Measurement and Correlation of Phase Equilibria in Aqueous Two

Article Cite This: J. Chem. Eng. Data 2018, 63, 625−634

pubs.acs.org/jced

Measurement and Correlation of Phase Equilibria in Aqueous TwoPhase Systems Containing Polyoxyethylene Cetyl Ether and Three Organic Salts at Different Temperatures Xueqing Yang,† Yang Lu,*,†,‡ Zhuo Sun,† Keyu Cui,‡ and Zhenjiang Tan*,† †

Jilin Provincial Key Laboratory for Numerical Simulation, Jilin Normal University, 1301 Haifeng Street, Siping, 136000, China Key Laboratory of Preparation and Application of Environmental Friendly Materials, Jilin Normal University, Ministry of Education, Changchun, 130103, China

‡

ABSTRACT: The polymer polyoxyethylene(20) cetyl ether (C56H114O21, POELE20) and three salts (K2C2O4, K2C4H4O6, and K3C6H5O7) were the phase-forming materials to build the aqueous two-phase system (ATPS) at the temperatures 288.15, 298.15, and 308.15 K. The data of the phase diagram including binodal curve data and tie-line data were determined and fitted by classical equations, and they obtained the satisfactory correlation effect. The phase-forming ability of salt composed of the same cation was investigated by three factors, namely, the valence of the anion, the Gibbs free energy of the anion, and the value of effective excluded volume (EEV). It was found that the phase-forming ability of salt strengthened when the values of said three factors went up. The results of the analysis on the data from the present work and that in our previous paper showed that the order of the phase-forming ability of salts was KOH < K2C2O4 < K2C4H4O6 < K2CO3 < K3C6H5O7 < K3PO4. The effect of temperature on phase-forming of the studied ATPSs was discussed through the phase diagram and EEV value, and it was showed that the increase in temperature is beneficial to separating two phases for ATPSs. For the investigated systems, the effect of temperature on the liquid−liquid equilibrium of ATPSs was studied by the phase diagram and the slope of the tie-line (STL), and it was found that the absolute value of the STL increased with rising temperature.

1. INTRODUCTION As a new green separation/enrichment technology, the aqueous two-phase extraction (ATPE) has many advantages, for example, being easy to operate, timesaving, highly efficient, green, and environmental friendly. ATPE has been applied in fields ranging from the quantitative separation and extraction of metal ions1−5 and the separation and purification of active biosubstance6−13 to the extraction of natural products.14−17 Currently, the aqueous two-phase system (ATPS) falls into four categories: polymer−salt ATPS,18−23 two-polymer ATPS,24,25 micromolecule alcohol−salt ATPS,26,27 and ion liquid−salt ATPS.28,29 The last three kinds of ATPSs are hard to convert from the laboratory prototype into mass production for the following reasons. First, the viscosity of the two-polymer system is high. Second, the micromolecule alcohol is extremely volatile. Finally, the cost of ion liquid is higher. One polymer of two-polymer ATPS is replaced with salt in polymer−salt ATPS. This results in the viscosity being reduced and the cost of system being cut down, and meanwhile, good biocompatibility is retained. Therefore, polymer−salt ATPS is worth developing and it has promising and prospecting application as the important branch in the ATPS field. Due to the heterogeneous nature of the phase-forming substances and target object, the determination of underlying data of ATPS is the prerequisite for the theoretical and applied research on ATPS. And the © 2018 American Chemical Society

calculation and correlation of experimental data is the foundation of overall research on the conditions of the phaseforming and liquid−liquid equilibrium. It was found that polyoxyethylene n-alkyl ether was an appropriate option for building polymer−salt ATPS because they were composed of two types of diametrically opposed components: polyoxyethylene (hydrophilic) and alkyl (hydrophobic). In our previous papers,30−37 the polyoxyethylene(10) lauryl ether (POELE10, C32H66O11) and polyoxyethylene(20) cetyl ether (POELE20, C56H114O21) were used in the ATPS, and the ATPSs composed of POELE10 and 14 kinds of salt have been given. The phase behaviors of the ATPSs containing POELE20 and six kinds of inorganic salt (KOH, K2CO3, K3PO4, Li2SO4, MgSO4, and ZnSO4) have been reported in our articles.31,32 Although the phase-forming ability of organic salt is weaker than the inorganic salt with the same valence, the organic salt has the merit of easy biodegradation. Therefore, the phase behaviors of the ATPSs containing POELE20 and organic salt will be studied in this paper. Received: September 18, 2017 Accepted: February 2, 2018 Published: February 7, 2018 625

