LiquidâLiquid Equilibrium and Physical Properties of Aqueous

Article pubs.acs.org/jced

Liquid−Liquid Equilibrium and Physical Properties of Aqueous Mixtures of Poly(ethylene glycol) with Zinc Sulfate at Different pH Values: Experiment, Correlation, and Thermodynamic Modeling Behnia Shahrokhi Chemical Engineering Department, Faculty of Engineering, Shomal University, P.O. Box 731, Amol, Mazandaran, Iran

Mohsen Pirdashti* Chemical Engineering Department, Faculty of Engineering, Shomal University, P.O. Box 731, Amol, Mazandaran, Iran

Poorya Mobalegholeslam Department of Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran

Abbas Ali Rostami Chemical Engineering Department, Faculty of Engineering, Shomal University, P.O. Box 731, Amol, Mazandaran, Iran ABSTRACT: The current study measured liquid−liquid equilibrium data for poly(ethylene glycol) (PEG) 1500 + zinc sulfate + water at 298.15 K and in various pH values (2.54, 3.57, and 4.70). Accordingly, the binodal curve was fitted to the Merchuk equation, and the tie-line compositions were fitted to the equations of Othmer−Tobias and Bancroft. Moreover, the study measured the refractive indices and densities of several homogeneous binary and ternary solutions. These solutions are used for calibration within a range of 0−35 mass % of PEG and 0−30 mass % of ZnSO4. Then, the viscosities, densities, electrical conductivities, and refractive indices of binary (PEG 1500 + water; zinc sulfate + water) and ternary (PEG 1500 + zinc sulfate + water) systems were measured and correlated. According to the results obtained from the density data, there was a linear variation of the polymer and the salt mass fractions. The viscosity data of PEG 1500 solutions were correlated as a function of the mass fractions by using a nonlinear equation. Also, the effects of the tie line lengths on the densities and viscosities of the aqueous two-phase systems were represented. Finally, the extended UNIQUAC, UNIFAC, and modified UNIQUAC-FV are used to predict the phase equilibria of mention systems. The fitted binary interaction parameters of the model were reported.

1. INTRODUCTION The liquid−liquid equilibrium (LLE) is one of the well-known processes for separating and purifying the biological products from the complex combinationin which they are produced by using aqueous two-phase systems (ATPSs).1−3 Generally, ATPSs may be created from a mixture of two polymers or one polymer and a salt in an aqueous medium separated into two phases. This phenomenon is useful in biotechnology for product separations and has also advantages over conventional extraction methods using organic solvents.4 Although ATPSs have complimentary properties, they have not been broadly adopted for either industrial or commercial purposes. This is due to some main reasons, including the lack of knowledge about LLE data, the physical and thermodynamics properties, the mechanisms that operate in dividing the equilibrium of macromolecules, the absence of a comprehensive theory anticipating the experimental © 2017 American Chemical Society

trends, and the empirical nature of the method. Therefore, the inadequacy of the knowledge in this field has motivated the researchers to study ATPSs.5,6 The design, optimization, and scale-up of the processes require the data from the phase diagram, composition, and the physical properties of the phase forming in ATPSs. Furthermore, these data are significant part of the model development since they predict the phase partitioning and also are highly required for the separation of biomolecule in an industrial process. LLE data for PEG + zinc sulfate are rare. Zafarani-Moattar and Hamzezadeh7 investigated the binodal curve for PEG 6000 + ZnSO4 at 298.15 K and observed the enlargement of the binodal Received: November 15, 2016 Accepted: February 14, 2017 Published: February 27, 2017 1106

DOI: 10.1021/acs.jced.6b00950 J. Chem. Eng. Data 2017, 62, 1106−1118

Journal of Chemical & Engineering Data

Article

Table 1. Pure Components Used in This Work chemical name

source

initial mole fraction purity

purification method

final mole fraction purity

analysis method

PEG 1500 zinc sulfate sodium hydroxide sulfuric acid

Merck Merck Merck Merck

0.99 0.99 0.99 0.95−0.97

crystallization fractional crystallization none none

0.999 0.9997

calibration curve calibration curve mass balance mass balance

(NaOH; mass purity > 0.99%), and sulfuric acid (95−97% H2SO4, GR > 95.0% for analysis) were obtained from Merck (Darmstadt, Germany) and used without further purification. All chemicals were dried for at least 24 h (413.15 K for salts and 313.15 K for polymers) in order to eliminate adsorbed water. Distilled deionized water was used to prepare the solutions. All of the other materials were of analytical grades. The source, initial mole fraction purity, purification method final mole fraction purity, and analysis method are presented in Table 1. 2.2. Apparatus and Procedure. In order to prepare the binary (PEG 1500 + water; zinc sulfate+ water) and ternary (PEG 1500 + zinc sulfate + water) systems, double-distilled deionized water was added to a 10 g proper mass of an individual solution in 15 mL graduated tubes through an analytical balance (A&D., Japan, model GF300) with an accuracy of ± 10−4 g. The conductivity of pure water was determined 0.0178 (± 0.0001) mS·cm−1. Then the tubes were put in a thermostatic bath (Memert., Germany, model INE400), and the densities, viscosities, electrical conductivities, and refractive indices of the solutions were measured. Accordingly, a constant temperature of 298.15 K with an uncertainty of 0.05 K could be accomplished. First, the densities of the solution including pure liquids and their mixtures were measured based on a double-distilled water and air calibration, using an Anton Paar oscillation U-tube densitometer (model: DMA 500) with a precision of ± 10−4 g.cm−3, Then, the viscosities of the solutions within a range of 0.5− 300 mPa·s at 298.15 K was measured by using an Anton Paar Lovis 2000 M viscometer of various capillary sizes (1.59−1.8 mm) with a precision of up to 0.5%. Besides, the viscosity uncertainties were measured so as to be ±0.001 mPa·s, and the JENWAY instrument (model: 4510) with an accuracy of 0.01 μS−1 was employed to measure the electrical conductivity at 298.15K. Finally, the refractive index was measured by a refractometer of CETI Belgium model with an accuracy of 0.0001nD. A titration method was adopted to ascertain the binodal curves. To make the solution turbid, titration process was conducted by adding the salt stock (titrant) to polymer solutions of particular concentrations was done. The mass could provide a concentration of each component (mixture composition). Then, proper amounts of the salt, water, and polymer were mixed in 15 mL graduated cylinder at 298.15 K to prepare 10 g of the feed samples based on the phase composition data attained from these experiments. Meanwhile, an appropriate ratio of zinc sulfate, sodium hydroxide, and sulfuric acid was mixed, respectively, so that the pH values of the salt solutions could be accurately adjusted via a pH meter with a precision of ±0.01 (827 pH, Lab, Metrohm, Swiss made). The contents of the test tubes were scrupulously put in vortexes for 5 min prior to their placement in the thermostatic bath of 298.15 K for 2 h. Later, the tubes were centrifuged (Hermle Z206A, Germany) at 6000 rpm for 5 min; therefore, the top and bottom samples could be effortlessly separated from the resultant nonturbid phases. Subsequently, the densities, viscosities, electrical conductivity, and refractive indices of both top and bottom phases were measured at 298.15 K, and the average values of the duplicate measurements in all of the

