The effect of temperature and molar mass on the (liquid + liquid) equilibria of (poly ethylene glycol dimethyl ether + di-sodium hydrogen citrate + water) systems: Experimental and correlation

Accepted Manuscript The effect of temperature and molar mass on the liquid–liquid equilibria of (poly ethylene glycol dimethyl ether + di-sodium hydrogen citrate + water) systems: Experimental and correlation Mohammed Taghi Zafarani-Moattar, Hemayat Shekaari, Parisa Jafari, Mahsa Hosseinzadeh PII: DOI: Reference:

S0021-9614(15)00308-0 http://dx.doi.org/10.1016/j.jct.2015.08.026 YJCHT 4372

To appear in:

J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

20 June 2015 9 August 2015 20 August 2015

Please cite this article as: M.T. Zafarani-Moattar, H. Shekaari, P. Jafari, M. Hosseinzadeh, The effect of temperature and molar mass on the liquid–liquid equilibria of (poly ethylene glycol dimethyl ether + di-sodium hydrogen citrate + water) systems: Experimental and correlation, J. Chem. Thermodynamics (2015), doi: http://dx.doi.org/10.1016/ j.jct.2015.08.026

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The effect of temperature and molar mass on the liquid–liquid equilibria of (poly ethylene glycol dimethyl ether + di-sodium hydrogen citrate + water) systems: Experimental and correlation Mohammed Taghi Zafarani-Moattar*, Hemayat Shekaari, Parisa Jafari, Mahsa Hosseinzadeh Physical Chemistry Department, University of Tabriz, Tabriz 51664, Iran

Abstract The liquid-liquid equilibrium for the {polyethylene glycol dimethyl ether 2000 (PEGDME2000) + di-sodium hydrogen citrate + H2O} system was studied at T = (298.15, 308.15 and 318.15) K and atmospheric pressure (≈ 85 kPa). The free energies, enthalpies and entropies of cloud points were calculated in order to investigate the driving force formation of this two-phase system. To investigate the effect of molar mass of the polymer on the binodals and tie-lines, similar measurements were also made at T = 298.15 K on this two-phase system consisting of the PEGDME with molar masses of 500 and 250 g.mol-1. The effective excluded volume model was used for representation of the phase-forming ability in PEGDME systems. An empirical and the Merchuk equations with the temperature dependency were used to correlate the binodal curves. The OthmerTobias and Bancraft and Setschenow equations, the osmotic virial and the extended NRTL models were used to fit the tie-line data.

Keywords: Liquid–liquid equilibrium; Poly ethylene glycol di-methyl ether; Di-sodium hydrogen citrate; EEV model; Extended NRTL model.

________________________________ *Corresponding author. Fax: +98 413 3340191. E-mail addresses: [email protected] (M. T. Zafarani-Moattar).

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1. Introduction Aqueous two-phase partitioning of biomolecules is a well-established process which was first introduced by Albertson [1]. The existent aqueous two-phase system (ATPS) included polymer-polymer aqueous two-phase system [2, 3], polymer-salt aqueous two-phase system [4, 5], ionic liquid- salt aqueous two-phase system [6, 7] and micro molecule organic solvent-salt aqueous two-phase system [8, 9]. Because organic solvent is volatile and instable, the price of ionic liquid is higher and the viscosity of system containing two polymers is larger, the application of these three types of aqueous two phase system in large-scale industrial production was affected. Whereas, the cost and viscosity polymer-salt aqueous two-phase system is cheaper, it has the advantage of good biocompatibility. These systems have many applications such as the pharmaceutical proteins [10, 11], purification of pharmaceutical enzymes [12]. Polyethylene glycol (PEG) which is a hydrophilic polymer has been used in the aqueous two-phase partitioning studies [4]. Poly ethylene glycol di-methyl ether (PEGDME) is a polymer that has a similar structure to the PEG, thus it can be used to form ATPSs with cosmotropic (i.e. water-structuring) salts. Vernau and Kula [13] have investigated the possible use of citrates as a substitute for inorganic salts. They found that sodium and potassium citrates also form aqueous two-phase systems with PEG which is suitable for protein extraction. In contrast to phosphate or sulfate, citrate is biodegradable and nontoxic and could be discharged into biological wastewater treatment plants. In this respect the liquid–liquid equilibria of aqueous two-phase system containing PEG and trisodium citrate [14, 15], PEG and tri-potassium citrate [16], PEG and di-sodium hydrogen citrate [4] and PEGDME and tri-potassium citrate [17] and have been studied, recently. However, there is no report on the liquid–liquid equilibria of aqueous PEGDME + disodium hydrogen citrate system in the literature. In this work, the binodal and tie-line data are reported for (PEGDME + di-sodium hydrogen citrate + water}) at different molar masses of PEGDME and working temperatures and atmospheric pressure (≈ 85 kPa). Furthermore, plait point of system has been calculated at each temperature using linear least square regression method; and based on cloud point values the free energies of the clouding process have been 2

estimated. In addition, the effect of molar mass and type of polymer on the phase forming ability was studied. For the investigated aqueous two-phase system (ATPS) two empirical statistic equations [18, 19] were used for reproducing the experimental binodal values. Also, the EEV model data were used to the effect of molar mass of polymer on the phase forming ability in these systems were studied. The experimental tie-line compositions obtained at the noted temperatures were fitted to Othmer-Tobias and Bancroft [20], Setschenow type equation [21], osmotic virial [22] model and extended NRTL [23] model.

2. Experimental 2.1. Materials and methods Poly ethylene glycol di-methyl ether (CAS No. 24991-55-7), of different molar masses (2000, 500, and 250) g·mol-1, were obtained from Merck. Di-sodium hydrogen citrate with CAS No. 6132-05-4) was obtained from Merck. The purity of the materials is shown in table 1. The polymers and salt were used without further purification, and double distilled deionised water was used.

