LiquidâLiquid Equilibrium of Two-Phase Aqueous Systems Composed

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Liquid−Liquid Equilibrium of Two-Phase Aqueous Systems Composed of PEG 400, Na2SO4, and Water at Different Temperatures and pH Values: Correlation and Thermodynamic Modeling Rui Gomes Nascimento,† Rafael da Costa Ilhéu Fontan,† Renata Cristina Ferreira Bonomo,† Cristiane Martins Veloso,§ Sérgio de Sousa Castro,‡ and Leandro Soares Santos*,† †

Department of Animal and Rural Technology, State University of Southwest of Bahia, 45700-000 Itapetinga, Bahia, Brazil Department of Exact and Natural Sciences, State University of Southwest of Bahia, Praça Primavera 40, Bairro Primavera, 45700-000, Itapetinga, Bahia, Brazil § Department of Natural Science, State University of Southwest of Bahia, 45083-900, Vitória da Conquista, Bahia, Brazil ‡

ABSTRACT: Liquid−liquid equilibrium (LLE) data were obtained for aqueous two-phase systems composed of polyethylene glycol (PEG) 400 g mol−1 + organic salt (Na2SO4) + water at different temperatures (293.15, 298.15, 303.15 and 308.15)/K, and pH values of 3.0, 4.0, and 5.0. The effect of temperature and pH on the binodal curves were evaluated, and it was verified that the increase of the variables resulted in a larger biphasic region. The saltingout effect was studied using the values of parameters of the effective excluded volume (EEV) model. The experimental results of LLE have been correlated using the UNIFAC model. The root-mean-square deviations between the experimental and predicted LLE compositions for the PEG 400 + Na2SO4 systems were very low. The UNIFAC model was able to represent satisfactorily the aqueous two-phase systems studied.

and consequently easy phase separation.13,16 Sodium sulfate is a salt that can be used in pharmaceutical and food field and has been widely used in the formation of aqueous two-phase systems. It is essential to determine liquid−liquid equilibrium data for an effective application of the ATPS, since this information allows a greater knowledge about the phase behavior in the systems and their physicochemical properties, besides facilitating the understanding of the mechanisms involved in the partitioning of biomolecules in ATPS.1,3,8 Several equilibrium data for the polyethylene glycol and sodium sulfate systems are available in the literature,1,11−14 including those formed by PEG 400 and sodium sulfate.15,16 However, despite the many published studies with equilibrium data for the systems containing PEG 400 and sodium sulfate, there is no report on equilibrium data for these systems at temperatures of 293.15, 298.15, 303.15, and 308.15 K associated with low pH values of pH 3, 4. and 5. Conditions are optimal for the stability of certain biomolecules such as pigments1 and proteins5 that can be commercially used in the pharmaceutical and food industries. Among these pigments, it is important to mention anthocyanins and betalains that have their optimal stability at low pH values. In this way, it is necessary to produce and study systems with these conditions.

1. INTRODUCTION Aqueous two-phase systems (ATPS) are formed by combination of low-miscible aqueous solutions (in specific concentrations) of polymer−polymer, salt−salt, polymer−salt, and alcohol−salt.1,2 Such systems can be used as an alternative to perform liquid− liquid extraction without the use of traditional organic solvents. This alternative has the advantages of low cost, low interfacial tension, its components are neither toxic nor flammable, and the possibility of large scale application and short time of phase separation.1−3 Aqueous two-phase systems have played an important role in the purification of several biological compounds (animal or plant cells, microorganisms, nucleic acids, enzymes, proteins, and pigments),1,4−6 in removal of metal ions6 and sulfide minerals,7,8 in nanoparticles recovery,9 and to remove organic pollutants from environments.10 The most common ATPS used for separation of biomolecules are composed of two polymers, especially polyethylene glycol (PEG) and dextran. However, the high cost of dextran and high viscosity of the polymer phase, which may interfere with the locomotion of the molecule of interest in the system, constitutes a major drawback of using this type of ATPS, and thus, polymersalt systems have constituted an important alternative.11−14 In these systems, PEG has been the predominant polymer, since it presents low cost and depending on its molar mass, low viscosity, as is the case of PEG 400, used in this work, while the salts of citrate, phosphate, and sulfate are the most used due to their ability to intensify hydrophobic behavior between the phases © XXXX American Chemical Society

Received: November 1, 2017 Accepted: February 20, 2018

A

DOI: 10.1021/acs.jced.7b00947 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Tie-lines were determined by a gravimetric method described by Merchuk et al.21 For the determination of the tie lines,

The information on the equilibrium data is very important because it allows one to evaluate the required amount of each component for the formation of the two phases but not expressed as one component affects the other8 or the contribution that each molecule provides to the system. There are some thermodynamic models that can estimate the contribution of the groups present in the systems, such as UNIFAC, UNIQUAC, ASOG, NRTL.17 However, the UNIFAC model has the advantage of determining the contribution parameters of the mixture group in two parts: residual and combinatorial. The residual part considers the energetic interactions formed by the functional groups when they separate and interact until the system comes into equilibrium and can be identified as an enthalpy contribution. The combinatorial part takes into account the differences in shape and size between the molecules in the mixture and can be identified as an entropic contribution. In this way, this model is ideal for the aqueous two-phase system.8,18 The thermodynamic modeling to estimate contribution groups has been studied for systems formed by PEG and sodium sulfate,19,20 but not to conditions that will be studied in this work. Therefore, this work is dedicated to obtaining phase equilibrium data for systems formed by PEG 400 + sodium sulfate + water at different temperatures and pH. The influence of temperature and pH on the equilibrium data was evaluated. The excluded effective volume (EEV) was used to describe the effect of salt exclusion. In addition, the UNIFAC model is used to predict the phase separation behavior of reference systems.

