Solvent Mixtures

Research Article

Jan Pavlıćˇek Grozdana Bogdanic´ Ivan Wichterle*

991

Simple Apparatus for the Measurement of Total Pressure of Polymer-Solvent Mixtures A new apparatus for determining the total pressure in binary systems with one nonvolatile component, such as polymer-solvent mixtures, was designed. In contrast to the ebulliometric method, it enables measurement of the pressure above solutions across wider concentration ranges. The apparatus was tested on mixtures of water and poly(ethylene glycol). The tested polymers had three nominal molar weights. The measurements were correlated with the UNIQUAC-free volume model described earlier and compared with the published data. The applicability of known predictive models on the measurements was also tested and it was found that the entropic free-volume model yielded the best prediction of vapor-liquid equilibria for the studied systems. Keywords: Binary systems, Polymer-solvent systems, Pressure, Static cells, Vapor-liquid equilibria Received: October 30, 2016; revised: February 11, 2017; accepted: February 21, 2017 DOI: 10.1002/ceat.201600597

1

Introduction

This study belongs to a series of continuing vapor-liquid equilibria (VLE) studies in diluted polymer-solvent systems. Earlier, VLE in polystyrene + butan-2-one [1], polystyrene + toluene [2], poly(methyl methacrylate) + acetone [3], poly(methyl methacrylate) + butan-2-one [4], poly(acrylic acid) + water [3], and in the solutions of co- and terpolymers of octadecyl acrylate and octadecyl methacrylate with styrene and 1-vinyl-2-pyrrolidone was investigated [5, 6]. For all those experimental measurements the ebulliometric method was used, which, however, cannot measure VLE in mixtures containing higher polymer concentrations. The aim of this study was to bridge that gap with a new setup and test its reliability.

2

Experimental Equipment and Procedure

With the newly designed apparatus the total pressure in binary mixtures with one nonvolatile component, such as polymer + solvent systems, can be measured. It enables measurement of the pressure above solutions over a wider concentration range. The schematic layout is shown in Fig. 1. The apparatus consisted of a thermostat with thermometer (ASL, model F250), an equilibrium cell (a 100 mL round glass flask with a stirrer driven by a very strong magnetic unit required for rather viscous systems), and a heated manifold for charging, degassing, and pressure measurement. The pressure was measured with an absolute heated capacitance unit (MKS Baratron, pressure up to 1000 Torr = 133 kPa). All connecting lines were wrapped in heating tape to keep them at temperatures higher than the system in order to eliminate solvent condensation.

Chem. Eng. Technol. 2017, 40, No. 5, 991–996

Figure 1. Schematic layout of the equilibrium measurement apparatus; (1) equilibrium cell; (2) thermostated bath; (3) magnetic stirrer; (4) cold trap; (P) pressure measurement; (T) temperature measurement; (R.P.) rotary pump; (W.P.) water ejector; (Paux), auxiliary pressure measurement; (V) volume buffer.

The mixtures used in the measurements were prepared in a detachable glass equilibrium flask by weighing the components to obtain an approximate volume of 50 mL. The mixture was then roughly degassed in an ultrasonic bath. Before starting the measurements, the whole system was evacuated several times to remove any remaining air. The final composition was determined by weighing the cell after the measurement was completed, because some amount of solvent always evaporates.

– Dr. Jan Pavlıćˇek, Dr. Grozdana Bogdanic´, Dr. Ivan Wichterle [email protected] Institute of Chemical Process Fundamentals, Czech Academy of Sciences, Rozvojova´ 135, 165 02 Prague, Czech Republic.

ª 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.cet-journal.com

Research Article

992

3

Then, the uncertainty in composition data can be estimated as better than 0.001 in weight fraction value. The equipment was first tested and calibrated for the vapor pressure of pure water. The accuracies of the temperature and pressure measurements were ±0.01 K and ±0.001 kPa, respectively. The lowest pressure limit for measurements is given by the accuracy of the MKS Baratron unit: it can be assumed as 0.01 kPa.