2.2. Apparatus and procedure The binodal curves were determined by the clouding point titration method as described in previous works [16, 17]. In this method, the composition of the mixture for each point on the binodal curve was determined from the amount of titrant added until turbidity was observed using an analytical balance (Shimatzu, 321-34553, Shimatzu Co., Japan) with a precision of ±1.10-7 kg. Feed samples (about 2×10-5 m3) were prepared in the vessel by mixing appropriate amounts of polymer, salt and water to determine tie lines. The thermostat (JULABO model MB, Germany) with an accuracy of ±0.02 K was set at the desired temperature, and the samples were stirred for 1 h. Then, the samples were placed in the thermostat and allowed to settle for at least 48 h so that they could be separated into two clear phases. After the separation of the two phases, the concentrations of di-sodium 3

hydrogen citrate in the top and bottom phases were determined by flame photometry (JENWAY PFP7, England). The concentration of PEGDME in both phases was determined by refractive index measurements performed at T = 298.15 K using a refractometer (ATAGO DR-A1, Japan) with a precision of ±0.0001. The uncertainty in refractive index measurement is ±0.0002. For dilute aqueous solutions containing a polymer and a salt, the relation between the refractive index, nD, and the mass fractions of polymer, wp, and salt, ws is given by:

nD = nw + ap wp + as ws

(1)

,

where nw is the refractive index of pure water which is set to 1.3325 at T = 298.15 K. ap and as are constants of polymer and salt, respectively, for which linear calibration plots of refractive index of the solution are obtained. However, it should be noted that equation (1) is only valid for dilute solutions. Therefore, before refractive index measurements, it was necessary to dilute the samples to be in the mass fraction range (C Range) presented in table 2. The uncertainty of the mass fraction of PEGDME achieved using equation (1) was better than 0.002. The values of these constants and respective correlation coefficient values, R, are given in table 2.

3. Results and discussion 3.1. Correlation and phase diagram For the aqueous (PEGDME + di-sodium hydrogen citrate) system, the binodal data and tie-line compositions determined experimentally at different polymer molar masses and proposed temperatures and atmospheric pressure of ≈ 85 kPa are given in tables 3 and 4, respectively. 3.2. Effect of temperature The effect of temperature on the phase-forming ability of the systems studied is also illustrated in figure 1 which shows that the two-phase area is expanded with an increase in temperature. This is attributed to the decrease in solubility or increase in phase-forming ability in the system studied.

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Additionally, to show the effect of temperature on the phase equilibrium compositions in the investigated system, the experimental tie-lines are compared in figure 2, for the temperatures T = (298.15 and 318.15) K, as an example. Figure 2, and the data collected in table 5 show that the slope and the length of the tie-lines increase with increasing temperature, similar to the one observed in our previous works [4, 19]. This is because the PEGDME becomes more hydrophobic with the increase in temperature [24]. Thus, by increasing temperature water is driven from the PEGDME-rich phase to the saltrich phase, so the PEGDME concentration at the PEGDME-rich phase increases, while the salt concentration decreases in the bottom phase.

3.3. Effect of polymer molar mass The molar mass of the polymer used influences the partitioning of proteins. The higher the molar mass of the polymer, the lower is the polymer concentration required for phase separation. As polymer concentration increases, differences in density, refractive index, and viscosity between the phases increase. Binoda curves shift towards the origin with the increase in PEGDME molar mass. The locus for the experimental binodals is shown in figure 3. In fact by increasing molar mass of PEGDME, the polymer becomes less hydrophilic and its solubility in water decreases; therefore, the salting out strength of PEGDME is increased by increasing molar mass of polymer. Also, in figure 4 the tie-line data are shown at molar masses M = (2000 and 250) g· mol−1 for the temperature T = 298.15 K . From the figure 4, it can be seen that the slope and length of tie-lines increased with an increase at polymer molar mass.

3.4. Effect of the Polymer PEGDME has a similar structure to poly ethylene glycol (PEG). In this regard, our interest lies in comparison of the phase forming ability of these polymers. The experimental binodal values for the (PEG2000 + Na2C6H6O7 + H2O) ternary system was reported by Zafarani-Moattar et al. [4]. The result of this comparison at T = 298.15 K is shown in figure 5. Considering that both of the polymers have the same molar masses, from this figure we can conclude that when we have di-sodium hydrogen citrate the salting-out of PEGDME is better than PEG. 5

4. Correlation 4.1. Binodal curve correlation In this work for the correlation of binodal data, we examined the performances of the temperature dependent Merchuk equation [18] which has been successfully used previously and the empirical equation that we proposed recently [19]: w1 = a.exp[b.( w2 ).5 − c.(w2 )3 ]

w1 = α + β ln( w2 ) + γ w2

(2)

,

(3)

,

here a, b, c are fitting parameters of Eq. (2) and α, β and
are the fitting parameters of Eq. (3). For the temperature dependency of fitting parameters of these equations we adopted a linear form for each parameter as a function of temperature [19]. The Merchuk equation and our previously proposed equation are used respectively in the form of Eqs (4) and (5) for fitting the binodal data of investigated system at different temperatures:

wp = [a0 + a1(T − T0 )]exp ([b0 + b1(T − T0 )] ws0.5 − [c0 + c1(T − T0 )] ws3 ) wp = [α0 + α1(T − T0 )] + [β0 + β1(T − T0 )]ln(ws ) + [γ 0 + γ1 (T − T0 )]ws

.

,

(4)

(5)

In Eqs (4) and (5), T is the absolute temperature and T0 is assumed to be the reference temperature, T0 = 273.15 K. Also a0, a1, b0, b1, c0 and c1 are independent temperature adjustable parameters of Eq. (4) and similarly α0, α1, β0, β1, γ0 and γ1 are independent temperature adjustable parameters of Eq. (5). The experimental binodal data for (PEGDME + di-sodium hydrogen citrate + water) system at T = (298.15, 308.15 and 318.15) K were fitted by non-linear leastsquares regression method to the Eqs. (4) and (5). The fitting parameters for these equations along with the corresponding standard deviation for each temperature are given in tables 5 and 6. The obtained standard deviations (sd) show that both of Eqs. (4) and (5) can be used to reproduce the binodal values; however, on the basis of the obtained 6

standard deviations, we conclude that the performance of Eq. (5) is better than the Eq. (4). 4.2. Tie-line correlation For the correlation of LLE values for the system investigated, we decided to use the Othmer-Tobias and Bancroft, Setschenow-type, and osmotic virial equations, and the extended NRTL model, which have different thermodynamic bases.

