Measurement and Correlation of Phase Equilibria in Aqueous Two

Article pubs.acs.org/jced

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Lauryl Ether and Tartrate Salt at Different Temperatures Yang Lu,†,‡ Tongfan Hao,† Ming Yan,‡ Juan Han,‡ Zhenjiang Tan,*,† and Yongsheng Yan*,†,‡ †

School of Computer Science, Jilin Normal University, 1301 Haifeng Street, Siping, 136000, China School of Chemistry and Chemical Engineering, Jiangsu University, 301 Xuefu Road, Zhenjiang, 212013, China

‡

ABSTRACT: The binodal curves of the aqueous two-phase system (ATPS) containing polyoxyethylene (10) lauryl ether (POELE10, C32H66O11) and three tartrate salts ((NH4)2C4H4O6, K2C4H4O6, and Na2C4H4O6) were determined at the temperatures (288.15, 298.15, and 308.15) K. The binodal data in the studied systems were fit by three known equations, and a satisfactory correlation effect was obtained. The liquid−liquid equilibrium (LLE) data for the investigated systems were calculated by computer software in terms of the lever rule and correlated by the Othmer−Tobias and Bancroft equations, respectively. The salting-out ability of salt was discussed from two different perspectives: anion and cation. The analysis on the Gibbs free energy of hydration of the ions and the binodal curves found that the saltingout ability of salt strengthened with the increase in absolute value of the Gibbs free energy of anion (cation) when the salt consisted of the same cation (or anion). The order of salting-out ability of salts with the same cation was KOH < K2C4H4O6 < K2CO3 < K2HPO4 < K3PO4, and the order of salting-out ability of salts with the same anion was (NH4)2HPO4 < K2HPO4 and (NH4)2C4H4O6 < K2C4H4O6 < Na2C4H4O6. The effect of temperature on the phase diagram of ATPS was studied. It was found that it is favorable to form the ATPS when the temperature rises and that the absolute value of the slope of the tie-line (STL) increased with the rising temperature. In the investigated systems, the effective excluded volume (EEV) is calculated at the different temperatures, and it was found that the greater value of EEV of the systems corresponds to the stronger phase formation of the ATPS.

1. INTRODUCTION In recent years, there is a trend to use the aqueous two-phase system (ATPS) as an effective liquid−liquid extraction technology.1−4 It is more widely used to separate and extract the biological materials, such as nucleic acids,5 proteins,6−8 viruses,9 antibiotics,10−12 and other biological molecules.13−15 The separation and extraction of all materials using ATPS is based on the study of the phase behavior of ATPS. Thus, in order to better design the extraction processes, the study of the phase behavior of the ATPS becomes more necessary. Nowadays, the ATPS mainly falls into the following four kinds: the polymer−polymer ATPS,16 polymer−salt ATPS,17 ionic liquid−salt ATPS,18 and micromolecule alcohol−salt ATPS.19,20 On the basis of analyzing and selecting, we found that nonionic surfactant polyoxyethylene (10) lauryl ether (POELE10, C32H66O11) was made up of the hydrophobic alkyl domain and hydrophilic polyoxyethylene tail. POELE10 is a substance that contains this feature, and it was an appropriate choice to form polymer−salt ATPS. In our previous articles,21,22 we have reported the phase behavior of the ATPS composed of POELE10 and five kinds of inorganic salts [KOH, K2CO3, K3PO4, K2HPO4, and (NH4)2HPO4] at different temperatures. © 2014 American Chemical Society

In this paper, we will study the liquid−liquid phase equilibria behavior of the ATPSs containing POELE10 and organic salts [(NH4)2C4H4O6, K2C4H4O6, and Na2C4H4O6] at T = (288.15, 298.15, and 308.15) K which have not been reported. First of all, the binodal data and tie-line data of the investigated systems will be given and be fit by using an appropriate fitting formula. Second, the effects of salt type and temperature on the phase diagram will be discussed. The discussion on the effect of salt will be elaborated from the perspective of the anion and cation, respectively. The relationship between the phase-forming ability of ATPS and the effective excluded volume of system will finally be studied.

