Thermodynamic Studies of the Aqueous Two-Phase System

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

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Thermodynamic Studies of the Aqueous Two-Phase System Containing Polyethylene Glycol Dimethyl Ether 2000 and Sodium Nitrite at (298.15, 308.15, and 318.15) K Mohammed Taghi Zafarani-Moattar,* Hemayat Shekaari, Parisa Jafari, and Fatemeh Gharekhani Physical Chemistry Department, University of Tabriz, Tabriz 5166616471, Iran

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S Supporting Information *

ABSTRACT: Liquid−liquid equilibrium data including binodals and tie-line compositions have been measured for aqueous ternary biphasic system containing polyethylene glycol dimethyl ether 2000 (PEGDME2000) and sodium nitrite at three temperatures (298.15−318.15) K and atmospheric pressure (≈ 85 kPa). The salting-out of the polymer by the salt was studied at different temperatures. Furthermore, the ΔGc, ΔHc, and ΔSc of the cloud points were computed at working temperatures from which it was found that the entropy is the driving force for phase separation. For representing the experimental binodal data two empirical equations with the temperature dependency were used. The Setschenow equation was utilized for correlating the measured tie-lines. Different versions of nonrandom two-liquid models were also selected in generating the obtained tie-lines. The plait point, and the characteristics of tie-lines (slope and the length) have been determined at working temperatures. The partitioning behavior of the iodine molecule in the above system was also studied.

1. INTRODUCTION Aqueous biphasic systems (ABSs) are environmentally suitable alternatives for liquid/liquid extractions. ABSs can be utilized in separation and preconcentration of proteins, DNA, dye molecules, ions, etc.1,2 In dissolving a solute in the ABS, two events may happen: unequal partition between the two phases or selective retention in one phase. Different factors such as temperature, pH, hydration environment etc are effective in the preference distribution of a solute in an ABS. The liquid−liquid equilibrium (LLE) data including binodal, tie-lines, and partition coefficient data that depend on temperature and medium pH are essential. Recently there were numerous studies about ABSs consisting of polymer + salt or ionic liquid.3,4 In these studies, special attention was paid to ABSs consisting of poly(ethylene glycol) (PEG) which is soluble in water. Poly(ethylene glycol) dimethyl ether (PEGDME) is a water-soluble polymer that can form a twophase system in aqueous solution with a suitable salt, so it can be utilized to separate biomolecules. Recently, the LLE of some aqueous (PEGDME + salt)5−9 and aqueous (PEGDME + ionic liquid) systems have been reported.10 In the literature, LLE data for an aqueous two-phase system consisting of PEGDME2000 and NaNO2 have not been studied. In this work, the binodal curves and the tie-lines for these systems at T = (298.15, 308.15 and 318.15) K have been reported. In addition, plait points of the phase diagram have also been determined at the studied temperatures. © XXXX American Chemical Society

Furthermore, the effect of temperature on the binodal curves and the tie-lines for the studied system was investigated and two temperature dependent empirical statistic equations11,12 were utilized to reproduce the obtained binodal data. To correlate the tie-line data, a temperature-dependent Setschenow type equation13 was utilized. The local composition models of e-NRTL14 and m-NRTL15 were utilized to model the obtained tie-line data. Additionally, the free energy, enthalpy, and entropy of cloud points for this system were determined in all temperatures to study driving force formation of this two- phase system. Finally, the partitioning behavior of the iodine molecule in the (PEGDME2000 + sodium nitrite + water) two-phase system was also studied. Previously the partitioning of iodine has been investigated in aqueous two-phase systems containing PEGDME and sodium nitrate5 and ABS containing poly(propylene glycol) (PPG)-block-PEG-block-PPG (PPG−PEGPPG) copolymer and sodium tartrate.16

2. MATERIALS AND METHODS 2.1. Materials. Polyethylene glycol dimethyl ether with an average molar mass 2000 (CAS NO. 9003-39-8) and sodium nitrite (CAS NO. 7757-83-7) were supplied from Merck. In Received: January 13, 2018 Accepted: June 13, 2018

A

DOI: 10.1021/acs.jced.8b00044 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

with correlation coefficients are also presented in Table 2. More details of the polymer mass fraction determination are given in the Supporting Information. The refractometer (ATAGO DR-A1, Co., Japan) with a precision of ±0.0001 was used. A precision better than 0.002 is obtained for the polymer mass fraction using the above method. The tie-line length, TLL, and slope of tie-line, STL, were determined by the following eqs 2 and 3:

Table 1 the purity of these chemicals were represented. PEGDME2000 and sodium nitrite were used as supplied by the Table 1. A Brief Summary of the Purity of the Used Materials material poly(ethylene glycol) dimethyl ether 2000 sodium nitrite iodine sodium thiosulfate

source

molecular formula

Merck

CH3(CH2CH2O) OCH3 NaNO2 I2 Na2S2O3

Merck Merck Merck

mass fraction purity >0.990

TLL = [(wptop − wpbot)2 + (wstop − wsbot)2 ]0.5

(2)

>0.980 >0.998 >0.990

S = (wptop − wpbot)/(wstop − wsbot)

(3)

here, wp and ws are mass percent of polymer and salt. Superscripts “top” and “bot” denote top and bottom phases, respectively. 2.2.2. Liquid/Liquid Partitioning Studies for Iodine in ABS. The PEGDME2000 and NaNO2 stock solutions were prepared based on weight/weight percent. The compositions of the five tie-lines to each temperature reported in Table 3 were

manufacturer. For preparing the solutions double distilled deionized water was used. 2.2. Apparatus and Procedure. 2.2.1. (Liquid−Liquid) Equilibrium (LLE). Binodal curves were measured by the titration method using an apparatus described previously.5,10 The aqueous polymer solution with known mass fractions (about 0.5 w/w) was titrated with aqueous salt solution in a vessel until turbidity occurred which is indicative of two-phase formation. The vessel was equipped with a thermostat with an uncertainty 0.05 K. In this experiment the titrant mass fractions were determined using an analytical balance (Shimadzu, AW220, GR220 Co., Japan) with a precision of ±10−7 kg. The uncertainty corresponding to the mass fractions of PEGDME and NaNO2 was 0.002. By mixing a known amounts of PEGDME2000, NaNO2, and H2O (about 2 0.10−5cm3) in the biphasic region, feed samples of tie-lines were prepared and then analyzed. The prepared samples were stirred for 1 h and then placed in a water bath the temperature of which was controlled with a precision of ±0.02 K. For separation of samples into clear two phases at least 48 h is required. The concentrations of NaNO2 in the top and bottom phases was analyzed by flame photometry (JENWAY PFP7, England) with an uncertainty of 0.002. The relation between refractive indexes of binary aqueous solutions of polymer or salt and the ternary aqueous solutions containing polymer and salt make it possible to determine mass fractions of polymer in both phases: nD = n w + a pwp + asws (1)

Table 3. Overall Composition of Aqueous Two-Phase System (PEGDME2000 + NaNO2 + H2O) To Distribute Iodine

Table 2. Values of the Parameters of eq 1 for the {PEGDME2000 (p) + NaNO2 (s) + H2O (w)} System constant

value

C range (w/w)

R2,a

PEGDME2000 NaNO3

ap as

0.1312 0.1115

0−0.10 0−0.06

0.9997 0.9984

T/K = 308.15

ws

wp

ws

wp

T/K = 318.15 ws

wp

1 2 3 4 5

0.3283 0.3343 0.3440 0.3484 0.3586

0.1399 0.1395 0.1401 0.1401 0.1400

0.3048 0.3103 0.3149 0.3203 0.3251

0.1789 0.1789 0.1788 0.1786 0.1787

0.2943 0.3046 0.3098 0.3156 0.3235

0.1897 0.1901 0.1901 0.1901 0.1902

prepared. Partitioning of 0.0014 g of iodine in each of prepared solutions was investigated. Each of these solutions was shaken for 30 min after which the phase separation quickly occurred. Vigorous shaking of each solution was followed by centrifugation (D-7200, Hettich, Co., American) at 2000 rpm for 15 min to ensure of phase separation completely. Then these solutions were placed in a water bath appointed by a thermostat (JULABO model MB, Co., Germany) at working temperature to reach equilibrium and achieve complete partitioning of iodine. The samples from the top and bottom phases were then removed for iodine determination by the titration method using sodium thiosulfate as described in our previous work.5 The starch solution was used to establish the end point in the titration. The distribution ratio can be easily determined by the ratio of concentration of the iodine in the top versus bottom phases. 2.3. Correlation. 2.3.1. Binodal Curve Correlation. In our previous works,5,9 for the correlation of binodal data at different temperatures we studied the capability of equation proposed by Merchuk11 and the one suggested previously12 with parameters which depend on temperature and found that eq 4 and eq 5 can be satisfactorily used, respectively: ÄÅ ÉÑ ÉÑ ÅÄÅÄÅÅ ÅÅ ÑÑ ÑÑ ÅÅÅ a1 b1 Å Å Ñ ÑÑ·(w )0.5 Å Å Ñ Å wp = ÅÅa0 + ÑÑ·expÅÅÅÅÅb0 + Ñ s ÅÅÇ (T − T0) ÑÑÖ (T − T0) ÑÑÑÖ ÅÅÇÅÅÇ ÉÑ ÅÄÅ ÑÉÑ ÑÑ c1 Å Ñ 3 Å Ñ ÑÑ·(ws) ÑÑÑÑ − ÅÅÅc0 + Ñ ÑÑ ÅÅÇ (T − T0) ÑÑÖ (4) ÑÖ

