Physical Properties and Liquid–Liquid Equilibrium of Aqueous Two

Article pubs.acs.org/jced

Physical Properties and Liquid−Liquid Equilibrium of Aqueous TwoPhase Systems Containing Poly(ethylene glycol) + Potassium Chloride + Sodium Polyacrylate Vanessa S. Sampaio,† Renata C. F. Bonomo,‡ Elias S. Monteiro Filho,§ Valéria P. R. Minim,† and Luis A. Minim*,† †

Department of Food Technology, Federal University of Viçosa, 36570-000, Viçosa, MG, Brazil Department of Animal and Rural Technology, State University of Southwest of Bahia, 45700-000, Itapetinga, BA, Brazil § Federal University of São João del-ReiUSL, MG 424-Km 47, 35701-970-Sete Lagoas, MG, Brazil ‡

ABSTRACT: Liquid−liquid equilibrium data and phase diagrams of aqueous two-phase systems (ATPS) composed by water + potassium chloride + poly(ethylene glycol) (PEG) + sodium polyacrylate (NAPA) of different molecular masses, (8000 or 15 000) g·mol−1, were determined at specific pH (7.0 and 9.0). The effects of pH and NAPA molecular mass on the equilibrium data and tie-lines were studied. It was found that an increase in molecular mass caused a decrease in the twophase region for the ATPS at pH 7.0, while at pH 9.0 no effect was observed. A change to the pH values of ATPS did not influence the equilibrium data of the systems studied. The universal quasichemical (UNIQUAC) activity coefficient model with the inclusion of a Pitzer−Debye−Hückel term was used to thermodynamically describe the solutions. The parameters obtained accurately reflected the experimental observations. The viscosity and density properties of the ATPS phases were obtained, and data were submitted to a linear regression analysis. A polynomial model presented good agreement with the experimental data.

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INTRODUCTION Traditional systems for liquid−liquid extraction (LLE) are widely used by industries in purification, extraction, and preconcentration processes of compounds of economic interest, and generally organic solvents are employed although they are toxic, carcinogenic, and flammable.1 For proteins and biomolecules, however, the classic liquid− liquid extraction method is not suitable for their extraction and purification due to the sensitivity of these components to denaturation promoted by organic solvents. In this context, aqueous two-phase systems (ATPS) are presented as an alternative to traditional liquid−liquid extraction methods, and these have many advantages including nontoxicity, noninflammability, and suitability for biotechnological applications.2 In addition, its constituents are commercially available and inexpensive.3 Among the different ATPS's studied, the most commonly used are those composed of polyethylene glycol−dextran (PEG−dextran) and PEG−salt and ionic liquids.2,4−6 An important aspect of these systems is the ability to manipulate the partition of a biomolecule by changing the ionic strength and pH of the system. Besides the chemical aspects, the extraction yield is independent of scale of the process, unlike other methods such as chromatographic bioseparation.7−10 A potentially interesting ATPS is formed by the polymer pair of PEG and sodium polyacrylate (NAPA). Little attention has been given to this system because two phases form only when © 2012 American Chemical Society

certain conditions are achieved, such as a complete dissociation of NAPA molecules (obtained at pH values above 7) and the addition of a sufficient amount of salt to the system, to facilitate the compartmentalization of highly charged polyelectrolytes in the phases. In general, this system presents the advantages of low viscosity, clear, well-defined phases, and recyclability. Moreover, PEG and NAPA polymers are harmless and relatively inexpensive.11,12 The NAPA polymer dissociates at pH greater than 5.0 and is completely charged at pH 7.0. Below pH 5.0, the NAPA polymer is discharged and precipitates in aqueous solutions. Therefore, adjusting the pH of the system allows for solubility modulation of the polymer. The main chain of the NAPA is hydrophobic, and its solubility is characterized by the presence of carboxyl groups (anions) on the polymer side chain.13 These groups are strongly hydrophilic when charged, so PEG and NAPA separate in two different phases. Johansson et al.14 measured equilibrium data for the aqueous PEG 4000 and 8000 + NAPA 240 000 system at different pH levels. Saravanan et al.15 determined the phase equilibrium compositions for the PEG 4000, 6000, and 10000 + NAPA 2100 in aqueous systems at 20 °C. In these earlier studies on the applicability of these systems for bioseparation, it was found that the systems are Received: August 3, 2012 Accepted: October 25, 2012 Published: November 6, 2012 3651