2. EXPERIMENTAL SECTION 2.1. Materials. Nonionic surfactant POELE10 was purchased from Aladdin Reagent Company (Shanghai, China), the quoted purity of which was greater than 0.99 mass fraction. The average molar mass, the critical micelle concentration (CMC), the hydrophilic lipophilic balance (HLB), and the melting point Received: January 4, 2014 Accepted: April 25, 2014 Published: May 6, 2014 1843

dx.doi.org/10.1021/je500009h | J. Chem. Eng. Data 2014, 59, 1843−1851

Journal of Chemical & Engineering Data

Article

Table 1. Sample Information chemical name POELE10 (NH4)2C4H4O6 K2C4H4O6 Na2C4H4O6 a

source

initial mole fraction purity

purification method

0.993

noa

0.990

noa

0.992

noa

0.991

noa

Aladdin Reagent Company Sinopharm Chemical Reagent Sinopharm Chemical Reagent Sinopharm Chemical Reagent

Table 3. Binodal Data for the POELE10 (1) + K2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa

Reagent was used without further purification.

Table 2. Binodal Data for the POELE10 (1) + (NH4)2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa 100w1

100w2

100w1

10.95 10.51 9.94 9.57 9.16 8.83 8.48 8.11 7.70 7.24

16.15 16.24 16.44 16.59 16.70 16.84 16.94 17.10 17.28 17.44

6.89 6.47 6.08 5.69 5.37 4.98 4.52 4.16 3.76 3.44

12.08 11.15 10.52 9.81 9.27 8.73 8.06 7.55 7.15 6.87

14.12 14.44 14.64 14.89 15.07 15.26 15.55 15.76 15.91 16.04

6.47 6.22 5.93 5.63 5.20 4.86 4.53 4.20 3.89 3.49

13.83 13.13 12.30 11.59 10.91 10.09 9.20 8.67 8.20

12.28 12.40 12.65 12.91 13.12 13.42 13.75 13.98 14.14

7.79 7.41 7.01 6.52 6.05 5.61 5.09 4.64 4.12

100w2

100w1

T = 288.15 K 17.61 2.99 17.79 2.58 17.96 2.24 18.16 1.90 18.31 1.64 18.48 1.50 18.70 1.22 18.87 0.93 19.04 0.70 19.21 0.55 T = 298.15 K 16.24 3.09 16.35 2.86 16.47 2.66 16.63 2.22 16.83 1.87 16.99 1.56 17.11 1.22 17.33 0.82 17.49 0.52 17.70 0.32 T = 308.15 K 14.30 3.68 14.49 3.27 14.67 2.91 14.87 2.40 15.06 1.98 15.25 1.63 15.54 1.34 15.72 1.01 16.03 0.72

100w2

100w1

100w2

19.44 19.67 19.85 20.06 20.25 20.36 20.60 20.95 21.23 21.50

0.42 0.34 0.24 0.17 0.12 0.10 0.08 0.04 0.02 0.01

21.77 21.93 22.17 22.42 22.71 22.96 23.15 23.41 23.83 24.25

17.89 18.02 18.13 18.39 18.64 18.83 19.04 19.41 19.74 20.02

0.26 0.19 0.14 0.12 0.10 0.09 0.05 0.04 0.02 0.02

20.21 20.51 20.79 20.96 21.18 21.37 21.61 21.90 22.35 22.56

16.30 16.52 16.75 17.10 17.45 17.74 18.05 18.45 18.83

0.36 0.20 0.06 0.05 0.03 0.02 0.01

19.29 19.63 19.99 20.34 21.99 22.89 23.72

100w1

100w2

100w1

14.65 13.69 12.50 11.56 10.81 9.97 9.13 8.52 7.91 7.26

13.31 13.61 13.95 14.33 14.54 14.86 15.26 15.51 15.81 16.08

6.89 6.38 6.03 5.70 5.38 4.92 4.49 3.97 3.49 3.10

17.35 16.50 15.69 14.63 13.89 13.17 12.41 11.81 10.93 10.37

10.22 10.35 10.53 10.81 11.00 11.26 11.53 11.72 12.03 12.27

9.86 9.44 8.88 8.43 7.82 7.30 6.66 6.27 5.60 4.96

17.93 16.97 15.98 15.11 14.31 13.70 13.04 12.45 11.89

8.71 8.82 9.07 9.30 9.47 9.60 9.80 9.93 10.15

10.90 10.05 9.62 9.16 8.49 7.85 7.11 6.30 5.53

100w2

100w1

T = 288.15 K 16.25 2.62 16.53 2.16 16.71 1.89 16.84 1.42 17.03 1.06 17.25 0.84 17.49 0.66 17.76 0.56 17.98 0.42 18.20 0.33 T = 298.15 K 12.50 4.35 12.69 3.79 12.89 3.55 13.12 3.13 13.36 2.56 13.65 2.28 13.96 1.85 14.17 1.50 14.51 1.23 14.89 1.01 T = 308.15 K 10.39 4.73 10.65 3.91 10.80 3.15 11.00 2.44 11.27 1.89 11.52 1.46 11.81 1.14 12.19 0.79 12.52 0.60