DOI: 10.1021/acs.jced.7b00831 J. Chem. Eng. Data 2018, 63, 625−634

Journal of Chemical & Engineering Data

Article

2. EXPERIMENTAL SECTION 2.1. Materials. Organic salts (K2C2O4·H2O, K2C4H4O6·1/2H2O, and K3C6H5O7·H2O) purchased from the Liaoji Trading Company (Siping, China) were analytical grade reagents (GR, min. 99% by mass fraction). The salts were placed in the dryer (normal temperature and pressure) before being used. And the crystal water was taken into account when the concentration of salt stock solution was calculated. The nonionic surfactant POELE20 was obtained from Zhengzhou Alfachem Co., Ltd. (Zhengzhou, China). The POELE20 was characterized as follows: the quoted purity of POELE20 was greater than 0.99 mass fractions, the critical micelle concentration (CMC) is 0.07 mg·L−1, the hydrophilic− lipophilic balance (HLB) is 11.5, the average molar mass is 1123.50 g·mol−1, and the melting point is 311.15 K. The concentration of POELE20 stock solution was obtained gravimetrically after being kept drying in a desiccator at 50 °C for roughly 2 days until the mass remained constant. All reagents were used directly in experiments without further processing. The double distilled water was used in experiments. 2.2. Apparatus and Procedure. A 50 mL glass vessel was used to determine the binodal data according to the turbidimetric method. The POELE20 solution was put into the vessel. The solution in the vessel was kept under constant temperature through coating the vessel by the water thermostat (HK-ZK1, YIKE Instrument Factory, Shanghai, China). The salt solution was dropped into the vessel, and one drop of water was added in the solution when the solution became cloudy. The mass fractions of two phase-forming matters (POELE20 and salt) were determined by using an analytical balance (BS124S, Beijing Sartorius Instrument Co., China) with a precision of ±1.0 × 10−7 kg. The next cloud point was determined following the above-mentioned processes. The tie-line data were obtained by using the following method. The feed samples were prepared by mixing the appropriate amounts of POELE20, salt (K2C2O4, K2C4H4O6, or K3C6H5O7), and water in the vessel. The samples were placed in a thermostat and kept for 6 h after the samples kept stirring for 15 min. The thermostat water bath was controlled at a constant temperature. The mass of POELE20 and salt in the top phase and bottom phase was determined when the mixed solution was separated into two clear phases. A flame photometer (TAS-968, Beijing Purkinje General Instrument Co., Ltd., China) was used to determine the mass of salt in two phases. The measurement uncertainties were statistically analyzed by estimating the corresponding mean standard deviation, with values equal to ±0.0003.38−40 The mass fraction of POELE20 in two phases was determined by a refractometer (WZS-I 811639, Shanghai, China) with a precision of ±0.0001. The relationships between the mass fractions of POELE20 (w1), the mass fractions of salt (w2), and the index of refraction of the mixed solution (nD) were represented by the following equation, and the precision of this method was 0.0006 nD = n0 + a1w1 + a 2w2

Table 1. Values of Parameters of eq 1 for Aqueous Solution of POELE20 + K2C2O4/K2C4H4O6/K3C6H5O7 at 298.15 K system

n0

a1

a2

POELE20 + K2C2O4 POELE20 + K2C4H4O6 POELE20 + K3C6H5O7

1.3339 1.3330 1.3342

0.1404 0.1395 0.1382

0.1459 0.1891 0.1741

determined at different temperatures. The binodal data of studied systems were determined and listed in Tables 2−4. The Table 2. Binodal Data for the POELE20(1) + K2C2O4(2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K and Pressure p = 0.1 MPaa 100w1

100w2

100w1

5.61 5.39 5.03 4.70 4.38 4.04 3.70

13.94 14.01 14.12 14.22 14.30 14.40 14.50

3.41 2.91 2.63 2.27 2.03 1.76 1.49

8.04 7.72 7.41 7.05 6.54 6.19 5.63 4.94

12.37 12.40 12.45 12.51 12.60 12.70 12.81 12.99

4.52 4.16 3.73 3.34 3.00 2.64 2.25 1.86

9.60 9.17 8.77 8.47 7.89 7.31 6.76

9.65 9.75 9.88 9.96 10.12 10.28 10.42

6.20 5.83 5.33 4.92 4.53 4.06 3.62

100w2

100w1

T = 288.15 K 14.61 1.24 14.79 1.03 14.90 0.84 15.10 0.69 15.21 0.45 15.33 0.31 15.51 0.22 T = 298.15 K 13.12 1.58 13.25 1.32 13.38 1.11 13.50 0.95 13.60 0.82 13.73 0.70 13.87 0.51 14.07 0.37 T = 308.15 K 10.58 3.07 10.71 2.65 10.87 2.17 11.01 1.79 11.14 1.48 11.31 1.24 11.47 0.88

