Calculation of liquid–liquid equilibrium in polymer electrolyte solutions using PHSC-electrolyte equation of state

Accepted Manuscript Title: Calculation of Liquid-Liquid Equilibrium in Polymer Electrolyte Solutions Using PHSC-Electrolyte Equation of State Authors: Masood Valavi, Mohammad Reza Dehghani, Farzaneh Feyzi PII: DOI: Reference:

S0378-3812(12)00587-0 doi:10.1016/j.fluid.2012.12.007 FLUID 9435

To appear in:

Fluid Phase Equilibria

Received date: Revised date: Accepted date:

22-5-2012 20-11-2012 6-12-2012

Please cite this article as: M. Valavi, M.R. Dehghani, F. Feyzi, Calculation of LiquidLiquid Equilibrium in Polymer Electrolyte Solutions Using PHSC-Electrolyte Equation of State, Fluid Phase Equilibria (2010), doi:10.1016/j.fluid.2012.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Calculation of Liquid-Liquid Equilibrium in Polymer Electrolyte

ip t

Solutions Using PHSC-Electrolyte Equation of State

cr

Masood Valavi, Mohammad Reza Dehghani1, Farzaneh Feyzi

us

Thermodynamics Research Laboratory, School of Chemical Engineering,

an

Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran

M

*Corresponding author: Tel. No: 00982177240496

d

Fax: +982173222772

te

Email address: [email protected]

Ac ce p

Postal address: School of Chemical Engineering Iran University of Science and Technology, Narmak,

Tehran 16846-13114, Iran

1

Corresponding Author: [email protected]

1 Page 1 of 47

Calculation of Liquid-Liquid Equilibrium in Polymer Electrolyte Solutions Using PHSC-

ip t

Electrolyte Equation of State Masood Valavi, Mohammad Reza Dehghani2,Farzaneh Feyzi

cr

Thermodynamics Research Laboratory, School of Chemical Engineering,

an

us

Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran

M

Abstract

In this work, the capability of the Perturbed Hard Sphere Chain (PHSC) equation of state

d

(EOS) in liquid-liquid equilibrium calculations of salt-polyethylene glycol (PEG)-water

te

systems is investigated. In order to present a comprehensive model, association as well as

Ac ce p

electrostatic contributions have been added to the original PHSC EOS. In this work 47 systems including PEG (with different molecular weights) and various salts have been modeled at different temperatures. Only two adjustable parameters between salt and PEG and between water and PEG have been employed. Good agreement between experimental data and calculation results is observed. Overall average deviation for all of the systems considered is 6.81%. This study shows that the PHSC EOS can be employed for correlation of phase behavior in aqueous two phase systems.

2

Corresponding Author: [email protected]

2 Page 2 of 47

Keywords: PHSC EOS; Polymer; ATPS; Electrolyte

ip t

1. Introduction Separation processes are one of the most important steps in biological engineering, and aqueous

cr

two phase system (ATPS) is one of the most favorable separation processes in this regard.

us

Albertson [1] first used ATPS for recovery of the bio-molecules. He showed that microorganisms and other biological molecules distribute between ATPS selectively. Later on

an

ATPS found many applications for separation of proteins. ATPS is categorized into two groups, polymer-polymer and polymer-salt aqueous solutions. The latter has some advantages

M

such as low price and low viscosity. In ATPS each phase contains 70% to 90% water and

d

addition of salts, with proper content of buffer, makes them an appropriate milieu for biological

te

molecules. Usually, bio-molecules such as proteins, lipids, nucleic acids, viruses and whole cells can be separated using ATPS [2]. Phase partitioning depends on the surface properties of

Ac ce p

the components such as size, charge and also the system properties such as pH, temperature and feed compositions. Among different polymers, PEG is the most applicable polymer for this purpose and, as a result, considerable experimental data on phase equilibrium of the systems containing PEG, salt and water can be found in the literature. A solution containing PEG accompanied with sulfate, potassium or citrate salts is the most favorable combination for ATPS, however, high molecular weight PEGs increase viscosity and density of the solution which has a negative effects on the economy of the separation process. A complete review on the available liquid-liquid equilibrium experimental data until 1995 is reported by Zaslavsey [3]. During recent years, ATPS has been received more attentions. In Table 1 a considerable

3 Page 3 of 47

part of the published works after 1995 are listed. Besides experimental studies, many attempts have been made on the prediction and correlation of phase partitioning over the past 10 years [4-8].Calculation of phase behavior in ATPS has inherent complexity due to the presence of

ip t

ions and polymers in aqueous solution. Among different methods, empirical equations and models based on local composition theories have been widely used for correlating the binodal

cr

curves as well as tie line compositions[4-8].The aforementioned methods need at least 3 up to

us

12 adjustable parameters. Gao et al. [9, 10] employed UNIFAC and UNIQUAC models for prediction and correlation of phase equilibrium in ATPS. They achieved good results in

an

correlation; however predictions were not satisfactory.

M

UNIQUAC-NRF proposed by Haghtalab and Asadollahi [11] was applied to the polymer– polymer systems. Later Haghtalab and Mokhtarani [12] utilized UNIFAC-NRF with the non-

te

ATPS.

d

random state as reference state then applied it for correlation of liquid-liquid equilibrium in

Ac ce p

NRTL model has been utilized in several studies for correlation of phase behavior in PEGelectrolyte systems [13-18]. As an example Haghtalab and Joda [2] used the modified NRTLNRF for modeling 15 systems containing Na2SO4,(NH4)2SO4,K2HPO4 and PEG. In a different approach, empirical equations with 3 or 4 adjustable parameters have been proposed for calculation of binodal curve as well as tie lines’ compositions[19-25]. Among various equations of state, PHSC has received more attention for modeling polymer solutions during recent years [26, 28-37]. PHSC was originally presented by Song et al.[26] later it was modified and applied to various systems by many authors. Lee and Kim [27] added the association contribution to the PHSC EOS for application in associating fluids. Favari et

