Measurement and Correlation of Phase Equilibria in Aqueous Two

Article pubs.acs.org/jced

Measurement and Correlation of Phase Equilibria in Aqueous TwoPhase Systems Containing Polyoxyethylene Lauryl Ether and Diammonium Hydrogen Phosphate or Dipotassium Hydrogen Phosphate at Different Temperatures Yang Lu,†,‡ Juan Han,† Zhenjiang Tan,*,‡ and Yongsheng Yan*,† †

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

‡

ABSTRACT: The phase diagrams for the systems containing polyoxyethylene lauryl ether (Brij35) and K2HPO4/(NH4)2HPO4 have been determined experimentally at three temperatures, (288.15, 298.15, and 308.15) K. Three experiential equations were used to correlate the binodal data. The liquid−liquid equilibrium (LLE) data of these systems obtained by the experimental method were fitted by using Othmer−Tobias and Bancroft along with simple Setschenow-type equations. Furthermore, the effect of temperature on the binodal curve for the disquisitive systems has been discussed, and it was found that two-phase region expands with the increase in temperature, which is corresponded to the value of the effective excluded volume (EEV) calculated according to the binodal model. In the investigated systems, the free energy (ΔG), enthalpy change (ΔH), and entropy change (ΔS) were calculated, and it indicated that the phase separation processes are endothermic and driven by the entropy increase. That the slope of tie-line increases with the rising temperature was mainly caused by the hydrophobicity of Brij35 which changes with the temperature being varied.

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INTRODUCTION As a new kind of green separation technology, the aqueous twophase system (ATPS) has drawn more attention nowadays, which had previously been generally used for the separation and purification of the biomolecules,1−4 antibiotics,5−9 and metal ions.10−12 The ATPS has been widely used in the field of extraction and purification because of its excellent properties, such as nontoxicity, the lower cost, and the possibility of largescale applications. Both phases of ATPS contain a lot of water, and therefore it provides relatively mild extraction conditions and is more suitable for the purification of biologically active substances. The initial ATPS is constituted at a certain critical concentration of polymer and polymer or polymer and salt. In recent years, there have been some new types of ATPS's, like the ionic liquid−salt ATPS and small molecule organic solvent−salt ATPS. However, few studies on surfactant polyoxyethylene-n-alkyl-ether (BrijX) and salt ATPS have been reported. Only Masumeh et al. have investigated ATPS's composed of surfactant polyoxyethylene cetyl ether (Brij58) and salts at different temperatures13,14 and concluded that the Brij58−salt ATPS's have a series of advantages compared with other systems, such as material saving, lower interface tension, and the ease of waste disposal. Kellermayer et al.15 have used surfactant Brij58 to separate lipids and proteins. As a nonionic surfactant, polyoxyethylene lauryl ether (Brij35, C32H66O11) contains a hydrophobic alkyl tail and a hydrophilic polyoxyethylene domain; thus Brij35 can be an © 2012 American Chemical Society

appropriate candidate for forming surfactant−salt ATPS's, which has huge potential for separating and purifying the biological materials. In this paper, the binodal data of the systems containing Brij35 and K2HPO4/(NH4)2HPO4 were determined at three temperatures of (288.15, 298.15, and 308.15) K and were correlated with three experiential equations. The effect of temperature and type of salts on the binodal curve was studied. The composition of two phases at equilibrium state was determined at different temperatures, and the data were also fitted using several equations. The slope of the tie-line was affected by the temperature change, due to the fact that the rising temperature leads to the variation of hydrophobicity of Brij35, which will be discussed in detail.

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EXPERIMENTAL SECTION Materials. Nonionic surfactants Brij35 with a quoted purity of greater than 0.99 mass fraction was purchased from Aladdin Reagent Company (Shanghai, China). The average molar mass, the critical micelle concentration (CMC), the hydrophilic lipophilic balance (HLB), and the melting point of the Brij35 is 626.86 g·mol−1, 0.09 mg·L−1, 16.9, and 300.15 K, respectively. K2HPO4 and (NH4)2HPO4 were obtained from the Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China), which were Received: April 16, 2012 Accepted: June 27, 2012 Published: July 12, 2012 2313

dx.doi.org/10.1021/je3004468 | J. Chem. Eng. Data 2012, 57, 2313−2321

Journal of Chemical & Engineering Data

Article

Table 1. Binodal Data for the Brij35 (1) + K2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa 288.15 K

a

298.15 K

308.15 K

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

18.8317 17.6598 16.6251 15.7716 15.0318 14.2079 13.4991 12.7324 12.1328 11.6097 10.9953 10.6179 10.0621 9.6350 9.2873 8.7454 8.1820 7.6044 7.1525 6.7597 6.3529 5.6970 5.1565 4.6672 4.0516 3.5414 3.1589 2.7645 2.1413 1.6090