100w2

100w1

100w2

15.68 15.88 16.02 16.17 16.43 16.63 16.85

0.12 0.07 0.04 0.03 0.02 0.01 0.12

17.04 17.29 17.45 17.65 17.87 18.13 17.04

14.17 14.34 14.45 14.54 14.63 14.73 14.91 15.09

0.29 0.10 0.08 0.03 0.02

15.24 15.60 15.94 16.27 16.58

11.71 11.87 12.10 12.29 12.50 12.67 12.93

0.50 0.18 0.09 0.07 0.05 0.03 0.02

13.26 13.62 13.96 14.18 14.36 14.52 14.95

a

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

binodal curves of three ATPSs at different temperatures were shown in Figures 1−3. Nine widely used empirical equations were used to fit the binodal data, and it was found that the following three equations were suitable for the present study

(1)

w1 = exp(a + bw2 0.5 + cw2 + dw2 2)

(2)

w1 = aw2 3 + bw2 2 + cw2 + d

(3)

w1 = a exp(bw2 0.5 − cw2 3)

(4)

where w1 and w2 are the mass fraction of POELE20 and salts and a, b, c, and d are the fitting parameters. Liu et al.19 used eq 3 to fit the binodal data of the Triton X-100 + sodium sulfate + water ATPS at five temperatures (293.15−313.15 K). The binodal data of polymer−salt ATPSs was correlated by the third-order polynomial equation (eq 3), and the equation analogue effect was good. Equation 4 was widely used to fit the binodal curves of many ATPSs.6,19,30,41−50 In this work, the experimental binodal data of three ATPSs were regressed and

where n0, a1, and a2 are constants; the values of the three parameters are given in Table 1 for the investigated ATPSs.

3. RESULTS AND DISCUSSION 3.1. The Binodal Data and Correlation. The ATPSs containing POELE20 and organic salts (K2C2O4, K2C4H4O6, or K3C6H5O7) were developed, and their phase diagrams were 626



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Table 3. Binodal Data for the POELE20(1) + K2C4H4O6(2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K and Pressure p = 0.1 MPaa 100w1

100w2

100w1

12.23 11.65 10.73 9.82 8.89 8.15 7.51 6.90

14.50 14.63 14.94 15.32 15.73 15.98 16.32 16.63

6.45 6.02 5.62 5.15 4.63 4.25 3.72 3.30

12.51 11.74 11.12 10.45 9.69 8.98 8.43 7.77 7.28

13.69 13.78 13.90 14.08 14.33 14.60 14.81 15.05 15.21

6.88 6.27 5.85 5.50 5.18 4.74 4.26 3.84 3.41

12.40 11.72 11.11 10.53 9.70 9.25 8.26 7.67

11.42 11.57 11.77 11.96 12.26 12.44 12.84 13.04

6.98 6.19 5.57 4.85 4.21 3.55 2.92 2.37

100w2

100w1

T = 288.15 K 16.83 2.97 17.01 2.62 17.21 2.14 17.41 1.74 17.67 1.30 17.84 0.94 18.16 0.60 18.37 0.37 T = 298.15 K 15.34 2.92 15.62 2.52 15.79 2.11 15.96 1.78 16.07 1.45 16.31 1.20 16.51 0.81 16.68 0.66 16.88 0.51 T = 308.15 K 13.35 1.93 13.68 1.57 13.94 1.28 14.30 1.05 14.62 0.71 14.95 0.48 15.31 0.26 15.63 0.10

Table 4. Binodal Data for the POELE20(1) + K3C6H5O7 (2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K and Pressure p = 0.1 MPaa

