Measurement and Correlation of the Electrical Conductivity of the Ionic

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Measurement and Correlation of the Electrical Conductivity of the Ionic Liquid [BMIM][TFSI] in Binary Organic Solvents Yanli Fu, Xianbao Cui,* Ying Zhang, Tianyang Feng, Jie He, Xuemei Zhang, Xue Bai, and Qinglong Cheng State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China S Supporting Information *

ABSTRACT: In this paper, the electrical conductivities of ionic liquid 1butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([BMIM][TFSI]) in mixed organic solvents of propylene carbonate (PC) + γbutyrolactone (GBL) and ethylene carbonate (EC) + dimethyl carbonate (DMC) were measured. The effects of mixed organic solvents with different ratios (1:0, 2:1, 1:1, 1:2, 0:1) on the electrical conductivity of ionic liquid were investigated. The organic solvents EC and DMC have a synergistic effect for the electrical conductivity of [BMIM][TFSI]−EC/DMC, and the optimal ratio of EC to DMC is 1:1; however, the organic solvents have no synergistic effect in [BMIM][TFSI]−PC/GBL. The concentration dependence of the electrical conductivity of the solution can be well fitted by the empirical Casteel−Amis equation. The effects of temperature on electrical conductivity can be described by the Vogel−Tamman−Fulcher (VTF) equation and the Arrhenius equation. The IL concentration dependence of the activation energy Ea and the pre-exponential factor A in the Arrhenius equation were also investigated, and fitted by empirical equations. On the basis of the VTF equation and the Arrhenius equation, a quasi-Arrhenius equation was proposed to describe the effects of temperature and composition on the electrical conductivity simultaneously in binary systems and ternary systems, and the correlation results agree well with the experimental results. conductivity of the mixture. Monti et al.15 measured the conductivity of 0.8 M NaTFSI in the mixtures of EC−PC and [BMIM][TFSI]−EC/PC; they found the conductivity can be slightly improved by adding 10−20% IL in the mixture. In addition, Taggougui et al.22 determined the conductivity of the mixed electrolyte hexyltrimethylammonium bis(trifluoromethylsulfonyl) imide ([N1116][NTf2])−EC/DEC [EC:DEC = 40%:60% (v/v)] in the presence of 1 M LiNTf2 as lithium salt and pointed out the conductivity increases as the volume fraction of IL decreases. The electrical conductivities of binary IL−organic solvent systems and multicomponent IL−organic solvent systems are primarily influenced by temperature and IL concentration. The relationship between the IL mole fraction and electrical conductivity can be described by the empirical Casteel−Amis equation.23−25 Besides, the Vogel−Tamman−Fulcher (VTF)26 and Arrhenius equations27 are usually applied to correlate the temperature dependence of electrical conductivity, and the VTF equation has a higher precision in a wide temperature range.28,29 Up to now, models to simultaneously describe the effects of temperature and IL concentration on electrical

1. INTRODUCTION Ionic liquids (ILs) are organic salts with low melting points (below 373 K), and most of the ionic liquids are in the liquid state at room temperature, so-called room temperature ionic liquids (RTILs).1,2 ILs have the properties of high electrical conductivity, nonflammable, negligible volatility, good thermal and electrochemical stability, wide electrochemical window, etc.,2−4 so they are good potential electrolytes in electrochemical processes, such as lithium batteries and super capacitors.5−12 Ionic liquid is usually mixed with organic solvents to reduce viscosity and improve electrical conductivity.13−19 For example, Rilo et al.16 dissolved 1-alkyl-3-methyl imidazolium tetrafluoroborate ([CnMIM][BF4], n = 2, 4, 6, 8) in ethanol and found the electrical conductivity of the solution was significantly improved compared to the pure IL. Zarrougui et al.20 measured the electrical conductivity of N-butyl-N-methylpyrrolidinium bis(trifluoro-methanesulfonyl) imide ([Pyr14][TFSI]) + methanol mixture, and they found there was a maximum value of electrical conductivity for the solution. Similarly, dissolved ionic liquid in mixed organic solvents can also improve the performance of the electrolyte. Guerfi et al.21 improved the safety and electrochemical performance of the electrolyte of EC−DEC−1 M LiPF6 by adding 1-ethyl-3-methylimidazolium bis(fluorsulfonyl)imide ([EMIM][TFSI]) and studied the ionic © XXXX American Chemical Society