area when the temperature was increased. Moreover, the temperature rise led to the increase in the volume values that were effectively excluded due to the high salting-out capability at high temperatures. Other researchers provided the equilibrium data for PEG 8000 + ZnSO4 at 298.15 K8 and PEG 4000 + ZnSO4 at 278.15, 288.15, 308.15, and 318.15 K.9 Their findings indicated that an increase (from 308.15 to 318.15 K) in the temperature expands the biphasic area. However, the effect of temperature was not very obvious on the equilibrium data of some systems such as poly(ethylene oxide) 1500 + ZnSO4 at 283.15, 298.15, and 313.15 K.10 Despite the focus of the many studies on the effect of temperature, the purpose of the current study is to gain the phase equilibrium data, binodal data, and their correlation for an ATPS, which includes PEG 1500 + zinc sulfate at the pH values of 2.54, 3.57, and 4.70. Accordingly, the study employs appropriate mathematic and thermodynamic models in order to save time and effort for experimental processes in various operational situations. The thermodynamic models describing the ATPSs are based on three groups, namely, lattice theory, local composition, and virial osmotic theory. In the first group, the molecules are supposed to be in a lattice (a room in form of rectangle). Moreover, the interaction of the enthalpy of mixing with neighboring molecules determined the enthalpy of mixing molecules.11 The local composition thermodynamic models describe the ATPSs in the second group. The most well-known members in the thermodynamic models are Wilson,12 nonrandom twoliquid (NRTL),13 and universal quasichemical (UNIQUAC).14 Besides, MNRTL-NRF,15 UNIQUAC-NRF,16 and the modified Wilson17,18 are the newly developed versions of these models that are more accurate and have been popular in the recent years. The third group of thermodynamic models takes a combination of theories into account to calculate the phase behavior of ATPS, using virial osmotic theory by McMillan and Mayer,19 the Hill theory,20 the solution and the VERS model,21 and extension of the Pitzer model.22 In order to model and correlate experimental LLE data, the modified UNIFAC-NRF model23 was applied, and the activity coefficients were utilized. To do this, the appropriate binary interaction parameters are needed since this LLE system is highly nonideal. Therefore at this paper, an attempt was made to measure and correlate the viscosity, density, electrical conductivity, and refractive index of binary (PEG 1500 + water; zinc sulfate + water) and ternary (PEG 1500 + zinc sulfate + water) systems, as well as the top and bottom phases of the two-phase system. The extended UNIQUAC, UNIFAC, and modified UNIQUAC-FV were applied to model the liquid−liquid equilibrium (LLE). Modeling involved the use of activity coefficients, but as this LLE system is strongly nonideal, the use of appropriate binary interaction parameters appeared necessary. These models were applied successfully to correlate the experimental LLE data.

2. EXPERIMENTAL EVALUATION 2.1. Materials. PEG with a mass average of 1500 g·mol−1, zinc sulfate (anhydrous GR > 99% for analysis), sodium hydroxide 1107



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above data were reported. The calibration approach was adopted to measure the polymer and salt concentrations via refractive indices and conductivities of both phases at 298.15 K. To this end, refractive index and conductivity calibration plots were prepared based on the recognized phase compositions, and then, the measured values were interpolated. The correlation of the physical properties in the ternary systems was obtained by a linear empirical expression. The aim of the researchers was to decrease the mathematical complexity without losing accuracy.

Φ′k =

G =G

LR

+G

SR

+G

com

⎛ϕ⎞ Z θ ln γi = ln⎜ i ⎟ + qi ln i + li 2 ϕi ⎝ xi ⎠ m m ⎡ ϕi ⎢ − ∑ xjlj + qi⎢1 − ln(∑ θτj ji) − xi j = 1 j=1 ⎣

li =

(1)

2AVd i b3

xp =

(2)

xs =

(3)

The mean ionic activity coefficient of electrolyte i can be written as: ln γ±LR =

|ZaZc|AI 0.5 1 + bI 0.5

θi =

(4)

where I is ionic strength, Vi is the molar volume of the nonionic component, and Za and Zc are the absolute charge number of anion and cation, respectively. Also, if the distances between the ions are less than 4 Å, A and b are obtained by: ⎛ d 0.5 ⎞ A = 1.32775 × 105⎜ ⎟ ⎝ (DT )1.5 ⎠

(5)

d 0.5 b = 6.359696 × (DT )0.5

(6)

∑ Φ′kDk

(7)

d=

∑ Φ′kdk

(8)

Z (ri − qi) − (ri − 1) 2

(11)

np vsns + n p + n w

(13)

vsns vsns + n p + n w

(14)

xiqi ∑i xiqi

(16)

where r and q are volumetric and surface parameters of van der Waals, respectively. Also, τij is the Boltzmann factor and defined as: ⎛ −aij ⎞ ⎟ τij = exp⎜ ⎝ T ⎠ (17) where T is the temperature and aij = uij − ujj. uij and ujj are interaction energy parameters of similar and nonsimilar components, respectively. It is obvious that τii = τjj = 1. 3.3. The Modified UNIQUAC-FV Model. In the modified UNIQUAC-FV model, the activity coefficient of component i is obtained as:26

D and d are the dielectric constant and the density of the mixture, respectively. The solution is considered as the mixture of a solvent and a pseudosolvent polymer and is calculated by: D=

j=1

where vs is the stoichiometric coefficient of zinc sulfate salt. ni is a number of moles of component i in each aqueous phase. Z shows the coordination number and set equal to 10. Subscripts w, p, and s show the water, polymer, and zinc sulfate, respectively. Volume fraction ϕi and surface fraction θi of each component are calculated by the following equations: xiri ϕi = ∑i xiri (15)

[1 + bI 0.5 − (1 + bI 0.5)−1

− 2 ln(1 + bI 0.5)]

∑

⎤ ⎥ m ∑k = 1 θkτkj ⎥⎦ θτ j ij

Subscripts i and j show the components of the systems. xi is the mole fraction of component i and can be calculated by the following equations in an electrolyte solution: nw xw = vsns + n p + n wGu (12)

3.1. Long-Range Interaction Contribution. As an expansion of the extended Debye−Hückel equation of Fowler and Guggenheim,27 the long-range interactions of nonionic components such as water−polymer are calculated as follows:28 ln γi LR =

m

(10)

In eq 1, GLR is the long-range interaction contribution standing for the electrostatic interactions between the ions. GSR is the short-range interaction contribution that reflects the nonelectrostatic interactions among each portion of the solution. Gcom represents the combinatorial contribution, and it elaborates the configuration entropy in the constituent particles of the system. Afterward, the activity coefficient of component i is provided as the sum of three contributions: ln γi = ln γi LR + ln γiSR + ln γicom

(9)

In this relation, ni is the number of moles. 3.2. The Extended UNIQUAC Model. The extended UNIQUAC equation was used to calculate the short-range interaction contribution of activity coefficient as follows:24

3. THERMODYNAMIC FRAMEWORK In this study, the extended UNIQUAC,24 UNIFAC,25 and modified UNIQUAC-FV26 are used to calculate the phase equilibria of ZnSO4 + PEG 1500 + H2O (pH = 2.54, 3.57, and 4.70) systems. The excess Gibbs energy, GE, is expressed as the sum of three contributions: E

nk Vk ∑i ≠ ion niVi

ln γi MUNIQUAC − FV = ln γiCom + FV + ln γiSR

(18)

