Lithium Salt Nature and Concentration Effect - ACS Publications

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Viscosity and Carbon Dioxide Solubility for LiPF6, LiTFSI, and LiFAP in Alkyl Carbonates: Lithium Salt Nature and Concentration Effect Yvon Rodrigue Dougassa,† Johan Jacquemin,‡ Loubna El Ouatani,§ Cécile Tessier,§ and Mérièm Anouti*,† †

Laboratoire PCMB (EA 4244), Université François Rabelais, Parc de Grandmont, 37200 Tours, France CenTACat, School of Chemistry and Chemical Engineering, Queen’s University Belfast, Belfast, BT9 5AG Northern Ireland, U.K. § SAFT-Direction de la Recherche, 111-113 Bld Alfred Daney, 33074 Bordeaux Cedex, France ‡

ABSTRACT: In this paper, we have reported the CO2 solubility in different pure alkyl carbonate solvents (EC, DMC, EMC, DEC) and their binary mixtures as EC/DMC, EC/EMC, and EC/DEC and for electrolytes [solvent + lithium salt] LiX (X = LiPF6, LiTFSI, or LiFAP) as a function of the temperature and salt concentration. To understand the parameters that influence the structure of the solvents and their ability to dissolve CO2, through the addition of a salt, we first analyzed the viscosities of EC/ DMC + LiX mixtures by means of a modified Jones−Dole equation. The results were discussed considering the order or disorder introduced by the salt into the solvent organization and ion solvation sphere by calculating the effective solute ion radius, rs. On the basis of these results, the analysis of the CO2 solubility variations with the salt addition was then evaluated and discussed by determining specific ion parameters Hi by using the Setchenov coefficients in solution. This study showed that the CO2 solubility has been affected by the shape, charge density, and size of the ions, which influence the structuring of the solvents through the addition of a salt and the type of solvation of the ions.

1. INTRODUCTION Standard lithium ion battery electrolytes are a mixture of organic solvents, such as carbonates, and lithium salts with perfluoroanions. In operating conditions, the oxidation reaction occurs at high potentials, therefore causing the formation of gases, especially CO2, by decomposition of the alkyl carbonates at high potentials. This phenomenon induces the increase in internal pressure inside the sealed cell, which causes a security problem. 1,2 Besides, the CO 2 formation modifies the composition and properties of the electrolyte affected by the solubility of the carbon dioxide present in these solutions. These effects, can be evaluated by better comprehension of parameters that affect the CO2 solubility in electrolyte. Lithium hexafluorophosphate (LiPF6) is the most common salt used as the reference in Li-ion batteries due to the combination of numerous properties.3−5 However, the thermal instability of this salt has been identified as a critical issue for the development of battery systems, in an electric vehicle or for stationary use. Thereby, in-depth studies have been conducted to select another safer lithium salt, including perfluoro anions, such as bis(trifluoromethylsulfonyl)imide (LiTFSI)6 and tris(pentafluoroethane)trifluorophosphate (FAP),3 as candidates for a more stable electrolyte. According to the structural and electronic differences between anions such as (PF6), (FAP), and (TFSI), the lithium salts, dissolved in an alkyl carbonate mixture, could affect the CO2 solubility in electrolytes. By comparing the effect of salting on the CO2 solubility in alkyl carbonate with and without a lithium salt, it is possible to analyze in detail the anion effect. The prior knowledge of the parameters which influence the structuring of solvents through © 2014 American Chemical Society