6.5456 6.8245 7.0864 7.2805 7.4479 7.6762 7.8891 8.1124 8.2808 8.3990 8.5778 8.6669 8.8425 8.9707 9.0735 9.2176 9.3856 9.5739 9.7531 9.8920 10.0283 10.2617 10.4768 10.6542 10.9045 11.1125 11.2457 11.4251 11.6899 11.9578

1.2695 1.0104 0.5948 0.4214 0.2907 0.1463 0.0821 0.0421 0.0216 0.0113 0.0072 0.0049 0.0040 0.0033 0.0031 0.0028 0.0025 0.0023 0.0021

12.1556 12.3310 12.6293 12.8276 13.0015 13.3284 13.6009 13.8471 14.0710 14.3323 14.6034 14.9263 15.1677 15.7179 15.9620 16.3277 16.6285 16.9956 17.4149

21.1295 20.2421 19.5994 18.9065 18.1601 17.4662 16.7378 16.0893 15.3086 14.6228 14.0423 13.5735 13.1510 12.4968 11.6765 11.0258 10.3679 9.7872 9.0083 8.4488 7.9894 7.2521 6.5245 5.8889 5.1075 4.3515 3.5395 2.9883 2.4329 2.0210

5.5655 5.7241 5.8791 6.0343 6.2296 6.4005 6.5714 6.7378 6.9387 7.0851 7.2072 7.3048 7.3943 7.5807 7.7629 7.9606 8.1166 8.2498 8.4947 8.6464 8.7696 8.9752 9.1752 9.3393 9.5528 9.7416 9.9990 10.2255 10.4272 10.6384

1.4471 1.0051 0.7470 0.3850 0.2790 0.1499 0.0818 0.0466 0.0175 0.0104 0.0083 0.0058 0.0045 0.0039 0.0036 0.0033 0.0028

10.9105 11.1531 11.3599 11.5863 11.8622 12.1528 12.4359 12.7227 13.0212 13.2780 13.5817 13.8756 14.2165 14.5831 14.8298 15.0833 15.5397

21.6440 20.8800 19.9970 19.2700 18.5860 17.8160 17.1440 16.4710 15.9540 15.3700 14.8410 14.2870 13.8070 13.3030 12.5510 11.8820 11.5500 10.9430 10.1930 9.6930 9.2830 8.6590 7.7370 7.1000 6.5760 5.8740 5.0200 4.4760 4.0990 3.7980

4.2320 4.2990 4.4120 4.5350 4.6350 4.8100 4.9360 5.1080 5.1970 5.3500 5.4690 5.6160 5.7320 5.8470 5.9950 6.1560 6.2290 6.3850 6.5710 6.6910 6.8020 6.9330 7.1530 7.2910 7.4440 7.5970 7.8130 7.9640 8.1230 8.2560

3.4510 2.8970 2.5620 2.1760 1.8440 1.5670 1.2960 1.0980 0.8600 0.6590 0.5240 0.3950 0.1810 0.0536 0.0363 0.0272 0.0190 0.0138 0.0099 0.0085 0.0077 0.0072 0.0066 0.0062 0.0058 0.0056 0.0054 0.0052 0.0051 0.0048

8.3980 8.6270 8.8280 9.0180 9.2200 9.4100 9.5650 9.7640 9.9630 10.1720 10.3390 10.5630 10.8700 11.1160 11.3390 11.5250 11.7590 11.9260 12.0870 12.2610 12.4030 12.6190 12.8230 13.0520 13.3970 13.6570 13.9580 14.1960 14.4170 14.8130

Standard uncertainties u are u(w) = 0.00001, u(T) = 0.05 K, and u(p) = 10 kPa.

formed, the concentration of Brij35 and salt were determined, respectively. The concentration of Brij35 in top and bottom phases was determined at 231 nm using UV−vis spectrometer (UV-2450, Shimadzu Corporation, Japan). The uncertainty in measuring the mass fraction of the Brij35 was found to be 0.001. The concentration of K2HPO4 in phases was determined by flame photometry (TAS-968, Beijing Purkinje General Instrument Co., Ltd., China), and the concentration of (NH4)2HPO4 in both phases was determined using conductivity measurements17,18 (DDSJ-308A, Shanghai Precision and Scientific Instrument Co., Ltd., China). The precision in the measurement of the mass fraction of the K2HPO4 was better than 0.0002. The relationship between the mass fraction of (NH4)2HPO4 and the conductivity is given by

analytical grade reagents (GR, min. 99 % by mass fraction). All reagents were used without further purification, and the water used in experiments was double-distilled. Apparatus and Procedure. The binodal data of the investigated systems were determined by using the cloud-point method.16 The vessel used to carry out the experiment was a glass vessel whose volume was 50 mL. The glass vessel was jacketed with a coat in which water was circulated using a water thermostat (DC-2008, Shanghai Hengping Instrument Factory, China). The temperature of the water in the jacket was controlled at the constant temperature. The Brij35 solution was added into the glass vessel from the stock solution with a known mass fraction. Then the salt solution with known mass fraction was dropped into the vessel until the mixed solution turned turbid. To verify the cloud point, one drop of water was taken into the compound to make the mixed solution clear. The above procedures were repeated to determine the following cloud point, and the cloud point was noted using an analytical balance (BS124S, Beijing Sartorius Instrument Co., China) with an uncertainty of 1.0·10−7 kg. To determine the data of the liquid−liquid equilibrium for the studied systems, the feed samples made by mixing Brij35, salt, and water at a proper ratio were taken into the vessel. The sample was kept stirring for 0.5 h and was placed in the thermostat water bath to settle for 48 h, in which water was controlled at a desired temperature. After the ATPS was