4 Page 4 of 47

al.[28] employed the simplified PHSC EOS for VLE, LLE and VLLE calculations in the systems containing polystyrene, cyclohexane and CO2. Doghieri et al. [29] adapted PHSC EOS within non-equilibrium thermodynamics framework to describe the solubility of small

ip t

penetrates in glassy polymers. Fermeglila et al. [30] used the PHSC EOS for evaluating phase behavior of hydrofluorocarbons, hydrocarbons as well as mixture of hydrocarbons and

cr

hydroflurocarbons. Hino et al. [31, 32] studied the screening effect in copolymer binary

us

mixtures. They calculated phase behavior of homo-polymer, copolymer as well as miscibility map (LCST, UCST). Later, Hino and Prausnitz utilized the PHSC EOS to represent the micro

an

phase separation transition in compressible di-block copolymer melts [33]. Ko et al. [34] combined the PHSC EOS with melting point depression theory to describe the phase behavior

M

of copolymer + electrolyte. Gupta and Prausnitz [35]evaluated the capability of this EOS for

d

prediction of phase behavior of polymer solutions in medium pressure range. Fermeglia et

te

al.[36]adapted this equation of state for evaluation of thermodynamic properties of pure hydro fluorocarbons. Chen et al.[37] applied chain referenced perturbed hard sphere EOS to correlate

Ac ce p

liquid-liquid equilibrium of solvent polymer systems. Recently, in our laboratory PHSC EOS has been improved through considering dipole-dipole, dipole- quadarupole and quadarupole quadarupole interactions [38].The modified version was successfully applied for calculating acid gas solubility in ionic liquids.

In this work, in the continuation of the previous researches, the PHSC EOS has been extended for application in polymer electrolyte solutions. The capability of the PHSC EOS in calculation of liquid-liquid equilibrium in ATPS has been examined. For this purpose modified PHSC EOS has been utilized to correlate compositions in two liquid phases for 47 systems using two adjustable parameters for each system. 5 Page 5 of 47

ip t

2. Theory In the PHSC model it is assumed that the molecules are made of chains of jointed tangent hard-

cr

spheres (or segments). This EOS uses the modified Chiew [39] and van der Waals EOSs as the

us

reference and perturbation terms, respectively. Compressibility factor is given by song et

an

al.[26] as follows:

M

Z PHSC ! Z ref ! Z pert

and

!

i, j

xi x j ri rj aij (T )

te

!! kT

Ac ce p

Z pert !

d

where:

Z ref ! 1 ! !

(1)

!

i, j

xi x j ri rj bij (T ) g ij hs ( d ij ) !

!

(2)

xi ( ri ! 1)[ g ij hs ( d ij ) ! 1]

(3)

i

In the above equations , k and r are defined as the number density, Boltzmann constant and the number of effective hard spheres per molecule, respectively. Meanwhile, a(T) reflects the attractive force between non-bonded segments and b(T) is the Van der Waals co-volume (or excluded volume) parameter per segment. These terms are defined by Song et al. [26]. The model parameters are presented in the appendix.

6 Page 6 of 47

Regarding polar substances, such as water and PEG, intermolecular association interactions between free electron pairs on the oxygen atoms, as well as bonding sites on the hydrogen atoms of the OH groups causes non-ideal behaviors. Therefore, it is necessary to consider the

ip t

hydrogen bonding interactions in thermodynamic modeling. In this regard, Lee and Kim [27] added association term to PHSC EOS to consider the hydrogen bonding effects. On the other

cr

hand, in electrolyte solutions, electrostatic interactions between ions should be taken into

us

account. Various theories such as Debye-Hückel, Pitzer-Debye-Hückel (PDH) and Mean Spherical Approximation (MSA) can be utilized for modeling electrostatic interactions between

an

charged particles. Unfortunately, the Debye-Hückel theory is valid just at low electrolyte concentrations, while the MSA theory is applicable in a wide range of concentrations. In this

M

study the restricted primitive MSA model is used to account for long range interactions.

te

Z ! Z PHSC ! Z association ! Z MSA

d

Considering the above facts, the compressibility factor in our model is defined as follows: (4)

Ac ce p

Chapman et al. [40]first extended the Wertheim theory and presented the Helmholtz energy change due to association. The compressibility factor change due to association can be derived using classical thermodynamic relations. The contribution of electrostatic interactions used is presented by Blum [41]. Mean spherical approximation theory (MSA) was applied to solve the Ornstein-Zernike (O.Z) integral equations. In this work, the restricted primitive version of this model for charged hard sphere mixtures has been utilized. In order to avoid repeating the formulas, the equations regarding association and MSA contributions are presented in appendix. 3 Phase equilibrium calculations

7 Page 7 of 47

Phase equilibrium calculations were performed using the equality of chemical potentials in two liquid phases:

! i I ! ! i II

i

II

ip t

! i I and !

(5) are the chemical potentials of component i in the upper and lower phases in ATPS.

cr

Required equations for calculation of chemical potential of PHSC-AS and restricted primitive

us

MSA were given by Shahriari et al. [38] and Lee and Kim [27] ,respectively.

an

In the systems containing polymer components, successive substitution flash calculation

may diverge. Heidemann and Michelsen [42] showed that this kind of instability in

M

successive substitution can occur whenever components in equilibrium show a strong deviation from ideality. They proposed a simple "damping" procedure for adapting K

lnK

j! 1

te

Ac ce p

the following equation:

d

factors (ratio of mole fractions).Koak [43] showed that K factors can be updated using

fi I ! lnK ! mln II fi

j

j

(6)

In the above equation m is the damping factor, introduced to ensure convergence of the procedure. fi is the fugacity of component i in equilibrium phases (I and II) at stage j. In this work, the damping factor for polymer is set to 0.5 and for salt and water is set to 0.005. 4. Results

8 Page 8 of 47

In the original PHSC EOS, three parameters including r ,δ and ε for pure non-associating components must be adjusted using pure thermo physical properties (e.g: density and vapor pressure). In the case of water and PEG, two more parameters must be adjusted ( k AB and !

AB

)

ip t

for considering association contribution. k AB represents volume of association bond and εAB shows association energy between two sites (A and B).Usually two or four hydrogen-bonding

cr

sites can be considered for water. We checked both cases and obtained better results using two

us

association sites on water molecules. Pure component parameters of water are adjusted to vapor pressure and liquid density data in temperature ranges of 283 to 401K. Vapor pressure and

an

liquid density of water have been correlated with 0.6% and 0.16% absolute relative deviation, respectively. The following objective function (OF) is used for calculation of pure water

i

2

! !! ! !

N

!

i

! ! il,calc ! ! il,exp !! ! il,exp !

! !! !

2

d

!

sat ! Pi ,sat calc ! Pi ,exp !! sat Pi ,exp !

