Prediction of phase diagrams for new pH-thermo sensitive recycling aqueous two-phase systems

Fluid Phase Equilibria 298 (2010) 206–211

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Prediction of phase diagrams for new pH-thermo sensitive recycling aqueous two-phase systems Yanjie Li, Xuejun Cao ∗ State Key Laboratory of Bioreactor Engineering, Department of Biochemical Engineering, East China University of Science Technology, 130 Meilong RD., Shanghai 200237, China

a r t i c l e

i n f o

Article history: Received 22 November 2009 Received in revised form 10 April 2010 Accepted 3 July 2010 Available online 21 July 2010 Keywords: Aqueous two-phase systems Thermo-sensitive polymer pH-sensitive polymer Flory–Huggins model COVE model

a b s t r a c t The recyclable aqueous two-phase systems formed by thermo-sensitive polymer (PNB ) and pH-sensitive polymer (PADB ) have been prepared by our laboratory. In this study, the Flory–Huggins model derived from the lattice theories and the COVE model based on the McMillan–Mayer solution theory were used for correlations and predictions of phase diagrams. The interaction parameters between the solvent and the polymers of the Flory–Huggins model were calculated from solubility parameters. The interaction parameters between the polymers and the COVE coefficients were determined by fitting experimental data. Simulation of Flory–Huggins model and COVE model indicates that the deviation between prediction values and experimental data is less than 0.50%. The COVE model was more effective than the Flory–Huggins model to this system. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Aqueous two-phase systems (ATPS) formed by two polymers or a polymer and a salt have some advantages in the purification of bioproducts and biocatalysis engineering [1]. However, the phase-forming polymers could not be recycled effectively and lead to high costs and environmental pollution, which has become an obstacle in industry. Our lab has been focusing on the development and application of the new recyclable ATPS polymers. PNB –PADB ATPS are new recycling ATPS, which were prepared by our laboratory [2,3]. PNB was copolymerized using N-isopropylacrylamide (NIPA), n-butyl acrylate (BA) as monomers, and 2,2 -azo-bisisobutyronitrile(AIBN) as initiator. It is a thermo-sensitive copolymer with a recovery of 99.1%. PADB was copolymerized with acrylic, 2-(dimethylamino)ethyl methacrylate (DMAEMA) and n-butyl methacrylate (BMA) as monomers. It is a pH-sensitive polymer which can be recycled by adjusting its isoelectric point (PI) to 4.1, with a recovery of 97.1%. The PNB –PADB recycling ATPS show potential application in bioseparation engineering and biocatalysis engineering areas. The knowledge of phase-forming and phase diagram is also needed for the engineering. There are two kinds of models describing the phase behaviors of aqueous two-phase systems in the literature, one based on lattice theories and the other on osmotic virial expansions [4].

∗ Corresponding author. Tel.: +86 21 64252695; fax: +86 21 64252695. E-mail address: [email protected] (X. Cao). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.07.001

The Flory–Huggins theory [5], the UNIQUIC model [6], the UNIFAC model [7], the Wilson model [8] and the Pitzer model [9] are some familiar ones for us. In this study, the Flory–Huggins model derived from the lattice theories and the COVE model [10,11] derived from the osmotic virial equations were used to predict the liquid–liquid phase behaviors of the PNB –PADB recycling ATPS at temperature 283.15 and 293.15 K. The work is very interesting for the development of the new systems. 2. Thermodynamic derivation 2.1. Flory–Huggins model The Flory–Huggins equation in its original form is [12]: H S G = − RT RT R

(1)

In which

 S =− ni ln ϕi R

(2)

i

and H = RT

  i

 ni mi

 i

ij ϕi ϕj

(3)

j>i

where ϕi and mi denote the volume fraction of component i and the ratio of the molar volume of component i to a reference volume, respectively. Here the reference volume was taken to be that

Y. Li, X. Cao / Fluid Phase Equilibria 298 (2010) 206–211

of component 3, water (thus m3 = 1). ij is the interaction parameter between components i and j, R is the gas constant and T is the temperature. ni is the amount of the component i. Flory–Huggins model proposed for the Gibbs energy of mixing is as follows:

⎛

⎞

i

j>i

where 0z refers to the pure solute. With Eqs. (7) and (9) we can get the chemical potential of the solvent as: −