Results and Data Processing

The total pressure of the systems containing water and poly(ethylene glycol) with nominal molecular weights of 1000, 3000, and 6000 g mol–1 (PEG1k, PEG3k, and PEG6k, respectively) was measured isothermally at 308.15 and 313.15 K. Tab. 1 specifies the chemicals used. The number-average and weight-average molecular weights (Mn1) and Mw, respectively) of the PEGs were determined using the light-scattering method (Wyatt Technology). The vapor pressure measurements are shown in Tab. 2, Tab. 3, and Tab. 4, expressed in terms of water activity,

Table 1. Description of compounds. CAS No.a)

Chemical name

Denoted as

Mw [g mol–1] nominal

b)

Mn [g mol–1]

Mw [g mol–1]

measured

measured

Purification

Poly(ethylene glycol)

b)

25322-68-3

PEG1k

1000

924

961

None


b)

25322-68-3

PEG3k

3000

3100

3441

None


b)

25322-68-3

PEG6k

6000

5665

5892

None

Water a)

7732-18-5

Redistillation

CAS No.: Chemical Abstract Service Registry Number; b) Manufacturer: Sigma-Aldrich.

Table 2. Total pressure (P1) and water activities (a1) over the water (1) + PEG1k (2) solutions at various weight fractions of water (w1). w1

P1 [kPa]

a1

T = 308.15 K

w1

P1 [kPa]

a1

T = 313.15 K

1.0000

5.637

1.0000

1.0000

7.387

1.0000

0.9004

5.601

0.9936

0.9004

7.341

0.9937

0.7982

5.559

0.9861

0.7982

7.289

0.9867

0.6510

5.452

0.9672

0.6510

7.150

0.9679

0.4977

5.209

0.9241

0.4977

6.850

0.9273


P1 [kPa]

a1

T = 308.15 K

w1

P1 [kPa]

a1

T = 313.15 K

1.0000

5.637

1.0000

1.0000

7.387

1.0000

0.8987

5.601

0.9935

0.8987

7.345

0.9943

0.7978

5.565

0.9873

0.7978

7.296

0.9876

0.7000

5.510

0.9775

0.7000

7.230

0.9787

0.5992

5.400

0.9580

0.5992

7.090

0.9597

0.4992

5.254

0.9321

0.4992

6.905

0.9347

– 1)


List of symbols at the end of the paper.


www.cet-journal.com

Research Article

993


P1 [kPa]

a1

w1

T = 308.15 K

P1 [kPa]

a1

T = 313.15 K

1.0000

5.637

1.0000

0.0000

7.387

1.0000

0.8973

5.607

0.9946

0.8973

7.350

0.9949

0.7988

5.575

0.9890

0.7988

7.310

0.9895

0.6971

5.517

0.9787

0.6971

7.244

0.9806

0.5922

5.415

0.9606

0.5922

7.110

0.9625

0.4978

5.275

0.9358

0.4978

6.940

0.9394

a1 = P1/P1, where P1 is the partial pressure and P1 is the vapor pressure of pure water, and plotted in Fig. 2. The obtained experimental data were correlated with the UNIQUAC-FV model, which was described earlier [4] and discussed previously [1, 2]. The pure component data used in the UNIQUAC-FV equations for each component included the molecular weight of the repeat unit (MRU), the area (Qi) and volume (Ri) of the repeat units based on tabulated values by rep Bondi [7], and the number of the repeat units (ni ). Input

Figure 2. Activity (a1) of water in the PEG + water system as a function of water weight fraction (w1). Experimental data: *, PEG6k, T = 313.15 K; 䊊, PEG6k, T = 308.15 K; ¢, PEG3k, T = 313.15 K; £, PEG3k, T = 308.15 K; ~, PEG1k, T = 313.15 K; ~, PEG1k, T = 308.15 K. Correlation: temperature interval (308.15 – 313.15) K; — PEG6k; – – PEG3k; - - - PEG1k.

