Hydrogen Bonding in Polymer Solution - Journal of Chemical

Article pubs.acs.org/jced

Hydrogen Bonding in Polymer Solution Chang-Hoon Bang, Hyun-Ki Choi, and Bong-Seop Lee* Department of Fire and Disaster Prevention Engineering, Kyungnam University, Changwon-si, Gyeongsangnam-do 51767, Republic of Korea ABSTRACT: The perturbed hard-sphere-chain-association (PHSC-AS) equation of state is applied to calculate the phase equilibrium of hydrogen bonding polymer systems. The pure parameters of polymers are estimated by regression of pressure−volume−temperature (PVT) data of pure molten-polymer. The calculation results show a good agreement with experimental data over the wide temperature (303 to 543 K) and pressure (1 to 2001 bar) range. The calculation results for vapor−liquid equilibrium (VLE) of polymer−solvent systems also show a good accuracy with ARD error of about 4% (a total of 354). The PHSC-AS model describes well the effects of various factors on vapor pressure of hydrogen-bonding polymer solution, such as temperature, solvents with different polarity (i.e., water, alcohols, acetone, amine), and the molecular weight and molecular structure of polymer. In addition, the infinite dilution weight fraction activity coefficient (WFAC) of strongly polar solvents such as water, alcohols, and acetic acid is calculated, and the calculated results show an acceptable performance. However, the LLE calculation shows a poor performance with PHSC-AS model.

1. INTRODUCTION The thermodynamics of polymeric systems plays an important role in the polymer industry and is often a key factor in polymer production, processing and material development, especially for the design of advanced polymeric materials.1,2 Especially, hydrogen bonding in polymer solution has attracted over time the intensive interest of researchers, and still remains a challenging problem in design polymer processing. Polymer solutions are in general more complex than mixture consisting of low-molecular-weight substances due to the large difference in the molecular sizes of between polymers and solvents. Unfortunately, the large value of free volume and/or concentration fluctuation often causes the pronounced density dependence of the phase behavior of polymer solutions at high temperatures.3,4 Therefore, for modeling of the phase behavior of polymer solutions, the equation of state (EOS) has been used widely instead of the excess Gibbs free energy (GE) model. Numerous studies have been performed to develop the EOS to be adaptable for polymer solutions. These studies can be classified into three general approaches: cubic EOS, lattice− fluid model, and perturbation model. The cubic EOS has been applied to the description of pressure−volume−temperature (PVT) for pure polymer and vapor pressure of polymer− solvent mixtures. The first attempt to apply a cubic EOS to polyethylene-ethylene systems was carried out by Sako et al.5 Kontogeorgis et al.6 correlated the vapor−liquid equilibrium (VLE) of polymer solutions with van der Waals EOS. Orbey and Sandler7 applied the PRSV EOS, along with the Wong and Sandler mixing rules to correlate VLE for polymer solutions. In order to determine pure polymer parameters, they assumed that the vapor pressure of pure polymer equals to 10−7 MPa. The lattice−fluid model was proposed by Sanchez and Lacombe8,9 © XXXX American Chemical Society

to describe the thermodynamic properties for liquid and gaseous mixtures. This model has long been applied to various polymer systems by many researchers10−14 and has been modified in the various types for a long time.15−17 Although the lattice−fluid models can be successfully applied to polymer solutions, many attentions have been paid to the development of off-lattice equations of state because the off-lattice EOS based on perturbation theory is able to be relatively easily developed by modifying the hard-sphere and dispersion term compared to lattice−fluid model. As a result, several off-lattice equations of state based on the perturbation theory have been proposed. Chapman et al.18 and Huang and Radoz19,20 derived the statistical associating fluid theory (SAFT) based on the thermodynamic perturbation theory pioneered by Wertheim.21 This theory has been further modified in a number of research works to develop the SAFT-LJ,22 SAFT-VR,23 and PC-SAFT24,25 models, among others. PC-SAFT model has been widely used to model phase behaviors of many polymer solutions for a wide range of temperatures, pressures and weight compositions.25−27 On the other hand, Song et al.28,29 developed a perturbed hardsphere-chain (PHSC) equation of state, starting from the modified Chiew equation of state30 for hard-sphere chains as the reference term and using a van der Waals-type perturbation term to account for attractive forces. Many authors31−33 have demonstrated that the PHSC EOS can represent, with good accuracy, the behavior of long-chain pure-component properties of polymers and is also suitable for describing the phase equilibria of polymer-containing mixtures despite the simplicity Received: April 27, 2016 Accepted: August 25, 2016