the addition of a salt, according to its nature and concentration, and the solubility of gases in these electrolytes, is necessary and has a considerable industrial and theoretical significance. In spite of this significance, relatively few papers describe parameters related to the dissolution of CO2 in electrolytes. Several authors present the CO2 solubility in standard electrolytes based on alkyl carbonate.7−11 However, as a general rule, these studies concern only pure alkyl carbonate solvents or sometimes their mixtures without lithium salts. We recently reported a series of papers concerning the influence of the nature of lithium salts (LiPF6, LiTFSI, and LiFAP), in an EC/DMC mixture, on the conductivity and self-diffusion coefficient of various species,12 and on CO2 solubility.9 In line with these studies, in this paper, we have expressed the salting effects, as a function of the concentration and nature of the anion (LiPF6 or LiTFSI or LiFAP), on viscosity and on the structure of the EC/DMC solvent mixture. On the basis of these results, the analysis of the comparative CO2 solubility according to the nature and concentration of the LiX salt (X = LiPF6, LiTFSI, or LiFAP) was discussed. The measurements presented in this paper address several aspects: • understanding the parameters, which influence the structuring of the solvents through the addition of a salt and the solvation of ions, by analyzing viscosity measurements Received: January 3, 2014 Revised: March 12, 2014 Published: March 17, 2014 3973

dx.doi.org/10.1021/jp500063c | J. Phys. Chem. B 2014, 118, 3973−3980

The Journal of Physical Chemistry B

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• extending the “specific ion parameters” denoted Hi, for CO2, to usual anions in formulated electrolytes for energy storage applications, to specifically evaluate the effect of gas generation on the long-time cycling of lithium ion batteries, • demonstrating how the nature of an anion, in relation to its volumetric or electronic properties, significantly determines the CO2 solubility with the Setchenov coefficient, kS

temperatures with degassed water and dehumidified air. Eleven readings were taken for each density measurement. The calibration of the viscometer was performed with ultrapure water. The density and viscosity were reported with uncertainty of better than 5 × 10−5 g cm−3 and 1%, respectively. The CO2 solubilities measured here were based on a chemical titration technique, with the experimental apparatus as described by our group elsewhere.8,9 It can be summarized as follows: in a glovebox, under a dry atmosphere, a known mass of electrolyte was first placed an equilibrium cell (EqC) equipped with a septum to avoid any air and moisture contaminations. The EqC was maintained at constant temperature, Texp, by being immersed in a water bath using a PID temperature controller (ΔT ± 0.1 K). The electrolyte was then saturated with CO2 at constant temperature for 1 h to reach the equilibrium. An argon flow was then used to displace the amount of dissolved CO2 from the equilibrium cell to the titration cell, which contains NaOH aqueous solution with a known concentration. The gas mixture was first passed through an ethanol bath at 193 K, to ensure that a solvent-free (Ar + CO2) gas is trapped from the gas stream. The displaced quantity of dissolved CO2 reacts then with NaOH solution, forming sodium carbonate (Na2CO3). The aqueous solution containing Na2CO3 and residual NaOH was finally titrated by adding a known concentration of HCl. The added volume VHCl, is directly linked to the amount, nliq 2 , of dissolved CO2 in the solution, nliq 2 = ΔVHCl·CHCl. 2.5. Data Analysis for CO2 Solubility Determination. The CO2 solubility is expressed in mole fraction of CO2 in solution, x2:

2. EXPERIMENTAL SECTION 2.1. Materials. Highly pure (GC grade, molecular purity >99.99%) ethylene carbonate (EC), dimethyl carbonate (DMC), ethyl methyl carbonate (EMC), and diethyl carbonate (DEC) purchased from Aldrich were used as received. The lithium salts such as lithium hexafluorophosphate (LiPF6) and lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) with highly purity (99.99%) were purchased from Sigma Aldrich and from Solvionic, respectively. All electrolytes based on these salts were formulated and stoked under a dry atmosphere in a glovebox. LiFAP based electrolytes were obtained from Merck, their purity is higher than 99.99%. LiFAP electrolytes were kept and used as received in a glovebox. 2.2. Mixture Preparation. All solvent mixtures were formulated under a dry atmosphere by mass using a Sartorius 1602 MP balance with an accuracy of ±1 × 10−4 g. During the study, samples were kept inside the glovebox before use. Alkyl carbonate mixtures have been prepared at 25 °C by mass and expressed in this study by mass fraction percentage (wt %) (as EC/DMC (50:50 wt %), EC/EMC (50:50 wt %), and EC/ DEC (50:50 wt %). Electrolytes are then prepared by adding the required mass of lithium salts, LiX (with X = PF6 or TFSI), to the solvent. The concentrations of lithium salts in solutions are reported here in molar concentration (mol·L−1). Before measurement, the water content of solvents and electrolytes were analyzed using coulometric Karl Fischer (Coulometer 831 - Metrohm) titration. The water content of samples is close to 10 ± 1 ppm. 2.3. Determination of CO2 Dissolution Methodology. The amount of CO2 dissolved in solutions is determined by a chemical titration methodology using the experimental setup as described previously.8,9 All gases used were obtained from (AGA/Linde Gas). The carbon dioxide with a mole fraction purity of 0.99995 and argon with a mole fraction purity of 0.999997 were used as received from the manufacturer. 2.4. Experimental Methods. Viscosity measurements were conducted from 283.15 to 333.15 K using an Anton Parr digital vibrating tube densitometer (model 60/602, Anton Parr, France) and an Anton Parr rolling-ball viscometer (model Lovis 2000M/ME, Anton Parr, France) regulated within ±0.02 °C. Dynamic viscosities were calculated by considering the effect of the sample density as a function of temperature and the buoyancy of the ball in sample. Consequently, density data are used to calculate a dynamic and kinematic viscosity by using the Lovis M/ME microviscosimeter according the recommendation of constructor. Simultaneous density and viscosity measurements were conducted for each sample, as both instruments are connected with hoses and simultaneously filled with the same sample. The temperature adjustments were ensured with the thermobalance using air/water circulation. The densitometer was first calibrated as recommended by the constructor at atmospheric pressure in the studied range of

x2 =

n2liq liq + n2liq nsolv

(1)

where nliq 2 is the moles of CO2 dissolved in the liquid solution liq liq and nliq solv = n1 + n3 is the amount of solvent in the liquid phase liq introduced in the equilibrium cell. Here, nliq 1 and n3 are the amount of solvents and lithium salt in the liquid solution, respectively. Henry’s law constants can be then calculated from the CO2 mole fraction solubility as KH = lim

x2 → 0

f2 (p ,T ,x 2) x2

≈

ϕ2(pexp ,Texp)pexp x2

(2)

where f 2 is the fugacity of the CO2 if the gas phase consists of pure CO2 and ϕ2 is its fugacity coefficient. ϕ2 is calculated at atmospheric pressure, pexp, and fixed temperature, Texp, using the compilation of Dymond and Smith.13

3. RESULTS AND DISCUSSION 3.1. Viscosity and Effects of the Nature and the Concentration of Salts. The effect of the addition of an ionic solute, such as lithium salts, to a binary mixture of solvents is complex because of the combination of intermolecular interactions that occur between the ions, the solvents, and the ion−solvent molecules. The viscosities of the solutions in binary EC/DMC (50/50, wt%) solutions at several concentrations of lithium salts LiX (X = PF6, TFSI, and FAP) were measured at temperatures ranging from 283.15 to 333.15 K and are summarized in Table 1. The experimental results of relative viscosities ηr = η/η0, where η and η0 are the viscosities of solution [LiX + (EC/DMC)] and solvent (EC/DMC), 3974



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Table 1. Viscosities η of EC/DMC (50/50, wt%) Electrolytes Containing C of Lithium Salt (LiPF6, LiTFSI, or LiFAP) as a Function of Temperature

