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Ind. Eng. Chem. Res. 2008, 47, 9596–9600
Modeling of the Phase Equilibrium for Aqueous Solutions of Brij 58 Surfactant and Three Salts Masumeh Foroutan* Department of Physical Chemistry, School of Chemistry, College of Science, UniVersity of Tehran, Tehran 14155-6455, Iran
Maryam Mohammadlou Department of Chemistry, Faculty of Science, Uremia UniVersity, Uremia, Iran
The osmotic virial model and the Flory-Huggins model, with the Debye-Huckel equation as an electrostatic term, have been used to correlate the liquid-liquid equilibrium data for an aqueous solution of polyoxyethylene cetyl ether surfactant (abbreviated as Brij 58) and three inorganic salts (containing NH4H2PO4, (NH4)2HPO4, and Brij58-KH2PO4) at 298.15 K. The results have shown that the maximum absolute deviation from experimental data is less than 0.6% and 1.4% for the osmotic virial model and the Flory-Huggins theory, respectively. These models are in good agreement with experimental data. 1. Introduction Liquid-liquid extraction utilizing aqueous two-phase systems (ATPS) has been used to separate and purify biological products from the complex mixtures.1-3 There are three types of ATPS (polymer-polymer, polymer-salt, and surfactant-salt ATPS) that have been used for the partitioning of biological materials. The modeling of the phase equilibria for polymer-polymer ATPS and polymer-salt ATPS has been investigated in many papers,4-19 but the modeling of surfactant-salt ATPS scarcely is found in the literature. Surfactants that have lipophilic and hydrophilic properties simultaneously then can be used extensively for the partitioning of biological material that usually have lipophilic properties. Recently, Kellermayer et al.20 used polyoxyethylene cetyl ether (abbreviated as Brij 58) as a nonionic surfactant to separate lipids and proteins. Wang et al. also investigated the partitioning of membrane proteins using surfactant-salt ATPS that contain Triton-X100 surfactant.21 To obtain new insights about the thermodynamics of a surfactant in aqueous solutions, we study the two-phase separation of aqueous solutions that contain a surfactant and salts. In the present work, it is shown that the phase behavior of surfactant-salt ATPS can be described accurately with the osmotic virial model and the Flory-Huggins model with the Debye-Huckel equation with temperature-dependent interaction parameters. These models extensively have been used for determination of liquid-liquid equilibrium (LLE) behavior of various systems.22-27 In addition, the effect of salt type on the LLE of these systems is studied. 2. Experimental Section 2.1. Materials. The nonionic surfactant Brij 58 was purchased from Sigma-Aldrich Co. and was used without further purification. The average ethylene oxide (EO) chain length was 20, the average molecular weight was 1124 g/mol, the critical micelle concentration (CMC) was 0.077 mg dm-3, the hydrophilic lypophilic balance (HLB) was 16, and the melting point was 311.15 K.28 The salts were obtained from Merck. The salts * To who correspondence should be addressed. Tel.: +98 21 61112896. Fax: +98 21 66495291. E-mail address: foroutan@ khayam.ut.ac.ir.
