sodium sulphate solution

Journal of Molecular Liquids 211 (2015) 924–933

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

A thermodynamic study on the phase behaviour of ethanol and 2-propanol in aqueous ammonium sulphate/sodium sulphate solution Yuliang Li ⁎, Yingjie Zhao, Rong Huang, Qianqian Cui, Xiaojia Lu, Huan Guo School of Environmental Science and Engineering, Chang'an University, 710064 Xi'an, China

a r t i c l e

i n f o

Article history: Received 10 May 2015 Received in revised form 6 August 2015 Accepted 10 August 2015 Available online 25 August 2015 Keywords: Liquid–liquid equilibrium Aqueous two-phase system Ethanol 2-Propanol Temperature

a b s t r a c t Liquid–liquid equilibrium (LLE) data for quaternary systems containing ethanol + 2-propanol + salt [(NH4)2SO4/Na2SO4] + water were experimentally determined at 308.15, 318.15 and 328.15 K. Binodal curves were fitted to four empirical nonlinear equations, whereas tie-lines were fitted to the Setschenow-type equation and its temperature-dependent expression as well as another two-parameter equation. All of the models were successfully correlated with the experimental data. Factors affecting the phase-forming abilities of the investigated systems were also studied, such as the temperature, mass fraction of ethanol in the alcohol mixture and type of salt. The effective excluded volume values for the studied systems also were determined to evaluate the phase separation abilities of investigated systems. These data can be used for the development and design of extraction processes utilizing such systems. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Aqueous two-phase systems (ATPSs), which are considered to be green separation systems and can be substituted for conventional methods (which usually consume large quantities of organic compounds), have often been a favoured technique for separation, extraction and enrichment. In essence, an ATPS is a system that exists in two phases and can be formed by two different water-soluble compounds, a polymer and a salt [1–4] or a hydrophilic organic solvent and a salt [5,6], under specific conditions. In the past few years, ATPSs have been applied widely for the separation, concentration and purification of DNA [7], antibodies [8,9], proteins [10,11], metal ions [12], drugs [13] and nanoparticles [14] due to their efficient, economical and environmentally friendly properties. Recently, many research groups have focused on ATPSs based on small-molecule organic solvents because of their extraction features, such as gentle reaction conditions, simple operation, strong adaptability and good selectivity. Furthermore, small-molecule organic solvents are cheap, easy to recycle, environmentally friendly and have low viscosities. All these features of small-molecule organic solvents have led to their increased use in ATPS research and applications. Thus, small-molecule organic solvent ATPSs, which combine both the advantages of traditional ATPSs and the aforementioned characteristics of small-molecule organic solvents, have been successfully used in the separation and purification of hesperidin [15] and pigments [16]. Furthermore, ATPSs based on small-molecule organic solvents have a unique advantage in the ⁎ Corresponding author. E-mail address: [email protected] (Y. Li).

http://dx.doi.org/10.1016/j.molliq.2015.08.021 0167-7322/© 2015 Elsevier B.V. All rights reserved.

extraction of biologically active substances due to their high moisture content, which can help the substances remain bioactive during the extraction process. Real data from small-molecule organic solvent ATPSs on the properties and equilibria of phase systems are necessary for the development, optimization, and scale-up of extraction processes. Recently, much work has been devoted to this type of ATPS. For example, ethanol + salt [(NH4)2SO4, NaOH, NaF, K2HPO4] ATPSs have been reported in the literature [17–20]. Binodal data for ethanol, 2-propanol and 1-propanol + magnesium sulphate/zinc sulphate + water systems have been experimentally determined at 303.15 and 313.15 K, respectively [21]. Furthermore, propyl alcohol-ammonium sulphate ATPS has been used in the treatment of p-aminophenol in water [22]. Other small-molecule organic solvent ATPSs, such as 1-butanol and acetone [15,23], have also been reported. However, the above studies focus on ATPSs that contain only one type of small-molecule organic solvent to form each ATPS, and this type of ATPS has demonstrated weaknesses with regard to application, such as the large amount of phase-forming materials used, high volatility of alcohol, and limited substances that are extracted using this type of ATPS. These shortcomings have limited the systems' applicability. To extend the variety of substances forming this type of ATPS and to identify extraction systems with better selectivity, efficiency and stability, quaternary ATPSs including two small-molecule organic solvents have been investigated in the context of ternary systems. For example, the ATPS composed of ethanol, acetone, (NH4)2SO4 and water has been studied and used in the extraction of tetracycline hydrochloride [24]. The results showed that this type of ATPS possesses some beneficial features, such as the small amount of phase-forming material used and the ease of forming an ATPS. Moreover, this ATPS can better extract

Y. Li et al. / Journal of Molecular Liquids 211 (2015) 924–933

tetracycline hydrochloride by adjusting the polarity of the system to be similar to that of the antibiotic. In addition, Chai [25] researched a new aqueous two-phase system using ethanol, n-propanol and ammonium sulphate/sodium dihydrogen phosphate and discussed the distribution behaviour of soluble oxytetracycline hydrochloride in this system. It has been found that the phase-forming velocity of binary alcohol is higher than a small-molecule alcohol, and oxytetracycline hydrochloride has been successfully extracted using this ATPS. Both of these ATPS applications with two different organic solvents showed that this type of ATPS can provide better selectivity for antibiotics in the extraction process compared with conventional ATPSs, which can improve the extraction rate of antibiotics. In addition, compared with ternary ATPSs based on a type of small-molecule alcohol, quaternary ATPSs based on binary alcohol can help to reduce the amount of phaseforming materials used and relieve secondary pollution when forming an ATPS with inorganic salt. However, studies concerning this type of quaternary ATPS are insufficient and require further development. In this work, phase diagrams and liquid–liquid equilibrium (LLE) data for the quaternary system ethanol + 2-propanol + (NH4)2SO4 + water were investigated at T = 308.15 K, 318.15 K, and 328.15 K, and the system ethanol + 2-propanol + Na2SO4 + water was examined at T = 308.15 K and at atmospheric pressure. In the above systems, ethanol and 2propanol were mixed in different proportions and formed homogeneous and stabilized solutions. The binodal curves were fitted to four nonlinear equations. The effective excluded volume (EEV) values obtained from the binodal models for the two systems at different temperatures were determined, and the effect of temperature and the mass fraction of ethanol in the mixture of alcohol and salts on the phase separation abilities of the systems were discussed. The findings are necessary for the design and optimization of extraction processes and can provide a possible basis for predicting the phase composition when data are not available. 2. Experimental section 2.1. Materials Analytical-grade (NH4)2SO4, Na2SO4, ethanol and 2-propanol were purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China), Tianjin Baishi Chemical Co., Ltd. (Tianjin, China), and Tianjin Fuyu Fine Chemical Co., Ltd. (Tianjin, China) respectively. All the above materials have a minimum mass fraction of 99.5%. Doubledistilled deionized water was also used in the experiments. 2.2. Apparatus and procedure Before the experiment, the mixtures of ethanol and 2-propanol were prepared by adding an appropriate amount of ethanol into the 2propanol until the mass fraction of ethanol reached 0.667 and 0.250 under stirring. In the following text, “MA” denotes the mass fraction of ethanol in the mixture of ethanol and 2-propanol. The values of MA1 and MA2 were 0.667 and 0.250, respectively. These mixtures of ethanol and 2-propanol were used throughout the follow-up experiments. The binodal curves were determined by the cloud point method. First, an alcohol mixture of known mass fraction was added to a vessel, and a salt solution of known concentration was then added dropwise using a small-sized pipette until the mixture became cloudy. Then, water was added dropwise to clarify the mixture, and the procedure was repeated until there was some precipitation at the bottom of the vessel for obtaining sufficient data for the construction of a phase diagram. The mass of the pipettes was determined before adding the solution as well as when each cloudy or clear point was reached using an analytical balance (model BS 124S, Beijing Sartorius Instrument Co., China) with a precision of ±1.0 × 10−7 kg. The mass fraction of each composition in the mixture was then calculated. The vessel was placed in a DC-2008 water thermostat throughout the process to keep the

