European Polymer Journal 73 (2015) 259–267

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European Polymer Journal

journal homepage: www.elsevier .com/locate /europol j

Measurement of solubility thermodynamic and diffusion kineticcharacteristic of solvents in PDMS by inverse gaschromatography

http://dx.doi.org/10.1016/j.eurpolymj.2015.10.0190014-3057/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.

Xia Yang a, Chen Jinxun a, Wu Zhen b, Wang Tao a, Li Jiding a,⇑a State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, ChinabOrdos Redbud Innovation Institute, Ordos 017000, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 16 July 2015Received in revised form 18 September 2015Accepted 12 October 2015Available online 22 October 2015

Keywords:Inverse gas chromatographySolubilityDiffusivityPolydimethylsiloxane

Inverse gas chromatography is a versatile and effective method for the characterizationof the solubility thermodynamics and diffusion kinetic of solvent–polymer systemwith the advantages of fast, low dosage of samples and large range of temperature.Polydimethylsiloxane (PDMS) is well known as an excellent polymer membrane materialfor its high permeability to gases and liquids and widely used in the separation and purifi-cation of bio-fermentation broth which was mainly consisted by acetone, butanol, ethanoland water. In this paper, the inverse gas chromatography method was applied to measuresolubility thermodynamics parameters like the infinite dilution activity coefficient andFlory–Huggins interaction parameter between those small molecules and PDMS. The infi-nite dilution diffusion coefficients were calculated by Van Deemter model over a temper-ature range of 373.2–413.2 K. The diffusion coefficient was fitted with the temperatureaccording to the Arrhenius correlation. The data could help the selection of membranematerial in pervaporation or gas separation and the analysis of mass transfer process.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Molecular solution/adsorption and diffusion is the important process in more and more polymer–solvent systems espe-cially for separation of polymer membrane pervaporation and gas permeation [1]. One of the most widely used polymermaterial in separation of organic-water separation (biofuel acetone–butanol–ethanol solution) is the crosslinked PDMSwhich has moderate selectivity and high permeability to many organics [2,3]. There is also a growing interest in using PDMSbased microfluidic chips for functions of bioanalysis in water and organic solvents [4]. In order to comprehend the masstransfer of the membrane [5] and provide academic guidance for the application of PDMS material, it is beneficial to inves-tigate the solution and diffusion characteristics of penetrants in the PDMS [6]. There are some experimental reports concern-ing application of PDMS membrane in penetrants pervaporation [7–9]. However, there are few reports for thethermodynamic and kinetic data of acetone, butanol, ethanol and water interaction with PDMS at the infinite condition.

The common experimental methods for solution/adsorption and diffusion incorporate experiments of swelling [10],gravimetric sorption/desorption [6,11] and pressure decay [12] with complex instruments and time consuming disadvan-tage. Inverse gas chromatography (IGC) is quick, convenient, accurate and low consumption of reagent compared withthe conventional research technique. The equilibrium swelling method needed several hours and the wiping process was

260 Y. Xia et al. / European Polymer Journal 73 (2015) 259–267

easy to cause weight error [10]. The gravitational [11] and pressure decay method [12] needed electronic balance and pres-sure sensor of high precision separately. Those methods became increasingly difficult when the mass transfer was slow orthe solvent was present in small amounts [13,14]. Therefore, IGC technology with the help of a common gas chromatographywas very suitable for the thermodynamic and kinetic data determination. Despite a long history and fast development in thelast 50 years, it is still evolving and quite attractive to chemical engineers, material scientists and analytical chemists in var-ious fields [15]. It has been widely applied not only in the determination of glass transition temperature and crystallinitydegree [16,17] at the beginning, but also in the measurement of activity coefficient, solubility parameters, diffusion con-stants, molar heat or enthalpies of mixing, the Flory–Huggins interaction parameters at infinite condition [18,19]. In addi-tion, IGC also helped the researchers settle the foundation for multicomponent at finite concentration [20–22] or highertemperature [23] and modify free-volume theory to describe solvent diffusion [24–26].

