Thermodynamic Equilibrium of Aqueous Two-Phase Systems

Article pubs.acs.org/jced

Thermodynamic Equilibrium of Aqueous Two-Phase Systems Composed of [C4mim]BF4 + MgCl2/Na2WO4 + H2O at Different Temperatures Tingting Wang,*,†,‡ Dan Zhang,‡ Yunfeng Cai,§ Juan Han,*,§ Qian Liu,∥ and Yun Wang∥ †

IP Research Center of Jiangsu Province, §School of Food and Biological Engineering, and ∥School of Chemistry and Chemical Engineering, Jiangsu University, Zhenjiang 212013, China ‡ Yancheng Entry-Exit Inspection and Quarantine Bureau, Yancheng 224000, People’s Republic of China ABSTRACT: Binodal data for the 1-butyl-3-methylimidazolium tetrafluoroborate ([C4mim]BF4) + salt (MgCl2/Na2WO4) + H2O systems were experimentally determined at T = (288.15, 298.15, and 308.15) K, respectively. The binodal data were successfully correlated by an empirical equation with four parameters. The liquid−liquid equilibrium data were given and satisfactorily correlated by the Othmer−Tobias and Bancroft equations, as well as a two-parameter equation. Additionally, the Chen-NRTL model, the Pitzer-Debye−Hückel equation, and the Flory− Huggins equation were used to determine and correlate the liquid−liquid equilibrium data for the studied systems, and good agreement was obtained with these thermodynamic models. The influences of the two salts and temperature on the phase equilibrium were investigated. The phase-separation ability of MgCl2 is stronger than that of Na2WO4. As the temperature of the systems decreases, the two-phase region shows an expansion trend.

1. INTRODUCTION

The basic data for determination of ILATPS is the premise of theory study and applied research. There is no complete theory of the phase separation for ILATPS at present. Therefore, the experimental work devoted to ILATPSs is far from enough. There is no report on the liquid−liquid equilibrium (LLE) data and complete phase diagram of aqueous [C4mim]BF4 + MgCl2/Na2WO4 systems in the literature. Correlation and prediction of experimental data are the foundation of research for the phase separation ability and LLE. The establishment of a variety of fitting empirical equations is a stable foundation for fitting binodal data in different aqueous two-phase systems. Empirical nonlinear expressions with three parameters15,16 or four parameters17 were the most frequently used for ATPSs. The four parameters always show a better correlation. At present, fitted equations for LLE mainly include the Othmer−Tobias and Bancroft equation, evaluating the accuracy of the experiment data, and Setschenow-type equations,18 evaluating the salt-out ability of different salts. Furthermore, there are some reports on the thermodynamic model of LLE in ATPSs. In the modified NRTL model,19,20 the widely used local composition model is the excess Gibbs free energy of ATPSs by three contributions, namely, short-range interaction contribution, long-range interaction contribution, and combinatorial contribution calculated by the Chen-NRTL model, Pitzer-Debye−Hückel (PDH) equation and Flory−

Aqueous two-phase systems (ATPSs), which could be formed when incompatible polymer−salts or polymer−polymers are dissolved in water over a critical concentration, are undoubtedly regarded as green systems and potentially capble of replacing conventional organic solvent extraction systems.1 With some prominent superiorities such as good biocompatibility, low energy consumption, short processing time, and relative reliability in scale-up, aqueous two-phase extraction (ATPE) has been applied to separation and purification in food chemistry,2 environmental chemistry,3 medical engineering,4 and fermentation engineering5 as an economical and efficient downstream processing method. Ionic liquids (ILs) have been entensively used during the analysis and separation processes because of their “green” characteristics, covering variable viscosity, nonvolatility, excellent solvation qualities, and high chemical and thermal stability.6 The IL-based ATPSs (ILATPSs), which were first reported by Gutowski and his co-workers, have won more and more appreciation in recent years for their prominent advantages and practical applications.7 Combining the benefits from both IL and ATPSs, ILATPSs contain many advantageous properties, including quick phase separation, high extraction efficiency, simple operation, and little emulsion formation and are environment friendly. Consequently, ILATPSs have been widely and successfully employed to deal with the separation of chloramphenicol,8 epitestosterone,9 sulfonamides,10 roxithromycin,11 penicillin,12 proteins,13 and amino acids.14 © 2016 American Chemical Society

