Liquid–liquid equilibrium correlation of aqueous two-phase systems composed of polyethylene glycol and nonionic surfactant

Thermochimica Acta 602 (2015) 78–86

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Liquid–liquid equilibrium correlation of aqueous two-phase systems composed of polyethylene glycol and nonionic surfactant Yang Liu a, * , Zhongyang Wu a , Yongjie Zhao b a b

Department of Biology & Guangdong Provincial Key Laboratory of Marine Biotechnology, Shantou University, Shantou, Guangdong 515063, PR China Department of Mechanical Engineering, College of Engineering, Shantou University, Shantou, Guangdong 515063, PR China

A R T I C L E I N F O

A B S T R A C T

Article history: Received 29 October 2014 Received in revised form 14 January 2015 Accepted 19 January 2015 Available online 1 February 2015

Phase diagrams of aqueous two-phase systems (ATPS) composed of polyethylene glycol 20000 (PEG 20000) + polyoxyethylene octyl phenyl ether (Triton X-100) or polyoxyethylene sorbitan monooleate (Tween 80) + water are determined at 273.15, 293.15 and 313.15 K, respectively. The liquid–liquid equilibrium (LLE) experimental data are correlated using the Flory–Huggins model derived from the lattice theories, and new interaction parameters (l12, l13 and l23) between any two compositions (the polymer(1) and the nonionic surfactant(2), the solvent(3)) in the ATPS are estimated at various temperature. Two kinds of fitting results are obtained when the surfactant molecules are regarded as single molecules or micellar molecules, respectively. It indicates that the interaction parameters (l12) between PEG and nonionic surfactant including Triton X-100 and Tween 80 decrease 52.3% and 105% as single molecules, while decrease 421% and 403% as micellar molecules by raising temperature, respectively. Moreover, the slightly better fitting effect can be observed if the surfactant molecules are regarded as the micellar molecules. The standard deviation between prediction values and experimental data of the components weight fraction is lower than 0.1% using the surfactant micellar parameters, showing the good descriptive quality and applicability of the Flory–Huggins model. ã 2015 Elsevier B.V. All rights reserved.

Keywords: Liquid–liquid equilibrium Nonionic surfactant PEG 20000 Flory–Huggins model The interaction parameter

1. Introduction Recently, the polymer/surfactant aqueous two-phase system (ATPS) [1–3] has been studied in the separation of biological materials, such as proteins, enzymes, and nucleic acids due to the extensive use of polymer and surfactant in pharmaceutical industry [4]. In this kind of ATPS, nonionic surfactant and polyethylene glycol (PEG) as a hydrophilic polymer are usually used to form the two-phase system. The surfactant molecules in the solution can self-organize and aggregate spontaneously to form the micelles with hydrophilic head-groups facing outwards and hydrophobic chains pointing inwards. The micelles and the PEG molecules in the solution can impel two phases formation due to the steric hindrance effect. The two compositions are concentrated in each phase, respectively, and the surfactant micelles can be regarded as the second phase composition [5–7]. In the polymer/nonionic surfactant ATPS, biomolecules partitioning depends largely on the hydrophobic interaction and excluded volume interaction due to the micelles structure existing.

* Corresponding author. Tel.: +86 754 86503093; fax: +86 754 86502726. E-mail address: [email protected] (Y. Liu). http://dx.doi.org/10.1016/j.tca.2015.01.013 0040-6031/ ã 2015 Elsevier B.V. All rights reserved.

Thus, the polymer/nonionic surfactant ATPS has an advantage of the hydrophobic biomolecules separation such as membrane proteins [8–10]. However, liquid–liquid equilibrium (LLE) data of the polymer/nonionic surfactant aqueous systems are relatively scarce, which would limit partly the universal application of this kind of ATPS. Previous studies on ATPSs show that the system temperature is usually important for the LLE of ATPS [11–13]. In polymer/nonionic surfactant ATPS, the micelles comprised by the nonionic surfactant molecules greatly care about the system’s temperature. The form and the amount of the micelles both in the surfactant-rich phase and in the polymer-rich phase vary with the system’s temperature [14–17], so the LLE of the polymer/nonionic surfactant ATPS would depend greatly on the system’s temperature. Moreover, the type of the nonionic surfactant molecule determines the micelles aggregation structure and number in ATPS, and then influences the LLE of the polymer/nonionic surfactant ATPS. In this paper, polyoxyethylene alkyl phenol (Triton X-100) and polyoxyethylene sorbitan monooleate (Tween 80) are selected to investigate the effect of the nonionic micelles type on the LLE of the polymer/nonionic surfactant ATPS. Using the Flory–Huggins model derived from the lattice theories, the temperature dependency of the interaction parameters is discussed when the surfactant molecules are

Y. Liu et al. / Thermochimica Acta 602 (2015) 78–86

[(Fig._1)TD$IG]

Table 1 The refractive index (N) of the mixed aqueous solution including PEG 20000 and surfactant with various concentrations at T = 293.15 K and pressure p = 0.1 MPa.a

Absorbance of 278nm or 240nm

1.6 Triton X-100 (278nm) Tween 80 (240nm)

1.4

N

1.2 1

0.6 y = 19.786x + 0.0196 R² = 0.9995

0.4 0.2 0 0

0.01

0.02

0.03

0.04

0.05

Surfactant concentration (w/w%) Fig. 1. The standard curves and fitting linear equations of Triton X-100 (278 nm) and Tween 80 (240 nm) aqueous solutions by spectrometer measurement, respectively.

regarded as single molecules or micellar molecules, respectively. The effect of temperature on the LLE of the polymer/nonionic surfactant ATPS has been studied further. 2. Experimental 2.1. Materials PEG 20000 (GR,
95% mass purity) was purchased from Merck (Shanghai, China). The non-ionic surfactant, Triton X-100 (polyoxyethylene octyl phenyl ether, GR,
95% mass purity) and Tween 80 (polyoxyethylene sorbitan monooleate, GR,
95% mass purity) were purchased from Amresco (Shanghai, China). The polymer and surfactants were used without further purification. Aqueous solutions were prepared with deionized and doubly distilled water. 2.2. Methods 2.2.1. Determination of the binodal curve Aqueous solutions of PEG 20000 and Triton X-100 (or Tween 80) with known concentrations were prepared beforehand and mixed in definite proportions, in such a way that the total mass of the system was around 10 g; masses were measured to within 0.1 mg. The three components solutions were well mixed by a turbine mixer in a capped plastic tube designed for centrifugation. The tubes were centrifuged at 2800  g for 20 min using a centrifuge of Universal 320R Hettich (Germany), and then were

