Liquid–liquid and liquid–liquid–solid equilibrium in Na2CO3–PEG–H2O

Fluid Phase Equilibria 180 (2001) 273–280

Liquid–liquid and liquid–liquid–solid equilibrium in Na2 CO3–PEG–H2 O M.E. Taboada a , J.A. Asenjo b , B.A. Andrews b,∗ a

b

Department of Chemical Engineering, University of Antofagasta, Angamos 601, Antofagasta, Chile Department of Chemical Engineering, Centre for Biochemical Engineering and Biotechnology, Millenium Institute for Advanced Studies in Cell Biology and Biotechnology, University of Chile, Beauchef 861, Santiago, Chile Received 23 August 2000; accepted 16 January 2001

Abstract The phase diagram was determined for the Na2 CO3 –PEG–H2 O system at 25◦ C using PEG (poly(ethylene glycol)) with a molecular weight of 4000. Compositions of the liquid–liquid and the liquid–liquid–solid equilibria were determined using calibration curves of density and index of refraction of the solutions, and atomic absorption (AA) and X-ray diffraction analyses were made on the solids. The solid phase in equilibrium with the biphasic region was Na2 CO3 ·H2 O. Binodal curves were described using a three-parameter equation. Tie lines were described using the Othmer–Tobias and Bancroft correlation’s. Correlation coefficients for all equations exceeded 0.99. The effects of temperature (25 and 40◦ C) and the molecular weight of the PEG (2000, 3000, and 4000) on the binodal curve were also studied, and it was observed that the size of the biphasic region increased slightly with an increase in these variables. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Liquid–liquid equilibria; Data; Phase diagram; PEG; Na2 CO3

1. Introduction Aqueous two-phase systems (ATPS) are formed by water plus two polymers, or by water with one polymer and an inorganic salt. In the latter, one of the polymers most frequently utilized is poly(ethylene glycol) (PEG) with which are formed two immiscible phases which normally contain mole fractions of water in excess of 80% [1]. This characteristic has allowed the use of these systems for the partitioning of a large number of biomaterials and metal ions [2–4]; several monographs are available on this topic [1,5–7]. Zaslavsky [1] presented a useful summary of experimental data and equilibrium diagrams for phases in systems formed by PEG, inorganic salts, and water. The principal inorganic salts discussed included ammonium phosphate, ammonium, sodium, and magnesium sulfates, potassium and sodium carbonates, and sodium and potassium hydroxides. Equilibrium diagrams for other salts have been reported [8–10]. ∗ Corresponding author. Tel.: +56-2-678-4710; fax: +56-2-699-1084. E-mail address: [email protected] (B.A. Andrews).

0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 3 5 4 - 5

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There are few data available on the ATPS of the present study, including results for only one region of the phase diagram [11]. These authors present data on parts of the phase diagrams for aqueous solutions of PEG with MgSO4 , Na2 SO4 , CaCO3 , (NH4 )2 SO4 and K3 PO4 . Binodal curves obtained from their tie line data are not precise and are only valid for the liquid–liquid equilibrium zone. It is seen that the effect of increasing the molecular weight of the PEG produces an increase in the binodal region. In the present study the phase diagram has been determined for the Na2 CO3 –PEG 4000–H2 O system at 25◦ C. The effect of temperature and molecular weight of the PEG on the binodal curve was also studied. The use of this system was interesting for the design of crystallization processes for carbonate salts using PEG as a co-solvent. 2. Experimental 2.1. Materials All reagents were from the Merck, and used as supplied with no further purification steps. Salts were reagent grade, and were dried in an oven for 48 h at 120◦ C before use. The polymer (mass-average molar mass 4000 g/mol) was in the form of solid powder (polydispersity index, as reported by the supplier, was 1.1). In drying for a week at 50◦ C, the polymers showed water content of 0.46 mass%. Distilled deionized water was used in all experiments (conductivity < 0.5 ␮S/cm). 2.2. Apparatus and procedures 2.2.1. Analytical methods The concentrations of Na2 CO3 were determined by sodium analysis using atomic absorption spectroscopy (AAS). The AAS measurements were performed using a Varian model SpectrAA 220 at a wavelength of 589 nm. Each mixture was prepared and analyzed in triplicate, and gave a mean accuracy of 0.7%. Analyses of error in chemical determinations of sodium for the quantification of Na2 CO3 showed there was no appreciable effect of PEG on the error. Absolute mean error was 1.31% with a standard deviation of 0.02% of the weight determination. The concentration of PEG was determined from density measurements at 25◦ C using an Anton Paar model DMA 38 densimeter. Each mixture was prepared and analyzed in triplicate. The relative accuracy of the weight fraction was 0.6%. Temperature was maintained within ±0.1◦ C of set points using a Haake Instrument Co. water bath. Since the density of phase samples depends on the PEG and salt concentrations, calibration plots of density versus polymer concentration were prepared for different concentrations of Na2 CO3 . The accuracy of the measured density was ±10−4 . The calibration was given by the following relation between the density (ρ) and the salt (WS ) and PEG (WP ) mass fractions: ρ = 0.9970 + 0.1739 WP + 1.0801 WS