Table 1. Parameters Rk and Qk of the Groups for the UNIFAC Model Rk

Qk

refs

CH2 ETHYL OH SO4 NA H2O

0.6744 1.5927 1.0000 2.8560 3.0000 0.9200

0.5400 1.3200 1.2000 2.0150 3.0000 1.4000

Magnussen, 198128 Ninni, 199929 Magnussen, 198128 Weast, 197330 Bondi, 196831 Magnussen, 198128

Table 2. Global Compositions and Phase Composition for Aqueous Two-Phase Systems PEG 400 (w1) + Sodium Sulfate (w2) + H2O (w3) at pH = 3.0, 4.0, and 5.0, Temperatures 293.15, 298.15, 303.15, and 308.15 K, and Pressure p = 0.1 MPaa global composition pH

3

4

2. EXPERIMENTAL SECTION 2.1. Materials. PEG 400 g mol−1 was purchased from Synth (Brazil) with a mass fraction of purity greater than 99% and used without further purification. Organic salt, sodium sulfate, was also purchased from the Brazilian company Synth with a mass fraction of purity greater than 99% and used without further purification. Distilled water was used in all experiments. 2.2. Methods. 2.2.1. Determination of Phase Diagrams and Tie Lines. Determination of the binodal curves was carried out using the turbidimetric titration method.18 Aqueous stock solutions at 70 wt % of PEG 400 and aqueous solutions at 22 wt % of Na2SO4 were prepared and used for the determination of aqueous biphasic systems. Initially, a few grams of the salt solution (approximately 1.0 g) was added to a glass tube and titrated with small aliquots of PEG 400 stock solution, approximately 0.05 g, until the solution became turbid, indicating the formation of a two phrases. A known amount of water was then added to the tube to recover the initial one-phase system. This procedure was repeated several times to obtain the binodal curve. The turbidimetric titration was performed in thermostatic bath (Tecnal, Brazil) with controlled temperature (293.15, 298.15, 303.15 or 308.15) K and the pH values were adjusted to 3.0, 4.0, 5.0, adding sulfuric acid. The total composition of the system was determined by measuring the amount of PEG added, using an analytical balance (Gehaka, Brazil). A nonlinear empirical equation, eq 1, was used to correlate the experimental binodal data of the PEG 400 + salt + water systems. [w1] = exp(a + b[w2]0.5 + c[w2] + d[w2]2 )

contribution group

5

3

4

5

3

4

5

3

4

(1)

where [w1] and [w2] represent the total compositions (in mass fraction) of PEG 400 and sodium sulfate, respectively, and a, b, c, and d are constants obtained by regression of the experimental data.

5

TL

w1

w2

1 2 3 1 2 3 1 2 3

0.3200 0.3400 0.3600 0.2800 0.3000 0.3200 0.2950 0.3100 0.3250

0.0700 0.0800 0.0900 0.0800 0.0900 0.1000 0.0750 0.0850 0.0950

1 2 3 1 2 3 1 2 3

0.3000 0.3150 0.3300 0.2800 0.3000 0.3200 0.2950 0.3100 0.3250

0.0800 0.0900 0.1000 0.0750 0.0850 0.0950 0.0750 0.0850 0.0950

1 2 3 1 2 3 1 2 3

0.2800 0.3000 0.3200 0.2600 0.2800 0.3000 0.2700 0.2900 0.3100

0.0800 0.0900 0.1000 0.0800 0.0900 0.1000 0.0800 0.0900 0.1000

1 2 3 1 2 3 1 2 3

0.2800 0.3000 0.3200 0.2500 0.2700 0.2900 0.2400 0.2600 0.2800

0.0800 0.0900 0.1000 0.0800 0.0900 0.1000 0.0800 0.0900 0.1000

top phase w1 293.15 K 0.3654 0.4045 0.4469 0.3449 0.3741 0.4053 0.3240 0.3538 0.3909 298.15 K 0.3473 0.3887 0.4346 0.3395 0.3733 0.3994 0.3177 0.3601 0.3807 303.15 K 0.3552 0.3952 0.4398 0.3062 0.3489 0.3764 0.3050 0.3494 0.3869 308.15 K 0.3422 0.3939 0.4347 0.3157 0.3640 0.4291 0.3113 0.3676 0.4176