parameters for water and PEG are listed in Tab. 5. The calculation procedure also requires water and PEG densities at the system temperature, which were estimated using the DIPPR data bank [8] for the solvent and the Tait equation parameters [9] for the polymers. The objective function for the optimization of the two UNIQUAC-FV energy parameters, A12 and A21, was defined as the sum of absolute percent deviations of activities. Tab. 6 shows the estimated set of interaction parameters for the temperature range 308.15–313.15 K together with the average absolute deviations from experimental activities. These parameters were used to predict activities and activity coefficients at infinite dilution (W¥ 1 ), for two isotherms, which are also included in Tab. 6. The interaction parameters, which are practically independent of temperature over a small temperature range, provided a good prediction. Fig. 2 illustrates the successful correlation of our data. For further analyses of the obtained data two group contribution predictive models developed earlier were selected: the simple activity coefficient entropic-FV [10] applying the group interaction parameter matrix developed by Hansen et al. [11], and the GC-Flory EoS [12] model. The GC-Flory model provided rather poor predictions, most likely due to the uncertainties in the group interaction parameters CH2O–H2O, which should be revised. Activity predictions with the entropic-FV model agreed well with the experimental data. The activities of the solvent were predicted within an average absolute deviation of < 0.01. These findings are presented in Tab. 6 and Tab. 7. In order to compare the results with published data for water + PEGs of similar molecular weights at similar temperatures to this work, determined by different methods [13–20], all cited literature data were correlated with the UNIQUAC-FV model. The results are summarized in Tab. 7, which shows PEG characteristics, system temperatures, number of experimental points, experimental method with references, correlated param-

Table 5. Input parameters of pure components: 1, water; 2, PEG. Solvent

MRU1 [g mol–1]

n1

R1

Q1

Polymer

MRU2 [g mol–1]

Water

18.02

1

0.920

1.400

PEG1k

44.06

rep


rep

n2

R2

Q2

21

33.4464

27.720

PEG3k

70

111.4890

92.400

PEG6k

129

205.4583

170.280


www.cet-journal.com

Research Article

994

Table 6. Correlation and prediction of VLE data for the water (1) + PEG (2) system using the UNIQUAC-FV and entropic-FV models. PEG characteristics –1

UNIQUAC-FV –1

Entropic-FV –1

a)

W1¥

Da1

W1¥

Mn [g mol ]

Mw/Mn

T [K]

n

Type of calculation

A12 [J mol ]

A21 [J mol ]

Da1

924

1.04

308.15 to 313.15

12

Correlation

1166.29

–1828.31

0.0002

308.15

6

Prediction

0.0003

5.66

0.0134

8.41

313.15

6

Prediction

0.0003

5.76

0.0141

8.75

12

Correlation

308.15

6

Prediction

0.0002

5.80

0.0041

9.06

313.15

6

Prediction

0.0002

5.90

0.0071

9.43

12

Correlation

308.15

6

Prediction

0.0004

6.00

0.0051

9.10

313.15

6

Prediction

0.0005

6.10

0.0085

9.46

3100

1.11

5665

a)

1.04

308.15 to 313.15

308.15 to 313.15

2323.67

–2323.67

3087.19

0.0001

–2600.22

0.0003

Da1 = S⏐acalc–aexp⏐/n is an average absolute deviation in calculated activity.

Table 7. Correlation and prediction of published VLE data for the water (1) + PEG (2) system using the UNIQUAC-FV and entropic-FV models. PEG characteristics –1

UNIQUAC-FV –1

Entropic-FV –1

W1¥

Da1b)

W1¥

Mn [g mol ] Mw/Mn

T [K]

n

Method

Ref.