Received: July 14, 2017 Accepted: March 20, 2018

A

DOI: 10.1021/acs.jced.7b00646 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Materials Description

a

materials

CAS

source

1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide propylene carbonate

174899-83-3 108-32-7

γ-butyrolactone

96-48-0

dimethyl carbonate

616-38-6

ethylene carbonate

96-49-1

Lanzhou Aolike Chemical Co. Ltd. Tianjin Guangfu Fine Chemical Institute Tianjin Guangfu Fine Chemical Institute Tianjin Guangfu Fine Chemical Institute Shanghai Macklin Biochemical Co., Ltd.

purity (mass fraction)

analysis method

>0.99 ≥0.99

GC,a KFb GC, KF

≥0.99

GC, KF

≥0.99

GC, KF

>0.99

LC,c KF

GC = Gas chromatography. bKF = Karl Fischer titration. cLC = Liquid chromatography.

carbonate (PC), γ-butyrolactone (GBL), dimethyl carbonate (DMC), and ethylene carbonate (EC) were analyzed by a gas chromatograph (Beifen Ruili SP-1000). The purity and source for all chemicals are listed in Table 1. Organic solvents were dried over 4 Å molecular sieves at room temperature (EC at 318.15 K) for 48 h, and their water contents were less than 200 ppm analyzed by Karl Fisher titration. The electrolytes were prepared by adding [BMIM][TFSI] to the organic mixtures of PC + GBL (PC:GBL = 1:0; 2:1; 1:1; 1:2; 0:1; mole ratio) and EC + DMC (EC:DMC = 1:0; 2:1; 1:1; 1:2; 0:1; mole ratio), respectively. Each component in the electrolytes was weighed by electronic balance (AL204, METTLER-TOLEDO), with an accuracy of ±1 × 10−4 g, and the minimal weight of the taken components was 0.1708 g. The electrical conductivities for [BMIM][TFSI]−PC/GBL mixtures were measured at temperature ranges from 293.15 to 353.15 K, and the electrical conductivities of [BMIM][TFSI]−EC/DMC mixtures were measured from 293.15 to 333.15 K. Each measurement was repeated five times, and then, average values were calculated. The electrical conductivity measurements were carried out by a digital conductivity meter (FE30, METTLER-TOLEDO) at a constant AC frequency of 50 Hz with the conductivity electrode (InLab710, METTLERTOLEDO). The cell constant was calibrated by 0.01 M KCl standard solution before each measurement. Temperature was controlled by a water thermostat (SYC-1015D, Gongyi city yuhua instrument Co., Ltd. China) with an accuracy of ±0.01 K. The relative standard uncertainty of electrical conductivity was 0.005.

conductivity have been rare. Lin et al.30−32 proposed a sixparameter empirical equation to correlate the relationship between conductivity and temperature and composition in IL aqueous solutions, while the correlated equations were simply established by fitting the electrical conductivity data with polynomials. Xu et al.28 proposed a four-parameter quasiArrhenius equation, which can only be well used in binary systems. Hence, for IL contained multicomponent systems, accurate models with improved theoretical basis need to be explored. The ionic liquid 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([BMIM][TFSI]) has a relatively wide electrochemical window and high conductivity at room temperature,33 and the anion TFSI− has a highly delocalized charge distribution and plasticizing effect.34,35 The organic solvents propylene carbonate (PC) and ethylene carbonate (EC) have a high dielectric constant, and dimethyl carbonate (DMC) has a low viscosity. The dielectric constant and viscosity of γ-butyrolactone (GBL) are in medium level. All of these organic solvents are commonly used in lithium-ion batteries. The mixtures of [BMIM][TFSI] and the above solvents are good candidates of electrolytes in electrochemical industry, so electrical conductivities of the mixtures are studied in this paper. Up to now, there have been no electrical conductivity data of [BMIM][TFSI]−PC/GBL and [BMIM][TFSI]−EC/DMC mixtures in the open literature. In this study, we measured the electrical conductivities of ternary mixtures of [BMIM][TFSI]−PC/GBL and [BMIM][TFSI]−EC/DMC over the whole composition range at different temperatures. The effects of organic solvent ratio, IL concentration, and temperature on the electrical conductivity were investigated. Furthermore, the effect of IL concentration was correlated by the empirical Casteel−Amis (CA) equation. The temperature dependence of the electrical conductivity was described by the VTF equation and the Arrhenius equation. At last, a quasi-Arrhenius equation was proposed to correlate the effects of both temperature and IL concentration on the electrical conductivity of multicomponent systems, and the equation has high precision and wide application.