925

temperature of the system constant. The temperature was maintained with an uncertainty of ±0.05 K. For determination of the tie-lines, known masses of ethanol, 2propanol, (NH4)2SO4/Na2SO4 and water in the biphasic region were mixed in vessels, vigorously stirred and placed in a temperaturecontrolled bath for at least 24 h until the mixture separated into two clear phases. The upper phase was carefully removed by pipette. The mass of the upper phase was determined by an analytical balance, and the mass of the lower phase was obtained by subtraction. Both the top phase and bottom phase were sampled for analysis. Before each analysis of the unknown sample, alcohol mixture solutions with concentrations in the range of 1%–50% w/w were prepared, and their refractive indexes were determined at the experimental temperatures using an Abbe refractometer (model WAY [2WAJ], Shanghai Physical Optics Instrument Co., Ltd.). Afterwards, the salt solutions with concentrations in the range of 0.1%–25% w/w were added to the above alcohol mixture solutions, and the corresponding refractive indexes were determined at the experimental temperatures. A comparison of the refractive indexes for the two groups of solutions revealed that there was no influence of salt on the refractive index when solved in the alcohol solutions. Standard curves of refractive index versus alcohol mixture concentration at different temperatures were then constructed. For the alcohol concentration measurement, the refractive indexes of both the top phase and bottom phase were determined using an Abbe refractometer with an uncertainty of ± 0.0002. We input the refractive indexes of both into the corresponding standard curve to obtain the concentration of the alcohol mixture in the phases. The mass fraction of water in both phases was determined via Karl Fischer titration. Finally, the mass fraction of salt [(NH4)2SO4/Na2SO4] in both the top phase and bottom phase was obtained from the law of mass conservation with an uncertainty of ±0.0001. The tie-line length (TLL), which shows the difference between the composition of two phases, and the slope of the tie-line (S), which reflects the phase-forming ability, were also calculated using the following equations at different compositions [26]:

TLL ¼


2
2 0:5 wt1 −wb1 þ wt2 −wb2



 S ¼ wt1 −wb1 = wt2 −wb2

ð1Þ

ð2Þ

where w1t, w1b, w2t and w2b represent the equilibrium mass fractions of the alcohol mixture and salt in the top and bottom phases, respectively. The tie-line data are provided in Table 1. 3. Results and discussion 3.1. Binodal data and correlation The binodal data of the quaternary system ethanol + 2propanol + (NH4)2SO4/Na2SO4 + water determined at T = 308.15, 318.15, and 328.15 K are presented in Table 2 and Figs. 1–3. The data were fitted using the empirical nonlinear expression developed by Merchuk et al. [27] as follows:   w1 ¼ a exp bw2 0:5 −cw2 3

ð3Þ

where w1 and w2 are the mass fractions of the alcohol mixture and the salt, respectively. This equation has been widely used for correlations of ionic liquid-based ATPSs [28] and polymer-based ATPSs [29]. The fitting parameters for this equation were determined from the correlation of experimental data obtained from the cloud point method. Coefficients a, b and c, along with the corresponding standard deviations (sd) and correlation coefficients (R2), are given in Table 3.

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Y. Li et al. / Journal of Molecular Liquids 211 (2015) 924–933

Table 1 Tie-line data for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPS at different temperatures and atmospheric pressure. T/K

Total system 100w1

100w2

Top phase

Bottom phase

100w1

100w1

100w2

TLL

S

T/K

100w2

Ethanol + 2-propanol + (NH4)2SO4 (MA1 = 0.667) T = 308.15 K 22.97 16.67 11.87 22.67 44.64 19.27 18.21 13.78 21.18 42.54 18.05 19.48 11.33 23.11 45.24 22.23 16.39 14.89 20.35 41.40 28.32 13.57 12.69 22.02 43.74 T = 318.15 K 27.45 13.96 14.06 21.73 39.93 33.44 10.71 13.20 22.46 40.90 25.08 15.08 15.07 20.90 38.64 18.63 19.19 13.61 22.11 40.31 25.85 15.51 11.86 23.64 42.42 T = 328.15 K 24.41 15.40 14.74 21.10 37.45 18.02 19.39 13.63 21.97 38.78 21.01 17.26 15.64 20.42 36.65 28.30 12.83 16.57 19.73 35.71 32.06 11.53 11.93 23.37 40.69

4.96 5.63 4.78 6.02 5.24 6.73 6.38 7.20 6.59 5.88 7.72 7.18 8.06 8.47 6.45

37.25 32.70 38.54 30.13 35.30 29.91 32.03 27.26 30.88 35.34 26.35 29.17 24.38 22.21 33.37

−1.85 −1.85 −1.85 −1.85 −1.85 −1.72 −1.72 −1.72 −1.72 −1.72 −1.70 −1.70 −1.70 −1.70 −1.70

Ethanol + 2-propanol + Na2SO4 (MA1 = 0.667) T = 308.15 K 21.21 10.73 7.68 21.26 21.28 11.07 6.51 22.61 17.34 13.24 9.43 19.42 21.96 10.32 7.06 21.96 17.92 14.01 5.84 23.45

25.40 26.83 22.99 26.04 27.89

7.47 6.73 8.83 7.13 6.22

22.46 25.79 17.20 24.09 27.99

−1.28 −1.28 −1.28 −1.28 −1.28

Ethanol + 2-propanol + (NH4)2SO4 (MA2 = 0.250) T = 308.15 K 30.57 10.93 13.76 18.29 47.56 34.29 9.72 12.63 19.18 49.30 22.99 15.32 10.97 20.57 51.76 34.94 11.13 8.86 22.52 55.33 33.05 10.73 11.43 20.17 51.09

3.50 3.17 2.75 2.22 2.86

36.90 40.02 44.51 50.71 43.27

−2.29 −2.29 −2.29 −2.29 −2.29

Standard uncertainty u is u(w) = ±0.001, u(T) = ±0.05 K, and u(p) = ±10 KPa.

To obtain a more accurate fitting result, another nonlinear empirical equation [30] of the following form was used to correlate the experimental binodal data:   w1 ¼ exp a þ bw2 0:5 þ cw2 þ dw2 2

ð4Þ

where w1 and w2 are the mass fractions of the alcohol mixture and the salt, respectively. The four fitting parameters a, b, c and d, along with the corresponding standard deviations (sd) and correlation coefficients (R2), are listed in Table 4. The following equation was also successfully applied to correlate the binodal data in this work:   w2 w2 w1 ¼ a1 exp − þ a2 exp − þc b1 b2

ð5aÞ

where w1 and w2 are the mass fractions of the alcohol mixture and the salt, respectively. Eq. (5a) has been extended to fit the binodal data of ATPSs based on hydrophilic organic solvents [31,32]. The fitting parameters a1, a2, b1, b2 and c, along with the corresponding standard deviations (sd) and correlation coefficients (R2), are given in Table 5. Eq. (5a) was over-parameterized when correlating the experimental binodal data in this work, so a simplified expression Eq. (5b) was proposed for the correlation of the experimental data, defined as follows:
w  2 þc w1 ¼ a exp − b

Table 2 Binodal data for the mixture of ethanol + 2-propanol (1) + salt (2) + water ATPSs at different temperatures and atmospheric pressure.

ð5bÞ

where w1 and w2 are the mass fractions of the alcohol mixture and the salt, respectively. The fitting parameters a, b and c, along with the corresponding standard deviations (sd) and correlation coefficients (R2), are listed in Table 6. A comparison with the association results obtained from the correlation of Eq. (5a) clearly demonstrates that there is no obvious influence on the association results when Eq. (5b) is used for the correlation.