bottom phase

w2

w1

w2

0.0330 0.0260 0.0207 0.0329 0.0281 0.0241 0.0439 0.0356 0.0278

0.1434 0.1302 0.1234 0.1654 0.1592 0.1543 0.1920 0.1818 0.1791

0.2213 0.2337 0.2402 0.2014 0.2350 0.2605 0.1853 0.2297 0.2436

0.0379 0.0291 0.0220 0.0339 0.0282 0.0248 0.0282 0.0207 0.0149

0.1579 0.1495 0.1451 0.1622 0.1588 0.1511 0.0725 0.0463 0.0470

0.2066 0.2269 0.2378 0.2184 0.2372 0.2760 0.2411 0.2731 0.2722

0.0332 0.0264 0.0204 0.0443 0.0344 0.0294 0.0415 0.0310 0.0245

0.1342 0.1350 0.1359 0.1342 0.1353 0.1446 0.1145 0.1118 0.1076

0.2207 0.2329 0.2408 0.2139 0.2359 0.2761 0.2510 0.2669 0.2988

0.0347 0.0261 0.0201 0.0344 0.0258 0.0182 0.0267 0.0196 0.0156

0.0995 0.0855 0.0734 0.0655 0.0508 0.0549 0.0189 0.0233 0.0174

0.2115 0.2392 0.2658 0.2463 0.2732 0.2952 0.2664 0.2868 0.3103

a

The standard uncertainties u are u(w) = 0.0001, u(T) = 0.05 K, and u(p) = 5 kPa. B



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different ATPS were prepared by weighting defined amounts of the components with composition greater than that of the binodal curve, to a final weight of 50 g, in graduated centrifuge tubes (50 mL). All system components were thoroughly agitated with a vortex mixer (Model AP-56, Phoenix Luferco, Brazil) and centrifuged at 3000 × g for 15 min at the respective temperature (Model Sp-701, Splabor, Brazil). The systems were left in a thermostatic water bath for 24 h for phase separation until reaching equilibrium. Volumes of the top and bottom phases were measured and phases were separated and characterized in terms of PEG 400, sodium sulfate, and water concentrations. All systems were prepared in duplicate. Tie-lines lengths (TLL) were determined according to eq 2. TLL = [(w1t − w1b)2 + (w2t − w2b)2 ]0.5

[w1]t = exp(a + b[w2]t 0.5 + c[w2]t + d[w2]t 2 )

(3)

[w1]b = exp(a + b[w2]b 0.5 + c[w2]b + d[w2]b 2 )

(4)

[w1]t − [w1] m = b [w1] − [w1]b mt

(5)

[w1] − [w1]t m = b [w1]b − [w1] mt

(6)

where subscripts “t”, “b”, and “m” represent the top phase, the bottom phase, and the mixture composition, and mt and mb are the weight of the top phase and bottom phase. The compositions measured for the tie lines were fitted to Othmer and Tobias22 correlation (eq 7) in order to verify the reliability.

(2)

where w1 and w2 are the mass fractions of PEG 400 and sodium sulfate in the top “t” and bottom “b” phases, respectively. 2.2.2. Quantification of System Components. After separation of phases from the prepared systems, with their correct pH values, the volume and mass of the upper and lower phases were measured. Using mass and volume, the composition of the phases was estimated by system of four eqs (eqs 3−6) and four unknown values [w1]t, [w1]b, [w2] t, [w2]b were determined.

⎛ 1 − W2 ⎞ ⎛ 1 − W1 ⎞ ln⎜ ⎟ = F + G ln⎜ ⎟ ⎝ W2 ⎠ ⎝ W1 ⎠

(7)

where w1 is mass fraction of PEG in the PEG rich-phase, w2 is mass fraction of Na2SO4 in the Na2SO4 rich-phase, and F and G are adjustable parameters.

Table 3. Values of Parameters (a, b, c, and d) of Equation 1 for ATPS PEG 400 + Sodium Sulfate + H2O at pH = 3.0, 4.0, and 5.0, T = 293.15, 298.15, 303.15, and 308.15 K, and Pressure p = 0.1 MPaa T/K

a

b

293.15 298.15 303.15 308.15

0.599 0.1659 −0.0332 0.1883

−13.5492 −8.2546 −5.4854 −8.4031

293.15 298.15 303.15 308.15

0.5279 −0.0879 −0.0332 0.358

−11.9740 −5.8078 −5.4854 −11.2774

293.15 298.15 303.15 308.15

0.1516 0.2192 −0.0145 0.7885

−8.3506 −11.0199 −6.6852 −18.1253

c pH 3.0 27.7112 10.4861 −0.574 9.2296 pH 4.0 18.0777 3.5287 −0.5741 17.9455 pH 5.0 11.0659 22.8031 4.5003 39.7724

d

R2

sdb

−46.7902 −9.9832 14.9585 −13.0375

0.9978 0.9930 0.9954 0.9984

0.0282 0.0257 0.0204 0.0267

−14.6565 3.2796 14.9586 −31.4398

0.9946 0.9916 0.9925 0.9893

0.0278 0.0246 0.0211 0.0267

−7.5055 −50.4037 1.0642 −78.5807

0.9996 0.9923 0.9985 0.9993

0.0200 0.0345 0.0313 0.0402

a Standard uncertainties u are u(w) = 0.0001, u(T) = 0.05 K, and u(p) = 5 kPa. bsd = (∑i n= 1(w1calc − w1exp)2/n)0.5, where w1 represent the mass calc fraction of PEG 400 and n and the number of binodal data, respectively. wexp 1 is the experimental mass fraction of PEG 400, w1 is the corresponding data calculated using eqs 3 and 4.