3. RESULT AND DISCUSSION 3.1. Experimental Data. The electrical conductivities for the ternary mixtures of [BMIM][TFSI]−PC/GBL (PC:GBL = 1:1) and [BMIM][TFSI]−EC/DMC (EC:DMC = 1:1) over the whole composition range at a wide temperature range were illustrated in Table S1 and Table S2 in the Supporting Information, respectively. Besides, the electrical conductivities for the above two mixtures with different ratios of organic solvents were shown in Table S3. The literature data for electrical conductivity of pure ionic liquid [BMIM][TFSI] have been reported by a number of groups.36−40 The comparison of our conductivity values for [BMIM][TFSI] with the available literature data was illustrated in Figure 1. The data from Vraneš et al. are in the same temperature range as ours, and the data are very close. However, our data have some deviations with those of Widegren et al. and Tokuda et al. Water content has some influences on the conductivity of ionic liquids; the deviation is mainly due to the water content in pure [BMIM][TFSI]. In our

2. EXPERIMENTAL SECTION The purity of the ionic liquid 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([BMIM][TFSI]) was checked by a high-performance liquid chromatograph (HPLC-Waters 490E), and it was further purified by evaporation at 363.15 K under high vacuum (0.5 kPa) for 10 h to remove water and low boiling point impurities; after that, the water content was less than 200 ppm measured by Karl Fisher titration. The purchased organic solvents propylene B



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Figure 1. Electrical conductivities of [BMIM][TFSI] vs temperature: ●, this work; □, Vraneš et al.;36 △, Vraneš et al.;37 ▽, Widegren et al;38 ◇, Tokuda et al.39

work, the water content of pure [BMIM][TFSI] was below 200 ppm, but it was less than 10 ppm in the study of Widegren et al. and Tokuda et al. and even less than 1 ppm in the work of Vraneš et al. More water in the ionic liquid results in larger values of the ionic liquid, so the electrical conductivity of [BMIM][TFSI] in our work is a little larger. The electrical conductivity values of binary mixtures [BMIM][TFSI]−PC and [BMIM][TFSI]−GBL are also available in the literature.37,40 Figure 2 illustrated the conductivity data vs IL mole fraction of this work and the literature at 318.15 K. It can be observed that the data of this work are in good agreement with the reported results, but the deviations at high IL concentration are a little larger. This is due to the fact that the electrical conductivity of pure IL [BMIM][TFSI] we measured is a little larger than the literature data. 3.2. The Effects of Composition on the Electrical Conductivity of Ternary Mixtures. 3.2.1. The Effects of IL Concentration on the Electrical Conductivity. The electrical conductivity of [BMIM][TFSI] in mixed solvents PC/GBL and EC/DMC (in constant mole ratio (1:1)) at different temperatures was illustrated in Figure 3. It can be seen that the electrical conductivities of the two solutions increase steeply to the maximum values with the increment of IL concentration at the solvent-rich region and then progressively decrease. The variation tendency can be clearly explained by the following equation proposed by Every et al.41 κ=

∑ niqiμi

Figure 2. Electrical conductivity of binary mixtures vs IL mole fraction at 318.15 K: (a) [BMIM][TFSI]−PC, ●, this work; □, Vraneš et al.;37 (b) [BMIM][TFSI]−GBL, ●, this work; □, Vraneš et al.40