A12 [J mol ] A21 [J mol ]

Da1b)

650

n/a

307.75

14

IP

[13, 15]

1004.73

–1929.83

0.0005

5.24

0.0077

8.26

1460

n/a

307.75

12

IP

[13, 15]

1634.87

–2035.12

0.0004

5.66

0.0038

8.99

2840

1.06

313.15

5

VPO

[13, 16]

2159.50

–2157.45

0.0001

6.10

0.0064

9.39

2840

1.06

313.15

16

VPO

[13, 17]

2084.97

–2123.97

0.0002

6.06

0.0026

9.39

5750

1.04

313.15

8

VPO

[13, 17]

2689.36

–2372.56

0.0001

6.19

0.0039

9.47

6000

n/a

308.15

23

VPO, IP

[14, 18]

3361.85

–2640.57

0.0001

5.91

0.0058

9.14

6000

n/a

308.15

23

IP

[14, 19]

2997.00

–2532.76

0.0007

5.89

0.0092

9.14

6000

n/a

313.10

4

IP

[13, 20]

2521.04

–2340.84

0.0016

6.22

0.0238

9.51

a)

a)

IP = isopiestic method, VPO = vapor pressure osmometry; b) Da1 = S⏐acalc–aexp⏐/n is an average absolute deviation in calculated activity.

eters, average deviations of correlated activities, and predicted activity coefficients at infinite dilution using the A12 and A21 interaction parameters of the UNIQUAC-FV model. Fig. 3 (at 308.15 K) and Fig. 4 (at 313.15 K) show perfect agreement between the correlated A12 and A21 parameters from the literature data plotted against each molecular weight of the PEGs and the parameters obtained from the correlation of our data in the 308.15–313.15 K range. For further analyses the prediction of the activities of water in mixtures with PEGs using the entropic-FV model was opted for. These results are also included in Tab. 7. In addition, Fig. 5 shows an example of comparison of our data and literature data [18, 19] and the prediction using the entropic-FV model for water activities for the ~6000 g mol–1 PEG as a function of water weight fraction at 308.15 K.


4

Conclusions

This simple setup enables precise determination of the vapor pressure of solutions containing higher polymer concentrations than can be measured with the ebulliometric method, which is limited by problems with smooth boiling, occurring, as a rule, if the polymer weight fraction in a mixture is higher than 15 %. New data were measured for aqueous systems containing three different poly(ethylene glycol)s, PEG1k, PEG3k, PEG6k, within 0 to 0.5 weight fraction of polymer. These were successfully correlated with the UNIQUAC-FV model and they complete published data sets, with which they are in good agreement. The entropic-FV model gave satisfactory predictions of VLE for the studied systems. Possible applications of more


www.cet-journal.com

Research Article

995

Figure 3. Dependence of the UNIQUAC-FV parameters A12 (squares) and A21 (circles) on molecular weight (Mn). £, 䊊, literature data at 308.15 K (Tab. 7); ¢, *, data from this work (Tab. 6).

Figure 5. Activity (a1) of water in the PEG6k (Mn ~ 6000 g mol–1) + water system as a function of water weight fraction (w1). Experimental data at 308.15 K: *, data from this work; 䊊, ref. [18]; ~, ref. [19]; — , predicted activities using the entropicFV model.

Symbols used

Figure 4. Dependence of the UNIQUAC-FV parameters A12 (squares) and A21 (circles) on molecular weight (Mn). £, 䊊, literature data at 313.15 K (Tab. 7); ¢, *, data from this work (Tab. 6).

sophisticated models that explicitly account for association, e.g., PC-SAFT, will be investigated in the subsequent studies. The future experimental setup will be slightly modified to include higher temperatures: the relative pressure unit MKS Baratron (pressure up to 10 Torr = 1.33 kPa), operating at temperatures up to 470 K, could be used as a zero indicator.

Mn Mw MRU n rep ni

[g mol–1] [g mol–1] [g mol–1] [–] [–]

P Pi P Qi

[kPa] [kPa] [kPa] [–]

Ri

[–]

T wi

[K] [–]

activity of component i UNIQUAC parameter for interaction i–j number-average molecular weight weight-average molecular weight molecular weight of the repeat unit number of experimental points number of the repeat units of component i total pressure pressure of component i vapor pressure of pure solvent area parameter for repeat unit of component i volume parameter for repeat unit of component i temperature weight fraction of component i

Greek letters D W¥ 1

i, j

This study was partially supported by the Czech Science Foundation (Grant No. 15-19542S).


