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Salt effect on aqueous two-phase system composed of nonylphenyl ethoxylate non-ionic surfactant
Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 611–614
Contents lists available at ScienceDirect
Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad
Salt effect on aqueous two-phase system composed of nonylphenyl ethoxylate non-ionic surfactant Alireza Salabat ∗ , Maryam Alinoori Chemistry Department, Arak University, P.O. Box 38156-879, Arak, Iran
article
info
Article history: Received 17 January 2008 Received in revised form 15 June 2008 Accepted 17 June 2008 Available online 11 July 2008 Keywords: Aqueous two-phase system Non-ionic surfactant Nonylphenyl ethoxylate Salt effect Phase diagram correlation
a b s t r a c t Phase diagrams of detergent-based aqueous two-phase systems composed of nonylphenyl ethoxylate (4-C9 H19 C6 H4 (OCH2 CH2 )9 OH, NP-9) non-ionic surfactant and various salt solutions were studied experimentally at 298.15 K. The salts used were magnesium sulfate, sodium sulfate and sodium chloride. The salting-out power of salts in these systems were determined and this power can be arranged with respect to the cations as Mg2+ > Na+ and anions as SO24− > Cl− . The experimental results of the phase diagrams were correlated using DH-NRTL model. It was found that, this model represent the experimental liquid–liquid equilibrium data of the surfactant aqueous two-phase systems with good accuracy. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Liquid–liquid extraction utilizing aqueous two-phase (ATP) systems have attracted considerable attention for the large-scale recovery and purification of bioproducts [1,2]. These two-phase systems usually can be made from aqueous solutions of two watersoluble polymers or a polymer and a salt. Extraction systems based on non-ionic surfactants have been described as an alternative to the standard polymer/polymer or polymer/salt systems [3–5]. Due to the higher content of water in both phases and lower interface tension in comparison with others, surfactant aqueous two-phase systems has more advantages, such as lower cost, experimental conveniences, ease of waste disposal and consequently shorter time for phase separation. These surfactant ATP systems are especially suitable for hydrophobic membrane protein separation especially [4]. Some investigations on the surfactant ATP systems and their application in biotechnology have been reported in literature [6,7]. Liquid–liquid phase diagram for Triton X-100–salt–water aqueous two-phase systems and partitioning of membrane proteins in these systems have been also measured at 293.15 K [8]. Nonylphenyl ethoxylate (NP-9) is a non-ionic surfactant, which to our knowledge there is no any report for liquid–liquid phase diagram of this surfactant with salt.
∗
Corresponding author. Tel.: +98 861 3664691; fax: +98 8614173406. E-mail addresses: [email protected], [email protected] (A. Salabat).
0364-5916/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2008.06.004
In this paper, for the first time we present experimental data for liquid–liquid phase diagrams of NP-9 +salts + H2 O systems at 298.15 K. The salts used were magnesium sulfate, sodium sulfate and sodium chloride. These liquid–liquid equilibrium (LLE) data could be useful in separation and purification of biomaterials and organic compounds. The obtained experimental results of the phase diagrams were correlated using Debye–Huckel (DH)-NRTL (Non Random Two Liquid) model. 2. Material and methods Nonylphenyl ethoxylate, of molecular weight 616.5 g mol−1 was purchased from Aldrich. Magnesium sulfate (GR, min 99.5%), sodium chloride (GR, min 99.5%) and sodium sulfate (GR, min 99%) were obtained from Merck. All chemicals were used without further purification. Experimental apparatus and aqueous two-phase equilibrium experiment were described previously [9]. The experiments were performed in 30 ml glass bottle. Aqueous two-phase systems were prepared from liquid surfactant and different salts containing magnesium sulfate, sodium sulfate or sodium chloride in triply distilled water. The total weight of these components for each sample was about 20 g. The mixtures were shaken for about 30 min and then placed in thermostat at 298.15 K for at least 24 h to ensure complete equilibration, as indicated by the absence of turbidity in each phase. After equilibration of the systems, the samples of approximately 6 ml from the upper and lower phases were taken out carefully for analysis and density measurement using syringes. Density of the top and bottom phase samples was measured with a
612
A. Salabat, M. Alinoori / Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 611–614
Mettler Toledo densimeter (DE51). The precision of the instrument is ±1 × 10−5 g cm−3 . The temperature of the vibrating tube in the densimeter was controlled to within (0.01 K). The concentration of MgSO4 was determined by magnesium analysis using atomic absorption spectroscopy (AAS). This measurement was carried out with Shimadzu Atomic Absorption Spectrophotometer AA-670 G. The concentrations of Na2 SO4 and NaCl were determined using atomic emission spectroscopy with a flame photometer (Perkin-Elmer). The measurements were performed in triplicate, with standard deviations of 0.2%. A double beam Perkin Elmer Lambda 15 UV-visible spectrophotometer was used for determination of NP-9 concentration in top and bottom phases. Absorbance of the samples was measured at λ = 258.6 nm. The water contents of the samples were measured with Kyoto mks-210 Karl Fisher instrument. The uncertainty in the mass percent for the top and bottom phases was less than ±0.3 for NP-9 and water. 3. Thermodynamic model In this work, the extended NRTL model (DH-NRTL) was used to correlate experimental liquid–liquid phase diagrams. In this model the excess Gibbs energy is calculated as a sum of two contributions, one is the long-range electrostatic interaction and the other is due to molecular interactions: GE = GEDH + GENRTL
Fig. 1. Phase diagram of the NP-9 + Na2 SO4 + H2 O system where the symbols represent the experimental data given in Table 1.