So in our research, the main sorption thermodynamic parameters of acetone, butanol, ethanol and water including infi-nite activity coefficient, solubility coefficient, the Flory–Huggins interaction parameter, solubility parameter, partial molarexcess free energy of mixture and enthalpy of sorption, Hansen polymer solubility parameter and dilution diffusion coeffi-cient of solvent were determined. Those might help the chosen of separation membrane according to the selective solutionand study of solution–diffusion mechanism [27,28].

2. Experimental

2.1. Materials

The PDMS with viscosity of 20 kg m�1 s�1 (density qm, 960.1 kg m�3) was achieved by Beijing Second Chemistry Companyof China. Acetone, butanol, ethanol, hexane, heptane and octane of chromatography grade were purchased from China Med-icine Group (Shanghai Chemical Reagent Corporation). Tetraethylorthosilicate of analytical grade was obtained from BeijingBeihua Fine Chemicals Company of China. The Chromosorb-G (average particle diameter ds, 2.12 � 10�4 m; density qs,747.4 kg m�3) was purchased from Shanghai No. 1 reagent manufactory of China. All the reagents were used without furtherpurification.

2.2. Packing column

The stainless steel column (lcol length, 2 m; di inner diameter, 3 mm) was immersed in the 10 wt% NaOH solution anddrawn by the pump to remove the greasy. The column was then processed by 10 wt% HCl solution to weaken the walladsorption after it is washed by the redistilled water. The support was carefully poured into the PDMS–heptane solution.The heptane was steadily and fully volatized for at least 48 h at 333 K after the addition of cross linking agent [8]. The coatedstationary phase was filled into the column carefully with an end connected to a vacuum pump (0.1 MPa) through a safetybottle. In that process, the column should be knocked continuously to disperse the support uniform. The coated support washeated at 353.2 K for 3 h to crosslink completely. The crosslinking degree was characterized by crosslink density which wasdetermined by physical method with the dynamic mechanical thermal analyzer of DMTA IV (Rheometric Scientific Ltd., USA)[29]. According to the kinetic theory of elasticity, the crosslink density was 4.2 � 10�5 mol�cm�3.

2.3. Procedure

Chromatographic measurements were carried on by GC-14C (Shimadzu Co. Ltd, Japan) equipped with the thermal con-ductivity detector (TCD). The flow vapor phase was solvent carried by inert gas hydrogen and the stationary phase was poly-mer membrane coating on the inert particles. Small volume of solvent was injected into the column oven as a disturbance viathe syringe. Then, the output signal of the detector was fed back to the computer with chromatographic workstation for fur-ther analysis. The temperature of the injection block and the detector were set about 50 K higher than the column temper-ature Tcol to avoid condensation.

The small pulse of solvent caused the partition of solvent in the polymer and the gas, and was determined by thedifference of retention time tr and dead time t0 measured by the paraffin series method [30]. The volumetric flow rate ofthe carrier gas Qg was determined by soap bubble flow meter and adjusted by the pressure drop. Then elution curves andthe peak width Wd was recorded under the various Tcol and Qg. The solubility data derived via IGC should correspond toequilibrium state, and the measurements of the adsorption should be performed under the condition of infinite dilutionof the sorbate. In other words, the partition of solvent depended mainly on its interaction energy with the polymer ratherthan the solvent concentration. So the tiny injection volume of 0.2 lL was chosen in all conditions. Every run was repeatedthree times at least.

Y. Xia et al. / European Polymer Journal 73 (2015) 259–267 261

3. Results and discussion

3.1. Solubility thermodynamics characteristic

3.1.1. Infinite dilute activity coefficientThe principle of IGC was based on the equilibrium partitioning of probe molecules between vapor and stationary phase.

