Fluid Phase Equilibria 228–229 (2005) 59–66
Prediction of gas solubility in battery formulations
P. Kolářa,∗ , H. Nakataa , J.-W. Shenb , A. Tsuboia , H. Suzukic , M. Ued
a
Mitsubishi Chemical Group, Science and Technology Research Center, Inc., Thermodynamic Properties Laboratory,
3-10 Ushiodori, Kurashiki, Okayama 712-8054, Japan
b Computational Modeling of Materials Laboratory, 1000 Kamoshida-cho, Aobadai, Yokohama 227-8502, Japan
c Battery System Design Laboratory, 8-3-1 Chuo Ami, Inashiki, Ibaraki 300-0332, Japan
d Battery Materials Laboratory, 8-3-1 Chuo Ami, Inashiki, Ibaraki 300-0332, Japan
Abstract
This paper describes the development of a thermodynamic model for predicting solubilities of nine gases (H2 , N2 , CO, Ar, O2 , CH4 , C2 H4 ,
C2 H6 , CO2 ) in battery electrolyte formulations composed of five organic carbonates (cyclic and linear) and lithium salts (LiPF6 ) between 283
and 363 K and <1 MPa. The PSRK equation of state by Holderbaum and Gmehling [Fluid Phase Equilib. 70 (1991) 251–265] was combined
with the NRTL expression for activity coefficients [H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144] and used for correlating available
gas solubility data. The prediction ability of the PSRK model was tested by correlating gas solubility data in propylene carbonate and predicting
the gas Henry’s constants in other carbonates. The PSRK predictions of missing combinations and multicomponent systems and were validated
by experimental measurements. The PSRK model is shown to predict gas solubilities in ternary battery formulations with accuracy within
10%.
The prediction of gas solubility was also tested using the quantum mechanical/COSMO-RS method by Klamt and Eckert [Fluid Phase
Equilib. 172 (2000) 43–72]. The COSMO-RS method did not require any prior experimental information and produced quantitatively correct
results for binary gas + carbonate systems.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Gas solubility; Prediction; PSRK; COSMO-RS; Lithium batteries
1. Introduction
Lithium-ion batteries currently represent the standard
power sources in portable electronic equipments such as
cellular phones, notebook computers, and video cameras.
The introduction of rechargeable lithium-ion batteries into
the market in the 1990s was a major technological breakthrough allowing to significantly decrease the size and
weight of portable electronic equipments and accelerate their
widespread use [1–3].
Despite the increasing compactness and reliability of
battery systems, improved designs of electrode and electrolyte materials are still necessary in order to overcome
∗
Corresponding author. Tel.: +81 86 457 2603; fax: +81 86 457 2989.
E-mail address: petr@yayoi.mt.m-kagaku.co.jp (P. Kolář).
0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.fluid.2004.10.019
their safety, capacity, cost, and size limitations [3]. In evaluating their performance, the battery’s cycle life, i.e. the ability
to withstand several hundreds of repeated charge–discharge
cycles, is tested. This testing is a much time-consuming
step in the development of new batteries since only a few
charge–discharge cycles can be carried out on a single battery
per day.
The reason for the gradual deterioration of the battery
performance over the cycle life is that the battery cell undergoes a number of irreversible electrochemical reactions
during charge–discharge cycles. These decomposition reactions may affect the electrical conductivity of the cell, and
cause generation of heat and evolution of gases due to the
increased electrical resistance. The gases may gradually accumulate in the small volume of the battery cell and exert significant pressures leading to battery swelling. The increased
60
P. Kolář et al. / Fluid Phase Equilibria 228–229 (2005) 59–66
Fig. 1. Lithium-ion batteries typically consist of a carbon anode and a lithium-transition metal cathode. The electrodes are in contact with a porous separator
and filled with a non-aqueous electrolyte having a high electrical conductivity (e.g., formulations consisting of mixed linear and cyclic organic carbonates, and
lithium salts with large anions, such as LiPF6 , LiBF4 , LiAsF6 , etc.).
temperature of the system may also lead to evaporation of
volatile solvent components, which will further affect the
electrolyte conductivity and increase the system pressure. In
the case of lithium-ion batteries, the gases generated by electrolyte decomposition typically consist of CO2 , CH4 , H2 ,
CO, ethane (C2 H6 ), and ethylene (C2 H4 ), each of the gases
having a widely different solubility in the liquid electrolyte.