k = a0 + a1w2

(1)

where k is the conductivity (μS·cm−1), w2 is the mass fraction of (NH4)2HPO4, and a0 and a1 are the coefficients, the value of which are 0.02997 and 0.80032. The precision of the mass fraction of (NH4)2HPO4 achieved using eq 1 is less than 0.0002. The density of the aqueous solutions of Brij35 with known mass fraction was determined with a density meter (model Anton Paar DMA-4100) with an uncertainty of 0.0001 g·mL−1 at a certain temperature which was controlled within 0.05 K 2314



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Table 2. Binodal Data for the Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa 288.15 K

a

298.15 K

308.15 K

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

100 w1

100 w2

17.5369 16.6700 15.7369 14.8723 14.0623 13.4403 12.7634 12.1358 11.4733 10.9538 10.4989 10.0858 9.6705 9.0309 8.4552 7.9320 7.3569 6.9645 6.5301 5.8361 5.2249 4.7352 4.1661 3.7572

6.6548 6.8726 7.1136 7.3518 7.5625 7.7134 7.9118 8.1352 8.3239 8.4899 8.6115 8.7236 8.8739 9.0819 9.2543 9.3909 9.6031 9.7066 9.8831 10.1282 10.3202 10.5349 10.7754 10.9393

3.2899 2.7977 2.3329 1.9579 1.4075 0.8279 0.5770 0.4072 0.2711 0.1333 0.0733 0.0616 0.0324 0.0221 0.0111 0.0082 0.0062 0.0055 0.0047 0.0040 0.0038 0.0034

11.0901 11.2867 11.5119 11.6737 11.9093 12.2611 12.5370 12.7219 12.9603 13.3398 13.6610 13.9887 14.1122 14.4103 14.7504 15.0673 15.3751 15.7845 16.2211 16.8247 17.4318 17.8459

19.7767 18.8023 17.8438 16.8655 16.0528 15.4235 14.6568 14.1155 13.5576 12.9575 12.4192 11.5556 10.7712 10.0549 9.4372 8.5397 7.7333 7.0214 6.3951 5.6940 4.8793 4.3039 3.6174 2.8602

5.8632 6.0373 6.2588 6.4870 6.6749 6.8180 7.0041 7.1146 7.2624 7.4334 7.5851 7.7893 8.0028 8.1983 8.3435 8.5620 8.7895 8.9912 9.2176 9.4493 9.7265 9.9635 10.2086 10.4730

2.2255 1.7804 1.3533 0.8342 0.5585 0.4541 0.2745 0.1934 0.1100 0.0531 0.0268 0.0213 0.0171 0.0098 0.0062 0.0046 0.0037 0.0029 0.0020

10.7153 10.8917 11.0927 11.3791 11.6658 11.7983 12.0712 12.3158 12.4789 12.7669 12.9746 13.1732 13.3817 13.6780 13.9079 14.1356 14.4814 14.7695 15.1539

20.2012 19.4574 18.6561 17.9588 17.3401 16.7549 16.1748 15.4932 14.8868 14.3895 13.8839 12.9670 12.1149 11.4119 10.5654 9.7831 9.3031 8.8147 8.3910 7.9738 7.3301 6.7552 6.2656 5.6026

5.1772 5.2993 5.4555 5.5965 5.7143 5.8178 5.9318 6.0902 6.2436 6.3492 6.4773 6.6739 6.8558 7.0168 7.2014 7.3768 7.5110 7.6568 7.7739 7.8854 8.0595 8.2434 8.3772 8.5905

4.9357 4.1740 3.6306 2.9821 2.4763 1.9465 1.4456 1.0336 0.8105 0.5713 0.3926 0.3236 0.1493 0.0850 0.0689 0.0502 0.0322 0.0172 0.0115 0.0072 0.0047 0.0035 0.0029

8.7841 9.0272 9.1919 9.3981 9.5702 9.7879 10.0224 10.2273 10.4443 10.6809 10.9230 11.1358 11.3673 11.5797 11.7136 11.9090 12.0965 12.3072 12.5807 12.8494 13.2898 13.6972 14.1509


using a water thermostat (DC-2008, Shanghai Hengping Instrument Factory, China).

