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Scientific RepoRts | 6:27449 | DOI: 10.1038/srep27449
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Theoretical Limits of Energy
Density in Silicon-Carbon
Composite Anode Based Lithium
Ion Batteries
Ranjan Dash1 & Sreekanth Pannala2
Silicon (Si) is under consideration as a potential next-generation anode material for the lithium ion
battery (LIB). Experimental reports of up to 40% increase in energy density of Si anode based LIBs
(Si-LIBs) have been reported in literature. However, this increase in energy density is achieved when
the Si-LIB is allowed to swell (volumetrically expand) more than graphite based LIB (graphite-LIB) and
beyond practical limits. The volume expansion of LIB electrodes should be negligible for applications
such as automotive or mobile devices. We determine the theoretical bounds of Si composition in
a Si–carbon composite (SCC) based anode to maximize the volumetric energy density of a LIB by
constraining the external dimensions of the anode during charging. The porosity of the SCC anode is
adjusted to accommodate the volume expansion during lithiation. The calculated threshold value of
Si was then used to determine the possible volumetric energy densities of LIBs with SCC anode (SCC-
LIBs) and the potential improvement over graphite-LIBs. The level of improvement in volumetric and
gravimetric energy density of SCC-LIBs with constrained volume is predicted to be less than 10% to
ensure the battery has similar power characteristics of graphite-LIBs.
For the past two decades, signicant eorts have been dedicated towards the development of high energy den-
sity LIBs1–3. e energy density of a LIB depends primarily on the specic capacities of cathode and anode, and
the operating voltage window at which the battery can be cycled1–3. Si has emerged as one of the promising
anode materials for high energy LIBs4,5. It is believed that a small amount of Si based material is currently used
in the anode of LIBs6. Si oers a suitable low voltage for an anode and a high theoretical specic capacity of
~4,200 mAh/g based on the formation of the Li22Si5 alloy, which is about 10 times higher than that of conventional
carbon based anodes (~372 mAh/g)4.
Today, the LIB capacity is limited by the capacity of cathode rather than the capacity of the anode1 with
the implication that any gains on anode capacity are proportionately reduced based on the overall cell compo-
sition. Commonly used cathodes such as lithium cobalt oxide (LCO), lithium nickel manganese cobalt oxide
(NMC), and lithium nickel cobalt aluminum oxide (NCA) have usable capacities of 140 mAh/g, 170 mAh/g,
and 185 mAh/g, respectively, which are lower than the widely used graphite anode (experimental capacity:
~330 mAh/g)7. us, despite Si having a signicantly larger capacity than graphite, the level of improvement in
gravimetric energy density on a cell level achieved using Si anode and existing cathodes is limited to a maximum
of ~41% (see Fig. S1a). is calculation does not take into account the issue of swelling; when mechanical eects
are taken into account, the possible capacity improvement becomes signicantly less.
Si has been a challenging anode material to work with because it expands volumetrically up to 400% upon full
lithium insertion to form the Li22Si5 alloy and conversely shrinks upon lithium extraction4,5,8,9. e other issue
with Si is its low ionic and electronic conductivity. Nano-sized Si particles combined with graphite and/or con-
ductive carbon (CC) are under investigation as a means to obtain a viable silicon based LIB anode4,10,11.
Signicant eort towards increasing the cycle life of Si anodes are currently being pursued with a reasonable
degree of success4. Up to 40% increase in gravimetric and volumetric energy density for Si-LIBs are reported in
various experimental works4,12; however, this improvement is achieved when the Si anode (and thus the cell) is
allowed to swell beyond practical limit. e increase in external volume (also referred to as swelling) of LIBs
1SABIC, 475 Creamery Way, Exton, PA 19341, USA. 2SABIC, 14100 Southwest Freeway, Sugar Land, TX 77478, USA.
Correspondence and requests for materials should be addressed to R.D. (email: Ranjan.Dash@SABIC.com)
Received: 02 February 2016
accepted: 18 May 2016
Published: 17 June 2016
OPEN
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Scientific RepoRts | 6:27449 | DOI: 10.1038/srep27449
either arising from gas generation from electrolyte decomposition or volume expansion of electrode is not desir-
able for use in practical applications such as automotive and mobile computing as space is at a premium13,14.
