phosphate potassium salt-based aqueous two phase systems

Journal Pre-proofs Equilibrium data and thermodynamic studies of L-tryptophanpartitionin alcohol / phosphate potassium salt-based aqueous two phasesystems Seyyed Mohammad Arzideh, Kamyar Movagharnejad, Mohsen Pirdashti PII: DOI: Reference:

S0021-9614(19)30733-5 https://doi.org/10.1016/j.jct.2020.106048 YJCHT 106048

To appear in:

J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

17 August 2019 2 January 2020 3 January 2020

Please cite this article as: S. Mohammad Arzideh, K. Movagharnejad, M. Pirdashti, Equilibrium data and thermodynamic studies of L-tryptophanpartitionin alcohol / phosphate potassium salt-based aqueous two phasesystems, J. Chem. Thermodynamics (2020), doi: https://doi.org/10.1016/j.jct.2020.106048

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Equilibrium data and thermodynamic studies of L-tryptophan partition in alcohol / phosphate potassium salt-based aqueous two phase systems

Seyyed Mohammad Arzideh Faculty of Chemical Engineering, Babol University of Technology, PO Box, 484, Babol, Iran Email: [email protected]

Kamyar Movagharnejad Faculty of Chemical Engineering, Babol University of Technology, PO Box, 484, Babol, Iran Email: [email protected]

Mohsen Pirdashti1 Chemical Engineering Department, Faculty of Engineering, Shomal University, PO Box 731, Amol, Mazandaran, Iran Email: [email protected]

1

Corresponding Author

Equilibrium data and thermodynamic studies of L-tryptophan partition in alcohol / phosphate potassium salt-based aqueous two phase systems

Abstract Experimental phase diagrams for {1-butanol/2-butanol/t-butyl alcohol+ potassium hydrogen phosphate (K2HPO4) + water} at 298.15 K have been determined, and their ability to separate an amino acid, L-Tryptophan, were measured. An excess Gibbs energy model has been proposed for modelling of aqueous two-phase systems (ATPS) containing light straight/branched alcohol, K2HPO4, and water. The hybrid ion-interaction and solvation model (HIS) was implemented to calculate the long-range ion-ion and middle-range ion-solvent interactions, and the UNIQUAC model was used for the short-range solvent-solvent interactions. The continuum characteristics such as density, dielectric constant, and solvation parameters were considered as mixed-solvent property dependent correlations. The proposed excess Gibbs energy model, HIS-UNIQUAC, has been found to describe the LLE data in a satisfactory precision of less than 0.331% for mass percent of experimental data. Moreover, the partitioning coefficient shows a perfect correlation (R2>0.982) with the long and middle range term of excess Gibbs energy model.

Keywords: Liquid–liquid equilibria; Separation; HIS-UNIQUAC model; Alcohols; K2HPO4; LTryptophan.

1. Introduction The knowledge of the thermodynamic behaviour of electrolyte solutions associated with mixed solvent especially alcohol-salt ATPSs (Aqueous two-phase systems) is of interest in many biological and environmental processes such as enzymes separation [1, 2], enantiomer separation [3], human antibodies' purification [4] and bio-product treatment [5]. Prediction of mean ionic activity in a mixed solvent electrolyte solutions of the biphasic system is required to have a reliable model in the wide range of solvent properties, salt concentrations, and temperatures. Recently, several pieces of researches have been done to model the ionic activity of mixed solvent electrolyte solutions [6-24].Most of them separate the excess Gibbs energy into three terms: the long-range interaction of species in response of electrostatic attractions, the middle range solute-solute or solute-solvent interactions, and the short-range solventsolvent interaction including a thermal and residual part. The Pitzer-Debye-Huckle (PDH) model included Debye-Huckle electrostatic interaction term and ion-ion middle range interaction was used successfully to predict the ionic activity of salt in mixed solvent solution in a wide range of ionic strength and mixed solvent properties [12, 19, 22]. The Coupled PitzerDebye-Huckle contribution of long-range ion-ion interaction and short-range ion-solvent interaction of the solvation effect were implemented as a three-characteristic model to electrolyte solutions with a versatile mixed solvent physical property [18, 25]. In these researches, the ion-ion and ion-solvent interaction account in the function of a physical property of water-co-solvent mixture like density, viscosity, dielectric constant. On the other side, the local composition model concurrently equipped with electrostatic contribution and ion-interaction models. Li et al. [7] calculated the excess Gibbs energy as the sum of Debye-Huckle theory, UNIQUAC short-range effects, and a contribution include the indirect impact of the charge interactions, e.g., the charge-dipole interactions and the charge-induced dipole interactions. Later, many studies performed using this model as modified LIQUAC [14], generalized LIQUAC [16], and revised LIQUAC [20]. Recently, solvent composition dependence and born contribution were considered an aid to improve the newest form of UNIQUAC models [10, 17]. The knowledge about the impact of mixed solvent property on the ion-ion, ion-solvent, and solventsolvent interaction in ATPS of K2HPO4 + straight and branch light alcohols is vital for much biological and environmental process design. Although, as a complete survey in the literature, Katayama et al. presented LLE data for ATPS of K2HPO4 with methanol, ethanol, 1-propanol, and 2-propanol in three different temperatures [26, 27], until now, the phase equilibrium data of straight and branch butanol in the aqueous solution of K2HPO4 has not reported. Consequently, in the present study, the experimental phase equilibrium of (water + 1-butanol/2-butanol/tbutyl alcohol + K2HPO4) in 298.15 K was investigated. Also, separation of L-Tryptophan was done in these systems, and the final pH and partition factor are reported. The proposed excess Gibbs energy

model (HIS-UNIQUAC) included in an original UNIQUAC term, the solvent property dependent PitzerDebye-Huckle contribution, born term, and an Ion-solvation short-range term. It was applied to describe the effect of mixed solvent characteristics of {water + light alcohol (methanol to butyl alcohol)} system. Finally, the impact of long-range, middle-range, and short-range of the excess Gibbs energy model on the partitioning coefficient of amino acid in all three orders is discussed.

2. Materials and methods 2.1. Materials To prepare the materials, we used 1-butanol, 2-butanol, tert-butanol, and potassium hydrogen phosphate (K2HPO4) with no further purification. The amino acid studied, L-tryptophan (Trp), was used without further purification. Distilled deionized water (conductivity= 0.056 μS∙cm-1) was used for the preparation of solutions. All the other materials had an analytical grade. The chemical name, CAS number (CAS), supplier, purification method, and purity are shown in Table 1.

Table 1. Source and purity of chemical reagents used in this work Chemical Name

CAS no.