Here, nD and nw are the refractive index of ternary solutions and pure water, respectively. The measured refractive index for pure water is 1.3325. The constants ap and as are attributed to polymer and salt, respectively, and are obtained from linear plots of the corresponding refractive index of binary aqueous solutions. Since eq 1 is only accurate at low concentrations, the taken samples from both phases were diluted as reported in Table 2 before measurements. The constants of eq 1 together

material

T/K = 298.15 tie-line

a 2

R represents the respective correlation coefficient value of the linear calibration plot of the refractive index against mass fraction for PEGDME2000 or NaNO2 at the mass fraction range (C range) of each material. B


Journal of Chemical & Engineering Data É ÄÅ É Ä ÄÅ β1 ÑÑÑÑ γ1 ÉÑÑÑ α1 ÑÑÑ ÅÅÅÅ ÅÅ ÅÅ Å Ñ Å Å Ñ wp = ÅÅα0 + ÑÑ + ÅÅβ0 + ÑÑ ln(ws) + ÅÅγ0 + ÑÑÑws ÅÇ ÅÇ T ÑÖ ÅÅÇ T ÑÑÖ T ÑÖ

Article

To determine GE,Comb and GE,LR, the Flory−Huggins expression19 and the Pitzer−Debye−Huckel20 were respectively utilized. To compute GE,SR, the e-NRTL,14 and mNRTL15 models were utilized. More details of these models are reported in the Supporting Information. In these models, the interaction parameters for PEGDME2000−water pairs, (τsw,τws) at T = (298.15, 308.15 and 318.15) K and NaNO2−water pairs (τw,ca,τca,w) at 298.15 K were obtained respectively from the literature.21,22 Because of lack of data for binary NaNO2−water at T = (308.15 and 318.15) K, the corresponding interaction parameters between NaNO2 and water (τw,ca,τca,w) pairs are considered as the adjustable parameters. Similarly for polymer-IL (τs,ca,τca,s) pairs interaction parameters are taken as the adjustable parameters. By correlation of obtained tie-line data, the adjustable parameters are almost obtained. As suggested by Renon and Prausnitz,23 α that is nonrandomness parameter in the NRTL model, has the values between 0.01 and 0.4.23 Different α values were tested to fit the available vapor−liquid data for the binary aqueous polymer and the obtained LLE data. The results show that better quality of fitting was achieved when the nonrandomness factors were set to 0.1, 0.1, and 0.02 for αwca, αsw, and αsca, respectively.

(5)

here, in these equation T and T0 indicate the absolute and the reference temperature (T0 = 273.15 K), respectively. The a0, a1, b0, b1, c0, and c1 are considered as adjustable parameters of eq 4 and the α0, α1, β0, β1, γ0, and γ1 are adjustable parameters of eq 5. The location of plait points at each temperature have been estimated using eq 6 along with the binodal curve: wp = f + gws

(6)

2.3.2. Tie-line Correlation. 2.3.2.1. Setschenow Equation. The first correlation equation which we used for the obtained tie-lines is the Setschenow equation.13 This equation is expressed as ij mptop yz j z lnjjj bot zzz = k p + ks(msbot − mstop) jm z k p {

(7)

here, ks is the salting-out coefficient, kp is a constant, and mp and ms represent the concentration of polymer and salt (in molality), respectively. By assuming very a simple dependency for each parameter to temperature in eq 7, eq 8 is obtained: ÉÑ ij mptop yz ÄÅÅÅ k p Ñ ks bot jj zz ÅÅ top Ñ lnjj bot zz = ÅÅ + (ms − ms )ÑÑÑÑ j m z ÅÅ T ÑÑÖ T (8) k p { Ç