inant factor; consequently, the maximum value of the electrical conductivity occurs and then the electrical conductivity decreases gradually. 3.2.2. The Effects of the Mole Ratio of Organic Solvents on the Electrical Conductivities of the Ternary Mixtures. The electrical conductivity data for [BMIM][TFSI]−PC/GBL (PC:GBL = 1:0; 2:1; 1:1; 1:2; 0:1) and [BMIM][TFSI]− EC/DMC (EC:DMC = 1:0; 2:1; 1:1; 1:2; 0:1) at 318.15 K are illustrated in Figure 4 and Figure 5. Figure 4 clearly shows that the maximum value of the electrical conductivity of IL + GBL (PC:GBL = 0:1) is the largest compared with other organic solvent ratios, while the value of the IL + PC (PC:GBL = 1:0) system is the smallest. In addition, the maximum value of electrical conductivity in the ternary mixture increases with the decreasing mole ratio of PC to GBL (increasing concentration of GBL) in the mixture. However, in [BMIM][TFSI]−EC/ DMC systems, the effect of the mole ratio of organic solvent on the electrical conductivity is different. Figure 5 shows that the maximum values of electrical conductivities of the ternary mixtures are larger than those of binary mixtures IL + EC (EC:DMC = 1:0) and IL + DMC (EC:DMC = 0:1), and the optimal ratio of EC to DMC is 1:1. It is owed to the optimal combination of high-dielectric-constant solvent (EC) with lowviscosity solvent (DMC), and the solvents have a synergistic

(1)

where n is the number of charge carriers of ion type i, q is the charge, and μ is the ion mobility of each species. The IL added to the organic mixtures increases the charge carriers in the solution, but it decreases the ion mobility, since it can increase the viscosity of the ternary mixture. The curve of electrical conductivity vs IL concentration is the result of the competition between the effects of increased charge carriers and the decreased ion mobility. In the low IL concentration region, the number of charge carriers plays a dominant role; therefore, electrical conductivity increases rapidly with the IL concentration. With the increment of IL mole fraction in mixed solvent, the ion mobility progressively becomes the predomC



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Figure 4. Electrical conductivity of [BMIM][TFSI]−PC/GBL mixtures vs IL mole fraction at 318.15 K with different PC/GBL ratios: ☆, 1:0; ▽, 2:1; ■, 1:1; △, 1:2; ○, 0:1. Lines () are results correlated by the Casteel−Amis equation.

Figure 3. Electrical conductivity of ternary mixtures vs IL mole fraction at various temperatures: (a) [BMIM][TFSI]−PC/GBL (PC:GBL = 1:1); (b) [BMIM][TFSI]−EC/DMC (EC:DMC = 1:1). ■, 293.15 K; ○, 298.15 K; ▲, 303.15 K; ▽, 308.15 K; ◆, 313.15 K; ◁, 318.15 K; ▶, 323.15 K; □, 328.15 K; ★, 333.15 K; ◇, 338.15 K; ●, 343.15 K; ☆, 348.15 K; ◀, 353.15 K. Lines () are results correlated by the Casteel−Amis equation.

Figure 5. Electrical conductivity of [BMIM][TFSI]−EC/DMC mixtures vs IL mole fraction at 318.15 K with different EC/DMC ratios: ☆, 1:0; ▽, 2:1; ■, 1:1; △, 1:2; ○, 0:1. Lines () are results correlated by the Casteel−Amis equation.

effect for the electrical conductivity of the IL contained ternary mixture. In contrast, PC and GBL possess both a high dielectric constant and a relatively high viscosity; they do not have a synergistic effect in the mixture of [BMIM][TFSI]−PC/GBL. Table S4 shows the dielectric constant and viscosity of these organic solvents. 3.2.3. Casteel−Amis Equation. The concentration dependence of electrical conductivity was usually described by the empirical Casteel−Amis equation23

respectively. The fitting curves are represented in Figures 3−5. Values of R2 are greater than 0.9980 and values of RMSE are less than 0.34 mS·cm−1, which indicates the Casteel−Amis equation has a good precision to describe the IL concentration dependence on electrical conductivities. Figure 3 and Tables S5 and S6 show that the parameters xκmax increase with increasing temperature. The reason is that rising temperature can reduce the solution viscosity and increase the charge carrier number by weakening ion aggregation; hence, the peak of electrical conductivity shifts toward the IL-rich region with increasing temperature. 3.3. The Temperature Dependence of Electrical Conductivities for Ternary Mixtures. 3.3.1. The Effects of Temperature on Electrical Conductivity. The effects of temperature on the electrical conductivities for the ternary systems of IL−PC/GBL (1:1) and IL−EC/DMC (1:1) are shown in Figure 6. It indicates the electrical conductivities of the mixtures increase with increasing temperature. At low IL