Source

Mass Fraction Purity a

1-butanol

71-36-3

Sigma-Aldrich

≥ 0.998

2-butanol

78-92-2

Sigma-Aldrich

≥ 0.998

2-methyl-2-propanol

75-65-0

Sigma-Aldrich

≥ 0.995

7758-11-4

Merck

≥ 0.990

73-22-3

Merck

≥ 0.990

7732-18-5

-

-

potassium phosphate dibasic l-tryptophan distillated water a

Purity stated by the manufacturer

2.2. Methods 2.2.1 Determination of phase diagrams The cloud-point titration method [28] was implemented to determine the binodal curves. All the apparatus and equipment used in this study were substantially similar to our previous work [28-30]. From the literature, there are two distinct aqueous and organic binodal curves for 1-butanol [17, 31, 32] and 2butanol [31, 33, 34], and there is a single binodal curve for 2-methyl-2-propanol [31, 33]. Thus we draw precisely all diagram phases. Due to determining the aqueous binodal curve, a known amount (10 g) of stock of 1-butanol (7wt%), 2-butanol (18 wt%), and 2-methyl-2-propanol (60 wt%), were prepared and the stock of K2HPO4 (60 wt%) added dropwise to agitated aqueous solution until it becomes cloudy. Then, the emulsion was diluted dropwise with deionized water until the solution turned clear. Due to

obtaining whole range binodal data, the procedure repeated until the alcohol mass fraction of the solution dramatically was diluted (wA<0.002). The mass measurements of binodal points were undertaken via an analytical balance (A&D., Japan, model GF300) with a precision of ± 10-4 g. The organic binodal curve for 1-butanol and 2-butanol was determined using a similar method. A known amount (20 g) of the solution of 1-butanol (80 wt%) and 2-butanol (65 wt%), was prepared and the solution of K2HPO4 (20 wt%) added dropwise to the agitated solution until it becomes cloudy. The emulsion was diluted dropwise with the same stock of the initial alcoholic solution until it turned transparent. The procedure was repeated until the salt mass fraction content of the solution was negligible (wS<0.0002). All procedures were done at 298.15 K using a 50 cm3 glass vessel, which was placed in a thermostatic bath (Memert., Germany, model INE400) with an uncertainty of ±0.05 K and atmospheric pressure (around 0.1 MPa) [29].

2.2.2. Determination of tie-lines For each ATPS, six samples of an appropriate amount of each alcohol, salt, and water were prepared in the biphasic region and were gravimetrically weighed (±0.0001 g) in the graduated tubes. The samples were shaken and centrifuged (Hermle Z206A, Germany) at 6000 rpm for 4 min at room temperature until resulted phases were cleared. Then, all tubes placed in the thermostatic bath with a temperature controller by a thermostat (Memert., Germany, model INE400) with an uncertainty of ±0.05 K for at least 12 h at the desired temperature. Accordingly, the top phase was carefully withdrawn until a layer of the material with a thickness of at least 0.5 mm was checked to be left above the interface, and then remained bottom phase was removed with a long needle. The phase compositions were determined by the gravimetric method proposed by Merchuk et al. [35]. For the aqueous binodal curve, the Eq. (1) was fitted to the experimental binodal data: wA = a ∙ exp(bwS0.5 − cwS3 )

(1)

The a, b, and c are the Merchuk adjustable parameters. For the organic binodal curve, in the case of 1butanol and 2-butanol, the salt mass fraction of solution was determined using a two-Gaussian function of alcohol mass fraction, Eq. (2), by fitting experimental binodal results: 2

2

(wA − b) (wA − e) wS = a ∙ exp (− ( ) ) + d ∙ exp (− ( ) ) c f

(2)

The wS and wA are the mass fraction of potassium hydrogen phosphate and alcohol respectively, and a to f are the adjustable parameters. The phase composition of each tie-line was determined through the simultaneous solving of binodal curves (Eqs. (1) and (2)) and the mass conservation of Eqs. (3) and (4):

𝑤𝑆𝐹 𝑀 − 𝑤𝑆𝑇 𝑀𝑇 − 𝑤𝑆𝐵 𝑀𝐵 = 0

(3)

𝑤𝐴𝐹 𝑀 − 𝑤𝐴𝑇 𝑀𝑇 − 𝑤𝐴𝐵 𝑀𝐵 = 0

(4)

where, wF is the mass fraction of the initial sample (feed) with a mass of M and wT, and wB have represented the mass fraction of the top and bottom phases, respectively. The MT and MB are the mass of obtained for the top and bottom phases.

2.2.3. L-Tryptophan partitioning The ability of individual ATPS to separate the Trp was determined at 298.15 K and atmospheric pressure. Three samples of an appropriate amount of each alcohol, salt, and Trp aqueous solution were prepared as same as described in the previous section. The weight percent (100wTrp) of the prepared solution of Trp was approximately 0.07794 wt% [36]. Additionally, the control samples were prepared at the same weight fraction with pure water. Moreover, the calibration curve constructed using the aqueous solution of Trp at different concentrations was reported in Figure S4. After separating the top and bottom phases, the pH of both solutions was measured precisely using a Metrohm 827 pH lab meter (Switzerland). Then, the individual phases were diluted using deionized water to eliminate the possible interferences of the alcohols and salt components on the analytical method. The concentration of Trp in both phases was determined using a UV-VIS spectrophotometer (Lambda 850, Perkin Elmer co.) at a wavelength of 279 nm [36] and using calibration curve previously established.

3. Thermodynamic model 3.1. Mixed solvent Reference state The main role of most ATPS's determined by manipulating the top and bottom phases ensure to achieve the partitioning ability. Hence, both phases have a different composition. In our study, salt-alcohol systems, two distinct aqueous-organic phases are observable. While the top phase, (aq+org)1, is enriched in an organic solvent and bottom phase, (aq+org)2, mostly composed of water as a solvent. So the molar chemical potential of aqueous-organic solution (μ±) definite as:

v

μ±(aq+org)1 = μ∗±(aq+org)1 + RT ln(mv±(aq+org)1 γ∗±(aq+org)1 )

(5)

v

μ±(aq+org)2 = μ∗±(aq+org)2 + RT ln(mv±(aq+org)2 γ∗±(aq+org)2 )

(6)

∗ Here 𝜇± , m±, γ±, R, T, and v denote the reference state of the mean chemical potential of electrolyte, the

mean molal concentration of ions, the mean ionic activity, the gas constant, temperature, and the sum of the stoichiometric coefficient of dissolved salt, respectively. The superscript * represents the molality scale and infinite diluted reference state. The reference state for both aqueous-organic phases is written as [16]:

v

v

v v ∞ μ∗±(aq+org)1 = μ∗±(org) − RT ln(M(org) γ∞ ±(org) ) + RT ln(M(aq+org)1 γ±(aq+org)1 ) v

v

v v ∞ μ∗±(aq+org)2 = μ∗±(aq) − RT ln(M(aq) γ∞ ±(aq) ) + RT ln(M(aq+org)2 γ±(aq+org)2 )

(7) (8)

The M stands for the molar mass of the solution and 𝛾±∞ is the infinite diluted activity coefficient in the molar base. From the equations (7) and (8), both phases have different reference state, and infinite dilute organic solution (μ∗±(org) ), and infinite dilute aqueous solution (μ∗±(aq) ). In this work, the uncharged gas ig

phase reference state (μMX ) is used to provide an analogy between the two phases' reference. So the discharge process from uncharged ions to infinite diluted solution formulate as follow:

ig

discharge v

μ∗±(org) = μMX + RT ln (γ±(org) ig

discharge v

μ∗±(aq) = μMX + RT ln (γ±(aq)

)

(9)

)

(10)

𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒

The "ig" refers to the gas phase of uncharged ions; the 𝛾±

is the activity coefficient due to the

discharging process and defined as:

discharge

γ±

= exp (

1 1 e2 zi2 vi (1 − ) (− )∑ ) Ms DS 8πε0 kT σi

(11)

The Ms and Ds, T, k, e, ε0, zi, and σi represent solvent (water or alcohol) molar mass and dielectric constant, temperature, Boltzmann constant, electron charge, vacuum permittivity, ionic charge, and Born radius of ions, respectively.