One of the main experimental parameters used to calculate all the thermodynamic parameters for IGC was specific retentionvolume of the solvent Vsr [8]. Quantitative determination of the specific retention volumes provides a convenient method ofdetermining thermodynamic quantities relating to the interaction of solute molecules with the polymer [16]. Vsr wasobtained by means of Eq. (1)

Vsr ¼Qgðtr � t0Þ

ms

273:2To

j ð1Þ

wherems was the mass of PDMS coated on the support material packed in the column, To the temperature of the flow meter.Since the gas was compressible, the pressure drop along the column might cause an increase of Qg in the pressure of the out-let (po) compared with the inlet value (pi). Then correction factor j was usually added for the correction of the Qg.

j ¼ 32ðpi=poÞ2 � 1

ðpi=poÞ3 � 1ð2Þ

Saturated vapor pressure of the solvents psat at different temperature was calculated from Antoine equation [7].Based on the balance partition of solvent between the carrier gas and polymer, the infinite dilution activity coefficients c1

(mass ratio) reflected the intermolecular interaction between the solvent and polymer [19,31]. The generalized equation wasas follows

c1 ¼ RTcol

VsrpsatMexp � psatðB11 � VmolÞ

RTcol

� �ð3Þ

where R was the gas constant, B11 second term of the Virial EOS given by

B11pc

RTc¼ 0:430� 0:886

Tc

Tcol� 0:694

Tc

Tcol

� �2

ð4Þ

and Vmol the molar volume of PDMS. From the recorded tr, t0 and Qg, the c1 was calculated based on Eq. (2). The c1 changingwith temperature was drawn in Fig. 1.

Fig. 1 showed that c1 values of solvents was in the order of acetone < ethanol < butanol < water. c1 gave an idea of thepolymer–solvent compatibility from 373.2 K to 413.2 K. Lower c1 meant the higher solubility. c1 of water was the highestobviously due to the PDMS being a hydrophobic polymer. c1 of all the four solvents decreased with increasing column tem-perature. The solubility was improved, because the increasing temperature caused the augment of mobility of the PDMSchains and weaken of the hydrogen bond between the molecules.

3.1.2. Infinite dilute partial molar excess free energy of mixtureThe solvent vapor sorption or solubility in a polymer was a thermodynamic process directly related to the change of the

free energy associated with the mixing process. Infinite molar excess free energy of mixture DG1mol was one of the criterions

370 380 390 400 410 420

20

30

40

50

60

70

80

γ∞

Tcol (K)

Fig. 1. Temperature dependence of infinite dilute activity coefficient with PDMS. (j acetone; butanol; ethanol; water).

262 Y. Xia et al. / European Polymer Journal 73 (2015) 259–267

for the mixing process. Based on the infinite activity coefficient, the infinite partial molar excess free energy of mixture DG1mol

at infinite dilution was calculated by Eq. (5). The change of DG1mol with temperature was drawn in Fig. 2.

DG1mol ¼ RT ln c1 ð5Þ

It was found in Fig. 2 that acetone had the smallest DG1mol and the order was acetone < ethanol < butanol < water. Larger

DG1mol meant more difficulty for the mixing process at the infinite condition. DG1

mol of all hydrophobic material–solvent mix-tures decreased with increasing temperature, which also meant that higher temperature made the mixing easier.

3.1.3. Infinite dilute partial molar mixing, adsorption and evaporation enthalpyMixing, adsorption and evaporation enthalpy of the solvent in PDMS was also one of the important thermodynamic

parameters, which showed the enthalpy change in the process of mixing/solution, adsorption and evaporation. Accordingto the Gibbs–Helmholtz equation, the value of the partial molar enthalpy of mixing DH1

mix at infinite dilution could bedirectly obtained from the slope of a fitting line derived from Eq. (6). The linear fitting of lnc1 with 1/T was shown inFig. 3. From the slope of the line, the DH1

mix was calculated and listed in Table 1.

DH1mix ¼ R

@ðlnðc1ÞÞ@ð1=TÞ

� �ð6Þ

From activity coefficient values of different temperatures, the enthalpy of solution/adsorption DH1ads was achieved by

Eq. (7). Fig. 4 illustrated the linear relationship of �lnVsr with 1/T. DH1ads was computed by the slope of fitted line and listed

in Table 1.

DH1ads ¼ �R

@ðlnðVsrÞÞ@ð1=TÞ

� �ð7Þ

The values of the enthalpy of vaporization of the solvent (enthalpy of phase change, precisely), DHvap, was the differenceof DH1

mix and DH1ads as Eq. (8) and listed in Table 1.