In eq 18, the first part stands for the combinatorial and the second one for the residual part. In this research modified the Freed-FV model was applied to calculate combinatorial activity coefficient. The activity coefficients of the components were calculated according to the following equation:

where Φ′k is volume fraction of nonionic component and is calculated by: 1108


Journal of Chemical & Engineering Data ln γiCom + FV = ln

ϕi xi

+

ϕ θ z qi ln i + li − i 2 ϕi xi

Article

⎛ θpHp,ca + θa + θwH w,ca ⎞ 1 ⎟⎟ ln γcSR = ln H w,c + Hc,w − ln⎜⎜ Zcqc θw + θa + θp ⎝ ⎠ ⎛ ⎞ θw(θp(Hca,w − Hp,w) + θw(Hca,w − 1)) ⎟⎟ − ⎜⎜ ⎝ (θw + θcHca,w + θaHca,w + θpHp,w)(θw + θc + θa + θp) ⎠ ⎛ θa(θp(1 − Hp,ca) + θw(1 − H w,ca)) ⎞ ⎟⎟ − ⎜⎜ ⎝ (θwH w,ca + θc + θpHp,ca)(θw + θc + θp) ⎠ ⎛ ⎞ θp(θp(Hca,p − 1) + θw(Hca,p − H w,p)) ⎟⎟ − ⎜⎜ ⎝ (θp + θwH w,p + θaHca,p + θcHca,p)(θw + θc + θa + θp) ⎠ (24)

∑ xjlj j

⎛ ϕ h ⎞2 ⎛ ϕ FV ⎞ ⎛ ϕ h − ϕ FV ⎞ ⎛ ϕ FV ⎞2 i i i i ⎟⎟ + 0.2⎜⎜ ⎟⎟ − 0.2⎜⎜ i ⎟⎟ + ln⎜⎜ h ⎟⎟ + ⎜⎜ x x ϕ ⎝ i i ⎠ ⎝ i ⎠ ⎝ ⎠ ⎝ xi ⎠ (19)

where Z shows the coordination number and set equal to 10, ri and qi are volumetric and surface parameters of van der Waals, respectively, and ϕhi denotes the fraction of hardcore volume associated with component i:

ϕi h =

xivih ∑j xjvjh

where the subscripts c, a, w, and p denote the cation, anion, water, and polymer, respectively. This equation can be expressed in the same forms as activity coefficient of the cation (c) by replacing the subscript of c with that of a and a with c. The mean ionic activity coefficient of an electrolyte (ZnSO4) with cation and anion can be calculated using the following relation:

(20)

where ϕFV i denotes the fraction of free volume associated with component i: ϕi FV =

xi(vi − vih) ∑j xj(vj − vjh)

ln γ±ZnSO =

(21)

vc ln γc + va ln γa

4

where xi is the mole fraction of component i, vi the molar volume of component i, and vhi the molar hardcore volume of component i. The short-range (ln γSR i ) part of the activity coefficient is defined as:

vc + va

(25) 25

3.4. The UNIFAC Model. The UNIFAC model uses the functional groups, which form the structures of compounds, and each group makes a unique contribution to the compound property. The interaction parameters, gained from a small number of groups using thermodynamically consistent data, can be used for multicomponent systems. The activity coefficient in the UNIFAC model is provided in terms of two parts, namely, the combinatorial part (γCi ) for entropy effects that is obtained from the differences in molecular size, and a residual part (γRi ) for energetic interactions between the functional groups in the mixture.

⎛ θpHp,w + (θc + θa)Hca,w + θw ⎞ 1 ⎟⎟ ln γwSR = 1 − ln⎜⎜ qw θw + θc + θa + θp ⎝ ⎠ ⎛ ⎞ θw((θa + θc)(1 − Hca,w) + θp(1 − Hp,w)) ⎟⎟ − ⎜⎜ ⎝ (θw + θcHca,w + θaHca,w + θpHp,w)(θw + θc + θa + θp) ⎠ ⎛ θc(θa(H w,ca − 1) + θp(H w,ca − Hp,ca)) ⎞ ⎟⎟ − ⎜⎜ ⎝ (θwH w,ca + θa + θpHp,ca)(θw + θa + θp) ⎠ ⎛ θa(θc(H w,ca − 1) + θp(H w,ca − Hp,ca)) ⎞ ⎟⎟ − ⎜⎜ ⎝ (θwH w,ca + θc + θpHp,ca)(θw + θc + θp) ⎠ ⎛ θp(θp(H w,p − 1) + (θa + θc)(H w,p − Hca,p)) ⎞ ⎟⎟ − ⎜⎜ ⎝ (θp + (θc + θa)Hca,p + θwH w,p)(θw + θc + θa + θp) ⎠ (22)

ln γi UNIFAC = ln γiC + ln γi R

(26)

The combinatorial part in the UNIFAC model is given by: ln γiC = 1 − ϕi + ln ϕi −

1 ln γpSR = ln H w,p + Hp,w qp

ϕi =

ri ∑j rjxj

ri =

∑ vk(i)R k

and

Fi =

⎛ ϕ ⎞⎞ ϕ Z ⎛ qi⎜⎜1 − i + ln⎜ i ⎟⎟⎟ Fi 2 ⎝ ⎝ Fi ⎠⎠ qi ∑j rx i j

qi =

and

(27)

(28)

∑ vk(i)Q k

(29)

where xi is the mole fraction of component i in the liquid phase and v(i) k is the number of groups of type k in component i. Rk represents the van der Waals group volume, and Qk represents the surface area. For group k and Z, the coordination number, defined in lattice theory, may have a value in range of 4 and 12 based on the type of packing. Moreover, the value of Z for typical liquids is 10. The residual part of the activity coefficient is gained from the following equation:

⎛ θwH w,p + θcHca,p + θaHca,p + θp ⎞ ⎟⎟ − ln⎜⎜ θw + θc + θa + θp ⎝ ⎠ ⎞ ⎛ θw((θa + θc)(Hp,w − Hca,w) + θw(Hp,w − 1)) ⎟⎟ − ⎜⎜ ⎝ (θw + θcHca,w + θaHca,w + θpHp,w)(θw + θc + θa + θp) ⎠ ⎛ θc(θa(Hp,ca − 1) + θw(Hp,ca − H w,ca)) ⎞ ⎟⎟ − ⎜⎜ ⎝ (θa + θpHp,ca + θwH w,ca)(θw + θa + θp) ⎠ ⎛ θa(θc(Hp,ca − 1) + θw(Hp,ca − H w,ca)) ⎞ ⎟⎟ − ⎜⎜ ⎝ (θc + θpHp,ca + θwH w,ca)(θw + θc + θp) ⎠ ⎛ ⎞ θp((θa + θc)(1 − Hca,p) + θw(1 − H w,p)) ⎟⎟ − ⎜⎜ ⎝ (θwH w,p + θcHca,p + θaHca,p + θp)(θw + θc + θa + θp) ⎠ (23)

ln γi R =

∑ vk(i)(ln ΓK − ln Γ(ki))

(30)

ln Γk = Q K [1 − ln(∑ θmψmk)] − m

∑ m

θmψkm ∑n θmψnm

(31)

where the group area fraction, θm and group mole fraction, Xm, are given by the equations: 1109



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Table 2. Density, ρ, Viscosity, η, Refractive Index, nD, and Electrical Conductivity, k, for the PEG 1500 (n) + Water Systema at 298.15 K and 0.1 MPa at Various Mass Fractions of PEG (1500), wP

a

wp

ρ (±0.0001) (g·cm−3)

η (±0.001) (mPa·s)

nD (±0.0001)

k (±0.0001) (mS·cm−1)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0.9970 1.0049 1.0129 1.0207 1.0292 1.0367 1.0457 1.0546

0.894 1.196 1.683 2.361 3.291 4.482 6.142 8.434

1.3327 1.3391 1.3458 1.3520 1.3590 1.3655 1.3726 1.3797

0.0178 0.0150 0.0123 0.0113 0.0101 0.0096 0.0090 0.0086

Standard uncertainties: u(wi) = 0.001; u(P) = 5 kPa; u(T) = 0.05 K.