3.2. Proposed gE Model The proposed excess Gibbs energy model, which is used in this study, consists of four contributions; the first contribution is a Pitzer–Debye–Huckel (G E,PDH) term [37] considering the long-range interaction effects. The Born term (G E,Born ) is used to describe the energy associated with the transfer of a point charge on each ion state in the mixed solvent to an infinitely dilute aqueous phase [38]. The solvation term (G E,Solvation) [25, 39] specified the ionic activity coefficient in a mixed-solvent electrolyte solution regarding the ionic solvation and the closest distance of approach between ions in a solution. Finally, an original UNIQUAC term (G E,UNIQUAC ) introduces by Abrams and Prausnitz [40] taken for short-range combinational and residual effects in the mixture. The summation of all terms gives the following excess Gibbs energy: GE G E,PDH G E,Born G E,Solvation G E,UNIQUAC = + + + RT RT RT RT RT

(12)

In 1980, Pitzer [37] established an excess Gibbs energy model based on limiting Debye-Huckel law [41] for long-range interaction: g E,PDH 4Ax Ix ⁄ =− ln (1 + ρIx1 2 ) RT ρ

(13)

where Ix = 1⁄2 ∑ zi2 xi represents the molar ionic strength, zi the ionic charge, ρ the closest approach parameter, and 𝐴𝑋 = 44290 𝑑𝑆0.5 ⁄(𝐷𝑆 𝑇)1.5 is the Debye-Huckel parameter on the mole fraction basis. The ds and Ds stand for the molar density and dielectric constant of the mixed solvent, respectively. The partial differentiation of gE respect to the moles of each species (ni) resulted in molar activity coefficients as 𝑅𝑇 ln 𝛾𝑖 = (𝜕𝑛 𝑇 𝑔𝐸 ⁄𝜕𝑛𝑖 ) 𝑇,𝑃,𝑛𝑗≠𝑖 . The long-range interaction, represented by the Debye-Huckle expression, is formulated in the McMillan-Mayer framework. Still, we carefully performed the framework conversion of the activity coefficient of this term from McMillan-Mayer to Lewis-Randall. The standard states can be considered for aqueous phase and organic phase within that the activity coefficient of an ion (𝛾𝑖𝐿𝑅 ) in an ideal dilute solution in water is the same as that in an ideal dilute solution of organic solvent (k): 𝛾𝑖𝐿𝑅 → 1 𝑎𝑠 𝑥𝑘 → 1

(14)

The asymmetrical activity coefficient for charged ions (i) was written as follow: 2 1 − 2 Ix ⁄zi2 ln γPDH = −Ax zi2 ( ln(1 + ρIx0.5 ) − Ix0.5 ) i ρ 1 + ρIx0.5

(15)

For equation (15), regardless of the solvent: 𝑙𝑛𝛾𝑖𝑃𝐷𝐻 → 0 𝑎𝑠

𝐼𝑥 → 0 ⇒ 𝛾𝑖𝑃𝐷𝐻 → 1

(16)

For the solvents j=1 and 2, Cardoso and O’Connell (1987) [6] suggested the long-range contributions (PDH) in the Lewis-Randall framework are given by:

ln 𝛾𝑗𝑃𝐷𝐻 = −(𝑣̅𝑗 ).

Π 𝑃𝐷𝐻 𝑅𝑇

(17)

This equation shows that each solvent has a portion of the effect on the osmotic pressure (ΠPDH) related to those partial molar volumes (𝑣̅𝑗 ). The partial differentiation of gE in equation (13) respect to the moles of each species (ni) of solvent molecules (j) for the long-range activity coefficient was obtained by:

ln γPDH = j

2Ax Ix1.5 4Ax Ix −1 ∂dS 3 ∂DS ln(1 + ρIx0.5 ) ( + ) 0.5 + ρ 2dS ∂xj 2DS ∂xj 1 + ρIx

(18)

In equation (18), the activity of the solvent is formulized in the Lewis-Randall framework to avoid inconsistency. The differentiate term of mixed-solvent molar density and dielectric constant are in the result of the molar differential on the Debye-Huckle constant (Ax). The Born effect in term of excess Gibbs energy [38] represented as: g E,Born e2 1 1 zi2 xi = ( − )∑ RT 2kT 4πε0 DS 4πε0 DW σi

(19)

where, DW, k, e, ε0, and σi represent the dielectric constant of water, Boltzmann constant, electron charge, vacuum permittivity, and Born radius of ions, respectively. The solvent (j) and solute (i) activity coefficient of Born term introduced by Pirahmadi et al.[17]:

ln γBorn =− j ln γBorn i

e2 1 ∂DS zi2 xi ∑ 2kT 4πε0 D2S ∂xj σi

(20)

e2 1 1 zi2 = ( − ) 2kT 4πε0 DS 4πε0 DW σi

(21)

The latter term is the solvation effect (ln γSV i ) on the ions surrounded by solvent molecules. Here, the ionic activity coefficient of the electrolyte solution was used as below [39]:

ln γSV i =

α si zi2 Im T

(22)

The "s" is the solvation parameter describing the solvation effects of ion-solvent, α is a distance parameter cited to ion-solvent distance, and Im stands for the ionic strength in the molal base. The solvent activity coefficient was obtained [42] using the Gibbs-Duhem theorem from Eq. (22):

ln γSV j =−

α S. (α⁄(α + 1))Im mMj (vc + va )T

(23)

The 𝑆 = ∑ 𝑠𝑖 𝑣𝑖 𝑧𝑖2 , vc and va are the stoichiometric constant of cation and anion, Mj represents the molar mass of solvents, and m the molality of the electrolyte. The original UNIQUAC contribution for excess Gibbs energy [40] is given here: 𝜙𝑗 𝜃𝑗 𝑔𝐸,𝑈𝑁𝐼𝑄𝑈𝐴𝐶 = ∑ 𝑥𝑗 ln + 5 ∑ 𝑞𝑗 𝑥𝑗 ln + ∑ 𝑞𝑗 𝑥𝑗 ln ∑ 𝜃𝑘 𝜓𝑘𝑗 𝑅𝑇 𝑥𝑗 𝜙𝑗 𝑗

𝑗

𝑗

(24)

𝑘

In Eq. (24), 𝜙, 𝜃 and 𝜓 are the surface fraction, volume fraction, and binary interaction defined as 𝜙 = 𝑥𝑖 𝑟𝑖 ⁄∑𝑖 𝑥𝑖 𝑟𝑖 , 𝜃 = 𝑥𝑖 𝑞𝑖 ⁄∑𝑖 𝑥𝑖 𝑞𝑖 and 𝜓𝑘𝑗 = 𝑒𝑥𝑝 (−