DHvap ¼ DH1mix � DH1

ads ð8Þ

Table 1 summarized the experimental values of enthalpy for mixing, adsorption and vaporization. It was shown that the

mixing was an endothermic process while the adsorption was an exothermic process.

3.1.4. Flory–Huggins interaction parameterFlory–Huggins theory usually described the dissolution of solvents in the polymer. Flory–Huggins interaction parameter

v characterized the interactions between the solvent and the polymeric stationary phase [32]. v was calculated by Eq. (9).Temperature dependence of v was figured in Fig. 5.

v ¼ ln c1 þ lnqqm

þ qmMqMm

� 1 ð9Þ

As shown in Fig. 5, the value order of v was acetone < butanol < ethanol < water. All the v decreased with increasing Tcol.Small v implied high interactions between the PDMS material and the studied solvents [33]. Values of the v indicated thatthe acetone was the most adequate for the polymer, while water was not favorable for PDMS.

10

11

12

13

ΔGm

∞(kJ/mol)

370 380 390 400 410 420Tcol (K)

Fig. 2. Temperature dependence of infinite dilute molar excess free energy with PDMS. (j acetone; butanol; ethanol; water).

2.40 2.45 2.50 2.55 2.60 2.65 2.702.5

3.0

3.5

4.0

4.5

1/Tcol(10-3K-1)

lnγ∞

Fig. 3. Plots of lnc1 versus 1/T with PDMS. (j acetone; butanol; ethanol; water).

Y. Xia et al. / European Polymer Journal 73 (2015) 259–267 263

3.1.5. Hansen solubility parameters of the polymerThe value of solubility parameter d which was derived from cohesion energy of a compound was important nowadays

which exhibited the ability of a polymer to be dissolved into a solvent. The indirect method had to be used for measuringthe solubility parameter, because the evaporation heat of the polymer could not be determined directly especially for thosecould not be evaporated. On the basis of the Flory–Huggins model and the Hildebrand–Scatchard solution theory, the solu-bility parameter of polymer phase dm could be estimated using the relationship between the Flory–Huggins parameter andthe solubility parameters of solvent and polymer as Eq. (10). vS was the entropic contribution and vH was the enthalpic con-tribution to v [31]. The entropic part was related to the free volume of the solvent, while the enthalpic one was related to theintermolecular forces between the polymer and the solvent.

v ¼ vS þ vH ¼ vS þVmol

RTðd� dmÞ2 ð10Þ

Rearranging Eq. (10) to get Eq. (11), dm of the PDMS material could be calculated from the slope of the plot of d2

2 � vRT2Vmol

(defined as Sp) to d or the intercept of the straight line with the known solvent d [34], which was exhibited in Fig. 6.

d2

2� vRT2Vmol

!¼ dmd� d2m

2þ vsRT2Vmol

!ð11Þ

As shown in Fig. 6, the average dm of PDMS from 373.2 K to 413.2 K was 6.045 after the linear fitting which showed thePDMS was very hydrophobic. The closer the solubility parameters of polymer and solvent were, the higher the compatibilitywas; so it was logical that acetone was the most compatible with PDMS.

3.2. Diffusion kinetic characteristic

The diffusion process was related to the rate of a penetrant going through a membrane. The infinite dilution diffusioncoefficient (mass ratio) could be calculated from the Van Deemter model, in which theoretical equivalent plate height Ht

could be calculated by

Ht ¼ AV þ BV

uþ CVu ð12Þ

The average linear velocity of carrier gas u was rectified by the pressure drop along the column and temperaturevariations between the column and soap film flow meter.

Table 1Experimentally derived enthalpy values.

Solvent DH1mix (kJ mol�1) DH1

ads (kJ mol�1) DHvap (kJ mol�1)

Acetone 22.12 �8.67 30.80Butanol 30.60 �9.04 39.64Ethanol 30.82 �4.03 34.85Water 26.65 �12.80 39.45

4.0

4.5

5.0

5.5

-lnV

sr(m3 /kg)

2.40 2.45 2.50 2.55 2.60 2.65 2.70

1/Tcol(10-3K-1)

Fig. 4. Plots of �lnVsr versus 1/T with PDMS. (j acetone; butanol; ethanol; water).