Received: November 26, 2015 Accepted: April 12, 2016 Published: April 21, 2016 1821

DOI: 10.1021/acs.jced.5b01010 J. Chem. Eng. Data 2016, 61, 1821−1828

Journal of Chemical & Engineering Data

Article

3. RESULT AND DISCUSSION

Huggins expression, respectively. The modified nonrandom two liquid (NRTL) model of phase separation has been successfully used to correlate liquid−liquid equilibrium (LLE) in polymer−salt ATPSs21 and ILATPSs.22 Herein, the phase equilibrium properties of 1-butyl-3methylimidazolium tetrafluoroborate ([C4mim]BF4) + magnesium chloride (MgCl2)/ sodium tungstate (Na2WO4) ATPSs were investigated at different temperatures (T = (288.15, 298.15, and 308.15) K). The binodal data and the LLE data were correlated by empirical equations. Additionally, the ChenNRTL model, the PDH equation, and the Flory−Huggins expression were used to correlate the phase behavior of the investigated systems. Moreover, the type of salts and temperature affecting the binodal curves and tie-lines (TLs) were discussed.

3.1. Binodal Data and Correlation. The binodal data for [C 4 mim]BF 4 + MgCl 2 /Na 2 WO 4 + H 2 O ATPSs were determined experimentally at T = (288.15, 298.15, and Table 2. Binodal Data for the [C4mim]BF4 (1) + MgCl2(2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and p = 0.1 MPaa T = 288.15 K

2. EXPERIMENTAL SECTION 2.1. Materials. [C4mim]BF4 was used without further purification. MgCl2·6H2O and Na2WO4·2H2O were analytical grade reagents. All other reagents were of analytical grade, and double distilled deionized water was used in the experiments. The sources for the chemicals used in this work as well as their purities are presented in Table 1. Table 1. Chemical Sample Descriptions chemical name [C4mim] BF4 MgCl2· 6H2O Na2WO4· 2H2O a

source Chenjie Chemical Co., Ltd. Sinopharm Chemical Reagent Sinopharm Chemical Reagent

initial mole fraction purity

purification method

0.99

nonea

0.99

nonea

0.99

nonea

Reagent was used without further purification.

2.2. Apparatus and Procedure. The phase diagram includes the binodal curve and the TLs. The binodal curves were determined by the cloud point method as described in the previous study.23 The compositions of the mixture for each point on the binodal curve was calculated by mass using an analytical balance (model BS 124S, Beijing Sartorius Instrument Co., China) with a precision of ±1.0 × 10−7 kg. The relative standard uncertainty was 0.01 in determining the mass fraction of both IL and salt by the titration method. The 50 mL glass vessel was placed in a DC-2008 water thermostat (Shanghai Hengping Instrument Factory, China) to maintain a constant temperature. The TLs were determined by a gravimetric method described by Merchuk. Appropriate quantities of [C4mim]BF4, MgCl2/ Na2WO4 and water were weighed and mixed in the centrifuge tubes to create a series of ATPSs. The tubes were subsequently put into the thermostated bath for 12 h to guarantee the formation of two distinct phases of the mixture. The bottom phase was collected, and the mass of the bottom phase (mb) was weighed directly, then the subtraction method was used to obtain the mass of the top phase (mt). The determination of each individual TL was conducted by applying the lever rule to the relationship between the top mass phase composition and overall system composition.21

T = 298.15 K

T = 308.15 K

100w1

100w2

100w1

100w2

100w1

100w2

93.10 91.57 78.04 77.04 68.03 62.84 59.41 56.35 53.52 49.70 47.52 44.39 39.52 36.52 34.26 32.65 29.83 27.77 26.30 24.95 23.37 22.14 21.00 19.79 19.02 17.76 16.97 15.71 15.13 14.35 13.48 12.69 11.81 11.05 9.95 8.69 6.55 5.13 4.51

0.21 0.26 0.65 0.69 0.94 1.07 1.17 1.28 1.36 1.55 1.62 1.77 2.01 2.21 2.42 2.63 3.00 3.36 3.71 4.02 4.47 4.90 5.52 6.14 6.62 7.18 7.80 8.56 9.18 9.77 10.62 11.40 12.39 13.27 14.92 17.00 19.50 21.10 22.50