A

DOI: 10.1021/acs.jced.6b00344 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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species; therefore, the activity of solvent and polymer should be known. The activity of solvent i is defined as

of dispersion term with van der Waals-type compared to SAFTfamily EOS. However, because the PHSC EOS cannot account for strong specific interactions such as hydrogen bonding, its application is limited in the polymer fluid systems with association phenomena such as self- and cross-association, which have a remarkable effect on the phase behavior of polymer solutions. In previous work,34,35 with an objective of extending of the PHSC to be adaptable for the associating fluids, we proposed the PHSC-AS (perturbed hard-sphere-chain-association) EOS. This model has been successfully applied to describe the phase equilibria such as VLE and liquid−liquid equilibria (LLE) of the binary system containing associating chemicals such as water, alcohols, amines, and carboxylic acids. In this work, our goal is to extend the PHSC-AS EOS to the hydrogen-bonding polymer solutions. Up to now, for simple polymer solutions containing nonpolar or slightly polar compounds, many EOSs have been used to compute the phase equilibria with reliable calculation results. However, the above-mentioned EOSs have rarely applied to more complex polymer systems containing strongly polar compounds such as water, alcohols, acetone, amine, and acetic acid. In this work, therefore, PHSC-AS EOS used to calculate the thermodynamic properties of hydrogenbonding polymer fluid such as PVT for pure polymer, VLE and infinite dilution weight fraction activity coefficient (WFAC) of strongly polar solvent in polymer. In addition, the calculation results with PHSC-AS EOS are compared to those with the PC-SAFT24,25 EOS, which is known to be useful for calculating phase equilibria of polymer systems.

ai =

xiϕi̅ ϕio

(1)

where ϕ̅ s and ϕos are the fugacity coefficients of solvent in the liquid-phase mixture and in the pure state, respectively, at the equilibrium temperature and pressure. The fugacity coefficient of component i in the mixture and in the pure state can be calculated from PHSC-AS EOS in which the molecule is assumed to be composed of a chain of freely jointed tangent hard-spheres. The PHSC-AS model consists of the reference term (ref) for hard-sphere chains, the van der Waals-type dispersion (disp) term and the association (assoc) term. Regarding the compressibility factor Z (P/ρkT), the equation of state is expressed as Z = Z ref + Z disp + Z assoc

(2)

The detail expression for reference and dispersion term are given in literature.28,29 The association term describing the hydrogen bonding interaction between association sites on molecules is given by the following relation based on the SAFT model20,36 ⎡ 1 1 ⎤⎛ ∂X A i ⎞ Z assoc = ρ ∑ xi ∑ ⎢ A − ⎥⎜ ⎟ ⎣X i 2 ⎦⎝ ∂ρ ⎠ i A i

(3)

The associating polymer has a lot of functional groups with association sites. By introducing the numbers of repeating units of polymer into the association term, the association term is easily extend to hydrogen-bonding polymer with many

2. THEORETICAL BACKGROUND For phase equilibria calculations of polymer solution, the condition for equilibrium requires the equality of activity for Table 1. Polymers Studied in This Work

B



κAiBj [−] C

2499.13 3278.97 299.49 266.83 255.63 282.60 259.58 324.55 368.73 266.23 0.015185 0.018180

κ

2471.09 3771.58 347.27 320.01 304.63 321.84 291.54 367.52 342.09 327.26 4.0119 3.3569 3.7227 3.6689 3.3617 3.5182 3.6859 4.0801