3. RESULTS AND DISCUSSION 3.1. Experimental Results. Tables 4 and 5, respectively, enlist the obtained binodal data and the tie-line compositions at T = (298.15, 308.15 and 318.15) K for the (PEGDME2000 + NaNO2 + water) system. 3.1.1. Effect of Temperature on the Binodal Curve. To see the effect of temperature on the phase-forming ability in the system studied, the binodal data presented in Table 4 have been plotted in Figure 1. Figure 1 reveals that an enhancement in temperature causes an expansion in the two-phase area. This

The following objective function was utilized to fit the obtained tie-lines: Of =

∑ ∑ ∑ ∑ (wTcal,p,l ,j − wTexp,p,l ,j)2 T

p

l

j

(9)

where wT,p,l,j is the weight percent of the component j in the phase p for lth tie-line at temperature T and superscripts “exp” and “cal” are the experimental and calculated values, respectively. 2.3.2.2. Local Composition Models. Previous studies10,17,18 in regard to the modeling of LLE data in aqueous two-phase systems show the good performance of the local composition models. In these models, the excess Gibbs energy, GE, has three contributions; long-range electrostatic, GE,LR, that represents the interaction between ions, the short-range GE,SR term considers interaction between all species, and the combinatorial GE,Comb term considers the differences between the shape and sizes of the components as GE = GE,Comb + GE,LR + GE,SR

Table 4. Experimental Binodal Data for {PEGDME2000 (p) + NaNO2 (s) + H2O (w)} System at T = (298.15, 308.15, and 318.15) K and Atmospheric Pressure (≈85 kPa)a T/K = 298.15

(10)

The following equation is utilized to calculate the activity coefficient of any component: ln γj =

E 1 jijj ∂Gm zyzz j z RT jj ∂nj zz k {T , P , ni ≠ nj

(11)

where j represents any component (electrolyte or nonelectrolyte). According to eqs 10 and 11 the activity coefficient of component i (polymer, ions, and water) has also the same three contributions: ln γ E = ln γ E,Comb + ln γ E,LR + ln γ E,SR

T/K = 308.15

T/K = 318.15

100 wpb

100 ws

100 wp

100 ws

100 wp

100 ws

32.23 31.92 31.26 30.27 29.06 27.39 25.85 24.28 22.68 21.09 19.57 17.99 16.65 15.39 14.15

21.51 21.67 21.93 22.3 22.76 23.32 23.96 24.57 25.23 25.88 26.57 27.19 27.80 28.42 28.95

34.61 34.41 34.09 33.35 32.30 31.01 29.48 27.81 26.28 24.63 23.03 21.39 19.79 18.28 16.81 15.57 14.36

20.24 20.28 20.43 20.71 21.09 21.54 22.10 22.66 23.35 24.01 24.64 25.34 25.96 26.66 27.24 27.99 28.62

35.33 35.00 34.23 33.20 31.86 30.30 28.57 26.93 25.15 23.39 21.72 20.16 18.59 17.18 15.83

19.12 19.27 19.59 19.98 20.54 21.11 21.71 22.39 23.06 23.79 24.55 25.22 25.88 26.52 27.10

The standard uncertainties σ for mass fraction, temperature, and pressure are σ (wi) = 0.002; σ (T) = 0.05 K and σ (p) = 1 kPa, respectively. bwp and ws represent mass fractions of polymer and salt, respectively. a

(12) C



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Table 5. Experimental Tie-Line Data for {PEGDME2000 (p) + NaNO2 (s) + H2O (w)} System at T = (298.15, 308.15 and 318.15) K and Atmospheric Pressure (≈ 85 kPa)a feed sample 100 wp′b

top phase 100 ws′

100 wp

19.89 19.92 19.89 19.90 19.86

27.17 28.05 28.65 29.34 29.89

30.72 34.41 36.01 37.31 38.28

19.88 19.88 19.87 19.88 19.90

26.19 27.08 28.08 29.20 29.96

31.10 33.82 36.21 38.27 40.30

21.08 21.06 21.11 20.98 21.06

25.43 26.33 27.34 28.23 29.32

34.46 37.20 39.31 41.36 43.99

bottom phase 100 ws

100 wp

T/K = 298.15 22.05 5.54 21.24 4.76 21.11 3.72 20.91 3.61 21.02 2.66 T/K = 308.15 21.52 5.32 20.82 3.89 20.05 3.44 19.90 3.28 19.68 2.94 T/K = 318.15 19.36 7.55 18.64 6.67 18.20 5.48 18.04 4.24 18.02 3.24

