Solid-liquid equilibria and thermo-physical properties of liquid electrolyte systems for lithium ion batteries

Fluid Phase Equilibria 473 (2018) 138e144

Contents lists available at ScienceDirect

Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Solid-liquid equilibria and thermo-physical properties of liquid electrolyte systems for lithium ion batteries Ha Young Oh, Ji-Eun Gu, So-Jin Park* Department of Chemical Engineering, College of Engineering, Chungnam National University, Daejeon, 305-764, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 February 2018 Received in revised form 24 May 2018 Accepted 31 May 2018 Available online 18 June 2018

Alkyl carbonate and g-butyrolactone (GBL) are attractive organic electrolyte materials that are stable over a wide range of operating voltages and ethylene sulfite (ES) is used as a supplementary film-forming electrolyte additive for lithium ion batteries (LIBs). This paper reports the solid-liquid phase equilibrium (SLE) data and the thermo-physical mixture properties such as the density, refractive index, excess and deviation properties for organic liquid electrolyte solutions of carbonate-based or GBL electrolytes containing ES. The SLE data were correlated with two activity coefficient models: NRTL and UNIQUAC. In addition, the extent to which the excess volume (V E Þ and molar refraction deviation (DR) of each of the binary systems correlated with the values calculated using the Redlich-Kister polynomial equations was determined. © 2018 Elsevier B.V. All rights reserved.

Keywords: Solid-liquid phase equilibrium Excess property Electrolyte Carbonate g-butyrolactone

1. Introduction The high electropositivity of lithium and the fact that it is the lightest metal among the solid elements have, together with its high energy density and high specific current capacity, led to the consideration of several combinations of organic solvents and lithium salts as the most promising liquid electrolyte materials for rechargeable batteries. Consequently, research and development of lithium ion batteries (LIBs), which have found use in various applications such as a power source for electric vehicles and as storage medium for electric energy generated by solar and wind sources, has been underway all over the world [1,2]. Research pertaining to LIBs focuses on the three basic components of these batteries: the anode, cathode, and electrolyte. In reality, even though in LIBs the electrodes are responsible for energy storage, the electrodes function in collaboration with a liquid or solid electrolyte capable of conducting lithium. Additionally, the electrolyte (or combination of electrolyte materials) largely contributes to characterizing LIBs in terms of their specific power, safety, life time, and performance at both low and high temperatures [3e6]. Therefore, the subsequent intensification of research into electrolytes and their additives, as one of the core elements of LIB technology, has been a major driving

* Corresponding author. E-mail address: [email protected] (S.-J. Park). https://doi.org/10.1016/j.fluid.2018.05.033 0378-3812/© 2018 Elsevier B.V. All rights reserved.

force behind the technological progress of LIBs [7]. A liquid electrolyte generally consists of a lithium salt, such as LiPF6 or LiN(CF3SO2)2 combined with linear and alkyl carbonates, because several lithium salts are highly soluble in these carbonates and the resulting conductivities are adequate for batteries. In addition, small amounts of other components, known as electrolyte additives, are incorporated in the electrolyte to improve its properties. For instance, ethylene sulfite (ES) or vinyl ethylene sulfite (VES), a film-forming electrolyte additive, are included in electrolyte formulations to increase the dielectric strength and enhance the electrode stability by facilitating the formation of a solid electrolyte interface (SEI) layer [8e10]. The selection of solvents for use in electrolyte formulations is therefore crucial to enhance the performance of LIBs. In practice, these solvent mixtures mainly contain ethylene carbonate (EC) or propylene carbonate (PC), which are used in combination with at least one of the following organic carbonates as co-solvents: dimethyl carbonate (DMC), diethyl carbonate (DEC), ethyl methyl carbonate (EMC), etc. The permittivity of these electrolyte mixtures is sufficiently high to allow lithium salts to dissociate in the mixture; furthermore, the low melting point of these electrolytes make them suitable for low-temperature applications. Apart from the aforementioned linear carbonates, g-butyrolactone (GBL) is another preferred electrolyte solvent for LIBs because of its similar electrochemical performance. However, its boiling point is much higher compared to that of linear carbonates such as DMC, DEC, and EMC and it would therefore be expected to enhance battery safety.