100w2

100w1

100w2

100w1

100w2

100w1

18.58 18.77 19.01 19.31 19.65 19.96 20.33 20.96

0.21 0.07 0.03 0.03 0.03

21.38 21.76 22.13 22.39 23.54

11.74 10.26 9.38 8.97 8.41 7.89 7.21

14.56 15.03 15.43 15.62 15.78 16.06 16.28

6.62 6.17 5.63 5.24 4.68 4.19 3.83

17.16 17.39 17.61 17.84 18.06 18.21 18.56 18.75 19.02

0.44 0.31 0.21 0.11 0.09 0.07

19.56 19.99 20.47 20.82 21.20 21.83

11.93 10.98 10.25 9.51 8.93 8.31 7.80 7.34 6.94

12.84 13.19 13.41 13.70 13.92 14.16 14.36 14.49 14.64

6.28 5.72 5.03 4.69 4.30 3.91 3.59 3.23 2.79

15.94 16.17 16.44 16.67 17.03 17.30 17.67 18.03

0.08 0.06 0.04 0.03 0.01

18.22 18.58 18.80 19.02 19.26

13.24 12.50 11.80 11.17 10.60 10.08 9.39 8.62

10.47 10.68 10.89 11.05 11.21 11.35 11.58 11.82

7.97 7.38 6.91 6.27 5.63 5.06 4.49 3.91


analyzed by computer and the fitting parameters a, b, c, and d of three euqations were given in Tables 5−7, where the square of correlation coefficients (R2) and the corresponding standard deviations (sd) were also shown. It was found that eq 3 has a higher goodness-of-fit than the other two equations by comparison of the correlation coefficients and standard deviations given in three tables. 3.2. Liquid−Liquid Equilibrium Data and Correlation. The tie-line data of the investigated systems were determined at three temperatures (288.15, 298.15, and 308.15 K) which were given in Tables 8−10. The corresponding tie-lines were shown in Figures 4−6. As the widespread empirical correlation equations, the Othmer−Tobias and Bancroft equations (eqs 5 and 6) were used to correlate the tie-line compositions of many ATPSs.22,31,32,42−44,51 In investigated systems, the tie-lines data was fitted by using these two equations

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

100w1

T = 288.15 K 16.54 3.43 16.74 2.94 16.98 2.35 17.11 2.00 17.31 1.46 17.45 0.97 17.63 0.34 T = 298.15 K 14.90 2.35 15.11 1.97 15.35 1.63 15.49 1.36 15.63 0.95 15.83 0.68 15.98 0.50 16.15 0.28 16.37 0.20 T = 308.15 K 12.06 3.40 12.27 2.86 12.44 2.35 12.70 1.96 12.98 1.62 13.20 1.14 13.44 0.82 13.74 0.46

100w2

100w1

100w2

17.83 18.13 18.47 18.69 19.03 19.52 20.26

0.23 0.12 0.06 0.05 0.04 0.02

20.76 21.02 21.28 21.63 21.99 22.57

16.65 16.85 17.13 17.32 17.70 17.98 18.21 18.46 18.83

0.11 0.09 0.06 0.04 0.02 0.02 0.02

19.14 19.43 19.96 20.21 20.65 21.26 22.18

13.98 14.27 14.55 14.75 14.99 15.36 15.64 15.98

0.20 0.12 0.07 0.05 0.02 0.01

16.48 16.74 17.14 17.56 17.99 18.45

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

a

⎛ 1 − w b ⎞n ⎛ 1 − w1t ⎞ 2 ⎟⎟ ⎟ = k1⎜⎜ ⎜ t b ⎝ w1 ⎠ ⎝ w2 ⎠

100w2

Figure 1. Binodal curves of the POELE10(1) + K2C2O4(2) + H2O(3) ATPSs at 288.15, 298.15, and 308.15 K. Solid line, reproduced by eq 3.

(5)

top phase and bottom phase), and k1, k2, n, and r were the fitting parameters whose values were shown in Table 11. The square of correlation coefficient values (R2) and standard deviations (sd) were shown in Table 11, and it was found that these two equations were qualified for the studied systems. 3.3. Effect of the Salt Type on the Binodal Curves. As an important affecting factor of phase-forming of ATPS, the effect of salt type on the binodal curves was studied. The anion

(6)

where w stands for the mass fraction of materials in ATPS, the subscripts “1”, “2”, and “3” respectively represent three substances of systems (POELE20, salt, and water), the superscripts “t” and “b” represent two phases of ATPS (the 627