264 Y. Xia et al. / European Polymer Journal 73 (2015) 259–267

u ¼ jQg

aTcol

Tfmð13Þ

where �a was the volume of gas phase per unit length

a ¼ Qgt0lcol

ð14Þ

The vortex diffusion term of AV characterized of peak widening caused by vortex turbulence and vertical diffusion term ofBVu relevant with the dispersion of solvent in the carrier gas could be neglected. Mass transfer resistance term CV was relevantwith the little gas resistance term Cg and membrane resistance term Cm which determined the time of balance between thephases.

CV ¼ Cg þ Cm ð15Þ

So Ht should be linearly dependent on u with a slope Cm, which could be calculated by

Cm ¼ 8p2

kl2mð1þ kÞ2D1

m

ð16Þ

k was the capacity factor

k ¼ tr � t0t0

ð17Þ

and lm was thickness of polymer coating on the particle with the assumption of spherical and uniform coating.

lm ¼ dsmmqs

6msqmð18Þ

370 380 390 400 410 420

9.0

9.5

10.0

χ

Tcol(K)

Fig. 5. Temperature dependence of interaction parameters of PDMS–solvent pairs. (j acetone; butanol; ethanol; water).

20 25 30 35 40 45 50

100

150

200

250

δ (MPa1/2)

S p(MPa)

Fig. 6. Plots of Sp versus d with PDMS. (h 373.2 K, 383.2 K, 393.2 K, 403.2 K, 413.15 K).

5.5

6.0

6.5

7.0

Ht (mm)

Ht (mm)

Ht (mm)

Ht (mm)

u (m/s) u (m/s)

u (m/s) u (m/s)

4

5

6

7

8

(A) Acetone (B) Butanol

5

6

7

8

0.07 0.08 0.09 0.10 0.11 0.07 0.08 0.09 0.10 0.11

0.07 0.08 0.09 0.10 0.11 0.07 0.08 0.09 0.10 0.1112

14

16

18

20

22

(C) Ethanol (D) Water

Fig. 7. Plots of Ht versus u in PDMS. (h 373.2 K, 383.2 K, 393.2 K, 403.2 K, 413.15 K).

Y. Xia et al. / European Polymer Journal 73 (2015) 259–267 265

with mm and ms the mass of the PDMS and support separately.According to the plate theory, Ht was given by

Ht ¼ Lnt

ð19Þ

nt was given by

nt ¼ 5:54tr

W1=2

� �2

ð20Þ

370 380 390 400 410 420

5

10

15

Tcol(K)

D∞(10-10m/s2)

Fig. 8. Temperature dependence of infinite dilution diffusion coefficient of solvents in PDMS. (j acetone; butanol; ethanol; water).

2.40 2.45 2.50 2.55 2.60 2.65 2.70-22.0

-21.5

-21.0

-20.5

lnD

∞ (10-10m/s2 )

1/Tcol(10-3K-1)

Fig. 9. Arrhennius plots for infinite dilution diffusion coefficient of solvents in PDMS. (j acetone; butanol; ethanol; water).

266 Y. Xia et al. / European Polymer Journal 73 (2015) 259–267

where W1/2 was the half peak width at the peak base [35]. The infinite dilute diffusion coefficient of solvent in polymer D1

could be obtained based on studying the effect of carrier gas velocity on a height equivalent to a theoretical plate combingwith Eqs. (12) and (16). From measurements of peak width and retention time, a plot of Ht versus u was prepared in Fig. 7.The slop Cm of linear fitting via Fig. 7 was applied for D1 of solvents calculation under different temperature. The results wereshowed in Fig. 8.

The order of the diffusion speed under the infinite dilution condition was water > ethanol > acetone > butanol as dis-played in Fig. 8. It was mainly owing to the difference in the size of the solvent molecules. The smaller the size of the mole-cule was, the larger the D1 was. In addition, the diffusivity of the solvents in the polymers was many orders of magnitudeslower than in normal gas or liquid systems.