⎡ ⎛ x ⎞a x IL − xκmax ⎤ ⎥ κ = κ max ⎜⎜ IL ⎟⎟ exp⎢b(x IL − xκmax)2 − a xκmax ⎥⎦ ⎢⎣ ⎝ xκmax ⎠ (2)

where κmax is the maximum electrical conductivity of the mixtures, xκmax is the corresponding mole fraction of IL, and a and b are the empirical parameters. The best fitting parameters κmax, xκmax, a, and b and the coefficient of determination (R2) and root-mean-square error (RMSE) are given in Tables S5−S7, D



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where κ∞ is the maximum electrical conductivity at infinite temperature, Ea,VTF is the activation energy for electrical conduction, R is the gas constant, and T0 is the glass transition temperature. The fitting results of ln κ versus 1000/(T − T0) are linear, as illustrated in Figure 7. The equation parameters and R2, RMSE

Figure 6. Electrical conductivities of ternary mixtures vs temperature at different IL mole fractions: (a) [BMIM][TFSI]−PC/GBL; (b) [BMIM][TFSI]−EC/DMC. ■, 0.05; ●, 0.1; ▲, 0.2; ▽, 0.3; ◆, 0.4; □, 0.5; ▶, 0.6; ○, 0.7; ★, 0.8; ◇, 0.9; ◀, 1.0. Lines are drawn to connect the data points.

concentration (x = 0.05, 0.1), the slopes of the electrical conductivities are less than those of others, which indicates that the electrical conductivity in such situations increases much slower with temperature. The reasonable explanation is that the IL almost completely dissociated in the solvent-rich region, thus the increase of electrical conductivity mainly due to the increase of ion mobility by rising temperature. When the IL concentration is greater than 0.1, the number of charge carriers in solutions increases. In addition, with the increase of IL concentration, IL gradually cannot be completely dissociated. Therefore, rising temperature can not only accelerate the ion mobility of each species but also contribute to the dissociation process, so that the electrical conductivities increase more rapidly. 3.3.2. Correlation of Temperature Effects by the Vogel− Tamman−Fulcher (VTF) Equation. The effects of temperature on the electrical conductivity of ionic liquid solution can be correlated by the Vogel−Tamman−Fulcher (VTF) equation.26 That is ⎡ −Ea,VTF ⎤ κ = κ∞ exp⎢ ⎥ ⎣ R(T − T0) ⎦

Figure 7. VTF plot of the electrical conductivity with temperature for (a) [BMIM][TFSI]−PC/GBL (PC:GBL = 1:1) and (b) [BMIM][TFSI]−EC/DMC (EC:DMC = 1:1) with IL mole fraction from 0 to 1: ■, 0.05; ●, 0.1; ▲, 0.2; ▽, 0.3; ◆, 0.4; □, 0.5; ▶, 0.6; ○, 0.7; ★, 0.8; ◇, 0.9; ◀, 1.0. Scattered points are experimental results, and lines () are plots of the VTF equation.

are listed in Table S8 and Table S9 with the values R2 ≥ 0.9995 and RMSE ≤ 0.11. This indicates the VTF equation fits the temperature dependency of electrical conductivity very well. The relationship between the value of VTF parameters (κ∞, Ea,VTF, and T0) and the mole fraction of IL is irregular, which is the same as previous work performed by Xu et al.28 Therefore, the VTF equation cannot describe the effect of IL concentration on electrical conductivity. 3.3.3. Correlation of Temperature Effects by the Arrhenius Equation. The Arrhenius equation has been utilized to describe the temperature dependence of electrical conductivity.41 It is expressed as follows

(3) E


Journal of Chemical & Engineering Data ⎡ −E ⎤ κ = A exp⎢ a ⎥ ⎣ RT ⎦

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relationship between VTF parameters and IL mole fraction is irregular, so it cannot be utilized to describe the concentration and temperature dependency for the electrical conductivity simultaneously. We found the values of Ea and A in the Arrhenius equation increase regularly with IL concentration, respectively, as shown in Figure 9 and Figure 10. Thus, proper

(4)

where A is the pre-exponential factor, Ea is the activation energy for ion transportation by migration, and R is the gas constant. The obtained conductivity data were fitted as a function of temperature using a linear fit of (ln κ) vs (1000/T). The results are illustrated in Figure 8. The best fit values of the activation

Figure 9. Natural logarithm of pre-exponential factor A vs IL mole fraction x for [BMIM][TFSI]−PC/GBL mixture: ●, experimental values; ---, calculated from eq 5; [BMIM][TFSI]−EC/DMC mixture: ■, experimental values; , calculated from eq 5.