100w2

100w1

100w2

18.50 18.79 19.00 19.36 19.71 19.94 20.18 20.39 20.69 20.88

0.27 0.19 0.11 0.07 0.05 0.02 0.01

21.12 21.38 21.77 22.04 22.43 23.29 23.61

15.22 15.61 15.74 16.07 16.45 16.67 17.01 17.31 17.60 17.80

0.78 0.59 0.32 0.20 0.09 0.05 0.03 0.02 0.01

18.09 18.35 18.65 18.98 19.36 19.85 20.34 20.63 21.35

12.92 13.40 13.92 14.41 14.87 15.23 15.57 16.00 16.30

0.30 0.17 0.08 0.05 0.02 0.01

16.68 17.01 17.60 18.02 18.54 18.95

a

Standard uncertainties u are u(w) = 0.0001, u(T) = 0.05 K, and u(p) = 10 kPa.

water thermostat (Shanghai Hengping Instrument Factory, China) with an uncertainty of ± 0.1 K. The POELE10 solution was put into the vessel, and then the salt solution was dropped into until the solution becomes cloudy. The mass fractions of POELE10 and salt were noted by using an analytical balance (BS124S, Beijing Sartorius Instrument Co., China) with an uncertainty of ± 0.1·10−7 kg. In order to determine the next cloud point, one drop of water was added, and the abovementioned processes were repeated. On the basis of the lever rule23−26 (eqs 1 and 2) and the optimal empirical formula (eqs 3 and 4) the liquid−liquid equilibrium data for the investigated systems were calculated using Microsoft Visual Basic 6.0. The uncertainty of this method for the calculation of tie-line data is 0.0004.

a


of the POELE10 are 626.86 g·mol−1, 0.09 mg·L−1, 16.9, and 300.15 K, respectively. Organic salts [(NH4 ) 2 C4 H 4O 6 , K2C4H4O6, and Na2C4H4O6] were analytical grade reagents (GR, min. 99 % by mass fraction), which were obtained from the Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China). All reagents were used without further purification. The doubledistilled water was used in experiments (Table 1). 2.2. Apparatus and Procedure. The bimodal data were determined with a 50 mL glass vessel by following the cloudpoint method. The vessel was equipped with a coat in which the water was kept at the desired temperature in a DC-2008

w1t = (1 + λ)w1 − λw1b w2t = (1 + λ)w2 − λw2b

(1)

(λ = m b / m t )

(2)

w1t = f (w2t)

(3)

w1b = f (w2b)

(4)

In the above equations, w represents the mass of fraction, the subscripts “1” and “2” stand for the POELE10 and salt, and the 1844



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Table 4. Binodal Data for the POELE10 (1) + Na2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa 100w1

100w2

100w1

16.13 15.52 14.94 14.44 13.83 13.31 12.78 11.80 11.35

7.47 7.59 7.72 7.81 7.93 8.07 8.21 8.46 8.61

10.72 10.01 9.10 8.13 7.66 7.22 6.71 6.27 5.70

14.10 13.08 12.61 12.06 11.64 10.92 10.39 9.93 9.19

9.39 9.51 9.58 9.71 9.81 9.99 10.14 10.28 10.49

8.56 8.05 7.34 6.80 6.31 5.87 5.14 4.58 4.18

13.78 13.16 12.67 12.06 11.43 10.84 10.41 9.98 9.58 9.18 8.62 8.08

9.69 9.83 9.97 10.13 10.33 10.52 10.65 10.81 10.91 11.06 11.25 11.44

7.60 7.29 7.04 6.73 6.33 6.06 5.76 5.35 5.18 4.88 4.58 4.35

100w2

100w1

T = 288.15 K 8.75 5.19 8.92 4.61 9.24 4.13 9.51 3.68 9.67 3.33 9.82 2.66 9.99 2.15 10.14 1.56 10.34 1.14 T = 298.15 K 10.68 3.77 10.83 3.28 11.11 2.76 11.28 2.31 11.46 1.91 11.62 1.51 11.90 1.16 12.14 0.84 12.31 0.57 T = 308.15 K 11.61 4.01 11.75 3.73 11.88 3.48 12.01 3.07 12.21 2.82 12.30 2.61 12.41 2.42 12.63 2.21 12.71 1.86 12.87 1.57 13.00 1.17 13.10 1.01