Concentration (%, w/w)

1.3330 1.3342 1.3358 1.3370 1.3384 1.3398 1.3411 1.3350 1.3363 1.3377 1.3390 1.3404 1.3416 1.3355 1.3371 1.3385 1.3398 1.3411 1.3425 1.3371 1.3380 1.3398 1.3411 1.3426 1.3440 1.3380 1.3392 1.3406 1.3420 1.3435 1.3447

y = 33.97x + 0.0041 R² = 0.9997

0.8

79

a

N

PEG 20000

Triton X-100

– 0 1.0 2.0 3.0 4.0 5.0 0 1.0 2.0 3.0 4.0 5.0 1.0 2.0 3.0 4.0 5.0 1.0 0 1.0 2.0 3.0 4.0 5.0 1.0 2.0 3.0 4.0 5.0 1.0

– 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 1.5 1.5 2.0 2.0 2.0 2.0 2.0 2.0 2.5 2.5 2.5 2.5 2.5 2.5 3.0 3.0 3.0 3.0 3.0 3.0

1.3330 1.3345 1.3361 1.3375 1.3388 1.3402 1.3415 1.3353 1.3367 1.3380 1.3396 1.3407 1.3421 1.3359 1.3373 1.3386 1.3400 1.3415 1.3427 1.3366 1.3382 1.3396 1.3411 1.3424 1.3439 1.3374 1.3388 1.3402 1.3416 1.3430 1.3444

Concentration (%, w/w) PEG 20000

Tween 80

– 1.0 2.0 3.0 4.0 5.0 1.0 1.0 2.0 3.0 4.0 5.0 1.0 1.0 2.0 3.0 4.0 5.0 1.0 1.0 2.0 3.0 4.0 5.0 1.0 1.0 2.0 3.0 4.0 5.0 1.0

– 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 1.5 1.5 2.0 2.0 2.0 2.0 2.0 2.0 2.5 2.5 2.5 2.5 2.5 2.5 3.0 3.0 3.0 3.0 3.0 3.0

Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 10 kPa.

left undisturbed for at least 24 h at 273.15, 293.15 and 313.15 K, respectively, in a thermostatic bath controlled within 0.05 K. The binodal curves represent the borderline between the one-phase and two-phase regions, which were determined by cloud-point measurements in the thermostatic bath with different temperature of 273.15  0.05, 293.15  0.05 and 313.15  0.05 K, respectively. Samples of 25% (w/w) PEG 20000 solution were prepared and carefully added drop-wise into 40% (w/w) Triton X-100 (or Tween 80) solution until the two-phase region was reached (turbid samples). Then water was added drop-wise until the one phase region was reached (transparent samples). The compositions where the change from a two-phase to a one phase system occurs lie on the binodal. A sample was regarded as monophasic when it

1.346

1.346

1.344

1.344

1.342

1.342

1.34

N

N

[(Fig._2)TD$IG]

1.338

1%Triton x-100 1.5%Triton x-100 2%Triton x-100 2.5%Triton x-100 3%Triton x-100

1.336 1.334

1 2 3 4 5 PEG20000 concentration (w/w%)

1% Tween 80 1.5% Tween 80 2% Tween 80 2.5% Tween 80 3% Tween 80

1.338 1.336 1.334

1.332 0

1.34

6

0

1 2 3 4 5 PEG20000 concentration (w/w%)

6

Fig. 2. The refractive index (N) of the mixed aqueous solution including PEG 20000 and surfactant with various concentrations. Left figure expresses PEG 20000 and Triton X100 solution, and right figure expresses PEG 20000 and Tween 80 solution.

80

Y. Liu et al. / Thermochimica Acta 602 (2015) 78–86

Table 2 Parameters (a0,a1, a2) of refractive index introduced into Eq. (1). a0, a1, a2 are the parameters fitted by the experimental refractive index of the mixed PEG 20000 and nonionic surfactant aqueous solution, a0 is actually the refractive index of pure water at T = 293.15 K and pressure p = 0.1 MPa. Component

a0

Water PEG 20000 Triton X-100 Tween 80

1.3330

a1

a2

100sda

0.1869 0.1443

0.0842 0.0163

0.1383

N

a sd ¼ ðSi¼1 ðncalcd  nexptl Þ2 =NÞ0:5 , where n and N represent the refractive index and the number of experimental data points, respectively.

was completely clear and no phase separation could be detected. The system was weighed repeatedly and the phase compositions at the phase boundary were calculated. Thus, the binodal curves of PEG 20000/Triton X-100 and PEG 20000/Tween 80 ATPSs could be obtained at various temperatures. 2.2.2. Determination of equilibrium constants Samples in the two phase region were carefully withdrawn from both phases. The Triton X-100 (or Tween 80) content was measured using UV–vis spectrophotometer of Model UVPC2501 (Shimadzu, Japan) in 278 nm (or 240 nm) where absorbance spectra of Triton X-100 (or Tween 80) aqueous solution has a highest absorbance peak, and the standard curves and fitting linear equations of respective surfactants aqueous solution are shown in Fig. 1. The mass fraction of PEG was determined by refractive index measure using an automatic Abbe refractometer of Model 2WAJ (Shanghai, China) at 298.15  0.05 K. The correlation between the refractive index (n) and the mass fraction of PEG (w1) and nonionic surfactant (w2) can be written as [18,19] n ¼ a0 þ a1 w 1 þ a2 w 2

(1)

The experimental refractive index of the mixed PEG 20000 and nonionic surfactant aqueous solution with various concentrations are displayed in Fig. 2. Through the linear calibration plots of the refractive index of the mixed solution, the parameters (a0, a1, a2) of Eq. (1) and standard deviations for PEG 20000 and nonionic surfactant aqueous solution are obtained in Table 1. Eq. (1) is only valid for mass fraction of w1  0.05 and w2  0.03 in the linear calibration range. The samples of ATPS should be diluted to the above mass fraction range and the uncertainty of the polymer mass fraction achieved using Eq. (1) was better than 0.0005.