Unusual swelling of LIBs in cell phones and laptops has also been reported to cause safety issues15–17. Similarly,
battery packs used in electric vehicles are in tight compression and thus external volume changes of LIBs are
undesirable16. Even though swelling of LIBs is undesirable, LIB module manufacturers have no choice but to
allow a volume expansion tolerance of ~5% to accommodate gases generated from electrolyte decomposition
without releasing these gases to the surrounding environment15. LIB swelling also causes structural damage
to the electrodes, delamination of the electrodes from the current collectors and separator, and other negative
eects, reducing cycle life. us, there is no room to allow for swelling of LIBs arising from volume expansion of
electrodes.
Figure1 provides a schematic to explain the swelling of graphite and SCC anode. Since the volume expansion
of graphite due to intercalation is low (~10%), any expansion may be incorporated within the porosity or void
spaces of the anode, which is typically about 30–35% (by volume)1 (see Fig.1a). e metal casing of LIBs cannot
withstand large dimensional changes and will rupture causing severe damage to the cell and triggering safety
issues15. e increase in volume of Si particles in an SCC anode with a low fraction of Si during charging can be
accommodated within the existing porosity of the anode so that there is no increase in thickness of anode upon
lithiation (see Fig.1b). However, the volume occupied by lithiated Si particles of an SCC anode with a large frac-
tion of Si cannot be incorporated within the existing porosity of anode, resulting in, an increase in the external
dimensions of the anode upon lithiation (see Figs1c and S1b).
e objective of this work is to determine the theoretical limits of the energy density of an LIB-SCC by
maximizing the fraction of Si (referred as “threshold value of Si”) that can be used in the anode without increas-
ing the external dimension of LIB beyond the accepted 5% swelling limit. e threshold or limiting value of Si
is calculated as the highest fraction of Si for which the anode does not change in size or shape due to the anode
particles’ increasing volume upon lithiation (Fig.1b). is requires that the porosity of the anode is adjusted to
accommodate the expansion of the Si. e threshold value of Si is determined by maximizing the volumetric
energy density of the LIB. As the threshold value of Si in the SCC anode will depend on the nal porosity of
lithiated anode, the threshold value is determined as a function of lithiated porosities. Based on the determined
threshold value of Si, the improvement in energy density over existing LIBs is calculated. e energy densities
of LIB were calculated for three types of cathode (LCO, NMC and NCA) and two types of anode (graphite and
SCC). is work is based on existing commercial cathode chemistries and does not address the improvements
that new and promising cathode chemistries can impart to the performance of LIBs. However, this work is easily
extensible to other cathode materials.
Figure 1. Schematic showing cross-section of anode before and aer charging for (a) graphite based anode,
(b) SCC anode with low amount of Si, and (c) SCC anode with high amount of Si. As can be seen, the anode
thickness remains unchanged for graphite and low Si based SCC anode. Swelling of anode is experienced for
anode with higher Si content (c).
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Scientific RepoRts | 6:27449 | DOI: 10.1038/srep27449
is work does not focus on charge-discharge cycling stability of Si anode, which has been the focus of the
majority of published articles on Si anodes for LIBs. Instead, this work focuses on system level limitations of
Si-LIBs arising from issues related to swelling of Si particles18–20. Most of the scientic papers published in Si
anode have not reported the amount of swelling of the anode or LIB for a number of reasons. Coin cells, which
are typically used by LIB researchers, have sucient free volume internally and thus no external change in dimen-
sions of cell is noticed during electrochemical cycling. Tests made on single-layer, low-capacity (<100 mAh)
pouch cells undergoes reversible volume changes during cycling; however, the volume change is hard to see
with the naked eye and thus does not get reported. Furthermore, the volumetric energy density/capacity values
reported in scientic articles are based on the volumes of cells in the discharged state rather than in the fully
charged state. e swelling issues become evident and problematic when LIBs are made using multiple-layered
high-capacity (>5 Ah) commercial pouch cells. Experimental observations of swelling of low-capacity LIBs may
also require instrumentation and techniques that are not typically used in battery research21.
is work adopts a system-level approach22,23, which is used to determine the extent of benets of Si-LIBs, and
can supplement understanding generated using experimental material-level analysis. e current work extends
the analysis presented in Obrovac et al.22 to determine the amount of Si in a SCC anode that would maximize the
volumetric capacity of a SCC-LIB. e model uses well-established experimentally derived properties as inputs.