100w1 100w2 100w1 100w2 100w1 100w2 100w1 100w2

Ethanol + 2-propanol + (NH4)2SO4 + water (MA1 = 0.667) T = 308.15 K 4.94 35.37 26.26 13.06 32.22 9.86 5.40 32.40 26.41 12.97 32.32 9.81 5.75 30.31 26.61 12.87 32.40 9.75 6.36 29.29 26.79 12.77 32.61 9.68 6.90 28.07 26.96 12.68 32.72 9.63 7.85 27.09 27.13 12.59 32.85 9.57 8.40 26.23 27.31 12.50 32.97 9.53 8.87 25.31 27.48 12.41 33.07 9.48 9.32 24.56 27.65 12.32 33.16 9.43 9.90 24.21 27.81 12.23 33.61 9.38 10.61 23.48 27.99 12.15 33.91 9.23 11.10 23.01 28.14 12.07 33.99 9.19 11.56 22.56 28.28 11.98 34.07 9.15 12.24 22.04 28.38 11.91 34.10 9.09 12.73 21.80 28.52 11.82 34.20 9.04 13.37 21.21 28.67 11.75 34.30 8.99 13.68 20.84 28.82 11.67 34.35 8.95 14.03 20.47 28.95 11.59 34.42 8.91 14.46 20.23 29.09 11.51 34.50 8.86 15.04 19.81 29.25 11.44 34.66 8.80 15.34 19.48 29.38 11.36 34.80 8.73 15.80 19.25 29.53 11.29 35.05 8.63 16.15 18.94 29.67 11.22 35.18 8.56 22.05 15.50 29.79 11.15 35.31 8.51 22.29 15.36 29.82 11.09 35.38 8.46 22.53 15.23 29.96 11.02 35.45 8.42 22.78 15.09 30.09 10.96 35.60 8.37 23.04 14.97 30.22 10.89 35.78 8.31 23.11 14.87 30.34 10.83 35.85 8.24 23.34 14.76 30.45 10.76 36.00 8.19 23.56 14.63 30.64 10.69 36.16 8.10 23.76 14.51 30.75 10.62 36.29 8.05 23.96 14.40 30.89 10.56 36.42 8.00 24.03 14.31 31.01 10.50 36.48 7.96 24.23 14.20 31.12 10.45 36.63 7.92 24.44 14.09 31.23 10.39 36.69 7.88 24.89 13.87 31.26 10.33 36.86 7.83 25.08 13.76 31.37 10.27 37.02 7.74 25.26 13.65 31.48 10.21 37.14 7.69 25.47 13.54 31.60 10.15 37.30 7.60 25.51 13.47 31.71 10.10 37.44 7.56 25.71 13.37 31.92 10.02 53.08 2.58 25.89 13.27 31.92 9.98 51.02 3.25 26.09 13.17 32.01 9.93 48.74 3.82 T = 318.15 K 5.70 35.09 25.22 13.92 31.72 10.27 6.29 31.91 25.35 13.78 31.91 10.19 7.01 30.05 25.54 13.67 32.11 10.11 8.14 27.89 26.23 13.34 32.34 10.03 9.00 27.05 26.64 13.06 32.34 9.98 9.79 26.03 26.91 12.94 32.50 9.90 10.28 25.20 27.17 12.82 32.59 9.84 11.06 24.39 27.33 12.72 32.76 9.77 11.68 23.81 27.46 12.62 33.01 9.69 12.53 23.04 27.76 12.50 33.06 9.63 13.29 22.38 27.88 12.40 33.24 9.56 13.83 21.92 28.11 12.30 33.39 9.49 14.49 21.37 28.38 12.19 33.46 9.43 15.35 20.67 28.68 12.00 33.72 9.30 16.02 20.14 28.80 11.91 33.86 9.23 16.35 19.89 29.03 11.81 34.00 9.17 17.31 19.16 29.14 11.73 34.15 9.10 18.27 18.43 29.25 11.58 34.29 9.04 18.74 18.10 29.38 11.50 34.38 8.99 19.23 17.74 29.60 11.40 34.75 8.90 19.75 17.38 29.71 11.32 34.90 8.83 20.28 17.00 29.85 11.24 34.98 8.79 20.82 16.64 30.06 11.14 35.11 8.73 21.31 16.30 30.27 11.04 35.27 8.66 21.84 15.94 30.46 10.95 35.33 8.62 22.31 15.63 30.70 10.85 35.46 8.56 22.80 15.31 30.80 10.78 35.60 8.50 23.23 15.03 30.90 10.71 35.73 8.44 23.79 14.69 31.11 10.62 35.85 8.38

46.74 45.25 44.22 42.90 41.43 40.61 39.81 39.03 38.34 37.87 37.17 36.30 34.99 34.42 33.90 33.20 30.02 29.40 26.07 25.65 25.15 24.66 24.28 23.82 23.36 22.99 22.57 22.17 21.78 21.38 21.02 20.68 20.34 19.99 19.58 19.21 18.85 18.49 18.18 17.83 17.55 17.16 16.83

4.23 4.66 5.10 5.49 6.03 6.37 6.68 6.99 7.28 7.39 7.66 8.09 8.69 8.90 9.12 9.48 11.11 11.43 13.26 13.46 13.75 14.04 14.23 14.49 14.76 14.94 15.18 15.41 15.63 15.86 16.09 16.29 16.50 16.70 16.97 17.22 17.44 17.66 17.87 18.10 18.28 18.57 18.82

36.24 36.41 36.52 36.66 36.71 36.84 36.94 37.05 37.20 37.23 37.35 37.41 37.51 37.60 37.77 37.92 38.02 38.12 38.16 38.49 38.61 38.87 38.99 39.20 39.90 40.22 40.48 41.25 41.62

8.19 8.13 8.08 8.03 7.99 7.94 7.90 7.85 7.80 7.76 7.71 7.67 7.62 7.58 7.52 7.47 7.39 7.35 7.27 7.21 7.14 7.08 6.98 6.91 6.70 6.49 6.37 6.27 6.14

(continued on next page)

Y. Li et al. / Journal of Molecular Liquids 211 (2015) 924–933 Table 2 (continued) T/K T = 318.15 K

Table 2 (continued)

100w1 100w2 100w1 100w2 100w1 100w2 100w1 100w2

23.87 24.09 24.42 24.90 T = 328.15 K 6.73 7.49 7.97 8.85 9.15 9.78 10.20 11.00 11.12 11.37 11.73 12.21 12.90 13.68 14.43 14.87 15.33 15.92 16.33 16.83 17.24 17.57 17.94 18.70 19.55 19.96 20.34 21.01 21.62 21.90 21.96 22.65 22.94 23.02 23.23 23.70 23.81 24.03 24.30 24.38 24.62

927

14.58 14.45 14.30 14.13 34.70 33.21 30.60 29.06 27.48 26.55 25.78 24.99 24.31 24.10 23.97 23.13 22.56 21.93 21.34 21.00 20.65 20.21 19.91 19.54 19.25 19.01 18.74 18.21 17.63 17.35 17.09 16.65 16.25 16.07 15.74 15.39 15.27 15.18 15.03 14.87 14.71 14.59 14.48 14.40 14.29

31.21 31.42 31.44 31.62 24.71 24.94 25.26 25.37 25.60 25.84 26.03 26.11 26.77 26.82 27.01 27.12 27.68 27.93 28.01 28.19 28.37 28.41 28.60 28.77 28.98 29.19 29.49 30.64 30.72 31.09 31.30 31.46 31.71 31.74 31.88 31.91 32.04 32.31 32.34 32.67 32.70 32.71 32.85 32.97 33.09