[–] [K]

[–] [–]

average absolute deviation activity coefficient of water at infinite dilution

Subscripts

Acknowledgment

The authors have declared no conflict of interest.

ai Aij

component

Abbreviations EoS FV

equation of state free volume


www.cet-journal.com

Research Article

GC PEG VLE

996

[10]

group contribution poly(ethylene glycol) vapor–liquid equilibria

[11]

References [1] [2] [3] [4] [5] [6] [7] [8]

[9]

J. Pavlıćˇek, G. Bogdanic´, I. Wichterle, Fluid Phase Equilib. 2016, 424, 41–43. DOI: 10.1016/j.fluid.2015.09.028 J. Pavlıćˇek, G. Bogdanic´, I. Wichterle, Chem. Biochem. Eng. Q. 2015, 29, 1–4. DOI: 10.15255/CABEQ.2015.2183 J. Pavlıćˇek, G. Bogdanic´, I. Wichterle, Fluid Phase Equilib. 2013, 358, 301–303. DOI: 10.1016/j.fluid.2013.08.036 J. Pavlıćˇek, G. Bogdanic´, I. Wichterle, Chem. Biochem. Eng. Q. 2014, 28, 447–450. DOI: 10.15255/CABEQ.2014.19388 G. Bogdanic´, I. Wichterle, J. Chem. Eng. Data 2011, 56 (4), 1080–1083. DOI: 10.1021/je101052a J. Pavlıćˇek, G. Bogdanic´, I. Wichterle, Fluid Phase Equilib. 2010, 297 (1), 142–148. DOI: 10.1016/j.fluid.2010.05.022 A. Bondi, Physical Properties of Molecular Crystals, Liquids, and Glasses, Wiley, New York 1968. T. E. Daubert, R. P. Danner, Data Compilation Tables of Properties of Pure Compounds, Design Institute for Physical Property Data, American Institute of Chemical Engineers (DIPPR/AIChE), New York 1985. P. A. Rodgers, J. Appl. Polym. Sci. 1993, 48 (6), 1061–1080. DOI: 10.1002/app.1993.070480613


[12] [13]

[14]

[15] [16] [17] [18] [19] [20]

G. M. Kontogeorgis, A. Fredenslund, D. P. Tassios, Ind. Eng. Chem. Res. 1993, 32 (2), 362–372. DOI: 10.1021/ie00014 a013 H. Hansen, B. Coto, B. Kuhlman, UNIFAC with Linearly Temperature-Dependent Group Interaction Parameter, SEP Publication No. 9212, Technical University of Denmark, Lyngby 1992. G. Bogdanic´, A. Fredenslund, Ind. Eng. Chem. Res. 1994, 33 (5), 1331–1340. DOI: 10.1021/ie00029a032 C. Wohlfarth, CRC Handbook of Thermodynamic Data of Aqueous Polymer Solutions, 1st ed., CRC Press LLC, Boca Raton, FL 2004. C. Wohlfarth, CRC Handbook of Phase Equilibria and Thermodynamic Data of Aqueous Polymer Solutions, 1st ed., CRC Press, Boca Raton, FL 2013. M. L. Lakhanpal, K. S. Chhina, S. C. Sharma, Indian J. Chem. 1968, 6 (9), 505–509. S. Hammer, A. Pfennig, M. Stumpf, J. Chem. Eng. Data 1994, 39 (3), 409–413. DOI: 10.1021/je00015a002 J. Gaube, A. Pfennig, M. Stumpf, J. Chem. Eng. Data 1993, 38 (1), 163–166. DOI: 10.1021/je00009a040 R. Sadeghi, Y. Shahebrahimi, J. Chem. Eng. Data 2011, 56 (4), 789–799. DOI: 10.1021/je100178s R. Sadeghi, R. Hosseini, B. Jamehbozorg, J. Chem. Thermodyn. 2008, 40 (9), 1364–1377. DOI: 10.1016/j.jct.2008.05.007 M. Herskowitz, M. Gottlieb, J. Chem. Eng. Data 1985, 30 (2), 233–234. DOI: 10.1021/je00040a033


www.cet-journal.com