Coulomb forces, the high term hydrodynamic effect, and interactions arising from changes in solute−solvent interactions with the concentration.22 The concentration range used in this study, up to 1 mol·L−1, is an overlapping range, in which the BC term is essential. The values of the B and D coefficients calculated from the adjustment of relative viscosity data according to eq 4 (Figure 1a) at 313.33 K, for example, are presented in Table 2 for various temperatures. As can be observed in this table, the B coefficient values are constant and range from (0.93 to 1.05) ± 0.02, whereas the D coefficient values increase monotonically with temperature and vary widely depending on the nature of the anion from 1.79 for LiFAP to 0.64 for LiTFSI. Finally, A reflects the viscous drag due to the ionic atmosphere. As expected, this parameter is insignificant because the C and C2 terms dominate in concentrated solutions. Generally, B coefficients are associated to the lyotropic behavior of the anions. This character is linked to the charge, size, and solvation of the ions, i.e., their ability to bond with the molecules of the solvent. In a group of identically charged ions, such as the anions studied in this paper, solvation increases as the ionic radius decreases. Because B and D coefficients are empirical parameters, there is no easy way to deduce interpretations for structural reorganization of the electrolyte; nevertheless, it is generally accepted that the value of the B coefficient represents the solute−solvent interaction and is a measurement of the order or disorder introduced by the solute into the solvent structure. However, there is no satisfactory theory establishing a relationship between the ionic B coefficients and the ionic effects on the structure of the solvent.23 To understand the structural entropy modification of the solvent, it is important to consider the contributions of the ionic solvate shell and the limitation of the ionic rotational entropy for multiatomic ions. With this approach, Krestov obtained the changes in the structure of the solvent beyond the solvation shell (ΔS),24 leading to “kosmotropic” and “chaotropic” terms linked directly to the solvent structure. For chaotrope ions, (η < η0), the ionspecific B coefficient is negative, whereas for kosmotropes ions, (η > η0) B is positive.23,25 In this case, all salts have a kosmotropic character. By comparing the B coefficient values of three LiX salts in EC/DMC solutions (Table 2), one can say that the identical forces of the solute−solvent interactions are due to identical positive B values (B = B+ + B−). This is probably due to the predominant contribution of lithium, i.e., B− ≪ B+. Petrella and Saccog26 have reported viscosity B coefficients for several salts

η/mPa·s for EC/DMC (50/50; wt%) + [LiX]/mol·L−1 T/K

C/mol·L−1

LiPF6

LiTFSI

LiFAP

283.15

0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00

1.532 2.188 2.895 4.144

1.532 2.056 2.512 3.190 4.028 1.192 1.562 1.871 2.289 2.888 0.967 1.237 1.465 1.812 2.150 0.766 0.957 1.118 1.390 1.699

1.533 2.039 2.898 4.091

298.15

313.15

333.15

1.192 1.654 2.243 3.143 4.152 0.967 1.322 1.752 2.266 3.005 0.766 1.024 1.342 1.672 2.169

1.193 1.559 2.210 3.210 4.250 0.967 1.243 1.729 2.302 3.073 0.766 0.968 1.281 1.693 2.144

respectively, have generally been analyzed with the empirical Jones−Dole equation:14 ηr = 1 + A C + BC

(3)

where A is the interionic coefficient, B is the solute−solvent interaction coefficient, and C is the concentration of the solute in mol·L−1. Although eq 3 is applicable to a dilute solution (C ≤ 0.1 mol·L−1), at higher concentrations (C ≥ 0.1 mol·L−1), B swamps out the effect of A. Jones and Talley,15 Kaminsky,16,17 Desnoyers and Perron,18 Desnoyers et al.,19 Feakins and Lawrence,20 and Robertson and Tyrrell21 added a quadratic term (Kaminsky or extended Jones−Dole equation): ηr = 1 + A C + BC + DC 2

(4)

2

The new DC term of eq 4 includes all the solute−solvent and solute−solute structural interactions that were not accounted for by the A√C and BC terms at high concentrations, such as the high terms of the long-range

Figure 1. Kaminski plot of (ηr − 1) as a function of salt concentrations at 313.15 K (a) and D coefficient variations as a function of temperature (b) for LiPF6 LiTFSI and LiFAP (b) lithium salt in EC/DMC (50/50, wt%). 3975



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Table 2. Kaminski Coefficients (B, D) and the Effective Solute Ions Radius (rs) for EC/DMC (50/50, wt%) Containing C (mol· L−1) of Lithium Salts (LiPF6, LiTFSI, or LiFAP) LiPF6

LiFAP

LiTFSI

T/K

B

D

rs/nm

B

D

rs/nm

B

D

rs/nm

283.15 298.15 313.15 333.15

1.07 1.07 1.07 1.07

1.55 1.35 1.01 0.73

0.56 0.55 0.52 0.49

0.88 0.92 0.91 0.93

1.79 1.62 1.27 0.89

0.57 0.56 0.54 0.51

0.96 0.91 0.92 0.93

0.64 0.45 0.30 0.14

0.40 0.36 0.32 0.25

Figure 3. Diagram representing the lithium salt solvation shell in the case of LiFAP (a) and LiTFSI (b).