H.Y. Oh et al. / Fluid Phase Equilibria 473 (2018) 138e144

139

customized self-built triple-glass jacketed still, which enables the melting or freezing process of a solid sample to be visually observed. The outermost exterior glass column of the glass jacket was maintained under vacuum to prevent moisture from freezing on the surface. The cooling/heating media were circulated through the center jacket of the glass still. The innermost equilibrium cell was not only heated or cooled but also insulated from the environment via the circulated cooling/heating media. The equilibrium cell was purged with nitrogen gas for dehumidification [19,20]. First, the mole fraction of each of the binary samples was gravimetrically determined using an A&D microbalance (HA202, Japan) with an accuracy of ±1  105 g. The standard uncertainty of the determined mole fraction was estimated to be less than ±1  104. The SLE point for the given composition was determined visually at the moment at which the last crystal of the mixture disappeared. The temperature at this SLE point was measured with a platinum resistance thermometer and a digital temperature readout box (ASL F250, UK). The standard uncertainty of the SLE temperature measurement was considered to be less than ±0.02 K. The values of V E and DR were calculated from the directly measured densities and refractive indices, respectively. The r of the pure components and those in mixtures were measured using a vibrating U-tube densitometer (Anton Paar model DMA 5000) under atmospheric pressure. This U-tube densitometer was calibrated using standard bi-distilled water and dried air before every measurement. According to the manufacturer's specification, the accuracy of r is ±5  106 g cm3 between 0 and 3 g cm3 and that of the temperature is ±0.01 K. The sample mixtures were prepared in narrow-mouth stoppered glass vials using a microbalance with a precision of ±1  105 g. The high-boiling-point component was first added to the vial to minimize evaporation losses. The experimental procedure was described in detail elsewhere [21]. The experimental systematic error in the r and mass measurements was estimated to be less than 1  105 g cm3 and 1  104 in the mole fraction, respectively. The nD was determined using a digital precision refractometer (KEM, model RA-520 N, Kyoto, Japan). The manufacturer stated the accuracy of the refractometer to be ±5  105 and ±1  104 in the ranges of 1.32e1.40 and 1.40e1.58 of refractive index values, respectively, and the accuracy of the temperature is ±5  102 K. The experimental procedure was described in detail elsewhere [22]. The values of DR were obtained from the measured nD data. The reproducibility of the measurement was checked with bidistilled water and the standard uncertainty (u) was estimated as uðnD Þ ¼ 1:5  104 g,cm4 ; uðTÞ ¼ 0:05K.

Many studies have used theoretical or empirical approaches to examine the properties of different electrolyte solutions. The results of these studies laid the foundation for subsequent advances in equilibrium and solution thermodynamics. Determining the dependence of the phase equilibrium and properties of solutions on the composition and temperature of these solutions remains an ongoing challenge for researchers in the chemical and physical sciences. This is because knowledge of these properties is of great importance to study the separation and interaction between the components of solutions [11]. Therefore, a good understanding of the phase equilibrium and thermodynamic properties of electrolyte mixtures for LIBs remains of interest and is helpful toward their utilization as electrolytes. In the present work, we determined the solid-liquid equilibrium (SLE) density (r), refractive index (nD ), excess volume (V E ), and molar refraction deviation (DR) at atmospheric pressure and different temperatures for the binary systems: DMC þ ES, EC þ ES, EMC þ ES, GBL þ ES. To the best of our knowledge, the experimental SLE and thermo-physical properties of the systems considered in this work have not yet been reported. The determined SLE data were correlated with the data calculated by the activity coefficient models NRTL [12] and UNIQUAC [13]. In addition, the calculated excess and deviation properties were modeled by known polynomial equations, namely the Redlich-Kister equations for binary fractions [14]. 2. Experiment 2.1. Materials DMC and EMC were purchased from Sigma Aldrich (USA, >99%) and GBL was provided by Junsei (Japan, >99%), whereas EC and ES were supplied by Acros Organics (USA, EC: >99%, ES: >98%). All of these chemicals were dried with 0.3 nm molecular sieves and used without any further purification. Subsequently these chemical compounds were analyzed by gas chromatography (GC) and their final purities were determined to exceed 99.9 mass %. The water contents of the chemicals were also checked using Karl-Fischer titrator (Metrohm 684 KF-Coulometer) and were found to be less than 5  105 g g1. The physical measurements of the chemicals are provided in Table 1 where they are compared with the values reported in the literature [15e18]. 2.2. Apparatus and procedure The SLE determination was carried out using a cryostat and a