4.2.1. Othmer-Tobias and Bancroft equations The Othmer-Tobias (Eq. (6a)) and Bancroft (Eq. (6b)) [20] have been used to correlate the tie-lines composition.  1 − wtop p  top  wp

  1 − wsbot   = k   , bot  ws  

(6a)

r

 wwtop   wwbot   bot  = k p  top  ,  ws   wp 

(6b)

where k, n, kp, and r represented fit parameters. Superscripts “top” and “bot” indicate top and bottom phases, respectively. Using the tie-line data reported in table 7, a linear dependency

of

the

log(wwbot wsbot ) against

top log[(1 − wtop p ) / wp ]

plots

against

log[(1 − wsbot ) / wsbot ] and

log(wwtop wtop obtained which indicated an acceptable p ) is

consistency of the results. The experimental LLE values were correlated to the Eq. (6) using the following objective function 2 , Of = ∑ ∑ ∑ ∑ ( wTcal, p ,l , j −wTexp , p ,l , j ) T

p

l

(7)

j

where, wT,p,l,j is the mass percent of the component j in the phase p for lth tie-line at working temperature. The superscripts “cal” and “exp” refer to the calculated and experimental values, respectively. In Eq. (7) the species j can be polymer, salt or solvent molecule. The corresponding correlation coefficient values, R2, and the values of the 7

fitted parameters together with the deviations are given in table 7. The R2 values obtained indicate that the measured tie-line values have acceptable consistency. On the basis of the deviations (Dev.) obtained, we conclude that Eqs. (6a) and (6b) can be satisfactorily used to correlate the tie-line results for the systems investigated.

4.2.2. Seteschenow type equation A Setschenow type equation is a relatively simple two-parameter equation, which can be derived from the binodal theory [21]. The equation has the following form:

 mtop  p ln  bot = k + k mbot − mstop ) ,  m  p s( s  p 

(8)

in which ks is the salting-out coefficient, kp is a constant and mp and ms are the molality of polymer and salt, respectively. Superscripts “top” and “bot” stand for polymer rich phase and salt rich phase, respectively. Following the previous works [15, 25], for the temperature dependence of fitting parameters of Eq. (8), here, we also adopted a simple form for each parameter and the obtained equation has the following form:

 mtop   k p ks bot  p ln  bot =  + ( ms − mstop )  .  m  T T   p 

(9)

The parameters of Eq. (9) at each temperature which were obtained from the correlation of the experimental LLE data at T = (298.15, 308.15 and 318.15) K are given in table 7 along with the corresponding standard deviations. Here, the objective function (Eq. (7)) was also used. On the basis of deviations reported in table 7, it is interesting to note that the Eq. (9) with only two parameters represents the experimental LLE values with excellent accuracy for the systems studied at the temperatures noted above.

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4.2.3. Osmotic virial equation In the osmotic virial equation adopted by Edmond and Ogston [15], the chemical potentials of polymer (p) and salt (s) µ i as a function of molality of polymer, mp, and salt, ms, can be written as:

∆µp = RT (ln mp + ln β ppmp + ln β ps ms ) ,

(10a)

∆µs = RT (ln ms + ln βss ms + ln β ps mp ) .

(10b)

Using the Gibbs–Duhem relation, the chemical potential for water (w) is then obtained as

∆µw = −RTVw ρw (mp + ms +

β pp 2

(mp )2 +

βss 2

(ms )2 + β ps mp ms ) .

(10c)

where βij is a constant characterizing the interaction between a molecule of component i and a molecule of component j and for βij a temperature-dependent function was assumed as follows:

β ij = β ij0 + β ij1 T .

(11)

The requirement for thermodynamic equilibrium is that the Gibbs energy is at a minimum. It can be shown from classical thermodynamics that a two-phase system at constant pressure and temperature containing component i (polymer, salt or water) at top (top) and bottom (bot) phases will obey the following constraints at equilibrium 



=  .

(12)

The interaction parameters βij are evaluated from the fitting of experimental LLE data to the Eq. (10) using the objective function (Eq. (7)) and the equilibrium condition:

( x jγ j )top = ( x j γ j )bot ,

(13)

9

in which and γ represented the mole fraction and activity coefficient, respectively. The fitting parameters of the osmotic virial equation along with the corresponding standard deviation are given in tables 7. On the basis of standard deviations reported in table 7 we conclude that the quality of fitting with the osmotic virial equation is fairly good. 4.2.4. Local composition NRTL models The local composition models are comprehensive molecular thermodynamics models for system with molecular and ionic species, molecules and ions of various size, and hydrophobic, hydrophilic and amphiphilic species. In this respect, the NRTL local composition model was extended by Zafarani-Moattar and Sadeghi [23] to represent the excess Gibbs energy of aqueous (polymer + electrolyte) solutions (E-NRTL). In local composition models, the excess Gibbs energy, GE, is expressed as the sum of three contributions:

G E = G E ,Comb + G E ,LR + G E ,SR ,

(14)

where GE,Comb is the combinatorial contribution, GE,LR is the long range interaction contribution and GE,SR

is the short-range interaction. The activity coefficient of

component i (polymer, ions and water) can also be considered as the sum of three contributions: ln γ E = ln γ E ,Comb + ln γ E , LR + ln γ E ,S R .

(15)

The Flory–Huggins expression [26], the Pitzer extension of the Debye–Hückel function (PDH) [27] and the extended NRTL (ENRTL) [23] model are used to calculate GE,Comb, GE,LR, and GE,SR(NRTL), respectively. The Flory–Huggins equation together with the necessary procedure for obtaining GE,Comb have been given previously [23]. In the required relations for calculating the combinatorial contribution to the excess Gibbs energy, GE,Comb, and consequently to the activity coefficient of the component i, a value of r = 1 was used for the number of segments of water and constituent salt ions. For the polymer, the value of the ratio of the molar volume of polymer to that of water was 10

considered. The value of = 14.9 has been frequently used for the aqueous electrolyte solutions [28]. The dielectric constants of Dw = (78.30, 74.82, and 71.51) were used for water at T = (298.15, 308.15, and 318.15) K, respectively [29]. In addition, for PEGDME, a dielectric constant D1 = 2.2 was calculated, according to the method proposed by van Krevelen and Hoftyzer [30]. Using the group contribution data reported by Zana [31], the molar volumes V = 1.660 × 10-3 m3·mol-1, V = 4.545 × 10-4 m3·mol-1 and V = 2.303 × 10-4 m3·mol-1 were calculated for PEGDME2000, PEGDME500, PEGDME250, respectively. In this work, non-randomness factor,  , of the E-NRTL was fixed to 0.1. For the short-range contribution, the E-NRTL [23] equation is used. Since the equation is lengthy, it is not given here. However, in this work in fitting the LLE data with E-NRTL model, the temperature dependency of parameters,  , is considered through the definition of parameter Aij as follows:

τ ij =

g ij − g ii RT

=

Aij RT

,

(16)

where gij and gii are energy of interaction between i–j and i–i species, respectively. The species i and j can be solvent molecules, salt or segments. The Aij is the temperature independent adjustable parameter. The procedure for obtaining the fitting parameters for E-NRTL model is exactly same as the one we presented for osmotic virial model. The E-NRTL local composition model used for the correlation of the LLE data has six interaction parameters. For binary aqueous polymer and di-sodium citrate solutions there are reliable values of water activity at T = (298.15, 308.15, and 318.15) K [32] and T = 298.15 K respectively [33]. So the binary interaction water–salt, salt–water, polymer–water and water– polymer parameters were calculated for E-NRTL model obtained from fitting of the LLE data at T = (298.15, 308.15, and 318.15) K; two remaining interaction parameters obtained from fitting the LLE data at T = (298.15, 308.15, and 318.15) K are shown in tables 8. In fitting LLE values to the E-NRTL, the objective function (Eq. (7)) and equilibrium condition (Eq. (13)) were also used. However, since there are no data for 11

binary of polymer solution at T = 318.15 K and salt solutions at T = 308.15 and 318.15 K, it is not possible to obtain the corresponding interaction parameters at this temperature. Therefore we decided to obtain all six interaction parameters of the E-NRTL model from the correlation of the LLE results at T = 308.15 and 318.15 K with the results given in table 8 to each of these models. On the basis of the standard deviations reported in tables 7 and 8, it is interesting to note that Eq. (9) with only two parameters represents the experimental LLE values with excellent accuracy for the system studied within the temperature range of 298.15 K to 318.15 K. To show the reliability of Eq. (9) in a better manner, the comparison between the experimental and correlated tie-lines is shown in figure 6 for the aqueous (PEGDME + di-sodium citrate) system at T = 298.15 K, as an example.

4. 3. Effective excluded volume model (EEV) The effective excluded volume model is based on statistical geometry methods from which effective excluded volume can be determined. This binodal model developed by Guan et al. [34] for aqueous polymer-polymer systems can also be used for the correlation of experimental binodal values for systems studied. The binodal equation for the aqueous polymer-salt system can be written as: * ln(v123

wp Mp

* ) + v123

ws =0 , Ms

(17)

* where v123 is the effective excluded volume (EEV). Mp and Ms are molar mass of polymer

and salt, respectively. In table 9 the EEV values obtained from the correlation of binodal data of some {PEGDME + di-sodium hydrogen citrate + water} systems at different polymer molar mass along with the corresponding standard deviation are given. In this work the interest * lies in the behaviour of the single fitted parameter, v123 , in the investigated systems which

should, at constant salt molar mass, be related to the salting-out strength of the polymer, as pointed out by Huddleston et al. [35]. From the EEV values and the position of the binodal curves shown in figure 3 we conclude that the higher salting-out strength, have larger values of EEV. In fact by 12

increasing molar mass of PEGDME, the polymer becomes less hydrophilic and its solubility in water decreases; Therefore, the salting out strength of PEGDME with higher molar masses increases. Also in figure 4, the tie-line data are shown at molar masses M = (250 and 2000) g·mol-1. From the figure 4 it can be seen that the slope and length of tie-lines increased with an increase at polymer molar mass.

4.4. Estimated plait point, slope and the length of tie-lines Somewhere in the binodal curve, we have a plait point where the length of the tieline has shrunk to zero, that is, when the two liquid phases become identical [36]. The location of the plait point for the system studied was estimated by extrapolation from the auxiliary curves satisfactorily fitted with the following linear equation:

wp = f + gws ,

(18)

where f and g represent the fitting parameters. For the system studied, the estimated values for the plait points along with the obtained fitting parameters for Eq. (18) and the corresponding correlation coefficients, R2, are listed in table 10. As an example, the locus of estimated plait point for (PEGDME2000 + di-sodium hydrogen citrate + water) system along with the used procedure is illustrated in figure 7 at T = 298.15 K. The tie-line length, TLL, and the slope of the tie-line, S, at different compositions and temperatures were calculated as follows: 2 2 top TLL =  ( w top − w bot − w sbot )  p ) + ( ws  p 

bot S = ( wtop p − wp )

(w

top s

0.5

,

(19)

− wsbot ) .

(20)

The results are also collected in table 4. Also shown in figure 4, the slope and TLL increases with an increase in polymer molecular mass.

3.6. The free energies of the cloud point (CP)

13

The Gibbs energy of phase separation (∆Gc) can be calculated from the following relation [37]:

∆G = RT ln Xp ,

(21)

Xp is the mole fraction concentration of PEGDME at the cloud-point. In table 11, the values of ∆Gc are presented. The enthalpy values of phase separation (∆Hc) were calculated by the relation,

∆H c =

d (∆Gc / T ) . d (1/ T )

(22)

The calculated ∆Hc values are presented in table 11 which are positive and show that the aqueous two-phase formation processes are endothermic. The following Gibbs–Helmoltz equation was used to calculate the entropy of phase separation (∆Sc),

∆S c =

∆H c − ∆G c . T

(23)

The calculated ∆Sc values are all positive and they are also collected in table 11. This shows that the increase of entropy is the driving force for the aqueous two-phase formation processes in the system studied at T = (298.15, 308.15 and 318.15) K. Previously we have also performed similar calculations on the aqueous two phase systems containing (PEG + di-sodium hydrogen citrate + water) [4] and (PEGDME2000 + sodium hydroxide + water) [25]; and for both of these systems positive ∆Hc and ∆Sc values were obtained at T = (298.15, 308.15 and 318.15) K.

5. Conclusions Liquid-liquid equilibrium for the (PEGDME + di-sodium hydrogen citrate + water) system was determined at temperatures (298.15, 308.15 and 318.15) K and atmospheric 14

pressure of ≈ 85 kPa. The experimental binodal values were satisfactorily correlated using an empirical equation and the Merchuck equation as a function of temperature with a linear temperature dependency in the form of (T- T0) K as a variable. We found that the empirical equation gives better results than the Merchuck equation in the correlation of binodal values. Comparison between the experimental results shows that the phaseseparation ability of the system studied increased with increasing the temperature and molar mass of polymer. Additionally, an Othmer–Tobias and Bancroft, Setschenow type equation, osmotic virial model and local composition based models (i.e. E-NRTL) were used for the correlation of the system studied. On the basis of the results obtained, it can be concluded that, the performances of all the models considered in the correlation are good. However, it was found that, the Setschenow type equation with only two parameters shows the best results in the correlation of tie-line compositions of the system studied. Furthermore the slope increases with an increase in polymer molar mass. Moreover, the Gibbs energies of the cloud point for this system studied with PEGDME 2000

were calculated. The results show that the increase of entropy is the driving force for

aqueous two-phase formation processes in this system.