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phase was submitted to two additional chloroform extractions for removing residual PEG. Finally, the tubes containing PEG + chloroform were dried at 105 °C for 12 h, and the PEG content was determined by weighing the tubes. The standard deviation of the PEG content was ± 0.1 mass %. The concentration of water was determined by freeze-drying (LV2000 TERRONI at 253.15 K for 24 h), as described by da Silva et al.19 The standard deviation of the water content was ± 0.01 mass %. All analytical measurements were performed in duplicate. Experimental data was used for model fitting and tie-line length (TLL) determination, as performed using eq 1

relatively inert (resulting in low protein denaturation), have a relatively low viscosity, and can separate by gravity within a few minutes. In this work, liquid−liquid equilibrium data of ATPS composed by PEG + NAPA + KCl + water with different molecular masses of NAPA were determined at pH 7.0 and 9.0. The universal quasichemical (UNIQUAC) activity coefficient model,16 modified by the presence of ionic species, was used to describe thermodynamically the solutions. The influence of NAPA molecular mass and pH on the phase diagram formation was also evaluated. The density and viscosity of the phases were measured, and a multiple polynomial model was fitted to the experimental data for its prediction.

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TLL = [(w2T − w2B)2 + (w3T − w3B)2 ]1/2

EXPERIMENTAL SECTION Materials. PEG with an average molecular mass of 2000 g·mol−1 (PEG) and NAPA with an average molecular mass of 8000 g·mol−1 (NAPA8, 0.45 mass fraction) and 15 000 g·mol−1 (NAPA15, 0.35 mass fraction) were purchased from Sigma Chemical Co. (St. Louis, MO) and used without further purification. All of the other reagents were of analytical grade with a minimum purity of 99 %. Aqueous Two-Phase Systems. The biphasic systems were prepared by weighing appropriate quantities of PEG (0.50 mass fraction), NAPA8 (0.45 mass fraction) or NAPA15 (0.35 mass fraction) and deionized water on an analytical balance (AUX220 Shimadzu, USA), with an uncertainty of ± 0.1 mg. The pH of the stock solutions was adjusted to 7.0 and 9.0 using a pH meter (Gehaka PG-100, Brazil) with uncertainty of ± 0.01. Both stock solutions of PEG and NAPA were supplemented with 150 mmol·L−1 KCl required for phase separation with low polymer concentrations.10 Typically, 40 g of the systems were prepared in 50 cm3 centrifuge tubes by weighing appropriate amounts of each component in the tubes on an analytical balance (AUX220 Shimadzu, USA) with uncertainty of ± 0.1 mg. The mixture was vigorously stirred for 2 min and then allowed to settle for 24 h at the temperature of 298.15 K to reach equilibrium. The temperature was controlled to within ± 0.05 K using a water bath at constant temperature (Phoenix II, Thermo Electron Corp., Germany). After reaching equilibrium, samples from the top and bottom phases were collected in duplicate to determine the composition of each phase using syringes and needles. The top phase was carefully sampled at a distance of at least 0.5 cm above the interface. Samples of the bottom phase were withdrawn using a syringe with a long needle. A minute air bubble was retained on the needle tip and expelled once in the bottom phase to prevent contamination from the top phase, paying special attention to not disturb the equilibrium. Phase Component Determination. Potassium chloride and NAPA were quantified by flame photometry (Photometer CELM FC- 180, Brazil), as described by Zafarani-Moattar and Sadeghi.17,18 The standard deviation of potassium chloride and NAPA measurements was ± 0.012 mass %. The PEG composition in both phases was determined by extraction with chloroform. Initially, a mass of ca. 2 g of each phase was weighed in centrifuge tubes, and the pH was adjusted to 11.0 by adding appropriated amounts of NaOH (1 mol·L−1) to ensure complete dissociation of polyacrylate molecules. Then, 3 mL of chloroform was added to the tubes which were mixed for 30 s in a vortex shaker and centrifuged at 4000g for 5 min. The chloroform bottom phase containing PEG was collected and stored in glass tubes, previously dried and weighed. The top