(1)
GEDH
where is the excess Gibbs energy calculated using Debye–Huckel equation and GENRTL is the excess Gibbs energy calculated using NRTL equation. Hence the activity coefficients is also calculated from the same two contributions as: ln γi = ln γiDH + ln γiNRTL .
(2)
The NRTL equation introduced by Renon et al. [10] is as follows
P
xj Gji τji
j
ln γiNRTL = P
+
xj Gii
P j
i
xj Gij
X
xj Gij
P
xk Gkj τkj
τij − kP
i
xj Gij
(3)
i
where
τij =
gij − gii
(4)
RT
Gij = exp(−αij τij )
(αij = αji )
(5)
where αij is the non-randomness factor; gij and gii are the energies of interaction between i–j and i–i species, respectively. Both gij and αij are inherently symmetric (gij = gij and αij = αji ). The electrostatic term of the activity coefficient of neutral molecule k based on Debye–Huckel equation of Fowler– Guggenheim [11] is given by: ln γkDH =
2AVk d b3
1 + bI 1/2 −
1
(1 + bI 1/2 )
− 2 ln 1 + bI 1/2
(6)
where k represents surfactant and water. The mean activity coefficient of a salt, γ± , is given by: ln γ±DH =
−|zc za |AI 1/2 1 + bI 1/2
(7)
mk0 zk20 .
(8)
where I =
1X 2
Fig. 2. Phase diagram of the NP-9 + MgSO4 + H2 O system where the symbols represent the experimental data given in Table 1.
k0
In these relation, Vk and zk0 are the molar volume of pure non-ionic component k and charge number of ion k0 , respectively; zc and za are the charge number of a cation and an anion, respectively; I the ionic strength on the molal scale; d, m and M are solvent density, molality and the molecular weight, respectively.