100 ws

STL

TLL

33.84 35.50 36.88 37.82 39.06

−2.14 −2.08 −2.05 −1.99 −1.98

27.80 32.90 35.94 37.71 39.93

33.09 34.88 36.13 37.45 38.45

−2.23 −2.13 −2.04 −1.99 −1.99

28.26 33.06 36.50 39.14 41.81

31.36 32.50 34.63 36.32 38.09

−2.24 −2.20 −2.06 −2.03 −2.03

29.46 33.52 37.61 41.38 45.42

The standard uncertainties σ for mass fraction, temperature, and pressure are σ(wi) = 0.002; σ (T) = 0.05 K; and σ(p) = 1 kPa, respectively. bwp′ and w′s are total mass fraction of polymer and salt in its feed samples, respectively, and S and TLL are the slope and tie-lines length at different concentrations calculated from eqs 2 and 3, respectively. a

Figure 1. Experimental binodal data for {PEGDME2000 (p) + NaNO2 (s) + H2O (w)} system at different temperatures: (purple ■) T = 298.15; (orange ▲) T = 308.15, and (blue ●) T = 318.15; () lines calculated binodal from eq 4.

Figure 2. Binodal curve, tie-lines, and plait point for the { PEGDME2000 (p) + NaNO2 (s) + H2O (w)} system at T = 298.15 K: (blue ●) experimental binodal data, (blue −−−) calculated binodal from eq 4, (−×−) tie-lines data, (--○--) calculated auxiliary curves, (green ) calculated from eq 6, and (red ■) plait point.

indicates that salting-out of PEGME is increased by increasing temperature. We attempted to draw these binodal data in a triangle diagram instead of ordinary x−y axes; however, these data occupy only very small region and are not visible in a triangle diagram. 3.1.2. Effect of Salt Type on the Binodal Positions. To investigate the anion influence on the formation of ATPSs with PEGDME 2000 , the obtained binodal curves of the {PEGDME2000 + sodium salts + water} system (salts are NaNO2 and other ones studied previously5,12,18,24−28) at 298.15 K are depicted in Figure 2. In Figure 2, for the salts with the same cation but different anions, the order of salting-

out capability of the anions is in the order of PO4−3 > HPO4−2 > CO3−2 > SO4−2 > Hcitrate−2 > OH− > NO2−2 > NO3−2. The salting-out ability of the anions depends on the Gibbs energy of hydration of ions (ΔGhyd). Marcus29 reported the ΔGhyd values of −2765, − 1818, − 1315, − 1080, −937, − 430, −330, and −300 kJ mol−1, respectively, for the above-mentioned anions. So, better salting-out of PEGDME2000 is observed with the anions which have more negative ΔGhyd value. 3.2. Correlation. 3.2.1. Binodal Curve Correlation. Table 6 enlists the results of fitting the binodal data reported in Table 4 to eqs 4 and 5 by the nonlinear least-squares regression D



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Table 6. Values of Parameters of eq 4, (ai, bi , ci), and eq 5, (αi , βi , γi) for {PEGDME2000 (p) + NaNO2 (s) + H2O (w)} System at T = (298.15, 308.15 and 318.15) K eq 4 T/K

a0

104.a1

b0

103.b1

105× c0

104× c1

47.9391

−3.1326

0.0374

1.3022

7.4798

−4.3213

298.15 308.15 318.15 overall

sda 0.25 0.55 0.45 0.42

eq 5 T/K

α0

10−3.α1

10−3.β0

10−3.β1

γ0

γ1

67.5639

5.0387

−5.6240

−2.0693

−1.9786

70.0402

298.15 308.15 318.15 overall

sd 0.24 0.42 0.33 0.33

exp 2 0.5 sd = (∑i N= 1(wcal p − wp ) /N) , where wp and N represented mass fraction of PEGDME2000 and number of binodal data, respectively.

a

method. According to the standard deviations (sd) values we conclude that both eqs 4 and 5 are suitable to correlate the binodal data; however, sd values show that the performance of eq 5 is slightly better compared to the Merchuk equation (eq 4). In Figure 1, the experimental and calculated binodal data obtained by eq 4 is illustrated. 3.2.2. Estimated Plait Point. The estimated values for the plait points are presented in Table 7 along with the values of Table 7. Values of Parameters Obtained from Setschenow Equation (kp, ks) (kg·K·mol−1) for {PEGDME 2000 (p) + NaNO2 (s) + H2O (w)} at T = (298.15, 308.15, and 318.15) K Steschenow type equation as a function of temperature (eq 8) T/K 298.15 308.15 318.15 overall