in ethylene carbonate at 40 °C, for Li+, B+ = 0.63 in EC, which is consistent with the values evaluated in this paper. At the same time, Table 2 shows that the values of the D coefficient sharply decrease with temperature. This means that, at high temperatures, the effect of solute−solvent (ion− solvent) and solute−solute (ion−ion) long-range Coulomb interactions on the experimental values of the viscosity of the solution becomes less essential. These features suggest that lithium is structure-ordering with a reverse viscosity temperature dependence. Figure 1b shows that the temperature dependence of ionic D coefficients dD/dT is always negative, which corroborates the idea of the structure-making role of the lithium ion. The sign of the dD/dT values provides important information regarding the structure-breaking and structuremaking roles of the solute in the solvent media rather than simply the D coefficient. The magnitude of the ionic D coefficient is then presumed to be proportional to the molar “hydrated volume” of the ion. Thomas27 has extended the Einstein relationship (eq 5) as follows: ⎤2 ⎡4 ⎤ ⎡4 η = 1 + 2.5⎢ πrs 3NA ⎥C + 4⎢ πrs 3NA ⎥ C 2 ⎦ ⎣3 ⎦ ⎣3 η0

obtained, in our previous work, by NMR (rs = 0.36 nm).12 However, they are consistent with the values obtained for LiTFSI (rs = 0.36 nm) such as provided in Table 2. Moreover, there is, in the case of LiTFSI, a significant effect of temperature on the radius of solvation halving between 283.15 and 333.15 K, whereas it remains almost constant in the case of LiFAP and LiPF6. The electrostriction caused by the ions of an electrolyte may be insignificant (for large ions) but always causes an increased pressure (reduction of the solvent volume). When the shapes of individual polyatomic ions considerably lose their sphericity (i.e., when they are not globular such as regular tetrahedral or octahedral shapes), the electrostriction becomes extremely difficult and cannot be achieved. Electrostriction occurs naturally near rod-like ions such as SCN− or plate-like ions such as CO32− or the large rod-like shape of the TFSI anion. It is likely that the charge density is very delocalized in the case of the TFSI anion and that its large size with a very elongated shape does not generate a rearrangement of the solvent mixture, which creates a significant void volume. We propose the shell solvation arrangement for LIFAP (a) and LiTFSI (b) in Figure 3. 3.2. Carbon Dioxide Solubility and Effect of the Nature and Concentration of the Salts. Measurements of viscosity as a function of the nature and concentration of the salt discussed in the first part of this study provide information on the structuring of the solvents by addition of a solute. The addition of CO2 can be also considered from a solute−solvent interactions point of view, and thus its solubility is influenced by the presence or absence of the lithium salt; in other words, the CO2 solubility can be discussed in the light of the results of the first section. Several studies show a direct correlation between viscosity and the solubility of the gas. Indeed, Chew and Connally30 presented a correlation to adjust the oil viscosity according to the gas solubility and Beggs and Robinson31 expressed this correlation in a mathematical form as ηs = k1(η0)k2 where k1 and k2 are predicted parameters

(5)

where rs is the effective solute ion radius and NA is the Avogadro constant. As shown by Breslau and Miller,28 this relationship can be used to represent the concentration dependence of the relative viscosity for concentrated electrolyte solutions if Vs = [4/3πrs3NA] is considered an adjustable parameter representing effective rigid molar volumes. By identifying eq 5 with the extended Jones−Dole equation (4), we can evaluate the effective solute ion radius, rs. The derived values of rs for LiX solutions are given in Table 2. We can see that the radiuses obtained for LiTFSI are smaller than for LiPF6 and LiFAP. The ion radius values obtained at 298.15 K in the concentration range 0.25−1.0 mol·L−1 for LiPF6 and LiFAP are 0.55 ± 0.01 nm for LiPF6 and LiFAP; these values are higher than the value derived by Matsuda with 0.37 nm29 or those 3976