4. Results and discussion The experimental liquid–liquid equilibrium results and phase densities for the NP-9 + salts aqueous two-phase systems are given in Table 1. In this table, wi represents mass fraction of solute i. The experimental phase diagrams for these systems are also shown in Figs. 1–3. In each system, the upper layer was the surfactant-rich, salt-poor phase, and the lower layer was the water-rich, salt-rich phase. As can be seen from the density data in Table 1, for all systems, phase density of the upper phase decreases with increasing tie-line length (TLL) and phase density of the bottom phase increases with increasing TLL. It is because that, with increasing TLL the surfactant concentration in the top phases increase and the salt concentration decreases. This trend for bottom phase is reverse. The tie lines are determined by connecting each corresponding set of total, bottom, and top phase points. The binodal curves were drawn through the top and bottom phase points. Near the critical point, the binodal curve is estimated on the bases of the location and trend of the top and bottom phase compositions. The effect of salt on the phase equilibrium curves of the surfactant ATP systems is given in Fig. 4. The results presented demonstrate that the salting-out power of the salts are as MgSO4 >
A. Salabat, M. Alinoori / Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 611–614
613
Table 1 Liquid–liquid equilibrium and phase density data for the NP-9 (1) + salt (2) + H2 O (3) aqueous two-phase system at 298.15 K Top phase
Bottom phase
100w1
100w2
100w3
d (g cm−3 )
100w1
100w2
100w3
d (g cm−3 )
76.10 70.46 54.97 50.87 47.42 45.23 44.11
1.04619 1.04604 1.04392 1.04383 1.04226 1.04168 1.04123
4.30 2.06 1.54 1.23 1.10 0.96 0.32
8.70 11.20 14.03 15.46 16.71 17.99 20.12
87.00 86.74 84.43 83.31 82.19 81.05 79.56
1.05080 1.06666 1.07477 1.07639 1.08668 1.09406 1.11740
5.20 4.80 2.12 1.87 1.23 0.87 0.59
75.80 71.30 51.90 48.33 45.57 42.24 39.11
1.05435 1.05406 1.05318 1.05271 1.05254 1.05187 1.05135
3.90 2.36 1.12 0.99 0.86 0.74 0.15
10.13 13.80 17.60 18.40 19.30 20.60 21.80
85.97 83.84 81.28 80.61 79.84 78.66 78.05
1.06358 1.06900 1.08945 1.09617 1.11365 1.12859 1.13575
6.36 5.31 2.90 2.16 1.58 1.36
66.24 59.49 49.90 43.14 39.62 36.64
1.07403 1.07373 1.07298 1.06854 1.06759 1.06432
3.30 2.30 2.10 2.07 1.45 0.98
16.35 17.70 18.41 19.40 20.36 22.79
80.35 80.00 79.49 78.52 78.19 76.23
1.07545 1.07661 1.08522 1.09314 1.12396 1.13260
NP-9 + MgSO4 + H2 O 19.30 26.31 43.46 48.00 51.80 54.11 55.46
4.6 3.23 1.57 1.13 0.78 0.66 0.43
NP-9 + Na2 SO4 + H2 O 19.00 23.90 45.98 49.80 53.20 56.89 60.30 NP-9 + NaCl + H2 O 27.40 35.20 47.20 54.70 58.80 62.00
Fig. 4. Effect of salt on the LLE behavior of NP-9 +salts+H2 O at 298.15 K; N5MgSO4 , Na2 SO4 , NaCl.
Fig. 3. Phase diagram of the NP-9 + NaCl + H2 O system where the symbols represent the experimental data given in Table 1.
Na2 SO4 > NaCl, because it depresses the binodal to lower polymer concentrations (Fig. 4). The salting-out power in these systems can be arranged for the respective cations as Mg2+ > Na+ and for the respective anions is as SO24− > Cl− , which is in agreement with lyotropic series given by Shaw [12]. There are two effective binary interaction parameters for a binary subsystem in the extended NRTL model. Therefore, six effective binary interaction parameters are required for a ternary system. The corresponding sets of binary interaction parameters were determined by minimizing the differences between the experimental and calculated mole fractions for each of the components over all the tie lines (same global initial mixture). The interaction parameters of DH-NRTL model, τij , were estimated by minimizing the following objective function: OF =
XXX Exp 2 (xCalc P ,l ,i − x P ,l ,i ) P
l
i
(9)
Table 2 Interaction parameters, τij , of the extended NRTL model and average deviation for NP-9 (1) + salts (2) + H2 O (3) systems at 298.15 K Salt
τ12
τ21
τ13
τ31
τ23
τ32
δ1
δ2
MgSO4 Na2 SO4 NaCl
19.94 8.21 0.51
4.45 31.99 15.18
−11.11 −11.62 −8.72
29.41 10.99 10.31
−10.749 −12.160 −6.986
8.15 20.88 14.73
0.6 0.8 1.1
0.4 0.5 0.3
and are reported in Table 2. The non-randomness parameter (αij ) was set as 0.2 for all calculation. In Eq. (9), xp,l,i is the molality of the component i in the phase p for lth tie-line. The experimental LLE data were correlated using Eq. (9) and the following equilibrium condition:
(xi γi )top = (xi γi )bot .
(10)
Using the estimated interaction parameters of the models, the phase diagrams for NP-9 +salts + H2 O systems were predicted. The average deviations of the predicted results by this model are reported in Table 2. The deviation, based on weight percent, is
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Fig. 5. Comparison of experimental and calculated phase diagram of NP-9 +MgSO4 + H2 O system with DH-NRTL model; N and solid lines: experiment, and dash lines: model
Fig. 7. Comparison of experimental and calculated phase diagram of NP-9 +NaCl + H2 O system with DH-NRTL model; N and solid lines: experiment, and dash lines: model.