(7)

te

OF !

N

M

parameters:

Ac ce p

The pure component parameters of water are listed in Table 2. In the case of polymers, three methods are suggested for calculation of model parameters: 1. fitting to liquid density data of polymers, 2. fitting to vapor pressure and liquid densities of low molecular weight compounds and extrapolation of the obtained parameters to heavy polymers, and 3. Using LLE experimental data of binary mixtures. PEG has two OH groups and two association sites have been considered on each; in overall, four association sites have been considered for PEG. Adjustable parameters have been estimated through fitting to liquid density of PEG600, 1000, 6000 with 0.22%,0.11%,0.21%

9 Page 9 of 47

absolute relative deviation. The following objective function was employed for adjustment of parameters:

!

i

! ! il,calc ! ! il,exp !! ! il,exp !

! !! !

2

ip t

OF !

N

(8)

cr

Estimated parameters of PEGs are presented in Table 1. Salt parameters were adjusted to the

us

mean ionic activity coefficient and liquid densities of aqueous electrolyte solutions. The following objective function was employed for obtaining ion parameters:

i

2

! !! ! !

N

!

i

! ! il,calc ! ! il,exp !! ! il,exp !

! !! !

2

an

!

! ! i ,calc ! ! i ,exp !! ! i ,exp !

(9)

M

OF !

N

In the above equation ! i ,calc and ! i ,exp are the calculated and experimental mean ionic activity

d

coefficient in aqueous electrolyte solution. The pure component parameters of electrolytes are

te

listed in Table 2.

Ac ce p

Binary interaction parameters between water and PEG as well as interaction parameters between salt and PEG have been adjusted using liquid-liquid equilibrium experimental data. These parameters were fitted to mass fraction of components in each phase considering equality of chemical potential for each component in two phases. The following objective function was utilized to correlate the component mass fractions in each phase:

M

OF !

N

! !

j ! 1 i! 1

!w

I ,exp ij

! wijI ,calc !

wijI ,exp

!

!w

II ,exp ij

! wijII ,calc !

wijII ,exp

(10)

In equation (11), wexp represents the experimental mass fraction and wcalc is the calculated mass fraction. M and N are the number of tie lines and components, respectively, and superscripts I 10 Page 10 of 47

and II, represent the two liquid phases in equilibrium. Adjusted binary interaction parameters are introduced in Table 3. Our results show that binary interaction parameter between water and PEG is biased around -0.07. Also in most cases binary interaction parameter between salt

ip t

and PEG is varied in the range of -0.2-0.2. Due to large differences between the size of PEG molecules and salt, binary interaction parameter between these components seems to have a

cr

reasonable value.

us

The ability of the PHSC EOS in correlation of liquid-liquid equilibrium has been checked using Figure 1 shows the algorithm and applied

an

Rachford-Rice flash calculation algorithm.

procedure for calculation of binary interaction parameters. The overall average relative

! !

!w

j ! 1 i! 1

I ,exp ij

! wijI ,calc !

wijI ,exp

!

2MN

!w

! wijII ,calc ! ! ! ! wijII ,exp ! ! ! ! !

II ,exp ij

d

N

te

M

(11)

Ac ce p

! ! ! %! w ! 100 ! ! ! ! !

M

deviation in phase equilibrium calculations is been calculated as below:

In Fig. 2, the binodal curve for PEG1000-(NH4)2SO4-water is depicted. As it can be seen the calculated compositions are in good agreement with the experimental data, also feed composition data seem to have good coincidence with the tie lines. Similar results are observed for other systems, the results are shown in Figs. 2 to 11. In Table 3, the numerical values of errors are presented.

5 .Conclusion

11 Page 11 of 47

In this work PHSC equation of state is used for modeling of ATPS containing polymer and electrolyte. In this regard, PHSC model has been extended to associative as well as electrolyte solutions. In our modification, restricted primitive MSA model is used for considering long

ip t

range electrostatic interactions. In order to check the ability of the model liquid-liquid equilibrium of PEG-salt-water for 47 systems are evaluated. ATPS containing PEG with

cr

various molecular weights (e.g: 400, 600, 1000, 1500, 2000, 3000, 4000) and electrolytes such

us

as sulfate, phosphate, carbonate and citrate are modeled. The results show that the overall average relative deviation is 6.81%. It is worth mentioning that only two adjustable parameters

an

have been used for correlation of LLE. In comparison with activity coefficient models which

Ac ce p

te

d

M

need 3 to 12 adjustable parameters, satisfactory results have been obtained in this work.

12 Page 12 of 47

ip t

Appendix : The attractive force parameter a(T) and the Van der Waals co-volume b(T)are defined by Song

Fa (

kT ) ! ij

Fb (

kT ) ! ij

3 ij

us

2! ! 3

3 ij

(2)

d

2! ! 3

M

and

bij (T ) !

(1)

an

aij (T ) !

cr

et al.[26] as follow:

te

where, ! ij is the segment diameter (in Angstrom) and ! ij is the dispersion energy parameter, Fa(kT/ε) and Fb(kT/ε) are the universal functions and can be calculated using empirical

Ac ce p

equations as below:

Fa (

kT kT kT 2 ) ! 1.8681exp[ ! 0.0691( )] ! 0.6715 exp[ ! 1.7317( ) 3 ] ! ! !

(3)

Fb (

kT kT 1 kT 3 ) ! 0.7303exp[ ! 0.1649( ) 2 ! 0.2697 exp[ ! 2.3973( ) 2 ] ! ! !

(4)

Classical mixing rules have been utilized for segment diameter and dispersion energy of binary mixtures:

13 Page 13 of 47

ij

!

ii

!!

jj

(5)

)

(6)

! ii! jj (1 ! kij )

cr

! ij !

1 (! 2

ip t

!

us

k ij is the adjustable binary interaction parameter. Radial distribution function g ijhs (d ij! ) was given

1 3 ! ij 1 ! ij ! ! 2 1 ! ! 2 (1 ! ! ) 2 (1 ! ! )3

te

Ac ce p

! !

! bib j 13 2/3 ( ) ! xi rb i i 4 bij

d

In the above equation:

! ij !

(7)

M

gij hs (dij ! ) !

an

by Boublick-Mansoori-Carnahan-Starling [44]:

! ! xi rbi i 4

(8)

(9)

Association term

Z associatio n is the contribution of association in compressibility factor which is given by Champan et al. [40] as follows: A

Z

association

! !