Therefore, the vapor pressures of the battery formulations and
the solubility of the evolved gases are important factors for
evaluating battery performance. Experimental measurement
of the gas solubility is difficult because of the large variety
of the generated gases, variable composition of the formulations, and a corrosive and hygroscopic nature of the battery
electrolytes (see Fig. 1).
This paper describes a thermodynamic model for predicting solubilities of nine key gases (H2 , N2 , CO, Ar, O2 , CH4 ,
C2 H6 , C2 H4 , CO2 ) in mixed battery formulations composed
of five organic carbonates (cyclic and linear) and lithium salts
(LiPF6 ) between 283 and 363 K and <1 MPa. The modeling procedure we apply is essentially similar to that used in
process development for thermodynamic modeling of multicomponent systems. It is shown that a relatively simple gas
solubility model may be developed, capable of predicting a
variety of multicomponent formulations using only binary
interactions.
predicted using only binary interactions. The PSRK EOS is
a combination of the following models:
(a) Soave–Redlich–Kwong equation of state [5]
P=
RT
a
−
v − b v(v + b)
(1)
(b) Modified Huron–Vidal first-order (MHV1) mixing rule
[6]
a
ai
1 gE
b
(2)
=
xi
+
+
xi ln
RTb
RTbi
q RT
bi
where b = xi bi and q = −0.64663 [4].
(c) Excess Gibbs energy model gE .
In this work, we use the NRTL activity coefficient
model [7] in place of the UNIFAC group contribution
model in the original PSRK EOS
xj Gji (uji /T )
gE
(3)
=−
xi
xj Gji
RT
where Gij is a combined interaction parameter, Gij =
exp(−0.3uij /T ).
In the total PSRK model, each pure component is described by two parameters ai and bi , and each binary system
is characterized by two interaction parameters uij and uji .
2. Development of gas solubility model
2.2. Pure component properties
2.1. Modeling procedure
The thermodynamic model for gas solubility used in this
work is the predictive Soave–Redlich–Kwong equation of
state (PSRK EOS) proposed by Holderbaum and Gmehling
[4]. The main feature of this model is that phase equilibria in multicomponent systems containing both subcritical
components (liquids), and near- or supercritical gases can be
Table 1 summarizes the basic physical properties of the
pure components in battery electrolyte formulations [8]. The
properties of EMC and LiPF6 were mostly unavailable in the
literature and Table 1 therefore lists our own measurements
(denoted as ‘MCC data’ throughout this paper). It can be
seen that despite their structural similarity, cyclic carbonates
(EC and PC) have largely different properties from linear
P. Kolář et al. / Fluid Phase Equilibria 228–229 (2005) 59–66
61
Table 1
Properties of pure carbonates and LiPF6
M (g/mol)
Tc (K)
Pc (bar)
Tb (K)
Tm (K)
ρL (g/cm3 )a
ηL (mPa s)a
εr (–)a
EC
88.063
806.0
67.7
521.4
309.6
1.338b
1.93b
89.8b
Propylene carbonate
PC
102.090
778.0
54.1
514.9
218.6
1.195
2.53
64.9
Dimethyl carbonate
DMC
90.079
548.0
45.0
363.2
273.7
1.069
0.573
2.8
Ethyl methyl carbonate
EMC
104.105
573.8c
39.3c
380.2f
219.2f
1.007f
0.66f
2.8f
Diethyl carbonate
DEC
118.133
576.0
33.9
401.8
230.2
0.969
0.748
2.82
Lithium hexafluorophosphate
LiPF6
151.903
855d
533e,f
468e,f
–
–
–
Compound
Alias
Ethylene carbonate
a
b
c
d
e
f
Structure
LiPF6
7.5d
Liquid-phase properties at 298 K.