Table 3. Density, ρ, Viscosity, η, Refractive Index, nD, and Electrical Conductivity, k, for the Zinc Sulfate + Water Systema at 298.15 K and 0.1 MPa at Various Mass Fractions of Salt, ws

a

ws

ρ (±0.0001) (g·cm−3)

η (±0.001) (mPa·s)

nD (±0.0001)

k (±0.0001) (mS·cm−1)

0.02 0.04 0.06 0.08 0.10 0.15 0.20 0.25 0.30

1.0081 1.0201 1.0318 1.0473 1.0606 1.0839 1.1084 1.1340 1.1599

0.902 0.943 0.981 1.006 1.086 1.172 1.295 1.515 1.678

1.3345 1.3364 1.3385 1.3403 1.3421 1.3470 1.3530 1.3585 1.3644

9.47 ± 0.1 15.49 ± 0.1 22.00 ± 0.1 27.20 ± 0.1 32.00 ± 1 43.60 ± 1 53.10 ± 1 61.30 ± 1 67.60 ± 1

Standard uncertainties: u(wi) = 0.001; u(P) = 5 kPa; u(T) = 0.05 K; u(pH) = 0.01.

Figure 1. Density, ρ, and viscosity, η, of the binary PEG 1500 + H2O system at 298.15 K as a function of the PEG 1500 mass fraction (wp).

θm =

Xm =

Q mX m ∑n Q nX n

4. RESULTS AND DISCUSSION 4.1. Physical Properties and Calibration Curves. The viscosities, densities, electrical conductivities, and refractive indices of the aqueous solutions of PEG 1500 + water and zinc sulfate + water at 298.15 K are given in Tables 2 and 3. Figures 1−4 indicate the linear and nonlinear improvement of the density and viscosity data are due to the increased PEG (1500) and mass fraction, respectively. The same results were also observed in the zinc sulfate + water system. According to the observations, the increased refractive indices of the salt and polymer solutions resulted from the increasing concentration. In addition, both of the modifications

(32)

∑j V m(i)Xj ∑j ∑n V n(i)Xj

(33)

where Vi is number of group of type of k in component i. The parameter ψmn contains the group interaction parameter, anm, according to the equation: ⎛ −a ⎞ ψnm = exp⎜ nm ⎟ ⎝ T ⎠

(34) 1110



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Figure 2. Refractive index, nD, and electrical conductivity, k, of the binary PEG 1500 + H2O system at 298.15 K and 0.1 MPa as a function of the PEG 1500 mass fraction (wp).

Figure 3. Density, ρ, and viscosity, η, of the binary zinc sulfate + H2O system at 298.15 K and 0.1 MPa as a function of the salt mass fraction (ws).

Figure 4. Refractive index, nD, and electrical conductivity (k) of the binary zinc sulfate + H2O system at 298.15 K and 0.1 MPa as a function of the salt mass fraction (ws).

increasingthe concentration. Compared to a 67.60 mS·cm−1 change in sulfate salt concentration, a negligible amount of 0.0090 mS·cm−1 resulted from the polymer solution conductivity when a change of 0−30% (w/w) occurred to the PEG (1500) concentration.

were clearly found to be linear. A great variation was seen between the electrical conductivities of the polymer and salt solutions. Although the electrical conductivity of the polymer solution is very lower than the electrical conductivity of salt, a decreased electrical conductivity was observed by 1111



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Table 4. Density, ρ, Viscosity, η, Refractive Index, nD, and Electrical Conductivity, k, for the Aqueous Single-Phase Systema (PEG 1500 (p) + Zinc Sulfate (s) + Water System) at 298.15 K and 0.1 MPa

a

ws

wp

ρ (±0.0001) (g·cm−3)

η (mPa·s)

nD (±0.0001)

k (mS·cm−1)

0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.5 2.0 2.5

0.5 1.0 1.5 2.0 0.5 1.0 1.5 1.0 0.5 0.5

1.0385 1.0425 1.0488 1.0584 1.0628 1.0703 1.0793 1.1020 1.1264 1.1594

1.351 ± 0.001 1.892 ± 0.001 2.716 ± 0.01 3.817 ± 0.01 1.520 ± 0.01 2.076 ± 0.01 3.247 ± 0.1 2.052 ± 0.01 2.012 ± 0.001 2.508 ± 0.01

1.3447 1.3509 1.3575 1.3645 1.3495 1.3560 1.3625 1.3615 1.3598 1.3657

17.4 ± 0.1 12.4 ± 0.1 9.5 ± 0.01 7.4 ± 0.01 26.3 ± 0.01 21.2 ± 0.01 16.2 ± 0.01 27.8 ± 0.01 42.7 ± 0.01 49.3 ± 0.01


Table 5. Some Proposed Semiempirical Relations to Predict the Physical Properties of Binary Systems

Table 8. Binodal Curve Data of the PEG 1500 + Zinc Sulfate + Water Systema at 298.15 K and 0.1 MPa at Different pH Values

coefficients of equation

pH = 2.54

binary system

a

equation

PEG 1500 + water

zinc sulfate + water

ρ = a + bwp a η= b − cwp (1 + e

)

nD = a + bwp k = a + bwp + cwp2 ρ = a + bws η = (a + bws)−1/c η = aebws nD = a + bws k = a(1 − e−bws) k = a(b − e−cws)

b

c

R2

0.9962

0.0164

0.9993

126.3545

4.9589

6.6288

0.9999

0.1332 0.0175

0.0134 −0.0547

0.0859

0.9996 0.9984

0.9981 1.0838 0.8526 0.0106 91.5087 94.4280

0.0572 −1.2110 0.2239 1.3318 0.4410 1.0119

0.6258

4.0341

0.9916 0.9958 0.9942 0.9981 0.9983 0.9992

Table 6. Some Proposed Semiempirical Relations to Predict the Physical Properties of Ternary Systemsa coefficients of equation

a

equation

a

b

C

R2

ρ = a + bws + cwp ρ = a + bews + cewp η = a + wbs + wcp η = a + bews + cewp nD = a + bws + cwp k = awbs wcp k = a + bws + cwp k = a + b ln ws + c ln wp