Table 1 Purity and physical properties of the chemicals at P ¼ 101.3 kPa. Chemical

Water content (ppm)

CAS-No.

GC analysis (wt. %)

r /g cm3 at 298.15 K

nD at 298.15 K

Exp.

Ref.

Exp.

Ref.

dimethyl carbonate ethyl methyl carbonate ethylene carbonatea ethylene sulfiteb g-butyrolactonec

47.0 41.0 13.0 7.0 43.0

616-38-6 623-53-0 96-49-1 3741-38-6 96-48-0

>99.9 >99.9 >99.9 >99.9 >99.9

1.06087 1.00688 1.31570d 1.43217 1.12497

1.06328e e 1.32199f 1.4158g 1.12454h

1.3662 1.3754 1.4172d 1.4449 1.4349

1.3671e e e e 1.4350h

Standard uncertainties u are uðrÞ ¼ 6  105 g,cm3 ; uðTÞ ¼ 0:01 K. Standard uncertainties u are uðnD Þ ¼ 1:5  104 g,cm4 ; uðTÞ ¼ 0:05 K. a IUPAC name: 1,3-dioxolan-2-one. b IUPAC name: 1,3,2-Dioxathiolane 2-oxide. c IUPAC name: Oxolan-2-one. d At 318.15 K. e Ref [15]. f Ref [16]. g Ref [17]. h Ref [18].

140

H.Y. Oh et al. / Fluid Phase Equilibria 473 (2018) 138e144

3. Results and discussion Solid-liquid equilibria for eutectic systems can be calculated by knowledge of the real behavior in the liquid phase and the pure component properties using Eq. (1)

xi ¼

1

"

( exp

gi

DHfus



R

1 1  Tmi T

 þ

DH trs



R

1 1  Ttrs T

)#

(1) If a solid-solid phase transition (like as one crystal phase can transform into another under the same condition) does not occur, enthalpy of transition of the last term in Eq. (1) can be neglected and simplified to Eq. (2) as follows [23]:

xi ¼

1

"

gi

( exp

DHfus R



1 1  Tmi T

)# (2)

where xi , gi is the liquid phase mole fraction and the activity coefficient, respectively, DH fus is the molar enthalpy of fusion, Tmi is the melting temperature, T is the absolute temperature, and R is the universal gas constant. The experimental SLE data for the binary systems DMC þ ES, EMC þ ES, EC þ ES, and GBL þ ES are listed and plotted in Table 2 and Figs. 1e4, respectively. As illustrated in Figs. 1e3, all the systems in this work showed a single eutectic point. These SLE data were regressed using models with a common activity coefficient: NRTL and the UNIQUAC equation. The solid lines represent the data calculated by using each of these two model equations. These common equations regressed the experimental SLE data well within 0.7 K of the RMSD temperature for all the systems that were considered. The regression values obtained

Fig. 1. SLE diagram for the binary system of DMC (1) þ ES (2)(C); solid curve was calculated from NRTL and UNIQUAC model.

with the NRTL model were slightly more accurate than those computed with the UNIQUAC model. The NRTL and UNIQUAC model parameters are listed in Table 3, along with the root-meansquare deviation (RMSD) between the experimental and calculated data. The RMSD was determined according to Eq. (3) [24].