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and cation are considered to be the fundamental factors affecting the ATPSs forming because they are combined to form salt. The phase diagrams of POELE20−(KOH, K2CO3, and K3PO4) ATPSs have been reported at different temperatures in the previous article.32 In the present work, the binodal curves of POELE20 and three organic salts (K2C2O4, K2C4H4O6, or K3C6H5O7) are given. The effect of salt type on the binodal curves will be discussed in terms of anion because these six salts (KOH, K2CO3, K2C2O4, K2C4H4O6, K3C6H5O7, and K3PO4) have the same cation and different anion. In Figure 7, the concentrations of two phase-forming substances (POELE20 and salts) were shown in terms of molality in order to clearly compare the effect of salt type on the binodal curves. It was found that the valence of the anion is an important factor affecting the phase-forming abilities of salt; namely, the phase-forming ability of salt composed of a higher valence anion is stronger when the salts are of the same cation. Therefore, the order of phase-forming abilities of these six salts is as follows: (KOH) < (K2CO3, K2C2O4, K2C4H4O6) < (K3C6H5O7, K3PO4). Further, the reason affecting the phaseforming ability of salt composed of the same valence anion was illustrated and it was found that the Gibbs free energy of hydration of ions (ΔGhyd)52 is also a factor affecting the phaseforming ability of salt. The Gibbs free energies of hydration of anions were given in Table 12 for the investigated salts.53−56 From the Gibbs free energies of hydration of anions in Table 12 and the binodal curves of ATPSs in Figure 7, we found that the more negative the Gibbs free energy in anions of the salt is, the stronger the salting-out ability of the salt is. However, this approach fails in the potassium citrate. Although the Gibbs free energy of C6H5O73− (ΔGhyd = 2793 kJ·mol−1) is more negative, it provided a two-phase region smaller than the PO43− (ΔGhyd = 2765 kJ·mol−1). The unexpected behavior of citrate was already observed in other polymer−salt ATPSs.53,57−59 These showed that the empirical rule for the formation of ATPS based on the Gibbs free energy did not live up to citrates. Therefore, for the studied ATPS, the phase-forming abilities of these salts followed this ordering: KOH < K2C2O4 < K2C4H4O6 < K2CO3 < K3C6H5O7 < K3PO4. 3.4. Effective Excluded Volume. Besides the valence of the ion and the Gibbs free energy of hydration of ions, it was found that the effective excluded volume (EEV) developed by Guan et al.60 also affects the phase-forming abilities of salts. The

Figure 2. Binodal curves of the POELE10(1) + K2C4H4O6(2) + H2O(3) ATPSs at 288.15, 298.15, and 308.15 K. Solid line, reproduced by eq 3.

Figure 3. Binodal curves of the POELE10(1) + K3C6H5O7(2) + H2O(3) ATPSs at 288.15, 298.15, and 308.15 K. Solid line, reproduced by eq 3.

Table 5. Values of Parameters of eq 2 for the POELE10(1) + K2C2O4/K2C4H4O6/K3C6H5O7(2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K T (K)

a

b

288.15 298.15 308.15

44.04 75.00 60.79

−456.0 −1087 −571.2

288.15 298.15 308.15

62.20 5.163 6.485

−486.5 −88.87 −94.71

288.15 298.15 308.15

53.23 53.13 60.47

−443.2 −449.6 −499.6

c POELE20 + K2C2O4 + H2O 1223 3400 1486 POELE20 + K2C4H4O6 + H2O 1045 278.9 288.2 POELE20 + K3C6H5O7 + H2O 998.4 1041 1150

R2

100sdα

−2427 −7568 −3127

0.9995 0.9810 0.9995

0.0402 0.3430 0.0674

−1453 −671.6 −738.0

0.9971 0.9973 0.9982

0.1900 0.1886 0.1667

−1493 −1686 −1935

0.9989 0.9996 0.9992

0.1125 0.0675 0.1159

d

exp 2 exp cal 0.5 sd = (∑ni=1 (wcal 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE20 in Tables 1−3 and w1 is the corresponding data calculated using eq 2. n represents the number of binodal data. a

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Table 6. Values of Parameters of eq 3 for the POELE10(1) + K2C2O4/K2C4H4O6/K3C6H5O7 (2) + H2O (2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K T (K)

a

b

288.15 298.15 308.15

−693.0 −728.4 2.144

379.6 380.8 42.80

288.15 298.15 308.15

65.88 −25.53 64.69

−18.61 39.00 −8.353

288.15 298.15 308.15

104.0 −49.64 15.27

−34.41 49.28 19.69

c POELE20 + K2C2O4 + H2O −69.32 −65.98 −12.43 POELE20 + K2C4H4O6 + H2O −1.512 −12.84 −3.651 POELE20 + K3C6H5O7 + H2O 0.4148 −13.86 −8.318

d

R2

100sdα

4.220 3.792 0.895

0.9997 0.9992 0.9997

0.0291 0.0696 0.0491

0.531 1.214 0.552

0.9986 0.9982 0.9998

0.1309 0.1568 0.0579

0.4667 1.196 0.7698

0.9978 0.9968 0.9997

0.1578 0.1993 0.0688

exp 2 exp cal 0.5 sd = (∑ni=1 (wcal 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE10 in Tables 1−3 and w1 is the corresponding data calculated using eq 3. n represents the number of binodal data. a