0.9974 1.0272 0.1946 0.6651 1.3325 19.9452 13.2365 23.1665

0.0610 0.0115 0.5039 0.0739 0.01049 0.6800 16.0058 17.0964

0.0142 0.0022 1.5478 0.4345 0.01302 −0.4214 −7.8019 −9.2219

0.9973 0.9288 0.9639 0.9466 0.9986 0.9944 0.9933 0.9654

n

R2

k1

r

R2

2.54 3.57 4.70

7224.05 1589.61 2271.98

−1.0166 −0.6981 −0.7019

0.9946 0.9938 0.9930

1.0004 0.8871 0.0107

2.1400 1.3025 9.7600

0.9936 0.9954 0.9911

100wp

100ws

100wp

100ws

46.50 34.84 32.91 27.08 24.92 19.82 17.64 17.41 13.80 12.27 11.82 8.57 8.41 7.77 5.86 5.70 3.94

3.80 5.80 7.51 9.76 11.03 14.30 15.85 16.44 19.07 20.82 21.01 24.16 24.31 25.46 27.41 27.52 30.28

40.54 35.78 33.79 31.03 30.25 20.86 20.48 17.62 17.30 16.92 16.45 16.11 12.45 6.50 6.58 6.53 6.49

2.71 3.19 4.36 4.54 5.64 9.86 11.22 13.17 13.32 14.33 13.93 14.88 18.11 22.55 24.82 24.84 24.86

45.00 35.50 32.08 29.16 22.93 22.70 20.16 20.01 19.00 14.27 13.97 13.50 4.12 4.23 4.25 4.17 3.99

1.40 3.35 4.29 4.88 8.59 7.83 9.50 10.90 10.17 16.85 16.49 17.64 27.97 28.02 28.22 28.32 28.65

Table 9. Values of Parameters of Equation 37 for PEG 1500 + Zinc Sulfate + Water at Different pH Values

Table 7. Values of the Parameters of Equations 1 and 2 for PEG 1500 + Zinc Sulfate + Water at Different pH Values k

pH = 4.70

100ws

a Standard uncertainties: u(wi) = 0.002; u(P) = 5 kPa; u(T) = 0.05 K; u(pH) = 0.01.

Bold equations indicate the fitting parameters for calibration curves.

pH

pH = 3.57

100wp

pH

a

b

c

R2

2.54

0.9899

−4.0240

32.4714

0.9961

3.57

0.6907

−3.4840

43.3562

0.9911

4.70

0.6965

−3.7678

32.1930

0.9947

Table 10. Effective Excluded Volume Parameter Correlation

The viscosities, densities, electrical conductivities, and refractive indices of the PEG 1500 + zinc sulfate + water systems are given in Table 4. Some experimental expressions are put forward in Tables 5 and 6 for the correlations of the physical properties of the binary and ternary systems (Figure 1−4). The purpose was to decrease the complexity of the model and increase its accuracy.

a

pH

EEV

LSEa

2.54 3.57 4.70

2120.11 2320.76 2350.06

0.0083 0.0250 0.0337

1

n

Least square error (min n ∑i = 1 (error)2 ).

Table 6 contains the fitting parameters for calibration curves (bold equations). The provided empirical equation was in agreement with the experimental binodal data with high accuracy. 1112



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Table 11. Fitting Parameter for Equation 1 and Statistics of Regression pH

K

B

R2

2.54 3.57 4.70

0.5556 0.7066 3.2554

−0.6220 −0.2911 8.0846

0.9877 0.9227 0.9530

4.2. Phase Diagram. The reliability of the measured tie-line compositions was ascertained by Othmer−Tobias (eq 36) and Bancroft (eq 37) correlation equations. ⎛ 1 − wpt ⎞ ⎛ 1 − wsb ⎞n ⎜⎜ ⎟⎟ = k ⎜ ⎟ ⎝ wsb ⎠ ⎝ wpt ⎠

(35)

⎛w ⎞ ⎛ wwb ⎞ ⎜ ⎟ = k1⎜⎜ wt ⎟⎟ ⎝ wsb ⎠ ⎝ wpt ⎠

(36)

r

Figure 6. Experimental binodal curves of PEG 1500 + zinc sulfate + water (light blue ☆) compared to PEG 4000 + zinc sulfate + water7 (blue ■), PEG 6000 + zinc sulfate + water9 (green ○) at 298.15 K.

where wpt is the mass fraction of PEG 1500 in the top phase, wsb is the mass fraction of ZnSO4 in the bottom phase, wwb and wwt are the mass fractions of water in the bottom and top phases, respectively, and k, n, k1, and r are the parameters. The values of the parameters are given in Table 7. Furthermore, the binodal data obtained from the turbidimetric titrations of PEG (1500) + zinc sulfate + water mixtures at 298.15 K at different pH values (2.54, 3.57, and 4.70) are presented in Table 8. For the binodal data correlation, the Merchuk equation29 can be suitably used to reproduce the binodal curves of the investigated systems. 0.5

wp = ae(bws

− cws3)

where MPEG and Msalt stand for the polymer and salt molecular weight, respectively. Moreover, V* is the effective excluded volume (EEV) of the salt into the PEG aqueous solution. As indicated in Table 10, a nonlinear regression was used to obtain the EEV values. Also the EEV increases with increasing pH. Although the performance of this model is worse than Merchuk,31 it has a stronger theoretical background (statistical geometry), which enables the evaluation of the salting-out effect in the different used salts. However, it should be noted that both models have been successfully adopted for the correlation of binodal data from polymer/polymer and polymer/salt ATPSs.7,31,32 To correlate the liquid−liquid equilibrium data, a simple twoparameter equation based on the binodal theory (Guan and co-workers30) was employed:

(37)

where a, b, and c represent the fitting parameters (Table 9) and wp and ws demonstrate the polymer and salt mass fractions, respectively. The binodal data of the above expression were correlated by least-squares regression. Besides, the obtained experimental data can also adapt to the equation provided by Guan and co-workers:30 ln(V* × WPEG/MPEG) + V* × Wsalt /Msalt = 0

top bot bot top ln(Wsalt /Wsalt ) = b + k(WPEG − WPEG )

(39)

In this equation b and k are fitting parameters that can be regarded as “effective” virial (or activity) coefficients and the salting-out coefficient of the salt. Wi is the mass fraction of PEG

(38)

Figure 5. Experimental and correlated binodal curves of PEG 1500 + zinc sulfate + water ATPSs at different pH values. 1113


TLL

1.25 1.22 1.16 1.08 0.95 0.94 0.94 0.92 0.93 0.79 0.71 0.58 47.90 49.39 50.38 56.60 45.18 49.76 52.18 57.15 47.73 54.51 59.52 72.78 2.488 2.886 3.747 4.809 3.198 3.647 3.968 4.514 2.953 3.462 3.734 4.195 1.2050 1.2123 1.2287 1.2546 1.2177 1.2369 1.2467 1.2674 1.2309 1.2680 1.3047 1.3835