2

 31=2 P P P  a ðexpÞ a ðcalÞ 2 x  x i a k ik ik 6 7 RMSD ¼ 4 5 6N

(3)

Table 2 SLE data of the binary systems for DMC, EMC, EC and GBL þ ES at P ¼ 101.3 kPa. Systems

x1

T/Ka

x1

T/Ka

(2)

dimethyl carbonate (1) þ ethylene sulfite (2)

0.0000 0.0501 0.1000 0.1997 0.3000 0.3500 0.4000

256.14 252.20(2) 249.02(2) 242.95(2) 235.78(2) 232.53(2) 237.92(1)

0.5000 0.5995 0.6987 0.7987 0.8999 0.9500 1.0000

246.47(1) 254.18(1) 261.12(1) 267.08(1) 272.39(1) 274.87(1) 277.52(1)

ethyl methyl carbonate (1) þ ethylene sulfite (2)

0.0000 0.0502 0.1000 0.1998 0.2999 0.4007 0.5000

256.14(2) 251.69(2) 248.95(2) 244.01(2) 238.48(2) 233.15(2) 227.05(2)

0.6001 0.7000 0.7300 0.7998 0.8999 0.9498 1.0000

219.49(2) 209.92(2) 210.80(1) 212.76(1) 216.73(1) 219.36(1) 221.68(1)

ethylene carbonate (1) þ ethylene sulfite (2)

0.0000 0.0503 0.1002 0.1502 0.2009 0.2402 0.2600 0.2702 0.2797

256.14(2) 251.92(2) 249.36(2) 246.60(2) 243.75(2) 241.93(2) 245.05(1) 246.36(1) 248.01(1)

0.3004 0.4000 0.4999 0.5987 0.6999 0.8000 0.9000 0.9501 1.0000

252.11(1) 264.22(1) 273.16(1) 281.73(1) 289.56(1) 296.68(1) 303.35(1) 306.46(1) 310.56(1)

g-butyrolactone (1) þ ethylene sulfite (2)

0.0000 0.0526 0.0997 0.2002 0.2962 0.4002 0.4998

256.14(2) 252.33(2) 250.04(2) 243.02(2) 236.19(2) 227.87(2) 220.05(2)

0.5987 0.6989 0.7993 0.8999 0.9496 1.0000 e

210.96(2) 215.00(1) 221.79(1) 226.15(1) 228.28(1) 231.28(1) e

Standard uncertainties u are uðxÞ ¼ 0:0005 uðTÞ ¼ 0:05K. a Solid phase component.

H.Y. Oh et al. / Fluid Phase Equilibria 473 (2018) 138e144

141

The calculated eutectic points from the NRTL parameters were x1 ¼ 0.3460/ T ¼ 232.03 K, x1 ¼ 0.7028/ T ¼ 209.61 K, x1 ¼ 0.2300/ T ¼ 240.74 K, x1 ¼ 0.6010/ T ¼ 209.42 K for the systems DMC þ ES, EMC þ ES, EC þ ES, and GBL þ ES, respectively. The determined values of VE and DR for the same binary systems are listed in Table 4 with the measured density and refractive indices for the pure and mixture components at 298.15 K. The excess volume, V E was calculated from Eq. (4) [25].

V E = cm3 ,mol1 ¼

Fig. 2. SLE diagram for the binary system of EMC (1) þ ES (2)(C); solid curve was calculated from NRTL and UNIQUAC model.

Fig. 3. SLE diagram for the binary system of EC (1) þ ES (2)(C); solid curve was calculated from NRTL and UNIQUAC model.

Fig. 4. SLE diagram for the binary system of GBL (1) þ ES (2) (C); solid curve was calculated from NRTL and UNIQUAC model.