EC properties at 313 K.
Estimated by the Constantinou–Gani group contribution method [9].
MCC data.
Assumed.
Decomposition.
carbonates (DMC, EMC, and DEC), in particular their boiling
and melting points, viscosity, and dielectric constants.
In the PSRK model, the pure component parameters ai
and bi are fitted to vapor pressure data using the following
relationships [4]:
ai = 0.42748
R2 Tci2
F (T ),
Pci
RTci
Pci
(4)
νiL
2
F (T ) = 1 + C1i 1 −
+ C3i 1 −
bi = 0.08664
T
Tci
T
Tci
3
2
+ C2i 1 −
information about the densities of the coexisting phases. The
PSRK EOS is known to be inaccurate for predicting of liquid densities, particularly for polar compounds. Problems
were also anticipated in estimating the density of LiPF6 solutions using the EOS. The liquid densities of the pure components were therefore represented by a Rackett-type equation
[8]
T
Tci
(5)
The calculation of phase equilibrium in the closed battery system is performed at a constant total volume, which requires
D2i
Mi
= L =
ρi
1+(1−T/D3i )D4i
D1i
(6)
and ideal mixing (vL = xi vi ) was assumed in liquid mixture calculations. The parameters D1 –D4 for pure LiPF6 were
fitted to MCC density data of several battery formulations
with a different LiPF6 content.
Fig. 2 compares the vapor pressure and liquid density correlations with experimental data [10]. The pure component
parameters for all the gases were taken from [4].
Fig. 2. Experimental and correlated vapor pressures (a) and densities (b) of pure organic carbonates. Symbols: Experimental data [10]; ( ): MCC data. Lines:
Data correlation using the PSRK (a) or Rackett models (b).
62
P. Kolář et al. / Fluid Phase Equilibria 228–229 (2005) 59–66
Table 2
Gas properties and number of available gas solubility data in organic carbonates [10]
H2
N2
CO
Ar
O2
CH4
C 2 H6
C 2 H4
CO2
Tc (K)
Pc (bar)
Tb (K)
EC
PC
DMC
EMC
DEC
33.2
126.2
132.9
150.8
154.6
190.6
282.4
305.4
304.2
13.0
33.9
34.8
48.7
50.5
46.0
50.4
48.8
73.8
20.7
77.4
81.7
87.3
90.2
111.8
169.3
184.5
215.6
–
3 GLE
–
–
–
3 GLE
3 GLE
–
5 HPV, 3 GLE
13 GLE, 4 HPV
3 GLE, 7 HPV
–
4 GLE
1 GLE
3 GLE, 4 HPV
8 GLE
3 GLE
50 GLE, 24 HPV
1 GLE
1 GLE
–
1 GLE
–
1 GLE
1 GLE
1 GLE
4 HPV
–
–
–
–
–
–
–
–
–
1GLE
1 GLE
–
1 GLE
–
1 GLE
1 GLE
1 GLE
3 HPV
Abbreviations of experimental datasets: GLE – gas solubility, HPV – high-pressure vapor–liquid equilibria.
2.3. Available gas solubility data
Table 2 summarizes the gas solubility data available in the
literature for the nine gases and four carbonates [10]. Most
solubility data are reported in PC, which is traditionally used
as an experimental substitute for EC due to the latter’s high
melting point (Table 1). No gas solubility data were found in
the literature for EMC and for solubilities of CO and O2 in
any of the carbonates. (Data [11] are thought to be in error).
Until very recently, no data had been available for any binary
combinations gas + DMC or DEC, however, two relevant sets
of measurements were published lately [12,13]. The database
of Henry’s constants and VLE data was also extended on
MCC data (CO2 , C2 H6 , CH4 , and N2 solubilities in EC and
PC).