3. Thermodynamic model The Flory–Huggins equation was usually used to describe the non-ideality of the liquid phases, such as polymer/polymer ATPS [20,21] or polymer/salt ATPS [22,23]. In this work, the Flory– Huggins equation was also used in the polymer/nonionic surfactant ATPS. This model proposed for the molar excess Gibbs free energy of mixing is as follows:
 DG ’ ¼ S i ln’i þ S S lij ’i ’j S ni mi (2) RT i mi i j>1 where ’i and mi denote the volume fraction of component i and the ratio of the molar volume of component i to a reference volume, respectively. The molar volume of component i is the molecular weight divided by mass density of component i. Here the reference volume was taken to be that of component 3, water (thus m3 = 1). The other components mi is the ratio of the molar volume of component i to the molar volume of water. The mi values of various components are listed in Table 2, the different mi values of the single molecules and the micellar molecules for the same surfactant molecules are displayed, especially. lij is the interaction parameter between components i and j, R is the gas constant and T is the temperature. ni is the molar amount of the component i. So the chemical potential difference of component i can be obtained by differentiation of the excess Gibbs energy of mixing to ni and be given as follows:

Dmi RT

¼ ln’i þ 1  mi S i

’i mi

þ mi S lij ’j  mi S S ljk ’j ’k j

(3)

j k>j

where Dmi is the excess chemical potential. Considering with the three components of PEG 20000(1), nonionic surfactant(2) and water(3), Eq. (3) can be written:

Dm1 RT

¼ ln’1 þ 1  ’1 

m1 m ’  1 ’ þ m1 l12 ’2 þ m1 l13 ’3 m2 2 m3 3

m1 l12 ’1 ’2  m1 l13 ’1 ’3  m1 l23 ’2 ’3

Dm2 RT

¼ ln’2 þ 1  ’2 

(4a)

m2 m ’  2 ’ þ m2 l12 ’1 þ m2 l23 ’3 m1 1 m3 3

m2 l12 ’1 ’2  m2 l13 ’1 ’3  m2 l23 ’2 ’3

[(Fig._3)TD$IG]

Fig. 3. Effect of temperature on binodal curves of ATPS composed of PEG 20000 and nonionic surfactant: ^, 273.15 K; *, 293.15 K;

4, 313.15 K.

(4b)

Y. Liu et al. / Thermochimica Acta 602 (2015) 78–86

81

Table 3 Physical property parameters of various components introduced into Eq. (2). Component

Molecular weight

Mass density (g/mL)

Molar volume (mL/mol)

mi

1:PEG 2:Triton X-100

20,000 647 90,000 [24] 1310 76,000 [24] 18

0.83 [20] 1.07 1.07 1.08 1.08 1.00

24038.46 604.67 84112.15 1224.30 70370.37 18.00

1335.47 33.59 4672.90 68.02 3909.47 1.00

Single molecule Micellar molecule Single molecule Micellar molecule

2:Tween 80 3:H2O

ð’T2l  ’B2l Þ 

Dm3 RT

¼ ln’3 þ 1  ’3 

m3 m ’  3 ’ þ m3 l13 ’1 þ m3 l23 ’2 m1 1 m2 2

m3 l12 ’1 ’2  m3 l13 ’1 ’3  m3 l23 ’2 ’3

(4c)

For top and bottom phases at LLE with constant temperature and pressure, the chemical potential (mi) of any component i in both phases are equal as follows:

mTi ¼ mBi

(5)

The superscript T and B mean top phase and bottom phase, respectively. So Eqs. (4a)–(4c) can be written: m1 ð’

B 2l 

’

T 2l þ

’ ’ T 1l

T 2;l 

’ ’ l B 1l

’

B 2l Þ 12 þ m1 ð

B 3l 

’

T 3l þ

’ ’ T 1l

T 3l 

(6a)

þm2 ð’B3l  ’T3l þ ’T2l ’T3l  ’B2l ’B3l Þl23 ¼ ðln’T2l  ln’B2l Þ

Table 4 Experimental binodal data of PEG 20000 (w1) + Triton X-100 (w2) + water ATPS at different temperatures and pressure p = 0.1 MPa.a w1

w2

w1

w2

w1

w2

T = 273.15 K 0.0110 0.2890 0.0204 0.2499 0.0259 0.2219 0.0401 0.1864 0.0455 0.1607 0.0479 0.1522

0.0541 0.0581 0.0632 0.0678 0.0683 0.0776

0.1281 0.1103 0.0941 0.0821 0.0744 0.0589

0.0818 0.0832 0.0908 0.0926 0.0930 0.0964

0.0491 0.0429 0.0359 0.0335 0.0317 0.0279

0.0960 0.0998 0.1011 0.1066 0.1145

0.0268 0.0238 0.0216 0.0182 0.0079

T = 293.15 K 0.0023 0.3909 0.0049 0.3403 0.0090 0.2729 0.0127 0.2594 0.0144 0.2488 0.0170 0.2317 0.0195 0.1937

0.0284 0.0327 0.0365 0.0408 0.0425 0.0445 0.0470

0.1790 0.1609 0.1470 0.1301 0.1239 0.1167 0.1080

0.0483 0.0513 0.0549 0.0585 0.0607 0.0641 0.0663

0.0946 0.0866 0.0776 0.0689 0.0599 0.0512 0.0471

0.0696 0.0780 0.0863 0.0970 0.1017 0.1031

a

þm3 ð’B2l  ’T2l þ ’T2l ’T3l  ’B2l ’B3l Þl23 ¼ ðln’T3l  ln’B3l Þ ð’T3l  ’B3l Þ 

0.1811 0.1439 0.1331 0.1163 0.1031

0.0337 0.0372 0.0388 0.0410 0.0437

0.0928 0.0820 0.0751 0.0682 0.0629

0.0456 0.0313 0.0214 0.0124 0.0067

(6c)

the subscript l denotes the tie line number. Eqs. (6a)–(6c) can be written in the matrix form Dl ¼ d

(7)

where

l ¼ ½ l12 l13 l23 T

(8)