were dried at 383.15 K for 24 h. All chemicals were used without further purification. 2.2. Apparatus and Procedure. A glass vessel, with a volume of 50 cm3, was used to perform the phase equilibrium determinations. The glass vessel was provided with an external jacket in which water at constant temperature was circulated using a thermostat. The temperature was controlled to within (0.01 K. The binodal curves were determined using a titration method. A salt solution of known concentration was titrated with the Brij 58 solution or vice versa, until the solution became turbid. To determine the tielines, feed samples (with a volume of ∼20 cm3) were prepared by mixing appropriate amounts of Brij 58, salt, and water in the vessel. The thermostat was set at a desired temperature, and the sample was stirred for 30 min. The mixture then was allowed to settle for 48 h. After separation of the two phases, the concentration of (NH4)2HPO4 and NH4H2PO4 in the top and bottom phases was determined using the phenate method.29 The concentration of KH2PO4 was determined using flame photometry as a spectroscopy method. The concentration of Brij 58 in both phases was determined from refractive index (nD) measurements that were performed at T ) 298.15 K, using a refractometer (Abbe Model 60, England) with a precision of (0.0001. The relationship between nD and the mass fractions of Brij 58 (w1) and salt (w2) is given by nD ) a0 + a1w1 + a2w2
(1)
The values of the coefficients a0, a1, and a2 are listed in Table 1. The precision of the mass fraction of Brij 58 achieved using eq 1 is SO42- > OH-
∑
(ln γ(k)DH )
(20)
We assumed that the Flory-Huggins interaction parameters are temperature-dependent; thus, we used the following simple relation:22
n
1 mz2 I) 2 i)1 i i
(ln γ(i)DH )
(19)
k)1 l)1
r1 + 1 + r1(φ2χ12 + φ3χ13) - r1(φ1φ2χ12 + Xr φ1φ3χ13 + φ2φ3χ23) (13a) r2 + 1 + r2(φ1χ12 + φ3χ23) - r2(φ1φ2χ12 + Xr φ1φ3χ13 + φ2φ3χ23) (13b)
)
VMkm (18) 1000 where w, ( m, ( x are the water, mean ionic (molality basis), and mean ionic (mole fraction basis) coefficients, respectively. For the Flory-Huggins model with the Debye-Huckel equation, calculations were performed by minimizing the following objective function: ln γ(m ) ln γ(x - ln 1 +
i)1
ln ai )
The results for the long-range interaction activity coefficient are converted to the mole fraction scale as follows:
(for k ) 1 and 3) (17)
System 2
System 3
w1
w2
w1
w2
w1
w2
0.0893 0.0721 0.0483 0.0342 0.0099 0.0049 0.0023 0.0019 0.0009 0.0004 0.0003
0.1123 0.1128 0.1137 0.1144 0.1159 0.1169 0.1180 0.1183 0.1208 0.1223 0.1249
0.0253 0.0241 0.0217 0.0193 0.0161 0.0091 0.0062 0.0020 0.0016 0.0012 0.0010
0.0896 0.0911 0.0977 0.1033 0.1119 0.1379 0.1503 0.1843 0.1938 0.1985 0.2031
0.0591 0.0463 0.0421 0.0320 0.0162 0.0126 0.0072 0.0035 0.0014 0.0009 0.0005
0.0512 0.0593 0.0641 0.0786 0.1145 0.1282 0.1533 0.1712 0.1841 0.1962 0.2118
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9599 Table 4. Tieline Data as Mass Fraction for Systems 1 (Aqueous Solution of Brij 58 + (NH4)2HPO4), 2 (Aqueous Solution of Brij 58 + NH4H2PO4), and 3 (Aqueous Solution of Brij 58 + KH2PO4) at 298.15 K Top Phase
Bottom Phase
w1
w2
0.0623 0.0534 0.0342
0.1135 0.1132 0.1144
0.0221 0.0209 0.0192
0.0964 0.0986 0.1012
0.0391 0.0359 0.0341
0.0692 0.0714 0.0716
w1
w2
0.0005 0.0006 0.0007
0.1237 0.1216 0.1203
0.0110 0.0012 0.0010
0.2102 0.1982 0.1970
0.0009 0.0006 0.0011
0.2013 0.1910 0.1783
System 1
System 2
System 3
Figure 5. Comparison of experimental and model (Flory-Huggins theory, combined with the Debye-Huckel equation) calculated tielines of the Brij 58 + (NH4)2HPO4 + H2O system at 298.15 K; w1 and w2 are the mass fractions for Brij 58 and salt, respectively ((×) experimental data and (O) calculated data)).
Table 5. Interaction Parameters βij of the Osmotic Virial Equation and Correlation Performance for the Systems βij (dm3 mol-1) system
β11
β12
β22
deviationa
Brij 58-NH4H2PO4 Brij 58-(NH4)2HPO4 Brij 58- KH2PO4
-0.2793 -0.3201 -2.5554
9.5114 1.5216 34.9499
-2.8281 -3.2894 -5.2169
0.0233 0.0059 0.0035
a
Deviation ) Fob/(6N), where N is the number of tielines.