Acknowledgment We are grateful to history of Tabriz research council for the financial support of this research.

15

References [1] P. A. Albertsson, partitioning of cell particles and macromolecules, 3rd rd. Wiley: New York, 1986. [2] T. Furuya, Y. Lawi, Y. Tanaka., et al, Fluid Phase Equilibria. 103 (1995) 119. [3] C. Grol3mann, R. Tintinger, J. Zhu., et al, Fluid Phase Equilib. 106 (1995) 111. [4] M.T. Zafarani-Moattar, P. Jafari, Fluid Phase Equilib. 337 (2013) 224. [5] J.C. Merchuk, B.A. Andrews and J.A. Asenjo, J. Chromatogr. B., 711 (1998) 285. [6] M. T. Zafarani-Moattar, Sh. Hamzezadeh, Fluid Phase Equilibria 304 (2011) 110– 120. [7] M. T. Zafarani-Moattar, Sh. Hamzezadeh, AICH 27 (4) (2011) 986. [8] Y. Wang, S. P. Hu, J. Han., et al, J. Chem. Eng. Data. 55 (11) (2010) 4574. [9] Y. Wang, S. P. Hu, Y. S. Yan., et al, CALPHAD, 33 (4) (2009) 726. [10] J. Perrson, H. O. Johansson, I. Galaev, B. Mattiasson, F. Tjerneld. Bioseparation. 9(2000) 105. [11] G. Tubio, L. Pellegrini, B. B. Nerli, G. A. Pico. J. Chem. Eng. Data. 51 (2006) 209. [12] A. Haghtalab, B. Mokhtarani, Fluid phase Equlib. 215 (2004) 151. [13] B. Y. Zaslavsky, Aqueous Two-Phase Partitioning, Physical Chemistry and Bioanalytical Application, Marcel Dekker, New York, 1995. [14] M.T. Zafarani-Moattar, R. Sadeghi, A.A. Hamidi, Fluid Phase Equilib. 219 (2004) 149. [15] M.T. Zafarani-Moattar, S. Emamian, S. Hamzehzadeh, J. Chem. Eng. Data 53 (2008) 456. [16] S. Hamzehzadeh, M.T. Zafarani-Moattar, Fluid Phase Equilib. 385 (2015) 37. [17] M.T. Zafarani-Moattar, V. Hosseinpour-Hashemi, J. Chem. Thermodyn. 32 (2011) 655. [18] J.C. Merchuk, B.A. Andrews and J.A. Asenjo, J. Chromatogr. B., 711 (1998) 285. [19] M. T. Zafarani-Moattar, E. Nemati-Kande, CALPHAD 34 (2010) 478. [20] D. F. Othmer, P. E. Tobias, Ind. Eng. Chem. 34 (1942) 690. [21] M. J. Hey, D. P. Jackson, Hong Yan, Polymer. 46 (2005) 2567. 16

[22] E. Edmond, A.G. Ogston, Biochem. J. 109 (1968) 569. [23] M. T. Zafarani-Moattar, R. Sadeghi, Fluid Phase Equilib. 203 (2002) 177. [24] H. Hartounian, E. Floeter, E. W. Kaler, S. I. Sandler, AIChE J. 39 (1993) 1976. [25] M. T. Zafarani-Moattar, H.Shekaari, M.Hosseinzadeh, P. Jafari, Fluid Phase Equilib. 203 (2002) 177. [26] P. J. Flory, J. Chem. Phys. 9 (1941) 660. [27] K. S. Pitzer, J. Am. Chem. Soc. 102 (1980) 2902. [28] J. m. Simonson, K. S. Pitzer, J. Phys. Chem. 90 (1986) 3009. [29] R. A. Robinson, R. H. Stokes, Electrolyte Solutions, 2nd ed., Butterworths, London, 1965. [30] D. W. van Krevelen, P. J. Hoftyzer, Properties of Polymers: Their Estimation and Correlation with Chemical Structure, 2nd ed., Elsevier, Amesterdam. 1976 (chapter 11). [31] R. Zana, J. Polym. Sci. 18 (1980) 121. [32] R. Sadeghi, Y. Shahebrahimi, J. Chem. Eng. Data, 56 (2011) 789. [33] S. Kazemi, M. T. Zafarani-Moattar, V. Taghivand, C.Ghotbi, Fluid phase Equilib 262 (2007) 137. [34] Y. Guan, T. H. Lilly, T. E. Treffry, Macromolecules 26 (1993) 3971. [35] J. G. Huddleston, F. D. Rogers, J. Chem. Eng. Data 48 (2003) 1230. [36] B. H. Lee, Y. Qin, J. M. Prausnitz, Fluid Phase Equilibria. 240 (2006) 67. [37] A. Dan, S. Ghosh, S. P. Moulik, J. Phys. Chem. B 112 (2008) 3617.

17

Table caption Table 1: Provenance and mass fraction purity of the materials used.

Table 2 : Values of parameters of the Eq. (1), ai, for the {PEGDME (p) +di-sodium hydrogen citrate (s) + H2O (w)} system.

Table 3: Experimental binodal results as mass fraction, wi , for the {PEGDME (p) +disodium hydrogen citrate (s) + water (w)} system at different molar masses at temperatures (298.15, 308.15 and 318.15) K and atmospheric pressure (≈ 85 kPa)a.

Table 4: Experimental tie-line values as mass fraction, wi, for {PEGDME (p) +di-sodium hydrogen citrate (s) + water (w)} system at different molar masses at temperatures (298.15, 308.15 and 318.15) K and atmospheric pressure (≈ 85 kPa)a.

Table 5: Values of parameters of Eq. (4), (ai, bi , ci ), Eq. (5), (αi , βi ,
i ), and for the {PEGDME2000 (p) +di-sodium hydrogen citrate (s) + water (w)} system at T = (298.15, 308.15 and 318.15) K.

TABLE 6: Values of parameters of Eq. (2), and Eq. (3), for {PEGDME (p) +di-sodium hydrogen citrate (s) + water (w)} systems with difference in molar mass at T =298.15 K.

TABLE 7: Values of parameters of Othmer-Tobias and Bancroft, (K, n, k , r), and Setschenow type, (kp, ks) (kg·K·mol-1), and osmotic virial equation, β (kg·mol-1), for {PEGME (p) +di-sodium hydrogen citrate (s) + water (w)} at different molar masses and temperatures (298.15, 308.15 and 318.15) K. .