100w2

100w1

100w2

10.53 10.76 10.97 11.14 11.30 11.65 11.92 12.23 12.57

0.79 0.44 0.23 0.15 0.07 0.04 0.02 0.01

12.86 13.24 13.53 13.86 14.22 14.52 14.82 15.28

12.49 12.72 13.03 13.28 13.54 13.77 14.00 14.24 14.49

0.34 0.18 0.12 0.05 0.03 0.02 0.01

14.72 15.02 15.30 15.70 16.10 16.71 17.37

13.27 13.43 13.53 13.73 13.86 13.99 14.10 14.22 14.40 14.57 14.79 14.95

0.80 0.57 0.45 0.29 0.15 0.12 0.09 0.05 0.03 0.02

15.16 15.42 15.56 15.89 16.15 16.40 16.58 16.74 16.97 17.07

Figure 2. Binodal curves of the POELE10 (1) + K2C4H4O6 (2) + H2O (3) ATPSs at (288.15, 298.15, and 308.15) K. △, 288.15 K; ○, 298.15 K; □, 308.15 K; solid line, reproduced by eq 6.

a


Figure 3. Binodal curves of the POELE10 (1) + Na2C4H4O6 (2) + H2O (3) ATPSs at (288.15, 298.15, and 308.15) K. △, 288.15 K; ○, 298.15 K; □, 308.15 K; solid line, reproduced by eq 6.

superscripts “t” and “b” stand for the top and bottom phase. The symbol “mt” and “mb” is the mass of solution in the top and bottom phases. The function f represents the optimal empirical formula. First, the appropriate amount of POELE10, salt, and water were added into the vessel and then it kept stirring for 15 min. Then, the sample was placed in the thermostat water bath of which the temperature was controlled at the constant temperature. Finally, the mass of the top phase and bottom phase was determined when the mixed solution was separated into two clear phases.

3. RESULTS AND DISCUSSION 3.1. Binodal Data and Correlation. The binodal data of the systems composed of POELE10 and organic salts [(NH4)2C4H4O6, K2C4H4O6, and Na2C4H4O6] were determined and are listed in Tables 2 to 4. The phase diagram for the three aqueous systems at different temperatures is shown in Figures 1 to 3. The binodal data were fit in accordance with the following three equations:

Figure 1. Binodal curves of the POELE10 (1) + (NH4)2C4H4O6 (2) + H2O (3) ATPSs at (288.15, 298.15, and 308.15) K. △, 288.15 K; ○, 298.15 K; □, 308.15 K; solid line, reproduced by eq 6. 1845



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Table 5. Values of Parameters of eq 5 for the POELE10 (1) + (NH4)2C4H4O6/K2C4H4O6/Na2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K T/K

a

288.15 298.15 308.15

34.17 53.33 50.99

288.15 298.15 308.15

5.323 79.19 54.16

288.15 298.15 308.15

73.62 76.82 61.56

b

d

R2

100SDa

−976.9 −1334 −1222

0.9977 0.9980 0.9994

0.16 0.16 0.10

−513.4 −1794 −1683

0.9971 0.9997 0.9995

0.22 0.10 0.12

−2336 −2630 −2946

0.9988 0.9989 0.9998

0.14 0.14 0.07

c

POELE10 + (NH4)2C4H4O6 + H2O 651.3 918.7 835.1 POELE10 + K2C4H4O6 + H2O −78.74 229.5 −603.5 1279 −444.8 1012 POELE10 + Na2C4H4O6 + H2O −608.9 1402 −644.0 1509 −564.7 1438 −288.9 −422.1 −391.2

exp 2 exp cal 0.5 SD = (∑ni=1(wcal is the corresponding data 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE10 in Tables 2 to 4 and w1 calculated using eq 5. n represents the number of binodal data.

a


a

b

288.15 298.15 308.15

119.7 62.37 −66.32

−47.62 −13.09 52.246

288.15 298.15 308.15

26.982 −23.69 −94.95

288.15 298.15 308.15

84.96 −76.92 15.47

d

R2

100SDa

0.3264 0.6297 1.111

0.9991 0.9992 0.9992

0.10 0.10 0.12

0.7152 0.7540 0.8935

0.9991 0.9990 0.9995

0.13 0.16 0.13

0.5008 0.9483 0.6552

0.9992 0.9990 0.9998

0.11 0.14 0.08

c

POELE10 + (NH4)2C4H4O6 + H2O 3.208 −3.001 −13.35 POELE10 + K2C4H4O6 + H2O 2.283 −5.064 27.29 −8.281 60.75 −12.82 POELE10 + Na2C4H4O6 + H2O −11.38 −3.468 60.74 −13.68 26.60 −8.705

exp 2 exp cal 0.5 SD = (∑ni=1(wcal is the corresponding data 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE10 in Tables 2 to 4 and w1 calculated using eq 6. n represents the number of binodal data.