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Table 3. CO2 Solubility in Pure Alkyl Carbonates and Their Mixtures as a Function of LiPF6 Concentration Expressed as a CO2 Mole Fraction, xCO2, at Atmospheric Pressure and 298 K 102·xCO2a

a

[LiPF6]/mol·L−1

PC

DMC

DEC

EMC

EC/DMC

EC/EMC

EC/DEC

EC/PC/3DMC

0.000 0.250 0.500 0.750 1.000

1.090 0.990 0.930 0.880 0.820

1.360 1.290 1.180 1.080 1.000

1.650 1.570

1.600 1.540 1.450

0.980 0.940 0.910 0.880 0.850

1.040 1.000 0.980

1.180 1.090

1.040 0.990 0.910 0.820 0.770

1.470 1.400

1.300

0.870

0.980 0.880

Precision and accuracy of the reported experimental data in Tables 3−5 are close to 1 and 15%, respectively.

Table 4. Experimental Values of CO2 Solubility in Selected Alkyl Carbonates and Their Mixtures as a Function of LiTFSI Concentration Expressed as a CO2 Mole Fraction, xCO2, at Atmospheric Pressure and 298 K 102·xCO2a −1

[LiTFSI]/mol·L 0.000 0.250 0.500 0.750 1.000 a

PC

DMC

EMC

DEC

EC/DMC

EC/EMC

EC/DEC

1.090 1.050 1.010 0.980

1.360 1.325 1.270 1.218 1.190

1.642 1.608 1.558 1.502 1.620

1.654 1.635 1.631 1.628 1.720

0.989 0.988 0.987 0.984 0.980

1.040 1.024 1.001 0.991 1.060

1.180 1.120 1.056 1.007 1.250

Precision and accuracy for experimental data in Tables 3−5 are close to 1 and 5%, respectively.

connected to the gas solubility xgas. k1 = a/(xgas + b)n and k2 = a′/(xgas + b′)p. The experimental carbon dioxide solubility values obtained at 298.15 K in the selected alkyl carbonates (PC, DMC, DEC, EMC) or their binary or ternary mixtures as a function of the salt concentration, expressed in mol·L−1 of LiX (X = PF6, FAP, or TFSI) are listed in Tables 3−5, where the solubility data are

LiTFSI-based electrolyte presents no trivial tendency (Table 4). As we show in our previously work,9 for this salt, a minimum CO2 solubility is observed for C close to 2 mol·L−1. However, a salting-in effect is observed for concentrations in TFSI lower than 1 mol·L−1. Several mechanisms can illustrate the salt effect on gas solubility in the electrolytes.33 In his original work, Hofmeister (1888) reported modifications of protein solubility caused by salts present in the solution, and built up the Hofmeister series (HS) by ordering various ions according to their effectiveness in this sense.34 In these studies, it is suggested that ions are strongly solvated by displacement of solvent molecules from the solvation sphere of the gas, leading to salting-out. This observation is very marked in the case of the PF6 anion, it is more nuanced with FAP and clearly lower in the case of TFSI. This hypothesis is supported by the fact that the solubility in solvent was generally driven by entropic effects; i.e., solvents that are more restructured by the addition of a salt-like PC are more affected by the addition of a salt. The contraction of the volume frequently observed by dissolution of the electrolytes in the solvent can also model the salting-out effect. The results discussed in the first section relating to the viscosity show a different behavior of the EC/DMC binary system in the case of addition of LiTFSI, explained by the size of the TFSI anion and the void volume resulting from the restructuring of solvent when LiTFSI is added. These observations may explain the different solubility of CO2 in the same system. In our study, the directed correlation between viscosities and gas solubility in these complex systems are not established; however, the logic of results of solubility can be viewed in light of the results of the first section. The effect of salt on the solubility of gases in solution is usually described by the Sechenov equation35 given by