′ Table 6. Interaction Parameters bkk of the Flory-Huggins + Debye-Huckel Equation and Correlation Performance for Three Systems: Brij 58 + (NH4)2HPO4 + H2O (System 1), Brij 58(1) + NH4 H2PO4 + H2O (System 2), and Brij 58(1) + KH2PO4 + H2O (System 3)
Figure 6. Comparison of experimental and model (Flory-Huggins theory, combined with the Debye-Huckel equation) calculated tielines of the Brij 58 + NH4H2PO4 + H2O system at 298.15 K; w1 and w2 are the mass fractions for Brij 58 and salt, respectively ((×) experimental data and (O) calculated data).
Value parameter
system 1
system 2
system 3
0 b12 1 b12 0 b13 1 b13 0 b23 1 b23
7.6276 × 1012 2.3886 × 1015 1.4607 × 1013 4.5742 × 1015 1.1238 × 1012 3.5192 × 1014
-3.1520 ×1015 -9.8704 ×1017 -1.2500 ×1014 -3.9143 ×1016 -4.5350 ×1015 -1.4201 ×1018
-8.8737 × 1013 -2.7788 × 1016 -3.0345 × 1014 -9.5025 × 1016 -7.2036 × 1014 -2.2558 × 1017
deviationa
1.3980
a
1.0268
0.3686
Deviation ) (Fob/6N) × 100; N is number of tie-lines. Figure 7. Comparison of experimental and model (Flory-Huggins theory, combined with the Debye-Huckel equation) calculated tielines of the Brij 58 + KH2PO4 + H2O system at 298.15 K; w1 and w2 are the mass fractions for Brij 58 and salt, respectively ((×) experimental data and (O) calculated data).
Figure 4. Comparison of experimental and model (osmotic virial) calculated tielines of the Brij 58 + KH2PO4 + H2O system at 298.15 K; w1 and w2 are the mass fractions for Brij 58 and salt, respectively ((×) experimental data and (O) calculated data).
They postulated that anions with a higher valence are better salting-out agents than anions with a lower valence, because the higher-valence anion hydrates more water than the lowervalence anion, thus decreasing the amount of water available
to hydrate PEG. This trend has been predicted theoretically by Kenkare.40 The osmotic virial model parameters obtained with the corresponding deviation (using eqs 2-6) have been collected in Table 5. The interaction parameters of the Flory-Huggins model, with the Debye-Huckel equation, have been reported in Table 6. Reasonable agreement between the calculated and experimental compositions was obtained. Based on the obtained deviations for these models, it can be concluded that the quality of the fitting for these systems is better when the osmotic virial equation has been used. To show the reliability of the osmotic virial model and Flory-Huggins theory (for the three Brij58-salt (NH4H2PO4, (NH4)2HPO4, and KH2PO4) aqueous systems), comparisons between the experimental and correlated tielines are shown in Figures 2-4 and Figures 5-7, respectively. The results showed that the average absolute deviation of the osmotic model and the Flory-Huggins theory, with the
9600 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008
Debye-Huckel equation, for three systems was less than 0.6% and 1.4%, respectively. These models could give a good representation of the phase behavior of aqueous solutions of Brij 58 surfactant and inorganic salts. 