Figure 8. Arrhenius plot of the electrical conductivity with temperature for (a) [BMIM][TFSI]−PC/GBL (PC:GBL = 1:1) and (b) [BMIM][TFSI]−EC/DMC (EC:DMC = 1:1) with IL mole fraction from 0 to 1: ■, 0.05; ●, 0.1; ▲, 0.2; ▽, 0.3; ◆, 0.4; □, 0.5; ▶, 0.6; ○, 0.7; ★, 0.8; ◇, 0.9; ◀, 1.0. Scattered points are experimental results, and lines () are plots of the Arrhenius equation.

Figure 10. Plot of the activation energy Ea vs IL mole fraction for the [BMIM][TFSI]−PC/GBL mixture: ●, experimental values; ---, calculated from eq 8; [BMIM][TFSI]−EC/DMC mixture: ■, experimental values; , calculated from eq 8.

energy (E a), pre-exponential factor (A), coefficient of determination (R2), and root-mean-square error (RMSE) are listed in Table S10 and Table S11. Figure 8 indicates the Arrhenius equation has a good accuracy for the electrical conductivity data at high temperaturel however, with the temperature decreasing, the deviation increases gradually.42 The range of the coefficient of determination R2 is from 0.9966 to 0.9991. Consequently, the behavior of the Arrhenius equation is not very good when applied at a wide temperature range, compared with the VTF equation (R2 ≥ 0.9995). Despite that the VTF equation predicts the electrical conductivity behavior with temperature more rigorously, the

models can be derived to describe Ea and A as functions of IL concentration. It is a practical approach to establish an accurate model to correlate the electrical conductivity with the temperature and mole fraction of IL. 3.4. Correlation of Electrical Conductivity Considering Composition and Temperature Simultaneously by the Quasi-Arrhenius Equation. The values of the pre-exponential factor (A) and activation energy (Ea) of the Arrhenius equation are usually considered as temperature independent and IL concentration dependent. In this part, the relationship between A, Ea, and IL mole fraction was explored. On the basis of the modification of the Arrhenius equation, a new model was F



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Ea = (ax−0.5 + b)x + d

proposed to correlate the electrical conductivity data with IL concentration and temperature. According to the variation trend of the pre-exponential factor (A) with the mole fraction of IL (x) in two ternary systems, we figured out an equation below

where a, b, and d are adjustable parameters and = d. The parameters a, b, and d and R2, RMSE are illustrated in Table 3, and the coefficients of determination R2 are 0.9974 and 0.9970. In Figure 10, all points fall on the fitting line, indicating the equation fits well with the activation energy data. Since the VTF equation can well describe the effects of temperature, the temperature term in the Arrhenius model is replaced by the temperature term (T − T0) in the VTF equation. After substitution of eq 5 and eq 8 into the Arrhenius equation with the modified temperature term, a new quasiArrhenius equation is proposed

(5)

ln A = m ln x + c

where c and m are the empirical constants. The fitting parameters and R2, RMSE were listed in Table 2. Figure 9 Table 2. Parameters c and m and R2, RMSE of eq 5 Fitted to the Pre-Exponential Factor (A) of the Arrhenius Equation in Ternary Systems solution

c

m

R2

RMSE

[BMIM][TFSI]−PC/GBL [BMIM][TFSI]−EC/DMC

10.75 11.52

1.343 1.652

0.9781 0.9715

0.1844 0.2599

⎡ (B x 0.5 + B x) + E 0 ⎤ 5 a ⎥ κ = B1x B2 exp⎢ − 4 T − B3 ⎣ ⎦

Ea0 = (B6 x 2′ + B7 )2

where x 2′ =

x2 , x 2 + x3

(10)

x2, and x3 are the mole fractions of organic

solvents. Considering eq 10, eq 9 can be converted to ⎡ (B x 0.5 + B x) + (B x ′ + B )2 ⎤ 5 6 2 7 ⎥ κ = B1x B2 exp⎢ − 4 T − B3 ⎣ ⎦

(11)