ARD (%) = 1/(NP∑i[(ρexp − ρcal)/ρexp]i) × 100. a

3. RESULTS AND DISCUSSION 3.1. Pure Component Parameters. To describe the phase behavior of a mixture with the PHSC-AS and PC-SAFT EOS, the molecular parameters for the pure compounds are required. For polymer with high molecular weight, the pure parameters are typically obtained from only pure PVT data. Other methodologies are seldom used. For example, Gross and Sadowski27 estimated pure-polymer parameters through simultaneous regression of both pure-polymer PVT data and LLE data of binary mixture and obtained successful LLE and VLE correlations for a variety of polymer−solvent systems. The method in which the pure parameters are estimated by extrapolating the pure component parameters of the n-alkane series has been studied in several literatures.5,19,24 Kouskoumvekaki et al.40 investigated two methods for various polymers. They observed that the pure-component parameters of polymer estimated by simultaneous regression of PVT data and binary mixture rather depend on the chosen binary system. The extrapolation method shows somewhat large error around 1.0% average absolute relative deviation (ARD) for most non-hydrogen bonding polymers because one pure component parameter (the size parameter, σ) is fitted to the pure PVT data. In order to obtain the satisfactory description for both of pure PVT behavior and the VLE for hydrogen-bonding polymer with molecular structure given in Table 1, in this work, the pure polymer parameters was estimated by regressing only

0.044 0.0552 0.0452 0.0455 0.0509 0.0457 0.0408 0.0305

(10)

55 187 198 150 60 129 17 160 956

κ

1−601 1−2001 1−1601 1−1200 1−900 1−2001 1−601 100−400 1−2001

κ

413−543 343−472 303−472 306−416 337−393 373−504 493−527 404−525 303−527

=

⎤3 ⎥ ⎢⎣ (σi + σj)/2 ⎥⎦ σσ i j

HDPE PEO41 PPO41 PVME42 PVAc43 PMMA41 PVAL41 PVPh44 Average

κ

⎡

ε /k [K]

A i Bi Aj Bj ⎢

ε/k [K]

A i Bj

(9)

σ [Å]

1 A iBi (ε + ε AjBj) 2

AiBj

ε A iBj =

Table 2. Pure Parameters for PHSC-AS and PC-SAFT EOS Estimated by Regressing PVT Data

where kij is the adjustable binary interaction parameter. The cross-association parameters, εAiBj and κAiBj can be defined as39

[−]

(8)

r/Mw [mol/g]

εij = (1 − kij) εiiεjj

ARD (%)

(7)

NP

1 (σi + σj) 2

PHSC-AS

σij =

m/Mw [mol/g]

where M w is the weight-average molecular weight of the polymer and Mmonomer indicates the molecular weight of repeating unit. The pair-potential parameters σij and εij between unlike segments in the mixture can be obtained by conventional combining rules

4.0126 3.0508 3.3953 3.4284 3.2069 3.3402 3.1556 3.5991

σ [Å]

(6)

P range [bar]

M monomer of repeating unit

0.028 0.0461 0.0375 0.0355 0.0374 0.0340 0.0413 0.0274

PC-SAFT

Mw

T range [K]

NGi =

0.2 0.1 0.2 0.1 0.1 0.1 0.6 0.1 0.1

(5)

where NGi is the number of functional groups with association sites in the chemical component i. In this work, the number of functional group of a polymer is defined as

41

Bj

εAiBj/k [K]

X A i = [1 + ρ ∑ xiNGi ∑ X BjΔA iBj ]−1

ε/k [K]

where a mole fraction of molecules not bonded at the association site A on the molecule of i component, XAi, is expressed as i

0.014924 0.022106

(4)

polymers

i

AiBj

⎡ 1 1 ⎤⎛ ∂X A i ⎞ Z assoc = ρ ∑ xiNGi ∑ ⎢ A − ⎥⎜ ⎟ ⎣X i 2 ⎦⎝ ∂ρ ⎠ i A

ARD (%)

functional group. The association term is defined as36−38

0.4 0.1 0.2 0.4 0.1 0.2 0.6 0.1 0.2

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Figure 1. Pressure−volume−temperature behavior of (a) PEO and (b) PVPh with PHSC-AS (solid line) and PC-SAFT (dashed line). The experimental data for PEO and PVPh are from Walsh and Zoller41 and Luengo et al.,44 respectively.