10−2·kp

10−2·ks

2.5361

4.4338

deva 0.02 0.06 0.09 0.06

Figure 3. Experimental binodal data for {PEGDME2000 (p) + salt (s) + water (w)} at T = 298.15 K. (dark blue −●−) Na3PO4;28 (purple −◇−) Na2HPO4;26 (red −▲−) Na2CO3;25 (light blue − ◆ −) Na 2 SO 4 ; 24 (green − ■ −) NaOH; 18 (orange − △ −) Na2Hcitrate;27 (green −○−) NaNO2 in this work; (blue-gray−□−) NaNO3.5

exp 2 dev = ∑p ∑l ∑j ∑T ((100wcal p,l,j,t − 100wp,l,j,t) /6N where wp,l,j,T is the mass fraction of the component j (i.e., polymer, salt, or water) in the phase p for lth tie-line at temperature T and N represents the number of tie-line data points. a

Table 8. Values of Parameters of eq 6, (f, g) and the Plait Points, for the {PEGDME2000 (p) + NaNO2 (s) + H2O (w)} System at T = (298.15, 308.15, and 318.15) K and Atmospheric Pressure (≈85 kPa)

parameters f and g and correlation coefficient values, R. In Figure 3, the locus of the estimated plait point for the studied system along with the procedure used is depicted as an example at T = 298.15 K. 3.2.3. Correlation of Tie-Line. 3.2.3.1. Setschenow Equation. To correlate the tie-lines for the (PEGDME2000 + NaNO2 + water) system at different temperatures, we selected Setschenow equation as a dependent temperature form. In this regard, the above objective function (eq 9) was utilized with the results reported in Table 8. Very small standard deviations given in Table 8 and also Figure 4 are indicative of excellent performance of the Setschenow equation (eq 9) with only two parameters in modeling tie-lines for the studied system at different temperatures. 3.2.3.2. Local Composition Models. In Table 9, the parameters of the used models together with standard deviations are reported. Deviations reported in Table 9,

T/K

f

g

R2

Plait point (wp%, ws%, ww%)

298.15 308.15 318.15

−17.2034 −25.7017 −6.7731

1.435 1.7123 1.3313

0.9625 0.9978 0.9849

(20.38,26.19,53.43) (26.20,19.20,54.60) (24.4,23.42,52.18)

show that both models have good capability for modeling the LLE data; however, the m-NRTL model show better quality of fitting compared with the e-NRTL model. 3.3. The Free Energies of the Cloud Point (CP). The Gibbs free energy (ΔGc), enthalpy (ΔHc), and entropy (ΔSc) of phase separation are very basic thermodynamic properties. To calculate ΔGc the following relation is used30 ΔGc = RT ln X p E

(13) DOI: 10.1021/acs.jced.8b00044 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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study is endothermic. The entropy changes were determined using the following eq 15: ΔSc =

4. CONCLUSIONS The phase diagrams for the (PEGDME2000 + NaNO2 + H2O) system were experimentally obtained at T = (298.15 to 318.15) K. The binodal data are represented with two nonlinear equations with a temperature dependence of parameter as 1/(T - T0) and found that both of these equations have good capability. The liquid−liquid phase behavior of the studied system is successfully modeled with the Setschenow equation and two versions of the NRTL models. The reported deviations reveal that the reliability of used models have the order: Setschenow

here, Xp is the concentration of PEGDME in mole fraction at the cloud point (CP). The computed ΔGc values at different CP (or T) are given in Table 10. Considering the eq 13, ΔHc values were calculated from the slope of the linear (leastsquares) plot of (ΔGc/T) against (1/T):31 d(ΔGc /T ) d(1/T )

(15)

The calculated ΔSc values presented in Table 10, are all positive. The positive entropy domenstrates that the increase of entropy is the driving force for aqueous two-phase formation process in the studied system. 3.4. Partitioning of Iodine. For the ABS system studied here, to examine the partitioning of the I2 molecule, five different tie-line lengths at T = (298.15, 308.15, and 318.15) K, reported in Table 3, were considered. The analysis of the iodine molecule indicated that in the chosen ABS and in different temperatures almost all the iodine extracted to the top phase and an undetectable amount of iodine was in the bottom phase. Similar results have been obtained using ABS containing (PPG−PEG-PPG) copolymer and sodium tartrate in which 100% of elemental iodine extracted to top phase containing the copolymer.16 However, a comparison of this result with a previous one8 in which the partitioning behavior of iodine has been studied in ABS containing PEGDME2000 and sodium nitrate, indicates that better partitioning of iodine is observed in ABS containing PEGDME2000 and sodium nitrite.