1 − 01 c2 c3 = + + A22 c2 c2 + 2A23 c2 c3 +A33 c3 c3 +A222 c2 c2 c2 M2 M3 RT V¯ 1 +3A223 c2 c2 c3 + 3A233 c2 c3 c3 + A333 c3 c3 c3

ϕ   G i ln ϕi + ij ϕi ϕj ⎠ ni mi =⎝ RT mi i

(4)

i

RT

= ln

j

c2 V¯ 2 V¯ 2 V¯ 2 − c2 − c3 + A22 (2M2 c2 − V¯ 2 c2 c2 ) M2 M2 M3

+A23 (2M2 c3 − 2V¯ 2 c2 c3 ) − A33 V¯ 2 c3 c3 +A222

 ϕj   i + mi ij ϕj − mi jk ϕj ϕk (5) = ln ϕi + 1 − mi RT mj j

+A233

As three components, we can get:

−m1 12 ϕ1 ϕ2 − m1 13 ϕ1 ϕ3 − m1 23 ϕ2 ϕ3

3 − 03

(6a)

3 2

M2 c2 c2 + V¯ 2 c2 c2 c2

+A223 (3M2 c2 c3 + 3V¯ 2 c2 c2 c3 )

k>j

m1 m1 1 ϕ2 − ϕ3 + m1 12 ϕ2 + m1 13 ϕ3 = ln ϕ1 + 1 − ϕ1 − RT m2 m3

(10)

The chemical potential of the solutes as: 2 − 02

The chemical potential difference for component i can be obtained by differentiation of the excess Gibbs energy of mixing with respect to the amount of the component, ni , and is given by the following equation:

j

207

RT

= ln

3 2

M2 c3 c3 + 3V¯ 2 c2 c3 c3

+ A333 V¯ 2 c3 c3 c3

(11a)

V¯ 3 V¯ 3 c3 V¯ 3 − c2 − c3 − A22 V¯ 3 c2 c2 M3 M2 M3

+A23 (2M3 c2 − 2V¯ 3 c2 c3 ) + A33 (2M3 c3 − V¯ 3 c3 c3 ) 2 m2 m2 ϕ1 − ϕ3 + m2 12 ϕ1 + m2 23 ϕ3 = ln ϕ2 + 1 − ϕ2 − RT m1 m3 −m2 12 ϕ1 ϕ2 − m2 13 ϕ1 ϕ3 − m2 23 ϕ2 ϕ3

+A222 V¯ 3 c2 c2 c2 + A223

(6b)

−m3 12 ϕ1 ϕ2 − m3 13 ϕ1 ϕ3 − m3 23 ϕ2 ϕ3

(6c)

2

M3 c2 c2 + 3V¯ 3 c2 c2 c3

+A233 (3M3 c2 c3 + 3V¯ 3 c2 c3 c3 ) +A333

3 m3 m3 ϕ1 − ϕ2 + m3 13 ϕ1 + m3 23 ϕ2 = ln ϕ3 + 1 − ϕ3 − RT m1 m2

3

3 2

M3 c3 c3 + V¯ 3 c3 c3 c3

(11b)

Here the components 2, 3 refer to the copolymers PNB and PADB , and 1 is the solvent, water. The pure component property Mi has been measured earlier and V¯ i was determined with group contribution. 2.3. Estimation of parameters

2.2. COVE model Following McMillan and Mayer, the osmotic pressure or equivalent the chemical potential of the solvent, 1 , can be expressed in terms of a virial expansion in the solute concentrations ci in [g/ml solution] as [10]: 1 − 01 = −RT V¯ i

 N c

i

Mi i=2

 N

+

i=2

N

j=2

Aij ci cj +

 N

N

N

i=2

j=2

k=2



Aijk ci cj ck + · · ·

(7)

where component 1 is the solvent and the components 2, 3, . . ., N are the solutes, copolymers PNB and PADB in this work. 01 refers to the pure solvent. Furthermore, V¯ i is the molar volume, Mi is the number-average molecular weight of the component i, and Aij and Aijk are the second and third osmotic virial coefficients characterizing the interactions between dissolved particles of the type i, j and k in the solution. Assuming additivity of the molar volumes, the concentration ci can be expressed [10], in terms of the mol fractions xi as: ci =

xi Mi = V¯

xi Mi

N

(8)

¯

xV i=1 i i

For the osmotic virial equation, the thermodynamic consistent expressions for the chemical potentials of the solutes, z , based on the Gibbs–Duhem equation are derived. The free energy of mixing of the pure components is zero, leading to