93.50 91.03 77.76 70.85 63.10 60.36 57.53 53.64 50.00 46.56 43.84 41.54 38.91 36.09 33.46 31.15 28.42 27.08 25.52 24.53 22.54 21.44 20.42 19.09 18.34 17.45 16.15 15.44 14.55 13.93 13.07 12.41 11.59 10.85 10.00 8.67 7.90 7.40 6.80

0.20 0.29 0.83 1.24 1.70 1.92 2.10 2.38 2.68 3.04 3.28 3.51 3.82 4.22 4.44 4.90 5.16 5.44 6.05 6.32 6.78 7.15 7.72 8.17 8.41 9.19 9.94 10.47 11.24 11.65 12.54 13.11 14.10 15.00 16.14 18.32 21.70 22.80 23.75

89.64 84.71 78.60 64.88 59.47 56.14 53.24 50.53 48.08 46.28 42.79 40.69 39.15 37.35 35.13 33.33 31.52 30.12 28.20 27.06 26.19 24.49 23.24 22.06 21.05 20.57 19.19 18.06 17.00 16.25 15.05 14.11 13.09 11.91 9.97 7.80 6.93 5.21 4.55

0.52 0.77 1.23 2.35 2.69 3.08 3.42 3.73 4.01 4.17 4.60 4.97 5.17 5.34 5.65 5.99 6.22 6.54 6.94 7.29 7.58 7.96 8.43 8.83 9.20 9.38 9.90 10.62 11.27 11.71 12.44 13.13 14.10 15.44 18.11 20.85 22.90 25.20 26.78

a Standard uncertainty u for each variable is u(T) = 0.05 K, u(p) = 10 kPa, and the relative standard uncertainty ur is ur(w) = 1%.

308.15) K (as shown in Table 2 and Table 3). The binodal data were fitted to the following equation: w1 = exp(a + bw20.5 + cw2 + dw22)

(1)

where w1 represents the mass fraction of IL and w2 represents the mass fraction of salts, and a, b, c, and d represent fitting parameters. Many researchers have employed this equation for the correlation of ILATPSs in the previous studies.24,25 The 1822



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fitting parameters and coefficient of determination (R2) together with their corresponding standard deviations (sd) are given in Table 4. Figures 1 and 2 show the binodal data for

Table 3. Binodal Data for the [C4mim]BF4 (1) + Na2WO4(2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and p = 0.1 MPaa T = 288.15 K

T = 298.15 K

T = 308.15 K

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

84.21 72.79 69.56 63.43 59.02 54.79 51.21 49.45 46.17 44.73 40.88 37.74 35.93 33.39 30.03 26.42 25.44 23.61 21.32 20.34 19.27 18.61 18.05 17.74 17.01 16.19 15.79 15.44 14.33 14.76 13.78 12.89 12.50 12.16 11.68 10.88 10.52 10.20

0.45 0.69 0.78 0.86 1.08 1.20 1.45 1.52 1.69 1.71 2.01 2.31 2.43 2.67 3.14 3.76 4.05 4.60 5.69 6.49 6.88 7.31 8.30 7.93 8.72 9.46 10.15 10.49 11.38 11.12 12.37 13.49 13.98 14.47 15.18 16.50 18.31 19.42

95.02 81.74 78.83 69.12 62.08 58.15 55.95 53.14 49.57 47.25 45.06 41.08 39.40 37.88 35.19 32.10 30.53 29.26 27.04 25.66 24.54 22.86 21.41 19.63 18.39 17.76 16.63 15.96 14.5 14.16 13.41 12.85 11.97 11.13 10.29 10.27 10.22 10.17 10.13

0.25 0.63 0.74 1.26 1.70 1.85 2.04 2.40 2.70 2.97 3.25 3.72 3.95 4.15 4.49 5.00 5.31 5.48 6.12 6.34 6.85 7.55 8.19 9.18 9.73 10.41 11.32 11.95 13.35 13.70 14.57 15.30 16.44 17.76 19.10 20.10 20.85 22.01 23.50