a

w1 = exp(a + bw20.5 + cw2 + dw22)

(5)

w1 = aw23 + bw22 + cw2 + d

(6)

w1 = a exp(bw20.5 − cw23)

(7)


where w1 is the mass fraction of POELE10, w2 is the mass fraction of salts, and a, b, c, and d are the fitting parameters. Equation 5 was used to fit the binodal data of the alcohol− citrate aqueous two-phase systems at 298.15 K by Wang et al.27 The third-order polynomial equation (eq 6) was used for the correlation of binodal data of PEG−salt ATPSs.28 The binodal curves of many ATPSs29−34 were correlated with eq 7. In our work, the bimodal data of the investigated systems were fit with using these three equations. The fitting parameters a, b, c, and d were determined through the regression analysis of experimental binodal data along with the square of correlation coefficients (R2) and the corresponding standard deviations (SD) of eqs 5 to 7 for the investigative systems are given in Tables 5 to 7, respectively. By comparing the correlation coefficients and standard deviations shown in Tables 5 to 7, it was found that eq 6 is satisfactorily used to correlate the binodal curves for the studied systems. 3.2. Liquid−Liquid Equilibrium Data and Correlation. For the investigated systems, the tie-line data were calculated in accordance with the application of the lever arm rule to the

288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15

a

b

c

R2

POELE10 + (NH4)2C4H4O6 + H2O 2.018 −3.172 385.2 0.9901 0.0003 122.3 840.2 0.9970 0.0249 8.640 724.7 0.9989 POELE10 + K2C4H4O6 + H2O 0.0026 15.36 681.4 0.9973 0.4613 −1.413 530.7 0.9973 1.328 −5.370 670.3 0.9989 POELE10 + Na2C4H4O6 + H2O 0.0219 9.438 1242 0.9966 0.0674 6.128 1435 0.9975 0.1495 2.821 1719 0.9987

100SDa 0.34 0.19 0.14 0.23 0.27 0.19 0.23 0.22 0.19

a exp 2 exp 0.5 SD = (∑ni=1(wcal 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE10 in Tables 2 to 4 and w1cal is the corresponding data calculated using eq 7. n represents the number of binodal data.

relationship between the mass phase composition and the overall system composition. It has been discussed that for the studied systems eq 6 was the optimal fitting equation in the sections above. The tie-line data calculated were showed in Tables 8 to 10 and the corresponding tie-lines are given in 1846



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Table 8. Tie-Line Data for the POELE10 (1) + (NH4)2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa total system 100w1

a

POELE10-rich phase 100w2

100wt1

salt-rich phase

100wt2

7.99 7.99 8.00 8.01

17.50 17.99 18.50 19.47

20.17 21.33 22.57 24.52

10.65 10.58 10.43 10.36

8.00 7.99 8.01 8.00

16.50 17.00 17.51 18.00

23.03 24.42 25.71 26.91

10.11 10.02 9.90 9.87

8.01 7.99 8.01 8.02

15.49 15.97 16.49 17.00

26.53 28.28 30.47 32.52

9.59 9.39 9.17 8.99

100wb1 T = 288.15 K 0.68 0.39 0.20 0.08 T = 298.15 K 1.02 0.53 0.29 0.19 T = 308.15 K 1.90 1.19 0.71 0.44

100wb2

slope (k)

average of slope

21.56 22.23 22.92 23.81

−1.7856 −1.7985 −1.7928 −1.8164

−1.7983

19.52 20.22 20.87 21.39

−2.3414 −2.3434 −2.3195 −2.3207

−2.3312

17.48 18.21 18.91 19.52

−3.1248 −3.0736 −3.0580 −3.0498

−3.0765


Table 9. Tie-Line Data for the POELE10 (1) + K2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa total system 100w1

a


100wt1

salt-rich phase

100wt2

8.03 8.01 7.94 7.99

16.48 17.00 17.40 18.00

21.10 24.32 27.63 29.92

11.30 10.41 9.54 8.96

7.84 7.87 8.00 8.00

16.48 17.00 17.49 18.00

29.22 30.55 32.34 34.22

8.92 8.84 8.73 8.63

8.00 8.00 7.99 7.99

14.50 15.01 15.48 16.03

29.20 30.77 32.29 33.95

7.55 7.45 7.30 7.09

100wb1 T = 288.15 K 2.35 1.11 0.65 0.07 T = 298.15 K 0.31 0.16 0.08 0.04 T = 308.15 K 0.28 0.15 0.10 0.04