Figure 1. Phase diagram in unit of mass fraction for PEG 400 (w1) + Na2SO4 (w2) at pH 3.0 (A), pH 4.0 (B), and pH 5.0 (C) and different temperatures: 293.15 K (●), 298.15 K (▽), 303.15 K (■), and 308.15 K(◇). C



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2.2.4. Thermodynamic Modeling. The UNIFAC model was used to describe the systems thermodynamically,24 which represents the activity coefficient, considering that the excess of Gibbs free energy, GE, is formed by a combinatorial term, GEcomb, which considers the size and the shape effect of the molecules, and a residual term, GEres, which takes into account molecular interactions.25

2.2.3. Effective Excluded Volume Determination. The effective excluded volume was calculated using mass fractions and experimental concentrations obtained in the preparation of the binodal curves. Data were adjusted in Origin 6 software applying the Levenberg-Marquadt numerical method, and the effective excluded volume was calculated by eq 8. ⎛ w ⎞ ⎛ w ⎞ * 2 ⎟ + ⎜V 213 * 1⎟ = 0 ln⎜V 213 M2 ⎠ ⎝ M1 ⎠ ⎝

⎛ GE ⎞ ⎛ G E ⎞ GE = ⎜ comb ⎟ + ⎜ res ⎟ RT ⎝ RT ⎠ ⎝ RT ⎠

(8)

where V213 * indicate the salt excluded volume and the salt effective volumetric fraction in the polymer phase, M and w represent the molecular mass and the mass fraction, and the indices “1” and “2” refer to the amount of PEG and salt in the phases, respectively. In order to verify the salting-out ability of the salts, the saltingout coefficient (k) was obtained by eq 9.1,23 ⎛ wt ⎞ ln⎜⎜ 1b ⎟⎟ = β + k(w2b − w2t) ⎝ w1 ⎠

E Gcomb = RT

∑ xi ln i

Φ*i z + xi 2

(10)

∑ qixi ln i

θi Φ*i

E Gres = −∑ qixi ln RT i

(∑ θj′τji)

(11)

(12)

in which the volume and area fractions are given by (9)

Φ*i =

where w is the mass fraction for the two components that form the systems, subscripts “1” and “2” refer to PEG 400 and sodium sulfate, respectively, and the superscripts “t” and “b” characterize upper and lower phases. β is characterized as the constant related to the activity coefficient.

rx i i ∑j rjxj

θi =

qixi ∑j qjxj

θi′ =

qi′xi ∑j qj′xj

(13)

The parameters r and q are parameters of the molecular structure of pure component, representing volume and surface area. For components i, the activity coefficient is given by

Figure 2. Phase diagram in unit of mass fraction for PEG 400 (w1) + Na2SO4 (w2) at temperature 293.15 K (A), 298.15 K (B), 303.15 K (C), and 308.15 K (D) and different pH values: 3.0 (●), 4.0 (▽), and 5.0 (■). D



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Figure 3. Linear dependency of the Othmer−Tobias equation at temperatures 293.15 K (A), 298.15 K (B), 303.15 K (C), and 308.15 K (D) and different pH values: 3.0 (▼), 4.0 (○), and 5.0 (●).

ln γi = ln

Φ*i Φ* θ z + qi ln i + li − i * xi xi 2 Φi

(∑ θj′τji) + qi′ − qi′ ∑ ∑

× ln

j

k

Table 4. Calculated Values of the Exclusion Volume of the Systems Formed by PEG 400 + Sodium Sulfate + Water at pH 3.0, 4.0, and 5.0 and Temperatures 293.15, 298.15, 303.15, and 308.15 Ka

∑ xjlj − q′ j

θj′ θk′τkj

(14)

where lj =

2 (rj − qj) − (rj − 1) z

(15)

The interaction energy is calculated using the interaction parameters obtained by the UNIFAC model, which considers the energy contribution that each chemical group exerts on the medium, the temperature, and the ideal gas constant. The interaction energy values can be obtained by equations: ⎛ Δuij ⎞ ⎛ aij ⎞ τij = exp⎜ − ⎟ = exp⎜ − ⎟ ⎝ T⎠ ⎝ RT ⎠

(16)

⎛ Δuji ⎞ ⎛ aji ⎞ τji = exp⎜ − ⎟ = exp⎜ − ⎟ ⎝ T⎠ ⎝ RT ⎠

(17)

pH

T (K)

V213* (g mol−1)

R2

sdb

3 4 5 3 4 5 3 4 5 3 4 5

293.15 293.15 293.15 298.15 298.15 298.15 303.15 303.15 303.15 308.15 308.15 308.15

415.26 445.53 498.29 411.34 459.53 488.29 760.64 769.43 788.55 781.62 769.43 788.55

0.9179 0.9307 0.9422 0.9498 0.9824 0.9943 0.9456 0.9179 0.9307 0.9498 0.9024 0.9299

0.0112 0.0063 0.0082 0.0052 0.0084 0.0085 0.0082 0.0058 0.0061 0.0051 0.0056 0.0051

a Standard uncertainties u are u(w) = 0.0001, u(T) = 0.05 K, and u(p) 2 0.5 = 5 kPa. bsd = (∑i n= 1(w − wexp 1 ) /n) , where w1 represent the mass fraction of PEG 400 and n and the number of binodal data, calc respectively. wexp 1 is the experimental mass fraction of PEG 400, w1 is the corresponding data calculated using eq 8.

where, Δuij and Δuji are the characteristic interaction energy parameters i−j, and are slightly temperature-dependent.