(1)

where w2T, w3T, w2B, and w3B are the top (T) and bottom (B) equilibrium mass fractions of PEG (2) and NAPA (3). The TLL was expressed in terms of mass fraction. Viscosity and Density Measurements. Density measurements were based on two replicates using a vibrating tube densimeter (Anton-Paar DMA-5000, Graz, Austria) with an accuracy of ± 5·10−6 g·cm−3 in the range of (0 to 3) g·cm−3. Instrument calibration was performed periodically under atmospheric pressure according to specifications, using deionized water and dried air. The viscosity of the phases, η, was evaluated in a rotational rheometer (HAAKE MARS Thermo Electron Corp., Germany) equipped with a thermostatic bath (Phoenix 2C30P, Thermo Electron Corp., Germany) and a concentric cylinder measuring 20 mm in diameter (Z 20 DIN) with annular gap of 0.85 mm. A total of 100 readings were obtained in 2 min at a constant shear rate of 100 s−1. The average value of η was obtained from the Data Manager software Rheonwin with an uncertainty of ± 0.01 mPa s. Analysis was performed at 298.15 K. Thermodynamic Modeling. In addition to the experimental data obtained, the UNIQUAC activity coefficient model was used to thermodynamically describe the solutions.16 Since the systems had ionic species in their compositions, a modification in the model was needed to take these ions into account. This model was chosen due to its broad applicability and acceptance, and several authors have successfully employed it.20−23 Original UNIQUAC represents the activity coefficient of a species in solution as the contribution of combinatorial and residual terms, according to eq 2:

ln γi = ln γiC + ln γi R

(2)

A proposed modification was the inclusion of a Pitzer−Debye− Hückel term according to the description given by Tashima et al.,24 to calculate the activity of ionic species in the solution.25 It essentially consists of expressing ion interactions by means of Coulombic forces. The model then becomes: ln γi = ln γiC + ln γi R + ln γiPDH

(3)

where ln γCi and γRi are the traditional terms in the UNIQUAC is described in eq 424 equation and γPDH i 3652

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Table 1. Density and Viscosity Values of Phases in the Systems Composed of PEG 2000 + NAPA8 at Different pH pH 7.0

pH 9.0

ρ/kg·m−3

ρ/kg·m−3

η/Pa·s

η/Pa·s

tie-line

top

bottom

top

bottom

top

bottom

top

bottom

1 2 3 4

1044.6 1043.2 1045.5 1048.3

1092.5 1109.1 1125.5 1138.9

0.00341 0.00392 0.00454 0.00462

0.00595 0.00709 0.00865 0.01130

1060.5 1043.2 1044.9 1047.8

1100.0 1102.7 1118.9 1134.4

0.00329 0.00354 0.00413 0.00483

0.00450 0.00644 0.00797 0.00965

Table 2. Density and Viscosity Values of Phases in the Systems Composed of PEG 2000 + NAPA15 at Different pH pH 7.0 ρ/kg·m

pH 9.0

−3

η/Pa·s

ρ/kg·m

−3

η/Pa·s

tie-line

top

bottom

top

bottom

top

bottom

top

bottom

1 2 3 4

1041.5 1043.7 1044,3 1046.7

1083.6 1102.7 1115.6 1128.7

0.00342 0.00378 0.00435 0.00515

0.00740 0.00983 0.01268 0.01630

1041.4 1041.5 1043.7 1047.4

1090.5 1103.8 1115.8 1130.9

0.00337 0.00379 0.00439 0.00525

0.00757 0.01010 0.01271 0.01690

⎤ ⎡ 2 I ln γiPDH = −Aϕzi2⎢ + ln(1 + b I )⎥ ⎦ ⎣1 + b I b ⎡ 2 + 2 ∑ mj⎢bi0, j + bi1, j 2 [1 − (1 + α I ) ⎣ α I j

interaction parameters according to the Simplex method in such a way that the overall deviation is minimized. Therefore, an objective function may be stated (eq 6), which incorporates all of these deviations:31 D

zi2 ⎡ ⎢1 2 2

⎛ ⎤ α 2I ⎞ exp(−α I )]⎥ − − ⎜1 + α I + ⎟ ⎦ αI ⎣ 2 ⎠ ⎝ ⎤ exp( −α I )⎥ ∑ ∑ mjmk b1j , k ⎦ j k