η (±0.01) (mPa·s)

and salt, and the superscripts in the equation indicate the top and bottom (bot) phases. The linear regression was used to find the values for b and k (Table 11). The experimental and correlated binodal curves of the study systems are shown in Figure 5. Figure 5 exhibits pH influence on the binodal curve of the aqueous two-phase PEG 1500 + zinc sulfate system. The figure indicates the descending binodal displacement by the moderate pH augmentation, which means that a lower concentrations of the phase polymers are required for the ATPS formation. Moreover, a comparable conduct has been illustrated in refs 33−35. The pH includes some function such as the solute charge, charged species ratio, and binodal location. The rise in pH level may lead to the salting-out phenomenon probably as a result of the salt’s promotion in water structure. Consequently, this phenomenon weakens the polymer hydrogen-bond interactions. The polymer solubility and reduced hydration might be due to the stronger affinity of salt ions toward water rather than the polymer. Finally, this process may lead to the exclusion of polymer from the rest of the solution.34 Also Figure 6 shows this binodal compared to the literature.7,9 With a lower molecular weight polymer, the two-phase region becomes smaller. Table 12 illustrates the tie-line data, equilibrium phase compositions, and physical properties of the top and bottom phases. Four feed solutions containing PEG 1500 + zinc sulfate + water were applied to perform the experiments at three pH values. The same table presents the experimental results for the feed solutions and the resulting coexistence of the phases. Furthermore, based on Table 12, the PEG concentration enhancement in the top phase is observed by an increment in salt composition at a constant pH. The salt hydration impact can explain this enhancement. The tie-line length (TLL) provides an empirical measurement of the compositions of the two phases, which can be calculated by the following equation:

3.82 3.92 3.82 3.37 6.30 5.62 5.46 5.75 3.89 3.72 3.37 3.01 10.68 12.92 16.54 18.15 9.45 10.15 11.62 16.20 9.18 9.38 9.90 10.80

34.05 35.26 38.04 42.53 35.51 38.94 40.63 44.04 38.41 44.70 50.98 64.36

ρ (±0.0001) (g·cm−3) 100wp η (±0.01) (mPa·s)

100ws

bottom phase

Article


4.70

3.57

(Cp top − Cp bottom)2 + (Cs bottom − Cs top)2

(40)

The slope of the tie-line (STL) is given by the ratio of the difference between the polymer (Cp) and salt (Cs) concentrations in the top and bottom phases as presented in eq 41: STL =

Cp top − Cp bottom Cs bottom − Cs top

(41)

The effects of pH on the equilibrium phase compositions, the slope, and length of the tie lines have been indicated for the PEG 1500 + zinc sulfate+ H2O system in Figure 7. TLL and STL would be increased in this system if the pH level is augmented, which may be because of the reduction in the solution hydrodynamic volume. Furthermore, a comparable conduct has been shown in refs 34 and 36. Waziri et al. (2003) and Shahbazinasab and Rahimpour (2012)34,37 reported the decreased intrinsic viscosity of the polymer solution caused by the pH reduction. Also, it should be noted that a decline in the results pH modifies the polymer chains, making their structure more compact as the intrinsic viscosity of a polymer solution is proportional to its hydrodynamic volume. In addition, based on the reports, the concentrations of the PEG and salt-rich phases increased and decreased, respectively, following the enhancement in the pH of an aqueous two-phase PEG−salt system. The study considered the effects of TLL on the densities, dynamic viscosities, and kinematic viscosities of the aqueous

a

1.0877 1.0883 1.0910 1.0934 1.0744 1.0770 1.0794 1.0809 1.0653 1.0697 1.0731 1.0753 4.05 3.91 4.01 3.90 2.81 2.66 2.64 2.02 3.37 2.00 2.49 1.41 41.17 42.09 43.36 45.23 37.48 39.68 41.24 44.40 36.31 37.61 37.89 39.55 23.00 25.00 27.00 30.00 23.00 25.00 27.00 30.00 23.00 25.00 27.00 30.00 2.54

18.00 18.00 18.00 18.00 18.00 18.00 18.00 18.00 18.00 18.00 18.00 18.00

100wp pH

100ws

100wp

100ws

top phase

−3

ρ (±0.0001) (g·cm )

TLL =

total system (% mass)

Table 12. Phase Composition, Tie-Line Data, and Physical Properties of the PEG 1500 + Zinc Sulfate + Water Aqueous Two-Phase Systema at 298.15 K and 0.1 MPa

−STL


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Figure 7. pH effects on the equilibrium phase compositions and slope and length of tie-lines for the PEG 1500 + zinc sulfate + H2O system.

Figure 8. Relationship between density difference (Δρ) and tie-line length (TLL) for the PEG 1500 + zinc sulfate + water system at different pH values.

Table 13. Values of the Parameters of the Modified UNIQUAC-FV and Extended UNIQUAC for the PEG 1500 (p) + Zinc Sulfate (ca) + water (w) System at pH = 2.54, 3.57, and 4.70 M UNIQUAC-FV pH 2.54 3.57 4.70

uwp

a

−209.36

upwa

AAD%c

−62.96

uwcab

0.089

ucawb

1525.33

155.24

AAD% −4

2.92 × 10

upca

ucap

SD%d

771.89

−554.86

2.11 × 10−2 5.00 × 10−2 6.99 × 10−2

E UNIQUAC 2.54 3.57 4.70 a

awpa

a

apw

175.12

−80.06

AAD%

awcab

acawb

AAD%

apca

acap

SD%

0.30

1757.1

−2455.5

1.22 × 10−3

12162.86

−130.09

18.51 × 10−2 22.03 × 10−2 21.78 × 10−2

Binary interaction parameters calculated from VLE (PEG + water) experimental data.38 bBinary interaction parameters calculated from VLE (salt +

water) experimental data.39 cAAD% =

100 NP

N

∑n =P 1

cal exp a wn − a wn exp a wn

, where N is the ( OF 6N )

, where NP is the number of experimental data points. dSD% = 100

number of tie lines.

UNIFAC,25 and modified UNIQUAC-FV26 models to connect the experimental data:

two-phase systems. Moreover, the TLL and pH enhancement resulted in the increment of density (Δρ) and reduction in viscosity (Δη) differences between the phases. Besides, a linear relationship was found in the density (Figure 8) and viscosity differences between the phases and TLL, and a comparable conduct has been explained in refs 33, 34, and 36. 4.3. Thermodynamic Modeling. The following objective function was minimized by the extended UNIQUAC,24

OF =

∑ ∑ ∑ (wpcal,l ,j − wpexp,l ,j)2 p

l

j

(42)

In eq 42, wp,l j is the weight fraction of the j species in the phase p for l-th tie-line. Furthermore, the species j can be a polymer, salt, or solvent molecule, and cal represents the measured values, 1115



Article

Table 14. Group Interaction Parameters (anm) of Our UNIFAC Model10 CH2 CH2CH2O OH Zn2+ (SO4)2− H2O

CH2

CH2CH2O

OH

Zn2+

(SO4)2−

H2O

0 2298.0 6159.7 −97.805 1947.8 324.99

1167.5 0 −285.50 7.3845 3.7225 0.12082

−1105.9 91.546 0 433.20 0.82830 16.431

−40.945 −38.395 699.55 0 1230.3 −459.54

156.28 43.125 −1343.5 66.845 0 −753.70

−471.26 −0.91698 325.88 70.687 −960.53 0

Table 15. Deviation (SD%) Values of Liquid−Liquid Equilibrium Calculation for PEG 1500 + Zinc Sulfate + Water Systems with Different pH Values Using UNIFAC, Extended UNIQUAC, and Modified UNIQUAC-FV Models systems

UNIFAC

extended UNIQUAC

modified UNIQUAC-FV

PEG 1500 + zinc sulfate + water system at pH 2.54 PEG 1500 + zinc sulfate + water system at pH 3.57 PEG 1500 + zinc sulfate + water system at pH 4.70

16.31 × 10−2

18.51 × 10−2

2.11 × 10−2

11.81 × 10−2

22.03 × 10−2

4.01 × 10−2

9.84 × 10−2

21.78 × 10−2

6.99 × 10−2

Figure 10. Liquid−liquid equilibrium of the system (PEG 1500 + zinc sulfate + water) at pH = 3.57, experimental results (orange circle), predictions with the modified UNIQUAC-FV model (black line), and extended UNIQUAC model (green line) and UNIFAC model (orange line).