𝑎𝑘𝑗 𝑇

) , respectively. The rj, qj, and akj are the volume,

surface area, and binary interaction parameters where 𝑎𝑘𝑗 ≠ 𝑎𝑗𝑘 , 𝑎𝑗𝑗 = 0. The UNIQUAC activity coefficient of solvent (j) and ions (i) are obtained from Eq. (25) [17]:

𝑈𝑁𝐼𝑄𝑈𝐴𝐶

ln 𝛾𝑗

=1−

𝜙𝑗 𝜙𝑗 𝜙𝑗 𝜙𝑗 + ln ( ) − 5𝑞𝑗 [ln ( ) + 1 − ] 𝑥𝑗 𝑥𝑗 𝜃𝑗 𝜃𝑗

𝜃𝑘 𝜓𝑗𝑘 + 𝑞𝑗 [1 − ln (∑ 𝜃𝑘 𝜓𝑘𝑗 ) − ∑ ] ∑𝑙 𝜃𝑙 𝜓𝑙𝑘 𝑘

𝑘

(25)

3.3. Physical properties calculation The density (ρ) of the (water + light alcohol) mixture was calculated using the Redlich-Kister [43] type equation: 𝑛

𝑀𝑆 𝑥𝑊 𝑀𝑤 𝑥𝐴 𝑀𝐴 = + + 𝑥𝑊 𝑥𝐴 ∑ 𝐵𝑝 (𝑥𝑊 − 𝑥𝐴 )𝑝 𝜌 𝜌𝑊 𝜌𝐴

(26)

𝑝=0

The 𝜌𝑊 , 𝜌𝐴 , 𝑀𝑤 , 𝑀𝐴 , 𝑥𝑊 , and 𝑥𝐴 represent the density, molar mass, and mole fraction of pure water and pure alcohol, respectively. The fitted values of Bp for the different aqueous-alcoholic system using from the experimental excess volume at 298.15 K [44-47] are given in Table S1. The Bp parameters for all alcohols are fitted up to five terms except 1-butanol and 2-butanol, where their mutual solubility makes an unrealistic correlation of excess volume for p greater than one. The dielectric constant (D) of the binary water-alcohol mixture at 298.15 K predicted using a combined form of the Jouyban-Acree model and the Abraham solvation parameters [48]. The born radius (σ) of cation and anion are considered approximately 0.425Å and 0.05Å greater than the ionic radius [49]. Therefore it accounts 1.805Å for K+ and 2.25Å for HPO2− 4 . The volume (r) and surface area (q) parameters of the UNIQUAC model for all components are obtained from the literature [14, 20, 50, 51] are listed in Table 2.

Table 2.The volume (r) and surface area (q) parameters of UNIQUAC model Name K+ 𝐇𝐏𝐎𝟐− 𝟒 Water Methanol Ethanol

R 0.4370 1.3290 0.9200 1.4311 2.1055

q 0.578 1.210 1.400 1.432 1.972

Ref. [20] [20] [50] [50] [50]

Name 1-Propanol 1-Butanol 2-Butanol Tert-Butanol

r 2.7800 3.4540 3.4535 3.9228

q 2.512 3.052 3.048 3.744

Ref. [14] [14] [50] [51]

Table 3. The fitting results of K2HPO4 and alcohols aqueous binary solution. System

Data Type

No. Data

a12

a21

s0

a0

%AARDa

44.94

0.722

Ref.

Water (1) + K2HPO4 (2)

Osmotic

27

594.4

-114.1

0.52

[52-54]

Water (1) + Methanol (2)

VLE

12

92.9

-90.2

3.46

[55, 56]

Water (1) + Ethanol (2)

VLE

15

8.1

100.2

1.25

[57]

Water (1) + 1-Propanol (2)

VLE

22

-80.4

286.9

2.32

[58, 59]

Water (1) + 1-Butanol (2)

LLE

6

-251.9

455.5

2.54

[60, 61]

Water (1) + 2-Butanol (2)

LLE

8

-211.7

699.1

3.13

[60, 62]

Water (1) + Tert-Butanol (2)

VLE

26

-97.6

404.8

1.64

[63]

a

Average absolute relative deviation

3.4. Solving Strategy In this study, the proposed model implemented to predict the experimental osmotic coefficient data of K2HPO4 + H2O [52-54] in a wide range of molality at 298.15 K. The value of approaching parameter, ρ, was chosen as a constant, 14.9, similar to previous studies [17, 23]. Also, the born term did not apply to osmotic coefficient data. The UNIQUAC model was used for the different aqueous-alcoholic systems using experimental binary VLE and LLE data [55-63]. The fitted parameters for K2HPO4 + H2O and alcohol +water systems are given at 298.15 K in Table 3. The adjustable parameters of the model for LLE data are mixed solvent solvation factor (S), mixed solvent distance parameter (α), and for the salt-alcohol interaction parameters (aS-A, aA-S). For the mixed solvent model, the solvation parameters of cation and anion were considered as "s", and it's written in terms of a mixed solvent characteristic variable that can be related to a physical property of water-alcohol mixture. Recently, the dielectric constant was used frequently as water-co-solvent characteristics property [18, 21, 25]. In this study, the polynomial correlation for the solvation parameter is proposed: 1 𝑠 = 𝑠0 + 𝑠1 𝐷𝑟 + 𝑠2 𝐷𝑟 2 + 𝑠3 𝐷𝑟 3 − (𝑠1 + 2𝑠2 + 3𝑠3 )𝐷𝑟 4 4

(27)

The s0 is the solvation parameter of the binary (K2HPO4 + H2O) system and the Dr defined as:

𝐷𝑟 =

𝐷𝑊 − 𝐷 𝐷𝑊 − 𝐷𝐴

(28)

where D stands for the mixed solvent dielectric constant at 298.15 K. The coefficient of the fourth-order term in Eq. (27) was defined based on the condition that the solvation parameter near the pure alcoholic phase is invariant. This concept is related to the small solubility of salt in the pure organic phase. Also, the distance parameter, α, was considered a function of the dimensionless dielectric constant of mixedsolvent: 𝑎 = 𝑎0 + 𝑎1 𝐷𝑟 , 𝑎 ≥ 0

(29)

The value of a0 is the distance parameter of the binary (K2HPO4 + H2O) system. The activity model, socalled "HIS-UNIQUAC", included the HIS contribution, the born term, and the UNIQUAC combinational and residual term was fitted by optimizing the solvation parameter correlations, distance parameter correlations, the salt-alcohol residual UNIQUAC interactions. The HIS-UNIQUAC activity model was applied to compute the activity coefficient (γi) of all components for the alcoholic top and

salty bottom phases. The mean salt activity coefficient is calculated from the individual activity coefficients of cation and anion using the following equation:

ln 𝛾±∗ =

𝑣+ 𝑣− ln 𝛾+∗ + ln 𝛾−∗ 𝑣 𝑣

(30)