Results and Discussion
Using simple mass balance calculations24, the density (in g/cc) of anode, ρ
A, specific gravimetric capacity
(in mAh/g) of anode, GA, porosity (in %) of unlithiated SCC anode, PA, and specic volumetric capacity (in mAh/
cc) of anode, V
A can be expressed in the form of eqns(1), (2), (3) and (4), respectively.
ρ=
−
+++
ρρρρ
−
−
−
−
−
−
−
−
()()()()
100 P
(1)
A
A
wwww
Si A
Si A
GA
GA
BA
BA
CC A
CC A
=
⋅+ ⋅
−−
G
(w s) (w s)
100 (2)
ASi ASiGAG
=
⋅+ ⋅
+
−−
−
P
(w 280) (w 10)
100
P
(3)
ASi AGAAL
=ρ ×
=−⋅.+ ⋅. +⋅ ⋅+ ⋅
+++
−−−− −
ρρρρ
−
−
−
−
−
−
−
−
()()()()
VG
[100 {(w28) (w 01)P }] {(ws)(ws)}
(4)
AAA
Si AGAALSiA Si GA G
wwww
Si A
Si A
GA
GA
BA
BA
CC A
CC A
Where wSi-A, wG-A, wB-A, and wCC-A are the weight fractions (in wt.%) of Si, graphite, binder, and CC, respec-
tively in anode; ρ
S-A, ρ
G-A, ρ
B-A, and ρ
CC-A are the true densities (in g/cc) of Si, graphite, binder, and conductive
carbons, respectively; sSi and sG are the specic gravimetric capacity (in mAh/g) of Si and graphite, respectively;
and, PA−L is the porosity (in %) of the lithiated anode.
By inputting the values, sSi = 3600 mAh/g, sG = 330 mAh/g, ρ
Si−A = 2.3 g/cc, ρ
G−A = 2.24 g/cc, and assigning a
variable for optimizing the relative weight of Si; wSi−A = x, eqn. (4) can be rewritten as eqn. (5).
=
−⋅.+ −− −⋅.+
+++
.⋅ +− −−⋅.
−− −
.
−− −
.ρρ
−−
−− −
−
−
−
()()
()
()
xx
xwx
V
[100 {( 28)((100 ww )01) P}]
[( 36) ((100 w)33)]
(5)
xx
A
BA CC AAL
23
100 ww
224
ww
BA CC A
BA CC ABA
BA
CC A
CC A
Figure2 is plotted using eqn. (5) for anode made using 5 wt.% SBR binder (ρ
B−A = 1.1 g/cc) and assuming no
CC i.e., wCC−A = 0 and complete expansion into the pores aer lithiation i.e., PA−L = 0. As the Si content increases,
the porosity required to accommodate volume expansion of Si increases. As expected, the specic gravimetric
capacity of anode also increases linearly with Si content (see Eqn. (2)); however, the specic volumetric capacity
of anode increases with Si content up to a limiting value and then decreases (see Fig.2). Increase in Si content
beyond this limiting value, Sit = 12.02 wt.% leads to decrease in specic volumetric capacity because any further
increase in Si content warrants increase in porosity required to compensate the volume expansion and thereby
reducing the density of anode (see Eqns(1) and (3)). Further, the decrease in density of anode leads to the sig-
nicant decrease in the weight of graphite with minimal changes in weight of Si, thereby impacting the specic
volumetric capacity of anode (see Fig. S2).