Figs. 3 and 4 confirm the expected trend for systems with
weak or no specific interactions, viz. that the gas solubility increases monotonically with the gas boiling point (cf.
Table 2). In the absence of any direct data, the binary interactions of CO and O2 with all the carbonates were assumed
to be the same as those of N2 and Ar, respectively. This substitution is commonly used in practice for gases with close
boiling points and critical properties in order to limit haz-
ardous measurements. As can be seen in Fig. 3b, using the
same interaction parameters, the predicted solubilities of the
individual gases are slightly different due to different pure
component fugacities (Eqs. (4) and (5)).
2.4. Prediction of missing interactions
The predictive capability of the PSRK model was tested
by correlating all available gas solubility data in PC and predicting the solubilities in other carbonates. Comparison of
the predictions (dashed lines) with data in Fig. 3a shows that
the PSRK model correctly predicts the decrease in the gas
solubility in EC as compared to PC. Nevertheless, the interaction parameters are necessary to adjust in order to obtain
good agreement with the experimental data (solid lines). The
likely reason for that is that EC is not simply homologous
with respect to PC. Lohmann and Gmehling [14] also found
it necessary to introduce a separate EC subgroup in their parameterization of modified UNIFAC (Dortmund) for organic
carbonates.
In the case of DMC, the prediction from PC is quantitative
for most of the gases and only interactions for H2 and C2 H4
need to be modified. This problem likely stems from the fact
Fig. 3. Experimental and correlated gas Henry’s constants in cyclic organic carbonates: (a) EC; (b) PC. Symbols: Literature data [10]; ( ): MCC data. Solid
lines are correlations using the PSRK model, dashed lines are predictions using PSRK parameters determined from gas + PC binary data.
P. Kolář et al. / Fluid Phase Equilibria 228–229 (2005) 59–66
63
Fig. 4. Experimental and correlated gas Henry’s constants in linear organic carbonates: (a) DMC; (b) DEC. Symbols: Literature data [12,13]. Solid lines are
correlations using the PSRK model, dashed lines are predictions using PSRK parameters determined from gas + PC binary data.
that in the fitting of PC + gas interactions the two parameters of the activity coefficient model are determined from a
limited number of Henry’s constant data (corresponding to
infinite dilution in pure solvent). This may lead to non-unique
values of the parameters, especially those for the reverse uij
pair. Additionally, in the case of C2 H4 there is some discrepancy between solubility data of C2 H4 and C2 H6 in PC (see
Fig. 3b). Consequently, the data fit obtained for C2 H4 may
not be optimal. The prediction for CO2 is reasonably good,
probably because the P-x-y data used for the fitting of the
parameters for CO2 + PC covered a wide range of conditions
(xCO2 < 0.4).
In the case of DEC, the prediction based on constant NRTL
interaction parameters is not sufficiently accurate (Fig. 4b).
For gases other than H2 and N2 , the PSRK model correctly
predicts a decrease in Henry’s constants as compared to
DMC, however, the experimental data indicate much higher
gas solubilities (i.e. lower Henry’s constants).
In all cases where data were available and the predictions
were of insufficient accuracy, the PSRK parameters were next
fitted to the experimental data. The parameters for EMC + gas
were then obtained by averaging the corresponding binary interaction parameters of DMC + gas and DEC + gas. All other
solvent + gas interactions were set to those for the corresponding PC + gas binaries.
In calculations with LiPF6 , the salt was in the first approximation assumed to behave as a non-volatile inert, in which
the gases have a negligible solubility (i.e. the coefficients Ci
in Eq. (5) for LiPF6 were set to zero and LiPF6 + gas interaction parameters set to uij = uji = 5000, resulting in the gas
Henry’s constants Hgas ≈ 1010 bar).