Table 7. Values of Parameters of eq 4 for the POELE20(1) + K2C2O4/K2C4H4O6/K3C6H5O7(2) + H2O + 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

a

b

c

POELE20 + K2C2O4 + H2O 25.31 −7.635 1192 9.972 −5.551 1517 2.738 −6.525 1434 POELE20 + K2C4H4O6 + H2O 0.0001 28.90 857.6 0.0004 21.64 965.3 0.0025 16.47 1121 POELE20 + K3C6H5O7 + H2O 1.539 −2.992 442.8 0.0010 19.45 1035 0.0094 12.70 1287

R2

Table 8. Tie-Line Data for the POELE20(1) + K2C2O4(2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K and Pressure p = 0.1 MPaa

100sdα total system

0.9969 0.9956 0.9935

0.0996 0.1686 0.2479

0.9975 0.9975 0.9983

0.1805 0.1857 0.1641

0.9856 0.9978 0.9984

0.4105 0.1676 0.1676

100w1

100w2

100wt1

7.00 7.00 7.00 6.99

13.75 13.99 14.25 14.49

15.18 19.42 22.29 24.66

7.00 7.00 7.00 7.00

12.75 13.01 13.26 13.49

20.41 23.36 26.09 29.14

7.00 7.00 7.00 7.00

11.00 11.25 11.50 11.75

23.16 25.51 27.84 30.55

exp 2 exp 0.5 sd = (∑ni=1 (wcal 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE20 in Tables 1−3 and wcal 1 is the corresponding data calculated using eq 4. n represents the number of binodal data. a

EEV represents the smallest spacing of species i which will accept an individual j molecule in an i−j binary system.60 This EEV based on the statistical geometry methods was originally used to compute the binodal data of ATPS composed of two types of polymers. In this work, this simplified EEV model was applied to the binodal data of these POELE20−salt ATPSs. The simplified EEV equation60 was written as ⎛ w ⎞ w * 2 ⎟ + V 213 * 1 =0 ln⎜V 213 M2 ⎠ M1 ⎝

POELE10-rich phase 100wt2

salt-rich phase 100wb1

100wb2

T = 288.15 K 12.07 4.30 14.31 11.50 2.88 14.83 11.16 1.91 15.29 10.88 1.29 15.61 T = 298.15 K 10.58 3.56 13.35 10.36 2.64 13.72 10.11 1.66 14.15 9.85 1.02 14.44 T = 308.15 K 8.56 3.60 11.51 8.46 2.85 11.85 8.37 2.04 12.21 8.26 1.31 12.58

slope (k)

average of slope

−4.856 −4.970 −4.938 −4.928

−4.923

−6.112 −6.170 −6.052 −6.113

−6.112

−6.627 −6.671 −6.704 −6.764

−6.691

a


In sum, the phase-forming ability of salt was affected by three aspects: the valence of the ion, the Gibbs free energy of ions, and the EEV value. The increase in the valence of the ion, the absolute value of the Gibbs free energy of ions, and the EEV value will strengthen the phase-forming ability of salt. 3.5. Effect of the Temperature on the Phase Diagram. The effect of temperature on the phase diagram can be divided into the effect on the binodal curve and the effect on the tielines. The effect of temperature on the binodal curve was studied by the phase diagram and EEV. The binodal curves of POELE20−salt (K2C2O4, K2C4H4O6, or K3C6H5O7) ATPSs at three temperatures (288.15−308.15 K) were shown in Figures 1−3. It was found that the binodal curves of the ATPS moved left when the temperature increased from 288.15 to 308.15 K. Meanwhile, it was shown that the EEV values of studied ATPSs increased with rising temperature shown in Table 13. This means that the POELE20−salt ATPSs are easier to form at the higher temperature. This impact is mainly caused by the effect of temperature on the hydrophobicity of POELE20. The

(7)

where w1 and M1 are the mass fraction and molecular weight of POELE20, w2 and M2 are the mass fraction and molecular weight of salt, and V*213 is the scaled EEV of salt. The EEV values obtained from the above equation for the investigated systems were shown in Table 13; at the same time, the square of correlation coefficients (R2) and standard deviations (sd) were also given there. The EEV values listed in Table 13 and the previous article32 showed the order of EEV values for the six POELE20−salt ATPSs is KOH < K2C2O4 < K2C4H4O6 < K2CO3 < K3C6H5O7 < K3PO4 when the systems are at the same temperatures. This order was consistent with the conclusion in the last section, which showed that the EEV value increased with the enhancement of the phase-forming ability of salt. 629