86.35 82.14 70.05 63.84 62.32 59.09 56.32 52.01 50.78 46.46 44.62 42.01 40.96 39.09 36.41 34.22 32.10 29.79 28.88 27.08 24.99 23.44 22.65 21.70 20.58 19.55 18.51 17.34 16.69 15.92 15.31 14.72 14.00 13.35 12.75 12.20 11.05 10.41 9.87

0.66 0.77 1.48 2.08 2.23 2.54 2.96 3.53 3.62 4.26 4.56 4.90 5.20 5.47 6.05 6.43 6.91 7.48 7.91 8.37 8.87 9.46 9.83 10.35 10.82 11.38 11.97 12.90 13.46 14.02 14.60 15.17 15.95 16.68 17.37 18.00 19.50 20.62 21.90

Figure 1. Phase diagram of [C4mim]BF4 (1) + MgCl2(2) + H2O (3) ATPS at different temperatures T = 288.15 K (■), 298.15 K (●), and 308.15 K (▲), the solid line represents the correlation according to eq 1.

Figure 2. Phase diagram of [C4mim]BF4 (1) + Na2WO4(2) + H2O (3) ATPS at different temperatures T = 288.15 K (■), 298.15 K (●), and 308.15 K (▲); the solid line represents the correlation according to eq 1.

[C4mim]BF4 + MgCl2/Na2WO4 + H2O ATPSs reproduced from eq 1 at three different temperatures. From the obtained coefficient of determination and standard deviations, we know

a

Standard uncertainty u for each variable is u(T) = 0.05 K, u(p) = 10 kPa, and the relative standard uncertainty ur is ur(w) = 1%.

Table 4. Values of Parameters of Equation 1 for the [C4mim]BF4 (1) + Na2WO4/MgCl2 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K T/K

a

b

288.15 298.15 308.15

0.3951 0.0510 −0.0241

−9.0669 −1.5886 0.3295

288.15 298.15 308.15

0.7120 0.1648 0.0601

−14.3605 −3.7632 −1.8158

c [C4mim]BF4 + MgCl2 + H2O 1.9443 −19.5842 −21.2360 [C4mim]BF4 + Na2WO4 + H2O 22.0769 −10.3805 −11.8783

d

R2

100sda

16.5434 51.8028 38.5847

0.9863 0.9980 0.9985

2.7270 1.0073 0.8009

−25.3637 33.7353 22.4812

0.9982 0.9990 0.9992

0.8029 0.6802 0.5647

i=1

Standard deviation (sd) = (∑n (w1 − w1exp)2 /n)0.5, where w1 and n represent the concentration (in weight percent) of [C4mim]BF4 and the cal number of binodal data, respectively. wexp 1 is the experimental mass faction of [C4mim]BF4, and w1 is the corresponding data calculated using eq 1. a

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Table 5. TL Data for the [C4mim]BF4 (1) + MgCl2(2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and p = 0.1 MPaa total system 100 w1

a

IL-rich phase 100 wt1

100 w2

salt-rich phase

100 wt2

100 wb1

36.43 39.98 40.08 39.98

13.26 12.00 11.04 13.46

88.94 86.35 82.27 92.50

0.37 0.41 0.48 0.32

4.95 5.35 6.34 4.67

37.29 37.39 38.00 38.09

13.65 14.49 13.01 15.11

86.33 90.14 83.91 93.07

0.48 0.31 0.58 0.23

8.00 7.50 8.45 6.91

45.12 44.95 45.01 44.98

14.02 12.06 13.11 11.21

88.04 80.93 84.16 77.69

0.58 1.10 0.87 1.33

4.77 6.00 5.40 7.01

100 wb2 T = 288.15 K 21.18 20.75 19.67 22.21 T = 298.15 K 21.50 22.50 20.90 23.53 T = 308.15 K 26.01 23.60 24.80 22.50