e concept of this threshold value of Si is further explained using some illustrative values for anodes made
using no CC i.e., wCC−A = 0 and no porosity aer lithiation i.e., PA−L = 0. e density, specic gravimetric and
specic volumetric capacity of anode made using 5 wt.% Si, 5 wt.% SBR binder and 90 wt.% graphite is 1.64 g/cc,
477 mAh/g, and 783 mAh/cc, respectively (see Table S3 and Fig. S2). e weight of Si, graphite and binder for a
1 cc electrode volume are 0.08 g, 1.48 g, and 0.08 g, respectively. e porosity of anode required to avoid increase
in external dimension of anode is 23%. When the Si amount in the anode increases to let’s say, 20%, the porosity
required to avoid swelling increases to 64%, thereby reducing the anode density to 0.78 g/cc (see Eqns(1) and (3)).
e weight of graphite for a 1 cc electrode volume decreases signicantly to 0.59 g, while the weight of Si increased
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Scientific RepoRts | 6:27449 | DOI: 10.1038/srep27449
slightly to 0.16 g. e specic gravimetric capacity increases to 968 mAh/g, whereas the specic volumetric capacity
decreases to 756 mAh/cc. Despite increase in the specic weight of Si from 0.08 g to 0.16 g, the specic volumetric
capacity decreases because of the decrease in the weight of graphite from 1.48 g to 0.59 g. At the threshold value
of Si, Sit = 12.02 wt.%, the specic volumetric capacity is maximum, i.e. 876 mAh/cc. e threshold value of Si is
independent of the thickness of Si anode and type of cathode material used but is dependent on the composition
of anode, density of binder and porosity of lithiated anode. e threshold value of Si decreases from 12.02 wt.% to
10.16%, 8.30% and 6.44%, for lithiated anode porosities of 10%, 20% and 30%, respectively (see Fig. S3).
e threshold value of Si that would maximize the volumetric capacity without any increase in the external
dimensions of anode can be determined by setting the rst derivative of eqn. (6) to zero:
′=⇒=fx x() 0Sit
Threshold value of Si was determined assuming sSi = 3600 mAh/g, sG = 330 mAh/g, ρ
S−A = 2.3 g/cc and
ρ
G−A = 2.24 g/cc. Figure S4 of Supplementary Information shows the threshold value of Si and volumetric capacity
of anode as a function of amount of binder and CC for dierent porosities of lithiated anode. e threshold value
of Si linearly increases with the amount of binder content with a constant slope of 0.068 and the intercept depends
on the amount of CC and porosities of lithiated anode. e threshold value of Si does not change drastically for
dierent amount of CCs. Calculations made using binder densities of 1.1 and 1.77 g/cc representing density of
SBR and PVDF, respectively, showed almost the same threshold value of Si. e threshold value depends more
on the amount of binder and porosity of lithiated anode than the type of binder. e threshold values for the
highest energy density is for the anode that does not contain binder and CC. e values are 11.68%, 9.82%,
7.96% and 6.10% for porosity of lithiated anode of 0%, 10%, 20% and 30%, respectively. e threshold value of
Si is independent of type and thickness of cathode assuming that the expansion of the anode is not absorbed by
the compression of the cathode. e maximum capacity of ~935 mAh/cc and ~712 mAh/g was obtained for SCC
anode with no binder and CC with the assumption that the porosity of the lithiated anode goes to 0. ese values
are more than twice of graphite anode (454 mAh/cc, 314 mAh/g). e threshold values for maximum volumetric
energy densities was found to be signicantly lower than what was determined without assuming no external
volume change. Such a low amount of Si can allow for exploration of more commercially viable manufacturing
approaches of Si. As the volume associated with Si content will be low (see Fig. S1b), the SCC material can be
porous Si mixed with graphite or porous Si-carbon composite.
Based on the determined threshold value of Si, the calculation was further extended to estimate the improve-
ment in capacity and energy density that can be achieved by moving from graphite to SCC anode for dierent
cathode materials (see Fig.3).
e specic electrolyte volume (in cc/cm2), vE and specic weight (in g/cc) of unit cell, wCell (in g) can be
expressed in the form of eqns(6) and (7), respectively.