10.55 10.47 10.42 10.34 14.22 14.11 13.99 13.84 13.73 13.62 13.53 13.46 13.14 13.07 12.98 12.91 12.75 12.66 12.59 12.52 12.44 12.38 12.30 12.22 12.14 12.05 11.83 11.26 11.16 11.00 10.92 10.77 10.64 10.59 10.54 10.49 10.44 10.33 10.29 10.21 10.13 10.09 10.04 9.99 9.89

35.91 36.05 36.10

8.34 8.29 8.24

41.96 42.33 42.82

6.03 5.91 5.75

33.22 33.41 33.51 33.62 33.73 33.84 33.95 34.04 34.11 34.20 34.29 34.38 34.47 34.58 34.68 34.78 34.89 34.99 35.18 35.28 35.29 35.67 35.69 35.76 35.85 35.93 36.02 36.35 36.45 36.63 36.81 36.91 37.07 37.16 37.25 37.32 37.38 37.48 37.58 37.68 37.75

9.84 9.78 9.71 9.66 9.61 9.55 9.51 9.46 9.40 9.35 9.30 9.24 9.20 9.16 9.11 9.06 9.02 8.97 8.88 8.84 8.81 8.64 8.61 8.57 8.53 8.49 8.45 8.32 8.25 8.16 8.08 8.02 7.95 7.89 7.86 7.82 7.79 7.74 7.70 7.67 7.64

37.82 37.89 37.96 38.10 38.19 38.33 38.65 38.70 38.93 39.11 39.25 39.38 39.48 39.60 39.80 40.04 40.34 40.56 40.75 40.91 41.06 41.22 41.38 41.56 41.73 42.03 42.20 42.44 42.64 43.11 43.30 43.62 44.04 44.31 44.68 44.91 45.51 46.18 47.16 47.56

7.61 7.57 7.54 7.48 7.45 7.38 7.29 7.19 7.11 7.04 6.99 6.93 6.88 6.83 6.76 6.68 6.51 6.45 6.37 6.30 6.23 6.14 6.10 6.04 5.98 5.87 5.80 5.72 5.63 5.48 5.38 5.28 5.15 5.05 4.95 4.82 4.69 4.53 4.31 4.02

5.79 5.71 5.63 5.57 5.50 5.42 5.35 5.27 5.21 5.13 5.07 5.00 4.93 4.86 4.80 4.73 4.65 4.57 4.51 4.45 4.39 4.33 4.27 4.22 4.15 4.08 4.01 3.94 3.86

46.05 46.37 46.57 47.03 47.25 47.69 47.97 49.03 49.95 51.24 51.80 52.27 52.73 53.29 53.89 54.39 54.89 55.73 56.48 57.13 58.16 58.89 66.21 66.32 66.73 67.01 67.75 73.08

3.77 3.69 3.61 3.53 3.45 3.37 3.28 3.03 2.92 2.83 2.74 2.67 2.60 2.51 2.42 2.35 2.28 2.17 2.07 1.98 1.86 1.77 1.32 1.22 1.13 1.02 0.93 0.88

Ethanol + 2-propanol + (NH4)2SO4 + water (MA2 = 0.250) T = 308.15 K 1.05 35.69 28.32 9.77 38.73 1.97 32.59 28.91 9.50 38.96 2.92 30.39 29.60 9.29 39.32 6.25 26.66 29.99 9.05 39.45 4.00 28.47 30.53 8.87 39.68 6.59 24.94 30.91 8.69 39.91 7.80 23.59 31.33 8.54 40.11 8.48 22.89 32.39 8.02 40.47 9.67 21.75 32.79 7.90 40.57 10.65 20.84 33.09 7.78 40.92 11.91 19.78 33.33 7.65 41.15 13.04 18.85 33.71 7.54 41.35 13.95 18.15 33.97 7.42 41.60 14.83 17.49 34.39 7.31 41.81 16.23 16.48 34.63 7.20 42.04 17.63 15.52 35.05 7.08 42.31 18.85 14.72 35.28 6.98 42.47 20.23 13.86 35.49 6.88 42.84 21.51 13.09 35.73 6.78 43.07 22.45 12.54 36.01 6.69 43.32 23.48 11.97 36.32 6.61 43.59 23.95 11.63 36.49 6.53 43.81 24.57 11.33 36.77 6.43 44.09 25.12 11.09 37.13 6.35 44.36 25.69 10.81 37.43 6.25 44.52 26.21 10.60 37.80 6.14 44.76 26.68 10.39 38.09 6.04 44.93 27.17 10.20 38.23 5.95 45.40 27.59 9.99 38.43 5.87 45.84

T/K

100w1 100w2 100w1 100w2 100w1 100w2 100w1 100w2

Ethanol + 2-propanol + Na2SO4 + water (MA1 = 0.667) T = 308.15 K 6.03 23.12 18.48 11.85 24.62 7.17 21.93 18.61 11.74 24.99 7.55 21.39 18.71 11.60 25.10 8.01 20.82 18.87 11.49 25.22 8.34 20.28 19.02 11.38 25.24 8.77 19.94 19.16 11.27 25.47 9.08 19.46 19.35 11.17 25.47 9.52 19.16 19.52 11.06 25.55 9.78 18.70 19.65 10.97 25.72 10.27 18.41 19.88 10.87 25.89 10.89 18.15 20.04 10.76 25.98 11.16 17.70 20.15 10.67 26.14 11.81 17.19 20.27 10.57 26.31 12.41 16.68 20.58 10.41 26.61 13.19 16.19 20.64 10.32 26.61 13.49 15.85 20.76 10.23 26.77 13.67 15.61 20.79 10.12 26.98 13.89 15.39 21.09 10.01 27.18 14.15 15.19 21.16 9.91 27.37 14.41 15.00 21.24 9.83 27.60 14.67 14.80 21.57 9.71 27.77 14.83 14.60 21.67 9.65 27.83 15.43 14.35 21.78 9.58 28.02 15.52 14.11 21.85 9.51 28.12 15.96 13.78 21.90 9.43 28.29 16.05 13.62 22.56 9.21 28.30 16.21 13.49 22.92 9.06 28.32 16.44 13.32 23.09 8.95 28.59 16.83 13.14 23.16 8.88 28.74 17.01 13.02 23.30 8.76 28.80 17.38 12.76 23.54 8.66 29.18 17.52 12.58 23.53 8.58 29.31 17.76 12.44 23.76 8.50 29.42 17.86 12.33 23.85 8.39 29.34 18.05 12.18 23.90 8.33 29.31 18.39 11.95 24.53 8.06

7.95 7.72 7.64 7.56 7.51 7.46 7.41 7.33 7.25 7.19 7.11 7.04 6.97 6.84 6.80 6.76 6.67 6.58 6.49 6.35 6.30 6.24 6.17 6.10 6.04 5.98 5.93 5.86 5.79 5.74 5.65 5.60 5.54 5.50 5.45

29.52 29.85 29.97 30.32 30.36 30.49 30.64 30.97 31.07 31.11 31.47 31.59 31.53 31.52 31.83 32.08 32.30 32.40 32.82 33.03 33.55 33.72 34.09 34.25 34.47 34.60 34.80 34.99 35.14 35.49 35.90 36.03 37.89 43.38 48.25

5.39 5.32 5.23 5.16 5.10 5.06 5.02 4.92 4.86 4.82 4.75 4.68 4.64 4.57 4.51 4.40 4.34 4.27 4.16 4.08 3.99 3.92 3.82 3.77 3.71 3.65 3.59 3.54 3.49 3.40 3.31 3.23 2.84 1.65 0.96

Standard uncertainty u is u(w) = ±0.001, u(T) = ±0.05 K, and u(p) = ±10 KPa.

Based on the obtained R2 and sd values in Tables 3–6, it can be concluded that Eqs. (3)–(5b) are satisfactory for correlating the binodal data of the investigated systems. Furthermore, Eq. (4) shows the most satisfactory accuracy among the four expressions due to its four fitting parameters.