3 A 4 D ¼ B5 C

(9)

2 3 a d ¼ 4b5 c

(10)

Table 5 Experimental binodal data of PEG 20000 (w1) + Tween 80 (w2) + water ATPS at different temperatures and pressure p = 0.1 MPa.a w1

0.0189 0.0219 0.0244 0.0281 0.0321

m3 T m ð’  ’B1l Þ  3 ð’T2l  ’B2l Þ l¼1;2;3;4 m1 1l m2

2

m2 ð’B1l  ’T1l þ ’T1l ’T2l  ’B1l ’B2l Þl12  m2 ð’B1l ’B3l  ’T1l ’T3l Þl13

T = 313.15 K 0.0012 0.3975 0.0051 0.3342 0.0115 0.2614 0.0154 0.2338 0.0186 0.2180

m3 ð’B1l ’B2l  ’T1l ’T2l Þl12 þ m3 ð’B1l  ’T1l þ ’T1l ’T3l  ’B1l ’B3l Þl13

B 3l Þ 13

m1 m1  ð’T2l  ’B2l Þ  ð’T3l  ’B3l Þ l¼1;2;3;4 m2 m3

w2

(6b)

’ ’ l B 1l

m1 ð’B2l ’B3l ’T2l ’T3l Þl23 ¼ ðln’T1l  ln’B1l Þ  ð’T1l  ’B1l Þ

w1

m2 T m2 T ð’  ’B1l Þ  ð’  ’B3l Þ l¼1;2;3;4 m1 1l m3 3l

w1

w2

w1

w2

w1

w2

T = 273.15 K 0.0250 0.2750 0.0351 0.2228 0.0446 0.1947 0.0560 0.1629 0.0649 0.1406

0.0712 0.0799 0.0892 0.0942 0.0990

0.1188 0.0948 0.0781 0.0669 0.0590

0.1019 0.1051 0.1060 0.1089 0.1119

0.0526 0.0477 0.0470 0.0430 0.0391

0.1148 0.1171 0.1191 0.1254

0.0358 0.0332 0.0309 0.0240

0.0367 0.0244 0.0155 0.0088 0.0053 0.0037

T = 293.15 K 0.0161 0.3357 0.0214 0.2881 0.0281 0.2521 0.0381 0.2284 0.0459 0.1836 0.0604 0.1552

0.0722 0.0748 0.0810 0.0825 0.0861 0.0922

0.1278 0.1197 0.1035 0.0993 0.0891 0.0813

0.0931 0.0961 0.0995 0.1008 0.1073 0.1130

0.0785 0.0722 0.0642 0.0619 0.0437 0.0380

0.1183 0.1211 0.1283 0.1300 0.1638 0.1970

0.0319 0.0288 0.0218 0.0204 0.0095 0.0058

0.0585 0.0683 0.0736 0.0803 0.0872

T = 313.15 K 0.0065 0.3869 0.0150 0.3034 0.0241 0.2579 0.0292 0.2328 0.0370 0.2025 0.0575 0.1425

0.0633 0.0640 0.0686 0.0774 0.0819 0.0824

0.1249 0.1169 0.1068 0.0852 0.0766 0.0735

0.0827 0.0857 0.0879 0.0922 0.0925 0.0961

0.0680 0.0590 0.0525 0.0411 0.0453 0.0362

0.0996 0.1032 0.1058 0.1121 0.1384 0.1967

0.0296 0.0265 0.0225 0.0217 0.0086 0.0050

Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 10 kPa.

a

w2

Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 10 kPa.

82

Y. Liu et al. / Thermochimica Acta 602 (2015) 78–86

Table 6 LLE data for systems composed of PEG 20000 (w1) + Triton X-100 (w2) + H2O (w3), from 273.15 to 313.15 K at pressure p = 0.1 MPa.a Tie line

TLL

Feed

Top phase

Bottom phase

w1

w2

w3

w1

w2

w3

w1

w2

w3

0.3272 0.3437 0.3882 0.4593

0.0600 0.0600 0.0700 0.0800

0.1500 0.1600 0.1600 0.1700

0.7900 0.7800 0.7700 0.7500

0.1012 0.1103 0.1308 0.1557

0.0207 0.0134 0.0021 0.0025

0.8781 0.8763 0.8671 0.8418

0.0139 0.0098 0.0078 0.0065

0.2875 0.3057 0.3189 0.3273

0.6986 0.6845 0.6733 0.6662

0.2519 0.2660 0.2774 0.3236

0.2891 0.3080 0.3155 0.3396

0.0480 0.0520 0.0480 0.0560

0.1400 0.1400 0.1600 0.1700

0.8120 0.8080 0.7920 0.7740

0.0838 0.0913 0.0959 0.1121

0.0179 0.0142 0.0113 0.0019

0.8983 0.8945 0.8928 0.8760

0.0138 0.0130 0.0124 0.0081

0.2599 0.2684 0.2759 0.3082

0.7266 0.7186 0.7117 0.6837

0.2854 0.3021 0.3167 0.3374

0.2907 0.3014 0.3012 0.3310

0.0500 0.0500 0.0500 0.0600

0.1400 0.1500 0.1600 0.1600

0.8100 0.8000 0.7900 0.7800

0.0878 0.0947 0.0980 0.1121

0.0073 0.0033 0.0029 0.0019

0.9049 0.9020 0.8991 0.8860

0.0081 0.0075 0.0067 0.0061

0.2813 0.2926 0.3061 0.3221

0.7106 0.6999 0.6872 0.6718

T = 273.15 K 1 2 3 4

0.2808 0.3090 0.3398 0.3575

T = 293.15 K 1 2 3 4 T = 313.15 K 1 2 3 4 a

STL

Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 10 kPa.