=
.⋅+⋅ +⋅
v
f((t P) (t P) (t P))
10000 (6)
ECC SS AA
=
⋅ρ +⋅ρ+ ⋅ρ +⋅ρ+ ⋅ρ
+.ρw
(t /2)(t)(t )(t)(t /2)
10000
v
(7)
Cell
Al Al AASSCACu Cu EE
Where f is electrolyte lling factor (in %); tC, tA, tS, tAl, and tCu are thickness (in μ m) of cathode, anode, separa-
tor, Al current collector, and Cu current collector, respectively; PC, PA, PA−L, and PS are porosity (in %) of cathode,
SCC anode, unlithiated SCC anode, and separator, respectively; and, ρ
Cu, ρ
Al, ρ
E, and ρ
S are density (in g/cc) of
Cu current collector, Al current collector, electrolyte, and separator, respectively. e specic areal capacity (in
Figure 2. Relationship between specic capacity of anode and amount of Si in the anode, wSi−A and
porosity of anode, PA for anode manufactured using 5 wt.% SBR binder (ρB−A = 1.1 g/cc) and no CC.
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Scientific RepoRts | 6:27449 | DOI: 10.1038/srep27449
mAh/cm2) of unit cell, SCell is determined by the capacity of 70 μ m thick cathode. e thickness of anode was
determined by equating the areal capacity of anode with that of cathode. e thickness of anode is determined
by the eqn. (8).
=.t
S
V
10000
(8)
ACell
A
e specic gravimetric (in mAh/g), GCell and volumetric (in mAh/cc), VCell capacity of unit cell is determined
using eqn. (9) and eqn. (10), respectively.
=G
S
w
(9)
Cell Cell
Cell
=++++ .V
S
(t /2)t tt (t /2)10000
(10)
Cell Cell
Al ASCCu
e energy density values are calculated by multiplication of capacity values with respective cell voltage. As the
Li+ intercalation potential of graphite (0.1 V) is lower than Si (0.37–0.45 V)10, the operational voltage for graphite
anode based LIBs will be higher than SCC anode based LIBs25,26. Because of the low amount of Si in SCC, it is
assumed that the operational voltage of graphite anode based LIB will be 0.1 V higher than SCC anode based LIB,
which is in agreement with experimental work5,27. e maximum improvement in capacity and energy density
that can be obtained by using SCC anode is for NCA based cathode. As the capacity and energy density of LIB
strongly depends on the porosity of the lithiated SCC anode, it is important that the particle size distribution and
other parameters that govern the packing density of lithiated anode is taken in to due consideration. Shape pre-
serving shell design of Si can be one of the potential approaches for maintaining the integrity of the Si particles via
conned porosity in its composite anode8,28. Minimal improvement in energy density and capacity of SCC-LIB
over graphite-LIB is seen when the porosity of lithiated SCC anode exceeds 30% (see Fig.3). e improvement in
capacity and energy density of SCC anode based LIBs over graphite anode based LIBs will be higher for thicker
cathodes and the value will depend on the thickness of cathode (see Fig. S5).
As the level of improvement that can be achieved with Si anode is limited because of its large volume and asso-
ciated electrode porosity change, other anode materials that can provide higher specic capacity than graphite
such as hard carbons, composite alloys, etc. will continue to be attractive as alternate anode materials27,29. Higher
capacity cathodes7 and approaches that can enable thicker cathode30 will increase the utilization of Si anode and
thus will provide higher level of improvement on a cell level.
e model was then extended to get an approximate eect of porosity changes on power density. At 22.5%
lithiated SCC anode porosity (equal to porosity of typical lithiated graphite anode), the power density of
SCC-LIBs will be equal to graphite anode based LIBs (see Fig.3). Currently, the power density of LIBs is limited
by lithium ion conductivity in the electrolyte and it is a strong function of electrode porosity. As the cathode
and separator porosities are assumed to be the same for SCC and graphite anode based LIBs, the power density
of SCC anode based LIB will be primarily limited by the porosity of lithiated anode. e decrease in porosity of
lithiated SCC anode will lead to decline in power density of SCC-LIB as compared to graphite-LIB. e decline
will be exponential and would depend on Bruggeman’s coecient31. e Bruggeman’s coecient and tortuosity
are dimensionless parameter and are related to electrode porosity as per eqn. (11).