!

i

xi !

Ai

1 1 !X j [ A ! ]( ) X 2 !!

(10)

14 Page 14 of 47

X A is defined as the mole fraction of molecules not bonded at site A, it is given as follows,

Ai B j

!

B

xi ! x j !

(11)

]

Bj

ip t

i

Ai B j ! 1

is the association strength and is expressed as:

! g ij hs (dij ! )[exp(

k AB and !

AB

!

Ai B j

KT

) ! 1]!

3 ij

k

cr

Ai B j

!

Ai B j

us

!

! [1 ! !

(12)

are association volume parameter and association energy between two sites A and

an

Aj

X

M

B. The cross association parameters are defined as:

k

Ai B j

!

!

Ai B j

! ! 2

Ai B j

d

!

k

Ai B j

k

Ai B j

[

! i! j 3 ] ! i! ! j ( ) 2

(13)

te

Ai B j

Ac ce p

!

(14)

Mean spherical approximation

The compressibility factor due to long range interactions between charged particles is given as below:

Z MSA ! !

1 ! 3 ! 2 Pn 2 ( ) (Restricted primitive MSA Pn=0) ! 8 ! P 3!

(15)

15 Page 15 of 47

where ! is the shielding parameter and can be calculated using following formula: 1 ( 1 ! 2! k ! 1) 2!

(16)

ip t

! !

e2 D kTv

!

xi z i 2

ion

(17)

us

k2 !

cr

Where:

In above equation, e is electron charge, zi is charge of ion. Also v represents summation of

an

stochiometric coefficients of ions. D is dielectric constant of solution and can be obtained from

xs Mws Ds

!

xs Mws s

d

s

(18)

te

D!

!

M

following equation [45]:

Ac ce p

In this work, PEG has been considered as pseudo-solvent. For PEG, a Dielectric constant of Dp=2.2 has been considered [46]. Also, dielectric constant of water is considered as function of temperature [84].

Dw ! 281 .67 ! 1.912T ! .0016644 T 2 ! 0.0000009592 T 3

(19)

16 Page 16 of 47

ip t

NOMENCLATURE

a(T): Attractive term

cr

b(T):Van der waals co volume

us

Fa (kT/ε): Universal function for a(T) term Fb (kT/ε): Universal function for b(T) term Radical distribution function

an

g ijhs (d ij! ) :

D=Dielectric constant

M

k:Boltzman constant

m: Damping factor

te

Kij: Binary interaction parameter

d

K: Mole fraction ratio in two phases

Ac ce p

M : Number of association sites on the molecule Mw: Molecular weight of water N : Total number of molecules P : Pressure

r:Segment number R : Gas constant

T : Absolute temperature v : Phase ratio of higher phase (

Lupperphase) ) F

V : Total volume wi: Weight fraction of component i 17 Page 17 of 47

XA : Mole fraction of the compound not bonded at the associating site A xi : Mole fraction of component i Z : Compressibility factor

! ij : Dispersion energy parameter AB

k AB

: Energy parameter of the association between sites A and B : Volume parameter of the association between sites A and B

: Segment diameter

M

ij

an

ρ: Number density (number of molecules in unit volume) !

us

!

cr

ip t

Greek Letters

fi: Fugacity of component i

Ac ce p

te

d

µi: Chemical potential of component i

18 Page 18 of 47

References

ip t

[1] P.A.Albertsson, Partition of Cell Particles and Macromolecules, 2rd ed.,Interscience/Wiley,1971. A.Haghtalab, M. Joda, Fluid Phase Equilib. 278(2009) 20-26.

[3]

B.Y.Zaslavsky,. Marcel Dekker, NewYork, (1995).

[4]

M.T.Zafarani-Moattar, R. Sadeghi. J. Chem. Eng. Data 49(2003) 297-300.

[5]

M.T.Zafarani-Moattar, J. Gasemi, Fluid Phase Equilib. 198(2002) 281-291.

[6]

M.T.Zafarani-Moattar, R. Sadeghi, A.A. Hamidi, Fluid Phase Equilib.219(2004)149-

an

us

cr

[2]

M

155.

M.T. Zafarani-Moattar, R. Sadeghi, Fluid Phase Equilib. 181(2001) 95-112.

[8]

K.Mishima, K.Nakatani,T.Nomiyama,K.Matsuyama,H.Nishigata, Fluid Phase Equilib.

Ac ce p

107(1995) 269-276.

te

d

[7]

[9]

Y.-L.Gao, Q.-H.Peng,Z.-C.-Li,Y.-G.Li, Fluid Phase Equilib. 63(1991)157-171.

[10]

Y.-L.Gao, Q.-H.Peng,Z.-C.-Li,Y.-G.Li, Fluid Phase Equilib. 63(1991)173-182.

[11]

A.Haghtalab, M.A.Asadolahi,Fluid Phase Equilib. 171 (2000)77–99.

[12]

A. Haghtalab, B. Mokhtarani, Fluid Phase Equilib. 180(2001) 139-149.

[13]

E.V.C.Cunha, M.N. Aznar, J. Chem. Eng. Data 54 (2009) 3242-3246.

[14]

R.A.G.Sé, , M. Aznar, J. Chem. Eng. Data 47 ( 2002) 1401-1405.

[15]

T.A. Graber, M.E. Gálvez, H.R. Galleguillos, J. Álvarez-Benedí, J. Chem. Eng. Data 49(2004)1661-1664. 19 Page 19 of 47

[16]

J.o.P. Martins, J.S.d.R. Coimbra, F.O.C. de Oliveira, G. Sanaiotti, C.s.A.S. da Silva, L.H.M. da Silva, M.d.C.H. da Silva, J. Chem. Eng. Data55(2009) 1247-1251. Aznar, Brazilian J. Chem. Eng.22(2005)463-470.

[18]

Y.-T. Wu, Z.-Q. Zhu, D.-Q. Lin, M. Li, Fluid Phase Equilib. 154(1999)109-122.

[19]

T. Murugesan, M. Perumalsamy, J. Chem. Eng. Data 50 (2005)1392-1395.

[20]

S.P. Amaresh, S. Murugesan, I. Regupathi, T. Murugesan,J. Chem. Eng. Data 53(2008)

cr

us

an

1574-1578.