(1)

Eq. (1) reproduced the results with maximum absolute deviations of 0.1%. Gonzales-Tello et al. [12], obtained the following equation for the density of concentrated aqueous solutions of PEG at 25◦ C. ρ = 0.99707 + 0.17441 WP

(2)

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275

They found that the density values were practically independent of the molecular mass of the PEG and are comparable to our result. In our work, Eq. (1) gave 1.1709 g/ml when W S = 0 and W P = 1. With Eq. (2) this value was 1.1714. The calibration was also verified using measurements of refractive index using a Mettler Toledo model #RE50 refractometer (±0.0001 nD). This way it was possible to obtain the percentage weight of PEG of a solution, knowing the density and/or the refractive index and the salt concentration obtained by AAS. The calibration for the index of refraction is shown in Eq. (3) n = 1.3325 + 0.2464 (WNa2 CO3 ) + 0.1447 (WPEG )

(3)

Eqs. (1) and (3) are valid only up to concentrations 25% PEG and 2% salt. Beyond these concentrations, linearity is not maintained, due to nearness to the biphasic zone. Average errors of 0.23% (refractive index) and 0.60% (density) were obtained on the Na2 CO3 –PEG–H2 O solutions using these equations. 2.2.2. Binodal curve The approximate location of the binodal curve was determined by adding a PEG solution to a Na2 SO4 solution until turbidity appeared indicating the beginning of the formation of a two-phase system. This corresponds to a point on the so-called binodal curve. This procedure appeared to be simple and accurate. A similar method was used by González-Tello et al. [8]. 2.2.3. Tie lines Equilibrium measurements were made by preparing mixtures of known overall mass composition by stirring for 24 h and allowing the solution to settle for another 24 h, at a constant temperature of 25±0.1◦ C to ensure that equilibrium was reached. At the end of each experiment, samples were taken from two phases and from three phases in different zones and analyzed. Longer stirring and settling periods did not result in any observable changes in the phase compositions. Feed compositions yielding roughly equal volumes of the top and the bottom phases were then calculated. Feed samples of 60–95 ml were prepared by mixing three components in 100 ml graduated Pyrex cylinders. These cylinders were capped using paraffin wax film. The cylinders were placed in a water bath with magnetic stirring at the desired temperature for 24 h. At the end of the 24 h the solution was allowed to settle for another 24 h at the same (constant) temperature to ensure that equilibrium was reached. At the end of each experiment, each phase’s volumes were recorded, and samples were taken from both phases and analyzed. The measurements of density in each phase were carried out immediately after sample withdrawal. The top phase was sampled first, with care taken to leave a layer of solution of at least 0.5 cm thick above the interface. The bottom phase was withdrawn using a syringe with a long needle. A tiny bubble of air was retained on the needle tip and expelled once in the bottom phase to prevent contamination from upper-phase material. The concentrations of salt and PEG in both phases were determined after mass dilution with water by a factor of approximately 2 (top phase) and 10 (bottom phase). After each determination the material balance for each component was checked. The average differences between compositions analyzed and compositions calculated from the material balances were 2.2%. 2.2.4. Liquid–liquid–solid zone In cases where precipitated salt was present (liquid–liquid–solid equilibrium), care was taken to ensure that the sample was withdrawn gently, with the needle tip well away from the salt crystals. The procedure

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Fig. 1. Binodal curve and tie-lines for PEG 4000 + Na2 CO3 + H2 O at 25◦ C.