Table 5. CO2 Solubility in Binary Mixtures as a Function of LiFAP Concentration Expressed as a CO2 Mole Fraction, xCO2, at Atmospheric Pressure and 298 K 102·xCO2a [LiFAP]/mol·L−1

EC/DMC

EC/EMC

EC/DEC

0 0.25 0.5 0.75 1

0.989 0.983 0.975 0.968 0.961

1.04 0.99 0.95 0.90 1.23

1.18 1.10 1.02 0.93 1.50

a

Precision and accuracy of the reported experimental data in Tables 3−5 are close to 1 and 8%, respectively.

reported in terms of their CO2 mole fractions. It can be observed that CO2 is more soluble in linear carbonates (EMC, DEC) than in cyclic carbonates (PC) (ΔxCO2 = 60%), such as already described by our group12 and others.7,32 This difference is less obvious (ΔxCO2 = 16%) when both are alkyl carbonate binary mixtures. Table 4 and Figure 4 show that the values of CO2 solubility in PC are in excellent agreement with the data published by Blanchard et al.11 We can also observe that the addition of a salt always reduces the solubility of CO2 (saltingout). This effect is more significant for LiPF6. As shown for LiPF6 and LiFAP (Tables 3 and 5), the CO2 solubility versus salt concentration C decreases linearly, indicating a salting-out effect independent of the salt concentration in solution for LiPF6. Comparatively, the

⎛ x* ⎞ log10⎜ i ⎟ = k SC ⎝ xi ⎠ 3977

(6)



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Figure 4. Sechenov plot of log10[(x*CO2 /xCO2)] in pure alkyl carbonate solutions as a function of the LiPF6 (a) and LiTFSI (b) lithium salt concentration at 298 K.

Figure 5. Sechenov plot of log10[(x*CO2 /xCO2)] in a binary mixture of alkyl carbonate solutions as a function of the concentration of LiPF6 (a), LiTFSI (b), and LiFAP (c) lithium salts at 298 K. Comparative Sechenov plot of litium salt in an EC/DMC binary mixture (d).

ion parameter Hi and ionic strength Ii, for each individual ion is summed:

where xi is the solubility expressed as the molar fraction of the gas in the salt solution, x*i is the solubility in the pure solvent, kS is Setchenov’s constant, and C is the salt concentration. Several concepts have been developed to describe the salting-out effect of gas in the presence of other dissociated complexes or without solute. The Schumpe model36 gives the most admitted approach based on the additivity of the solubility expressed by the ratio of gas in a pure solvent and in the salt solution in logarithmic scale according to composition. In this model, the individual contribution of single ions to the overall effect of the salt can be described by eq 7 in which the product of a specific

⎛ x* ⎞ log10⎜ i ⎟ = ⎝ xi ⎠

∑ HiIi i

(7)

Several parameters can affect the specific ion parameter Hi, such as the gas or solvent nature and the temperature. Hi, can be obtained directly from the experimentally determined Setchenov coefficients, kS, for the single electrolytes at fixed 3978



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Table 6. Setchenov Constants, ksc, and Ion-Specific Constants of Anion H(X) for the Salting-Out of CO2 in an Alkyl Carbonate or Its Mixtures with a Lithium Salt LiX (X = PF6, TFSI, and FAP) at Atmospheric Pressure and 298 Ka

a

electrolytes

ksc(LiPF6)

PC DMC DEC EMC EC/DMC EC/EMC EC/DEC EC/PC/3DMC

0.127 0.131 0.070 0.088 0.125 0.072 0.121 0.129

ksc(LiFAP)

ksc(LiTFSI)

H(PF6)

0.137 0.083 0.013

0.063 0.060 0.053 0.006 0.003 0.029 0.093

0.254 0.262 0.141 0.176 0.251 0.144 0.242 0.258

H(FAP)

H(TFSI)

0.274 0.165 0.025

0.126 0.119 0.107 0.013 0.007 0.059 0.186

Precision and accuracy for ksc are close to 1 and 8%, respectively.

temperature.36 Li+ is arbitrarily chosen as a reference ion as zero, e.g., HLi+ = 0. For completely dissociated strong electrolytes, the ionic strength is expressed by Ii =