In Eq. (30) v+ and v− are the stoichiometric coefficients of the K + and HPO2− 4 , and v equals to the sum of the anion and cation stoichiometric coefficients. At the equilibrium condition (constant temperature and pressure), the chemical potential of electrolyte in the top organic phase (1) is equal to those in the aqueous bottom phase (2). Thus, using the Equations (5)-(11), the corrected distribution coefficient for electrolyte (𝐾± ) was calculated: 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒

∞ ∞ 2 𝑀 𝛾±,𝑎𝑞 𝑀𝑇 𝛾±,𝑇 𝑥±𝑇 𝛾±𝐵 𝑜𝑟𝑔 𝛾±,𝑜𝑟𝑔 𝐾± = 𝐵 = 𝑇 ∙ [( ) ( ) ( 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 )] ∞ ∞ 𝑀𝐵 𝛾±,𝐵 𝑀𝑎𝑞 𝛾±,𝑎𝑞 𝑥± 𝛾± 𝛾

(31)

±,𝑜𝑟𝑔

The distribution coefficient for solvent (water or alcohol), 𝐾𝑠 , calculates quickly from:

𝐾𝑠 =

𝑥𝑠𝑇 𝛾𝑠𝐵 = 𝑥𝑠𝐵 𝛾𝑠𝑇

(32)

Moreover, the Rachford-Rice equation based on the molar balance of all components in both phases is used: (𝐾𝑊 − 1)𝑧𝑊 (𝐾𝐴 − 1)𝑧𝐴 (𝐾± − 1)𝑧± + + =0 1 + (𝐾𝑊 − 1)𝛽 1 + (𝐾𝐴 − 1)𝛽 1 + (𝐾± − 1)𝛽

(33)

The zW, zA, and z± represent the initial mole fraction of water, organic matter, and mean mole fraction of ions, respectively. Calculating the phase ratio (β) from Eq. (33) by an iterative method such as NewtonRaphson yields a compositional determination of the top and the bottom phases. The objective function of liquid-liquid equilibria (𝑂𝐹𝐿𝐿𝐸_𝐶𝑎𝑙𝑐 ) that should be minimized was defined as: 𝑛𝑐

𝑂𝐹𝐿𝐿𝐸_𝐶𝑎𝑙𝑐

𝐾𝑖𝑙+1 = ∑ (1 − 𝑙 ) 𝐾𝑖 𝑖=1

2

(34)

where 𝐾𝑖𝑙 stands for the distribution ratio of component i computed in iteration l. The optimization procedure followed by comparing the simulated value and experimental LLE data of nc components (water, alcohol, and salt) by minimization of an objective function [17] to estimate parameters:

2

2 1⁄2

𝑇,𝐸𝑥𝑝 𝐵,𝐸𝑥𝑝 𝑇,𝐶𝑎𝑙𝑐 𝐵,𝐶𝑎𝑙𝑐 𝑛𝑐 ∑𝑁 − 𝑤𝑖,𝑗 ) + (𝑤𝑖,𝑗 − 𝑤𝑖,𝑗 ) ) 𝑗=1 ∑𝑖=1 ((𝑤𝑖,𝑗

𝑂𝐹𝑃𝑎𝑟_𝑒𝑠𝑡 = 100

(35)

2𝑛𝑐 𝑁 (

)

This objective function ensures to obtain the closest calculated tie-line to the experimental tie-line, and N is the number of tie-lines data. Fitting ternary LLE data vitally needs to choose a fast and robust optimization method to enable to adjust of the multivariable objective function. Recently, particle swarm optimization (PSO) used for the estimation of binary interaction parameters in the activity model for liquid-liquid equilibrium [64]. The

PSO algorithm is reliable as it accurately finds the global minima/maxima of their input function. The applicability of this method was successfully approved in their study. The PSO also needs no initial guess, strongly recommended for LLE calculation [64]. The particle swarm optimization algorithm uses the swarms (initial population) moving through the direction, which is determined respect to both individuals and entire swarms' best position. The best function value was used for guiding the swarms, and it's repeated until getting a favourable solution. In our study, the PSO was applied to minimized objective function introduced by Eq. (35) and stopping criteria are defined based on the approaching degree of particles (TolX) based on the iterative measures according to a predefined closure function:

𝑇𝑜𝑙𝑋 =

100 𝑣 𝑀𝑎𝑥(𝑠𝑖 ) − 𝑀𝑖𝑛(𝑠𝑖 ) ∑ ( ) 𝑣 𝑀𝑒𝑎𝑛(𝑠𝑖 ) 𝑖=1

(35)

The si is the value of swarmed particle in the ith dimension of variable space (v). These criteria ensured the optimization algorithm not only reaches the desired value of the objective function but also it rejects all of the local solutions to achieve the optimized global value. Table 4 shows the selected parameters for the PSO algorithm. In this table, the cognitive and social component determines the ratio of movement around the individuals and the entire swarms' best position and velocity factor imply the acceleration of particles in movement. In the aim of our study, the number of particles in the swarm (Npart), velocity factor (vl), and range factor (Rf) of variables are defined

adjustable and need to tune them. Figure S1-S3 depicts the convergence graphic of the HIS-UNIQUAC model for the (1-butanol + K2HPO4+ water) system. From these figures, the optimum value of the adjusted parameters are Npart=60, vl=0.8, and Rf=100. Table 4. Parameter used in the PSO algorithm PSO parameter

Value

Number of particles in swarm (Npart )

30-180

Number of iterations

10000

Number of decision variables (NVar)

6

Cognitive component (c1 )

2.0

Social component (c2 )

2.0

Velocity factor (vl)

0.6-1.2

Inertia weight

1.0

Initial Upper and Lower bond of variables

[-1 1;-1 1;-100 100;-100 100;-100 100;-1 0]

Range factor (Rf)

(1-100)

4. Results and discussion 4.1. Phases diagrams and correlations The experimental binodal data of the systems composed of alcohol (1-butanol/2-butanol/tert-butanol), K2HPO4, and water at 298.15 K are shown in Table 5. Due to mutual solubility, it can be seen that the biphasic area of 1-butanol and 2-butanol ATPS systems are segregated. The binodal results were fitted using Eq. (1) and (2), the adjusted parameters and degrees of closure (R2 and SD) are present in Table S2. For all of the systems, the coefficient of determination is sufficiently approached to unity (R2>0.992), and the standard deviations satisfactory are so little (SD<0.0032).