Liquid−liquid equilibrium data were used to estimate the interaction parameters of the group contribution through the E



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UNIFAC model, implemented in Fortran code TML-LLE 2.0,26 based on the method proposed by Nelder and Mead.27 The method consists in the minimization of a concentration-based objective function S, defined by D

S=

3.1. Effect of Temperature on the Equilibrium Phase Diagram. The graphical analysis of the systems formed by PEG 400 + sodium sulfate + water (Figure 1) showed no significant variation of the biphasic region with increasing temperature. In relation to the PEG 400 + sodium sulfate + water systems (Figure 1a,c), other authors32 studying the effect of temperature at 293.15, 313.15, and 333.15 K in systems composed by PEG (400, 4000, 6000) + sodium sulfate + water, observed that an increase in temperature caused the displacement of binodal

M N−1

∑ ∑ ∑ {(xijkI,exp − xijkI,calc)2 + (xijkII,exp − xijkII,calc)2 } k

j

i

(18)

where D is the number of data sets, N and M are the numbers of components and tie lines in each data set, respectively. Superscripts I and II refer to the two liquid phases in equilibrium, while the superscripts “exp” and “calc”, refer to the experimental and calculated values of the liquid phase concentration. Using the interaction parameters estimated by the above method, the comparison of the experimental and predicted data of each component in each of the two phases was done through the root-mean-square deviation (δx), given by

Table 6. Estimated Interaction Parameters and Interaction Energies Related to the System at pH 3.0, 4.0, and 5.0 and Temperatures 293.15, 298.15, 303.15, and 308.15 K

δx = 100 M

×

N−1

∑ j ∑i

I,exp II,exp I,calc 2 II,calc 2 {(xijk − xijk ) + (xijk − xijk )}

2MN (19)

where D is the number of data sets, N and M are the numbers of components and tie lines in each data set, respectively. Superscripts I and II refer to the two liquid phases in equilibrium, while the superscripts “exp” and “calc”, refer to the experimental and calculated values of the liquid phase concentration. The values of the volume (Rk) and the surface area (Qk) of each group contribution used as input parameters in Fortran code TML-LLE for molecular simulation using the UNIFAC model were obtained in the literature and are presented in Table 1.

3. RESULTS AND DISCUSSION Three global points were used for each system composed by PEG 400 + sodium sulfate + water, which are presented in Table 2. The values obtained for the fit parameters “a”, “b”, “c”, “d”, and the coefficients of determination (R2) for the systems studied are shown in Table 3. On the basis of the R2 values, it can be concluded that the equation has been satisfactorily adjusted to the experimental data. Table 5. Values of the Parameters Adjusted for Equation 8 for the PEG 400 + Sodium Sulfate + Water Systems at pH 3.0, 4.0, and 5.0 and Temperatures T = 293.15, 298.15, 303.15, and 308.15 K pH

T (K)

K

B

R2

sda

3 4 5 3 4 5 3 4 5 3 4 5

293.15 293.15 293.15 298.15 298.15 298.15 303.15 303.15 303.15 308.15 308.15 308.15

11.195 33.889 33.115 64.948 34.207 14.679 6.071 13.049 15.501 8.03 12.43 24.50

−1.678 0.1607 0.0481 0.3138 0.1201 −15.322 −0.1696 0.5739 0.0412 −0.1859 −1.063 −3.54

0.9952 0.9973 0.9698 0.9927 0.9768 0.998 0.992 0.9157 0.9785 0.999 0.969 0.9989

0.0158 0.0081 0.0290 0.0179 0.0232 0.0168 0.0117 0.0518 0.0291 0.0048 0.1052 0.1776

b,calc 2 sd = (∑i =n 1(wt,calc − wt,exp − wb,exp )2/n)0.5, where n 1 1 ) + (w1 1 represent the number of tie-lines.

a

F

T/K

pH

group i

group j

aij

aji

293.15 293.15 293.15 293.15 298.15 298.15 298.15 298.15 303.15 303.15 303.15 303.15 308.15 308.15 308.15 308.15 293.15 293.15 293.15 293.15 298.15 298.15 298.15 298.15 303.15 303.15 303.15 303.15 308.15 308.15 308.15 308.15 293.15 293.15 293.15 293.15 298.15 298.15 298.15 298.15 303.15 303.15 303.15 303.15 308.15 308.15 308.15 308.15