S=

⎛ ⎞3/2 1 e2 2πNAρs ⎜ ⎟ 3 ⎝ 4πε0DkBT ⎠

∑∑ ∑ m

n

i

2 ⎡⎛ I,ex I,calc ⎞ ⎢⎜ wi , n , m − wi , n , m ⎟ · ⎢⎜ ⎟ σ wiI,n,m ⎠ ⎣⎝

⎛ w II,ex − w II,calc ⎞2 ⎤ i ,n,m i ,n,m ⎟ ⎥ + ⎜⎜ ⎟⎥ II σ wi , n , m ⎝ ⎠⎦

1/2

(4)

In γPDH term, α and b are model constants (2.0 and 1.2 i kg1/2·mol−1/2, respectively),26 I is the ionic strength, and zi is the absolute charge value of species i. b0i,j and b1i,j are symmetric (i.e., b0i,j = b1i,j) adjustable parameters, available in the literature.27,28 Aϕ is the Debye−Hückel parameter, calculated according to eq 5: Aϕ =

N K−1

/4N (6)

in which wi,n,m is the mass fraction of component i in the tie line n of data group m. The superscripts I and II stand for phases I or II, respectively, and superscripts ex and calc stand for experimental and calculated data points, respectively, D is the total number of data groups, N is the total number of tie lines in each group m, and K is the number of components in the mth data group. Subscripts i, n, and m represent the compound, tie line, and group number, respectively. σwIi,n,mand σwIIi,n,m are the average standard deviations observed in the compositions of the two liquid phases.

(5)

NA is Avogadro’s number, ρs is the solvent density, e is the electron charge, ε0 is the vacuum electric permittivity, D is solvent dielectric constant, k is the Boltzmann’s constant, and T is the absolute temperature. Once the equations are stated, the interaction parameters must be estimated from the experimental data. This task may be accomplished using a nonlinear regression method. In this case, the Nelder−Mead Simplex method was employed.29 The ionic species were each treated as solution components in the PDH term. In fact, this treatment is not necessary since the liquid−liquid equilibrium is correctly described without the electrostatic interaction term but may improve the results as ion concentrations are increased.30 Parameter regression proceeds accordingly to the algorithm expressed below. A reasonable initial guess should be provided; then a liquid−liquid flash is carried out, and the calculated compositions are compared to the experimental compositions. From this comparison, it is possible to obtain an overall deviation from all of the systems studied between experimental and calculated values. The algorithm then changes the

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RESULTS AND DISCUSSION Viscosity and Density. A series of experiments were performed to determine viscosity, η, and density, ρ, of the upper and lower phases of the systems under study. Tables 1 and 2 include the experimental values of duplicate measurements for the ATPS phases studied. For all phases, the standard deviations of density and viscosity were less than 5.3 kg·m−3 and 0.08 mPa·s, respectively. The densities and viscosities of the phases increased as the mass fraction of the system components and molecular weight of NAPA increased, while the changes in pH affected only the density of systems containing NAPA8 at a 5 % significance. According to Saravanan et al.31 and Albertsson,32 high-viscosity differences between phases are beneficial in operational terms, because they decrease the time of phase separation. The values of density and viscosity encountered were close to those found by Minim et al.33 for ternary mixture (PEG + NAPA + water) at 298.15 K. The difference in density between phases of the 3653