D1 of different temperature was correlated by Arrhenius formula as Eq. (21) and drawn in Fig. 9.

ln D1 ¼ � E1D

RTþ ln D1

0 ð21Þ

From Fig. 9, the apparent activation energy E1D and pre-exponential factor D1

0 were computed in Table 2. The E1D might be

regarded as the energy of the dissolved molecule jumping into the adjacent free volume among the polymer chain. In theinfinite dilute solution, the diffusing species did not often encounter polymer molecules, so the diffusion rate was limited

Table 2E1D and D1

0 of the solvents in PDMS.

Solvent ED (kJ mol�1) D0 (10�6 m s�2)

Acetone 32.18 2.974Butanol 35.55 1.133Ethanol 27.76 1.338Water 25.05 6.074

Y. Xia et al. / European Polymer Journal 73 (2015) 259–267 267

by the energy required for the diffusing species to escape from its present station and move into the surrounding. The affinitydifference made little contribution to the diffusion coefficient [36]. The bigger molecule polymer generally meant the largerE1D . Water had the lowest E1

D with the smallest collision diameter. The infinite dilute diffusion coefficient under othertemperature could be calculated according to Eq. (21) with the obtained data in Table 2.

4. Conclusion

Solution and diffusion of main components of acetone, butanol, ethanol and water in PDMS materials at infinite dilutionwere studied by IGC. The retention time and peak width of the test probe molecules were recorded. The specific retentionvolume was converted to compute the solubility and diffusion characteristic of the solvent–polymer system. The value orderof mass-based infinite dilution solvent activity coefficient and partial molar excess free energy of mixture ace-tone < ethanol < butanol < water showed that acetone had the best compatibility with PDMS, while the water was the worstsolubility. The positive mixing enthalpy indicated the mixing process was an endothermic process, while the negativeadsorption showed the adsorption was an exothermic process. The smallest Flory–Huggins interaction parameter alsoproved that the acetone had the strongest interaction with PDMS. According to the Flory–Huggins model and the Hilde-brand–Scatchard solution theory, Hansen’s solubility parameter of cross-linked PDMS was 6.045. At last, the infinite dilutediffusion coefficients were calculated. Water and ethanol had larger D1 than acetone, while butanol had the smallest D1 forits large molecule size. Obviously, the solubility difference and diffusion speed difference provided the possibility of PDMS asmembrane separation for the mixture of acetone, butanol, ethanol and water.

As a fast and reliable method of achieving physicochemical properties and thermodynamic data in solvent–polymer sys-tems, the IGC method do solve the disadvantage of time-consuming and painstaking gravimetric for sorption/desorptionexperiments. Those thermodynamics and kinetic parameters can also offer the data to the theoretical models for gasseparation, pervaporation and reverse osmosis.

Acknowledgements

The financial supports of National Natural Science Foundation of China (21576150), Science Foundation of TsinghuaUniversity (20131089399) and the Special funds for technological development research of Research Institutes fromNational Ministry of Science and Technology (2013EG111129) are greatly appreciated.