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RESULTS AND DISCUSSION Binodal Data and Correlation. The binodal data of the systems containing Brij35 and K2HPO4/(NH4)2HPO4 were determined at three temperatures, which were given respectively in Tables 1 and 2. The binodal curves for the investigated systems were plotted in Figures 1 and 2. Three experiment equations (eqs 2 to 4) were used to correlate all of the binodal data. 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)

Figure 1. Binodal curves of the Brij35 (1) + K2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K. ○, 288.15 K; △, 298.15 K; □, 308.15 K; solid line, reproduced by eq 2.

The variables w1 and w2 represent the mass fraction of Brij35 and salts, and a, b, c, and d are fitting parameters. Wang et al.19 used eq 2 to fit the binodal data of the systems composed of micromolecule organic solvent and salts at 298.15 K and obtained desirable results. The binodal data of poly(ethylene glycol) (PEG)−salts ATPS's20 were correlated using the thirdorder polynomial equation (eq 3). Equation 4 was generally applied to the correlation of the binodal curves of ATPS's.21−26 Tables 3 to 5 represent the values of fitting parameters in these equations along with the square of correlation coefficients (R2) and the corresponding standard deviations (SDs) for those systems, respectively. Although three equations showed good relativity in the investigated systems, we found that the eq 2 was more appropriate to fit the binodal curves by comparing

the square of correlation coefficients and the corresponding SDs of every system which is listed in three tables. Effect of Temperature on the Hydrophobicity of Brij35. Following Zafarani-Moattar et al.,27 the excess specific volume (VE) is determined according to this equation (eq 5). VE =

⎛w w ⎞ 1 − ⎜⎜ 1 + 2 ⎟⎟ ρ ⎝ ρ1 ρ2 ⎠

(5)

where ρ represents the density of the aqueous solutions of Brij35, w is the mass fraction, and the subscripts “1” and “2” stand for the Brij35 and water. The VE of the aqueous solutions 2315



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systems were given in Table 7. According to the values of V*213 listed in Table 7, it was found that EEV increased with the rising temperature, which was caused by the variation in hydrophobicity of Brij35. In fact, Brij35 is more hydrophobic with the increase in temperature, as a result, salt is easier to exclude the Brij35 from salt-rich phase to Brij35-rich phase. So with Brij35 being controlled at the same concentration, the concentration of the salt at which the ATPS is formed turns lower with the rising temperature. Effect of the Temperature on Binodal Curves. The binodal curves of the Brij35-K2HPO4 ATPS and those of the Brij35-(NH4)2HPO4 ATPS at the (288.15, 298.15, and 308.15) K were respectively plotted in Figures 1 and 2. It has been found that the binodal curve travels toward the axis of the coordinate with the temperature rising from 288.15 K to 308.15 K. In other words, the rising temperature will lead to the expansion of two-phase region. This phenomenon was observed in most of polymer−salt ATPS's, such as PEG− salts29−32 and PPG−salt33−35 ATPS's. However, there are some exceptions; namely, the binodal curves of some systems (e.g., the PVP-salt ATPS's36,37) were hardly influenced by the temperature changes. That is because the hydrophobicity of some polymer strengthens with the rising temperature and that causes the decrease of polymer hydration power. Thus, it is concluded that with the temperature being rising, the critical concentration of salt above which the two phases formed will decreases and that is in line with the results obtained from the EEV. Rahmat et al.38 consider the clouding as the mark of the separation of phase; the free energy of the two-phase (ΔG) formation can be obtained according to the follow equation

Figure 2. Binodal curves of the Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K. ○, 288.15 K; △, 298.15 K; □, 308.15 K; solid line, reproduced by eq 2.

of Brij35 at the temperatures T = (283.15 to 313.15) K were listed in Table 6. Zafarani-Moattar et al. held that the behavior of VE is attributed to the intermolecular interactions between the hydrogen atom of the water and the oxygen atoms of the polymer and difference between the size of water and polymer. At the low temperatures the more negative value of VE is consistent with the strong hydrogen bond interactions between polymer and water. Instead, the hydrogen bond interactions are weakened at the higher temperatures, and less negative values of VE are obtained. Therefore, we may conclude that the Brij35 becomes more hydrophobic with the increasing temperature according to the values of VE in Table 6. Effective Excluded Volume and Phase-Separation Abilities of Salts. The effective excluded volume (EEV) is determined from the binodal model developed by Guan et al.28 on the base of statistical geometry for ATPS containing two polymers. In the present work, we applied EEV to the surfactant−salt ATPS so as to study the effect of temperature on the phase-separation abilities of ATPS. The equation for our investigated systems is written as ⎛ w ⎞ w * 2 ⎟ + V 213 * 1 =0 ln⎜V 213 M2 ⎠ M1 ⎝

ΔG = RT ln(X )

(7)

where X is the mole fraction concentration of salt and the value of ΔG is listed in Table 8. The enthalpy change (ΔH) is calculated by processing the free energy at different temperatures from the slope of linear dependency of the plots ΔG/T against 1/T using this equation ΔH =

d(ΔG /T ) d(1/T )

(8)

The value of ΔH is shown in Table 8. The entropy change (ΔS) is calculated using the Gibbs−Helmholtz equation (eq 9), and the value is also given in Table 8.