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very good for all of the systems studied. In all cases, the determination coefficient (R2) exceeded 0.85. Phase Equilibrium. The phase compositions for the aqueous two-phase systems formed by different molecular masses of NAPA and varying pH values are shown in Tables 4 and 5. All concentrations are expressed in mass fraction. For each PEG/NAPA/pH combination, four tie lines were determined. The tie lines were obtained by linear regression of the corresponding set of overall bottom phase and top phase concentrations. This new aqueous two-phase system has a higher PEG concentration in the upper phase and higher NAPA concentration in the bottom phase. For most systems, the PEG concentration in the bottom phase is very small, and in some cases PEG is almost excluded from this phase, while the opposite behavior is observed in the top phase. The same behavior was observed by Johansson et al.35 when evaluating the effect of salts on the phase equilibrium of system containing PEG and NAPA. Equilibrium diagrams for PEG and NAPA at 298 K for the ATPS are shown in Figures 1 and 2. At pH 7.0 it can be observed that the increase in the molecular weight of NAPA caused a slight reduction of the biphasic area in all concentration ranges analyzed. At pH 9.0 no change in the biphasic area was observed when the NAPA molecular weight was increased. Similar behavior was observed for the PEG + maltodextran ATPS.36 The effect of pH on phase separation is observed in Figures 3 and 4, which summarize the phase diagrams corresponding to ATPS with NAPA8 and NAPA15 at different pH values, respectively. There was no displacement of the biphasic region for the pH levels studied. Similar behavior was observed for systems containing PEG + NAPA at pH 5.5 and 7.3.14 Table 6 shows the experimental values of TLL for the different pH values evaluated. For each system studied, it is observed that the TLL changed slightly upon variations to the pH with respect to each total composition evaluated. Nascimento et al.,37 studying the liquid−liquid equilibrium of system composed of UCON 2000 + sodium phosphate, observed in all pH levels studied that the TLL increased as the overall composition increased. Thermodynamic Modeling. A set of parameters was obtained as displayed in Table 7. With these parameters, the experimental data can be described within a mean deviation of 3 %. From this set, a slight change may be observed from pH 7 to pH 9, reflecting the small difference between system compositions. In general, parameters tended to decrease from pH 7 to pH 9, indicating lower interactions in the latter case. Also, for a given pH the differences between NAPA8 and

systems studied ranged from (4.5 to 8.0) %. These values were higher than that found by Albertsson (1971)32 for systems containing PEG + dextran whose difference in density ranged from (2.5 to 6.0) %. The obtained values were also higher than those found for systems containing PEG with different molecular weights and ammonium sulfate ((3.0 to 4.5) %).34 The general linear model (eq 7) was adjusted to the experimental data of density (ρ) and viscosity (η) as a function of PEG concentration (w1), NAPA concentration (w2), and pH (w3). ψ = β0 + β1w1 + β2w2 + β3w3 + β4 w1w2 + β5w1w3 + β6w2w3

(7)

where ψ is the thermophysical property. An analysis of variance (ANOVA) for the models was performed, and the model significance was examined via Fisher’s statistical test (F-test) by determining significant differences between sources of variation in experimental results, that is, the significance of regression, the lack of fit, and the multiple determination coefficients (R2). Parameters with less than 95 % significance (p > 0.05) were excluded and added to the error term. All statistical analyses were performed using the statistical package Statistical Analysis System version 9.0 (SAS Institute Inc., Cary, NC). Table 3 presents the values of Table 3. Adjusted Models for Calculating Densities and Dynamic Viscosities of Phases in the Systems Composed of PEG 2000 + NAPA8 and PEG 2000 + NAPA15 NAPA8 Top phase: ρ = 1052.16 − 0.8825x1 − 2.0419x3 + 0.1905x2x3 η = 11794 + 0.1405x1 Bottom phase: ρ = 1035.65 − 40.72x1 + 8.259x2 − 4.865x1x2 η = −5.7239 + 9.354x1 + 1.325x2 − 0.9403x1x2 NAPA15 Top phase: ρ = 1019.4 + 0.6763x1 + 3.0004x2 η = 0.8569 + 01919x1 Bottom phase: ρ = 978.71 + 8.706x2 η = −15.9244 + 1.845x2