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL ETHYL

OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O OH SO4 Na H2O

585.88 980.67 1254.3 412.07 545.68 963.1 1101.3 319.95 444.88 937.21 1053.10 309.24 291.65 698.18 832.80 373.38 542.67 1142 1346.8 426.49 500.27 1229.9 1232.9 345.37 491.95 1070.80 1048.70 315.73 599.49 806.70 1179.00 344.43 504.45 1142.7 1387.3 291.66 591.06 989.9 992.67 498.23 591.06 989.90 992.67 498.23 375.03 1031.90 1061.90 519.34

−2203.7 −1970 1015.1 −1235.1 −2953.1 −2735.6 590.2 −1821.7 −2994.20 −2794.30 601.50 −1905.00 −2857.80 −2598.90 656.05 −1910.90 −2211.4 −1974.2 667.19 −1380.1 −2272.1 −2053.9 644.54 −1266.7 −2909.00 −2664.70 656.68 −1952.90 −2800.40 −2528.60 619.80 −1911.00 −2720.8 −2494.6 622.56 −1759.9 −2672.2 −2417.1 512.88 −1782.8 −2672.20 −2417.10 512.88 −1782.80 −2927.50 −2676.00 457.58 −2062.00



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addition of sulfuric acid to a solution of sodium sulfate increases the amount of H+ ions in the medium forming a new type of monovalent anion, HSO4−. Thus, the lower the pH the lower the concentration of divalent ions, which increases the HSO4−/SO42− ratio. The importance of the presence of a higher concentration of divalent salts ions, in comparison to monovalent ones, is associated with a higher hydration capacity of this anion resulting in less water available for PEG hydration. 3.3. Othmer and Tobias Correlation. The linear dependence between the graphs in [(1 − wa/wa)] versus ln [(1 − wb/wb)] (eq 7) is shown in Figure 3 at the respective temperatures and pH values, discussed in this paper. It is noteworthy that the values of R2 are greater than 0.9222, in all systems; therefore, it can be stated that the experimental data were thermodynamically consistent. In addition, these values express the reliability of the methodology used to obtain the experimental data. 3.4. Effect of Excluded Volume. In order to better study the binding capacity of sodium sulfate with water, the excluded volume, which can be defined as a kind of void spaces available for molecular interactions, was calculated for systems formed at 293.15 K, 298.15 K, 303.15 K, and 308.15 K and at pH values 3.0, 4.0, and 5.0 for the respective tie lines. The values of the excluded volume are represented in the Table 4. The equilibrium conditions and the distribution of the components in the systems are usually influenced by the present of

curves, expanding the biphasic region, which implies in a smaller concentration of the salt and the polymer required to form an ATPS. A general analysis of the driving forces governing system behavior is necessary in order to allow a more comprehensive understanding of the influence of temperature on the equilibrium of the phases. As temperature increases, molecular agitation occurs, breaking and forming bonds during the phase separation process, thus increasing the enthalpy variation. However, the configurational entropy of the polymer also increases due to the process of chain folding, expelling the water molecules that previously formed solvation layers around the PEG molecules enabling the molecules to reach innumerable possibilities of rearranging.33,34 Thus, water transfer occurs from the upper to the lower phase. In other words, the phase separation is facilitated as temperature rises, because a greater difference in the physical-chemical properties is observed between the phases of the system. 3.2. Effect of pH Value on the Equilibrium Phase Diagram. Phase diagrams of PEG 400 + sodium sulfate at pH 3.0, 4.0, and 5.0 at temperatures of 293.15 K, 298.15 K, 303.15 and 308.15 K, respectively, are shown in Figure 2. The biphasic region expands with an increase in pH. Such behavior can be explained on the basis of the fact that sulfate anions are ionic chemical species of oxidation state 2−, originated from sulfuric acid of molecular formula SO42−.35 The

Figure 4. Tie-line in unit of mass fraction for PEG 400 (w1) + Na2SO4 (w2) ATPS at pH 3.0, and temperatures: (A) 293.15, (B) 298.15, (C) 303.15 and (D) 308.15 K. Tie-line 1, (−●−) experimental data, (--○--) data predicted by the UNIFAC model; tie-line 2, (−■−) experimental data, (--□--) data predicted by the UNIFAC model; and tie-line 3, (−▲−) experimental data, (--Δ--) data predicted by the UNIFAC model. G



Article

where the higher k value gives a higher volume of salt exclusion. For the same temperature, the values of k were higher at the higher pH values, which explain the higher effect of excluded volume of the PEG 400 + Na2SO4 systems. In addition, the increased EEV values reflects in the phase diagram by a leftward shift in the position of the binodal curve, which corresponds to a decrease in the single-phase mixture area. Thus, a decrease in the salt concentration required to form a two-phase system indicates the higher salting-out strength.41,42 3.5. Modified Universal Functional Group Activity Coefficient (UNIFAC) Model. Table 6 shows the parameters, aij and aji, of interaction between molecular groups obtained through molecular simulation. The values of the interaction energy were calculated using eq 15 with the values of the parameters aij shown in Table 6. According to the interaction energy values shown in Table 6, it was observed that as the pH value increases, a reduction of the interaction energy of the ETHYL contribution group with the salt contribution groups occurs. This is due to the higher concentration of ions with higher valence in the system. Molecules that have higher valence need more hydration, and possibly the salt molecules will migrate to the phase with the higher amount of available water, which is not the polymer phase, and consequently the energy of interaction between PEG (w1) and SALT (w2)