(6)

where w1 and w2 are the mass fraction of Brij35 and salts, M1 and M2 are molar mass of Brij35 and salts, and V*213 is the scaled EEV of salt, respectively. The values of V*213 along with the square of correlation coefficient (R2) and SDs for the studied

ΔS =

ΔH − ΔG T

(9)

Table 3. Values of Parameters of Equation 2 for the Brij35 (1) + K2HPO4/(NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K T/K

a

288.15 298.15 308.15

36.92277 33.88888 20.76488

288.15 298.15 308.15

39.59151 35.11090 32.76918

b

c

d

Brij35 (1) + K2HPO4 (2) + H2O (3) −32.05305 8.68079 −0.20518 −31.40847 9.15858 −0.24880 −19.72374 6.34032 −0.22128 Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) −34.77796 9.44387 −0.22238 −31.91387 9.09791 −0.23814 −31.04575 9.29846 −0.27071

R2

100 SDa

0.99919 0.99951 0.99974

0.15912 0.14917 0.09943

0.99911 0.99938 0.99955

0.15910 0.15488 0.13601

exp 2 exp cal 0.5 SD = (∑ni=1(wcal 1 − w1 ) )/n) , where w1 is the experimental mass fraction of Brij35 in Tables 1 and 2 and w1 is the corresponding data calculated using eq 2. n represents the number of binodal data. a

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a

b

c

288.15 298.15 308.15

−0.00282 0.00685 −0.01484

0.37036 0.12513 0.75967

288.15 298.15 308.15

−0.00491 0.00594 0.00040

d

Brij35 (1) + K2HPO4 (2) + H2O (3) −9.28328 64.92648 −7.15620 56.28412 −11.99935 59.91524 Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) 0.42992 −9.7209 65.14902 0.15275 −7.37525 56.71721 0.37774 −9.61194 59.93275

R2

100 SDa

0.99733 0.99661 0.99712

0.28888 0.39353 0.37160

0.99551 0.99836 0.99834

0.35744 0.25219 0.26192

exp 2 exp cal 0.5 SD = (∑ni=1(wcal 1 − w1 ) )/n) , where w1 is the experimental mass fraction of Brij35 in Tables 1 and 2 and w1 is the corresponding data calculated using eq 3. n represents the number of binodal data. a


a

288.15 298.15 308.15 288.15 298.15 308.15

b

R2

c

Brij35 (1) + K2HPO4 (2) + H2O (3) 11.42893 0.38748 0.00185 0.99805 11.05013 0.44758 0.00253 0.99832 37.79637 −0.17457 0.00314 0.99905 Brij35 (1)+ (NH4)2HPO4 (2) + H2O (3) 6.92075 0.57577 0.00198 0.99787 13.16066 0.35269 0.00235 0.99823 19.99162 0.17136 0.00292 0.99846

Table 7. Values of Parameters of Equation 6 for the Brij35 (1) + K2HPO4/(NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K

100 SDa

T/K

0.25014 0.28036 0.14037

288.15 298.15 308.15

0.24896 0.26596 0.25544

288.15 298.15 308.15

exp 2 exp 0.5 SD = (∑ni=1(wcal 1 − w1 ) )/n) , where w1 is the experimental mass fraction of Brij35 in Tables 1 and 2 and wcal 1 is the corresponding data calculated using eq 4. n represents the number of binodal data.

V213 * /g·mol−1

R2

Brij35 (1) + K2HPO4 (2) + H2O (3) 1400.00 0.99721 1535.85 0.99920 1750.40 0.99970 Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) 1101.13 0.99682 1201.50 0.99929 1867.94 0.99928

100 SDa 0.01062 0.00878 0.01064 0.01620 0.01268 0.02222

exp 2 exp 0.5 SD = (∑ni=1(wcal 1 − w1 ) )/n) , where w1 is the experimental mass fraction of Brij35 in Tables 1 and 2 and w1cal is the corresponding data calculated using eq 6. n represents the number of binodal data.

a

a

On the basis of the calculated data reported in Table 8, it was found that the free energy has a negative value and the value of enthalpy change is greater than zero. Therefore, the phase separation processes are endothermic and driven by entropy increase, which is consistent with the conclusion for aqueous solutions of electrolytes and PEG obtained by da Silva and Loh,39 who hold that the phase separation for aqueous solutions of PEG and salt was accompanied by an enthalpy increase according to the enthalpy of electrolyte solution in aqueous PEG solutions and in pure water measured with calorimetry. Effect of the Salt on Binodal Curves. In addition to the temperature, the type of salt is also an important factor to affect the formation of ATPS. The phase capacity of salt is related to the salting-out strength, which is sensitive to the anion and cation of salts. The salting-out capacity of salt with the same cation depends mainly on the anion, and the salting-out strength of salt increases with the valence of anion rising, which is suitable for most of the ATPS. The cation will also affect the salting-out strength of salt; in the present work, we studied the salting-out ability of K2HPO4 and (NH4)2HPO4 at 298.15 K,