Figure 9. Liquid−liquid equilibrium of the system (PEG 1500 + zinc sulfate + water) at pH = 2.54, experimental results (gray circle), predictions with the modified UNIQUAC-FV model (gray line), and extended UNIQUAC model (green line) and UNIFAC model (red line).

whereas the experimental values are shown with exp superscript. Finally, in order to correlate the liquid−liquid equilibrium records, the equilibrium condition was employed. (xiγi)top = (xiγi)bottom

Figure 11. Liquid−liquid equilibrium of the system (PEG 1500 + zinc sulfate + water) at pH = 4.70, experimental results (yellow circle), predictions with the modified UNIQUAC-FV model (black line) and extended UNIQUAC model (green line) and UNIFAC model (orange line).

(43)

Apparently, the sum of mole fractions of the three components in every phase should be equal to integrity to make the mass balance equation useful for checking the measured values. Mole fraction measured values are acquired from the mentioned equations and a proper activity coefficient model. In the current research whenever was possible, the authors used the available binary experimental data reported in the literature to fit binary parameters of mentioned models. Ninn et al.38 measured the binary interaction parameters of extended UNIQUAC and modified UNIQUAC-FV model for the waterpolymer system by minimizing the difference between the experimental vapor−liquid equilibrium data. Likewise, they measured

the values obtained by this model, and the binary interaction parameters of water + salt binary system have been measured in the same procedure through the related VLE experimental data provided in the ref 39. In this research, the interaction parameters of salt and polymer for the extended UNIQUAC and modified UNIQUAC-FV models were obtained from the experimental data of the LLE. The comparison of the interaction parameters of the VLE data showed a good agreement with the LLE system in all of the mentioned models. The fitting parameters of the extended UNIQUAC, modified UNIQUAC-FV models, 1116



Article

Figure 12. Comparison of calculated weight percentage of water, modified UNIQUAC-FV, extended UNIQUAC and UNIFAC models, with experimental data (PEG 1500 + zinc sulfate + water).

ORCID

together with the respective deviations, are summarized in Table 13. Moreover, interaction parameters of UNIFAC model were calculated on the basis of the interaction parameters of Leandro Rodrigues de Lemoset al. which were published before;10 the obtained interaction parameters are listed in Table 14. Table 15 shows the deviation of experimental data with three different models of modified UNIQUAC-FV, extended UNIQUAC, and UNIFAC models. Figures 9−12 shows the composition of the salt, polymer, and water obtained by the extended UNIQUAC, modified UNIQUAC-FV, and UNIFAC models besides the experimental values. However, the modified UNIQUAC-FV model is superior to the other two models.

Mohsen Pirdashti: 0000-0002-8862-0583 Abbas Ali Rostami: 0000-0002-3180-658X Notes

The authors declare no competing financial interest.

■

(1) Albertsson, P. A. Partitioning of Cell Particles and Macromolecules, 3rd ed.; Wiley-Interscience: New York, 1986. (2) Walter, H.; Brooks, D. E.; Fisher, D. Partitioning in Aqueous TwoPhase Systems; Academic Press: New York, 1985 (3) Zaslavsky, B. Y. Aqueous Two-Phase Partitioning, Physical Chemistry and Bioanalytical Applications; Marcel Dekker: New York, 1995. (4) Hatti-Kaul, R. Methods in Biotechnology: Aqueous Two-Phase Systems: Methods and Protocols; Humana Press Inc.: Totowa, NJ, 2000. (5) Lu, Y.-M.; Yang, Y.-Z.; Zhao, X.-D.; Xia, C.-B. Bovine Serum Albumin Partitioning in Polyethylene glycol (PEG)/Potassium Citrate Aqueous Two-Phase Systems. Food Bioprod. Process. 2010, 88, 40−46. (6) Rocha, M. V.; Nerli, B. B. Molecular Features Determining Different Partitioning Patterns of Papain and Bromelain in Aqueous Two-Phase Systems. J. Bio. Macromol. 2013, 61, 2−204. (7) Zafarani-Moattar, M. M. T.; Hamzehzadeh, S. Liquid-liquid equilibria of aqueous two-phase systems containing polyethylene glycol and sodium succinate or sodium formate. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2005, 29, 1−6. (8) Hey, M. J.; Jackson, D. P.; Yan, H. The Salting out Effect and Phase Separation in Aqueous Solutions of Electrolytes and Poly (ethylene glycol). Polymer 2005, 46, 2567−2572. (9) de Oliveira, R. M.; Francisco, K. R. Liquid-Liquid Equilibrium of Aqueous Two-Phase Systems Containing Poly(ethylene) Glycol 4000 and Zinc Sulfate at Different Temperatures. J. Chem. Eng. Data 2008, 53, 919−922. (10) de Lemos, L. R.; da Rocha Patrício, P.; Rodrigues, G. D.; de Carvalho, R. M. M.; da Silva, M. C. H.; da Silva, L. H. M. Liquid−liquid equilibrium of aqueous two-phase systems composed of poly(ethylene oxide) 1500 and different electrolytes ((NH4)2SO4, ZnSO4 and K2HPO4): Experimental and correlation. Fluid Phase Equilib. 2011, 305, 19−24. (11) Baskir, J. A; Hatton, T. A.; Suter, U. W. thermodynamics of the partitioning of biomaterials in two-phase aqueous polymer systems: Comparison of lattice model to experimental data. J. Phys. Chem. 1989, 93, 2111−2122.