Table 5. The mass percent (100wi) of the experimental binodal data for top (T) and bottom (B) of the systems composed of 1-butanol/2-butanol/tert-butanol (A) + K2HPO4 (S) + water at 298.15 K and 0.1 MPa a. 1-butanol

2-butanol

Tert-butanol

100𝒘𝑻𝑺 †

100𝑤𝐴𝑇

100𝑤𝑆𝐵

100𝑤𝐴𝐵

100𝑤𝑆𝑇

100𝑤𝐴𝑇

100𝑤𝑆𝐵

100𝑤𝐴𝐵

100𝑤𝑆

100𝑤𝐴

0.014 0.055 0.082 0.163 0.251 0.330 0.353 0.183 0.106 0.025

79.865 82.340 83.625 86.332 88.003 89.852 91.265 93.272 94.287 96.361

2.162 3.426 7.451 12.099 12.347 14.074 19.863 21.066 26.510 30.718 36.903

6.636 6.511 5.757 4.417 4.454 3.961 2.739 2.352 1.438 0.855 0.349

0.007 0.018 0.033 0.046 0.098 0.148 0.235 0.272 0.311 0.286 0.232

66.747 69.646 72.806 76.612 80.395 82.172 85.838 87.028 88.184 89.989 92.028

1.201 3.762 4.383 9.133 11.926 15.629 21.064 23.943 25.013 28.143 32.017

13.238 9.974 9.744 6.943 5.914 4.615 2.999 2.242 1.989 1.342 0.760

0.019 0.100 0.241 0.639 1.054 2.187 3.762 4.383 9.133 15.629 21.064

92.243 78.774 67.499 52.851 39.938 28.258 18.220 16.963 7.903 3.339 1.972

37.410 39.810 47.111

a Standard † w:

0.327 0.215 0.114

0.115 0.015

93.914 96.914

36.393 39.633 43.827 48.332

25.013 32.017 36.393 39.633 43.827 48.332 54.837

0.345 0.168 0.057 0.015

1.432 0.738 0.563 0.469 0.340 0.244 0.170

uncertainties u are u (wT) = 0.0002, u (wB) = 0.0017, u (T) = 0.05 K, and u (P) = 5 kPa.

mass fraction

The LLE determination was conducted through the lever rule by solving Eqs. (1) - (4) in the measured known mass of top and bottom phases. The tie-lines of each system are plotted in Figures 1-3 and the mass percent of the tie-lines are presented in Table 5. The Liquid-Liquid Equilibrium data plotted in Figures 1-3 were correlated to the HIS-UNIQUAC model consist of the original UNIQUAC, PDH, and Born terms. They show that for all three systems, the proposed models successfully could predict both top and bottom region for branched butanol in the presence of K2HPO4.

Table 6. The mass percent (100wi) of tie-line (TL) data of K2HPO4 (S) + 1-butanol/2-butanol/tert-butanol a (A) + water systems at 298.15 K and 0.1 MPa . TL

Feed 100𝑤𝐴 †

Top 100𝑤𝑆

100𝑤𝐴

Bottom 100𝑤𝑆

100𝑤𝐴

100𝑤𝑆

0.02 0.07 0.27 0.34 0.24 0.09

5.34 3.08 1.73 0.83 0.25 0.04

7.94 18.55 24.88 30.30 36.68 44.04

0.07 0.08 0.18 0.21 0.30 0.26

7.10 4.14 1.71 0.52 0.19 0.03

8.91 17.03 26.35 34.39 39.38 45.97

0.98 0.47 0.30 0.17 0.11 0.05

2.04 1.14 0.76 0.55 0.39 0.31

20.01 26.78 32.35 37.54 44.05 49.23

K2HPO4 + 1-butanol + water 1 2 3 4 5 6

44.83 40.00 36.50 32.00 37.55 43.19

3.76 10.00 14.99 20.00 21.98 23.98

80.13 82.91 88.28 91.49 92.74 94.58 K2HPO4 + 2-butanol + water

1 2 3 4 5 6

38.03 35.00 28.00 30.13 29.32 29.38

5.02 10.00 18.00 22.41 26.66 31.25

77.47 78.53 84.13 85.04 89.69 91.12 K2HPO4 + tert-butanol + water

1 2 3 4 5 6 a Standard † w:

28.05 32.39 35.12 37.96 41.03 44.00

8.05 11.97 14.97 18.02 21.00 24.04

43.45 56.66 64.13 72.19 77.85 85.60

uncertainties u are u (wT) = 0.0003, u (wB) = 0.0038, u (T) = 0.05 K, and u (P) = 5 kPa. mass fraction

Figure 1. Experimental versus HIS-UNIQUAC correlations for the mass percent tie lines of the ternary system {1-butanol + K2HPO4+ water} at 298.15 K; (●) binodal data, (□) mutual solubility of 1-butanol water system [17],( Δ-Δ) experimental tie-line data, (+-.-+) HIS-UNIQUAC model.

Figure 2. Experimental versus HIS-UNIQUAC correlations for the mass percent tie lines of the ternary system {2-butanol + K2HPO4+ water} at 298.15 K; (●) binodal data, (□) mutual solubility of 2-butanol water system [60, 62],( Δ-Δ) experimental tie-line data, (+-.-+) HIS-UNIQUAC model.

Figure 3. Experimental versus HIS-UNIQUAC correlations for the mass percent tie lines of the ternary system {Tert-butanol + K2HPO4+ water} at 298.15 K; (●) binodal data, ( Δ-Δ) experimental tie-line data, (+-.-+) HIS-UNIQUAC model.

4.2. Fitting results and the adjusted parameters of HIS-UNIQUAC model The optimized values of Sn, α1, and aij fitted by LLE data of alcohol + K2HPO4 + water systems for methanol to tert-butanol at 298.15 K are given in Table 7. Also, the model ability, based on the deviation introduced in Eq. (35), to predict the LLE data is represented in this table.

Table 7. The adjusted parameters of HIS-UNIQUAC (M1) water (1) + alcohol (2) + K 2HPO4 (3) systems and comparison with the prediction ability of modified extended UNIQUAC (M2), and original extended UNIQUAC (M3) using Eq. (35) in mass percent (%Δw) at 298.15 K. s1

s2

s3

α1

a23

a32

M1

M2

M3

Ref.

Methanol

1305.0

1662.3

-1586.6

-2.20

298.1

-61.1

0.111

0.335

2.058

[26]

Ethanol

1244.4

5119.9

-8057.6

-2.70

157.0

-18.5

0.286

0.294

2.962

[26]

1-Propanol

9043.1

-32041.9

49311.8

-8.60

14.2

-347.7

0.352

0.676

3.438

[27]

1-Butanol

31611.7

-52616.8

17162.8

-17.99

108.7

2547.7

0.128

0.698

9.565

2-Butanol

39521.1

-58438.8

11446.4

-24.23

304.5

3932.1

0.331

1.425

6.941

Tert-Butanol

58039.3

-80528.4

5647.8

-6.01

152.7

3864.9

0.290

1.579

3.400

0.250

0.835

4.727

Overall

Table 8. The sensitivity analysis of adjusted HIS-UNIQUAC model parameters in 95% confidence level for alcohol + K2HPO4 + water systems. s1

s2

s3

α1

a23

a32

Methanol

±1.12

±2.23

±0.89

±0.15

±2.23

±8.22

Ethanol

±2.17

±2.49

±4.15

±1.01

±15.7

±1.11

1-Propanol

±4.13

±2.93

±2.55

±0.95

±9.31

±1.91

1-Butanol

±6.52

±2.51

±3.09

±6.11

±9.58

±7.98

2-Butanol

±1.03

±3.25

±2.72

±0.33

±3.59

±9.36

Tert-Butanol

±5.29

±1.91

±3.26

±1.69

±6.26

±0.84

The sensitivity analysis of the obtained parameters, represented in Table 8, demonstrates that for the confidence level of 95%, the sensitivity of 26 parameters is less than 5%, and sensitivity of 9 parameters is less than 10%, and one parameter has the sensitivity of less than 20%. Results from the information imply in Table 7 that the proposed model able to predict the aqueous biphasic systems as well as the %Δw in the range of (0.111-0.331) % while the prediction of modified extended UNIQUAC [17] model and original extended UNIQUAC [9] model were in the range of (0.294-1.579) % and (2.058-9.565) %, respectively. The original extended UNIQUAC [9] has not enough reliability because it considers alcohol as a solute [17], an unrealistic concept. These results indicate our proposed model is a suitable candidate for the prediction of activity coefficients of components in mixed-solvent systems.