which is plotted in Figure 3. These two salts have the same anion and different cations which were both monovalent cations. From Figure 3, it was found that the phase capacity of K2HPO4 is similar to that of (NH4)2HPO4. That is because K+ have the same salting-out strength as (NH4)+ in the case of the same anion, which was suggested by other literature.13 Liquid−Liquid Equilibrium Data and Correlation. For the systems composed of Brij35 and K2HPO4/(NH4)2HPO4, the liquid−liquid equilibrium (LLE) data determined at T = (288.15, 298.15, and 308.15) K were given in Tables 9 and 10, respectively. The tie-line of the investigated systems at three temperatures were plotted in Figures 4 and 5, respectively. The LLE data was correlated using the Othmer−Tobias and Bancroft40 equation (eqs 10 and 11) which were empirical correlation equations for the tie lines. ⎛ 1 − w b ⎞n ⎛ 1 − w1t ⎞ 2 ⎟⎟ ⎟ = k1⎜⎜ ⎜ t b ⎝ w1 ⎠ ⎝ w2 ⎠

(10)

Table 6. VE of the Aqueous Solutions of Brij35 for Different Brij35 Mass Fractions (w1) at the Temperatures T = (283.15 to 313.15) Ka T/K VE/mL·g−1 VE/mL·g−1 a

283.15

288.15

293.15

298.15

303.15

308.15

313.15

−0.02253

−0.02138

−0.02022

−0.01907

−0.01979

−0.01871

−0.01762

−0.01653

w1 = 0.1 −0.02600

−0.02485

−0.02369 w1 = 0.2

−0.02306

−0.02197

−0.02088

Standard uncertainties u are u(w) = 0.00001, u(T) = 0.05 K, and u(p) = 10 kPa. 2317



Article

Table 8. Free Energy Changes (ΔG), Entropy Changes (ΔS), and Enthalpy Changes (ΔH) for Clouding of K2HPO4 and (NH4)2HPO4 in the Presence of Brij35 for Different Mass Fractions (Wp) and Temperatures T = (288.15, 298.15, and 308.15) K ΔG/kJ·mol−1 (ΔS/kJ·mol−1·K−1) ΔH/kJ·mol Wp = 0.05 Wp = 0.10 Wp = 0.15

7.99 9.84 10.78

Wp = 0.05 Wp = 0.10 Wp = 0.15

5.34 5.95 5.54

−1

T = 288.15 K

T = 298.15 K

Brij35 (1) + K2HPO4 (2) + H2O (3) −3.03 (0.0383) −3.29 −4.30 (0.0491) −4.62 −5.30 (0.0558) −5.65 Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) −3.57 (0.0309) −3.85 −4.88 (0.0376) −5.22 −5.96 (0.0399) −6.29

T = 308.15 K

(0.0379) (0.0485) (0.0551)

−3.79 (0.0382) −5.28 (0.0491) −6.42 (0.0558)

(0.0308) (0.0375) (0.0397)

−4.19 (0.0309) −5.64 (0.0376) −6.76 (0.0399)

empirical correlation equations were widely used to fit the tieline compositions of various kinds of ATPS's.19,25,26,41 The fitted parameters, along with the square of correlation coefficient values (R2) and SDs for the studied systems are given in Table 11, which presents the satisfactory correlative degree. The LLE data of the investigated systems were fitted by the another equation (eq 12) so as to study the law of the LLE compositions. w2t = (r + k 32)w1t −

k 32

(12)

where wt1 and wt2 are the mass fraction of Brij35 and salts in the Brij35-rich phase, wb3 is the mass fraction of water in the saltrich phase, and k3 and r are the fitting parameters, respectively. This equation has been used for correlating the tie-line data of the polyvinylpyrrolidone42 and polyoxyethylene cetyl ether13 systems. The fitted parameters along with the square of correlation coefficient (R2) and SDs are presented in Table 12. The simple Setschenow-type equation (eq 13) on the basis of binodal theory43 was also used to correlate the tie-line data.

Figure 3. Binodal curves of the Brij35 (1) + K2HPO4/(NH4)2HPO4 (2) + H2O (3) ATPS's at 298.15 K. ○, K2HPO4; ×, (NH4)2HPO4.