100wb2

slope (k)

average of slope

18.77 19.83 20.36 21.33

−2.5126 −2.4657 −2.4959 −2.4152

−2.4723

19.17 19.80 20.38 20.88

−2.8225 −2.7743 −2.7711 −2.7920

−2.7900

17.07 17.66 18.19 18.78

−3.0405 −3.0020 −2.9593 −2.9024

−2.9761


coefficient values (R2) and standard deviations (SD) are shown in Table 11. 3.3. Effect of the Salt Type on the Binodal Curves. Salt is an important factor affecting ATPS formation. The salt consists of the anion and cation, and the anion and cation are the fundamental elements affecting the phase diagram of ATPSs. We have reported the phase diagram of POELE10− (KOH, K2CO3, K2HPO4, (NH4)2HPO4, K3PO4) ATPSs at different temperatures in a previously published article.21,22 In the present work, the binodal curves of POELE10 and three organic salts are given. In order to clearly compare the effect of anion and cation on the binodal curves, the concentrations of POELE10 and all salts are shown in terms of molality in Figures 7 and 8, respectively. Figure 7 shows that the salts of ATPSs have the same cation and a different anion. From the figure, it was found that the phase-forming abilities of the salt in general strengthened with the increase in the valence of anion. In fact, the phase-forming ability of salt is proportional to its salting-out ability, which is related to the Gibbs free energy of

Figures 4 to 6. In the investigated systems, the tie-lines composition was correlated with using the Othmer−Tobias and Bancroft35 equations (eqs 8 and 9), which were widespread empirical correlation equations for the tie-lines of many systems.27,33,34,36 ⎛ 1 − w b ⎞n ⎛ 1 − w1t ⎞ 2 ⎟⎟ ⎟ = k1⎜⎜ ⎜ t b ⎝ w1 ⎠ ⎝ w2 ⎠

(8)

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

(9)

where w is the mass fraction, the subscript “1”, “2”, and “3” stand for the POELE10, salt, and water, respectively; and the superscripts “t” and “b” represent the top phase and bottom phase; and k1, k2, n, and r were the fitting parameters. The values of the parameters along with the square of correlation 1847



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Table 10. Tie-Line Data for the POELE10 (1) + Na2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa total system 100w1

a


100wt1

salt-rich phase

100wt2

8.00 8.00 8.01 7.98

12.50 13.01 13.50 13.98

22.42 25.37 28.20 30.31

8.24 7.97 7.74 7.63

8.01 8.00 8.01 8.00

11.99 12.50 12.99 13.49

24.10 27.18 29.23 31.57

8.00 7.77 7.64 7.51

8.00 8.01 7.99 7.99

11.01 11.51 12.00 12.49

28.44 30.84 33.22 35.90

6.25 6.13 6.02 5.91

100wb1 T = 288.15 K 2.06 1.17 0.73 0.38 T = 298.15 K 1.80 0.99 0.51 0.26 T = 308.15 K 1.24 0.51 0.24 0.04

100wb2

slope (k)

average of slope

14.28 15.01 15.54 16.17

−3.3728 −3.4401 −3.5187 −3.5073

−3.4597

13.55 14.25 14.90 15.49

−4.0215 −4.0451 −3.9576 −3.9268

−3.9877

12.59 13.29 13.86 14.41

−4.2934 −4.2390 −4.2093 −4.2243

−4.2415


Figure 4. Tie lines of the POELE10 (1) + (NH4)2C4H4O6 (2) + H2O (3) ATPSs at (288.15, 298.15, and 308.15) K. △, dashed line, 288.15 K; ○, dotted line, 298.15 K; □, solid line, 308.15 K.

Figure 5. Tie lines of the POELE10 (1) + K2C4H4O6 (2) + H2O (3) ATPSs at (288.15, 298.15, and 308.15) K. △, dashed line, 288.15 K; ○, dotted line, 298.15 K; □, solid line, 308.15 K.

Na +( −365 kJ ·mol−1) > K+( −295 kJ·mol−1)

hydration of the anions (ΔGhyd).37 It shows that the more negative the Gibbs free energy38 in the anions of the salt is, the stronger the salting-out ability of the salt will be. As observed in Figure 7, the salting-out ability of these salts follows this ordering.