Table 3. Calculation Results for VLE of Polymer Solutions with PHSC-AS and PC-SAFT Modelsa PHSC-AS systems PEO/waterb

PPO/waterb PVAc/methanolc

PVAc/ethanolc

PVAc/propanolc

PVAc/butanolc

PEO/methanold PEO/ethanold PPO/methanole PVME/waterf PVAc/waterc PVAc/propanamineb PMMA/waterb PVPh/acetoneg

PVAL/methanolc PVAL/waterc c c f b b e

overall a

PC-SAFT

N

T [K]

εcross/k [K]

κcross [−]

kij

Δ (%)

εcross/k [K]

κcross [−]

kij

Δ (%)

11 19 11 6 6 11 9 9 7 12 5 6 7 6 10 10 8 5 6 12 10 7 4 11 16 16 16 16 16 15 3 10 4 4 10 5 8 7 354

293.10 313.10 333.10 303.15 323.15 313.20 333.20 353.20 313.20 333.20 353.20 313.20 333.20 353.20 313.20 333.20 353.20 303.15 303.15 298.15 355.65 313.15 313.15 313.15 318.15 313.15 308.15 303.15 298.15 293.15 383.15 363.15 373.15 383.15 366.65 303.15 303.15 303.15 293−383

1245.41

0.015463

0.038255

0.016926

1424.78

0.027393

2464.45

0.021569

2860.31

0.035274

2623.31

0.010651

2720.40

0.030076

2640.59

0.006334

2260.82

0.017664

2654.12

0.009084

2595.58

0.008073

2612.58 2386.16 2240.25 1061.52 1160.26 857.26 1578.92 3942.24

0.022562 0.011287 0.023326 0.007208 0.011262 0.084133 0.021708 0.018643

2.4 0.7 2.2 3.0 2.9 1.3 2.6 3.1 1.8 5.6 1.8 3.0 8.4 1.6 8.1 3.6 3.9 3.9 6.9 0.9 15.9 7.1 3.7 7.1 1.0 0.9 0.8 0.7 0.6 0.4 7.5 3.6 2.0 5.2 13.6 16.5 19.4 5.9 4.1

1330.51

1092.71

−0.0236 −0.0238 −0.0215 −0.0194 −0.0169 0.0244 0.0188 0.0294 0.0263 0.0163 0.0138 0.0225 0.0138 0.0125 0.0138 0.0088 0.0063 0.0005 0.0127 0.0251 0.0357 −0.0157 0.0266 0.0551 0.0029 0.0041 0.0054 0.0067 0.0087 0.0111 −0.0584 0.0202 0.0210 0.0181 0.0669 0.0391 0.0406 0.0331

2852.22 2351.97 2858.50 1617.99 1262.97 687.66 1834.56 4363.71

0.042595 0.036418 0.017503 0.002111 0.028445 0.04659 0.039742 0.025848

−0.0183 −0.0188 −0.0205 −0.0319 −0.0338 0.0381 0.0363 0.0538 0.0556 0.0463 0.0431 0.0419 0.0338 0.0338 0.0481 0.0438 0.0400 −0.0113 0.0090 0.0443 −0.0658 −0.0134 0.0097 0.0471 0.0213 0.0213 0.0213 0.0213 0.0213 0.0238 −0.1397 −0.0394 −0.0338 −0.0394 0.0113 −0.0338 −0.0319 −0.0450

8.3 4.8 3.0 7.7 5.3 1.8 3.4 3.1 2.2 7.5 1.9 1.5 8.6 1.9 7.5 3.7 4.3 6.2 8.3 3.4 7.0 5.2 2.8 8.8 0.7 0.7 0.7 0.6 0.5 0.5 7.7 5.2 5.5 2.4 7.1 5.4 4.7 6.1 3.9

Note: Δ (%) = 1/(N∑[(Xexp − Xcal)/Xexp]i) × 100, where X = activity of solvent or partial pressure of solvent. bHao et al.54 cPalamara et al.55 Jung et al.56 eKim et al.57 fStriolo and Prausnitz.58 gLuengo et al.59

d

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Figure 2. Vapor−liquid equilibria of the PVPh (Mw = 3000)/acetone system at 293 K (open circle), 298 K (open squares), 303 K (open triangles), 308 K (filled circle), 313 K (filled squares), and 318 K (filled triangles) with PHSC-AS (solid line) and PC-SAFT (dashed line). The experimental data are from Luengo et al.59

Figure 4. Vapor−liquid equilibria of the PVAL/water system (triangle,54 14 700 g/mol; squares,54 67 000 g/mol; and circles,57 88 000 g/mol) at 303.15 K with PHSC-AS (solid line) and PC-SAFT (dashed line).

Figure 5. Vapor−liquid equilibria of the various polymer/water systems (squares, PVA; triangles, PMMA; and circle, PEO) at 313.15 K with PHSC-AS (solid line) and PC-SAFT (dashed line). The experimental data for PMMA and PEO and for PVAc are from Hao et al.54 and Palamara et al.,55 respectively.