18

TABLE 8: Values of parameters of E-NRTL, as a function temperature independent form,  , and temperature independent form, Aij (J·mol-1), for the {PEGDME (p) +disodium hydrogen citrate (s) + water (w)} system at temperatures (298.15, 308.15 and 318.15) K. TABLE 9: Effective excluded volumes as determined by regression of the statistical geometry model for the {PEGDME (p) + di-sodium hydrogen citrate (s) + water (w)} systems at T = 298.15 K. Table 10: The values of parameters of Eq. (18), ( f, g ) and the plait points for the {PEGDME (p) +di-sodium hydrogen citrate (s) + H2O (w)} system at working temperature. Table 11: The Gibbs energy change, ∆Gc/( kJ·mol-1), entropy changes, ∆Sc /( J·K-1·mol-1), enthalpy changes, ∆Hc /( kJ·mol-1), for the clouding point of PEGDME2000 in the presence of di-sodium hydrogen citrate at different salt mass fraction, ws , and T = ( 298.15, 308.15 and 318.15) K.

19

Figure caption Figure 1: Experimental binodal results for the {PEGDME2000 (p) +di-sodium hydrogen citrate (s) + H2O (w)} system at different temperatures: (▲) T = 298.15; (■) T = 308.15 and (●) T = 318.15 K, and (solid line) the calculated from Eq. (3).

Figure 2: Effect of temperature on the equilibrium phase compositions for the {PEGDME2000 (p) +di-sodium hydrogen citrate (s) + H2O (w)} system. Experimental tielines at: (▬○▬) T = 298.15 and (---×---) T =318.15 K.

Figure 3. Plot of mass percent polymer against mass percent salt to show binodal curves for the {PEGDME (p) +di-sodium hydrogen citrate (s) + H2O (w)} two-phase system at different polymer molar masses: (♦) PEGDME2000; (●) PEGDME500; (▲) PEGDME 250 and T = 298.15 K; and (solid line) the calculated from Eq. (3).

Figure 4. Effect of type of polymer via plot of mass percent polymer against mass percent salt to illustrate the effect of polymer molar mass on the slope and length of tie-lines of the {PEGDMEn (p) +di-sodium hydrogen citrate (s) + H2O (w)} system: (○) PEGDME2000; (×) PEGDME250; (—), tie-lines were obtained by connecting the experimental equilibrium phase composition values.

Figure 5. Binodal curves for {PEGDME2000 (1) + Na2C6H6O7 (2) + H2O (3)}(

▬▲▬),

{PEG2000 (p) + Na2C6H56O7 (s) + H2O (w)}, [17], ( ▬□▬), at T = 298.15 K. Figure 6: Experimental and correlated tie-lines and experimental binodal result for {PEGDME2000 (p) +di-sodium hydrogen citrate (s) + H2O (w)} system at T = 298.15 K. 20

(▬□▬) experimental tie-lines; (---×---) calculated tie-lines using the temperature dependent Setschenow type equation (Eq. (9)).

Figure 7: Binodal curve, tie-lines and plait point for the {PEGDME2000 (p) +di-sodium hydrogen citrate (s) + H2O (w)} system at T = 298.15 K: (●) experimental binodal, (▬▬) calculated binodal from Eq. (3), (▬□▬) tie-lines, (---×---) calculated auxiliary curves and (■) plait point.

21

Materiala Poly ethylene glycol dimethyl ether2000 Poly ethylene glycol dimethyl ether500 Poly ethylene glycol dimethyl ether250 Poly ethylene glycol2000 Di–sodium hydrogen citrate

Molecular formula C H3O(C2H4O)nCH3 C H3O(C2H4O)nCH3 C H3O(C2H4O)nCH3 HO(C2H5O)n H Na2C6H6O7

Table 1 Provenance and mass fraction purity of the materials used. a

Both material were supplied from Merck.

22

Mass fraction purity >0.990 >0.990 >0.990 >0.990 >0.990

Table 2 Values of parameters of the Eq. (1), ai, for the {PEGDME (p) +di-sodium hydrogen citrate (s) + H2O (w)} system. Material PEGDME2000 PEGDME 500 PEGDME 250 Na2C6H6O7 a

Constant ap ap ap as

Value 0.1311 0.1278 0.1188 0.1537

C Range( w/w) 0 to 0.15 0 to 0.10 0 to 0.10 0 to 0.08

R2a 0.9999 0.9999 0.9997 0.9999

where, R, represented the respective correlation coefficient value of the linear

calibration plot of the refractive index against mass fraction for PEGDME or di-sodium citrate at the mass fraction range (C range) of each material.

23

Table 3 Experimental binodal results as mass fraction, wi , for the {PEGDME (p) +di-sodium hydrogen citrate (s) + water (w)} system at different molar masses at temperatures (298.15, 308.15 and 318.15) K and atmospheric pressure (≈ 85 kPa)a. T/K = 298.15 PEGDME500 b p

PEGDME250 100 ws 27.40 23.65 22.38 17.43 15.46 14.12 12.51 11.18 10.08 9.23 8.40 7.76

100 w 6.23 9.81 11.30 17.28 19.72 21.87 24.31 26.28 28.30 29.76 31.44 32.75

100 ws 37.41 36.46 35.25 33.69 31.80 30.56 28.61 26.77 24.72 23.09 20.87 19.23 17.27 15.60 13.76 12.42 11.05 10.02 8.97 8.17

100 wp 2.78 3.16 3.76 4.63 5.74 6.82 8.68 10.12 12.52 14.33 16.60 18.59 21.00 22.98 25.31 27.12 29.17 30.92 32.57 34.13

PEGDME2000 T/K = 298.15 100 wp

33.22 31.89 30.05 28.22 26.69 24.50 22.62 21.30 19.27 17.54

100 ws 5.83

6.30 6.86 7.52 8.09 8.96 9.75 10.47 11.47 12.39

T/K = 308.15 100 ws 3.32

100 wp

43.24 34.69 29.58 27.22 24.28 21.90 19.42 17.38 15.31 13.58

5.25 6.90 7.71 8.86 9.86 11.10 12.08 13.26 14.20

24

T/K = 318.15 100 wp

44.27 39.37 34.08 31.71 28.49 22.91 20.57 17.92 15.33 13.36

100 ws 3.17

4.12 5.35 5.98 6.95 8.88 9.88 11.06 12.44 13.45

16.26 14.56 13.29 11.71 10.49 9.20 8.23 7.28 a

13.15 14.12 14.97 15.98 16.75

11.88 10.55 9.19 8.17 7.18

15.23 16.06 16.93 17.56 18.23

11.42 9.97 8.57 7.56 6.61

15.34 16.15 16.78 17.42

17.59 18.26 19.01

The standard uncertainties σ for mass fraction, temperature and pressure are: u (wi) =

0.002; u (T) = 0.05 K and u (p) = 0.5 kPa, respectively. b

14.51

wp and ws represented mass fractions of polymer and salt, respectively.