electrolytes. It is known that salt type and concentration are effective factors in phase separation. As shown in Table 4, the excluded volume of systems in higher pH values (higher concentration of divalent ions) are significantly higher than those with higher concentration of monovalent ions. This happens because the higher the concentration of divalent ions, the greater the hydration capacity of the salt molecules and thus they will have more free configurational sites for interaction with the water molecules, thus, the higher the excluded volume. The same behavior was observed in equilibrium data for systems formed by PEG (2000, 4000) + sodium chloride + water.36 In other studies when they studied the effect of the volume of exclusion in systems composed of ionic liquid and salts, it was realized that the higher the concentration of divalent ions in molecules of salts, the greater the hydration capacity of the molecules, thus, the higher the volume excluded37,38 In order to verify the effect of the salts in the structure of water molecules, the salting-out coefficient of salts (k) was determined. The adjusted parameters β and k are presented in Table 5. On the basis of the values of R2, it can be concluded that eq 9 presents satisfactory accuracy for tie-lines data correlation for the investigated systems. Some researchers have demonstrated the relationship of the effect of excluded volume with the salting-out coefficient (k),39,40

Figure 5. Tie-line in unit of mass fraction for PEG 400 (w1) + Na2SO4 (w2) ATPS at pH 4.0, and temperatures: (A) 293.15, (B) 298.15, (C) 303.15, and (D) 308.15 K. Tie-line 1, (−●−) experimental data, (--○--) data predicted by the UNIFAC model; tie-line 2, (−■−) experimental data, (--□--) data predicted by the UNIFAC model; and tie-line 3, (−▲−) experimental data, (--Δ--) data predicted by the UNIFAC model. H



Article

Figure 6. Tie-line in unit of mass fraction for PEG 400 (w1) + Na2SO4 (w2) ATPS at pH 5.0, and temperatures (A) 293.15, (B) 298.15, (C) 303.15, and (D) 308.15 K. Tie-line 1, (−●−) experimental data, (--○--) data predicted by the UNIFAC model; tie-line 2, (−■−) experimental data, (--□--) data predicted by the UNIFAC model; and tie-line 3, (−▲−) experimental data, (--Δ--) data predicted by the UNIFAC model.

will decrease. This fact is related to the excluded volume, because the higher the hydration capacity of the salt molecules, the greater the number of free configurational sites for interaction with water molecules and the larger the value of excluded volume. Phase compositions were estimated from the interaction parameters values (Table 6) and compared with experimental compositions, as shown in Figures 4−6. Table 7 presents the mean deviations of each system calculated by eq 19. As can be seen in Table 7 and Figures 4−6, the UNIFAC model had an excellent representation for the analyzed systems, presenting a very low overall mean deviation. For the systems containing PEG 400 (Figures 4−6), the calculated data practically overlap with the experimental ones, better representing this system. This can be attributed to the fact that PEG 400 contains a smaller ethylene chain in relation to PEGs of larger molar mass, and the program need to fit less calculated data to the experimental ones.

Table 7. Deviations in the Compositions of the Systems by Thermodynamic Modeling (UNIFAC) systems

δx (%)

PEG 400 + sodium sulfate + water, pH 3, T = 293.15 K PEG 400 + sodium sulfate + water, pH 3, T = 298.15 K PEG 400 + sodium sulfate + water, pH 3, T = 303.15 K PEG 400 + sodium sulfate + water, pH 3, T = 308.15 K PEG 400 + sodium sulfate + water, pH 4, T = 293.15 K PEG 400 + sodium sulfate + water, pH 4, T = 298.15 K PEG 400 + sodium sulfate + water, pH 4, T = 303.15 K PEG 400 + sodium sulfate + water, pH 4, T = 308.15 K PEG 400 + sodium sulfate + water, pH 5, T = 293.15 K PEG 400 + sodium sulfate + water, pH 5, T = 298.15 K PEG 400 + sodium sulfate + water, pH 5, T = 303.15 K PEG 400 + sodium sulfate + water, pH 5, T = 308.15 K overall mean deviation

3.18 3.12 3.11 3.24 2.97 2.54 2.33 2.98 2.88 2.16 2.16 2.25 2.74

verified that higher values of temperature and pH favor the two-phase formation, increasing the biphasic region. The experimental binodal data were satisfactorily correlated with the Merchuk equation. The data were correlated with the UNIFAC models to determine the activity coefficient. The findings of the thermodynamic model is adequate and acceptable, and the UNIFAC model

4. CONCLUSIONS New experimental results were presented for the liquid−liquid equilibrium data of the PEG 400, sodium sulfate (Na2SO4), and water systems at different temperatures (293.15 K, 298.15 K, 303.15 K, 308.15 K) and pH values (3.0, 4.0, and 5.0). It was I