[(Fig._4)TD$IG]

Fig. 4. Comparison of the experimental tie-line data with calculated from the Flory–Huggins model for PEG 20000/Triton X-100 ATPS at 273.15 K, 293.15 K and 313.15 K, respectively. Hollow circular symbols, solid circular symbols and red triangle symbols denote experimental, calculated tie lines as Triton X-100 single molecules and calculated tie lines as Triton X-100 micelles, respectively. Curve line denotes binodal curve. Straight lines are shown to guide the eyes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Y. Liu et al. / Thermochimica Acta 602 (2015) 78–86

[(Fig._5)TD$IG]

83

Fig. 5. Comparison of the experimental tie-line data with calculated from the Flory–Huggins model for PEG 20000/Tween 80 ATPS at 273.15 K, 293.15 K and 313.15 K, respectively. Hollow circular symbols, solid circular symbols and red triangle symbols denote experimental, calculated tie lines as Tween 80 single molecules and calculated tie lines as Tween 80 micelles, respectively. Curve line denotes binodal curve. Straight lines are shown to guide the eyes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

m1 T ð’  ’B2l Þ m2 2l

Bl1 ¼ m2 ð’B1l  ’T1l þ ’T1l ’T2l  ’B1l ’B2l Þl¼1;2;3;4

(13a)

Bl2 ¼ m2 ð’B1l ’B3l  ’T1l ’T3l Þ l¼1;2;3;4

(13b)

Bl3 ¼ m2 ð’B3l  ’T3l þ ’T2l ’T3l  ’B2l ’B3l Þ l¼1;2;3;4

(13c)

C l1 ¼ m3 ð’B1l ’B2l  ’T1l ’T2l Þ l¼1;2;3;4

(14a)

(11c)

C l2 ¼ m3 ð’B1l  ’T1l þ ’T1l ’T3l  ’B1l ’B3l Þl¼1;2;3;4

(14b)

Al1 ¼ m1 ð’B2l  ’T2l þ ’T1l ’T2;l  ’B1l ’B2l Þ l¼1;2;3;4

(12a)

C l3 ¼ m3 ð’B2l  ’T2l þ ’T2l ’T3l  ’B2l ’B3l Þl¼1;2;3;4

(14c)

Al2 ¼ m1 ð’B3l  ’T3l þ ’T1l ’T3l  ’B1l ’B3l Þl¼1;2;3;4

(12b)

al1 ¼ ðln’T1l  ln’B1l Þ  ð’T1l  ’B1l Þ  m1  ð’T3l  ’B3l Þ l¼1;2;3;4 m3 bl1 ¼ ðln’T2l  ln’B2l Þ  ð’T2l  ’B2l Þ  m2  ð’T3l  ’B3l Þ l¼1;2;3;4 m3

(11a)

m2 T ð’  ’B1l Þ m1 1l

m cl1 ¼ ðln’T3l  ln’B3l Þ  ð’T3l  ’B3l Þ  3 ð’T1l  ’B1l Þ m1 m3  ð’T2l  ’B2l Þ l¼1;2;3;4 m2

Al2 ¼ m1 ð’B2l ’B3l  ’T2l ’T3l Þl¼1;2;3;4

(11b)

so l can be achieved:

(12c)

l ¼ Dþ d

(15)

where D+ is the Moore–Penrose inverse matrix. The calculation can be performed by using readily available matrix-oriented software

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Y. Liu et al. / Thermochimica Acta 602 (2015) 78–86

like MATLAB. Thus, the LLE calculations were carried out with the minimization of the Gibbs free energy deduced by Eqs. (2)–(15). LLE also subject to conservation of mass in the ATPS as follows:

’T3 ¼ 1  ’T1  ’T2

(16a)

’B3 ¼ 1  ’B1  ’B2

(16b)

’T1 þ ’B1 ¼ M

(17a)

’T2 þ ’B2 ¼ N

(17b)

M and N are the total volume fraction of PEG 20000(1) and nonionic surfactant(2), respectively, in ATPS. So Eqs. (6a)–(6c) can be expressed concisely:

’T1l 1 ln  2l13 ð2’T1l  MÞ m1 M  ’T1l 1  ’T1l  ’T2l ¼ ln ð1  M  NÞ þ ’T1l þ ’T2l þ ðl13 þ l23  l12 Þð2’T2l  NÞ

(18a)

’T2l 1 ln  2l23 ð2’T2l  NÞ m2 N  ’T2l 1  ’T1l  ’T2l ¼ ln ð1  M  NÞ þ ’T1l þ ’T2l þ ðl13 þ l23  l12 Þð2’T1l  MÞ

(18b)

STL ¼

To verify the reliability of Flory–Huggins model with known l12, l13 and l23, Eqs. (18a) and (18b) can be solved to determine the calculated values of ’T1l and ’T2l by minimizing the following objective function F obl ¼

ln

1  ’T1l  ’T2l þ ðl13 þ l23  l12 Þð2’T2l  NÞ ð1  M  NÞ þ ’T1l þ ’T2l

’T1l 1 þ 2l13 ð2’T1l  MÞ  ln m1 M  ’T1l þ

!2

1  ’T1l  ’T2l ln þ ðl13 þ l23  l12 Þð2’T1l ð1  M  NÞ þ ’T1l þ ’T2l

MÞ 

temperature increase. It can be attributed to the quite different cloud point temperature of the two nonionic surfactants. The cloud point temperature of Triton X-100 is 65  C and it is much lower than the cloud point temperature of Tween 80 (>100  C), so the biphase formation of PEG 20000/Triton X-100 ATPS is more obviously influenced by the temperature [14,25]. Another important line in ATPS phase diagram is the tie line, and the two important parameters are the tie line length (TLL) and the slope of the tie line (STL). The composition concentrations (including total, top phase and bottom phase) of the four tie lines determined by the methods in Section 2.2.2 in PEG 20000/Triton X100 ATPS and in PEG 20000/Tween 80 ATPS at different temperatures are shown in Tables 3 and 4, respectively. TLL and STL listed in Tables 3 or 4 can be calculated according to the following Eqs. (20) and (21), respectively. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  T 2  2 TLL ¼ w1  wB1 þ wT2  wB2 (20)

’T2l 1 ln þ 2l23 ð2’T2l  NÞ m2 N  ’T2l

!2 ! min

(19)

The optimization problem can be solved by the MATLAB1 optimization tool box. 4. Results and discussion 4.1. Binodal curve and tie lines For the two kinds of ATPSs composed of PEG 20000 and nonionic surfactants including Triton X-100 or Tween 80, the binodal data compositions determined experimentally at (273.15, 293.15 and 313.15) K are given as the scatter plots in Fig. 3, respectively. In the figures, it can be seen that the effects of temperature on the two-phase formation of the two studied ATPSs are different. The loci for the experimental binodals of PEG 20000/ Triton X-100 ATPS displayed in Fig. 3 demonstrate that the biphase areas are expanded with increasing temperature. To PEG 20000/ Tween 80 ATPS, the biphase areas have no obvious change by the