Figure 3. Vapor−liquid equilibria of the PVAc (Mw = 167 000 g/mol)/ alcohol (diamonds, methanol; squares, ethanol; triangles, propanol; and circles, butanol) systems at 313.2 K with PHSC-AS (solid line) and PC-SAFT (dashed line). The experimental data are from Palamara et al.55

repeating unit of polymer) and H (of the hydroxyl group of alcohol, amine, and water). Such cross-association was evidenced by experimental measurements38,45−47 with the FT-IR spectrum analysis method. In this work, the cross-association parameters (i.e., εAB/k and κAB) were estimated by fitting the all VLE data for polymer−solvent mixtures and were considered as temperature-independent parameters. The calculated results for VLE are reported in Table 3 with kij at each temperature. PHSC-AS and PC-SAFT models show a similar results with ARD error of approximately 4.1% and 3.9%, respectively. Based on the fact that the association between molecules can be expressed through the equilibrium constant, Gupta et al.48 and Kontogeorgis et al.49 identified the direct relationships (i.e., εAB/k ≈ −ΔHassoc) between association energy parameters εAB/k and enthalpy of hydrogen bonding −ΔHassoc/R. The crossassociation energy parameters for PVAc/alcohol systems are distributed in the range from 4.9 to 5.3 kcal/mol, and from 4.5 to 5.7 kcal/mol for PHSC-AS and PC-SAFT EOSs,

pure PVT data.41−44 The estimated pure component parameters for PHSC-AS and PC-SAFT are reported in Table 2. The calculated densities with PHSC-AS and PC-SAFT EOSs show a good accuracy over a wide temperature range (303 to 543 K) and pressure range (1 to 2001 bar) with ARD error of 0.13% and 0.21%, respectively. Figure 1 shows that both models provide a good description of the PVT behavior for PEO and PVPh in the molten state up to high pressure (2001 bar) and temperature (543 K). 3.2. Vapor−Liquid Equilibria. The estimated pure polymer parameters are applied to calculate the VLE for polymer/solvent systems in which the hydrogen bonding between polymer and solvent exists. Then, the pure parameters for solvents (i.e., alcohols, propanamine, acetone, and water) are obtained from previous work.34 Although PEO, PPO, PVAC, and PVME are not selfassociating compounds, there is a cross-association interaction between O (of functional group O and COO in E



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respectively. The estimated parameters are in very good agreement with experimental values38,45−47 based on the chemical association theory. Pimentel et al.45 reported the crossassociation enthalpy for low molecular weight phenol-methyl acetate and -ethyl acetate mixtures, which range from 4.8 to 5.7 kcal/mol. Moskala et al.46 reported the value of 5.1 kcal/mol by measuring the degree of cross-association in PVPh/PVAc blend with the FT-IR spectrum analysis method for the enthalpy of hydrogen bonding due to cross-association between the hydroxyl group (OH) in PVPh and the ester group (COO) in PVAc. Widom et al.47 obtained the cross-association enthalpy value of 7.0 kcal/mol for phenol/acetone system with the FT-IR spectrum analysis method. For comparative purposes of the performance of the PHSC-AS and PC-SAFT EOS, the calculated results are presented in Figures 2−5. Figure 2 illustrates the partial vapor pressure of acetone mixed with PVPh in wide temperature range. Two models allow an equally good description with very high precision. As shown in Figure 3, the partial vapor pressure for PVAc/alcohol systems is accurately represented according to the increase of alkyl chain length on alcohols (i.e., methanol, ethanol, propanol, and butanol). In general, the molecular weight of polymer with degree of polymerization exerts an influence on the phase behaviors. As can be seen in Figure 4, the activity of water decreases with increase of the molecular weight of the PVAL (i.e., 14 700, 67 000, and 88 000 g/mol) because of the enhancement of hydrogen bonding between the water and hydroxyl (OH) group in the repeating units of PVAL. The calculation results by two models also show the

Table 4. Calculation Results for Infinite Dilution WFAC of Strongly Polar Solvent ARD (%) polymer PEO