was the same as for determining tie lines. Crystals were filtered off and then analyzed using X-ray diffraction. 3. Results and discussion 3.1. Binodal curve The binodal curve is plotted in Fig. 1 together with tie lines. The equilibrium data are listed in Table 1. For the system studied, the density of the top phases was close to 1.1 g/ml while that of the bottom phases ranged from 1.1 to 1.3 g/ml. The density difference between the phases increased with the tie line length. Table 1 also lists the value of the partition coefficient (K) of the salt, defined as the fraction of salt retained in the bottom phase divided by the salt in the top phase. High values of K indicate there is a good Table 1 Tie lines for the sodium carbonate (1) + water (2) + PEG (3) system at 25◦ C at various initial mass fraction w Initial component

Top phase

Bottom phase

Partition coefficient K

w1

w3

w1

ρ (g/ml)

w3

w1

ρ (g/ml)

w3

0.0800 0.0803 0.0802 0.1125 0.1500 0.1007

0.1500 0.2001 0.2499 0.2501 0.2000 0.3976

0.1306 0.1427 0.1690 0.2365 0.2135 0.2680

1.0756 1.0802 1.0851 1.0976 1.0935 1.1052

0.3678 0.4195 0.4563 0.5516 0.5191 0.6235

0.0120 0.0089 0.0067 0.0034 0.0041 0.0020

1.1289 1.1491 1.1761 1.2482 1.2240 1.2972

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

10.88 16.03 25.22 69.56 52.07 134.00

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Fig. 2. Effect of molecular weight of PEG on the binodal curve at 25◦ C.

separation of the salt. The percentage of sodium carbonate recovered in the bottom phase was 99.26% for the tie line farthest from the water origin. Fig. 1 shows that when PEG is added to the saturated solution, the solubility of the salt decreases. Observation of the equilibrium lines shows that whatever the addition of salt, there is an alteration in the composition of both immiscible phases. The binodal curve was fitted using the following non-linear expression of Mistry et al. [13] 3 lnXPEG = a + bX0.5 sal + cXsal

(4)

where XPEG and Xsal represent the mass% values for PEG and salt, respectively. The parameters were a = 4.432, b = −0.726 and c = −0.003 obtained using Newton’s method. Error in the regression coefficient between experimental and calculated values using this equation was 0.9989. The fitting of Eq. (4) was performed using “Tablecurve”, a program that automatically fits 200 different equations to a set of experimental data and classifies the resulting equations according to the R2 values. The form of the equation is therefore, empirical. Fig. 2 shows the effect of varying the molecular weight of the PEG from 2000 to 6000. There was a greater effect when the variation was between 2000 and 4000. The binodal curves for molecular weights between 2000 and 4000 tended to superimpose for salt concentrations greater than 10% in weight and for PEG concentrations greater than 35%. The binodal zone increased with increase in molecular weights. González-Tello et al. [8] observed similar tendencies for magnesium sulfate, and Ho-Gutierrez et al. [14] for sodium sulfate. When concentrations of salt exceed 13% by weight, with PEG near 60%, the binodal curve for PEG 2000 tends to be the same as those of PEG 4000 and 6000. Fig. 3 shows the effects of raising the temperature from 25 to 40◦ C, where, for salt concentrations between 3 and 8% by weight, only a very slight increase in the binodal region is observed.

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Fig. 3. Effect of temperature on the binodal curve with PEG 4000.

3.2. Tie lines Tie line compositions are given in Table 1. The phase concentrations are also plotted in the phase diagram in Fig. 1. The tie lines are determined by connecting each corresponding set of total, top and bottom phase compositions. The coexisting phases are close in composition. A mass balance was obtained for each component, comparing the initial mass with the amounts in the bottom and top phases. The mass of each component was calculated from volume, density and equilibrium composition measurements. The average relative error for the mass balance was 2.2%. Empirical equations are used to model the equilibrium results of the traditional liquid–liquid extraction, and which correspond to the Othmer–Tobias correlation’s (Eq. (5)) and Bancroft potential equation (Eq. (6)) [8].





1 − w3t w3t w2b w1b






1 − w1b =k w1b




= k1

w2t w3t

n (5)

r (6)

where w3t represents the mass fraction of PEG in the top phase, w1b represents the mass fraction of Na2 CO3 in the bottom phase, w 2b represents the mass fraction of water in the bottom phase, and w 2t represents the mass fraction of water in the top phase; k, n, k1 and r represent parameters to be determined. Linearization of both equations produces acceptable consistency in the results. The values obtained for these parameters are 4.295, 1.036, 4.129 and 0.970, respectively. The linear regression index of Eqs. (5) and (6) was 0.991 for both. In the liquid–liquid–solid zone, the solids proved to be Na2 CO3 ·H2 O (thermonatrite).

