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. 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