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polyethylene Glycol and various salts at 25 °C. J. Chem. Eng. Data 1992, 57, 268−274. (13) Salabat, A. The influence of salts on the phase composition in aqueous two-phase systems: experiments and predictions. Fluid Phase Equilib. 2001, 187-188, 489−498. (14) Martins, J. P.; Carvalho, C. D. P.; Silva, L. H. M. D.; Coimbra, J. S. D. R.; Silva, M.D.C.H.D.; Rodrigues, G. D.; Minim, L. A. Liquid−liquid equilibria of an aqueous two-phase system containing poly (ethylene) glycol 1500 and sulfate salts at different temperatures. J. Chem. Eng. Data 2008, 53 (1), 238−241. (15) Martins, J. P.; Coimbra, J. S. D. R.; de Oliveira, F. C.; Sanaiotti, G.; da Silva, C. A.; da Silva, L. H. M.; da Silva, M. D. C. H. Liquid− liquid equilibrium of aqueous two-phase system composed of poly (ethylene glycol) 400 and sulfate salts. J. Chem. Eng. Data 2010, 55 (3), 1247− 1251. (16) de Araujo Sampaio, D.; Mafra, L. I.; Yamamoto, C. I.; Andrade, E. F.; Souza, M. O.; Mafra, M. R.; Castilhos, F. Aqueous two-phase (polyethylene glycol + sodium sulfate) system for caffeine extraction: Equilibrium diagrams and partitioning study. J. Chem. Thermodyn. 2016, 98, 86−94. (17) Iqbal, M.; Tao, Y.; Xie, S.; Zhu, Y.; Chen, D.; Wang, X.; Huang, L.; Peng, D.; Sattar, A.; Shabbir, M. A. B.; Hussain, H. I. Aqueous two-phase system (ATPS): an overview and advances in its applications. Biol. Proced. Online 2016, 18, 1−18. (18) Albertsson, P. A. Partition of Cell and Macromolecules; John Wiley: New York, 1986. (19) Castro, B. D.; Aznar, M. Liquid-liquid equilibrium of water+ PEG 8000+ magnesium sulfate or sodium sulfate aqueous two-phase systems at 35° C: experimental determination and thermodynamic modeling. Brazilian. Braz. J. Chem. Eng. 2005, 22, 463−470. (20) Se, R. A.; Aznar, M. Liquid− liquid equilibrium of the aqueous two-phase system water+ PEG 4000+ potassium phosphate at four temperatures: experimental determination and thermodynamic modeling. J. Chem. Eng. Data 2002, 47, 1401−1405. (21) Merchuk, J. C.; Andrews, B. A.; Asenjo, J. A. Biomedical Sciences and Applications. J. Chromatogr., Biomed. Appl. 1998, 711, 285−293. (22) Othmer, D. F.; Tobias, P. E. Ind. Eng. Chem. 1942, 34, 693−696. (23) Han, J.; Yu, C.; Wang, Y.; Xie, X.; Yan, Y.; Yin, G.; Guan, W. Liquid−liquid equilibria of ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate and sodium citrate/tartrate/acetate aqueous twophase systems at 298.15 K: Experiment and correlation. Fluid Phase Equilib. 2010, 295, 98−103. (24) Guo, W.; Ma, J.; Wang, Y.; Han, J.; Li, Y.; Song, S. Liquid−liquid equilibrium of aqueous two-phase systems composed of hydrophilic alcohols (ethanol/2-propanol/1-propanol) and MgSO4/ZnSO4 at (303.15 and 313.15) K and correlation. Thermochim. Acta 2012, 546, 8−15. (25) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (26) Aznar, M.; Stragevitch, L.; Davila, S. G. Liquid−liquid equilibria: A comparison between original and modified UNIFAC. Lat. Am. Appl. Res. 1998, 28, 135−138. (27) Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Computer Journal 1965, 7, 308−313. (28) Magnussen, T.; Rasmussen, P.; Fredenslund, A. UNIFAC parameter table for prediction of liquid-liquid equilibriumsnd. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 331−339. (29) Ninni, L.; Camargo, M. S.; Meirelles, A. J. A. Water Activity in Poly(ethylene glycol) Aqueous Solutions. Thermochim. Acta 1999, 328, 169−176. (30) Weast, R. C.; Handbook of Chemistry and Physics, 53rd ed.; Chemical Rubber Co. 1972; pp 32−39. (31) Bondi, A. A. Physical Properties of Molecular Crystals, Liquids, and Glasses; John Wiley & Sons, Inc.: New York, 1968. (32) Oliveira, R. M. Phase equilibration of biphasic aqueous systems composed of polyethylene glycol, zinc sulfate, copper sulfate and sodium citrate under different temperatures. Masters Dissertation, Universidade Feceral de Viçosa, Viçosa, Brazil, 2006.

presented excellent results, with low deviations between the experimental and calculated compositions. In this way, interaction parameters can be employed for prediction of phase behavior in the investigated binary system. Besides that, it was observed that the salting-out coefficient follows the same behavior of the excluded volume.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +55 (77) 991397137. Fax: +55 (77)32618681. ORCID

Leandro Soares Santos: 0000-0001-7431-318X Funding

This work was supported by CNPq, FAPESB, and Capes agencies of Brazil. Notes

The authors declare no competing financial interest.

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REFERENCES

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