⎛

cz V¯ z  z − 0z = RT ⎝ln + Mz N

i=2



V¯ z 2Aiz Mz − Mi

 ci +

N N   3

2 i=2 j=2

Haasen [13,14] divided the total solubility parameter ıt into three parts as follows: ı2t = ı2d + ı2p + ı2h

(12)

where ıd , ıp and ıh refer to the dispersion component, polarization component and hydrogen-bonding component, respectively, that we can get with group contribution as: ıd =

F di

(13a)

Vi

2 1/2 F ) pi ıp =

(13b)

1/2 E hi ıh =

(13c)

(

Vi

Vi

where Fdi , Fpi , Ehi , and Vi , respectively, are the dispersion, polarization and hydrogen-bonding components of the molar attract constant F of the atoms or groups for the repeat structural unit that can be added [15]. With the total solubility parameter ıt , we can get the interaction parameters between the solvent and the polymers 12 and 13 of the Flory–Huggins equation as below:

Aijz Mz − V¯ z Aij ci cj −

N N N    i=2 j=2 k=2

⎞ V¯ z Aijk ci cj ck ⎠

(9)

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Y. Li, X. Cao / Fluid Phase Equilibria 298 (2010) 206–211

Table 1 Experimental phase compositions for PNB –PADB ATPS at 283.15 and 293.15 K. 283.15 K (wt%)

293.15 K (wt%)

Top phase

Bottom phase

Top phase

Bottom phase

PADB

PNB

PADB

PNB

PADB

PNB

PADB

PNB

1.51 1.11 0.61 0.43 0.23

4.33 4.95 6.00 6.90 7.88

3.71 3.88 4.23 4.62 5.03

1.29 1.16 1.01 0.81 0.75

1.21 0.90 0.58 0.43 0.23

4.30 4.95 6.01 6.89 8.27

3.52 3.75 4.20 4.62 5.25

1.13 1.02 0.90 0.81 0.75

12 =

2 V¯ 1 (ı1 − ı2 ) RT

(14)

13 =

2 V¯ 1 (ı1 − ı3 ) RT

(15)

The parameters between the polymers 23 and the seven COVE parameters were obtained though the minimization of the following objective function:



OF =

r i=1

exp

(Ki

− Kicalc )

4. Results and discussion

2

r

can be calculated directly from the known stock solutions. Samples from each phase are taken out with micro-sampler, and are diluted to a concentration range in the calibration curve. All the samples and the calibration are measured by SEC, a three-column system (TSKgel G3000PWXL × 3) is used. The eluant is water and the flow rate is 0.7 ml/min. All the measurements are performed at 20 ± 0.1 ◦ C.

(16)

4.1. Experimental results

where r is the number of experimental points. Singular value decomposition (SVD) method was used for minimizing this objective function [16]. Some salts also partitioned between the phases, and then, the standard chemical potential, 0i is not exactly the same in two phases. In this study, the salt concentration is dilute so that the effect could be neglected [17]. The fitted parameters used to construct the phase diagram can be used only for phosphate buffer solutions (pH 7).

Because the pH-sensitive copolymer PADB become turbid in the acidic environment, phase diagram experiment was carried out at fixed pH 7.0 according to the previous study. The compositions of PNB –PADB in aqueous two-phase systems at 283.15 and 293.15 K are given in Table 1. The phase diagrams of all studied systems are shown in Fig. 1. PNB enriches in top phase and PADB in bottom phase.

3. Experiments

There are two pure substance parameters, Mi and V¯ i , which are needed for the calculation. The number-average molecular weights of the two copolymers Mi have been determined before, here Mn PNB = 2200 Da and Mn PADB = 37, 000 Da. The value of the molar volume V¯ i can be estimated by group contribution method, = 40, 500 cm3 /mol [20]. The here V¯ P = 2751 cm3 /mol and V¯ P

3.1. Materials and methods 3.1.1. Preparation of polymers PNB : The copolymerization of BA and NIPA was carried out in benzene with AIBN as initiator. After shaken for 24 h under nitrogen atmosphere at 65 ◦ C, the product was dissolved in acetone and deposited in hexane. Finally, it was dried in a vacuum [3,18]. PADB : Acrylic Acid, DMAEMA and n-Butylmethacrylate were added to the purified water at room temperature with APS and NaHSO3 as initiator. And then it was shaken for 24 h under the nitrogen atmosphere in a temperature controlled water bath at 60 ◦ C. The deposit was washed by absolute alcohol and dried in the vacuum [19]. The molecular weights of PNB and PADB were determined using membrane osmometry (Germany). Phase composition in ternary polymer–polymer–buffer systems was measured by Size-Exclusion High-Performance Liquid Chromatography (SEC), using a threecolumn systems comprised of one Bio-Gel TSK-4030-cm column and two Bio-Gel TSK-3030-cm columns in series. All measurements were performed at 25 ± 0.01 ◦ C.