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Fig. 4. Phase diagram for PEG Na2 CO3 –PEG 4000–H2 O at 25◦ C.

3.3. Phase diagram for Na2 CO3 –PEG 4000–H2 O a 25◦ C Fig. 4 shows the complete phase diagram for the system plotted on triangular coordinates. The letters L and S denote liquid and solid phases, respectively. Most of the phase diagram consists of either a solid–liquid–liquid or solid–solid–liquid region. Region 1L represents unsaturated solutions. The biphasic zone is labeled 2L. The two liquid regions occupy a small portion of the total phase diagram, although the coexisting phases are generally quite different in composition. There are two single liquid–solid regions, one with a liquid rich in water and another with a liquid rich in PEG. Any addition of sodium carbonate would alter the compositions of the two immiscible phases. The 1S + 2L region represents the crystallization field of sodium carbonate monohydrate, which is an advantage with respect to working without PEG, given that at 25◦ C a decahydrated salt is crystallized if one works with salt and water. The system is saturated with salt and the composition of each liquid phase remains constant although the relative quantity of the two liquids changes, as predicted by the two-phase rule. The 1S + 1L region contains the monohydrated salt in equilibrium with PEG saturated solutions. Next there exist two zones of two solids and a liquid. In one of these the solids include the monohydrated salt and an anhydrous salt in equilibrium with a PEG saturated solution. In the second zone, the solids include an anhydrous salt, solid PEG, and the same solution (SP ) that corresponds to the solubility of PEG in water at 25◦ C, the value of which, experimentally measured, was 68.2% by weight. The eutectic points FI and FS were 0.01% (PEG) and 26.80% (salt) in the bottom phase, and 62.30% (PEG) and 0.20% (salt) in the top phase. There exists a zone of insignificant size, which is not visible in the diagram, as it is practically superposed by the ordinate. This corresponds to crystals in equilibrium with a saturated sodium carbonate solution

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which varies between the solubility of the salt in water (23.17% by salt weight [15]) to the invariant FI (0.01% PEG and 26.80% salt). Acknowledgements Financial support from Conicyt (Fondecyt Project 1990907) and the Millenium Institute for Advanced Studies in Cell Biology and Biotechnolgy (P 99-031-F) is gratefully acknowledged. References [1] B.Y. Zaslavsky, Aqueous Two Phase Partitioning Physical Chemistry and Bioanalytical Applications, Marcel Dekker, New York, 1995. [2] J.A. Asenjo, A.S. Schmidt, F. Hachem, B.A. Andrews, J. Chromatogr. 668 (1994) 47–64. [3] A.S. Schmidt, B.A. Andrews, J.A. Asenjo, Biotechnol. Bioeng. 50 (1996) 1–9. [4] R.D. Rogers, C.B. Bauer, A.H. Bond, Sep. Sci. Technol. 30 (1995) 7–9, 1203–1217. [5] P.A. Albertsson, Partition of Cell Particles and Macromolecules, Wiley, New York, 1986. [6] B.A. Andrews, J.A. Asenjo, in: E.L. Harris, S. Angal (Eds.), Protein Purification Methods. A Practical Approach, IRL Press, Oxford, 1989. [7] S. Bamberger, D.E. Brooks, K.A. Sharp, J.M. Van Alstine, T.J. Weber, Partitioning in Aqueous Two Phase Systems, Academic Press, New York, 1985. [8] P.G. González-Tello, F. Camacho, G. Blazquez, F.J. Alarcón, J. Chem. Eng. Data 41 (1996) 1333–1336. [9] L.H. Meller da Silva, J. Coimbra, A.A. Meirelles, J. Chem. Eng. Data 42 (2) (1997) 398–401. [10] T.A. Graber, M.E. Taboada, A. Carton, S. Bolado, J. Chem. Eng. Data 45 (2) (2000) 182–184. [11] S.M. Snyder, K.D. Cole, D. Szlag, J. Chem. Eng. Data 37 (1992) 268–274. [12] P.G. González-Tello, F. Camacho, G. Blázquez, J. Chem. Eng. Data 39 (1994) 611–614. [13] S.L. Mistry, A. Kaul, J.C. Merchuk, J.A. Asenjo, J. Chromatogr. A 741 (1996) 151–163. [14] I. Ho-Gutiérrez, E. Cheluget, J.H. Vera, M. Weber, J. Chem. Eng. Data 39 (1994) 245–248. [15] H.R. Perry, Chemical Engineers Handbook, Vol. I, McGraw-Hill, New York, 1994.