R2 = 0.97 R2 = 0.85 R2 = 0.86 R2 = 0.90

R2 = 0.92 R2 = 0.96 R2 = 0.94 R2 = 0.93

polynomial coefficients obtained from the regression for density and viscosity of the studied systems. The agreement between experimental and predicted values for density and viscosity was

Table 4. Liquid−Liquid Equilibrium Data for PEG 2000 (w1) + NAPA8 (w2) + Potassium Chloride (w3) + Water (w4) Systems for Specific pH (7 to 9) total composition

top phase

bottom phase

pH

w1

w2

w3

w4

w1

w2

w3

w4

w1

w2

w3

w4

7.0

0.0750 0.0850 0.0950 0.1060 0.0700 0.0800 0.0900 0.1000

0.0750 0.0850 0.0950 0.1070 0.7090 0.0800 0.0900 0.1000

0.0110 0.0110 0.0110 0.0110 0.0110 0.0110 0.0110 0.0110

0.8390 0.8190 0.7990 0.7770 0.8480 0.8290 0.8090 0.7890

0.1156 0.1472 0.1844 0.2225 0.1106 0.1401 0.1664 0.1889

0.0449 0.0423 0.0418 0.0424 0.0452 0.0426 0.0402 0.0398

0.0063 0.0059 0.0048 0.0037 0.0076 0.0067 0.0044 0.0045

0.8312 0.8149 0.7686 0.7313 0.8369 0.8177 0.8074 0.7758

0.0274 0.0148 0.0121 0.0079 0.0211 0.0150 0.0154 0.0119

0.1141 0.1451 0.1592 0.1731 0.1295 0.1451 0.1540 0.1711

0.0085 0.0107 0.0134 0.0153 0.0114 0.0114 0.0120 0.0128

0.8494 0.8292 0.8151 0.8046 0.8494 0.8280 0.8190 0.8045

9.0

3654

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Table 5. Liquid−Liquid Equilibrium Data for PEG 2000 (w1) + NAPA15 (w2) + Potassium Chloride (w3) + Water (w4) Systems for Specific pH (7 to 9) total composition

top phase

bottom phase

pH

w1

w2

w3

w4

w1

w2

w3

w4

w1

w2

w3

w4

7.0

0.0750 0.0860 0.0950 0.1050 0.0750 0.0850 0.0940 0.1050

0.0750 0.0850 0.0950 0.1050 0.0760 0.0850 0.0940 0.1060

0.0110 0.0110 0.0110 0.0110 0.0110 0.0110 0.0110 0.0110

0.8380 0.8180 0.7980 0.7780 0.8380 0.8180 0.8000 0.7780

0.1353 0.1562 0.1875 0.2192 0.1226 0.1615 0.1809 0.2257

0.0432 0.0434 0.0402 0.0395 0.0457 0.0402 0.0401 0.0428

0.0070 0.0041 0.0039 0.0016 0.0053 0.0013 0.0019 0.0056

0.814 0.796 0.768 0.740 0.8268 0.7971 0.7772 0.7261

0.0270 0.0182 0.0119 0.0052 0.0222 0.0082 0.0080 0.0069

0.1251 0.1423 0.1535 0.1739 0.1271 0.1476 0.1553 0.1721

0.0121 0.0126 0.0129 0.0130 0.0129 0.0119 0.0127 0.0141

0.8385 0.8185 0.8216 0.8078 0.8462 0.8422 0.8340 0.8170

9.0

Figure 1. Influence of NAPA molecular weight on the phase diagram of the PEG (1) + NAPA (2) system at 298.15 K and pH 7. ●, NAPA (8000 g·mol−1); △, (15 000 g·mol−1).

Figure 3. Influence of pH on the phase diagram of the PEG (1) + NAPA (8000 g·mol−1) (2) system at 298.15 K. ●, pH 7; △, pH 9.

Figure 4. Influence of pH on the phase diagram of the PEG (1) + NAPA (15 000 g·mol−1) (2) system at 298.15 K. ●, pH 7; △, pH 9.

