radius on capacity fading in lithium-ion batteries
Research on anode particle radius on capacity fading in lithium-ion batteries has been done
previously. Rai [21] postulated that batteries with smaller anode particle sizes generate better
capacity. The authors postulated that smaller particles(graphite) allow quicker lithium-ion
intercalation and deintercalation due to the short distances for lithium-ion transport within the
particles. There is no agreed-upon consensus for optimal particle size in lithium-ion batteries though
particles less than 150 nm are mainly used. Wu [22] investigated the effect of silicon particle size in
the micrometer range when used as a lithium-ion battery anode. The authors have found out in
their study that particle size of 3μm shows better outcomes with respect to the 20 μm particle size
with an initial capacity of 800 mAh/g and retention of 600 mAh/g after 50 cycles. Buqa [23]
investigated three different graphite particle sizes (6, 15 and 44 µm) and showed that smaller
particles could achieve better capacity retention. Several authors like Drezen [24] and Fey [25] have
postulated that smaller particles improve capacity retention. Mei has [26] postulated that energy
and power density increase with smaller particle sizes due to lower overpotential. Mei [26] has also
postulated that smaller particle size increases the surface area for reaction. Our focus was to study
the effect of the anode particle radius on the capacity fading in lithium-ion batteries taking into
consideration lithium losses during cycling.
Figure 3 shows the capacity fading of a lithium-ion battery with cycling for various anode particle
radii. The model assumes zero lithium loss during the process of cycling. Four different anode
particle radii (0.5, 1, 2 and 2.5 m) were considered for analysis. It is seen that the least capacity
fading (high relative capacity) is seen for an anode particle radius of 0.5 m. Relative capacity is
defined as the capacity of the battery at any point of time divided by the initial capacity of the
battery. It can be seen that as the anode particle radius increases from 0.5 to 2.5 µm, the relative
capacity decreases over 2000 cycles.
Figure 3. Capacity fading with cycling for various anode particle radius with zero lithium loss
Figure 4 shows the capacity fading in a lithium-ion battery cycling for four different particle radii
(0.5, 1, 2 and 2.5 m) with 10 percent lithium loss during cycling. During charge-discharge cycling,
there is more lithium loss during initial cycles. A comparison of Figures 3 and 4 shows that the
capacity loss is seen to be less without cyclable lithium loss compared to 10 % initial lithium loss as
the number of cycles increases. This is clearly shown in Figure 5. It is seen from Figure 5 that there
is less capacity loss of around 3 % when we go from zero percent lithium loss to 10 percent lithium
loss during cycling.
http://dx.doi.org/10.5599/jese.1147
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372 CAPACITY FADING OF Li-ION BATTERIES
366
Figure 4. Capacity fading with cycling for various anode particle radius with lithium loss
Figure 5. Comparison of relative capacity with and without lithium loss
Figures 6 and 7 show the capacity loss in the battery as a function of the anode reaction rate
constant.
Figure 6. Capacity loss with cycling for various anode reaction rate constant without lithium loss
The anode reaction rate constant indicates the intercalation/deintercalation reaction rate
constant. Figure 6 shows that when the intercalation/deintercalation reaction rate constant is the
Jha and Krishnamurthy J. Electrochem. Sci. Eng. 12(2) (2022) 359-372
http://dx.doi.org/10.5599/jese.1147 367
highest, the capacity loss is the lowest. With increasing intercalation/deintercalation reaction rate,
the rate of lithium transport increases, effectively increasing the capacity of the battery. While
Figure 6 shows the capacity loss when there is no initial cyclable lithium loss during cycling, Figure 7
shows the capacity loss when there is 10 % initial lithium loss during cycling.
Figure 8 shows the comparison of the capacity losses when there are 0 and 10 % lithium losses
during cycling. The figure shows that when the initial lithium loss during cycling increases from zero
percent to 10 percent, there is a 4 % differential in the capacity loss due to side reactions.
Figure 7. Capacity loss with cycling for various anode reaction rate constants with 10 % Li loss during cycling
Figure 8. Comparison of capacity loss for 0 % Li loss and 10 % Li loss
Effect of anode radius on lithium-ion concentration at the anode/SEI interphase
Figure 9 shows the concentration of lithium ions at the anode/SEI interphase as a function of
anode particle radius (4 different particle radii are shown in the figure). It is seen that the highest
concentration of lithium ions at the anode/SEI interphase occurs at the smallest particle radius.