Figure 4. Experimental and correlated tie-line data along with experimental and calculated binodal data for {PEGDME2000 (p) + NaNO2 (s) + water (w)} system at T = 298.15 K: (−○−) experimental tie-lines; (red −×−) calculated tie-lines using temperature dependent Setschenow eq (eq 8); (blue ●) experimental binodal data, and (blue ) calculated binodal from eq 4.

ΔHc =

ΔHc − ΔGc T

(14)

In Table 10, ΔHc values are positive in all cases; and this reveals that the aqueous two-phase formation process under

Table 9. Values of Parameters of E-NRTL and M-NRTL, as a Function Temperature Independent Form, τij, for the {PEGDME2000 (p) + NaNO2 (s) + Water (w)} System at T = (298.15, 308.15, and 318.15) K

a,b

The highlighted partitions were calculated according to the water activity data of aqueous solution PEGDME200021 and NaNO2,22 respectively. ARD% is calculated as

c

Np − 1

ARD% = (1/Np)

∑ i=0

ij a cal − a exp jj w w jj j a wexp k

yz zz × 100 zz z {

where Np is the number of experimental points. F



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Table 10. Free Energy Changes, ΔGc/(kJ mol−1), Entropy Changes, ΔSc/(J mol−1·K−1), and Enthalpy Changes, ΔHc/(kJ mol−1), for Clouding of PEGDME2000 in the Presence of NaNO2 for Salt Mass Fraction, ws, at Temperatures T = (298.15, 308.15 and 318.15) K T/K= 298.15 −3