Article

Table 9. Tie-Line Data for the POELE20(1) + K2C4H4O6(2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K and Pressure p = 0.1 MPaa total system

POELE10-rich phase

100w1

100w2

100wt1

6.99 6.99 7.00 6.99

16.75 16.98 17.25 17.50

15.71 19.37 21.93 24.53

7.00 7.01 6.99 7.00

16.00 16.25 16.51 16.78

21.65 24.06 26.66 29.26

7.00 7.00 7.00 7.00

14.26 14.50 14.75 15.01

30.70 32.68 35.07 37.46

100wt2


100wb2

T = 288.15 K 13.34 4.40 17.77 12.20 3.08 18.52 11.49 2.05 19.15 10.74 1.34 19.69 T = 298.15 K 11.24 2.55 17.38 10.69 1.96 17.83 10.12 1.24 18.35 9.49 0.60 18.83 T = 308.15 K 6.65 1.80 15.86 6.28 1.12 16.26 5.79 0.84 16.65 5.33 0.34 16.99

slope (k)

average of slope

−2.555 −2.580 −2.595 −2.591

−2.580

−3.101 −3.088 −3.085 −3.065

−3.085

−3.131 −3.150 −3.146 −3.172

−3.150

Figure 4. Tie lines of the POELE20(1) + (NH4)2C4H4O6(2) + H2O(3) ATPSs at 288.15, 298.15, and 308.15 K.


Table 10. Tie-Line Data for the POELE20(1) + K3C6H5O7(2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K and Pressure p = 0.1 MPaa total system

POELE10-rich phase

100w1

100w2

100wt1

7.00 7.00 6.99 7.00

16.50 16.74 17.01 17.24

14.04 17.28 19.89 22.10

6.99 7.00 7.00 6.99

15.02 15.26 15.51 15.75

19.64 22.02 24.22 26.53

7.00 7.00 7.00 6.99

13.25 13.49 13.76 14.00

27.30 28.66 30.02 31.77

100wt2


100wb2

T = 288.15 K 14.14 4.73 17.28 13.33 3.32 17.99 12.72 2.44 18.55 12.25 1.78 19.01 T = 298.15 K 10.90 3.45 16.10 10.37 2.57 16.61 9.95 1.81 17.13 9.50 1.35 17.49 T = 308.15 K 7.31 2.10 14.71 7.15 1.44 15.18 6.97 0.89 15.65 6.66 0.54 16.03

slope (k)

average of slope

−2.970 −3.000 −2.997 −3.009

−2.994

−3.102 −3.105 −3.117 −3.145

−3.117

−3.408 −3.397 −3.366 −3.344

−3.379

Figure 5. Tie lines of the POELE20(1) + K2C4H4O6(2) + H2O(3) ATPSs at 288.15, 298.15, and 308.15 K.


change in the hydrophobicity of POELE20 with temperature was discussed through the excess specific volume in our published paper.32 The excess specific volume was developed to use in the system of polypropylene glycol 400 and water by Zafarani-Moattar et al.61 We have introduced this method into POELE10/POELE20−salt ATPSs32,37 to compute the excess specific volume in order to study the hydrophobicity of two polymers. It was confirmed that the POELE20 will become more hydrophobic when the system temperature increases. Then, the two-phase system is easier to form when more water comes into the bottom phase from the top phase.

Figure 6. Tie lines of the POELE20(1) + K3C6H5O7(2) + H2O(3) ATPSs at 288.15, 298.15, and 308.15 K.

The effect of temperature on the tie-lines of studied ATPSs was also discussed, and the tie-lines of ATPSs composed of POELE20 and salts (K2C2O4, K2C4H4O6, or K3C6H5O7) at three temperatures were shown in Figures 4−6, respectively. In 630



Article

Table 11. Values of Parameters of eqs 5 and 6 for the POELE20(1) + K2C2O4/K2C4H4O6/K3C6H5O7(2) + H2O(3) ATPSs at T = 288.15, 298.15, and 308.15 K T (K)