4.2. Flory–Huggins model

NB

ADB

interaction parameters between the solvent and the polymers (12 , 13 ) calculated from solubility parameters ı with Eqs. (14) and

3.2. Phase-diagram measurements Two-phase systems are prepared by mixing different ratios of known stock solutions of PNB and PADB in salt-water (pH = 7 phosphate buffer, 0.1 M) in volumetrically marked centrifuge tubes. Water is then added to a total system to the weight of 5 g. All the tubes are placed in a constant-temperature to allow the phases separation and equilibrate for 24 h. The total solution concentrations

Fig. 1. Phase diagrams of PNB –PADB aqueous two-phase systems at 283.15 and 293.15 K.

Y. Li, X. Cao / Fluid Phase Equilibria 298 (2010) 206–211

209

Table 2 The absolute deviations (ADs) and average absolute deviations (AADs) between experimental data and prediction calculated with Flory–Huggins equation for PNB –PADB ATPS at 283.15 and 293.15 K. 283.15 K (wt%)

293.15 K (wt%)

PADB

PNB

PADB

PNB

Exp

Cal

ADs

Exp

Cal

ADs

Exp

Cal

ADs

Exp

Cal

ADs

Top phase 0.23 0.43 0.61 1.11 1.51

0.15 0.41 0.79 1.13 1.48

0.08 0.02 0.18 0.02 0.03

4.33 4.95 6.00 6.90 7.88

4.47 5.06 5.83 6.86 7.73

0.14 0.11 0.17 0.04 0.15

0.23 0.43 0.58 0.90 1.21

0.21 0.40 0.65 1.06 1.51

0.02 0.03 0.07 0.16 0.30

4.30 4.95 6.01 6.89 8.27

4.50 5.20 6.11 6.86 7.57

0.20 0.25 0.11 0.03 0.70

Bottom phase 3.71 3.88 4.23 4.62 5.03

3.74 3.89 4.17 4.62 5.15

0.03 0.01 0.06 0.01 0.12

0.75 0.81 1.01 1.16 1.29

0.75 0.81 1.01 1.16 1.29

0 0 0 0 0

3.52 3.75 4.20 4.62 5.25

3.90 4.02 4.31 4.61 4.94

0.38 0.27 0.11 0.01 0.31

0.75 0.81 0.90 1.02 1.13

0.75 0.81 0.90 1.02 1.13

0 0 0 0 0

AADs

0.05

0.06

0.17

0.13

absolute deviations are listed in Table 2. It could be seen from Table 2 that the absolute deviations of most data are less than 0.5% at 293.15 K, and less than 0.2% at 283.15 K. Even the maximum absolute deviation at 283.15 K is only 0.17%, which shows that Flory–Huggins model can predict phase diagram of PNB –PADB ATPS well.

4.3. COVE correlation

(15) are: 12 = 0.6656, 13 = 0.6771. The parameter between the polymers 23 is 0.1209, determined by fitting the LLE data at 293.15 K. These parameters are used to predict the phase behaviors at 283.15 and 293.15 K, which are shown in Figs. 2 and 3. The

To predict a phase diagram of ATPS, it had better that the model parameters could be easily obtained from VLE data, and then these parameters were used for predictions. There are not any known VLE data, because the PNB –PADB ATPS are firstly developed, so the LLE data has to be used to correlate the parameters. The correlation results and the deviations are listed in Table 3, which shows that the deviations of most data correlation are less than 0.3%. From Figs. 4 and 5, we can see that it has good correlation in the range of low concentrations. The bigger deviations appear in high concentrations, probably because the polydispersity and molecular-weight distribution have a considerable influence on the phase behavior now. Table 4 shows that the COVE parameters are temperature dependent, and that the same finding was also suggested before [11].

Fig. 3. Prediction of phase diagram for PNB –PADB aqueous two-phase systems with Flory–Huggins equation at 293.15 K.