1 1 C iz i 2 = C iνiz i 2 2 2

solvent with LiPF6 and LiTFSI and show a linearity over a wide concentration range for all of the solvents studied. The slope from the experimental points represented by the best linear fit for dilute solution (C → 0) provided Setchenov’s coefficient, kS, noted in Table 4. From these values and unknown Hi for Li+ (HLi+ = 0), all other ion-specific constants Hi can be calculated from eq 9 of either anion. These data are given in Table 6. The type of salting effect can be inverted with a change in the gas partial pressure, and this inversion cannot be described by the Sechenov equation. Last but not least, due to its empirical character, the Sechenov equation cannot predict whether a salt will increase the solubility (salting-in) or will decrease it (salting-out).

(8)

where C is the concentration of salt and νizi, respectively, for the individual ion. The relationship between the specific ion parameters, Hi, and the specific coefficient kS can be then obtained by combining eq 6 into eq 8: kS =

1 2

∑ Hiνiz i 2 i

(9)

As shown by Lang,37 Hi can be obtained experimentally from the Setchenov coefficients of either a cation or an anion. Depending on the sign of kS, the solubility of the gas can be either decreased (salting-out), for a positive kS, or increased (salting-in), for a negative kS. The Setchenov’s constants can be interpreted in terms of entropic change induced by the CO2 solubility according to the nature of the anion. The aim is to answer the question, “What is the correct solubility behavior due to ions in solvents that is not subject to linearity constraints?” The applicability of theses approach is based on the correlation between the Setschenov coefficient of a salt and changes in the volume of the solution. Furthermore, salt affects the solubility according to the charge densities of their ions. Those with high charge densities caused a salting-out effect (positive kS) and they tend to reduce the nonpolar gas solubility in a solvent; comparatively, ions having low charge densities induce an increase in the solubility of nonpolar gases and, as a consequence, a salting-in effect (negative kS). Although these theories can predict the efficacy of ions as salting-out agents, they fail to predict the salt-induced variation of the gas solubility, as well as the key governing the particular salt effect on different nonpolar molecules. Ions may play a major role in favoring or disfavoring the polarizing power of solvent molecules by orienting them toward the electrolyte solute (salting-in and salting-out, respectively), according to the ionic charge density. A determinant parameter here is the individual dipole moment for a solvent molecule in solution, which is not defined if the interactions consist of multiple interactions, as such. In the case of (lithium salt/alkyl carbonate) solutions, solvation and dipolar ordering are coupled. The plots, i.e., log10(x*i /xi) vs concentration, C, representing low Setchenov are presented in Figures 4 and 5 for a pure

4. CONCLUSION In this paper, the viscosities and CO2 solubility in an alkyl carbonate solvent in mixtures with a lithium salt LiX (X = LiPF6, LiTFSI, or LiFAP) have been measured as a function of the salt concentration and temperature. A series of calculated microscopic properties were deducted from the processing of experimental data by the extended Jones−Dole or Setchenov theories. This study showed that the CO2 solubility has been influenced by several aspects of the solvent and added lithium salt: • The shape, charge density, and size of the ions, which influence the structuring of the solvents through the addition of a salt and the type of solvation of the ions, such as visualized by the processing of viscosity measurements. A singular behavior of viscosity variation in the case of LiTFSI addition to binary system EC/ DMC, explained by the size of the TFSI anion and the void volume resulting from the restructuring of solvent may explain the particular solubility of CO2 in the same system. • Specific ion parameters Hi for CO2 solubility at 298.15 K, determined with the Setchenov coefficient, kS. These values can be used to predict the salt effect in the presence of generated gases for energy storage application. The aim is to specifically evaluate the harmful effect of gas generation on the long-time cycling of lithium ion batteries. With this study, it is possible to conclude that the nature of anions of salt in the electrolyte formulation, in relation to their volumetric or electronic properties, significantly determine the viscosity and CO2 solubility. 3979



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AUTHOR INFORMATION

Corresponding Author

*M. Anouti: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support for this work was provided by the SAFT France Company and “Conseil régional of région centre”. REFERENCES

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