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

ln(w2t /w3b)

(11)

⎛ wt ⎞ ln⎜⎜ 2b ⎟⎟ = β + k4(w1b − w1t) ⎝ w2 ⎠

where w is the mass fraction, the subscripts “1”, “2”, and “3” represent the Brij35, salt, and water, respectively; and the superscripts “t” and “b” stand for the top phase and bottom phase; and k1, k2, n, and r are the fitting parameters. The two

wt1

(13)

wb1

where and are the mass fraction of Brij35 in the top and bottom phases; wb2 and wt2 areis the mass fraction of salt in the

Table 9. Tie-Line Data for the Brij35 (1) + K2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa total system 100 w1

a

Brij35-rich phase 100 w2

100

wt1

100

salt-rich phase wt2

10.995 10.997 10.991

9.016 9.520 10.006

20.569 24.678 28.112

6.390 5.712 5.304

10.969 11.000 10.968 10.974

8.521 9.009 9.550 10.042

25.084 28.156 31.058 34.174

4.978 4.706 4.492 4.332

10.979 10.982 11.008 10.992

8.006 8.518 9.004 9.535

28.078 30.160 33.083 36.148

4.080 3.992 3.794 3.638

100

wb1

T = 288.15 K 2.527 1.573 0.666 T = 298.15 K 1.123 0.751 0.360 0.171 T = 308.15 K 0.390 0.105 0.047 0.025

100 wb2

slope (k)

average of slope

11.530 12.213 12.896

−3.51075 −3.55649 −3.61761

−3.56162

11.053 11.669 12.253 12.781

−3.94642 −3.94082 −3.95762 −4.03041

−3.96882

10.444 11.042 11.615 12.092

−4.35113 −4.26020 −4.22583 −4.27164

−4.2772

Standard uncertainties u are u(w) = 0.00001, u(T) = 0.05 K, and u(p) = 10 kPa. 2318



Article

Table 10. Tie-Line Data for the Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K and Pressure p = 0.1 MPaa total system 100 w1

a

Brij35-rich phase 100 w2

100 wt1

salt-rich phase

100 wt2

10.981 10.993 10.989 10.985

9.002 9.501 10.005 10.514

21.327 25.514 28.862 31.984

5.562 4.573 3.985 3.502

10.998 11.005 10.986 10.981

8.505 8.998 9.511 10.01

23.203 27.754 32.397 35.038

4.970 4.044 3.032 2.636

10.998 10.997 10.990 10.989

8.009 8.502 9.016 9.492

28.290 31.168 35.153 37.615

3.200 2.987 2.321 2.090

100 wb1 T = 288.15 K 2.308 1.052 0.656 0.317 T = 298.15 K 1.849 0.601 0.369 0.300 T = 308.15 K 1.197 0.837 0.447 0.237

100 wb2

slope (k)

average of slope

11.938 12.892 13.505 14.080

−2.98372 −2.94094 −2.96342 −2.99402

−2.97053

11.318 12.208 12.876 13.403

−3.36780 −3.33062 −3.26051 −3.23216

−3.29777

10.798 11.432 12.057 12.644

−3.56947 −3.59987 −3.57195 −3.55180

−3.57327


parameters of this equation along with the square of correlation coefficient values (R2) and SDs for the studied systems are given in Table 13. The value of salting-out coefficient given in the Table 13 increases with the rise in temperature, which demonstrates that the salting-out strength gets better when temperature is elevatory. The salting-out strength enhancing leads to the increase in the value of salting-out coefficient, which is consistent with what we previously described. From the R2 and SD showed in Tables 11 to 13, it was found that eq 13 was more appropriate to correlate the LLE data for our systems. Effect of Temperature on the Tie-Line. The tie-line of the Brij35-K2HPO4 ATPS and that of the Brij35-(NH4)2HPO4 ATPS at different temperatures were plotted in Figures 4 and 5, respectively. From the two figures, it was found that the absolute value of the slope of the tie-line increases with the temperature rising, which is consistent with the value of the slope listed in Tables 8 and 9. In present work the slope of the tie-line (STL) was expressed as STL = ΔY/ΔX, where ΔX and ΔY represent the concentration of salt and Brij35 in the top phase minus that of salt and Brij35 in bottom phase. As in the cases mentioned earlier, the increase in temperature causes the hydrophobicity of Brij35 increasing, which prompts the water to come into the bottom phase from the top phase. With the temperature increasing, the concentration of salt in bottom phase decreases, and by contrast, that in top phase increases, which leads to the decrease in the value of ΔX; on the other hand, the concentration of Brij35 increases in the top phase and decreases in the bottom phase causing the value of ΔY to increase. It stands to reason, then, that the absolute value of “STL” will increase with the increase in the value of ΔY and decrease in the value of ΔX. The tie-line length (TLL), as one of predominant influence on the separation of materials using aqueous two-phase systems, changes regularly with the variation of the temperature. From Figures 3 and 4, it was found that the tie-line length increases with the temperature rising.

Figure 4. Tie lines of the Brij35 (1) + K2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15 )K. solid line, ×, 288.15 K; dot line, △, 298.15 K; dash line, ○, 308.15 K.

Figure 5. Tie lines of the Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K. solid line, ×, 288.15 K; dot line, △, 298.15 K; dash line, ○, 308.15 K.