M.E. Taboada, O.A. Rocha, T.A. Graber, B.A. Andrews,J. Chem. Eng. Data 46

M

[21]

ip t

[17]

T.A. Graber, M.E. Taboada, A. Cartón, S. Bolado,J. Chem. Eng. Data 45 (2000)182-184.

[23]

B. Ma, M. Hu, S. Li, Y. Jiang, Z. Liu,J. Chem. Eng. Data 50(2005) 792-795.

[24] [25]

te

d

[22]

Ac ce p

(2001)308-311.

L.P. Malpiedi, C. Fernández, G. Picó, B. NerliJ. Chem. Eng. Data 53(2008) 1175-1178.

P. González-Tello, F. Camacho, G. Blázquez, F.J. Alarcón,J. Chem. Eng. Data 41(1996)1333-1336.

[26]

Y.Song, S.M. Lambert, J.M. Prausnitz, Ind. Eng. Chem. Res. 33(1994) 1047-1057.

[27]

B.S. Lee, K.C. Kim, Korean J. Chem. Eng. 24 (2007) 133–147.

[28]

F.Favari, A. Bertucco, N. Elvassore, M. Fermeglia ,Chem. Eng. Sci. 55(2000) 2379-2392.

20 Page 20 of 47

[29]

F.Doghieri, M.G.D. Angelis, M.G. Baschetti , G.C. Sarti, Fluid Phase Equilib. 241(2006) 300-307. M.Fermeglia, A. Bertucco, S. Bruni, Chem. Eng. Sci. 53 ( 1998)3117-3128.

[31]

T.Hino, Y. Song, J.M. Prausnitz, Macromol. 28(1995)5709-5716.

[32]

T.Hino, Y. Song, J.M. Prausnitz,Macromol. 28(1995)5717-5724.

[33]

T.Hino, J.M. Prausnitz, Macromol. 31(1998) 2636-2648.

[34]

S.J.Ko, Elect. Acta 49(2004) 461-468.

[35]

R.B.Gupta, J.M. Prausnitz, Ind. Eng.Chem. Res. 35 (1996)1225-1230.

[36]

M.Fermeglia, A. Bertucco, D. Patrizio,Chem. Eng. Sci. 52 (1997)1517-1527.

[37]

X.Chen, Fluid Phase Equilib. 237(2005) 162-169.

[38]

R.Shahriari, M.R. Dehghani, B. Behzadi,Fluid Phase Equilib. 313(2012) 60-72.

[39]

Y.C.Chiew, Mol. Phys. 70 (1990)129-143.

[40].

W.G.Chapman, , K.E.Gubbins,, G.Jackson,M.Radosz, Ind. Eng. Chem. Res. 29(1990) 1709-1721.

[41]

L.Blum, J. Chem. Phys. 61 (1974) 2129-2136.

[42]

R.A.Heidemann, M.L. Michelsen, Ind. Eng. Chem. Res.34(1995) 958-966.

[43]

N.Koak, Some computational and experimental aspects of polymer solution phase

Ac ce p

te

d

M

an

us

cr

ip t

[30]

behavior. Phd thesis ,Calgary,Alberta, 1997. [44]

G.A. Mansoori, N.F.Carnahan, K.E. Starling, T.W. Leland, J. Chem. Phys. 54 (1971)

1523-1525.

21 Page 21 of 47

[45]

Y. Song , C.-C.Chen, Ind. Eng. Chem. Res., 48 (2009) 7788-7797.

[46]

M.T.Zafarani-Moattar , S. Hamzehzadeh, S. Hosseinzadeh, Fluid Phase Equilib.

ip t

268(2008)142-152.

A. Haghtalab, B. Mokhtarani, Fluid Phase Equilib. 215(2004) 151-161.

[48]

J.O.P. Martins, F.o.C. de Oliveira, J.S.l. dos Reis Coimbra, L.H.M. da Silva, M.d.C.H. da

cr

[47]

us

Silva, I.S.B. do Nascimento, J. Chem. Eng. Data 53(2008) 2441-2443.

J.G.Huddleston, H.D. Willauer, R.D. Rogers,J. Chem. Eng. Data 48 (2003) 1230-1236.

[50]

M.Perumalsamy, T. Murugesan, Fluid Phase Equilib. 244 (2006)52-61.

[51]

I.Regupathi, C.K. Srikanth, N. Sindhu, J. Chem. Eng. Data 56(2011)3643-3650.

[52]

M.Jayapal, I. Regupathi, T. Murugesan, J. Chem. Eng. Data 5 (2006)56-59.

[53]

R.M. de Oliveira, J.S.d.R. Coimbra, K.R. Francisco, L.A. Minim, L.H.M. da Silva,

Ac ce p

te

d

M

an

[49]

J.A.M. Pereira, J. Chem. Eng. Data 53( 2008) 919-922. [54]

M.E. Taboada, H.R. Galleguillos, T.A. Graber, S. Bolado, J. Chem. Eng. Data 50 (2004)264-269.

[55]

T.A. Graber, M.E. Taboada, J.A. Asenjo, B.A. Andrews, J. Chem. Eng. Data 46 (2001) 765-768.

[56]

C.P. Carvalho, J.S.R. Coimbra, I.A.F. Costa, L.A. Minim, L.H.M. Silva, M.C. Maffia., J. Chem. Eng. Data 52(2007)351-356.

22 Page 22 of 47

[57]

I. Regupathi, S. Murugesan, R. Govindarajan, S.P. Amaresh, M. Thanapalan, J. Chem. Eng. Data 54 (2009)1094-1097. J.O.P. Martins, F.o.C. de Oliveira, J.S.l. dos Reis Coimbra, L.H.M. da Silva, M.d.C.H. da

ip t

[58]

Silva, I.S.B. do Nascimento, J. Chem. Eng. Data 53(2008) 2441-2443. B.D.C.a.M. Aznar, Brazilian J. Chem. Eng. 22(2005) 464-470.

[60]

L.A. Ferreira, J.A. Teixeira, J. Chem. Eng. Data, 56 (2010) 133-137.

[61]

S.Alireza, Calphad30(2006) 296-300.

[62]

L.H.M.d.Silva, J.S.R. Coimbra, and A.J.d.A. Meirelles, J. Chem. Eng. Data 42(1997)

an

us

cr

[59]

398-401.

M.E.Taboada, J.A. Asenjo, and B.A. Andrews,Fluid Phase Equilib. 180 (2001) 273-280.