TLL

S

mt

mb

0.8653 0.8351 0.7831 0.9052

−4.04 −3.98 −3.96 −4.01

1.3034 1.2829 1.2476 1.3465

3.1029 2.7272 2.7524 2.6555

0.8110 0.8556 0.7815 0.8925

−3.73 −3.73 −3.71 −3.70

1.5834 1.6018 1.5508 1.7001

3.5497 3.5037 3.5492 3.4078

0.8707 0.7824 0.8232 0.7378

−3.27 −3.33 −3.29 −3.34

1.6039 1.6208 1.6112 1.6878

2.4006 2.3757 2.3888 2.3122


Table 6. TL Data for the [C4mim]BF4 (1) + Na2WO4(2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and p = 0.1 MPaa total system 100 w1

a

IL-rich phase

100 w2

100

wt1

100

salt-rich phase wt2

40.07 39.99 39.67 40.11

9.70 10.99 9.00 10.45

71.44 75.88 68.41 73.83

0.70 0.61 0.77 0.65

38.92 40.11 40.06 39.98

14.54 12.99 12.01 11.33

83.33 78.18 75.73 72.95

0.57 0.78 0.89 1.02

38.71 38.96 39.65 38.00

12.03 11.24 10.25 12.95

71.12 68.32 65.25 73.28

1.53 1.75 2.01 1.37

100 wb1

100 wb2

T = 288.15 K 10.78 18.08 10.26 19.35 11.22 17.05 10.48 18.80 T = 298.15 K 10.14 23.40 10.18 21.95 10.25 20.78 10.23 20.06 T = 308.15 K 10.29 21.07 10.60 20.39 11.10 19.46 9.96 21.85

TLL

S

mt

mb

0.6310 0.6824 0.5946 0.6590

−3.49 −3.50 −3.51 −3.49

1.6520 1.7043 1.5897 1.6879

2.3510 2.2957 2.4153 2.3211

0.7667 0.7122 0.6843 0.6555

−3.21 −3.21 −3.29 −3.29

1.9034 1.6786 1.6705 1.5509

3.2330 2.3236 2.3341 2.4491

0.6389 0.6066 0.5689 0.6655

−3.11 −3.10 −3.10 −3.09

1.9009 1.9683 2.0080 1.8879

2.7515 2.6380 2.5983 2.7121


The superscripts “b” and “t” stand for the bottom phase and the top phase, respectively. The obtained TL data at T = (288.15, 298.15, and 308.15) K for the [C4mim]BF4 + MgCl2/Na2WO4 + H2O ATPSs are given in Table 5 and Table 6, respectively. The tie-line length (TLL), and the slope of the tie-line (S) at three different temperature shown in the tables are calculated by following equations:

that eq 1 is appropriate for the calculation of the binodal data for the [C4mim]BF4 + MgCl2/Na2WO4 + H2O ATPSs. 3.2. LLE Data and Correlation. Previous studies have successfully applied the lever rule to the calculation of the LLE data of ILATPSs.26,27 Herein, LLE compositions were calculated by MATLAB according to eq 1 and the lever rule: w1t = exp[a + b(wwt )0.5 + cw2t + d(w2t)2 ]

(2)

w1b

(3)

= exp[a +

b(wwb )0.5

+

cw2b

+

d(w2b)2 ]

w1t − w1

m = b b mt w1 − w1 w2 − w2t w2b − w2

wt1,

wb1,

=

wt2

(6)

S = (w1t − w1b)/(w2t − w2b)

(7)

where w 1t , w 1b , w 2t , and w 2b represent the equilibrium compositions of IL (1) and salt (2). The superscripts “b” and “t” stand for the bottom phase and the top phase, respectively. In this work, the TL data were correlated by using several models. Of all the empirical equations proposed to correlate the TL data for ILATPSs, the Othmer−Tobias (eq 8) and Bancroft (eq 9) were the most widely used,

(4)

mb mt

TLL = [(w1t − w1b)2 + (w2t − w2b)2 ]0.5

(5)

wb2

where and represent the equilibrium compositions of IL (1) and salt (2), in the top phase and the bottom phase. 1824