−4

T/K = 308.15 −4

ws

10 ΔHc

10 ΔGc

ΔSc

10 ΔGc

ΔSc

10 ΔGc

ΔSc

0.22 0.23 0.24 0.25

6.472 6.360 6.359 6.479

−1.287 −1.318 −1.350 −1.382

64.884 65.554 66.612 68.108

−1.348 −1.380 −1.413 −1.446

64.748 65.434 66.492 67.970

−1.417 −1.449 −1.483 −1.519

64.887 65.556 66.615 68.111

(6) Zafarani-Moattar, M. T.; Hosseinpour-Hashemi, V. (Liquid + liquid) equilibrium of the ternary aqueous system containing poly ethylene glycol dimethyl ether 2000 and tri-potassium citrate at different temperatures. J. Chem. Thermodyn. 2012, 48, 75−83. (7) Sadeghi, R.; Kahaki, H. B. Thermodynamics of aqueous solutions of poly ethylene glycol di-methyl ethers in the presence or absence of ammonium phosphate salts. Fluid Phase Equilib. 2011, 306, 219−228. (8) Zafarani-Moattar, M. T.; Nikjoo, D. Phase Diagrams for Liquid− Liquid and Liquid− Solid Equilibrium of the Ternary Poly (ethylene glycol) Dimethyl Ether 2000+ Sodium Carbonate+ Water System. J. Chem. Eng. Data 2009, 54, 2918−2922. (9) Zafarani-Moattar, M. T.; Shekaari, H.; Jafari, P. Aqueous twophase system based on cholinium chloride and polyethylene glycol dimethyl ether 250 and it use for acetaminophen separation. J. Chem. Thermodyn. 2017, 107, 85−94. (10) Zafarani-Moattar, M. T.; Shekaari, H.; Jafari, P. Design of Novel Biocompatible and Green Aqueous two-Phase Systems containing Cholinium L-alaninate ionic liquid and polyethylene glycol di-methyl ether 250 or polypropylene glycol 400 for separation of bovine serum albumin (BSA). J. Mol. Liq. 2018, 254, 322−332. (11) Merchuk, J. C.; Andrews, B. A.; Asenjo, J. A. Aqueous twophase systems for protein separation: Studies on phase inversion. J. Chromatogr., Biomed. Appl. 1998, 711, 285−293. (12) Zafarani-Moattar, M. T.; Nemati-Kande, E. Study of liquid− liquid and liquid−solid equilibria of the ternary aqueous system containing poly ethylene glycol dimethyl ether 2000 and tri-potassium phosphate at different temperatures: Experiment and correlation. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2010, 34, 478−486. (13) 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. (14) Zafarani-Moattar, M. T.; Sadeghi, R. Measurement and correlation of liquid−liquid equilibria of the aqueous two-phase system polyvinylpyrrolidone−sodium di-hydrogen phosphate. Fluid Phase Equilib. 2002, 203, 177−191. (15) Sadeghi, R. A modified segment-based nonrandom two-liquid model for the calculation of vapor−liquid equilibrium of aqueous polymer−salt solutions. Chem. Eng. Sci. 2006, 61, 7786−7794. (16) Samaddar, P.; Chakraborty, A.; Sen, K. Block copolymer as a novel functional phase in an aqueous biphasic system for species selective iodine extraction. RSC Adv. 2005, 5, 44204−44210. (17) Zafarani-Moattar, M. T.; Nemati-Kande, E. Study of liquid− liquid and liquid−solid equilibria of the ternary aqueous system containing poly ethylene glycol dimethyl ether 2000 and tri-potassium phosphate at different temperatures: experiment and correlation. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2010, 34, 478−486. (18) Zafarani-Moattar, M. T.; Shekaari, H.; Hosseinzadeh, M.; Jafari, P. Aqueous two-phase system of polyethylene glycol dimethyl ether 2000 and sodium hydroxide at different temperatures: Experiment and correlation. Fluid Phase Equilib. 2014, 376, 225. (19) Flory, P. J. Thermodynamics of high polymer solutions. J. Chem. Phys. 1941, 9, 660. (20) Pitzer, K. S. Electrolytes. From dilute solutions to fused salts. J. Am. Chem. Soc. 1980, 102, 2902−2906.

> m-NRTL > e-NRTL. In addition, the plait point, STL and TLL are evaluated at working temperatures. Also the driving force for phase splitting behavior in this system is studied by calculating the changes in thermodynamic functions (free energy, enthalpy, and entropy) of the cloud point which indicated that the increase of entropy is responsible for phase separation. Partitioning studies of the iodine molecule in ABS containing PEGDME2000 and sodium nitrite indicated that iodine molecules are entirely extracted to the top phase.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00044. Details for determination of polymer and salt concentrations; details of correlation to local composition models (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Fax: +98 413 3340191. E-mail: [email protected]. ORCID

Mohammed Taghi Zafarani-Moattar: 0000-0002-2174-1639 Hemayat Shekaari: 0000-0002-5134-6330 Funding

We are grateful to University of Tabriz research council for the financial support of this research. Notes

The authors declare no competing financial interest.

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T/K = 318.15 −4

REFERENCES

(1) Albertsson, P. A. Partitioning of Cell Particles and Macromolecules, 3rd ed.; Wiley: New York, 1986. (2) Frerix, A.; Schönewald, M.; Geilenkirchen, P.; Müller, M.; Kula, M.-R.; Hubbuch, J. Exploitation of the Coil−Globule Plasmid DNA Transition Induced by Small Changes in Temperature, pH Salt, and Poly (ethylene glycol) Compositions for Directed Partitioning in Aqueous Two-Phase Systems. Langmuir 2006, 22, 4282−4290. (3) Diniz, R. S.; Souza, E. C., Jr.; Coimbra, J. S.R.; de Oliveira, E. B.; da Costa, A. R. Liquid−liquid Equilibria of Aqueous Two-Phase Systems Containing Sodium Hydroxide + Poly(ethylene glycol) of (1450, 4000, or 10 000) g·mol−1 at (288.2, 298.2, and 308.2) K. J. Chem. Eng. Data 2012, 57, 280−283. (4) Zafarani-Moattar, M. T.; Hamzehzadeh, S.; Nasiri, S. A new aqueous biphasic system containing polypropylene glycol and a watermiscible ionic liquid. Biotechnol. Prog. 2012, 28, 146−156. (5) Zafarani-Moattar, M. T.; Shekaari, H.; Gharekhani, F. Study of phase equilibria of aqueous two phase system containing poly ethylene glycol di-methyl ether 2000 and sodium nitrate at different temperatures and application of this system in separation of iodine. J. Chem. Thermodyn. 2017, 113, 20−28. G



Article

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Thermodynamic Studies of the Aqueous Two-Phase System

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