Fig. 1. Effect of the salting-out ability of salts on binodal curves for alcohol mixture (MA1 = 0.667) (1) + salt (2) + water (3) ATPSs at 308.15 K: ○ (NH4)2SO4; ■ Na2SO4.

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Y. Li et al. / Journal of Molecular Liquids 211 (2015) 924–933 Table 3 Parameters of Eq. (3) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4 Ethanol + 2-propanol + Na2SO4 MA2 = 0.250 Ethanol + 2-propanol + (NH4)2SO4 a

N

T/K

a

b

c

R2

sda

308.15 318.15 328.15 308.15

90.1285 97.1381 91.5890 67.5401

−0.3130 −0.3388 −0.3152 −0.3489

4.6096E−05 3.4462E−05 4.0315E−05 5.8845E−05

0.9981 0.9977 0.9951 0.9997

0.16 0.18 0.52 0.02

308.15

99.4799

−0.3934

4.8334E−05

0.9958

0.99

2

exp exp 0:5 sd ¼ ð∑ðwcal is the experimental mass fraction of the alcohol i −wi Þ =NÞ , where wi i¼1

is the corresponding data calculated using Eq. (3). “N” represents the mixture and wcal i number of binodal data points. Fig. 2. Effect of the mass fraction of ethanol in the alcohol mixture on binodal curves for alcohol mixture (1) + (NH4)2SO4 (2) + water (3) ATPSs at 308.15 K: ● MA1 = 0.667; ▲ MA2 = 0.250; solid line, obtained by correlating experimental binodal data using Eq. (4).

3.2. Effective excluded volume (EEV) and salting-out ability In this paper, the effective excluded volume theory based on the statistical geometry method developed by Guan et al. [33] for aqueous polymer–polymer systems was used to correlate the binodal data and calculate the EEV of the studied systems. This EEV theory is based on the concept that macroscopically, any molecular species in a solution is randomly distributed and that every system composition on the binodal curve could form a geometrically saturated solution of each solute in the presence of the other. The EEV values for the systems composed of different salts [(NH4)2SO4/Na2SO4] and the same alcohol mixture (MA1 = 0.667), as well as the systems composed of different alcohol mixtures (MA1 = 0.667, MA2 = 0.250) and the same salt ((NH4)2SO4), determined at T = 308.15 K, were calculated to investigate the salting-out abilities of salts and the phase-forming abilities of the differently proportioned alcohol mixtures. For the correlation of

Fig. 3. Effect of temperature on binodal curves for alcohol mixture (MA1 = 0.667) (1) + (NH4)2SO4 (2) + water (3) ATPSs: ■ 308.15 K; ▲ 318.15 K; ★ 328.15 K; solid line, obtained by correlating experimental binodal data using Eq. (4).

ATPSs composed of ethanol, 2-propanol, (NH4)2SO4/Na2SO4 and water, the effective excluded volume model can be written as follows:  w2 w1 ln V 213 þ f 213 þ V 213 ¼0 M2 M1

ð6aÞ

 w2 w1 ¼0 ln V 213 þ V 213 M2 M1

ð6bÞ

where V*213, f213, M1 and M2 are the scaled EEV of the salts, the volume fraction of the unfilled effective available volume after tight packing of salt molecules into the network of alcohol molecules, the molar mass of the alcohol mixture and the molar mass of salt, respectively. The values of V*213 and f213 obtained from the correlation of the experimental binodal data, along with the R2 and sd values, are given in Tables 7 and 8. In previous studies, Eq. (6a) was proposed to correlate binodal data from polymer–polymer systems because of the obvious differences between two components. The values of f213 are related to the relative geometric shape, size, and interactions of different molecules. Thus, in polymer–polymer systems, f213 could be small enough to be neglected without any obvious influence. From Table 7, it can be seen that f213 was small enough to be neglected for the investigated system. Meanwhile, there was no significant difference between the association coefficients (R2) and standard deviations (sd) derived from these two equations. Thus, a simplified Eq. (6b) was used to correlate the binodal data. However, compared with the results of Eqs. (3)–(5b) concerning binodal data fitting, the EEV model still does not fit the data as well as the four nonlinear empirical equations. The EEV represents the smallest spacing of a given alcohol that will accept an individual salt, so it reflects the compatibility of the two components in studied systems. Therefore, the EEV should be related to the salting-out ability and is extensively used to evaluate the salting-out ability of salts in polymer–salt systems [34]. In general, the value of EEV increases with increased salting-out ability. In this work, the EEV model was used to evaluate the salting-out abilities of two salts [(NH4)2SO4, Na2SO4] in ATPSs composed of the same alcohol mixture (MA1 = 0.667) at T = 308.15 K. From Table 8, it can be observed that the EEV values of these two salts follow the order Na2SO4 N (NH4)2SO4, meaning that the salting-out ability of Na2SO4 is higher than that of (NH4)2SO4. To study in greater depth the relationship between EEV and salting-out ability, the binodal curves of the ATPSs composed of the alcohol mixture MA1 = 0.667, salt (NH4)2SO4/Na2SO4 and water at T = 308.15 K are plotted in Fig. 1. These binodal curves, which are the solubility curves for the studied systems, provide the minimum concentration of two components required to form the ATPSs. In this figure, the three coordinate axes respectively represent the mass fractions of the alcohol mixture,

Y. Li et al. / Journal of Molecular Liquids 211 (2015) 924–933

929

Table 4 Parameters of Eq. (4) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. T/K

a

b

c

d

R2

sda

Ethanol + 2-propanol + Na2SO4

308.15 318.15 328.15 308.15

4.4625 3.8005 3.8249 4.3376

−0.3346 0.1909 0.2010 −0.5192

0.0251 −0.0903 −0.0965 0.0631

−1.8600E−03 −2.1808E−04 −6.8884E−05 −2.7300E−03

0.9991 0.9995 0.9981 0.9996

0.01 0.04 0.20 0.02

MA2 = 0.250 Ethanol + 2-propanol + (NH4)2SO4

308.15

4.7138

−0.5603

0.0640

−2.6000E−03

0.9969

0.73

System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4

a

Definition is given in Table 3.

water and salt; the region below the binodal curve indicates the separated two-phase area, whereas the region above the binodal curve represents the homogeneous system. From Fig. 1, it can be observed that the area of the separated two-phase region of the ATPS containing Na2SO4 is greater than that of the (NH4)2SO4-based ATPS; this relationship follows the order of the systems' EEV values. This phenomenon reflects that an increase in EEV drives the binodal curve towards the top of the phase diagram, which directly causes the corresponding increase in the two-phase region and a decrease in the concentration of salt required to form an ATPS; in other words, the salting-out ability becomes stronger. The molar Gibbs free energy of hydration (ΔGhyd) of the constituent ions of salt, proposed by Marcus [35,36], also has been used to evaluate the salting-out ability. Salts were observed to salt-out better when the Gibbs free energy of the salt ions decreased; in other words, the more negative the ions, the stronger the salting-out abilities of their salts. In this work, the salts (NH4)2SO4 and Na2SO4 share the same anion (SO24 −), but the ΔGhyd of Na+ (ΔGhyd = − 365 kJ · mol−1) is greater −1 than the ΔGhyd of NH+ ). Thus, the salting4 (ΔGhyd = −285 kJ · mol out ability of Na2SO4 is greater than that of (NH4)2SO4, which is in agreement with the order obtained from the EEV model.