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Table 7. Values of Parameters of eq 8 and 9 for the [C4mim]BF4 (1) + MgCl2/ Na2WO4 (2)+ H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K

a

T/K

k1

n

k2

288.15 298.15 308.15

4.9647 × 10−5 5.6705 × 10−5 0.0030

5.9652 6.1128 3.6897

4.5964 4.2886 4.1874

288.15 298.15 308.15

0.0114 0.0064 0.0127

2.3454 2.9405 2.6342

5.7278 4.8913 4.5464

r MgCl2 0.1313 0.1421 0.2247 Na2WO4 0.3923 0.3365 0.3530

R21

R22

100sd1a

100sd2a

0.9716 0.9971 0.9840

0.9812 0.9981 0.9862

0.5543 0.1579 0.4995

0.6123 0.1748 0.5023

0.9885 0.9732 0.9946

0.9876 0.9713 0.9948

0.2689 0.5711 0.1970

0.4290 0.8461 0.2788

Standar deviation (sd) is calculated as follows: i=1 top 2 bot bot 2 0.5 sd = [∑ ((witop , j ,cal − wi , j ,exp) + (wi , j ,cal − wi , j ,exp) )/2N ] N

where N is the number of TLs and j = 1 and j = 2, sd1 and sd2 represent the mass percent standard deviations for IL and salt, respectively.

⎡⎛ 1 − w b ⎞⎤ n ⎡⎛ 1 − w t ⎞⎤ 1 2 ⎥ ⎢⎜ ⎟⎟ ⎟⎥ = k1⎢⎜⎜ b ⎢⎣⎝ w1t ⎠⎥⎦ ⎣⎢⎝ w2 ⎠⎥⎦

⎛ wb ⎞ ⎛ w t ⎞r ⎜⎜ 3b ⎟⎟ = k 2⎜ 3t ⎟ ⎝ w1 ⎠ ⎝ w2 ⎠

Table 8. Values of Parameters of eq 10 for the [C4mim]BF4 (1) + Na2WO4/MgCl2 (2)+ H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K

(8)

(9)

in which wt1 is the mass fraction of [C4mim]BF4 in the top phase; wb2 is the mass fraction of the salt in the bottom phases; wb3 and wt3 are the mass fractions of water in the bottom and top phases, respectively; and k1, n, k2, and r are the fitted parameters provided in Table 7. In conclusion, good agreement was obtained using these two models. An equation with two parameters (eq 10) was also used to correlate the TL data.28,29 k denotes salting-out coefficient, and β denotes the constant related to the activity coefficient. Superscripts “t” and “b” stand for the top phase and the bottom phase, respectively: ⎛ wt ⎞ ln⎜⎜ 2b ⎟⎟ = β + k(w1b − w1t) ⎝ w2 ⎠

a

E,LR

E,SR

288.15 298.15 308.15

4.3950 9.9690 7.7305

288.15 298.15 308.15

4.2669 7.0852 5.4247

β MgCl2 −0.3690 3.9649 2.6836 Na2WO4 −0.6598 −1.4763 0.6715

R2

100sda

0.9963 0.9941 0.9726

0.2437 0.4395 1.0042

0.9994 0.9983 0.9989

0.0667 0.0817 0.1158

Standard deviation (sd) is calculated as follows: j=1 i=1 3

N

where N is the number of TLs and j is the components in each phase.

The PDH equation, Flory−Huggins equation, and the indispensable procedures for obtaining GE,LR and GE,Comb have been reported in our previous work.36 It is the same as those presented about polymer−salt ATPS. In regard to GE,LR, the dielectric constant of [C4mim]BF4 was assumed to be D = 12.9.37 The dielectric constant of D = 78.34 was also used for water.38 According to the GE,Comb, the molar volume of [C4mim]BF4 is 0.269 nm.39 For an ILATPS, the extended NRTL equation for GE,SR is expressed as

(10)

(11)

E,SR ⎡ XILGsw τsw + (Xc + Xa)Gca,w τca,w ⎤ G NRTL ⎥ = nw⎢ ⎢⎣ X w + XILGsw + (Xc + Xa)Gca,w ⎥⎦ RT

E,Comb

where G , G , and G are the long-range interaction contribution, the short-range interaction contribution, and the combinatorial contribution, respectively. While the activity coefficient of component i (IL, ions, and water) can also be considered as the sum of three contributions: ln γi = ln γi LR + ln γiSR + ln γiComb

k

top 2 bot bot 2 0.5 sd = [∑ ∑ ((witop , j ,cal − wi , j ,exp) + (wi , j ,cal − wi , j ,exp) )/6N ]