[64]

R. Azimaie, G.R.P. , V.T. , M. Vossoughi, C. Ghotbi, Phys. Chem. Liq. 48(2010) 764-

te

772.

d

M

[63]

C.P. Carvalho, I. A. F. Costa, L. A. Minim, M.Cristina,Quim. Nova. 31(2008) 209-213.

[66]

K. S. Nascimento, A. M. Azevedo, B. S. Cavada, M.R. Aires-Barros, Sep. Sci.Tech.

Ac ce p

[65]

45(2010) 2180-2186. [67]

M.van Berlo, K.C.A.M. Luyben, L.A.M. van der Wielen, J. Chrom. B: Bio. Sci. Appl. 711(1998) 61-68.

[68]

J.G.L.F. Alves, J. Brenneisen, L. Ninni, A.J.A. Meirelles, G. Maurer, J. Chem. Eng. Data 53(2008) 1587-1594.

[69]

M.T.Zafarani-Moattar, A.A. Hamidi,J. Chem. Eng. Data 48(2003) 262-265.

23 Page 23 of 47

M. Hu, Q. Zhai, Y. Jiang, L. Jin, Z. Lin,J. Chem. Eng. Data 49 (2004) 1440-1443.

[71]

M.Perumalsamy, A. Bathmalakshmi, T. Murugesan, J. Chem. Eng. Data52(2007) 11861188.

ip t

[70]

M.T.Zafarani-Moattar, S.Hamzehzadeh,Calphad 29 (2005) 1-6.

[73]

G. Tubío, L. Pellegrini, B.B. Nerli, G.A. Picó,,J. Chem. Eng. Data 51(2005) 209-212.

[74]

H.Rasa, M. Mohsen-Nia, and H. Modarress, J.Chem. Therm. 40(2008) 573-579.

[75]

M.Mohsen-Nia, H. Rasa, H. Modarress,J. Chem. Eng. Data 53(2008) 946-949.

[76]

J.M.Smith, H.C.Vanness , M.M.Abbott, Introduction to chemical engineering

M

an

us

cr

[72]

[78] [79]

Y.Tsujita, T.Nose, T.Hata, Polymer J. (1973) 5, 201-208.

Ac ce p

[77]

te

d

thermodynamics. McGraw-Hill, (2005).

P.a.O.S. Novonty, Amer. Chem. Soc. 33 (1988) 58-63.

A.Robinson, H.Stockes, Electrolyte Solutions. 2nd ed.,London Butterworth,London, (1965).

[80]

N.Voros, P. Proust, A. Fredenslund, Fluid Phase Equilib. 90(1993) 333-353.

[81]

S.M.Snyder, K.D. Cole, D.C. Szlag,J. Chem. Eng. Data 37(1992) 268-274.

[82]

S.Hammer, A. Pfennig, M. Stumpf, J. Chem. Eng. Data 39 (1994) 409-413.

24 Page 24 of 47

[83]

R.M. de Oliveira, J.S.d.R. Coimbra, L.A. Minim, L.H.M. da Silva, M.P. Ferreira Fontes,J. Chem. Eng. Data 53 (2008) 895-899.

te

d

M

an

us

cr

ip t

B.S. Lee, K.C. Kim, Korean J. Chem. Eng. 26 (2009) 1733–1747.

Ac ce p

[84]

25 Page 25 of 47

Table1

PEG MW

Salt

Haghtalab and

1500 ,4000

Na2SO4,K2HPO4

4000

Na2 C4H4O6

Zafarani-Moattar et

8000

Na2SO4,MgSO4

1500

Li2SO4,Na2SO4,MgSO4

M

Anzar(2009)

al(2003)

Perumalsamy and

298.15,308

[46]

3400

298.15,323

[13]

305.65,278

[48]

313.15

te

1000,2000,

Ac ce p

Huddleston et

[47]

283.15,298,

d

Martins et al(2008)

298.15

,318.15

an

al(2008) Chunha and

Ref.

us

Mokhtarani(2004)

T (K)

cr

Author

ip t

Reported experimental data on PEG-salt-water systems after 1995

K3PO4,K2CO3,(NH4)2S

298.15

[49]

O4,Li2SO4,ZnSO4,MnS O4,NaOH

2000

Na3C3H5O(COO)3

298,308,318

[50]

2000

NH4 C3H5O(COO)3

298.15,303.1

[51]

Murugesan(2006)

Regupathi et al(2011)

5,308.15,313. 15,318.15 Jayapal et al(2007)

2000

K3 C3H5O(COO)3

298.15,308.1

[52]

26 Page 26 of 47

5,318.15 Murugesan and

2000

Na3 C3H5O(COO)3

Perumalsamy(2005)

313, 318 4000

ZnSO4

283,288,308,

al(2008)

[53]

318

K2HPO4

4000

283,288,293,

cr

Se and Aznar(2002)

[19]

ip t

De Oliveira et

298,303,308,

[14]

(NH4)2HPO4

an

4000

298,303,308,

[20]

318

4000

KCl,NaCl

298,303

[54]

Graber et al(2004)

4000

Li2SO4

278,298,318

[15]

Taboada et al(2001)

4000

Na2SO4

298

[21]

Graber et al(2001)

4000

NaNO3

298

[55]

Martins et al(2009)

400

Na2SO4,MgSO4

298,308,318

[16]

4000

Li2SO4,Na2SO4,K2HP4

278,298,308,

[56]

d

Ac ce p

Carvalho et al(2007)

M

Taboada et al(2005)

te

Amaresh et al(2008)

us

303

Regupathi et al(2009)

Zafarani-Moattar and

6000

318 NH4 C3H5O(COO)3

298,303,308,

[57]

313,318

6000

NaOH

298,308,318

[4]

6000

(NH4)2HPO4,

298,308,318

[7]

298,308,318

[6]

Sadeghi(2003) Zafarani-Moattar and Gasemi(2001) Zafarani-Moattar et

NH4H2PO4 6000

Na3 C3H5O(COO)3

27 Page 27 of 47

al(2004) Martins et al(2008)

6000

Li2SO4,Na2SO4,MgSO4,

283,298,313

[58]

308

[59]

296

[60]

298,308,318

[23]

298

[61]

298,308,318

[7]

K2HPO4

277,298,313

[62]

Na3 C3H5O(COO)3

278,283,288,

[53]

ZnSO4 8000

MgSO4

8000

Na2SO4

Ma et al(2005)

400,1000

Cs2CO3

Salabat(2006)

1000,6000

Na2SO4,K2HPO4,

ip t

Castro and

Ferreira and

cr

Aznar(2005)

an

us

Teixeira(2011)

(NH4)2SO4 1000,6000

d

Sadeghi(2001)

Na2HPO4,NaH2PO4

M

Zafarani-Moattar and

8000,10000

De Oliveira et

1500,4000

al(2008)

te

Silva et al(1997)

Taboada et al(2001)

4000

Na2CO3

298

[63]

2000,6000,

NaNO3

298

[55]

Ac ce p

298,308,318

Graber et al(2001)

10000

Azimaie et al(2010)

1500

MgSO4

308,313,318

[64]

Carvalho et al(2008)

1500

Na3C3H5O(COO)3,

278,298,308.