investigated at T = 308.15 K are plotted in Fig. 2. In this figure, the binodal curve moves upwards in the phase diagram when MA decreases, indicating that the separated two-phase region of the ATPS composed of the alcohol mixture MA2 = 0.250 is larger than that of the ATPS composed of the alcohol mixture MA1 = 0.667. This behaviour reflects that a decrease in MA promotes a corresponding increase of the two-phase region and a decrease in the concentration of the alcohol mixture required to form ATPSs; in other words, as the mass fraction of ethanol in the alcohol mixture decreases, the phase-separation ability of the alcohol mixture increases, which is consistent with the conclusion drawn from the EEV values. In previous studies, it was found that the phase-separation ability of hydrophilic alcohols can be ranked in the following order: 2-propanol N ethanol. This ranking provides strong evidence for our conclusion [5,32]. In these papers, the “hydrogen bond” interaction between the alcohol molecules and water molecules, the “ion–dipole” interaction of the salts, and the forces acting between alcohol molecules (which are always neglected) were used to investigate and evaluate the phaseseparation ability of alcohol. Eventually, it was concluded that the phase-separation ability of 2-propanol is higher than that of ethanol. 3.4. Effect of temperature on binodal curves

3.3. Effect of the mass fraction of ethanol in the alcohol mixture on the EEV values The scaled EEV of ATPSs composed of different solvents and the same salt vary because of differences in the size, shape, and interaction of the molecules in the systems at the same temperature [5,6]. From Table 8, it can be observed that the EEV value of the ATPS composed of alcohol mixture MA2 = 0.250, (NH4)2SO4 and water is higher than that of the ATPS composed of alcohol mixture MA1 = 0.667, (NH4)2SO4 and water at T = 308.15 K, which indicates that the former alcohol mixture is more easily excluded from the salt-rich phase than the latter and that it forms an ATPS more easily. In other words, the phase-separation abilities of alcohols increase with an increase in EEV of the ATPS under the same experimental conditions. To further investigate the relationship between phase-separation ability and the ratio of ethanol in the alcohol mixture, the binodal curves for ethanol + 2propanol (MA1 = 0.667, MA2 = 0.250) + (NH4)2SO4 + H2O

In this work, the effect of temperature on the phase-forming ability of an ethanol + 2-propanol (MA1 = 0.667) + (NH4)2SO4 + water system at T = 308.15, 318.15, and 328.15 K is illustrated in Fig. 3. The locus for the experimental binodal data shown in Fig. 3 indicates that the region below the binodal curve increases with decreased temperature at (NH4)2SO4 concentrations greater than 25%, whereas the binodal curves for this system at the three temperatures are similar for mass fractions of (NH4)2SO4 below 25%. In other words, the separated two-phase region becomes larger as temperature decreases when the concentration of (NH4)2SO4 is greater than 25% by mass fraction in the system. This behaviour occurs mainly because the solubility of (NH4)2SO4 decreases as temperature decreases from 328.15 K to 308.15 K, correspondingly weakening the hydration of salt ions, which could lead to weaker competition for water molecules in the salt. Thus, the alcohol molecules attract more water and drive more water out of the salt-rich phase and into the alcohol-rich phase, causing the salt concentration in the salt-

Table 5 Parameters of Eq. (5a) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. T/K

a1

b1

a2

b2

c

R2

sda

Ethanol + 2-propanol + Na2SO4

308.15 318.15 328.15 308.15

34.1156 33.0703 33.2387 56.8805

17.9142 18.0214 17.7209 26.5585

34.1156 33.0703 33.2387 18.3994

17.9157 18.0216 17.7195 2.0000

−6.9569 −5.7134 −5.3107 −17.9783

0.9981 0.9988 0.9970 0.9998

0.16 0.10 0.32 0.01

MA2 = 0.250 Ethanol + 2-propanol + (NH4)2SO4

308.15

47.9177

0.6884

63.6002

12.2975

−0.9742

0.9986

0.32

System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4

a

Definition is given in Table 3.

930

Y. Li et al. / Journal of Molecular Liquids 211 (2015) 924–933

Table 6 Parameters of Eq. (5b) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4 Ethanol + 2-propanol +

R2

c

sda

T/K

a

b

308.15 318.15 328.15 308.15

68.2312 66.1406 66.4776 46.2440

17.9149 −6.9569 0.9981 0.16 18.0215 −5.7134 0.9988 0.10 17.7205 −5.3112 0.9970 0.31 12.2021 0.4575 0.9932 0.43

Na2SO4 MA2 = 0.250 Ethanol + 2-propanol +

308.15 65.6567

9.3350

3.6827 0.9870 3.06

Table 8 Parameters of Eq. (6b) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. T/K

V*213

R2

sda

Ethanol + 2-propanol + Na2SO4

308.15 318.15 328.15 308.15

2.6051 2.5789 2.5778 3.4482

0.9695 0.9783 0.9771 0.9869

1.04E−03 6.89E−04 9.62E−04 3.35E−04

MA2 = 0.250 Ethanol + 2-propanol + (NH4)2SO4

308.15

3.0178

0.9890

8.37E−04

System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4

a

Definition is given in Table 3.

(NH4)2SO4 a

Definition is given in Table 3.

3.5. Tie-line data and correlation

rich phase to rise while the alcohol-rich phase becomes more dilute. Therefore, to a certain extent, the water-absorbing capacity of alcohol molecules is higher than the hydration of salt ions as temperature decreases when the concentration of (NH4)2SO4 is greater than 25%. According to the three binodal curves in the phase diagram, the phaseseparation ability of the alcohol mixture MA1 = 0.667 at different temperatures follows the order 308.15 K N 318.15 K N 328.15 K in this system when the salt concentration is greater than 25% by mass fraction. However, when the salt concentration is less than 25% by mass fraction, the amount of salt in the system is low enough that decreases in temperature have a relatively minor effect on salt solubility; as a result, the hydration of salt ions in the system is less sensitive to changes in temperature. Thus, the phase diagram binodal curves of the system at different temperatures change little in this situation. Furthermore, it can be observed from Table 8 that the EEV value of the ATPS consisting of the alcohol mixture MA1 = 0.667, (NH4)2SO4 and H2O increases with decreasing temperature, which could support the above conclusion that decreased temperatures can promote the system's phase-forming ability. However, the effect of temperature on the quaternary hydrophilic alcohol-based ATPSs investigated differs from the effect on ternary systems. In an ATPS composed of ethanol/2-propanol/1-propanol, MgSO4/ ZnSO4 and water, temperature had no significant effect on the binodal curve within the investigated range [21]. Furthermore, it has been reported that temperature plays a positive role in forming the ATPS consisting of 2-propanol, NaOH and water [18]. In this study, the effect of temperature on the systems investigated may relate to the type of salt, i.e., a stronger phase-forming salt makes the system less sensitive to temperature than a weaker one. Moreover, the effects of temperature on ionic liquid (IL)–salt ATPSs and polymer–salt ATPSs also differ from the conclusions drawn here. In polymer–salt ATPSs, an increase in temperature causes the expansion of the two-phase area [37], whereas in IL–salt ATPSs, the two-phase area decreases with increasing temperature [38].

The liquid–liquid equilibrium (LLE) compositions, tie-line lengths (TLL) and average tie-line slopes (S) of the ATPSs composed of ethanol, 2-propanol, salt [(NH4)2SO4/Na2SO4] and water determined at three different temperatures are listed in Table 1 and Figs. 4 and 5. In this paper, a simple two-parameter model, a Setschenow-type equation, was used to estimate the accuracy of the tie-line compositions. This equation based on binodal theory was proposed by Hey et al. [39], and it has been widely used for fitting the tie-line data of IL–salt ATPSs and polymer–salt ATPSs. The equation can be enumerated as follow:

ln

ct1 cb1

!



 ¼ kMA cb1 −ct1 þ ks cb2 −ct2 :

ð7Þ

In the above equation, c1, c2, kMA, and ks represent the molality of the alcohol mixture, the molality of the salt, a parameter relating the activity coefficient of the alcohol mixture to its concentration, and the saltingout coefficient, respectively. The two superscripts “t” and “b” represent the top phase and the bottom phase, standing for the salt-rich phase and alcohol-rich phase, respectively. Assuming that the first term on the right side of this equation can be ignored relative to the second term, a Setschenow-type equation can be obtained, meaning that kMA b b ks because the absolute value of (c1b − c1t) exceeds that of (c2b − c2t). The salting-out coefficients, ks, along with the corresponding intercepts, correlation coefficients (R2) and standard deviations (sd), are listed in Table 9. From this table, it can be observed that the Setschenow-type equation can be satisfactorily applied to the correlation of tie-line data for the investigated systems.