References

[1] C. Etxabarren, M. Iriarte, A. Etxeberria, C. Uriarte, J.J. Iruin, J. Appl. Polym. Sci. 89 (8) (2003) 2216–2223.[2] G. Cocchi, M.G. De Angelis, F. Doghieri, J. Membr. Sci. 492 (2015) 612–619.[3] G. Cocchi, M.G. De Angelis, F. Doghieri, J. Membr. Sci. 492 (2015) 600–611.[4] J.N. Lee, C. Park, G.M. Whitesides, Anal. Chem. 75 (23) (2003) 6544–6554.[5] I. Vankelecom, S. DeBeukelaer, J.B. Uytterhoeven, J. Phys. Chem. B 101 (26) (1997) 5186–5190.[6] A. Randová, L. Bartovská, P. Izák, K. Friess, J. Membr. Sci. 475 (2015) 545–551.[7] I.H. Romdhane, R.P. Danner, AIChE J. 39 (4) (1993) 625–635.[8] C.W. Zhao, J.D. Li, Z. Jiang, C.X. Chen, Eur. Polym. J. 42 (3) (2006) 615–624.[9] S. Zhao, W.W. Zhang, F. Zhang, B. Li, Polym. Bull. 61 (2) (2008) 189–196.[10] B.L. Shi, C.S. Feng, Y.L. Wu, J. Membr. Sci. 245 (1–2) (2004) 87–93.[11] I. De Bo, H. Van Langenhove, J. De Keijser, J. Membr. Sci. 209 (1) (2002) 39–52.[12] R. Pourdarvish, R.P. Danner, J.L. Duda, J. Appl. Polym. Sci. 108 (3) (2008) 1407–1413.[13] R.K. Surana, R.P. Danner, F. Tihminlioglu, J.L. Duda, J. Polym. Sci., Part B: Polym. Phys. 35 (8) (1997) 1233–1240.[14] R.Y. Qin, H.P. Schreiber, Langmuir 10 (11) (1994) 4153–4156.[15] S. Mohammadi-Jam, K.E. Waters, Adv. Colloid Interface Sci. 212 (2014) 21–44.[16] J.M. Braun, J.E. Guillet, Macromolecules 8 (6) (1975) 882–888.[17] P. Mukhopadhyay, H.P. Schreiber, Macromolecules 26 (24) (1993) 6391–6396.[18] N. Belov, Y. Yampolskii, M.C. Coughlin, Macromolecules 39 (5) (2006) 1797–1804.[19] Q.G. Zhang, Q.L. Liu, J. Lin, J.H. Chen, A.M. Zhu, J. Mater. Chem. 17 (46) (2007) 4889–4895.[20] P.K. Davis, J.L. Duda, R.P. Danner, AIChE J. 51 (11) (2005) 2930–2941.[21] M.J. Debarro, S.B. McGregor, C.J. Glover, Ind. Eng. Chem. Res. 27 (6) (1988) 1066–1073.[22] P.F. Lito, A.L. Magalhaes, J. Gomes, C.M. Silva, J. Chromatogr., A 1290 (2013) 1–26.[23] W.S. McGivern, J.A. Manion, J. Chromatogr., A 1218 (46) (2011) 8432–8442.[24] Y.Q. Shi, X.W. Wang, G.W. Chen, J. Appl. Polym. Sci. 61 (8) (1996) 1387–1394.[25] Z.P. Smith, R.R. Tiwari, M.E. Dose, K.L. Gleason, T.M. Murphy, D.F. Sanders, G. Gunawan, L.M. Robeson, D.R. Paul, B.D. Freeman, Macromolecules 47 (9)

(2014) 3170–3184.[26] N. Ramesh, P.K. Davis, J.M. Zielinski, R.P. Danner, J.L. Duda, J. Polym. Sci., Part B: Polym. Phys. 49 (23) (2011) 1629–1644.[27] I.M. Balashova, E. Meco, R.P. Danner, Fluid Phase Equilib. 366 (2014) 69–73.[28] R.P. Danner, Fluid Phase Equilib. 362 (SI) (2014) 19–27.[29] S. Ray, S.K. Ray, J. Membr. Sci. 270 (1–2) (2006) 132–145.[30] N.S. Wu, G.S. Wu, M.Y. Wu, J. Chromatogr. Sci. 44 (5) (2006) 244–246.[31] D. Patterso, Y.B. Tewari, H.P. Schreibe, J.E. Guillet, Macromolecules 4 (3) (1971) 356–359.[32] D.G. Gray, J.E. Guillet, Macromolecules 6 (2) (1973) 223–227.[33] K. Demirelli, I. Kaya, M. Coskun, Polymer 42 (12) (2001) 5181–5188.[34] H. Eser, F. Tihminlioglu, Fluid Phase Equilib. 237 (1–2) (2005) 68–76.[35] J.R. Conder, C.L. Young, Physicochemical Applications of Gas Chromatography, Wiley, New York, 1979.[36] C.Y. Zeng, M. Huang, H. Zhao, J.C. Zhou, J.D. Li, J. Appl. Polym. Sci. 123 (1) (2012) 124–134.