P

i xi Mi

rm



Xxi Mi  i

ri

(4)

where ri , rm ; and Mi are the densities of the pure component and mixture, and the molar mass, respectively. The experimental VE values determined for the DMC þ ES, EC þ ES and EMC þ ES systems show negative deviation from ideal behavior as illustrated in Fig. 5 The negative values of VE could be caused by their intermolecular interaction, considering that alkyl carbonate is basically a polar molecule, which probably associates mainly through the intermolecular interactions of CH/O or O/HO [26], and that ES is a hydrogen bond acceptor. Moreover, despite the relatively high polarity of GBL (dipolar moment; 4.12 D and dielectric constant; 42 at 298.15 K), the GBL þ ES system exhibits positive V E values for the entire range of concentrations, even though their positive deviation from ideality was not large. These positive values may be discussed in terms of the different molecular sizes and/or molecular structures (linear and cyclic). Furthermore, the free volume effect caused by the geometrical and structural differences between two molecules may also partly contribute to positive V E values. The V E of the DMC þ ES, EMC þ ES, and GBL þ ES systems were determined at 298.15 K, whereas that of EC þ ES was determined at 318.15 K because the melting point of EC is approximately 310.6 K. The negativity increases in the order in which the difference in density in the mixtures increases. Namely, the negativity of deviation increases in the order of EC þ ES < DMC þ ES < EMC þ ES, even though the EC þ ES system was measured at a different temperature. The DR of all of these systems was determined at the same temperatures. As shown in Fig. 6, the DMC þ ES and GBL þ ES systems showed positive deviation across the entire ranges of concentration, whereas EMC þ ES and EC þ ES showed negative deviation. The molar refraction (R) is a measure of the total polarizability of 1 mol of substance and deviation in the refractive index is used to explain the nature of solute-solvent interactions. In terms of the properties of a mixture, DR is more informative than the deviation in the refractive index because it takes into account the electronic perturbation of molecular orbitals during the liquid mixing process. Usually, DR is dependent on the temperature, pressure, and refractive index and R is directly related to the dispersion forces. Therefore, the positive values of DR for the DMC þ ES and GBL þ ES systems indicate that the dispersion forces are higher in the mixtures than in the pure liquids whereas the negative values of the EMC þ ES and EC þ ES systems indicate the presence of interactions amongst the components of the mixture. The values of DR were calculated from Eq. (5) using the molar refractivity of the pure and mixed components and the volume fraction of the component [27].

DR= cm3 ,mol1 ¼ Rm 

X fi Ri i

(5)

142

H.Y. Oh et al. / Fluid Phase Equilibria 473 (2018) 138e144

Table 3 Activity coefficient model parameters and the RMSD between the calculated and experimental data for each binary system. Models

Systems

Aij/cal$mol1

Aji/cal$mol1

a

RMSD (K)

NRTL

dimethyl carbonate (1) þ ethylene sulfite (2) ethyl methyl carbonate (1) þ ethylene sulfite (2) ethylene carbonate (1) þ ethylene sulfite (2) g-butyrolactone (1) þ ethylene sulfite (2)

741.159 85.725 278.478 354.940

455.092 388.549 244.318 476.272

0.27 0.30 0.31 0.30

0.34 0.67 0.69 0.56

UNIQUAC

dimethyl carbonate (1) þ ethylene sulfite (2) ethyl methyl carbonate (1) þ ethylene sulfite (2) ethylene carbonate (1) þ ethylene sulfite (2) g-butyrolactone (1) þ ethylene sulfite (2)

473.064 108.265 227.990 219.589

713.235 122.049 253.394 224.929

e e e e

0.58 0.69 0.69 0.60

Table 4 Densities, excess molar volumes, refractive indices and deviations in molar refractivity for the binary systems of {DMC þ ES, EMC þ ES, GBL þ ES} at 298.15 K and {EC þ ES} at 318.15 K and P ¼ 101.3 kPa. x1