> NH4 +( −285 kJ ·mol−1)

In summary, the ion (anion or cation) of salts with the more negative Gibbs free energy requires a lower concentration to promote the formation of ATPSs, which means that the binodal curve tends toward to the axis and the biphasic region expands with increasing the absolute of the negative Gibbs free energy of ions. 3.4. Effect of the Temperature on the Phase Diagram. The binodal curves for the three aqueous systems at different temperatures are shown in Figures 1 to 3, from which it was concluded that the binodal curves of the ATPS were moving toward the axes when the temperature rises from 288.15 K to 308.15 K. This means that the ATPS is easier to form at higher temperatures. The effect of temperature on the binodal curves springs from the effect of temperature on the hydrophobicity of POELE10. The POELE10 becomes more hydrophobic with increasing temperature, which was confirmed with using the

PO4 3 −( −2765 kJ·mol−1) > HPO4 2 −( −1789 kJ ·mol−1) > CO32 −(− 1315 kJ ·mol−1) > C4 H4O6 2 − ( −1090 kJ ·mol−1) > OH−( −430 kJ ·mol−1)

The salts of ATPSs fall into two groups (K2HPO4/ (NH4)2HPO4, (NH4)2C4H4O6/K2C4H4O6/Na2C4H4O6) in Figure 8. The salts contain the same anion, and they also have different cations in each group. The salting-out abilities of these salts are also related to the Gibbs free energy of hydration of the cations: the salting-out ability of the salt is more powerful when the value of Gibbs free energy in anions of the salt is more negative. Thus, the ordering of the salting-out ability of these salts goes as follows. 1848



Article

excess specific volume developed by Zafarani-Moattar et al.32 in our previously published article.22 Thus, the two-phase area of the POELE10−salt ATPS expands with rising temperature. The tie-lines of POELE10−[(NH 4 ) 2 C 4 H 4 O 6 /K 2 C 4 H 4 O 6 / Na2C4H4O6] ATPSs at different temperatures were plotted in the Figures 4 to 6, respectively. In this work the slope of the tie-line (STL) was expressed as STL = ΔY/ΔX, where ΔX presents the concentration of the salt in the top phase minus that of the salt in the bottom phase, and ΔY presents the concentration of POELE10 in the top phase minus that in the bottom phase. Tables 8 to 10 found that the absolute value of STL increases with the rising temperature, which is observed visually from Figures 4 to 6. In sum, the increase in the temperature will lead to the expansion of the two-phase area of the phase diagram and the increase in the absolute value of STL. 3.5. Effective Excluded Volume and Phase-Separation Abilities of Salts. The effective excluded volume (EEV) is calculated with the binodal model that was developed by Guan et al. based on the statistical geometry methods.39 This binodal model was originally used in the systems containing two types

of polymers. In our paper, we applied this simplified model to the aqueous surfactant−salt systems, and the corresponding equation is written as ⎛ w ⎞ w * 2 ⎟ + V 213 * 1 =0 ln⎜V 213 M2 ⎠ M1 ⎝

(10)

where w1 and w2 are the mass fractions of POELE10 and salts, V*213 is the scaled EEV of salt, and M1 and M2 are molecular masses of POELE10 and salts, respectively. For the investigated systems, the EEV values along with the square of correlation coefficients (R2) and standard deviations (SD) are given in Table 12, in which the value of EEV of three salts at the constant temperature is Na2C4H4O6 > K2C4H4O6 > (NH4)2C4H4O6. This illustrated that the phase-forming ability of salt strengthened with rising the value of EEV of salts, which is consistent with the previous discussion in Section 3.3. Meanwhile, for the same ATPS, the value of EEV of salt increased with the temperature changing from 288.15 K to 308.15 K. That means that the increase in temperature is beneficial to

Figure 7. Effect of the anion of the salt on the binodal curves at temperature T = 298.15 K. ▲, magenta, POELE10−K3PO4 ATPS; ●, red, POELE10−K2HPO4 ATPS; ★, green, POELE10−K2CO3 ATPS; ■, blue, POELE10−K2C4H4O6 ATPS; ▼, black, POELE10−KOH ATPS.

Figure 6. Tie lines of the POELE10 (1) + Na2C4H4O6 (2) + H2O (3) ATPSs at (288.15, 298.15, and 308.15) K. △, dashed line, 288.15 K; ○, dotted line, 298.15 K; □, solid line, 308.15 K.