5. Conclusion The Flory-Huggins theory, with the Debye-Huckel equation, and the osmotic virial model have been used to correlate the equilibrium data of the Brij 58-salt (KH2PO4, (NH4)2HPO4, and NH4H2PO4) aqueous two-phase systems. These models were determined to correlate the experimental data with calculated data with good accuracy. The deviations reported in Tables 5 and 6 show that, in each case, the quality of fitting is better with the osmotic virial model. Furthermore, the effect of salt type on the binodals has been studied. Literature Cited (1) Albertsson, P. A. Partitioning of Cell Particles and Macromolecules, 3rd Edition; Wiley: New York, 1986. (2) Walter, H.; Brooks, D. E.; Fisher, D. Partitioning in Aqueous TwoPhase Systems; Academic Press: New York, 1985. (3) Zaslavsky, B. Y. Aqueous Two-Phase Partitioning: Physical Chemistry and Bioanalytical Applications; Marcel Dekker: New York, 1995. (4) Rosa, P. A. J.; Azevedo, A. M.; Ferreira, I. F.; de Vries, J.; Korporaal, R.; Verhoef, H. J.; Visser, T. J.; Aires-Barros, M. R. Affinity partitioning of human antibodies in aqueous two-phase systems. J. Chromatogr., A 2007, 1162, 103– 113. (5) Pico´, G.; Romanini, D.; Nerli, B.; Farruggia, B. Polyethyleneglycol molecular mass and polydispersivity effect on protein partitioning in aqueous two-phase systems. J. Chromatogr., B 2006, 830, 286–292. (6) Walker, S. G.; Dale, C. J.; Lyddiatt, A. Aqueous two-phase partition of complex protein feed stocks derived from brain tissue homogenates. J. Chromatogr., B 1996, 680, 91–96. (7) da Silva, L. H. M.; Meirelles, A. J. A. Phase equilibrium in polyethylene glycol maltodextrin aqueous two-phase systems. Carbohydr. Polym. 2000, 42, 273–278. (8) Furuya, T.; Yamada, S.; Zhu, J.; Yamaguchi, Y.; Iwai, Y.; Arai, Y. Measurement and correlation of liquid-liquid equilibria and partition coefficients of hydrolytic enzymes for DEX T500 + PEG20000 + water aqueous two-phase system at 20 °C. Fluid Phase Equilib. 1996, 125, 89–102. (9) Kataoka, T.; Nagao, Y.; Kidowaki, M.; Araki, J.; Ito, K. Liquidliquid equilibria of polyrotaxane and poly (vinyl alcohol). Colloids Surf., B 2007, 56, 270–276. (10) Peng, Q.; Li, Z.; Li, Y. Experiments correlation and prediction of protein partition coefficient in aqueous two-phase systems containing PEG and K2HPO4-KH2PO4. Fluid Phase Equilib. 1995, 107, 303–315. (11) Mishima, K.; Matsuyama, K.; Ezawa, M.; Taruta, Y.; Takarabe, S.; Nagatani, M. Interfacial tension of aqueous two-phase systems containing poly(ethylene glycol) and dipotassium hydrogenphosphate. J. Chromatogr., B 1998, 711, 313–318. (12) Gao, Y.; Peng, Q.; Li, Z.; Li, Y. Thermodynamics of ammonium sulfate polyethylene glycol aqueous two-phase systems experiment and correlation using extended uniquac equation. Fluid Phase Equilib. 1991, 63, 157–171. (13) Perumalsamy, M.; Murugesan, T. Prediction of liquid-liquid equilibria for PEG 2000-sodium citrate based aqueous two-phase systems. Fluid Phase Equilib. 2006, 24, 52–61. (14) Haraguchi, L. H.; Mohamed, R. S.; Loh, W.; Pessoˆa Filho, P. A. Phase equilibrium and insulin partitioning in aqueous two-phase systems containing block copolymers and potassium phosphate. Fluid Phase Equilib. 2004, 215, 1–15. (15) Salabat, A.; Moghadasi, M. A.; Zalaghi, P.; Sadeghi, R. Liquid + liquid equilibria for ternary mixtures of polyvinylpyrrolidone + MgSO4 + water at different temperatures. J. Chem. Thermodyn. 2006, 38, 1479–1483. (16) Sadeghi, R.; Rafiei, H. R.; Motamedi, M. Phase equilibrium in aqueous two-phase systems containing poly vinylpyrrolidone and sodium citrate at different temperatures experimental and modeling. Thermochim. Acta 2006, 451, 163–167.