r /g cm3

VE/cm3 mol1

nD

DR/cm3 mol1

1.4407 1.4365 1.4283 1.4202 1.4123 1.4044 1.3965 1.3889 1.3811 1.3737 1.3700

0.0075 0.0125 0.0241 0.0323 0.0377 0.0379 0.0342 0.0303 0.0211 0.0139 0.0083

1.4405 1.4361 1.4279 1.4200 1.4127 1.4056 1.3991 1.3927 1.3867 1.3810 1.3782

0.0614 0.1158 0.1974 0.2535 0.2817 0.2850 0.2664 0.2283 0.1704 0.0933 0.0349

1.4358 1.4350 1.4333 1.4315 1.4297 1.4278 1.4259 1.4238 1.4217 1.4196 1.4185

0.0263 0.0466 0.0794 0.1045 0.1203 0.1245 0.1210 0.1072 0.0794 0.0447 0.0218

1.4443 1.4437 1.4425 1.4414 1.4402 1.4392 1.4382 1.4373 1.4365 1.4356 1.4353

0.0007 0.0014 0.0019 0.0022 0.0025 0.0028 0.0030 0.0029 0.0024 0.0009 0.0003

dimethyl carbonate (1) þ ethylene sulfite (2) 0.0499 0.0997 0.2002 0.2999 0.4000 0.4997 0.6004 0.6998 0.8009 0.9002 0.9505

1.41239 1.39260 1.35325 1.31496 1.27701 1.23988 1.20289 1.16691 1.13050 1.09566 1.07806

0.0496 0.0857 0.1519 0.2085 0.2445 0.2671 0.2695 0.2486 0.1781 0.1140 0.0586

ethyl methyl carbonate (1) þ ethylene sulfite (2) 0.0498 0.0994 0.1993 0.2998 0.3996 0.5008 0.5995 0.7001 0.8002 0.8995 0.9501

1.40465 1.37800 1.32676 1.27843 1.23317 1.18988 1.14994 1.11121 1.07473 1.04017 1.02308

0.0532 0.0961 0.1660 0.2268 0.2663 0.2881 0.2901 0.2559 0.2073 0.1183 0.0484

Fig. 5. (VE cm3$mol-1) for the binary systems at 298.15 K; C, DMC (1) þ ES (2); , EMC (1) þ ES (2); GBL (1) þ ES (2); and at 318.15 K; , EC (1) þ ES (2); solid curves were calculated using the Redlich-Kister equation.

ethylene carbonate (1) þ ethylene sulfite (2) 0.0492 0.0998 0.2011 0.3000 0.4024 0.5005 0.5994 0.6997 0.8005 0.8996 0.9494

1.40348 1.39966 1.39176 1.38361 1.37481 1.36604 1.35686 1.34714 1.33700 1.32662 1.32121

0.0306 0.0453 0.0700 0.0820 0.0878 0.0879 0.0828 0.0701 0.0523 0.0290 0.0127

g-butyrolactone (1) þ ethylene sulfite (2) 0.0501 0.1008 0.2006 0.2991 0.4102 0.4994 0.5998 0.7010 0.7995 0.9002 0.9495

1.41736 1.40119 1.36954 1.33859 1.30397 1.27638 1.24554 1.21473 1.18491 1.15470 1.13997

0.0252 0.0424 0.0738 0.0949 0.1088 0.1143 0.1124 0.0982 0.0778 0.0429 0.0240

Standard uncertainties u are uðxÞ ¼ 0:0005, uðrÞ ¼ 6  105 g,cm3 .uðnD Þ ¼ 1:5  104 g,cm4 .

Fig. 6. DR (cm3$mol-1) for the binary systems at 298.15 K;C, DMC (1) þ ES (2); , EMC (1) þES (2); , GBL (1) þ ES (2)and at 318.15 K; , EC (1) þ ES (2); solid curves were calculated using the Redlich-Kister equation.

" Rm ¼

n2D  1 n2D þ 2

#P

i xi Mi

rm

 (6)

H.Y. Oh et al. / Fluid Phase Equilibria 473 (2018) 138e144

143

Table 5 Redlich-Kister parameters and standard deviations of V E and DR for the binary systems of DMC þ ES, EMC þ ES at 298.15 K and EC þ ES at 318.15 K. A1 VE

A2

dimethyl carbonate (1) þ ethylene sulfite (2) 1.0790 0.2368 ethyl methyl carbonate (1) þ ethylene sulfite (2) 1.1551 0.2511 ethylene carbonate (1) þ ethylene sulfite (2) 0.3525 0.0410 g-butyrolactone (1) þ ethylene sulfite (2) 0.4564 0.0363