[65]

K2HPO4

318

Na3 C3H5O(COO)3

298

Nascimentoet

600

[66]

al(2010)

28 Page 28 of 47

Van Berlo et al(1998)

2000,4000,

NH4NH2CO3

298

[67]

Na3 C3H5O(COO)3

298

[68]

Alves et al(2008)

600,1500,3 000

Malpiedi et al(2008)

600,1000,2

Na2C4H4O6

8000

8000

Zaffarani-Moattar and

6000

Perumalsamyetal

6000

Ac ce p

(2007)

Zaffarani-Moattar and

298

[69]

Cs2SO4

298,308,318

[70]

Na3 C3H5O(COO)3

293,303,313

[71]

Na(HCOO)

298

[72]

Na3 C3H5O(COO)3

295,310,323

[73]

MgSO4

295,301,305,

[74]

d

4000

te

Hu et al(2004)

[25]

K3C3H5O(COO)3

Hamidi(2003)

6000

[24]

298

M

al(1996)

MgSO4

an

1000,3350,

us

000,

Gonzalez-Telloet

298

cr

000,4000,6

ip t

1000

,NaC4H6O4

Hamzehzadeh(2005) Tubio et al(2006)

600,1000,1 450,3350, 8000

Rasa et al(2008)

10000

311

29 Page 29 of 47

Mohsen-Niaet

20000

CuSO4

290,299,308, 317

ip t

al(2008)

[75]

Table2

! /k

k AB

!

AB

/k

Ref.

an

!

us

r

450.82

1247.38

0.03766

[76]

426.05

1928.58

0.00395

[77]

749.18

-

-

[78, 79]

4.9657

1810.48

-

-

[78, 79]

d

Component

cr

Pure component parameters used in this work

1837.66

-

-

[78, 79]

3.6716

749.18

-

-

[78, 79]

4.0847

1932.97

-

-

[78, 79]

1

4.2139

1840.59

-

-

[78, 79]

1

3.6851

1031.28

-

-

[78, 79]

1

3.8923

1011.80

-

-

[78, 79]

1

3.5191

1117.96

-

-

[78, 79]

Na3 C3H5O(COO)3

1

6.2293

790.92

-

-

[78, 79]

Na2CO3

1

3.9899

1890

-

-

[78, 79]

1.6384

2.8921

PEG

0.0144Mw

4.7997

(NH4)2SO4

1

3.2171

MgSO4

1

Na2SO4

1

K2HPO4

1

Li2SO4

1

ZnSO4 NaCl NaNO3

te

3.8921

Ac ce p

K3PO4

M

Water

30 Page 30 of 47

Table3 Binary interaction parameters and overall relative deviation obtained in this study for ATPS

PEG

kwater-PEG

ksalt-PEG

T(K)

1000

-0.0709

0.1557

298

1540

-0.0714

0.1503

2000

-0.0733

0.1675

4000

-0.0726

0.1292

1000

-0.0753

1000

-0.0722

M

Salt

1000 1000

Na2SO4

298

1.53

[9]

298

0.67

[9]

298

8.13

[9]

0.1833

288

10.1

[80]

0.1914

298

6.19

[80]

-0.0688

0.2065

308

7.38

[80]

-0.0669

0.2002

318

6.95

[80]

-0.0753

0.1661

288

3.60

[80]

d

an

us

[9]

Ac ce p

2000

0.5

te

(NH4)2SO4

%! w Ref.

cr

MW

ip t

systems.

2000

-0.0683

0.1777

308

3.83

[80]

2000

-0.0657

0.2201

318

6.83

[80]

1500

-0.0782

-0.1896

298

13.4

[58]

1500

-0.0698

-0.2257

298

0.66

[47]

400

-0.0665

-0.2047

298

0.84

[16]

1000

-0.0712

-0.1963

298

3.44

[81]

1500

-0.0664

-0.2177

298

8.87

[58]

400

-0.0634

-0.2004

308

0.75

[16]

31 Page 31 of 47

0.14

[16]

3000

-0.0822

-0.1782

293

10.7

[82]

4000

-0.0768

-0.2034

298

8.41

[47]

1500

-0.0709

0.2055

298

2.44

[47]

4000

-0.0734

0.1877

298

5.56

[47]

1000

-0.0851

0.2523

277(pH=7)

8.91

[62]

1000

-0.0821

0.2904

298(pH=7)

10.5

[62]

1000

-0.0712

0.2125

277(pH=9)

[62]

400

-0.1112

-0.0629

us

2.79

298

5.23

[16]

400

-0.1119

-0.0441

308

8.76

[16]

1000

-0.1071

-0.0862

298

5.84

[81]

1500

-0.0765

-0.2994

283

9.42

[58]

1500

-0.0725

-0.2890

298

14.8

[58]

-0.0699

-0.2704

313

17.1

[58]

-0.0698

-0.2889

298

7.85

[49]

2000

-0.0808

0.1052

298

7.51

[49]

2000

-0.0696

-0.1802

298

4.22

[55]

1500

-0.0850

-0.1932

298

6.25

[65]

1500

-0.0723

0.1797

318

10.4

[83]

1500

-0.0721

0.1817

308

4.55

[83]

600

-0.0565

0.1463

298(pH=6)

4.93

[66]

600

-0.0578

0.1487

298(pH=8)

1.l6

[66]

1000

-0.0584

0.1037

288

5.18

[80]