The electrical conductivity data of [BMIM][TFSI]−PC/GBL and [BMIM][TFSI]−EC/DMC mixtures with different ratios of organic solvents (1:0, 2:1, 1:1, 1:2, 0:1) were fitted by eq 11. The correlated parameters Bi, R2, and RMSE are reported in Table 4. The values of the coefficient of determination are 0.9973 and 0.9800, respectively, which indicate that the electrical conductivity data of ternary mixtures can be well correlated by the quasi-Arrhenius model. In addition, the electrical conductivity data in the literature included 11 binary systems and 1097 data points were also correlated by eq 11. The results were illustrated in Table 5, and the values of R2 are more than 0.9980 or even exceed 0.9990. In conclusion, the quasi-Arrhenius equation (eq 11) can well describe the effects of temperature and IL concentration on electrical conductivity, for both the binary and ternary systems.

(6)

where Ea0 is the infinitesimal dilution activation energy produced by the pure solvent, Ea,IL is the molar energy related to the ionic interactions, and the second term Ea,ILx in eq 6 represents the contribution of IL at a molar fraction x to the activation energy. Figure 10 illustrates the activation energies (Ea) of the solutions increase with the mole fraction of IL, but the slope at each spot decreases progressively with the increasing mole fraction of IL. With the increasing concentration of IL in the solution, the reinforcement of ion−solvent and ion−ion interactions leads to the increase of Ea. According to eq 6, the derivative dEa/dx is Ea,IL, which represents the slope. That means the molar energy related to the ionic interactions Ea,IL decreases with IL mole fraction. Hence Ea,IL is a function of IL mole fraction. As a result, a model is obtained to express the relationship between Ea,IL and the mole fraction of IL x Ea,IL = ax−0.5 + b

(9)

where κ is the electrical conductivity of mixtures, x is the mole fraction of IL, and Bi are empirical parameters. In eq 9. E0a is constant for the binary systems, since it is only related to pure organic solvent. However, it is a variable and related to the compositions of organic solvents in the IL contained ternary mixtures. Thus, an empirical equation is proposed to describe E0a of a solution of IL dissolved in mixed organic solvents

shows the values of A increase monotonically with IL concentration from the diluted IL region (x = 0.05) to pure IL and the values for IL−EC/DMC mixtures are greater than those for IL−PC/GBL mixtures. According to the study of Petrowsky et al.,43 the pre-exponential factor increases monotonically with increasing dielectric constant of the solution, so it may be due to the higher dielectric constant of EC. Figure 10 shows the relationship between the activation energy (Ea) and the IL mole fraction in the two ternary mixtures. An appropriate model can be built to describe the behavior of Ea at different compositions. According to the quasi-lattice theory, the interrelation between activation energy (Ea) and IL mole fraction can be calculated by the following equation44 Ea = Ea,ILx + Ea0

(8)

E0a

4. CONCLUSIONS The electrical conductivities of ternary systems of [BMIM][TFSI]−PC/GBL and [BMIM][TFSI]−EC/DMC were measured. The electrical conductivity of ionic liquid [BMIM][TFSI] is greatly improved by the mixed organic solvent. Moreover, conductivity data of the solution increase sharply to a maximum

(7)

Therefore, according to eq 6 and eq 7, the activation energy Ea can be correlated by the following equation

Table 3. Parameters a, b, and d and R2, RMSE of eq 8 Fitted to the Activation Energy (Ea) of the Arrhenius Equation in Ternary Systems solution

a

b

d

R2

RMSE


9.105 7.705

10.28 12.89

4.202 5.287

0.9974 0.9970

0.1958 0.2626

G



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Table 4. Parameters Bi and R2, RMSE of eq 11 for the Electrical Conductivity (κ) of Ternary Mixtures solution

B1

B2

B3

B4

B5

B6

B7

R2

RMSE


17711 29849

1.246 1.773

41.73 56.01

1881 2826

−316.4 −705.4

0.7978 −11.11

23.16 5.491

0.9973 0.9800

0.3850 0.9777

Table 5. Parameters Bi and R2, RMSE of eq 11 for the Electrical Conductivity (κ) of Binary Mixtures solution b