ðwT1  wB1 Þ ðwT2  wB2 Þ

(21)

As Tables 3 and 4 show, STL generally increases by TLL increasing in both PEG 20000/Triton X-100 ATPS and PEG 20000/ Tween 80 ATPS. Especially, the rising of STL with TLL increase is more obvious in lower temperature condition. The STL change for polymer/nonionic surfactant ATPS was probably due to the transfer of water from the top phase to the bottom phase with TLL increase. Namely, the polymer concentration increase in the top phase is more than the surfactant concentration increase in the bottom phase [19,26]. In higher temperature condition, the polymer molecules move faster so that the steric exclusion interaction between the polymer molecules and water molecules is smaller than the interaction in lower temperature condition, which causes STL of the two ATPSs in 313.15 K no significant change as in 273.15 K. Tables display that TLL vary within 0.25–0.36 and STL vary within 0.28–0.46 in PEG 20000/Triton X-100 ATPS, while TLL vary within 0.23–0.42 and STL vary within 0.31–0.41 in PEG 20000/ Tween 80 ATPS. It is indicated that STL has larger changes with the variation of TLL in PEG 20000/Triton X-100 ATPS than in PEG 20000/Tween 80 ATPS. It is because that the mutual solubility of Triton X-100 and water is more greatly affected by the experimental temperature (from 273.15 to 313.15 K) than the mutual solubility of Tween 80 and water [27]. Thus, the two surfactants concentrations in bottom phases have different variation depending on the temperature condition, so the two kinds of STL in PEG 20000/Triton X-100 ATPS and PEG 20000/ Tween 80 ATPS display different variation range. 4.2. Flory–Huggins model correlation LLE calculations were carried out through the minimization of the Gibbs free energy provided by Eq. (2). LLE data of the two kinds of ATPSs in Tables 3 and 4 are correlated with the phase equilibrium condition for the ATPS, such as chemical potential equal and mass constant for any composition of bottom and top phases at constant temperature and pressure. The optimal parameters l12, l13 and l23 in PEG 20000/Triton X-100 ATPS and PEG 20000/Tween 80 ATPS at various temperature were obtained through the Moore–Penrose inverse matrix provided by Eq. (15), respectively. Two kinds of fitting results are compared when the surfactant molecules are regarded as single molecules or micellar molecules. The predicted volume fraction of the components i from Flory–Huggins model can be obtained by Eq. (19). The weight fraction of component i (wi) can be expressed

Y. Liu et al. / Thermochimica Acta 602 (2015) 78–86

85

Table 7 LLE data for systems composed of PEG 20000 (w1) + Tween 80 (w2) + H2O (w3), from 273.15 to 313.15 K at pressure p = 0.1 MPa.a Tie line

TLL

Feed

Top phase

Bottom phase

w1

w2

w3

w1

w2

w3

w1

w2

w3

0.3278 0.3731 0.4095 0.4074

0.0600 0.0700 0.0800 0.0800

0.1800 0.1800 0.1800 0.1900

0.7600 0.7500 0.7400 0.7300

0.1005 0.1282 0.1489 0.1527

0.0557 0.0240 0.0074 0.0070

0.8438 0.8478 0.8437 0.8403

0.0163 0.0118 0.0095 0.0037

0.3126 0.3360 0.3478 0.3727

0.6711 0.6522 0.6427 0.6236

0.2349 0.3245 0.3706 0.4009

0.3340 0.3526 0.3911 0.3857

0.0600 0.0700 0.0800 0.0800

0.1800 0.1800 0.1800 0.2000

0.7600 0.7500 0.7400 0.7200

0.0983 0.1232 0.1478 0.1535

0.0698 0.0327 0.0121 0.0087

0.8319 0.8441 0.8401 0.8378

0.0239 0.0153 0.0128 0.0092

0.2926 0.3388 0.3572 0.3828

0.6835 0.6459 0.6300 0.6080

0.3010 0.3529 0.3705 0.4102

0.3199 0.3494 0.3430 0.3478

0.0600 0.0700 0.0700 0.0800

0.1800 0.1900 0.2000 0.2000

0.7600 0.7400 0.7300 0.7200

0.1100 0.1320 0.1350 0.1480

0.0321 0.0134 0.0127 0.0082

0.8579 0.8546 0.8523 0.8438

0.0183 0.0156 0.0148 0.0132

0.3188 0.3466 0.3631 0.3956

0.6629 0.6378 0.6221 0.5912

T = 273.15 K 1 2 3 4

0.2704 0.3330 0.3679 0.3949

T = 293.15 K 1 2 3 4 T = 313.15 K 1 2 3 4 a

STL

Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 10 kPa.

by the volume fraction (’i) and the ratio of the molar volume (mi) of component i as the following Eq. (22)

’i ¼

wi  mi w  mi =S i Mi Mi i

(22)

where Mi denotes the molar mass of component i. The standard deviation based on the Flory–Huggins model parameters obtained by the following Eq. (23) for the two kinds of polymer/nonionic surfactant ATPSs in two surfactant molecular states are collected in Tables 5 and 6. 3

4

Sd ¼ S S ½ðwTi;l;exp  wTi;l;cal Þ2 þ ðwBi;l;exp  wBi;l;cal Þ2 

(23)

i¼1 l¼1

where wi,l is the weight fraction of the component i for the lth tieline, the subscript exp and cal stand for calculated and experimental, respectively. It is concluded that reasonable agreement between calculated and experimental compositions are obtained from the standard deviation values which are all lower than 0.1%. Especially, Table 8 Correlation of parameters of ATPS in two surfactant molecular states containing PEG 20000 and Triton X-100 from 273.15 to 313.15 K. Surfactant

Temperature (K)

l13

l23

Sd, Eq. (23)