25

Table 4 Experimental tie-line values as mass fraction, wi, for the {PEGDME (p) +di-sodium hydrogen citrate (s) + water (w)} system at different molar masses at temperatures (298.15, 308.15 and 318.15) K and atmospheric pressure (≈ 85 kPa)a.

Feed sample b

Top phase

T /K = 298.15 Polymer

Bottom phase

slope

TLL

PEGDME500

100 wp′

100 ws′

100 wp

100 ws

100 wp

100 ws

20.00 20.00 19.99 20.01 20.03 20.00

17.40 19.18 20.98 22.75 24.55 26.34

30.25 34.78 38.06 40.50 43.36 45.70

9.22 7.44 6.68 6.01 5.40 4.93

4.88 2.71 1.56 0.76 0.32 0.13

29.69 33.37 35.80 38.37 40.64 42.79

-1.2397 -1.2368 -1.2536 -1.2285 -1.221 -1.2035

32.60 41.24 46.69 51.25 55.62 59.25

23.16 23.18 22.78 23.11 23.18 23.17

18.38 20.87 23.00 25.84 28.38 30.08

35.87 39.46 43.92 48.38 52.65 55.12

7.92 7.08 5.66 4.79 4.00 3.59

4.22 2.83 1.98 1.32 0.99 0.58

34.44 37.41 40.67 43.73 46.60 48.69

-1.1934 -1.2077 -1.1979 -1.2083 -1.2128 -1.2094

41.30 47.55 54.63 61.08 66.96 70.77

4.54 2.88 1.53 0.84 0.40 0.33

22.77 25.98 29.75 32.98 36.08 39.26

-1.67 -1.62 -1.53 -1.46 -1.40 -1.34

32.25 39.15 46.42 51.53 55.75 59.83

PEGDME250

PEGDME2000 T /K =298.15 23.15 23.09 23.12 23.10 23.12 23.13

11.47 13.59 15.68 17.79 19.88 22.13

32.21 36.20 40.37 43.36 45.80 48.33

6.19 5.44 4.33 3.86 3.72 3.53

T/K = 308.15

26

24.92 25.03 24.99 24.99 25.02 24.99

10.62 12.72 14.86 16.93 18.97 21.16

32.36 37.66 41.22 45.05 48.48 51.01

6.13 4.73 3.83 3.15 2.80 2.64

4.63 2.53 1.75 1.22 0.84 0.57

22.61 27.06 30.27 33.38 36.28 39.04

-1.68 -1.57 -1.49 -1.45 -1.42 -1.39

32.26 41.62 47.51 53.24 58.23 62.20

2.93 2.03 1.17 0.74 0.74 0.47

23.47 26.10 28.92 31.23 33.88 37.87

-1.72 -1.70 -1.68 -1.69 -1.64 -1.59

36.03 42.69 49.60 54.97 59.39 65.52

T/K = 318.15 17.99 18.00 18.02 18.03 18.02 18.02 a

7.98 8.99 10.00 10.97 11.99 13.03

34.09 38.81 43.81 48.05 51.45 55.94

5.38 4.44 3.59 3.24 2.98 2.95

The standard uncertainties σ for mass fraction, temperature and pressure are: u (wi) =

0.002; u (T) = 0.05 K and u (p) = 0.5 kPa, respectively. b

w'p and ws' are total mass fraction of polymer and salt in its feed samples, respectively;

and also tie-line length (TLL) and Slope at different concentrations calculated from Eqs. (19) and (20).

27

Table 5 Values of parameters of Eq. (4), (ai, bi , ci ), Eq. (5), (αi , βi ,
i ), and for the {PEGDME2000 (p) +di-sodium hydrogen citrate (s) + water (w)} system at T = (298.15, 308.15 and 318.15) K. T/K

a0

a1

b0

.b1

10-4.c0

10-3.c1

0.4661

2.0084

2.0084

Sda

(Eq. (4)) 97.8271

298.15 308.15 318.15 Overall T/K

α0

0.6178

α1

-0.4568

β0

β1

γ0

10-3.γ1

0.4661

2.0084

2.0084

0.18 0.45 0.36 0.33 Sda

(Eq. (5)) 97.8271

0.6178

-0.4568

298.15 308.15 318.15 Overall a

0.12 0.27 0.13 0.17

exp 2 0.5 sd = (∑i =1 ( wcal , where wp and N represented mass fraction of p − wp ) / N ) N

PEGDME2000 and number of binodal data, respectively.

28

TABLE 6 Values of parameters of Eq. (2), and Eq. (3), for {PEGDME (p) +di-sodium hydrogen citrate (s) + water (w)} systems with difference in molar mass at T =298.15 K. (Eq. (2))

PEG500 PEG250

a

b

c.105

sd

135.0809 110.9075

-0.6101 -0.5217

31.305 17.89

0.14 0.12

(Eq. (3))

PEG500 PEG250

α

β

γ

sd

77.6042 67.6901

-27.594 -19.6447

0.0316 -0.4621

0.13 0.12

29

TABLE 7 Values of parameters of Othmer-Tobias and Bancroft, (K, n, k , r), and Setschenow type, (kp, ks) (kg·K·mol-1), and osmotic virial equation, β (kg·mol-1), for {PEGME (p) +disodium hydrogen citrate (s) + water (w)} at different molar masses and temperatures (298.15, 308.15 and 318.15) K.