Figure 2. Influence of NAPA molecular weight on the phase diagram of the PEG (1) + NAPA (2) system at 298.15 K and pH 9. ●, NAPA (8000 g·mol−1); △, (15 000 g·mol−1).

reflecting its high concentration in both phases. As expected, the strongest attractive interaction was with the salt (or more specifically its ions). Both NAPA8 and NAPA15 interacts positively with PEG2000, meaning repulsion in relative terms. On the other hand, the salt interacts positively with PEG2000 and negatively with both NAPA8 and NAPA15. From a molecular point of view, interactions between noncharged components are much less intense than between the charged ones. This does not mean different values of their interaction

NAPA15 are small. The results indicate that, at pH 7, NAPA8 interacts more weakly with PEG 2000 than NAPA15, while at pH 9 the inverse is observed. However, since the variation is small, this may be justified by the numerical technique employed to estimate the parameters. Considering water as the key component, it is possible to first notice its negative interaction with all of the components, 3655

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deviations, but also accurately reflect the experimental observations.

Table 6. TLL Values for PEG + NAPA ATPS at Different pH Values NAPA8

■

NAPA15

tie-lines

pH 7.0

pH 9.0

pH 7.0

pH 9.0

1 2 3 4

11.216 16.758 20.835 25.140

12.296 16.236 17.838 22.036

13.592 16.978 20.906 25.266

12.958 18.718 20.776 25.415

Corresponding Author

*E-mail: [email protected]. Tel.: +55-31-3899-1617. Fax: +55-313899-2208. Funding

This work was supported by the CNPq and FAPEMIG agencies of Brazil.

Table 7. Interaction Parameter Values of the Modified UNIQUAC Modela

Notes

The authors declare no competing financial interest.

pH 7.0

■

i j

1

2

3

4

897.72 X 0 175.28 5.0671 29.37 pH 9.0

AUTHOR INFORMATION

1843.6 −370.15 −518.93 0 −1999 −150.77

5 1229.7 −1189.1 −563.86 −122.4 0 −1340.8

6 −59.521 −221.38 −231.18 −335.42 −316.44 0

1 2 3 4 5 6

0 −201.09 −212.12 −26.29 3.0881 54.497

932.24 0 X 453.04 646.41 19.83

j

1

2

3

4

5

6

1 2 3 4 5 6

0 −199.05 −183.44 −23.215 −21.896 51.518

717.38 0 X 493.97 457.14 47.768

683.28 X 0 52.627 53.975 0.10222

1143.5 −563.06 −1309.9 0 −1463.9 −1431.6

1143.0 −557.58 −1303.0 −292.0 0 −1304.5

−60.297 −201.42 −215.07 −448.83 −425.94 0

REFERENCES

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i

The indices 1 to 6 stand for PEG, NAPA8, NAPA15, K+, Cl−, and H2O, respectively.

a

parameters, listed in Tables 1 and 2, since for charged species the specific interactions are calculated in a different term of the equation. One should notice that the PDH term, as formulated in this work, does not have any adjustable parameters. But, since there is already an additional summation to the total ln γi, this reflects on the parameters of the residual term. Some authors argue that this treatment is not necessary since the liquid−liquid equilibrium is correctly described without the electrostatic interaction therm, but as the concentration of ions are increased the results may improve.38 For instance, Perumalsamy and Murugesan (2006)39 noticed better correlation of LLE data using UNIQUAC with a Debye−Hückel term, relative to the original equation.

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CONCLUSIONS The physical property values increased with the increase in solute mass fraction and molecular weight of NAPA, while the change to pH did not influence these properties. The simple polynomial functions presented good agreement with the experimental data, and thus the estimation of ρ and η using the models developed in this work is recommended, considering the range of pH and concentrations investigated. The effect of pH on equilibrium data of all systems under study was quite small. An increase in the molecular weight of NAPA caused a slight decrease in the two-phase area for all concentration ranges analyzed at pH 7.0. The UNIQUAC parameters obtained represent not only a good fit in terms of mean 3656

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Journal of Chemical & Engineering Data

Article

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