(17) Li, M.; Zhu, Z. Q.; Wu, Y. T.; Lin, D. Q. Measurement of phase diagrams for new aqueous two-phase systems and prediction by a generalized multicomponent osmotic virial equation. Chem. Eng. Sci. 1998, 53, 2755–2767. (18) dos Santos Tada, E.; Loh, W.; de Alcaˆntara Pessoˆa-Filho, P. Phase equilibrium in aqueous two-phase systems containing ethylene oxide-propylene oxide block copolymers and dextran. Fluid Phase Equilib. 2004, 218, 221–228. (19) Pei, Y.; Wang, J.; Liu, L.; Wu, K.; Zhao, Y. Liquid-liquid equilibria of aqueous biphasic systems containing selected imidazolium ionic liquids and salts. J. Chem. Eng. Data 2007, 52, 2026–2031. (20) Kellermayer, M.; Ludany, A.; Miseta, A.; Koszegi, T.; Berta, G.; Bogner, P.; Hazlewood, C. F.; Cameron, I. L.; Wheatley, D. N. Release of potassium, lipids, and proteins from nonionic detergent treated chicken red blood cells. J. Cell Physiol. 1994, 159, 197–204. (21) Xie, H. G.; Wang, Y. J.; Sun, M. Modeling of the partitioning of membrane protein and phase equilibria for Triton X-100-salt aqueous twophase systems using a modified generalized multicomponent osmotic virial equation. J. Process Biochem. 2006, 41, 689–696. (22) Zafarani-Moattar, M. T.; Sadeghi, R. measurement and correlation of liquid-liquid equilibria of the aqueous two phase system poly vinylpyrrolidonesodium dihydrogen phosphate. Fluid Phase Equilib. 2002, 203, 177–191. (23) Toshiyuki, K.; Yohei, N.; Masatoshi, K.; Jun, A.; Kohzo, I. Liquidliquid equilibria of polyrotaxane and poly (vinyl alcohol). Colloids Surf., B 2007, 56, 270–276. (24) Markku, L.; Ismo, M.; Jari, T.; Erkki, P. Liquid-liquid equilibria in ternary systems of linear and cross-linked water-soluble polymers. Fluid Phase Equilib. 2002, 201, 381–399. (25) de Alcaˆntara Pessoˆa Filho, P.; Maurer, G. An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions. Fluid Phase Equilib. 2008, 269, 25–35. (26) Foroutan, M.; Zarrabi, M. Activities of water, polymer and salt in liquid-liquid equilibria of polyvinylpyrrolidone and (NH4) 2HPO4/ (NH4)H2PO4 buffer using the Flory-Huggins model with Debye-Huckel and Pitzer-Debye-Huckel equations and the osmotic virial model: Effects of pH and temperature. Fluid Phase Equilib. 2008, 266, 164–171. (27) Zafarani, M. T.; Sadeghi, R.; Hamidi, A. A. Liquid-liquid equilibria of an aqueous two-phase system containing polyethylene glycol and sodium citrate: experiment and correlation. Fluid Phase Equilib. 2004, 219, 149–155. (28) Solarzano, L. Determination of ammonia in natural waters by the phenol hypochlorite method. Limnol. Oceanogr. 1969, 14, 799. (29) Cheluget, E. L.; Gelinas, S.; Vera, J. H.; Weber, M. E. Liquidliquid equilibrium of aqueous mixtures of poly propylene glycol with NaCl. J. Chem. Eng. Data 1994, 39, 127–130. (30) Edmond, E.; Ogston, A. G. An approach to the study of phase separation in ternary aqueous systems. J. Biochem. 1968, 109, 569–576. (31) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (32) Zana, R. Partial molal volumes of polymers in aqueous solutions from partial molal volume group contributions. J. Polym. Sci. 1980, 18, 121–126. (33) You, T. W.; Dong, Q. L.; Zi, Q. Z.; Le, H. M. Prediction of liquidliquid equilibria of polymer-salt aqueous two-phase systems by a modified Pitzer virial equation. Fluid-Phase Equilib. 1996, 124, 67–79. (34) Foroutan, M.; Hedari, N.; Mohammadlou, M.; Jafar Sojahrood, A. Effect of temperature on the liquid-liquid equilibrium for aqueous solution of nonionic surfactant and salt: experimental and modeling. J. Chem. Thermodyn. 2008, 40, 1077–1081. (35) Marcus, Y. J. Chem. Soc., Faraday Trans. 1993, 89, 713–718. (36) Fowler, R. H.; Guggenheim, E. A. Statistical Thermodynamics; Cambridge University Press: New York, 1956. (37) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd Edition; Butterworths: London, 1959. (38) Ali, H.; Babak, M. On extension of UNIQUAC-NRF model to study the phase behavior of aqueous two phase polymer-salt systems. Fluid Phase Equilib. 2001, 180, 139–149. (39) Ananthapadmanabhan, K. P.; Goddard, E. D. Aqueous biphase formation in polyethylene oxide-inorganic salt systems. Langmuir 1987, 3, 25–31. (40) Kenkare, P. U.; Hall, C. K. Modeling of phase separation in PEGsalt aqueous two-phase systems. AIChE J. 1996, 42 (12), 3508–3522.
ReceiVed for reView March 22, 2008 ReVised manuscript receiVed August 27, 2008 Accepted October 9, 2008 IE800467Y