Smaller anode particles allow lithium ions to intercalate and deintercalated quickly due to the short
diffusion path for lithium ion transport within the particles. This leads to a higher concentration of
lithium ions at the anode/SEI interphase.
Figure 10 shows the concentration of lithium ions at the anode/SEI interphase as a function of
the reaction rate constant for lithium intercalation. With the increasing rate constant of
deintercalation, the concentration of lithium ions at the anode/SEI interphase is seen to increase.
http://dx.doi.org/10.5599/jese.1147
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372 CAPACITY FADING OF Li-ION BATTERIES
368
Figure 9. The concentration of lithium ions at the anode/SEI interphase as a function of anode particle radius
Figure 10. The concentration of lithium ions at the anode/SEI interphase as a function of the anode reaction
rate constant
Figure 11 shows the concentration of lithium ions at the anode/SEI interphase varying with anode
radius in the first and the 2000th cycle.
Figure 11. The concentration of lithium ions at the anode/SEI interphase in the first and 2000th cycle
Jha and Krishnamurthy J. Electrochem. Sci. Eng. 12(2) (2022) 359-372
http://dx.doi.org/10.5599/jese.1147 369
During the charging cycle, lithium from the cathode moves to the anode and hence the
concentration of lithium ions at the anode/SEI interphase increases. The lithium ions move from the
anode to the cathode during the discharging cycle. Hence, the concentration of lithium ions at the
anode/SEI interphase is seen to go from maximum to zero. As the battery cycles, lithium ions are
lost in the intercalation deintercalation process. Hence, the concentration of lithium ions at the
anode/SEI interphase is lower in the 2000th cycle than in the 1st cycle.
The potential drop across the SEI layer as a function of anode particle radius
Figure 12 shows the effect of anode particle radius on the potential drop across the SEI layer. The
figure analyses the effect of four different particles sizes on the potential drop across the SEI layer.
The least potential drop across the SEI layer occurs when the anode particle size is the smallest. As
explained earlier, smaller anode particle sizes lead to higher intercalation deintercalation rates
leading to higher current densities. Given a constant power output, this indicates a lower potential
drop across the cell and hence a lower potential drop across the SEI layer.
Figure 12. Potential drop over the SEI film with cycle number for various anode particle radius
Figure 13 shows the effect of the anode reaction rate constant on the potential drop across the
SEI layer.
Figure 13. Potential drop over the SEI layer as a function of anode reaction rate constant
http://dx.doi.org/10.5599/jese.1147
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372 CAPACITY FADING OF Li-ION BATTERIES
370
The graph shows that the potential drop across the SEI layer increases with decreasing rate
constant. The anode reaction rate constant indicates the rate of intercalation deintercalation of
lithium ions in the anode particles. When the anode reaction rate constant is lower, the
intercalation/deintercalation of lithium ions in the anode is reduced, giving rise to a lower current
density. Given a constant power output, this indicates an increased potential drop across the cell
and, hence, a potential drop across the SEI layer. This is shown in Figure 13.
Figure 14 shows the comparison of modelling predictions with experimental data [3,11].
Modeling predictions are found to compare well with experimental data. The model comparisons
are made for 1 C discharge at 45 oC operating conditions for the lithium-ion battery cell. The
parameters used for data fitting are shown in Table 1.
Figure 14. Comparison of modelling predictions with experimental data of capacity fading percentage at 1C
discharge rate and 45 °C [3,11]
Conclusion
A 1-dimensional mathematical model is developed to study the effect of anode particle radius
and anode reaction rate constant on capacity fading of a Li-ion battery. Simulation results predict
that for the smallest anode particle radius of 0.5 m, capacity fading is less in comparison to 2.5 m.
Smaller anode particle radii lead to faster lithium intercalation/deintercalation rates leading to
higher current densities and lesser capacity fade. Smaller anode particle radii also lead to increasing
anode surface area for reaction. The anode reaction rate constants are also found to play a major
role in the capacity fading of lithium-ion batteries. It is found that the higher the anode reaction rate
constant, the lesser is the capacity fade in the battery. Model results are compared with
experimental data and found to compare well.