5. Conclusion In the present work, we have measured the LLE data for three ternary systems of NP-9 +salts + H2 O at 298.15 K. The salts used for investigation of the salt effect are MgSO4 , Na2 SO4 and NaCl. The results show that the salting-out power in these systems can be arranged as MgSO4 > Na2 SO4 > NaCl. The salting-out power for the respective cations is as Mg2+ > Na+ and for the respective anions is as SO24− > Cl− , which is in agreement with lyotropic series. The experimental results of the phase diagrams were correlated using the DH-NRTL model. The calculated average deviation between experimental and calculated phase diagrams revealed that the DH-NRTL model is a good model for the correlation and calculation of the LLE data in these systems. References
Fig. 6. Comparison of experimental and calculated phase diagram of NP-9 +Na2 SO4 + H2 O system with DH-NRTL model; N and solid lines: experiment, and dash lines: model.
defined by the following equation:
δi =
N 1 X
N i=1
|wical − wiexp |
(11)
where N is the number of experimental points and the superscripts ‘exp’ and ‘cal’ denote the experimental and calculated values, respectively. On the basis of the obtained deviations, it can be concluded that DH-NRTL model is a suitable model for correlation of the LLE data in these systems. The comparison of experimental tie line data with those calculated from the DH-NRTL model is shown in Figs. 5–7.
[1] P.A. Albertsson, Partition of Cell Particles and Macromolecules, Wiley, New York, 1986. [2] A. Greve, M.R. Kula, J. Chem. Technol. Biotechnol. 50 (1991) 27–39. [3] Ragini Hatti-Kaul, Aqueous Two-Phase Systems, Methods and Protocols, Humana Press, 2000. [4] H. Tani, T. Kamidate, H. Watanabe, Anal. Sci. 14 (1998) 875–888. [5] K. Selber, F. Tjerneld, A. Collen, T. Hyytia, T. Nakari-Setala, M. Bailey, Process Biochem. 39 (2004) 889–896. [6] W.J. Horvath, C.W. Huie, Talanta 39 (1992) 487–492. [7] M.D. Womack, D.A. Kendall, R.C. MacDonald, Biochim. Biophys. Acta. 733 (1983) 210–217. [8] H.G. Xie, Y.J. Wang, M. Sun, Process Biochem. 41 (2006) 689–696. [9] A. Salabat, Fluid Phase Equilib. 187–188 (2001) 489–498. [10] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [11] R.H. Fowler, E.A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, New York, 1956. [12] D.J. Shaw, Introduction to Colloid and Surface Chemistry, 4th edn, Butterworth, London, 1992.
Contents lists available at ScienceDirect
Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad
Salt effect on aqueous two-phase system composed of nonylphenyl ethoxylate non-ionic surfactant Alireza Salabat ∗ , Maryam Alinoori Chemistry Department, Arak University, P.O. Box 38156-879, Arak, Iran
article
info
Article history: Received 17 January 2008 Received in revised form 15 June 2008 Accepted 17 June 2008 Available online 11 July 2008 Keywords: Aqueous two-phase system Non-ionic surfactant Nonylphenyl ethoxylate Salt effect Phase diagram correlation
a b s t r a c t Phase diagrams of detergent-based aqueous two-phase systems composed of nonylphenyl ethoxylate (4-C9 H19 C6 H4 (OCH2 CH2 )9 OH, NP-9) non-ionic surfactant and various salt solutions were studied experimentally at 298.15 K. The salts used were magnesium sulfate, sodium sulfate and sodium chloride. The salting-out power of salts in these systems were determined and this power can be arranged with respect to the cations as Mg2+ > Na+ and anions as SO24− > Cl− . The experimental results of the phase diagrams were correlated using DH-NRTL model. It was found that, this model represent the experimental liquid–liquid equilibrium data of the surfactant aqueous two-phase systems with good accuracy. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Liquid–liquid extraction utilizing aqueous two-phase (ATP) systems have attracted considerable attention for the large-scale recovery and purification of bioproducts [1,2]. These two-phase systems usually can be made from aqueous solutions of two watersoluble polymers or a polymer and a salt. Extraction systems based on non-ionic surfactants have been described as an alternative to the standard polymer/polymer or polymer/salt systems [3–5]. Due to the higher content of water in both phases and lower interface tension in comparison with others, surfactant aqueous two-phase systems has more advantages, such as lower cost, experimental conveniences, ease of waste disposal and consequently shorter time for phase separation. These surfactant ATP systems are especially suitable for hydrophobic membrane protein separation especially [4]. Some investigations on the surfactant ATP systems and their application in biotechnology have been reported in literature [6,7]. Liquid–liquid phase diagram for Triton X-100–salt–water aqueous two-phase systems and partitioning of membrane proteins in these systems have been also measured at 293.15 K [8]. Nonylphenyl ethoxylate (NP-9) is a non-ionic surfactant, which to our knowledge there is no any report for liquid–liquid phase diagram of this surfactant with salt.