1500

ZnSO4 NaNO3 K3PO4

Ac ce p

2000

Na3 C3H5O(COO)3

an

cr

ip t

318

M

Li2SO4

-0.1973

d

MgSO4

-0.0612

te

K2HPO4

400

32 Page 32 of 47

298

19.1

[83]

1000

-0.0713

-0.2232

288

7.24

[80]

1000

-0.0676

-0.2211

298

9.15

[80]

1000

-0.0642

-0.2236

308

5.69

[80]

1000

-0.0614

-0.2169

318

6.52

[80]

4000

-0.0753

-0.0810

313

9.81

[54]

cr

ip t

0.1515

an M d te Ac ce p

NaCl

-0.07812

us

Na2CO3

4000

33 Page 33 of 47

Figure Captions

ip t

Figure 1. Rachford-Rice algorithm and procedure to calculate binary interaction parameters. Figure 2. Binodal curve for (NH4)2SO4+PEG1000 system at 298K. Dashed lines are tie line

cr

compositions and solid line is calculated binodal curve. (○): experimental data [9], (□): feed

us

compositions.

Figure 3. Binodal curve for (NH4)2SO4+PEG1540 system at 298K. Dashed lines are tie line

an

compositions and solid line is calculated binodal curve. (○): experimental data [9], (□): feed

M

compositions.

Figure 4. Binodal curve for (NH4)2SO4+PEG2000 system at 298K. Dashed lines are tie line

te

compositions.

d

compositions and solid line is calculated binodal curve. (○): experimental data [9], (□): feed

Ac ce p

Figure 5. Binodal curve for (NH4)2SO4+PEG4000 system at 298K. Dashed lines are tie line compositions and solid line is calculated binodal curve. (○): experimental data [9], (□): feed compositions.

Figure 6. Binodal curve for Na3C3H5O(COO)3+PEG600 system at 298K. Dashed lines are tie line compositions and solid line is calculated binodal curve. (○): experimental data[66] , (□): feed compositions. Figure 7. Binodal curve for Na3C3H5O(COO)3+ PEG1500 system at 298K. Dashed lines are tie line compositions and solid line is calculated binodal curve. (○): experimental data [83], (□): feed compositions. 34 Page 34 of 47

Figure 8. Binodal curve for MgSO4+PEG400 at 298K. Dashed lines are tie line compositions and solid line is calculated binodal curve. (○): experimental data[48] , (□): feed compositions.

ip t

Figure 9. Binodal curve for Li2SO4+PEG1500. At 283K. Dashed lines are tie line compositions and solid line is calculated binodal curve. (○): experimental data[48] , (□): feed compositions.

cr

Figure 10. Binodal curve for Li2SO4 + PEG2000. At 298 K . Dashed lines are tie line

us

compositions and solid line is calculated binodal curve. (○): experimental data[48] , (□): feed compositions.

K2HPO4+PEG4000 at 298K .Dashed lines are tie line

an

Figure 11. Binodal curve for

compositions and solid line is calculated binodal curve. (○): experimental data [47] , (□): feed

Ac ce p

te

d

M

compositions.

35 Page 35 of 47

Figure 1

ip t

Input: T,P ,Zi , initial guess for Ki, kij (interaction parameters)

cr

Calculate phase ratio using:

us

z i ( K i ! 1) ! 0 1 ! v ( K i ! 1)

!

zi K i 1 ! v(Ki ! 1)

No

te

d

xiII !

Modification by optimization procedure

M

zi xiI ! 1 ! v( K i ! 1)

an

Calculate mole fractions in each phase:

Is this criteria implemented?

Ac ce p

! iI

Is OF minimum?

!

1!

i

! iII

Yes

!!?

M

OF !

N

! !

j! 1 i! 1

!w

! wijI ,calc !

I ,exp ij

I ,exp ij

w

!

!w

! wijII ,calc !

II ,exp ij

II ,exp ij

w

No

Yes

Modify K:

LnK

j! 1

fI ! LnK ! mLn iII fi

j

Output:

j

Mass fractions

36 Page 36 of 47

Figure 2

ip t

0.35

0.3

cr

0.25

us

0.2

0.15

an

0.1

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Ac ce p

te

d

0 0.06

M

0.05

37 Page 37 of 47

ip t

Figure 3

0.35

cr

0.3

us

0.25

0.2

an

0.15

0.1

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Ac ce p

te

d

0 0.04

M

0.05

38 Page 38 of 47

cr

ip t

Figure 4

us

0.35

an

0.3

M

0.25

0.2

d

0.15

te

0.1

Ac ce p

0.05

0 0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

39 Page 39 of 47

Figure 5

ip t

30

cr

25

us

20

an

15

10

6

8

10

d

4

12

14

16

Ac ce p

te

0

M

5

40 Page 40 of 47

ip t

Figure 6

0.45

cr

0.4

us

0.35 0.3

an

0.25 0.2

M

0.15 0.1

0.05

te

0

0.1

0.15

0.2

0.25

0.3

0.35

Ac ce p

0

d

0.05

41 Page 41 of 47

cr

ip t

Figure 7

us

45 40

an

35 30

M

25 20

te

d

15 10

Ac ce p

5 0

0

5

10

15

20

25

30

35

42 Page 42 of 47

Figure 8

ip t

0.4

cr

0.35

us

0.3 0.25

an

0.2 0.15

M

0.1

0.05

0.1

te

0

0.15

0.2

0.25

Ac ce p

0

d

0.05

43 Page 43 of 47

Figure 9

ip t

0.5 0.45

cr

0.4

us

0.35 0.3

an

0.25 0.2

M

0.15 0.1

0.05

0.1

te

0

0.15

0.2

0.25

Ac ce p

0

d

0.05

44 Page 44 of 47

cr

ip t

Figure 10

us

0.4 0.35

an

0.3

M

0.25 0.2

d

0.15

te

0.1

Ac ce p

0.05 0 0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

45 Page 45 of 47

Figure 11

ip t

0.35

0.3

cr

0.25

us

0.2

an

0.15

0.1

0.06

0.08

0.1

d

0.04

0.12

0.14

0.16

0.18

Ac ce p

te

0 0.02

M

0.05

46 Page 46 of 47

High lights

Ac ce p

te

d

M

an

us

cr

ip t

! PHSC EOS have been used for correlation of LLE in aqueous two phase systems. ! Mean spherical approximation theory has been couple with PHSC model. ! 47 polymer-electrolyte systems have been modelled in this work.

47 Page 47 of 47