DR

dimethyl carbonate (1) þ ethylene sulfite (2) 0.1526 0.0282 ethyl methyl carbonate (1) þ ethylene sulfite (2) 1.1363 0.1228 ethylene carbonate (1) þ ethylene sulfite (2) 0.5008 0.0269 g-butyrolactone (1) þ ethylene sulfite (2) 0.0109 0.0070

" Ri ¼

n2D;i  1

#  Mi

ri

n2D;i þ 2

xV fi ¼ P i i j xj V j

A3

A4

A5

sst/cm3 mol1

0.1365

0.1359

0.2528

0.0056

0.0138

0.2152

e

0.0053

0.0477

0.1494

0.0864

0.0017

0.0403

0.0527

e

0.0010

0.0503

0.0521

0.0708

0.0008

0.1368

0.1090

0.2407

0.0043

0.0019

0.0771

e

0.0010

0.0122

0.0145

0.0149

0.0001

EC þ ES, and GBL þ ES, respectively.

(7)

(8)

where Rm , Ri , fi , nD , nD;i , and Vi represent the molar refractivity of the mixture and pure component i, the volume fraction of pure component i in the mixture, the refractive index of the mixture and pure component i, and the molar volume of pure component i, respectively. The determined VE and DR values were regressed with the following Redlich-Kister polynomial.

V E ; DR ¼ x1 x2

n X

Ai ðx1  x2 Þi1

(9)

i¼1

where x is the mole fraction, Ai is the fitted Redlich-Kister parameter, and n signifies the number of fitted parameters. The Akaike Information Criteria (AIC) [28], which was used to optimize the number of Redlich-Kister parameters, is as follows:

AIC ¼ N ln SR þ 2n

(10)

where N denotes the number of data points, SR is the sum of squares of the residuals, and n is the number of parameters. We only considered fewer than seven parameters to allow for convenient application in the engineering field and decided the number of parameters that produced the smallest AIC value. The fitted parameters and their corresponding standard deviations of the fit, sst , are listed in Table 5. The sst is defined as:

sst ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi uP  u N X calc  X exp 2 t i i i ðN  nÞ exp

(11)

where Xicalc and Xi are the calculated and experimental values of component i, respectively, N is the number of experimental points, and n is the number of model parameters. The mean deviations of the V E values were 0.0056, 0.0053, 0.0017, and 0.0010 cm3 ,mol1 for the DMC þ ES, EMC þ ES, EC þ ES, and GBL þ ES mixtures, respectively. On the other hand, DR is 0.0008, 0.0054, 0.0013, and 0.0001 cm3 ,mol1 for the same systems DMC þ ES, EMC þ ES,

4. Conclusions The SLEs for the respective mixtures DMC þ ES, EMC þ ES, EC þ ES, and GBL þ ES exhibit a single eutectic point. The eutectic points regressed by the least-squares method are x1 ¼ 0.3460/ T ¼ 232.03 K, x1 ¼ 0.7028/ T ¼ 209.61 K, x1 ¼ 0.2300/ T ¼ 240.74 K, x1 ¼ 0.6010/ T ¼ 209.42 K for the systems DMC þ ES, EMC þ ES, EC þ ES, and GBL þ ES, respectively. They are in good agreement with the values obtained with the common g E models, NRTL and UNIQUAC, within 0.7 K of RMSD. The values of V E for the same binaries were found to be negative for the entire composition ranges except for the GBL þ ES system. The negative V E values were considered to be caused by intermolecular interaction between the polar alkyl carbonate and associated molecules and ES, which is a hydrogen bond acceptor. The positive deviation of the GBL þ ES system could be discussed in terms of different molecular sizes and/or different molecular structures (linear and cyclic). The negativity of V E for the systems containing alkyl carbonate increases in the order in which the density difference among the mixtures increases; namely, the negative deviation increases in the order of EC þ ES < DMC þ ES < EMC þ ES. The values of DR for the DMC þ ES and GBL þ ES systems were positive, contrary to those of the other systems. The negativity and positivity of DR can be understood in terms of the difference in the dispersion forces between the pure and mixture components; therefore, the dispersion forces of the mixtures DMC þ ES and GBL þ ES are higher than those of the respective pure components. The experimental values of V E and DR were regressed very well with the Redlich-Kister polynomials within 0.006 cm3 ,mol1 . References [1] L. Xing, W. Li, C. Wang, F. Gu, M. Xu, C. Tan, J. Yi, J. Phys. Chem. B 113 (2009) 16596e16602. [2] H. Zhao, S.J. Park, F. Shi, Y. Fu, V. Battaglia, P.N. Ross Jr., G. Liu, J. Electrochem. Soc. 161 (2014) A194eA200. [3] S. Menne, J. Pires, M. Anouti, A. Balducci, Electrochem. Commun. 31 (2013) 39e41. [4] D. Belov, D.T. Shieh, J. Solid State Electrochem. 16 (2012) 603e615. [5] P. Ping, Q. Wang, D. Kong, C. Zhang, J. Sun, C. Chen, J. Electroanal. Chem. 731 (2014) 119e127. [6] S.C. Kinoshita, M. Kotato, Y. Sakata, M. Ue, Y. Watanabe, H. Morimoto, S.I. Tobishima, J. Power Sources 183 (2008) 755e760. [7] A. Balducci, S.S. Jeonga, G.T. Kima, S. Passerini, M. Winter, M. Schmuck, G.B. Appetecchi, R. Marcilla, D. Mecerreyes, V. Barsukove, V. Khomenkoe, I. Cantero, I. De Meatza, M. Holzapfel, N. Tran, J. Power Sources 196 (2011) 9719e9730.