Figure 4.The experimental alcohol yield factor versus calculated value by the proposed model (●) was compared with modified extended UNIQUAC () and original extended UNIQUAC (▲) models.

Moreover, in Fig. 4, the simulated (𝑌𝐴,𝑠𝑖𝑚 ) yield of alcohol,(𝑀𝑇 𝑤𝐴𝑇 )⁄(𝑀𝐹 𝑤𝐴𝐹 ), by the proposed model versus experimental value (𝑌𝐴,𝑒𝑥𝑝 ) was compared with modified extended UNIQUAC and original extended UNIQUAC models. The plot shows that the proposed model gives a favorable prediction (R2=0.9981) than two other models. The adjusted parameters of solvation correlations, Equations (27) - (29), given in Table 7, reveal the vital role of mixed-solvent dependent function to fit the solvation and distance parameters. The negative values of α1 show that for all alcohols, the distance parameters varied between a0 = 0.722 (Water + K2HPO4 binary system) to zero for the higher alcoholic phase. It seems that the solvation mechanism (a ≈ 0) would be independent of ionic strength in the organic region and its activity calculated directly from the solvation factor. Moreover, increasing the alcohol chain carbon and decreasing the branched carbon empower this phenomenon. In Figure 5, the solvation factor for the straight and branched alcohols as a co-solvent in different dimensionless dielectric constant is plotted. The solvation factor stands on s0 = 44.94 (Water + K2HPO4 binary system) near the aqueous region, and its behaviour tends to be flat near the alcoholic region. Generally, the lighter alcohol makes a lower solvation factor in a mixed-solvent mixture.

Figure 5. The solvation factor of water + alcohol + K2HPO4 for different dimensionless dielectric constant in mixed-solvent.

4.3. Gexterms From the salty solution to an aqueous-alcoholic mixture, biphasic boundary consists of a wide range of solutions accompany with different molecular interactions. Role of excess Gibbs energy terms on the whole range of binodal curve assists in studying LLE behaviour precisely. In Fig. 7, the magnitude excess Gibbs energy of each term of the HIS-UNIQUAC model was plotted for solubility data of tert-butanol + K2HPO4 + water at 298.15 K. In this figure, the horizontal axis is the salt mole fraction (xs) of the binodal curve, and the vertical axis indicates the value of Gex ⁄RT of PDH, solvation, and original UNIQUAC terms.

Figure 6. the magnitude of excess Gibbs energy terms of HIS-UNIQUAC model versus salt mole fraction of the binodal curve of water + Tert-butanol + K2HPO4 at 298.15 K.

The impact of long-range electrostatic interaction increases at salty solutions (107% for xs=0.11189 or ws=0.54837), which ions are occupying everywhere of solvent inter-structural space. The plot shows that the short-range interactions, the UNIQUAC combinational and residual terms, have a significant role for top phase solutions (23.34% for xs=0.00111 or ws=0.00639). For such a solution, the lower amount of salt intrinsically reduced the ionic interaction, and water-alcohol short forces reveal as a critical determinant. The solvation mechanism is toward a diversified behaviour. For the alcoholic solution, the excess Gibbs energy of solvation makes a significant positive deviation (80.2% for xs=0.00111) while it has a negative deviation for the salty solution (-14.19% for xs=0.11189). The portion of the surrounded solvent increases

through the lower ionic strength of the alcoholic phase and the ions solvated completely. The more ionic strength provides competition between long-range interaction, attracting the ions each other, and solvent covering the ions.

Figure 7. the magnitude of excess Gibbs energy terms of HIS-UNIQUAC model in 𝑚𝑠 ⁄𝑚𝑎 = 5𝑒 − 5 for top phase of water + Alcohol + K2HPO4 at 298.15 K.

Figure 8. the magnitude of excess Gibbs energy terms of HIS-UNIQUAC model in 𝑚𝑠 ⁄𝑚𝑎 = 5 for top phase of water + Alcohol + K2HPO4 at 298.15 K.

Effect of the straight and branch alcohols on the magnitude of excess Gibbs energy term for the top and bottom phases were studied and are presented in Figures 7 and 8. Calculations conducted at the constant molality ratio of salt to alcohol, 𝑚𝑠 ⁄𝑚𝑎 = 5 and 𝑚𝑠 ⁄𝑚𝑎 = 5𝑒 − 5 for the top and bottom phases, respectively. However, it's clearly from Figure 8 that the solvation effect and the short-range interactions are the dominant terms for the alcoholic phase in all systems. The magnitude of the excess Gibbs energy terms in Figure 8 is confirmed the result from Figure 6, where the long-range interactions and solvation have the principle importance. Moreover, it can be seen that the presence of different co-solvent in the salty phase impresses tall terms of excess Gibbs energy.

4.4. Partitioning of L-Tryptophan The results obtained for the partition coefficients of Trp between the alcoholic phase and the salty phases (𝐾 = 𝐶𝑇 ⁄𝐶𝐵 ) and final pH, at 298.15 K and constant initial alcohol content of the feed (wA ≈ 0.1) and different salt concentration in the feed are reported in Table 9. The results show that increasing the TLL makes a dramatic decrease in the partition coefficient. Also, the systems contain T-Butanol and 2Butanol show better separation than 1-Butanol.

Table 9. Partition coefficients (K) of Trp in ternary system of alcohol (A) + K2HPO4 (S) + water and final pH a of top (T) and bottom (B) phase at 298.15 K and at 0.1 MPa . Feed 100wA

Top 100wS

100wA

Bottom 100wS

100wA

Top

100wS

TLL (%)

pHT

pHB

CTrp

Bottom

/(10-3 mole∙dm-3)

K

1-Butanol + K2HPO4 +water 10.00

8.00

80.13

0.02

5.34

8.31

75.26

9.30

8.77

25.1

1.3

19.1

10.03

16.00

82.91

0.07

3.08

17.58

81.72

9.52

9.10

10.9

1.4

7.71

10.00

24.00

88.28

0.27

1.73

26.48

90.43

9.81

9.17

2.4

1.5

1.62

2-Butanol+ K2HPO4 +water 10.00

8.00

74.36

0.06

7.19

8.33

67.68

9.60

9.21

42.6

1.3

32.5

10.00

16.00

78.65

0.09

3.99

17.26

76.61

9.81

9.26

11.2

1.4

8.30

10.00

24.00

83.25

0.16

1.72

26.45

85.66

9.63

9.36

5.2

1.2

4.44

T-Butanol+ K2HPO4 +water 10.15

12.00

31.70

1.81

3.40

15.03

31.23

10.25

9.27

50.1

1.3

38.5

10.00

16.00

43.56

0.97

2.04

19.98

45.66

9.95

9.23

12.1

1.4

8.55

24.00

59.94

0.39

1.02

28.19

65.15

9.48

9.45

3.8

1.3

3.02

10.00 a Standard

uncertainties u are u (wT) = 0.0005, u (wB) = 0.0024, u(pH)= 0.03, u (C)=0.5×10-3 mole/dm3, u (T) = 0.05 K, and u (P) = 5

kPa. † w: mass fraction

The long-range electrostatic (PDH), solvation (Solv), and short-range (SR) terms of excess Gibbs energy were calculated using the proposed activity model for the top and bottom phases at given LLE data in Table 9. The logarithm of partition coefficients was plotted against the change of excess Gibbs energy (ΔGE) terms from top to bottom phases are shown in Fig. 9-11.