Table 11. Values of Parameters of eqs 8 and 9 for the POELE10 (1) + (NH4)2C4H4O6/K2C4H4O6/Na2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K T/K

k1

n

288.15 298.15 308.15

0.3201 0.2636 0.1007

1.950 1.794 2.140

288.15 298.15 308.15

0.0443 0.1092 0.1208

3.026 2.161 1.898

288.15 298.15 308.15

0.0208 0.0404 0.0366

2.851 2.346 2.188

k2

r

R12

POELE10 + (NH4)2C4H4O6 + H2O 2.009 0.4736 0.9963 2.396 0.4974 0.9988 3.238 0.3997 0.9924 POELE10 + K2C4H4O6 + H2O 3.005 0.2742 0.9614 3.025 0.4310 0.9772 3.259 0.5119 0.9996 POELE10 + Na2C4H4O6 + H2O 4.189 0.2983 0.9901 4.273 0.3703 0.9930 4.857 0.4088 0.9906

R22

100SD1a

100SD2a

0.9976 0.9994 0.9960

0.31 0.14 0.46

0.51 0.21 0.71

0.9535 0.9795 0.9999

1.68 0.82 0.07

3.87 1.27 0.08

0.9866 0.9893 0.9947

0.86 0.82 0.67

1.89 1.56 0.95

top 2 bot bot 2 0.5 SD = [(∑Ni=1((wtop i,j,cal − wi,j,exp) + (wi,j,cal − wi,j,exp) )/2N] , where N is the number of tie lines and j = 1 and j = 2. SD1 and SD2 represent the mass percent standard deviations for POELE10 and salt, respectively. a

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formation of ATPS strengthened with the increase in the value of EEV.

■

AUTHOR INFORMATION

Corresponding Author

*Y.Y.: E-mail:[email protected]. Tel.: +86-051188790683. Fax: +86-0511-88791800. Funding

This work was supported by the National Natural Science Foundation of China (Nos. 21076098 and 21206059), Ph.D. Programs Foundation of Ministry of Education of China (No. 20133227120006), the Natural Science Foundation of Jiangsu Province (No. BK2011529), China Postdoctoral Science Foundation funded project (No. 2013M531284), Doctor Innovation Programs Foundation of Jiangsu Province (No. CXLX12_0645), Jiangsu Postdoctoral Science Foundation funded project (No. 1101036C), the Programs of Senior Talent Foundation of Jiangsu University (Nos. 11JDG029 and 12JDG079), Siping Science and Technology Development Program Foundation (No. 2012042), the Natural Science Foundation of Jilin Province (No. 20130101179JC_15), and Science and Technology Research Foundation of Jilin Province Department of Education (No. 2014_158).

Figure 8. Effect of the cation of the salt on the binodal curves at temperature T = 298.15 K. □, black, POELE10−K2HPO4 ATPS; ○, red, POELE10−(NH4)2HPO4 ATPS; ★, magenta, POELE10− Na2C4H4O6 ATPS; ▲, blue, POELE10−K2C4H4O6 ATPS; ▼, green, POELE10−(NH4)2C4H4O6 ATPS.

Table 12. Values of Parameters of eq 10 for the POELE10 (1) + (NH4)2C4H4O6/K2C4H4O6/Na2C4H4O6 (2) + H2O (3) ATPSs at T = (288.15, 298.15, and 308.15) K T/K 288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15

V213 * /g·mol−1

R2

POELE10 + (NH4)2C4H4O6 + H2O 906.0 0.9850 963.0 0.9655 1031 0.9325 POELE10 + K2C4H4O6 + H2O 1147 0.9627 1332 0.9841 1495 0.9750 POELE10 + Na2C4H4O6 + H2O 1378 0.9888 1392 0.9714 1573 0.9835

Notes

The authors declare no competing financial interest.

■

SDa

ACKNOWLEDGMENTS We are grateful to Computing Center of Jilin Province for essential support.

0.09 0.09 0.19

■

0.09 0.08 0.13

REFERENCES

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exp 2 exp 0.5 SD = (∑ni=1(wcal 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE10 in Tables 2 to 4 and wcal 1 is the corresponding data calculated using eq 10. n represents the number of binodal data. a

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4. CONCLUSION In this paper, the binodal data and the tie-line data of the ATPS consisted of POELE10 and organic salts [(NH4)2C4H4O6, K2C4H4O6, and Na2C4H4O6] at different temperatures were given. These experimental data were correlated with the empirical equation, and it produced good effects. First, the relationship between the salting-out ability of salt and the Gibbs free energy of hydration of the ions was discussed. It was found that, in regard to the salts with the same cation, their salting-out abilities are stronger when the Gibbs free energy of their anion is more negative. In the same way, the more negative the Gibbs free energy of cation of salt is, the stronger the salting-out ability of salt is for those salts containing the same anion. Second, raising the temperature of the system will lead to the expansion of the two-phase region and the increase in the absolute value of slope of the tie-line. Finally, the EEV of value was given and analyzed, and it was found that the phase 1850



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