The fitting parameters, the standard deviations, and R2 are listed in Table 8, indicating that eqs 10 can satisfactorily correlate the LLE data. 3.3. Correlation of the Thermodynamic Model Equation. According to the previous Chen-NRTL model30 and modified Wilson model,31 The excess Gibbs free energy is expressed as the sum of three contributions:32 GE = GE,LR + GE,SR + G E ,Comb

T/K

⎡ X w Gwsτws + (Xc + Xa)Gca,sτca,s ⎤ ⎥ + rnIL⎢ ⎢⎣ X w Gws + XIL + (Xc + Xa)Gca,s ⎥⎦ ⎡ X w Gw,caτw,ca + XILGs,caτs,ca ⎤ ⎥ + ncZc⎢ ⎢⎣ X w Gw,ca + XILGs,ca + Xa ⎥⎦

(12)

The Pitzer’s extension of the Debye−Hü ckel function (PDH),33 the extended NRTL model,34 and the Flory− Huggins expression35 are used to calculate GE,LR, GE,SR, and GE,Comb, respectively.

⎡ X w Gw,caτw,ca + XILGs,caτs,ca ⎤ ⎥ + naZa⎢ ⎢⎣ X w Gw,ca + XILGs,ca + Xc ⎥⎦ 1825

(13)



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Table 9. Values of Parameters of Extended Local Composition NRTL Model for the [C4mim]BF4 (1) + Na2WO4/MgCl2 (2)+ H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K T/K

τs,ca

τsw

τca,s

288.15 298.15 308.15

0.6174

1.3386

0.4324

288.15 298.15 308.15

0.2420

1.0233

0.3946

τca,w

τws

τw,ca

100Deva

0.8844

0.0372

1.0953

0.0834 0.1002 0.0989

1.4437

0.3188

1.2757

0.0928 0.0863 0.0896

Na2WO4

MgCl2

a

l=1

p=1

Deviation (Dev) = (Fab/6N ) × 100 , where OF = ∑N ∑2

j=1

cal 2 ∑3 (wlexp , p , j − wl , p , j) and N stands for the number of the TLs.

In regard to the above relations, the subscripts s, IL, w, ca, a, and c stand for the segment of IL, IL, water, salt, anion, and cation, respectively. N and X represent the number of moles and the effective local mole fraction, respectively.

Xi = φiK i

(14)

(Ki = Zi for ions and Ki = 1 unity for IL and solvent) where φi is the segment fraction. The energy parameters of G and τ are given by

Gm ′ m = exp( −ατm ′ m) τm ′ m =

gm ′ m − gmm RT

(15)

τj , ca = τjc , ac = τja , caτca , j = τcj = τaj (16)

Here, g represents the energy of interaction and α represents the no randomness factor. The species m and m′ in the above relations can be solvent molecules or segments, and the species j can be solvent molecule or IL. The LLE data of ILATPSs in this work were correlated with using the following equilibrium equation: (xjγj)t = (xjγj)b

Figure 3. Effect of type of salts on binodal curves at different temperatures. The [C4mim]BF4 (1) + Na2WO4 (2) + H2O (3) ATPSs: 288.15 K (□); 298.15 K (○); 308.15 K (△); The [C4mim]BF4 (1) + MgCl2 (2) + H2O (3) ATPSs: 288.15 K (■); 298.15 K (●); 308.15 K (▲).

partial experimental TLs of the [C4mim]BF4+ MgCl2/Na2WO4 ATPSs are compared in Figure 4 for the three different temperatures T = 288.15, 298.15, and 308.15 K. In the temperature range considered, an increase in the temperature results in the slight increase of the absolute values of the slopes of the TLs. In regard to the salting-out, a decrease in temperature can increase the ability of the phase separation in the investigated ATPSs. [C4mim]BF4 becomes more hydrophobic as the temperature increases. Thus, as the temperature increases, water in the [C4mim]BF4-rich phase tends to transfer to the salt-rich phase. 3.5. Phase-Separation Abilities of Salts. Salt plays an important role in the formation of ATPS. The phase diagrams in previous literature reveal that the closer the binodal curves move to the axis, the stronger the salting-out ability is.40,41 As observed in Figure 3, the phase-separation ability of MgCl2 is stronger than that of Na2WO4 as a whole. As the temperature increases, the gap of the binodal curves of the two salts is widening. It also means that the order for ability of the phase separation, MgCl2 > Na2WO4, is more obvious in a higher temperature. Tables 5 and 6 provide the absolute values of the TL slopes. The slope for the [C4mim]BF4 + MgCl2 ATPS is larger than that for the [C4mim]BF4 + Na2WO4 ATPS under isothermal conditions. As compared to that for the [C4mim]BF4 + Na2WO4 ATPS, water in the [C4mim]BF4 + MgCl2 ATPS is driven out more from the [C4mim]BF4-rich phase to the salt-