Nomenclature
s The electric potential at electrode
e Electrolyte potential
∆SEi The potential losses due to SEI layer
CLi Concentration of lithium in the electrode particles
Ce Electrolyte salt concentration
e Electrolyte conductivity
F Activity coefficient for the salt
Jha and Krishnamurthy J. Electrochem. Sci. Eng. 12(2) (2022) 359-372
http://dx.doi.org/10.5599/jese.1147 371
t+ Transport number for Li+
isum Sum of all electrochemical current sources
Qe, Qs Arbitrary electrolyte and electrode current source
e Electrolyte volume fraction
De Electrolyte salt diffusivity,
Re Total Li+ source term in the electrolyte
is Current density in electrode
s Electrical conductivity of electrode
rp Particle radius
CLi,max Total concentration of reaction sites,
Ds Salt diffusivity at electrode
RLi Molar flux of lithium at the particle surface
Av Specific surface
Rl,src Additional reaction sources that contributes to total species source
RSEI Film resistance
0 Film thickness
∆ Film thickness change
SEI Film conductivity
Η Activation over potential
Eeq Equilibrium potential of cell
Qcell,0 Battery cell capacity
a , c Anode and cathode transfer coefficient
ka , kc Reaction rate constant for anode and cathode
Acknowledgement: The authors would like to acknowledge BITS Pilani, Hyderabad and Council for
Scientific and Industrial Research, CSIR Grant No: (No:22/0784/19/EMR II), which helped us in
publishing this article.
Data availability statement: Data used for this paper can be provided on request
References
[1] B. S. Haran, P. Ramadass, R. E. White, B. N. Popov, Seventeenth Annual Battery Conference
on Applications and Advances, Proceedings of Conference (Cat. No. 02TH8576), Long Beach,
CA, USA, 2002, 13-18. https://doi.org/10.1109/BCAA.2002.986361.
[2] X. Han, M. Ouyang, L. Lu, J. Li, Energies 7(8) (2014) 4895-4909.
https://doi.org/10.3390/en7084895
[3] B. Y. Liaw, E. P. Roth, R. G. Jungst, G. Nagasubramanian, H. L. Case, D. H. Doughty, Journal of
Power Sources 119–121 (2003) 874-886. https://doi.org/10.1016/S0378-7753(03)00196-4.
[4] V. Ramadesigan, K. Chen, N. A. Burns, V. Boovaragavan, R. D. Braatz, V. R., Journal of the
Electrochemical Society 158 (2011) A1048. https://doi.org/10.1149/1.3609926.
[5] A. M. Colclasure, K. A. Smith, R. J. Kee, Electrochimica Acta 58 (2011) 33-43.
https://doi.org/10.1016/j.electacta.2011.08.067.
[6] M. B. Pinson, M. Z. Bazant, Journal of the Electrochemical Society 160 (2013) A243-A250.
https://doi.org/10.1149/2.044302jes.
[7] B. Ziv, V. Borgel, D. Aurbach, J.-H. Kim, X. Xiao, B.R. Powell, Journal of the Electrochemical
Society 161 (2014) A1672-A1680. https://doi.org/10.1149/2.0731410jes.
[8] L. Liu, J. Park, X. Lin, A.M. Sastry, W. Lu, Journal of Power Sources 268 (2014) 482-490.
https://doi.org/10.1016/j.jpowsour.2014.06.050.
[9] J. Guo, Z. Li, T. Keyser, Y. Deng, Proceedings of the 2014 Industrial and Systems Engineering
Research Conference, Montréal, Canada (2014) 913-919.
http://dx.doi.org/10.5599/jese.1147
https://doi.org/10.1109/BCAA.2002.986361
https://doi.org/10.3390/en7084895
https://doi.org/10.1016/S0378-7753(03)00196-4
https://doi.org/10.1149/1.3609926
https://doi.org/10.1016/j.electacta.2011.08.067
https://doi.org/10.1149/2.044302jes
https://doi.org/10.1149/2.0731410jes
https://doi.org/10.1016/j.jpowsour.2014.06.050
J. Electrochem. Sci. Eng. 12(2) (2022) 359-372 CAPACITY FADING OF Li-ION BATTERIES
372
[10] S. Ramesh, B. Krishnamurthy, Journal of the Electrochemical Society 162 (2015) A545-A552.
https://doi.org/10.1149/2.0221504jes.