Fig. 4. Correlation of phase diagram for PNB –PADB aqueous two-phase systems with COVE model at 283.15 K.

Fig. 2. Prediction of phase diagram for PNB –PADB aqueous two-phase systems with Flory–Huggins equation at 283.15 K.

210

Y. Li, X. Cao / Fluid Phase Equilibria 298 (2010) 206–211

Table 3 The absolute deviations (ADs) and average absolute deviations (AADs) between experimental data and prediction calculated with COVE equation for PNB –PADB ATPS at 283.15 and 293.15 K. 283.15 K (wt%)

293.15 K (wt%)

PADB

PNB

PADB

PNB

Exp

Cal

ADs

Exp

Cal

ADs

Exp

Cal

ADs

Exp

Cal

ADs

Top phase 0.23 0.43 0.61 1.11 1.51

0.21 0.51 0.55 1.11 1.50

0.02 0.08 0.06 0.01 0.01

4.33 4.95 6.00 6.90 7.88

4.39 4.91 5.95 6.99 8.96

0.06 0.04 0.05 0.09 1.08

0.23 0.43 0.58 0.90 1.21

0.21 0.43 0.69 0.90 1.20

0.02 0.00 0.11 0.00 0.01

4.30 4.95 6.01 6.89 8.27

4.32 4.90 5.78 6.92 7.57

0.02 0.05 0.22 0.03 0.70

Bottom phase 3.71 3.88 4.23 4.62 5.03

3.72 3.86 4.37 4.57 5.33

0.01 0.02 0.15 0.05 0.30

0.75 0.81 1.01 1.16 1.29

0.75 0.81 1.01 1.16 1.29

0 0 0 0 0

3.52 3.75 4.20 4.62 5.25

3.54 3.70 4.20 4.71 4.94

0.02 0.05 0.00 0.09 0.31

0.75 0.81 0.90 1.02 1.13

0.75 0.81 0.90 1.02 1.13

0 0 0 0 0

AADs

0.07

0.13

0.06

0.10

Table 4 Interaction parameters of COVE model at 283.15 and 293.15 K.

283.15 K 293.15 K

A22 (ml mol/g2 )

A23 (ml mol/g2 )

A33 (ml mol/g2 )

A222 (ml2 mol/g3 )

A223 (ml2 mol/g3 )

A233 (ml2 mol/g3 )

A333 (ml2 mol/g3 )

2.525 × 10−3 1.941 × 10−3

1.924 × 10−3 2.351 × 10−3

−1.027 × 10−2 −1.060 × 10−2

−5.432 × 10−2 −1.526 × 10−2

−3.529 × 10−2 −1.768 × 10−2

−2.688 × 10−2 −2.312 × 10−2

3.955 × 10−2 5.637 × 10−2

F G H mi ni R S T V¯ i W xi

Fig. 5. Correlation of phase diagram for PNB –PADB aqueous two-phase systems with COVE model at 293.15 K.

5. Conclusions

molar attract constant molar Gibbs free energy of mixing enthalpy the ratio of the molar volume of component i to a reference volume amount of component i gas constant entropy temperature partial molar volume of component i molecular weight mole fraction of component i

Greek letters chemical potential of component i i ij Flory–Huggins interaction parameters between components i and j volume fraction of component i ϕi ı solubility parameter

The new ATPS formed by thermo-sensitive polymer (PNB ) and pH-sensitive polymer (PADB ) are very promising in bioseparation engineering and biocatalysis engineering. Their phase diagram has been predicted by Flory–Huggins model and COVE model. The interaction parameters of Flory–Huggins model calculated from the solubility parameters were the first time to be used to correlate the LLE of the new ATPS, and the COVE parameters were obtained by fitting the LLE data. The two models show good agreements between the calculation data and the experimental data. The work is valuable for the design and application of this new ATPS in industry.

Superscripts i, j, k components i, j and k d, p, h dispersion component, polarization component and hydrogen-bonding component n number-averaged 1 solvent water 2 copolymer PADB 3 copolymer PNB

List of symbols

Acknowledgments

Aij Aijk ci

This project was supported by National Medicine Novelty Project of China (2009ZX09306-001) and the National Special Fund for State Key Laboratory of Bioreactor Engineering (2060204). Authors appreciate the above National funds.

second osmotic virial coefficient third osmotic virial coefficient amount of substance concentration of component i

Y. Li, X. Cao / Fluid Phase Equilibria 298 (2010) 206–211

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