■

CONCLUSION The binodal data and liquid−liquid equilibrium data of ATPS's composed of Brij35 + K2HPO4 /(NH4)2HPO4 + H2O were

top and bottom phase, respectively; the fitting parameters k4 and β are the salting-out coefficient and activity coefficient. The 2319



Article

Table 11. Values of Parameters of Equations 10 and 11 for the Brij35 (1) + K2HPO4/(NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K T

k1

n

288.15 K 298.15 K 305.15 K

5.25121 12.15290 20.97635

3.23527 2.64102 2.24419

288.15 K 298.15 K 305.15 K

11.10401 6.09228 14.82620

2.90910 3.06167 2.43677

k2

R22

100 SD1a

100 SD21a

0.99157 0.99873 0.97886

0.55679 0.37487 1.49538

1.30358 0.61039 2.18166

0.99943 0.99531 0.99140

0.38657 0.83267 0.99845

0.54158 1.52203 1.52752

R1 2

r

Brij35 (1) + K2HPO4 (2) + H2O (3) 5.36426 0.26095 0.99088 5.52294 0.35358 0.99833 5.80524 0.42812 0.97466 Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) 4.87573 0.31363 0.99738 5.40941 0.30992 0.99495 5.74116 0.39449 0.99124

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, j = 1 and j = 2, and SD1 and SD2 represent the mass percent standard deviations for Brij35 and salt, respectively. a

■

Table 12. Values of Parameters of Equation 12 for the Brij35 (1) + K2HPO4/(NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K T 288.15 K 298.15 K 305.15 K 288.15 K 298.15 K 305.15 K

k3

r

R2

100 SD1a

Brij35 (1) + K2HPO4 (2) + H2O (3) 4.71818 −22.52018 0.95999 0.87285 6.11165 −37.46189 0.95142 1.04511 6.92830 −48.09395 0.98034 0.61893 Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) 4.36353 −19.45897 0.96527 1.36174 4.08247 −17.19008 0.98026 1.07934 5.42002 −29.65829 0.82379 2.94911

Corresponding Author

*E-mail: [email protected]; tel.: +86-0434-3291953; fax: +86-0434-3291953 (Z.T.). E-mail: [email protected]; tel.: +860511-88790683; fax: +86-0511-88791800 (Y.Y.).

100 SD2a 0.85671 1.00701 0.59586

Funding

This work was supported by the National Natural Science Foundation of China (No. 21076098), the Natural Science Foundation of Jiangsu Province (Nos. BK2010349 and BK2011529), China Postdoctoral Science Foundation funded project (No. 20110491352), Ph.D. Innovation Programs Foundation of Jiangsu Province (No. CX2211_0584), Jiangsu Postdoctoral Science Foundation funded project (No. 1101036C), and the Programs of Senior Talent Foundation of Jiangsu University (No. 11JDG029).

1.34989 1.07264 2.92481

top top 2 bot 2 0.5 SD = [∑Ni=1((wi,j,cal − wi,j,exp ) + (wi,j,cal − wbot i,j,exp) )/2N] , where N is the number of tie lines,j = 1 and j = 2, and SD1 and SD2 represent the mass percent standard deviations for Brij35 and salt, respectively. a

Notes

Table 13. Values of Parameters of Equation 13 for the Brij35 (1) + K2HPO4/(NH4)2HPO4 (2) + H2O (3) ATPS's at T = (288.15, 298.15, and 308.15) K T 288.15 K 298.15 K 305.15 K 288.15 K 298.15 K 305.15 K

k4

β

R2

100 SD1a

Brij35 (1) + K2HPO4 (2) + H2O (3) 3.17636 −0.01995 0.99751 0.13560 2.83879 −0.12407 0.99342 0.24809 3.12254 −0.07869 0.99556 0.17262 Brij35 (1) + (NH4)2HPO4 (2) + H2O (3) 4.96075 0.17875 0.99997 0.02102 6.05370 0.49452 0.98864 0.44512 5.86300 0.39676 0.98431 0.40660

AUTHOR INFORMATION

The authors declare no competing financial interest.

■

100 SD2a

REFERENCES

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0.04117 0.06421 0.04657 0.01009 0.24720 0.19918

top top 2 bot 2 0.5 SD = [∑Ni=1((wi,j,cal − wi,j,exp ) + (wi,j,cal − wbot i,j,exp) )/2N] , where N is the number of tie lines, j = 1 and j = 2, and SD1 and SD2 represent the mass percent standard deviations for Brij35 and salt, respectively. a

determined at (288.15, 298.15, and 308.15) K. The binodal data for these systems were satisfactorily described by the proposed equations, and the tie-line compositions for the studied systems were satisfactorily correlated with Othmer− Tobias and Bancroft along with the simple Setschenow-type equations. Additionally, the effect of temperature on the binodal curves was studied, and it was found that the two phases are more likely to form at higher temperatures for the investigated systems, which corresponds to the value of EEV calculated by eq 6. The increase in temperature will enhance the hydrophobicity of Brij35, which makes the slope of the tieline rise. Finally, the formation of aqueous two-phase system was endothermic and driven by entropy increase from the calculated free energy (ΔG), enthalpy change (ΔH), and entropy change (ΔS). 2320



Article

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Measurement and Correlation of Phase Equilibria in Aqueous Two

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