[11] S. Ramesh, K.V. Ratnam, B. Krishnamurthy, International Journal of Electrochemistry 2015
(2015) 1-9. https://doi.org/10.1155/2015/439015
[12] J. Xu, R. D. Deshpande, J. Pan, Y.-T. Cheng, V. S. Battaglia, Journal of the Electrochemical
Society 162 (2015) A2026-A2035. https://doi.org/10.1149/2.0291510jes
[13] A. H. N. Shirazi, M. R. Azadi Kakavand, T. Rabczuk, Journal of Nanotechnology in Engineering
and Medicine 6(4) (2015) 041003. https://doi.org/10.1115/1.4032012
[14] R. Singhvi, R. Nagpal, B. Krishnamurthy, Journal of the Electrochemical Society 163 (2016)
A1214-A1218. https://doi.org/10.1149/2.0601607jes.
[15] J. Liang Cheng, X. Hai LI, Z. Xing Wang, H. Jun Guo, Transactions of Nonferrous Metals Society
of China 27 (2017) 1602-1607. https://doi.org/10.1016/S1003-6326(17)60182-1.
[16] A. Tomaszewska, Z. Chu, X. Feng, S. O’Kane, X. Liu, J. Chen, C. Ji, E. Endler, R. Li, L. Liu, Y. Li, S.
Zheng, S. Vetterlein, M. Gao, J. Du, M. Parkes, M. Ouyang, M. Marinescu, G. Offer, B. Wu,
eTransportation 1 (2019) 100011. https://doi.org/10.1016/j.etran.2019.100011
[17] S. Gantenbein, M. Schönleber, M. Weiss, E. Ivers-Tiffée, Sustainability 11(23) (2019) 6697.
https://doi.org/10.3390/su11236697
[18] D. Lee, B. Koo, C. B. Shin, S. Y. Lee, J. Song, I. C. Jang, J. J. Woo, Energies 12(22) (2019) 4386.
https://doi.org/10.3390/en12224386
[19] S. Khaleghi Rahimian, M. M. Forouzan, S. Han, Y. Tang, Electrochimica Acta 348 (2020)
136343. https://doi.org/10.1016/j.electacta.2020.136343
[20] C. Inc., Batteries & Fuel Cells Module User’s Guide, COMSOL Multiphysics Help (2012).
[21] A. K. Rai, B. J. Paul, J. Kim, Electrochimica Acta 90 (2013) 112-118.
https://doi.org/10.1016/j.electacta.2012.11.104
[22] H. Wu, G. Chan, J.W. Choi, I. Ryu, Y. Yao, M.T. Mcdowell, S.W. Lee, A. Jackson, Y. Yang, L. Hu,
Y. Cui, Nature Nanotechnology 7(5) (2012) 310-315. https://doi.org/10.1038/nnano.2012.35
[23] H. Buqa, D. Goers, M. Holzapfel, M. E. Spahr, P. Novak, Journal of the Electrochemical Society
152(2) (2005) A474-A481. https://doi.org/10.1149/1.1851055
[24] T. Drezen, H. E. Kwon, P. Bowen, I. Teerlinck, M. Isono, I. Exnar, Journal of Power Sources 174
(2007) 949-953 https://doi.org/10.1016/j.jpowsour.2007.06.203
[25] G. T. K. Fey, Y. G. Chen, H. M. Kao, Journal of Power Sources 189 (2009) 169-178.
https://doi.org/10.1016/j.jpowsour.2008.10.016
[26] W. Mei, H. Chen, J. Sun, Q.Wang, Sustainable Energy and Fuels 3 (2019) 148-165
https://doi.org/10.1039/C8SE00503F
©2021 by the authors; licensee IAPC, Zagreb, Croatia. This article is an open-access article
distributed under the terms and conditions of the Creative Commons Attribution license
(https://creativecommons.org/licenses/by/4.0/)
https://doi.org/10.1149/2.0221504jes
https://doi.org/10.1155/2015/439015
https://doi.org/10.1149/2.0291510jes
https://doi.org/10.1115/1.4032012
https://doi.org/10.1149/2.0601607jes
https://doi.org/10.1016/S1003-6326(17)60182-1
https://doi.org/10.1016/j.etran.2019.100011
https://doi.org/10.3390/su11236697
https://doi.org/10.3390/en12224386
https://doi.org/10.1016/j.electacta.2020.136343
https://doi.org/10.1016/j.electacta.2012.11.104
https://doi.org/10.1038/nnano.2012.35
https://doi.org/10.1149/1.1851055
https://doi.org/10.1016/j.jpowsour.2007.06.203
https://doi.org/10.1016/j.jpowsour.2008.10.016
https://doi.org/10.1039/C8SE00503F
https://creativecommons.org/licenses/by/4.0/)