Table 7 Parameters of Eq. (6a) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4 Ethanol + 2-propanol + Na2SO4 MA2 = 0.250 Ethanol + 2-propanol + (NH4)2SO4 a

T/K

V*213

f213

R2

sda

308.15 318.15 328.15 308.15

2.6464 2.7672 2.6713 3.4461

−0.0078 −0.0353 −0.0168 0.0123

0.9703 0.9859 0.9797 0.9914

1.01E−03 4.47E−04 8.55E−05 2.19E−04

308.15

3.0006

0.0016

0.9890

8.32E−04

Definition is given in Table 3.

Fig. 4. Effect of the mass fraction of ethanol in the alcohol mixture on tie-lines for alcohol mixture (1) + (NH4)2SO4 (2) + water ATPSs at 308.15 K: ■ MA1 = 0.667; Δ MA2 = 0.250.

Y. Li et al. / Journal of Molecular Liquids 211 (2015) 924–933

931

Table 10 Parameters of Eq. (8) for the mixture of ethanol and 2-propanol (1) + (NH4)2SO4 (2) + water ATPSs at different temperatures. System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4 a

T/K

10−3ks

KMA

R2

sda

308.15 318.15 328.15

3.6829 3.4488 3.5200

123.0392 86.2797 76.9894

0.9994 0.9993 0.9993

1.35E−05 1.06E−05 2.18E−05

Definition is given in Table 9.

correlation using the temperature-dependent Setschenow equation were not changed. In our study, a relatively simple equation with two parameters also was used to correlate the tie-line data, which can be derived from the binodal theory as follows [33]:

ln Fig. 5. Effect of temperature on tie-lines for alcohol mixture (MA1 = 0.667) (1) + (NH4)2SO4 (2) + water ATPSs: ■ 308.15 K; ☆ 318.15 K; Δ 328.15 K.

Recently, for the temperature dependency of fitting parameters of the Setschenow equation, Zafarani-Moattar et al. adopted a simple form for each parameter and used the equation to correlate the experimental LLE data of their polymer–salt ATPSs determined at different temperatures [40,41]. According to their work, we adopted a simple form for each parameter of the Setschenow equation, as follows:

ln

ct1 cb1

! ¼

kMA ks
b t  þ c −c T T 2 2

ð8Þ

where ks is the salting-out coefficient, kMA is a constant, and c1 and c2 represent the molality of the alcohol mixture and the salt, respectively. The two superscripts “t” and “b” represent the top phase and the bottom phase, standing for the salt-rich phase and alcohol-rich phase, respectively. The experimental LLE data of ethanol + 2-propanol (MA1 = 0.667) + (NH4)2SO4 + water system at T = 308.15, 318.15, and 328.15 K were correlated using Eq. (8), and the fitting parameters ks, kMA along with correlation coefficients (R2) and standard deviations (sd) are listed in Table 10. From Table 10, it can be observed that the fitting parameters ks and kMA were slightly different at the three temperatures. On the basis of the standard deviations (sd) and correlation coefficient values (R2), the temperature-dependent Setschenow equation shows that the experimental LLE data achieved good accuracy for the studied system at T = 308.15, 318.15, and 328.15 K. Compared to the fitting results using the previous Setschenow equation, the sd and R2 derived from the

wt2 wb2

!


 ¼ β þ k wb1 −wt1

ð9Þ

where k is the salting-out coefficient and β is the constant most closely related to the activity coefficient. The superscripts “t” and “b” represent the top phase and the bottom phase, respectively. This equation was successfully used to correlate the tie-line data for polymer–salt ATPSs [4,42] and IL–salt ATPSs [43]. The fitting parameters of Eq. (9), together with the correlation coefficients (R2) and the standard deviations (sd), are provided in Table 11. This expression shows strong agreement when correlated with the experimental tie-line data. On the basis of the standard deviations (sd) and correlation coefficient values (R2) presented in Tables 9–11, it can be concluded that Eqs. (7)–(9) represent the experimental LLE data with good accuracy for the investigated system, especially the two-parameter equation, which performs with the most satisfactory accuracy among the three equations. Moreover, the results show good reliability of the experimental tie-line data and calculation methods used. 3.6. Effect of the mass fraction of ethanol in the alcohol mixture on tie-lines In this work, the alcohol mixture in the systems containing ethanol, 2-propanol, salt [(NH4)2SO4/Na2SO4] and water was enriched in the bottom phase, which we call the alcohol-rich phase; the top phase was shown to be the complementary salt-rich phase. To show the effect of the mass fraction of ethanol in the alcohol mixture on the phase equilibrium compositions for the investigated system, the experimental tie-lines for the ATPSs consisting of two alcohol mixtures (MA1 = 0.667, MA2 = 0.250), (NH4)2SO4 and water determined at T = 308.15 K are described in Fig. 4. The absolute value of the slope for the tie-lines of the system containing the alcohol mixture MA1 = 0.667 is less than that of the system with MA2 = 0.250, suggesting that some water transfer occurs from the top phase to the bottom

Table 9 Parameters of Eq. (7) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. T/K

ks

Intercept

R2

δ(ks)b

δ(intercept)c

sda

Ethanol + 2-propanol + Na2SO4

308.15 318.15 328.15 308.15

11.9515 10.8400 10.7268 14.3390

0.3993 0.2712 0.2346 0.2885

0.9994 0.9993 0.9993 0.9984

0.15 0.14 0.14 0.28

0.02 0.02 0.01 0.03

1.35E−05 1.06E−05 2.18E−05 1.01E−04

MA2 = 0.250 Ethanol + 2-propanol + (NH4)2SO4

308.15

14.2064

0.4282

0.9987

0.26

0.03

6.45E−05

System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4

a

N

2 2

b bot bot 0:5 sd ¼ ð∑ð100wtop −100wtop i; j; exp Þ þ ð100wi; j;cal −100wi; j; exp Þ =6NÞ , where N is the number of tie-lines and j is the number of components in each phase. δ(ks) is the standard deviation i; j;cal

i¼1

for the fitting parameters of “ks”. δ(intercept)c is the standard deviation of the fitting parameters of the “intercept”.

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Table 11 Parameters of Eq. (9) for the mixture of ethanol and 2-propanol (1) + salt (2) + water ATPSs at different temperatures. System MA1 = 0.667 Ethanol + 2-propanol + (NH4)2SO4 Ethanol + 2-propanol + Na2SO4 MA2 = 0.250 Ethanol + 2-propanol + (NH4)2SO4 a

T/K

k

β

R2

sda

308.15 318.15 328.15 308.15

0.0484 0.0467 0.0459 0.0633

−0.0651 −0.0342 −0.0357 −0.0728

0.9999 0.9999 0.9999 0.9996

1.17E−06 4.68E−07 4.57E−06 1.62E−05

308.15

0.0524

−0.1193

0.9997

1.71E−05

Definition is given in Table 9.