103k1

n

k2

288.15 298.15 308.15

2.255 0.3214 1.686

4.287 5.026 3.718

4.515 5.308 5.983

288.15 298.15 308.15

6.665 6.061 5.054

4.359 4.098 3.661

288.15 298.15 308.15

3.655 7.225 69.78

4.737 3.841 2.075

R12

r

POELE20 + K2C2O4 + H2O 0.1669 0.9970 0.1309 0.9908 0.1934 0.9994 POELE20 + K2C4H4O6 + H2O 3.427 0.1642 0.9941 3.722 0.1890 0.9992 4.415 0.2256 0.9925 POELE20 + K3C6H5O7 + H2O 3.558 0.1468 0.9986 3.899 0.1964 0.9938 3.993 0.4088 0.3961

R2 2

100sdα1

100sdα2

0.9952 0.9906 0.9997

0.7216 0.5631 0.1291

2.952 1.804 0.2860

0.9907 0.9994 0.9938

0.5479 0.1554 0.3999

2.152 0.3998 0.8256

0.9943 0.9953 0.5477

0.3279 0.3849 0.6668

1.735 1.054 0.8844

top bot bot 2 2 0.5 sd = [∑Ni=1 ((wi,j,cal − wtop i,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 POELE20 and salt, respectively. a

Table 13. Values of Parameters of eq 7 for the POELE20(1) + K2C2O4/K2C4H4O6/K3C6H5O7(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

Figure 7. Effect of anion of salt on the binodal curves at temperature T = 298.15 K.

R2

POELE20 + K2C2O4 + H2O 845.7 0.9635 939.4 0.9613 1102 0.9761 POELE20 + K2C4H4O6 + H2O 1187 0.9676 1276 0.9600 1424 0.9826 POELE20 + K3C6H5O7 + H2O 1602 0.9664 1746 0.9545 2042 0.9749

sdα 0.0898 0.0748 0.0932 0.0886 0.0800 0.0897 0.0525 0.0597 0.0508

exp 2 exp 0.5 sd = (∑ni=1 (wcal 1 − w1 ) /n) , where w1 is the experimental mass fraction of POELE20 in Tables 1−3 and wcal 1 is the corresponding data calculated using eq 7. n represents the number of binodal data. a

this paper, the following equation was used to express the slope of the tie-line (STL) STL = ΔY /ΔX

V213 * (g·mol−1)

experimental data, and a good effect was obtained. Second, this Article dwelled on crucial factors affecting the phaseforming ability of salt. It was found that three factors, namely, the Gibbs free energy of ions, the valence of ions, and the EEV value, all affected the phase-forming ability of salt. More specifically, with salts of the same cations, the phase-forming ability of salt will be greater if these three factors increase (the absolute value Gibbs free energy of the anion, the valence of the anion, and the EEV value). Finally, the effect of temperature on the phase diagram was studied through the binodal curve, EEV value, tie-line, and STL. It was found that the two-phase area in the phase diagram will expand and the absolute value of the STL will rise by the observation of the binodal curve and tielines. For the same ATPS, the EEV value and the absolute value of STL all increased with rising temperature, which is shown from the data in related tables. Thus, we could draw the conclusion that higher temperature is beneficial for the formation of studied ATPSs.

(ΔX = |x t − x b| , ΔY = |y t − y b |) (8)

where x and y represent the concentration of salt and POELE20 and “t” and “b” represent the top phase and the bottom phase. The STL values for the investigated ATPSs were given in Tables 7−9. It was found that the absolute value of STL increases as the temperature goes up in three tables and Figures 4−6. In summary, when the system temperature goes up in the investigated ATPSs, the two-phase area in the phase diagram will expand and the absolute value of STL will rise.

4. CONCLUSION In this paper, the POELE20−salt (K2C2O4, K2C4H4O6, or K3C6H5O7) ATPSs were built, and their binodal data and tieline data were determined at different temperatures. First, the classical empirical equations for the bindal data and tie-line data were introduced into this work to correlate with the Table 12. Gibbs Free Energies (ΔGhyd) of Anions anion ΔGhyd (kJ·mol−1)

OH− −430

C2O42− −673

C2H4O62− −1102 631

CO32− −1315

C6H5O73− −2793

PO43− −2765



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Article

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Phone: +86-0434-3291935. Fax: +86-0434-3291953. ORCID

Yang Lu: 0000-0002-5782-5375 Funding

This work was supported by the National Natural Science Foundation of China (No. 21606099, 21406090, and 21407058), the Natural Science Foundation of Jiangsu Province (No. BK20141289 and BK20131258), the Natural Science Foundation of Jilin Province (No. 20150520062JH), and Science and Technology Research Foundation of Jilin Province Department of Education (No. JJKH20170376KJ). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

■

REFERENCES

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

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Measurement and Correlation of Phase Equilibria in Aqueous Two

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