NP 9

343.4−423.7

30.4

36.9

ethanol

31

340.5−398.2

23.6

4.1

1-propanol

24

343.2−398.2

7.0

5.8

2-propanol

2

343.2−373.2

10.5

3.8

1-butanol

31

343.4−423.7

14.6

6.7

2-butanol

5

343.4−352.4

16.0

4.6

65

323.15−413.15

15.2

11.6

167

323.15−423.7

16.2

9.5

7.5

15.9

water overall PVAC

methanol

15

353.2−433

4.9

27.9

22

353.2−433

17.6

25.6

2-propanol

15

393.2−473.2

13.7

12.9

1-butanol

26

353.2−473.2

9.0

30.0

2-butanol

7

393.2−423.2

8.6

4.7

102

353.2−353.2

10.7

22.1

methanol

363−473

11.0

29.2

ethanol

1

423

49.0

63.8

2-propanol

3

423−473

37.6

13.4

1-butanol

3

423−473

40.4

20.9

acetic acid grand overall

353.2−433

1-propanol

overall a

17

PHSC-AS PC-SAFT

ethanol

overall PMMA

T range [K]

solvent methanol

16

3

423−473

18.4

8.2

26

363−473

19.8

25.3

423

340−473

10.2

10.7

ARD (%) = 1/(NP∑[(ln Ω∞exp − ln Ω∞cal)/ln Ω∞exp]i) × 100.

Figure 6. Infinite dilution WFAC of solute in (a) PEO, (b) PVAC, and (c) PMMA solutions using PHSC-AS EOS. The experimental data are from Hao et al.52 F



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parameter between polymer and solvent was ignored (i.e., kij = 0), and the cross-association parameter is used as an adjustable parameter. The value for cross-association parameter is obtained from VLE calculation. However, for some polymer−alcohol systems in which cannot obtain crossassociation parameters from VLE calculation, those values in PHSC-AS model are assumed to be same with self-association parameters for alkanol, whereas the PC-SAFT model used lower values than self-association parameters, by a factor of about 0.85. Meanwhile, because the dimerization energy of acetic acid is expected to be stronger than the hydrogen bonding energy between PMMA and acetic acid, crossassociation parameters between them used the value of about 70% for self-association of acetic acid. Figures 6 and 7 represent the calculation results with PHSC-AS and PC-SAFT, respectively, which provide a direct illustration of the calculation performance of the both models. For PEO, PVAC, and PMMA, the predictive accuracy of both models is fairly good, but both models gave poor calculations of infinite dilution WFAC of water solvent. This result may be caused by one of two reasons: one is the ignorance of introduction of binary interaction parameter because the experimental Ω∞ of water in PEO increase considerably with the temperature changes, the other is the experimental uncertainty. The experimental WFACs at infinite dilution of water solvent according to molecular weight of polymer show more significant variation. For example, the experimental Ω∞ of water in PEO with molecular weight of 4 000 000 g/mol and 400 g/mol

decrease of activity of water with the molecular weight of PVAL. PC-SAFT EOS shows significantly better accuracy for PVAL/water system than PHSC-AS EOS. In addition, Figure 5 indicates that the two models capture well the difference of activity of water in different polymer solutions according to molecular structure of polymer. 3.3. Infinite Dilution Weight Fraction Activity Coefficient. Infinite dilution activity coefficients can be obtained by extrapolating finite concentration activity data to zero concentration of solute. The experimental infinite dilute activity coefficients of solute in polymer solution are reported in weight fraction base, which is defined as50,51 ∞

Ω∞ = lim ws → 0

M p ϕs̅ as = ws Ms ϕso

(11)

∞

where Ω is the infinite dilution WFAC of solute (s) in polymer solution. The WFAC at infinite dilution of strongly polar solvents such as water, alcohols, and acid were calculated by PHSC-AS and PC-SAFT models. To avoid mathematical errors, a solvent weight fraction of 1 × 10−7 was used as being equivalent to zero. The calculation results of infinite dilution WFAC Ω∞ for PEO-, PVAC- and PMMA-solvent systems are given in Table 4. All the experimental data are obtained from the polymer solution data collection.52 In general, the binary interaction parameter kij is a function of molecular weight and temperature. In the calculation of WFAC, for the simplicity of calculation and the investigation of the importance of crossassociation between polymer and solvent, the binary interaction

Figure 7. Infinite dilution WFAC of solute in (a) PEO, (b) PVAC, and (c) PMMA solutions using PC-SAFT EOS. The experimental data are from Hao et al.52 G