phase when the mass fraction of ethanol in the alcohol mixture increases. The reason for this transfer may be that the hydration abilities of ethanol and 2-propanol increase as the homologous phaseseparation ability decreases [44]; that is, the interaction force between the alcohol molecules and water molecules is stronger when the alcohol's phase-separation ability decreases. Therefore, when the MA value increases, the amount of 2-propanol in the alcohol mixture will decrease, which weakens the phase-separation ability of the alcohol mixture and correspondingly strengthens its hydration ability. The alcohol molecules can then attract more water molecules and become enriched in the bottom phase, finally resulting in the alcohol-rich phase becoming diluted while the salt concentration in the salt-rich phase increases. Thus, as the mass fraction of ethanol in the alcohol mixture increases, the absolute value of the slope for the tie-lines decreases. This behaviour suggests that the phase-separation ability of the alcohol mixture in the investigated system decreases with increasing MA values. 3.7. Effect of temperature on tie-lines The tie-lines for the systems consisting of the alcohol mixture MA1 = 0.667, (NH4)2SO4 and water determined at T = 308.15, 318.15, and 328.15 K are illustrated in Fig. 5 to demonstrate the influence of temperature on the tie-lines. As shown in Fig. 5, the tie-lines at the three temperatures are all parallel. This phenomenon occurred because temperature has little influence on the phase equilibrium compositions, so there is no significant change in the slope of the tie-lines with increased temperature. This situation mainly occurs because when the salt concentration in the system with the alcohol mixture MA1 = 0.667, (NH4)2SO4 and water is lower than 25% by mass fraction, the system will be less sensitive to changes in temperature, and the liquid–liquid equilibrium condition will be maintained. 4. Conclusions Liquid–liquid equilibrium data have been determined for ethanol + 2-propanol (MA1 = 0.667, MA2 = 0.250) + salt ((NH4)2SO4/Na2SO4) + H2O ATPSs at T = 308.15, 318.15, and 328.15 K. The Merchuk equation and three other equations were successfully used to correlate binodal data, and tie-lines were described by the Setschenow-type equation and a two-parameter equation. The Setschenow-type equation was adopted to the temperaturedependent expression and was also used to correlate the experimental LLE data. All the fitted results show good agreement with the experimental data, which reflects the good reliability of the experimental data and calculation methods used. The effect of temperature on the binodal curves of the investigated systems was determined: as temperature decreases, the separated two-phase area increases when the salt concentration is greater than 25% by mass fraction because the decrease in solubility of (NH4)2SO4 causes the hydration of salt ions to correspondingly weaken, whereas systems with a salt concentration less

than 25% are less sensitive to temperature. The effect of the salt and differently proportioned alcohol mixture on the phase-forming ability also has been studied based on EEV values obtained from the binodal model. Salting-out ability can be ranked as Na2SO4 N (NH4)2SO4, and the phaseseparation ability of the alcohol mixture was strengthened as the mass fraction of ethanol in the alcohol mixture decreased. Conflict of interests None of the authors of the manuscript have a direct financial relation with the commercial identity mentioned in this paper. Acknowledgements This work was sponsored by the National Natural Science Foundation of China (No. 41472220); the Research and Development Project of Science and Technology for Shaanxi Province (Nos. 2013JQ2019 and 2015KJXX-25), the Fundamental Research Funds for the Central Universities (Nos. 310829153507, 2014G3292007 and 310829151143), Project funded by China and Shaanxi Postdoctoral Science Foundation (Nos. 2014M552400), and the National Training Projects of the University Students’ Innovation and Entrepreneurship program (Nos. 201510710071 and 201510710077). References [1] Alireza Salabat, The influence of salts on the phase composition in aqueous twophase systems: experiments and predictions, Fluid Phase Equilib. 187–188 (2001) 489–498. [2] Rahmat Sadeghi, Measurement and correlation of phase equilibria for several PVP + salt aqueous two-phase systems at 303.15 K, Fluid Phase Equilib. 237 (1) (2005) 40–47. [3] Pedro P. Madeira, Xin Xu, Youting Wu, et al., Liquid–liquid equilibrium of aqueous polymer two-phase systems using the modified Wilson equation, Ind. Eng. Chem. Res. 44 (7) (2005) 2328–2332. [4] Mohammed Taghi Zafarani-Moattar, Parinaz Seifi-Aghjekohal, Liquid–liquid equilibria of aqueous two-phase systems containing polyvinylpyrrolidone and tripotassium phosphate or dipotassium hydrogen phosphate: experiment and correlation, Calphad 31 (4) (2007) 553–559. [5] Yun Wang, Shiping Hu, Juan Han, et al., Measurement and correlation of phase diagram data for several hydrophilic alcohol + citrate aqueous two-phase systems at 298.15 K, J. Chem. Eng. Data 55 (11) (2009) 4574–4579. [6] Yun Wang, Shiping Hu, YongSheng Yan, et al., Liquid–liquid equilibrium of potassium/sodium carbonate + 2-propanol/ethanol + water aqueous two-phase systems and correlation at 298.15 K, Calphad 33 (4) (2009) 726–731. [7] Hans-Olof Johansson, Tiago Matos, Juliana S. Luz, et al., Plasmid DNA partitioning and separation using poly (ethylene glycol)/poly (acrylate)/salt aqueous twophase systems, J. Chromatogr. A 1233 (2012) 30–35. [8] Wu. Qiang, Dongqiang Lin, Qilei Zhang, Dong Gao, Shanjing Yao, Evaluation of poly(ethylene glycol)/hydroxypropyl starch aqueous two-phase system for the separation of monoclonal antibodies from cell culture supernatant, J. Sep. Sci. 37 (2014) 447–453. [9] Ana M. Azevedo, A. Gabriela Gomes, Paula A.J. Rosa, et al., Partitioning of human antibodies in polyethylene glycol sodium citrate aqueous two-phase systems, Sep. Purif. Technol. 65 (1) (2009) 14–21. [10] Chiyang He, Shehong Li, Huwei Liu, et al., Extraction of testosterone and epitestosterone in human urine using aqueous two-phase systems of ionic liquid and salt, J. Chromatogr. A 1082 (2) (2005) 143–149. [11] Celeste C. Ibarra-Herrera, Oscar Aguilar, Marco Rito-Palomares, Application of an aqueous two-phase systems strategy for the potential recovery of a recombinant protein from alfalfa (Medicago sativa), Sep. Purif. Technol. 77 (1) (2011) 94–98. [12] Ratthaya Lertlapwasin, Nakara Bhawawet, Apichat Imyim, et al., Ionic liquid extraction of heavy metal ions by 2-aminothiophenol in 1-butyl-3-methylimidazolium hexaflorophosphate and their association constants, Sep. Purif. Technol. 72 (1) (2010) 70–76. [13] T. Agasøster, Aqueous two-phase partitioning sample preparation prior to liquid chromatography of hydrophilic drugs in blood, J. Chromatogr. B Biomed. Sci. Appl. 716 (1–2) (1998) 293–298. [14] Luis Henrique Mendes da Silva, M.C.H. da Silva, J.A. Júnior, et al., Hydrophobic effect on the partitioning of [Fe(CN)5(NO)]2− and [Fe(CN)6]3− anions in aqueous twophase systems formed by triblock copolymers and phosphate salts, Sep. Purif. Technol. 60 (1) (2008) 103–112. [15] Hongju Zhu, Yu ding, Yawei Jia, Hesperidin extraction from orange peel with new aqueous two-phase system, J. Food Sci. Biotechnol. 32 (9) (2013) 995–1001. [16] Xingli Liu, Taihua Mu, Hongnan Sun, Miao Zhang, Jingwang Chen, Optimisation of aqueous two-phase extraction of anthocyanins from purple sweet potatoes by response surface methodology, Food Chem. 141 (2013) 3034–3041.

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Glossary N: number of solubility data N: number of tie-lines T: temperature (K) MA: mass fraction of ethanol in alcohol mixture TLL: tie-line length S: slope of the tie-line w: mass fraction ks, k: salting-out coefficient β: interaction parameter V*213: scaled EEV of salt f213: volume fraction M: molar mass a, b, c, d, a1, b1, a2, b2: fitting parameters R2: correlation coefficient sd: standard deviation Super/subscript

b: bottom phase t: top phase cal: calculated value exp: experimental value 1: the mixture of ethanol and 2-propanol 2: salt 3: water