Single molecule

273.15 293.15 313.15

l12 0.1720 0.1160 0.0820

0.5511 0.3916 0.2723

0.8637 0.8214 0.8395

0.000267 0.000947 0.000329

Micelles

273.15 293.15 313.15

0.042 0.1452 0.2188

0.4704 0.2129 0.0427

0.6095 0.563 0.5469

0.000242 0.000898 0.000305

Table 9 Correlation of parameters of ATPS in two surfactant molecular states containing PEG 20000 and Tween 80 from 273.15 to 313.15 K. Surfactant

Temperature (K)

l12

Single molecule

273.15 293.15 313.15

0.0440 0.000206 0.00203

Micelles

273.15 293.15 313.15

0.0558 0.1197 0.2806

l13

l23

Sd, Eq. (23)

0.5596 0.7247 0.000583 0.4599 0.7068 0.000248 0.4634 0.7238 0.000315

the less standard deviation values are obtained if the surfactant molecules are regard as the micellar molecules. Tables 5 and 6 show that the interaction parameters between the polymer and nonionic surfactant (l12) in two ATPSs are much lower than the parameters between the nonionic surfactant and water (l23) or the parameters between the polymer and water (l13), especially in PEG 20000/Tween 80 ATPS. This result exactly accords with the Flory–Huggins theory that the different compositions molecules would rearrange to decrease the energy in the mixed solution [28]. The lower l12 values easily impel the molecular rearrangement. The l12 values in PEG 20000/Triton X-100 ATPS are higher than the l12 values in PEG 20000/Tween 80 ATPS at various temperatures, which indicate that the interaction between PEG 20000 and Triton X-100 is stronger than the interaction between PEG 20000 and Tween 80. The l12 and l13 values in the two kinds of ATPS decrease with the temperature increasing. The result corresponds with the traditional law because of the inverse proportion between l and temperature [28]. The interaction parameters between the macromolecule solute and the solvent such as l13 and l23 could imply the soluble ability of the solvent to the macromolecules [6,28,29]. Namely, the l value is more lower and the macromolecules dissolve more easily in the solvent. Thus, data in Tables 5 and 6 indicate that PEG 20000 has a better solubility in the aqueous solution than the micelles composed by the nonionic surfactant (Triton X-100 or Tween 80). Moreover, the l23 values have not obvious variation with the temperature increasing, which implies that the micelles solubility does not vary at the investigated temperatures. To show the reliability of the Flory–Huggins model, comparison between the experimental and correlated tie lines of PEG 20000/ Triton X-100 and PEG 20000/Tween 80 ATPS are shown in Figs. 4 and 5 at 273.15, 293.15 and 313.15 K, respectively. It could be seen from figures that the Flory–Huggins model can predict phase diagram of the polymer/nonionic surfactant ATPS in reasonable agreement. Moreover, the better fitting effect can be observed obviously if the surfactant molecules are regard as the micellar molecules. It indicated that the thermodynamic state of surfactant micellar is more specifically suited to correlate by the Flory– Huggins model (Tables 7–9). 5. Conclusions

0.4498 0.6239 0.000161 0.2579 0.5935 0.000236 0.1643 0.5333 0.000316

The phase diagrams of two kinds of polymer/nonionic surfactant ATPSs (PEG 20000 + Triton X-100 + water and PEG

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20000 + Tween 80 + water) have been investigated at different temperature. The biphase areas are significantly expanded with increasing temperature in PEG 20000/Triton X-100 ATPS. It is indicated that the experimental temperature has an obvious effect on the two phases formation of PEG 20000/Triton X-100 ATPS due of the low cloud point of Triton X-100 in aqueous solution. Flory– Huggins model has been applied to correlate the thermodynamic variables of polymer/nonionic surfactant ATPS and the interaction parameters of the two kinds of ATPSs in two surfactant molecular states including the single molecules and the micellar molecules have been obtained, respectively. The better fitting effect by the Flory–Huggins model can be observed in the surfactant ATPS if the surfactant molecules are regard as the micellar molecules. The interaction parameters between the polymer and surfactant (l12) and the interaction parameters between the polymer and water (l13) in ATPS have obviously decreased with temperature increasing, respectively, while the interaction parameters between the nonionic surfactant and water (l23) have not obvious variation with temperature increasing. It indicates that temperature plays a key role in the interaction between the polymer and the nonionic surfactant or water in these ATPSs.

[9]

[10]

[11]

[12]

[13]

[14]

[15]

Acknowledgments

[16]

This work is supported by the National Natural Science Foundation of China (No. 21476135), Outstanding Young Teachers Training Program in Guangdong Higher Education Institutions (No. Yq2013076), Science and Technology Planning Project of Guangdong Province, China (No. 2012B060400006), Education Department Projects of Guangdong Province, China (Nos. 2012KJCX0052, 920-38030337).

[17] [18]

[19]

[20]

References [21] [1] C. Kepka, J. Rhodin, R. Lemmens, F. Tjerneld, P.-E. Gustavsson, Extraction of plasmid DNA from Escherichia coli cell lysate in a thermoseparating aqueous two-phase system, J. Chromatogr. A 1024 (2004) 95–104. [2] H. Everberg, U. Sivars, C. Emanuelsson, C. Persson, A.-K. Englund, L. Haneskog, P. Lipniunas, M. Jörntén-Karlsson, F. Tjerneld, Protein pre-fractionation in detergent–polymer aqueous two-phase systems for facilitated proteomic studies of membrane proteins, J. Chromatogr. A 1029 (2004) 113–124. [3] B. Boruah, B. Gohain, P.M. Saikia, M. Borah, R.K. Dutta, Acid-base equilibrium of neutral red in aqueous nonionic surfactant–polymer systems, J. Mol. Liquids 160 (2011) 50–56. [4] N.A. Alsmadi, A.S. Wadajkar, W. Cui, K.T. Nguyen, Effects of surfactants on properties of polymer-coated magnetic nanoparticles for drug delivery application, J. Nanopart. Res. 13 (2011) 7177–7186. [5] B. Lindman, A. Khan, E. Marques, M.G. Miguel, L. Piculell, K. Thalberg, Phase behavior of polymer–surfactant systems in relation to polymer–polymer and surfactant–surfactant mixtures, Pure Appl. Chem. 65 (1993) 953–958. [6] M. Foroutan, N. Heidari, M. Mohammadlou, A.J. Sojahrood, (Surfactant + polymer) interaction parameter studied by (liquid + liquid) equilibrium data of quaternary aqueous solution containing surfactant, polymer, and salt, J. Chem. Thermodyn. 41 (2009) 227–231. [7] F. Spyropoulos, W.J. Frith, I.T. Norton, B. Wolf, A.W. Pacek, Sheared aqueous two-phase biopolymer–surfactant mixtures, Food Hydrocolloid. 22 (2008) 121–129. [8] R. Hu, X. Feng, P. Chen, M. Fu, H. Chen, L. Guo, B.F. Liu, Rapid, highly efficient extraction and purification of membrane proteins using a microfluidic