∗
Corresponding author. Tel.: +98 861 3664691; fax: +98 8614173406. E-mail addresses: [email protected], [email protected] (A. Salabat).
0364-5916/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2008.06.004
In this paper, for the first time we present experimental data for liquid–liquid phase diagrams of NP-9 +salts + H2 O systems at 298.15 K. The salts used were magnesium sulfate, sodium sulfate and sodium chloride. These liquid–liquid equilibrium (LLE) data could be useful in separation and purification of biomaterials and organic compounds. The obtained experimental results of the phase diagrams were correlated using Debye–Huckel (DH)-NRTL (Non Random Two Liquid) model. 2. Material and methods Nonylphenyl ethoxylate, of molecular weight 616.5 g mol−1 was purchased from Aldrich. Magnesium sulfate (GR, min 99.5%), sodium chloride (GR, min 99.5%) and sodium sulfate (GR, min 99%) were obtained from Merck. All chemicals were used without further purification. Experimental apparatus and aqueous two-phase equilibrium experiment were described previously [9]. The experiments were performed in 30 ml glass bottle. Aqueous two-phase systems were prepared from liquid surfactant and different salts containing magnesium sulfate, sodium sulfate or sodium chloride in triply distilled water. The total weight of these components for each sample was about 20 g. The mixtures were shaken for about 30 min and then placed in thermostat at 298.15 K for at least 24 h to ensure complete equilibration, as indicated by the absence of turbidity in each phase. After equilibration of the systems, the samples of approximately 6 ml from the upper and lower phases were taken out carefully for analysis and density measurement using syringes. Density of the top and bottom phase samples was measured with a
612
A. Salabat, M. Alinoori / Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 611–614
Mettler Toledo densimeter (DE51). The precision of the instrument is ±1 × 10−5 g cm−3 . The temperature of the vibrating tube in the densimeter was controlled to within (0.01 K). The concentration of MgSO4 was determined by magnesium analysis using atomic absorption spectroscopy (AAS). This measurement was carried out with Shimadzu Atomic Absorption Spectrophotometer AA-670 G. The concentrations of Na2 SO4 and NaCl were determined using atomic emission spectroscopy with a flame photometer (Perkin-Elmer). The measurements were performed in triplicate, with standard deviations of 0.2%. A double beam Perkin Elmer Lambda 15 UV-visible spectrophotometer was used for determination of NP-9 concentration in top and bottom phases. Absorbance of the samples was measured at λ = 258.6 nm. The water contents of the samples were measured with Kyoto mks-210 Karl Fisher instrument. The uncertainty in the mass percent for the top and bottom phases was less than ±0.3 for NP-9 and water. 3. Thermodynamic model In this work, the extended NRTL model (DH-NRTL) was used to correlate experimental liquid–liquid phase diagrams. In this model the excess Gibbs energy is calculated as a sum of two contributions, one is the long-range electrostatic interaction and the other is due to molecular interactions: GE = GEDH + GENRTL
Fig. 1. Phase diagram of the NP-9 + Na2 SO4 + H2 O system where the symbols represent the experimental data given in Table 1.
(1)
GEDH
where is the excess Gibbs energy calculated using Debye–Huckel equation and GENRTL is the excess Gibbs energy calculated using NRTL equation. Hence the activity coefficients is also calculated from the same two contributions as: ln γi = ln γiDH + ln γiNRTL .