PEGDME500 PEGDME250

K 0.8381 0.7614

T/K 298.15 308.15 318.15

0.7070 0.6135 0.3765

PEGDME500 PEGDME250

Othmer-Tabias and Bancroft equations (Eq. (6)) T/K = 298.15 n R2 k1 r 1.1682 0.998 1.2724 0.8012 1.3396 0.998 1.2852 0.7202 PEGDME2000

R2 0.996 0.999

Dev 1.28 0.66

0.8825 0.995 1.6033 1.0855 0.994 0.9984 0.999 1.7069 0.986 0.999 1.3771 0.993 2.1016 0.7106 0.998 Steschenow type equation as a function of temperature (Eq. (9)) T/K = 298.15 kp ks -1.9162 2.8164 0.0452 1.2564 PEGDME2000 0.02465 0.0553

0.94 0.30 0.60

T/K 298.15 308.15 318.15 overall

a

Dev 0.07 0.06

0.26 0.35 0.38 0.33 Osmotic virial equation as a function of temperature (Eq. (10)) T/K = 298.15 β β1 β2 0 4.1154 2.011 3.225 0.2812 -0.3171 -0.8123 PEGDME2000

PEGDME500 PEGDME250

10

−2

0

× β1

-1.0696

1

10 +4 . β1 3.0686

10

−1

1

10 3. β 2 9.0160

0

× β2

-2.8753

T/K 298.15

0

β3 -9.1371

Dev 0.23 0.24 1

10 +3. β 3 2.5000

Dev

0.30

30

308.15 318.15 Overall a

0.27 0.46 0.34

exp 2 Dev = ∑ p ∑ l ∑ j ∑ T ((100 wcal p ,l , j ,T − 100 w p ,l , j ,T ) / 6 N ) ), where wp,l,j,T is the mass

fraction of the component j (i. e. polymer, salt or water ) in the phase p for l th tie-line at temperature T and N represents the number of tie line data.

TABLE 8 Values of parameters of E-NRTL, as a function temperature independent form,  , and temperature independent form, Aij (J·mol-1), for the {PEGDME (p) +di-sodium hydrogen citrate (s) + water (w)} system at temperatures (298.15, 308.15 and 318.15) K. . E-NRTL, as a function of temperature, τ ij T /K

τ ws

τ sw

ARD% a τ wca

τ caw

ARD%

τ sca

τ cas

Dev

PEGDME250 298.15

1.307

-0.7515

0.04

1.5603

-0.2022

0.06

-0.5073

5.5190

1.11

-0.0125

0.5259

0.04

PEGDME500 1.5603 -02022

0.06

0.3330

21.100

1.88

0.06

1.5200 -2.1248 -15.488

1.6216 4.497 28.0259

2.30 1.89 1.84

PEGDME2000 298.15 308.15 318.15

-0.441 0.8959 3.0201

0.5213 -0.4159 -2.1711

0.04

1.5603 -1.0621 -14.992

-0.2022 0.6618 384.994

E-NRTL, as a function of temperature, Aij PEGDME2000 T /K

Α sw .10−3

Α ws .10 −3

Α sca .10−6

Α cas .10−4

Α wca .10 −6

Αcaw ×10−3

-2.301

4.641

-4.5885

0 .9604

-4.51

4.530

298.15 308.15 318.15 Overall

Dev

4.07 1.14 2.97 2.72

31

a

N p −1  a cal − a exp ARD % = (1/ N p ) ∑  w exp w aw i =0 

  ×100 where Np is the number of experimental points. 

The highlighted partitions were calculated according to the water activity data of aqueous solution of PEGDME [35] and Na2C6H6O7 [36].

TABLE 9 Effective excluded volumes as determined by regression of statistical geometry model for the {PEGDME (p) + di-sodium hydrogen citrate (s) + water (w)} systems at T = 298.15 K. PEGDME + di-sodium hydrogen citrate +water

EEV/(g·mol-1`)

R2

sd

PEGDME2000 PEGDME500 PEGDE250

27.739 12.007 9.557

0.992 0.986 0.980

0.17 0.17 0.08

32

Table 10 The values of parameters of Eq. (18), (f, g) and the plait points for the {PEGDME (p) +di-sodium hydrogen citrate (s) + H2O (w)} system at working temperatures (298.15, 308.15 and 318.15) K. f

g

R2

298.15

10.8204

0.9708

0.991

(21.07,10.56,89.49)

308.15

6.5008

1.1492

0.999

(19.3,11.14,91.84)

318.15

-1.1391

1.5372

0.988

(16.78,11.65,94.87)

T/K

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

PEGDME2000

T/K = 298.15 PEGDME500

-4.4433

1.1751

0.998

(16.63, 17.93, 65.44)

PEGDME250

-11.8501

1.3775

0.999

(17.21, 21.10, 61.69)

33

ws

∆Hc / kJ·mol

T / K = 298.15

T / K = 308.15

T / K = 318.15

-1

∆Gc/ kJ·mol

∆Sc/ -1

-1

J·K ·mol

∆Gc/ -1

kJ·mol

∆Sc/ -1

-1

J·K ·mol

∆Gc/ -1

kJ·mol

∆Sc/ -1

J·K -1·mol-1

0.07

2.64

-14.99

59.13

-15.55

59.04

-16.17

59.13

0.09

3.83

-15.59

65.14

-16.19

64.97

-16.89

65.14

0.11

5.30

-16.16

71.97

-16.80

71.72

-17.60

71.97

0.13

11.54

-16.74

94.85

-17.44

94.06

-18.35

93.95

0.15

14.11

-17.35

105.53

-18.14

104.67

-19.19

104.68

Table 11 The Gibbs energy change, ∆Gc/(kJ·mol-1), entropy changes, ∆Sc /(J·K -1·mol-1), enthalpy changes, ∆Hc /(kJ·mol-1), for the clouding point of PEGDME2000 in the presence of disodium hydrogen citrate at different salt mass fraction, ws , and T = ( 298.15, 308.15 and 318.15) K.

34

Figure. 1 50 45 40 35 100 wp

30 25 20 15 10 5 0 0

5

10 100 ws

35

15

20

Figure 2 60 55 50 45 40

100 wp

35 30 25 20 15 10 5 0 0

4

8

12

16

20 24 100 w s

36

28

32

36

40

44

Figure 3 40 35 30

100 wp

25 20 15 10 5 0 0

5

10

15

20 100 ws

37

25

30

35

40

Figure. 4 60 55 50 45 40

100 wp

35 30 25 20 15 10 5 0 0

5

10

15

20

25

30

100 ws

38

35

40

45

50

55

Figure. 5 50 45 40 35

100 wp

30 25 20 15 10 5 0 2

7

12

100 ws

39

17

22

Figure. 6 60

50

100 wp

40

30

20

10

0 0

10

20

30 100 ws

40

40

50

Figure. 7

60

50

100 w p

40

30

20

10

0 0

5

10

15

20

25 100 ws

41

30

35

40

45

►Liquid-liquid equilibrium of (PEGDME+ di-sodium hydrogen citrate+ H2O) was studied. ►The effect of temperature and polymer molar mass on the LLE were investigated. ►Binodal data were fitted with two temperature dependent semi-empirical equations. ►EEV model was used for study the effect of molar mass of polymer on the binodal. ►Several equations including NRTL model were used to fit tie-lines.

42