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are about 1742 at 398.85 K and 16.152 at 393.15 K, respectively, whereas in PEO with molecular weight of 7500 g/mol is 42.452 at 393.15 K. 3.4. Liquid−Liquid Equilibria. The estimated pure polymer parameters are applied to calculate the LLE for HDPE/alcohol systems in which the hydrogen bonding among alcohol molecules exists. For the PHSC-AS and PC-SAFT EOS, the binary interaction parameters are available in the attractive perturbation term. For investigation of estimated pure parameter fore polymer, we used the zero value of binary interaction parameter. The results are shown in Figure 8. Though PHSC-AS model is able to predict the UCST phase behavior of HDPE/ alcohol solution but can not obtain the satisfactory results despite adjustment of binary interaction parameter. Furthermore, the HDPE/alcohol solutions are shown LCST phase behavior with the negative value of binary interaction parameter. On the other hand, PHSC-AS EOS described the

LCST phase behavior with binary interaction parameter kij = −0.15, but does not obtain a satisfying result as shown in Figure 9. Such unsatisfied results with SAFT-family EOS is often found.27,40 The possible one way for improving the performance of LLE calculation is found in literature.27,53 When pure-polymer parameters are adjusted only to liquid-density data, it is known that adjusted parameters often take on unreasonable values, which leads to unsatisfying descriptions of phase equilibria for polymer mixtures. Therefore, Sadowski group27,53 estimated pure-polymer parameters through the simultaneous regression of both pure-polymer PVT data and binary phase equilibria data, such as the VLE, and mentioned that purecomponent parameters obtained in this method are suitable for different mixtures. Therefore, to obtain the satisfying results for LLE calculation, such a method for PHSC-AS EOS will apply to the polymer solution with hydrogen bonding phenomena. On the other hand, PC-SAFT EOS model shows much more successful description for the UCST phase behavior of HDPE/ alcohol solution and LCST phase behavior of PVPh/acetone solution with adjustable binary interaction parameter. Our next goal is the improvement of LLE phase behaviors of hydrogen bonding polymer solutions with PHSC-AS EOS.

4. CONCLUSION In this work, the PHSC-AS EOS was extended to the PVT and VLE phase behaviors for hydrogen-bonding polymers such as PEO, PPO, PVME, PMMA, PVAc, PVAL, and PVPh. The calculated results were compared with those by PC-SAFT EOS. Both models represent well PVT relation for pure moltenpolymer and VLE for polymer/solvent systems. The crossassociation energy parameter estimated from the VLE data shows a close to the experimental data from FT-IR spectral analysis. Both of two models describe well the effects of various factors on activity (or partial vapor pressure) of solvent in hydrogen-bonding polymer solution, such as temperature, solvent with different polarity, and the molecular weight and molecular structure of polymer. In addition, PHSC-AS and PC-SAFT models represent the infinite dilution WFAC of strongly polar solvents such as water, alcohols, and acetic acid quantitatively. Despite simple the dispersion term of PHSC-AS EOS, PHSC-AS and PC-SAFT model provide the similar accuracy for PVT, VLE, and WFAC at infinite dilution. However, the LLE calculation shows a poor performance with PHSC-AS model but PC-SAFT model is correlated much more successfully.

Figure 8. Liquid−liquid equilibrium for HDPE with n-alkanols. The experimental data are from Nakajima et al.60 Two lines with different types are the correlations with PHSC-AS (red color, kij is 0 for all alcohols) and PC-SAFT (blue color; kij is 0.014 for pentanol, 0.01 for heptanol, 0.0052 for nonanol) for each of the three solvents (pentanol highest, nonanol lowest). Polymer molecular weight is 20 000 g/mol.

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The authors declare no competing financial interest.

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REFERENCES

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Figure 9. Liquid−liquid equilibrium for PVPh with acetone. The experimental data are from Kim and Kim.38 Two lines with different types are the correlations with PHSC-AS (red color, kij is −0.15 for all systems) and PC-SAFT (blue color; kij is 0.02 for 6912 g/mol, 0.06 for 14 378 g/mol, and 0.065 for 24 267 g/mol) for each of the three molecular weights (6912 g/mol highest, 24 267 g/mol lowest). H



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Hydrogen Bonding in Polymer Solution - Journal of Chemical

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