(2)
The NRTL equation introduced by Renon et al. [10] is as follows
P
xj Gji τji
j
ln γiNRTL = P
+
xj Gii
P j
i
xj Gij
X
xj Gij
P
xk Gkj τkj
τij − kP
i
xj Gij
(3)
i
where
τij =
gij − gii
(4)
RT
Gij = exp(−αij τij )
(αij = αji )
(5)
where αij is the non-randomness factor; gij and gii are the energies of interaction between i–j and i–i species, respectively. Both gij and αij are inherently symmetric (gij = gij and αij = αji ). The electrostatic term of the activity coefficient of neutral molecule k based on Debye–Huckel equation of Fowler– Guggenheim [11] is given by: ln γkDH =
2AVk d b3
1 + bI 1/2 −
1
(1 + bI 1/2 )
− 2 ln 1 + bI 1/2
(6)
where k represents surfactant and water. The mean activity coefficient of a salt, γ± , is given by: ln γ±DH =
−|zc za |AI 1/2 1 + bI 1/2
(7)
mk0 zk20 .
(8)
where I =
1X 2
Fig. 2. Phase diagram of the NP-9 + MgSO4 + H2 O system where the symbols represent the experimental data given in Table 1.
k0
In these relation, Vk and zk0 are the molar volume of pure non-ionic component k and charge number of ion k0 , respectively; zc and za are the charge number of a cation and an anion, respectively; I the ionic strength on the molal scale; d, m and M are solvent density, molality and the molecular weight, respectively.
4. Results and discussion The experimental liquid–liquid equilibrium results and phase densities for the NP-9 + salts aqueous two-phase systems are given in Table 1. In this table, wi represents mass fraction of solute i. The experimental phase diagrams for these systems are also shown in Figs. 1–3. In each system, the upper layer was the surfactant-rich, salt-poor phase, and the lower layer was the water-rich, salt-rich phase. As can be seen from the density data in Table 1, for all systems, phase density of the upper phase decreases with increasing tie-line length (TLL) and phase density of the bottom phase increases with increasing TLL. It is because that, with increasing TLL the surfactant concentration in the top phases increase and the salt concentration decreases. This trend for bottom phase is reverse. The tie lines are determined by connecting each corresponding set of total, bottom, and top phase points. The binodal curves were drawn through the top and bottom phase points. Near the critical point, the binodal curve is estimated on the bases of the location and trend of the top and bottom phase compositions. The effect of salt on the phase equilibrium curves of the surfactant ATP systems is given in Fig. 4. The results presented demonstrate that the salting-out power of the salts are as MgSO4 >
A. Salabat, M. Alinoori / Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 611–614
613
Table 1 Liquid–liquid equilibrium and phase density data for the NP-9 (1) + salt (2) + H2 O (3) aqueous two-phase system at 298.15 K Top phase
Bottom phase
100w1
100w2
100w3
d (g cm−3 )
100w1
100w2
100w3
d (g cm−3 )
76.10 70.46 54.97 50.87 47.42 45.23 44.11
1.04619 1.04604 1.04392 1.04383 1.04226 1.04168 1.04123
4.30 2.06 1.54 1.23 1.10 0.96 0.32
8.70 11.20 14.03 15.46 16.71 17.99 20.12
87.00 86.74 84.43 83.31 82.19 81.05 79.56
1.05080 1.06666 1.07477 1.07639 1.08668 1.09406 1.11740
5.20 4.80 2.12 1.87 1.23 0.87 0.59
75.80 71.30 51.90 48.33 45.57 42.24 39.11
1.05435 1.05406 1.05318 1.05271 1.05254 1.05187 1.05135
3.90 2.36 1.12 0.99 0.86 0.74 0.15
10.13 13.80 17.60 18.40 19.30 20.60 21.80
85.97 83.84 81.28 80.61 79.84 78.66 78.05
1.06358 1.06900 1.08945 1.09617 1.11365 1.12859 1.13575
6.36 5.31 2.90 2.16 1.58 1.36
66.24 59.49 49.90 43.14 39.62 36.64
1.07403 1.07373 1.07298 1.06854 1.06759 1.06432
3.30 2.30 2.10 2.07 1.45 0.98
16.35 17.70 18.41 19.40 20.36 22.79
80.35 80.00 79.49 78.52 78.19 76.23
1.07545 1.07661 1.08522 1.09314 1.12396 1.13260
NP-9 + MgSO4 + H2 O 19.30 26.31 43.46 48.00 51.80 54.11 55.46
4.6 3.23 1.57 1.13 0.78 0.66 0.43
NP-9 + Na2 SO4 + H2 O 19.00 23.90 45.98 49.80 53.20 56.89 60.30 NP-9 + NaCl + H2 O 27.40 35.20 47.20 54.70 58.80 62.00
Fig. 4. Effect of salt on the LLE behavior of NP-9 +salts+H2 O at 298.15 K; N5MgSO4 , Na2 SO4 , NaCl.