[EMIM][DCA]−PC [EMIM][DCA]−GBLb [BMIM][BF4]+ANc [HexMIM][BF4]+ANc [BMIM][Tf]+ANc [BMP][BF4]+ANc [EMIM][BF4]+ANc [BMPyrr][TFSI]−PCd [1BPy][BF4]−MeOHe [1B3MPy][BF4]−EtOHe [1B4MPy][BF4]−MeOHe a

B1

B2

B3

B4

B5

B′ a

R2

RMSE

1880 3829 4047 5830 7265 4636 1712 226.9 629.1 370.6 709.0

0.8712 1.090 0.9219 0.9625 0.9801 0.9425 0.7239 0.5422 0.3640 0.4900 0.3602

163.7 128.7 94.86 66.59 46.61 95.05 134.0 180.6 190.1 209.5 168.3

364.5 768.6 766.0 1100 1278 765.2 159.4 84.49 −336.9 −440.0 −398.9

−12.84 −86.24 503.1 650.3 455.0 656.6 483.7 228.4 694.0 618.0 800.9

256.2 200.8 162.4 215.4 273.5 165.2 165.5 180.2 244.3 278.1 311.8

0.9996 0.9990 0.9994 0.9993 0.9993 0.9991 0.9981 0.9984 0.9985 0.9981 0.9980

0.3887 0.6505 0.4622 0.3859 0.4075 0.5615 1.093 0.1342 0.6916 0.3078 0.7256

B′ = (B6 + B7)2. bBinary system in ref 28. cBinary system in ref 46. dBinary system in ref 45. eBinary system in ref 47.

value at low IL concentration and then decrease gradually, and there is an optimal IL concentration. The effects of the ratio of organic solvents on the electrical conductivity were investigated. The organic solvents EC and DMC have a synergistic effect for the electrical conductivity of [BMIM][TFSI]−EC/ DMC, and the optimal ratio of EC to DMC is 1:1. The electrical conductivity of [BMIM][TFSI]−PC/GBL increases with decreasing ratio of PC to GBL, and the data of the ternary mixture are greater than that of [BMIM][TFSI]−PC and less than that of [BMIM][TFSI]−GBL at a specified temperature. The concentration dependence of the electrical conductivity of the solution can be well fitted by the empirical Casteel−Amis equation, and the effects of temperature on electrical conductivity can be described by the VTF equation and the Arrhenius equation. The IL concentration dependence of the activation energy Ea and pre-exponential factor A in the Arrhenius equation was also investigated and fitted by empirical equations. On the basis of the VTF equation and the Arrhenius equation, a quasi-Arrhenius equation was proposed to describe the effects of temperature and IL concentration on the electrical conductivity simultaneously in binary systems and ternary systems, and the quasi-Arrhenius equation has high accuracy.

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(PC:GBL = 1:1) and [BMIM][TFSI]−EC−DMC (EC:DMC = 1:1) mixtures (Tables S8 and S9); parameters and R2, RMSE of the Arrhenius equation fitted to the temperature dependency of the electrical conductivity of [BMIM][TFSI]−PC−GBL (PC:GBL = 1:1) and [BMIM][TFSI]−EC−DMC (EC:DMC = 1:1) mixtures (Tables S10 and S11) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Phone/Fax: +8622-27404493. ORCID

Xianbao Cui: 0000-0001-6080-2628 Funding

This work was financially supported by National Natural Science Foundation of China (NSFC Grant No. 21776201). Notes

The authors declare no competing financial interest.

■

REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00646. Experimental conductivity data for [BMIM][TFSI]− PC−GBL (PC:GBL = 1:1) and [BMIM][TFSI]−EC− DMC (EC:DMC = 1:1) with IL mole fraction and temperature (Tables S1 and S2); experimental conductivity data for [BMIM][TFSI]−PC−GBL (PC:GBL = 1:0; 2:1; 1:2; 0:1) and [BMIM][TFSI]−EC−DMC (EC:DMC = 1:0; 2:1; 1:2; 0:1) with IL mole fraction x at 318.15 K (Table S3); dielectric constant and viscosity of organic solvent (Table S4); parameters and R2, RMSE of the Casteel−Amis equation fitted to the electrical conductivity of [BMIM][TFSI]−PC−GBL and [BMIM][TFSI]−EC−DMC mixtures (Tables S5−S7); parameters and R2, RMSE of the VTF equation fitted to the electrical conductivity of [BMIM][TFSI]−PC−GBL H



Article

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