(17)

Here, b is the bottom phase and t is the top phases, respectively. The model parameters of the extended NRTL equation were estimated by minimizing the following objective function: OF =

∑ ∑ ∑ (wpcal,l ,j − wpexp,l ,j)2 p

l

j

(18)

where wp,l,j refers to the weight fraction of the component j (ionic liquid, solvent molecule, or salt) in the phase p for lth TL. The superscripts cal and exp are the calculated and experimental values, respectively. According to the above extended NRTL model, the six binary adjustable model parameters of the experimental LLE data and the corresponding deviations are given in Table 9. From the obtained deviations, it can be concluded that this model is adapted to the representation of the LLE data for these studied ILATPSs. 3.4. The Effect of Temperature on the Binodal Curves and TLs. Figure 3 illustrates the binodal curves for the [C4mim]BF4 + MgCl2/Na2WO4 + H2O measured at T = (288.15, 298.15 and 308.15) K. The region above the curves represents the two-phase region, while the region below the curves refers to homogeneous solutions. On the basis of the locus for the experimental binodals, it is evident that the onephase area expands as the temperature increases. Moreover, 1826



■

Article

AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86 051188795397. E-mail: [email protected]. *Tel.: +86 051188780201. E-mail: [email protected]. Funding

This work was supported by the National Natural Science Foundation of China (Nos. 31470434, 21406090, 21407058, and 21576124), the Special Financial Grant from the China Postdoctoral Science Foundation (No. 2015T80510), the grants from the project of General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China (No. 2015IK139), the Science Foundation of Jiangsu Entry-exit Inspection Quarantine Bureau of China (Nos. 2015KJ27 and 2015KJ28), the Project of science and technology development plan of Taicang (No. TC2015NY05), and the Programs of Senior Talent Foundation of Jiangsu University (No.15JDG173). Notes

The authors declare no competing financial interest.

■

REFERENCES

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Figure 4. TLs of the [C4mim]BF4 + salt (MgCl2(a); Na2WO4(b)) ATPS at T = 288.15 K (●); 298.15 K (▲); 308.15 K (■).

rich phase. This trend indicates that water serves as a more preferable solvent for [C4mim]BF4 as dissolved in Na2WO4 aqueous solution than dissolved in MgCl2. The salting-out ability of salts is connected with the fitting parameter k in eq 10. With the increase of k, the salting-out ability of salts increases.42,43 According to the parameter k values listed in Table 8, we can draw a conclusion that the salting-out ability of the salts investigated in this work follows the order: MgCl2 > Na2WO4, which also agrees with the phaseseparation ability proved by the binodal curves in Figure 3.

4. CONCLUSIONS For IL ([C4mim]BF4) + salt(MgCl2/ Na2WO4) + water ATPSs, binodal data and TL data were measured at T = (288.15 K, 298.15 K, and 308.15 K). The binodal data were fitted by the empirical equation with four parameters, and the TL data were fitted by the Othmer−Tobias and Bancroft equations, as well as the two-parameter equation. The extended NRTL model, the Pitzer’s extension of the Debye−Hückel function (PDH), and the Flory−Huggins expression were also used to correlate the TL data. All the equations used exhibit a satisfactory correlation. The effects of the two salts and temperature on phase separation were discussed. The order of the phase-separation ability of the two salts is MgCl2 > Na2WO4. The two-phase area expands as the temperature decreases, while the slope of the TL decreases slightly as the temperature increases. 1827



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Thermodynamic Equilibrium of Aqueous Two-Phase Systems

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