τ=
−−
−α
−
(P )
(11)
AL AL
()
AL
Figure 3. Improvement in unit cell (a) capacity and (b) energy density of SCC-LIBs over graphite-LIBs for
three dierent cathode – LCO, NMC and NCA.
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Scientific RepoRts | 6:27449 | DOI: 10.1038/srep27449
e conductivity of lithium ions and thus the power density of LIB is inversely proportional to tortuosity.
For electrode packed with spherical spheres, the Bruggeman’s coecient is 1.532. Based on experimental obser-
vation33, a Bruggeman’s coefficient of 2.5 (average of the anisotropic coefficients for graphite and note that
Bruggeman’s coecient in our denition includes the porosity in the numerator) is used to determine the decline
in power density (see Fig.4). us, in order to have similar power characteristics, the improvement in capacity
and energy density of various cathodes–SCC anode based LIBs over graphite-LIBs is between 7.5–12.5% and
5–10%, respectively (see Figs3 and 4). e improvement in capacity and energy density of SCC based LIB over
graphite-LIBs for lower lithiated anode porosity (< 22.5%) will come at a cost of lower power density.
Conclusions
A theoretical model was developed and used to obtain the amount of Si in SCC anodes required for maximizing
the volumetric energy density of LIBs without allowing for any increase in the external dimension of anode dur-
ing charging of the LIB. e result indicates that the amount of Si permitted in an anode is signicantly lower
than scenarios the external dimensional change of the anode is allowed. e threshold or limiting value of Si that
would maximize volumetric energy density was determined to be 11.68 wt.%. e maximum capacity of the SCC
anode with no volume expansion constraint was determined to be ~935 mAh/cc and ~712 mAh/g. e theoret-
ical limit for gravimetric and volumetric energy density of SCC-LIB was obtained for NCA based cathodes and
the values were ~14% and ~21%, respectively, higher than graphite-LIBs. Once a practical acceptable lithiated
porosity based on power requirements is introduced in the model, the level of improvement in gravimetric and
volumetric energy density of SCC-LIBs gains can further drop down to as low as ~7% and ~8%, respectively.
Method
Calculations for threshold values of Si, capacity and energy density of LIBs were performed using Microso Excel
2013 and equations were derived based on simple mass/capacity balance. e unit cell of LIB dened in this work
consists of cathode, anode, separator and halves of positive and negative current collector. Halves of current
collectors are used because a single current collector is shared by two layers of cathodes or anodes. Table S1 of
Supplementary Information summarizes the values used in the model. It is assumed that electrolyte occupies 90%
of combined porosity of cathode, pre-lithiated anode, and separator. Table S2 of Supplementary Information sum-
marizes all the symbols and associated units used in the model. While a common cathode thickness30 of 70 μ m
was primarily used in the model, calculations were also performed for cathode thickness of 35 μ m, 100 μ m and
200 μ m (see Fig. S5).
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Acknowledgements
e authors would like to thank SABIC for providing support for this work and for agreeing to release the study
for broader distribution. e views and opinions of the authors expressed herein do not state or reect those
of SABIC. e authors would also like to thank Mark Armstrong and Deepak Doraiswamy for reviewing the
manuscript and helpful discussions.
Author Contributions
R.D. conceived, designed, and performed the research and wrote the paper. S.P. performed some aspects of the
research, and co-wrote the paper.
Additional Information
Supplementary information accompanies this paper at http://www.nature.com/srep
Competing nancial interests: e authors declare no competing nancial interests.
How to cite this article: Dash, R. and Pannala, S. eoretical Limits of Energy Density in Silicon-Carbon
Composite Anode Based Lithium Ion Batteries. Sci. Rep. 6, 27449; doi: 10.1038/srep27449 (2016).
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