Figure 9. The logarithm of partition coefficients of Trp versus the difference of long-range electrostatic interaction of two phases.

Figure 10. The logarithm of partition coefficients of Trp versus the difference of solvation power of two phases.

Figure 11. The logarithm of partition coefficients of Trp versus the difference of short-range interaction of two phases. Results show that the difference in short-range interaction of two phases has no change for different feed composition, and it may have little effect on the partition coefficient of Trp for all systems. However, its partitioning has significant dependence on the change of long-range and solvation terms from the top phase to the bottom phase. In a while, the linear correlation of this behaviour was fitted for all three alcohols as follows: 𝐸 𝐸 1-Butanol: 𝑅𝑇 ln(𝐾) = 29.67∆𝐺𝑃𝐷𝐻 + 7.264∆𝐺𝑆𝑜𝑙𝑣

, 𝑅 2 = 0.991

(36)

𝐸 𝐸 2-Butanol: 𝑅𝑇 ln(𝐾) = 11.67∆𝐺𝑃𝐷𝐻 + 10.07∆𝐺𝑆𝑜𝑙𝑣

, 𝑅 2 = 0.982

(37)

𝐸 𝐸 T-Butanol: 𝑅𝑇 ln(𝐾) = 10.19∆𝐺𝑃𝐷𝐻 + 17.15∆𝐺𝑆𝑜𝑙𝑣

, 𝑅 2 = 0.996

(38)

Consequently, the long-range electrostatic interactions and solvation mechanism have a major impact (R2>0.982) on the separation of Trp in these systems. As can be seen, the difference of the long-range interaction and solvation mechanism between two phases has an inverse impact on the branched alcohol partitioning capacity.

4. Conclusion In this work, the binodal data and the liquid-liquid equilibrium (LLE) tie-line for (water + 1-butanol / 2butanol / t-butyl alcohol + K2HPO4) systems were experimentally obtained at 298.15 K. The binodal data were fitted using Merchuk Equation and a two-Gaussian correlation with satisfactory correlation

coefficients, R2>0.992. The partition coefficient of L-Tryptophan (Trp) in these systems was measured at a constant initial alcohol content of the feed, and the final pH of both phases was reported. The maximum partitioning occurs in the lower TLL, about 19.05, 32.49, and 38.55 for 1-butanol, 2-butanol, and t-butyl alcohol, respectively. The LLE tie-lines were correlated to a proposed excess Gibbs energy model for aqueous organic mixed solvent electrolyte solutions, HIS-UNIQUAC, which consists of the original UNIQUAC, PDH, solvation, and Born terms. HIS-UNIQUAC model was able to correlate the tie-lines of (water + alcohol + K2HPO4) at 298.15 K for a satisfactory mass percent deviations of 0.128% for 1butanol, 0.331% for 2-butanol, and 0.290% for Tert-butanol. The effect of mixed-solvent characteristics such as dielectric constant on the solvation term of the organic-aqueous solution was discussed. The more alcoholic solution makes a stronger solvation power for present anion and cation. Also, in the organic phase, the ionic strength dependence of the solvation term was ignored, and the solvation effect show as a constant behaviour. It can be summarized that cosolvent which could form a powerful binding with water molecules able to provide a sufficient condition to accommodate charged ions. Moreover, the partition coefficient of Trp for all three alcohols has a significant correlation with the difference of long-range interaction and solvation terms from the top phase to the bottom phase. It can be concluded that the long-range electrostatic interaction and solvation mechanism plays an essential role in biphasic biomolecules separation systems.

Acknowledgment The authors would like to express their special thanks of gratitude to John M. Prausnitz; Professor of Chemical Engineering at the University of California, Berkeley who gave us the golden opportunity to do this wonderful project on the equilibrium thermodynamics by his important considerations and suggestions in order to improve the thermodynamics model, and for always pointing out the relevance of the results. We are really thankful to him.

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Highlights: 

Phase diagram for ATPS of 1-Butanol/2-Butanol/Tert-Butanol with K2HPO4 were determined.



L-Tryptophan partitioning was investigated.



The hybrid ion-interaction and solvation model (HIS) was firstly combined with modified extended UNIQUAC model to describe LLE data.



The proposed model (HIS-UNIQUAC) presented more accurate results.



The partitioning factor represented a correlation with the long-range electrostatic and solvation term of proposed model.

Graphical Abstract

Equilibrium data and thermodynamic studies of L-tryptophan partition in alcohol / phosphate potassium salt-based aqueous two phase systems

Seyyed Mohammad Arzideh Faculty of Chemical Engineering, Babol University of Technology, PO Box, 484, Babol, Iran Email: [email protected]

Kamyar Movagharnejad Faculty of Chemical Engineering, Babol University of Technology, PO Box, 484, Babol, Iran Email: [email protected]

Mohsen Pirdashti2 Chemical Engineering Department, Faculty of Engineering, Shomal University, PO Box 731, Amol, Mazandaran, Iran Email: [email protected]

2

Corresponding Author

Conflict of Interest and Authorship Conformation

Dear Editor, We have prepared a manuscript for The Journal of Chemical Thermodynamics that shows the phase diagrams and compositions and thermodynamics analysis of L-tryptophan partition, which is an important topic in Aqueous Two Phase System. This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue. All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version. The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript. The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:

Sincerely, Authors

Seyyed Mohammad Arzideh

Faculty of Chemical Engineering, Babol University of Technology, PO Box, 484, Babol, Iran

Kamyar Movagharnejad

Faculty of Chemical Engineering, Babol University of Technology, PO Box, 484, Babol, Iran

Mohsen Pirdashti

Chemical Engineering Department, Faculty of Engineering, Shomal University, PO Box 731, Amol, Mazandaran, Iran

Research Highlight: 

Phase diagram for ATPS of 1-Butanol/2-Butanol/Tert-Butanol with K2HPO4 were determined.



L-Tryptophan partitioning was investigated.



The hybrid ion-interaction and solvation model (HIS) was firstly combined with modified extended UNIQUAC model to describe LLE data.



The proposed model (HIS-UNIQUAC) presented more accurate results.



The partitioning coefficient represented a correlation with the long-range electrostatic and solvation term of proposed model.