Fig. 3. Phase diagram of the NP-9 + NaCl + H2 O system where the symbols represent the experimental data given in Table 1.
Na2 SO4 > NaCl, because it depresses the binodal to lower polymer concentrations (Fig. 4). The salting-out power in these systems can be arranged for the respective cations as Mg2+ > Na+ and for the respective anions is as SO24− > Cl− , which is in agreement with lyotropic series given by Shaw [12]. There are two effective binary interaction parameters for a binary subsystem in the extended NRTL model. Therefore, six effective binary interaction parameters are required for a ternary system. The corresponding sets of binary interaction parameters were determined by minimizing the differences between the experimental and calculated mole fractions for each of the components over all the tie lines (same global initial mixture). The interaction parameters of DH-NRTL model, τij , were estimated by minimizing the following objective function: OF =
XXX Exp 2 (xCalc P ,l ,i − x P ,l ,i ) P
l
i
(9)
Table 2 Interaction parameters, τij , of the extended NRTL model and average deviation for NP-9 (1) + salts (2) + H2 O (3) systems at 298.15 K Salt
τ12
τ21
τ13
τ31
τ23
τ32
δ1
δ2
MgSO4 Na2 SO4 NaCl
19.94 8.21 0.51
4.45 31.99 15.18
−11.11 −11.62 −8.72
29.41 10.99 10.31
−10.749 −12.160 −6.986
8.15 20.88 14.73
0.6 0.8 1.1
0.4 0.5 0.3
and are reported in Table 2. The non-randomness parameter (αij ) was set as 0.2 for all calculation. In Eq. (9), xp,l,i is the molality of the component i in the phase p for lth tie-line. The experimental LLE data were correlated using Eq. (9) and the following equilibrium condition:
(xi γi )top = (xi γi )bot .
(10)
Using the estimated interaction parameters of the models, the phase diagrams for NP-9 +salts + H2 O systems were predicted. The average deviations of the predicted results by this model are reported in Table 2. The deviation, based on weight percent, is
614
A. Salabat, M. Alinoori / Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 611–614
Fig. 5. Comparison of experimental and calculated phase diagram of NP-9 +MgSO4 + H2 O system with DH-NRTL model; N and solid lines: experiment, and dash lines: model
Fig. 7. Comparison of experimental and calculated phase diagram of NP-9 +NaCl + H2 O system with DH-NRTL model; N and solid lines: experiment, and dash lines: model.
5. Conclusion In the present work, we have measured the LLE data for three ternary systems of NP-9 +salts + H2 O at 298.15 K. The salts used for investigation of the salt effect are MgSO4 , Na2 SO4 and NaCl. The results show that the salting-out power in these systems can be arranged as MgSO4 > Na2 SO4 > NaCl. The salting-out power for the respective cations is as Mg2+ > Na+ and for the respective anions is as SO24− > Cl− , which is in agreement with lyotropic series. The experimental results of the phase diagrams were correlated using the DH-NRTL model. The calculated average deviation between experimental and calculated phase diagrams revealed that the DH-NRTL model is a good model for the correlation and calculation of the LLE data in these systems. References
Fig. 6. Comparison of experimental and calculated phase diagram of NP-9 +Na2 SO4 + H2 O system with DH-NRTL model; N and solid lines: experiment, and dash lines: model.
defined by the following equation:
δi =
N 1 X
N i=1
|wical − wiexp |
(11)
where N is the number of experimental points and the superscripts ‘exp’ and ‘cal’ denote the experimental and calculated values, respectively. On the basis of the obtained deviations, it can be concluded that DH-NRTL model is a suitable model for correlation of the LLE data in these systems. The comparison of experimental tie line data with those calculated from the DH-NRTL model is shown in Figs. 5–7.
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