144

H.Y. Oh et al. / Fluid Phase Equilibria 473 (2018) 138e144

[8] A. Li, P. Du, Z. Chen, R. Zhao, W. Huang, L. Zou, D. Huang, H. Chen, Ionics 21 (2015) 2431e2438. [9] W. Yao, Z. Zhang, J. Gao, L. Li, J. Xu, Z. Wang, Y. Yang, Energy Environ. Sci. 2 (2009) 1102e1108. [10] L. Xing, W. Li, M. Ku, T. Li, L. Zhou, J. Power Sources 196 (2011) 7044e7047. [11] R.K. Shukla, A. Kumar, U. Srivastava, K. Srivastava, V.S. Gangwar, Arab. J. Chem. 9 (2016) S1357eS1367. [12] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135e144. [13] D. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116e128. [14] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345e348. [15] F. Comelli, R. Francesconi, J. Chem. Eng. Data 39 (1994) 560e564. [16] R. Naejus, D. Lemordant, R. Coudert, J. Chem. Thermodyn. 29 (1997) 1503e1515. [17] P.G. Sears, W.C. O'Brien, J. Chem. Eng. Data 13 (1968).

[18] T. Mathuni, J.I. Kim, S.J. Park, J. Chem. Eng. Data 56 (2011) 89e96. [19] S.H. Shin, I.Y. Jeong, Y.S. Jeong, S.J. Park, Fluid Phase Equil. 376 (2014) 105e110. [20] S.H. You, I.Y. Jeong, I.C. Hwang, S.J. Park, Fluid Phase Equil. 383 (2014) 21e26. [21] S.J. Park, R.H. Kwon, Y.Y. Choi, Fluid Phase Equil. 361 (2014) 130e134. [22] I.Y. Jeong, R.H. Kwon, S.J. Park, Y.Y. Choi, J. Chem. Eng. Data 59 (2014) 289e294. [23] A. Jakob, R. Joh, C. Rose, J. Gmehling, Fluid Phase Equil. 113 (1995) 117e126. [24] K.H. Lee, S.H. You, S.J. Park, Kor. J. Chem. Eng. 33 (2016) 2982e2989. [25] T.M. Aminabhavi, B. Gopalakrishna, J. Chem. Eng. Data 40 (1995) 856e861. [26] Y. Wang, P.B. Balbuena, J. Phys. Chem. A 105 (2001) 9972e9982. [27] K.H. Lee, S.J. Park, Y.Y. Choi, Kor. J. Chem. Eng. 34 (2017) 214e224. [28] H. Akaike, IEEE Trans. Automat. Contr. 19 (1974) 716e723.