3. Model validation
3.1. CO2 solubility in EMC (or EC) + LiPF6
The solubility of CO2 in EMC + LiPF6 solutions was measured in a high-pressure apparatus (AKICO Ltd., Tokyo,
Japan) at 298, 323, 343, and 363 K. Known amounts of CO2
and EMC + LiPF6 mixtures were charged into the equilibrium
cell (602 cm3 ) using piston pumps so that the liquid level in
Fig. 5. Experimental and predicted total pressures in CO2 + EMC + LiPF6 mixtures: (a) LiPF6 = 0 mol/l; (b) LiPF6 = 0.75 mol/l; (c) LiPF6 = 1.25 mol/l. Symbols:
MCC data; Lines: PSRK model.
64
P. Kolář et al. / Fluid Phase Equilibria 228–229 (2005) 59–66
101.3 kPa. The two mixtures with LiPF6 mass concentrations
0 and 12.5% contained the same mass ratio of EMC/EC = 1.8.
The gas solubilities in both solutions were predicted using the
binary parameters for gas + EC and gas + EMC developed in
Section 2.4. The PSRK model predicted the gas solubility
data with accuracy within 10%. In the investigated mixtures,
the gas solubilities were relatively high and the effect of the
salt could be predicted well assuming that it mainly acts as
a diluent in the solution. However, this preliminary assumption may not be generally valid since the salt is known to
dissociate in the formulations. The effect of LiPF6 on the
gas solubility is likely more complex and requires further
investigation.
Fig. 6. MCC data (symbols) and predicted (lines) solubilities of CO2 and
CH4 in EC + EMC + LiPF6 ternary mixtures at 298 K and gas partial pressures 101.3 kPa.
the cell reached 40%. Both phases were then stirred and the
total pressure in the system was monitored until equilibrium
was attained. In a similar manner, the solubility of CO2 in
EC + LiPF6 binary mixtures was measured at 343 and 363 K
and LiPF6 molar concentrations 0 and 1.25 mol/l. LiPF6 solutions are highly hygroscopic and may generate corrosive
hydrogen fluoride on decomposition. Consequently, all their
handling was carried out under a sealing blanket of dry nitrogen.
Fig. 5 shows the experimental data at LiPF6 molar concentrations 0, 0.75, and 1.25 mol/l. Lines show the prediction by the PSRK model described in Section 2.4, in which
the EMC + CO2 binary interactions were obtained by averaging the binary interaction parameters of DMC + CO2 and
DEC + CO2 .
3.2. CO2 and CH4 solubility in EC + EMC + LiPF6
Fig. 6 compares PSRK predictions with MCC experimental data of CO2 and CH4 solubilities in the ternary system EC + EMC + LiPF6 at 298 K and gas partial pressures
4. Gas solubility prediction using COSMO-RS
The binary gas solubilities in the organic carbonates were
also predicted using the COSMO-RS method, which combines quantum mechanical information with novel developments in statistical thermodynamics [15,16]. Using the
COSMO-RS method, the calculation of gas solubilities is
based on the molecular structure only and it does not require any prior experimental information about the investigated systems. In our calculations, the sigma profiles for all
the components were taken from the COSMO-RS database
and the computations performed using COSMOtherm ver.
1.2, release 7.02 [17].
Figs. 7 and 8 show that COSMO-RS correctly predicts the
order and magnitude of the gas solubilities in all the carbonates including the temperature dependence of the Henry’s
constants. Some differences are observed for near-critical
gases with very high solubilities (CO2 , C2 H4 , C2 H6 ). As
shown in Fig. 5, the dependence of CO2 solubility on the
pressure is nonlinear, which may also explain the scatter
of the Henry’s constants obtained by different experimental methods (Fig. 7b). Regarding the C2 gases, COSMO-RS
Fig. 7. Experimental and predicted gas Henry’s constants in cyclic organic carbonates: (a) EC; (b) PC. Symbols: see Figs. 3 and 4. Dashed lines: COSMO-RS
method.
P. Kolář et al. / Fluid Phase Equilibria 228–229 (2005) 59–66
65
Fig. 8. Experimental and predicted gas Henry’s constants in linear organic carbonates: (a) DMC; (b) DEC. Symbols: see Figs. 3 and 4. Dashed lines: COSMO-RS
method.
consistently indicates that C2 H4 exhibits a higher solubility
in the organic carbonates than C2 H6 . This result may help to
resolve the problem of the conflicting data for these gases.