5. CONCLUSION New experimental results were presented for the liquid−liquid equilibrium data of the PEG 1500 + zinc sulfate+ water system at various pH values of 2.54, 3.57, and 4.70 at 298.15 K. It was found that the two-phase area was expanded with increasing pH. Also, it was observed that with pH enhancement, the slope of the equilibrium tie-lines decrease and length of tie lines increase for the mentioned biphasic system. The experimental binodal data were satisfactorily correlated with the Merchuk equation. Moreover, the densities, viscosities, electrical conductivities, and refractive indices of the binary and ternary mixtures of the aqueous two-phase PEG 1500 + zinc sulfate+ water systems were measured and correlated at 298.15 K. Furthermore, the study developed some empirical models in order to present the physical properties of binary and ternary systems. The models could precisely reproduce the experimental data. The data were correlated with the extended UNIQUAC, UNIFAC, and modified UNIQUAC-FV models to determine the activity coefficient. The findings of the three thermodynamics models are adequate and acceptable, in that the obtained binary interaction parameters can be employed for prediction of phase behavior in the investigated quaternary system.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 1117



Article

(12) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−142. (13) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21, 116−128. (14) Wilson, G. M. Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Soc. 1964, 86, 127−130. (15) Haghtalab, A.; Joda, M. Modification of NRTL-NRF model for computation of liquid−liquid equilibria in aqueous two-phase polymer− salt systems. Fluid Phase Equilib. 2009, 278, 20−26. (16) Haghtalab, A.; Mokhtarani, B. The new experimental data and a new thermodynamic model based on group contribution for correlation liquid-liquid equilibria in aqueous two-phase systems of PEG and (K2HPO4 or Na2SO4). Fluid Phase Equilib. 2004, 215, 151−161. (17) Xu, X.; Madeira, P. P.; Teixeira, J. A.; Macedo, E. A. A new modified Wilson equation for the calculation of vapor−liquid equilibrium of aqueous polymer solutions. Fluid Phase Equilib. 2003, 213, 53−63. (18) Sadeghi, R. A modified Wilson model for the calculation of vapour + liquid equilibrium of aqueous polymer+ salt solutions. J. Chem. Thermodyn. 2005, 37, 55−60. (19) McMillan, W. G.; Mayer, J E. The Statistical Thermodynamics of Multicomponent Systems. J. Chem. Phys. 1945, 13, 276−305. (20) Hill, T L. Theory of solutions. II. osmotic pressure virial expansion and light scattering in two component solutions. J. Chem. Phys. 1959, 30, 93−97. (21) Haghtalab, A.; Mokhtarani, B.; Maurer, G. Experimental Results and Thermodynamic Modeling of the Partitioning of Lysozyme, Bovine Serum Albumin, and r-Amylase in Aqueous Two-Phase Systems of PEG and (K2HPO4 or Na2SO4). J. Chem. Eng. Data 2003, 48, 1170−1177. (22) Perez, B.; Malpiedi, L. P.; Tubío, G.; Nerli, B.; Filho, P. A. P. Experimental determination and thermodynamic modeling of phase equilibrium and protein partitioning in aqueous two-phase systems containing biodegradable salts. J. Chem. Thermodyn. 2013, 56, 136−143. (23) Pirdashti, M.; Movagharnejad, K.; Mobalegholeslam, P.; Curteanu, S.; Leon, F. Phase Equilibrium and Physical Properties of Aqueous Mixtures of Poly (vinyl pyrrolidone) with Trisodium Citrate, Obtained Experimentally and by Simulation. J. Mol. Liq. 2016, 223, 903−920. (24) Pirdashti, M.; Movagharnejad, K.; Rostami, A. A.; Bakhshi, H.; Mobalegholeslam, P. Liquid-liquid equilibria, electrical conductivity, and refractive indices of Poly (ethylene glycol)+sodium sulfate+ guanidine hydrochloride aqueous two phase systems: correlation and thermodynamic modeling. Fluid Phase Equilib. 2016, 417, 29−40. (25) Paksoy, H.Ö .; Ö rnektekin, S.; Balcl, B.; Demirel, Y. The performance of UNIFAC and related group contribution models Part I. Prediction of infinite dilution activity coefficients. Thermochim. Acta 1996, 287, 235−249. (26) Pirdashti, M.; Movagharnejad, K.; Mobalegholeslam, P.; Pirdashti, H. Liquid-liquid equilibrium of poly (ethylene glycol) 4000+ sodium sulfate+ urea/guanidine hydrochloride aqueous two-phase systems at different pH: Experimental results and thermodynamic modeling. Fluid Phase Equilib. 2016, 427, 460−475. (27) Fowler, R. H.; Guggenheim, E. A.; Statistical Thermodynamics, Chap. 9; Cambridge University: Cambridge, 1941. (28) Wu, Y.-T.; Lin, D.-Q.; Zhu, Z.-Q. Thermodynamics of aqueous two-phase systemsThe effect of polymer molecular weight on liquid− liquid equilibrium phase diagrams by the modified NRTL model. Fluid Phase Equilib. 1998, 147, 25−43. (29) Merchuk, J. C.; Andrews, B. A.; Asenjo, J. A. queous Two-Phase Systems for Protein Separation Studies on Phase Inversion. J. Chromatogr., Biomed. Appl. 1998, 711, 285−293. (30) Guan, Y.; Lilley, T. H.; Treffry, T. E. A new excluded volume theory and its application to the coexistence curves of aqueous polymer two-phase systems. Macromolecules 1993, 26, 3971−3979. (31) Silverio, S. C.; Rodriguez, O.; Teixeira, J. A.; Macedo, E. A. The effect of salts on the liquid-liquid phase equilibria of PEG 600 salt aqueous two-phase systems. J. Chem. Eng. Data 2013, 58, 3528−3535.

(32) Huddleston, J. G.; Willauer, H. D.; Rogers, R. D. Phase diagram data for several PEG salt aqueous biphasic systems at 25 C. J. Chem. Eng. Data 2003, 48, 1230−1236. (33) Porto, T. S.; Pessôa-Filho, P. A.; Neto, B. B.; Filho, J. L. L.; Converti, A.; Porto, A. L. F.; Pessoa, A. P. Removal of Proteases from Clostridium Perfringens Fermented Broth by Aqueous Two-Phase Systems (PEG/citrate). J. Ind. Microbiol. Biotechnol. 2007, 34, 547−552. (34) Shahbazinasab, M-K.; Rahimpour, F. Liquid−Liquid Equilibrium Data for Aqueous Two-Phase Systems Containing PPG725 and Salts at Various pH Values. J. Chem. Eng. Data 2012, 57, 1867−1874. (35) Costa, A. R. D.; Coimbra, J. S. D.R.; Ferreira, L. A.; Marcos, J. C.; Santos, I. J. B.; Marleny, D. A.; Saldaña, M. D. A.; Teixeira, J. A. C. Partitioning of Bovine Lactoferrin in Aqueous Two-Phase System Containing Poly(Ethylene Glycol) and Sodium Citrate. Food Bioprod. Process. 2015, 95, 118−124. (36) Perumalsamy, M.; Murugesan, T. Phase Compositions, Molar Mass, and Temperature Effect on Densities, Viscosities, and LiquidLiquid Equilibrium of Polyethylene Glycol and Salt-Based Aqueous Two-Phase Systems. J. Chem. Eng. Data 2009, 54, 1359−1366. (37) Waziri, S. M.; Abu-Sharkh, B. F.; Ali, S. A. The Effect of pH and Salt Concentration on the Coexistence Curves of Aqueous Two-Phase Systems Containing a pH Responsive Copolymer and Polyethylene Glycol. Fluid Phase Equilib. 2003, 205, 275−290. (38) Ninni, L.; Camargo, M. S.; Meirelles, A. J. A. Water activity in poly(ethylene glycol) aqueous solutions. Thermochim. Acta 1999, 328, 169−176. (39) Guendouzi, M. E.; Mounir, A.; Dinane, A. Water activity, osmotic and activity coefficients of aqueous solutions of Li2SO4, Na2SO4, K2SO4, (NH4)2 SO4, MgSO4, MnSO4, NiSO4, CuSO4, and ZnSO4 at T= 298.15 K. J. Chem. Thermodyn. 2003, 35, 209−220.

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