[22]

[23]

[24]

[25]

[26]

[27] [28] [29]

continuous-flow based aqueous two-phase system, J. Chromatogr. A 1218 (2011) 171–177. H. Everberg, T. Leiding, A. Schiöth, F. Tjerneld, N. Gustavsson, Efficient and nondenaturing membrane solubilization combined with enrichment of membrane protein complexes by detergent/polymer aqueous two-phase partitioning for proteome analysis, J. Chromatogr. A 1122 (2006) 35–46. M. Roobol-Bóza, V. Dolby, M. Doverskog, Å. Barrefelt, F. Lindqvist, U.C. Oppermann, K.K.V. Alstine, F. Tjerneld, Membrane protein isolation by in situ solubilization, partitioning and affinity adsorption in aqueous two-phase systems purification of the human type 1 11b-hydroxysteroid dehydrogenase, J. Chromatogr. A 1043 (2004) 217–223. J.P. Martins, J.S.R. Coimbra, F.C. Oliveira, G. Sanaiotti, C.A.S. Silva, L.H.M. Silva, M.C.H. Silva, Liquid–liquid equilibrium of aqueous two-phase system composed of poly(ethylene glycol) 400 and sulfate salts, J. Chem. Eng. Data 55 (2010) 1247–1251. M.T. Zafarani-Moattar, R. Sadeghi, Effect of temperature on the phase equilibrium of aqueous two-phase systems containing polyvinylpyrrolidone and disodium hydrogen phosphate or trisodium phosphate, Fluid Phase Equilibr. 238 (2005) 129–135. M. Foroutan, N. Heidari, M. Mohammadlou, A.J. Sojahrood, Effect of temperature on the (liquid + liquid) equilibrium for aqueous solution of nonionic surfactant and salt: experimental and modeling, J. Chem. Thermodyn. 40 (2008) 1077–1081. I. Fischer, M. Franzreb, Direct determination of the composition of aqueous micellar two-phase systems (AMTPS) using potentiometric titration – a rapid tool for detergent-based bioseparation, Colloid Surf. A 377 (2011) 97–102. C.W. Ooi, C.P. Tan, S.L. Hii, A. Ariff, S. Ibrahim, T.C. Ling, Primary recovery of lipase derived from Burkholderia sp. ST8 with aqueous micellar two-phase system, Process Biochem. 46 (2011) 1847–1852. Z. Wang, J.-H. Xu, W. Zhang, B. Zhuang, H. Qi, Cloud point of nonionic surfactant Triton X-45 in aqueous solution, Colloid Surf. B 61 (2008) 118–122. B. Lindman, G. Karlström, Nonionic polymers and surfactants: temperature anomalies revisited, C. R. Chim. 12 (2009) 121–128. M. Perumalsamy, T. Murugesan, Phase compositions, molar mass, and temperature effect on densities, viscosities, and liquid–liquid equilibrium of polyethylene glycol and salt-based aqueous two-phase systems, J. Chem. Eng. Data 54 (2009) 1359–1366. Y. Liu, Z. Wu, J. Dai, Phase equilibrium and protein partitioning in aqueous micellar two-phase system composed of surfactant and polymer, Fluid Phase Equilibr. 320 (2012) 60–64. E.S. Tada, W. Loha, P.A. Pessôa-Filho, Phase equilibrium in aqueous two-phase systems containing ethylene oxide–propylene oxide block copolymers and dextran, Fluid Phase Equilibr. 218 (2004) 221–228. H.-O. Johansson, G. Karlström, F. Tjerneld, C.A. Haynes, Driving forces for phase separation and partitioning in aqueous two-phase systems, J. Chromatogr. B 711 (1998) 3–17. M.T. Zafarani-Moattar, R. Sadeghi, Measurement and correlation of liquid– liquid equilibria of the aqueous two-phase system polyvinylpyrrolidone– sodium dihydrogen phosphate, Fluid Phase Equilibr. 203 (2002) 177–191. M. Foroutan, M. Zarrabi, Quaternary (liquid + liquid) equilibria of aqueous twophase polyethylene glycol, poly-N-vinylcaprolactam, and KH2PO4: experimental and the generalized Flory–Huggins theory, J. Chem. Thermodyn. 40 (2008) 935–941. U. Sivars, F. Tjerneld, Mechanisms of phase behaviour and protein partitioning in detergent/polymer aqueous two-phase systems for purification of integral membrane proteins, Biochim. Biophys. Acta 1474 (2000) 133–146. Ç. Batıgöç, H. Akbaş, M. Boz, Thermodynamics of non-ionic surfactant Triton X-100-cationic surfactants mixtures at the cloud point, J. Chem. Thermodyn. 43 (2011) 1800–1803. J.P. Martins, C.P. Carvalho, L.H.M. Silva, J.S.R. Coimbra, M.C.H. Silva, G.D. Rodrigues, L.A. Minim, Liquid–liquid equilibria of an aqueous two-phase system containing poly(ethylene) glycol 1500 and sulfate salts at different temperatures, J. Chem. Eng. Data 53 (2008) 238–241. C.A. Miller, Dissolution rates of surfactants, Adv. Polym. Sci. 218 (2008) 3–24. A.D. Diamond, J.T. Hsu, Aqueous two-phase systems for biomolecule separation, Adv. Biochem. Eng. Biot. 47 (1992) 89–135. F. Simonet, C. Garnier, J.-L. Doublier, Description of the thermodynamic incompatibility of the guar–dextran aqueous two-phase system by light scattering, Carbohyd. Polym. 47 (2002) 313–321.