5. Conclusions
Gas solubility and vapor pressure are important properties of battery formulations consisting of non-aqueous mixtures of polar organics with high dielectric constants and
conducting salts. The present work shows that the standard
procedure for thermodynamic modeling of multicomponent
systems may also be applied to complex formulations used
in product development. The procedure consists of building
up of a thermodynamic model from its simpler subsystems
(unary, binary, ternary, etc.) and, whenever possible, validating the model predictions against experimental data at each
level.
In this work, we obtained good predictions for ternary
and higher systems using only binary interactions, which allowed us to significantly reduce the experimental effort for the
model development. In the preliminary gas solubility model,
it was found sufficient to assume that LiPF6 behaves as a nonvolatile inert with respect to the gases. The effect of the salt
is likely more complex, and its impact on the gas solubility
is being further studied.
The present work also shows the potential of the quantum
mechanical/COSMO-RS method for predicting interactions
for which no data are available. The gas solubilities predicted
by COSMO-RS were found in good agreement with the available data for all the tested binary systems gas + carbonate.
List of symbols
a
energy parameter of the SRK equation of state
b
size parameter of the SRK equation of state (covolume)
C
coefficient in vapor pressure correlation, Eq. (5)
D
g
M
P
R
T
u
v
x
coefficient in density correlation, Eq. (6)
molar Gibbs energy
molecular weight
pressure
gas constant (R = 8.31441 J/mol K)
temperature (K)
interaction parameter in NRTL model, Eq. (3)
molar volume
mole fraction
Greek letters
ε
relative permittivity (dielectric constant)
η
viscosity
ρ
density
Subscripts and superscripts
b
boiling point
c
critical property
E
excess property
i,j
component index
L
liquid
m
melting point
References
[1] G. Pistoia, Lithium Batteries: New Materials, in: Developments and
Perspectives, Elsevier, Amsterdam, 1994.
[2] D. Linden, T.B. Reddy, Handbook of Batteries, 3rd ed., McGrawHill, New York, 2002.
[3] J.O. Besenhard, Handbook of Battery Materials, Wiley-VCH, 1999.
[4] T. Holderbaum, J. Gmehling, Fluid Phase Equilib. 70 (1991)
251–265.
[5] G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203.
[6] M.L. Michelsen, Fluid Phase Equilib. 60 (1991) 213–219.
[7] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144.
[8] T.E. Daubert, R.P. Danner, Physical and Thermodynamic Properties
of Pure Chemicals: Data Compilation, American Institute of Chemical Engineers, New York, 1989–2003.
66
P. Kolář et al. / Fluid Phase Equilibria 228–229 (2005) 59–66
[9] B. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases
and Liquids, 5th ed., McGraw-Hill, New York, 2001.
[10] Dortmund Databank, version 2003. DDBST GmbH, Oldenburg, Germany. http://www.ddbst.com/.
[11] W.R. Baird, R.T. Foley, J. Chem. Eng. Data 17 (1972) 355–
357.
[12] O. de la Iglesia, A.M. Mainar, J.I. Pardo, J.S. Urieta, J. Chem. Eng.
Data 48 (2003) 657–661.
[13] J. Im, M. Kim, J. Lee, H. Kim, J. Chem. Eng. Data 49 (2004)
243–245.
[14] J. Lohmann, J. Gmehling, J. Chem. Eng. Jpn. 34 (2001) 43–51.
[15] A. Klamt, F. Eckert, Fluid Phase Equilib. 172 (2000) 43–72.
[16] R. Putnam, R. Taylor, A. Klamt, F. Eckert, M. Schiller, Ind. Eng.
Chem. 42 (2003) 3635–3641.
[17] COSMOlogic GmbH and Co., KG, Leverkusen, Germany.
http://www.cosmologic.com/.