The membranes (Nafion and LDPE) in binary liquid mixtures benzene + methanol – sorption and swelling

European Polymer Journal 45 (2009) 2895–2901

Contents lists available at ScienceDirect

European Polymer Journal

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

The membranes (Nafion and LDPE) in binary liquid mixturesbenzene + methanol – sorption and swelling

A. Randová a,*, L. Bartovská a, Š. Hovorka a, K. Friess a, P. Izák b

a Department of Physical Chemistry, Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republicb Institute of Chemical Process Fundamentals, Rozvojová 135, 165 02 Prague 6, Czech Republic

a r t i c l e i n f o

Article history:Received 20 March 2009Received in revised form 9 June 2009Accepted 29 June 2009Available online 2 July 2009

Keywords:MembraneSwellingSorptionSeparation factorsSpecific volume

0014-3057/$ - see front matter � 2009 Elsevier Ltddoi:10.1016/j.eurpolymj.2009.06.023

* Corresponding author. Fax: +420 220 444 333.E-mail addresses: [email protected] (A. Randov

(L. Bartovská), [email protected] (Š. Hovorka)(K. Friess), [email protected] (P. Izák).

a b s t r a c t

Sorption studies provide valuable information about the interactions of the components ofthe liquid mixture with the polymer. In the present paper, the behaviour of Nafion andlow-density polyethylene membranes in binary mixtures benzene + methanol was exam-ined with respect to their application in separation processes. The individual sorption iso-therms, the separation factors, and the composition of the swollen membranes werederived from the experimental data. The results confirm that Nafion as a polar materialsorbs the more polar component of the mixture (methanol) preferentially to the less polarcomponent (benzene) whereas non-polar polyethylene prefers non-polar benzene in thewhole concentration range. Volume measurements of the swollen membranes indicatethat the ideal sorption behaviour cannot be considered for the selected systems.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Since large amounts of solvents are used in industrialapplications, the minimisation of their environmental im-pacts calls for the improvement of current technologiesfor solvent regeneration or finding new possibilities in thisfield. However, the distillation process, commonly used forthe solvents separation, is energy-consuming, and itsselectivity may be limited by the vapour–liquid equilib-rium, especially in cases of azeotropic mixtures. If the pro-cess can be replaced by the membrane separation, thesedifficulties might be overcome. The problem is the choiceof suitable membrane. It is necessary to consider the selec-tivity of the membrane, as well as its price and durability.The sorption data may help when designing the separationprocess and choosing the suitable membrane.

The aim of this work is to compare the selectivity of twomembranes of different nature for non-polar–polar organic

. All rights reserved.

á), [email protected], [email protected]

mixtures as such as benzene + methanol, often encoun-tered for instance in the pharmaceutical industry. Nafionusually shows a high selectivity for organic mixtures. Onthe other hand, with hydrophobic membranes, such aspolyethylene, one cannot expect a very high selectivity,as they do not possess any functional groups to create adifference in interaction between the two components ofthe separated mixture. Nevertheless polyethylene in therole of the separation membrane is a very cheap material.

Both materials under study are used in the form of thefoil. Nafion is a polymer with perfluorovinyl pendant sidechains ended by sulphonic acid groups (Fig. 1a). Thepoly(tetrafluoroethylene) backbone guarantees an out-standing chemical stability in both reducing and oxidizingenvironments. The sulphonic exchange groups on the sidechains have very high acidity [1,2]. Nafion membrane isused in fuel cells, membrane reactors, gas dryers, produc-tion of NaOH, electrodialyses, etc. [3–7]. Polyethylene is asmooth-chained polymer with simple structural unit(Fig. 1b). In numerous applications the membranes are im-mersed in liquid, which significantly affects their proper-ties (namely swelling and transport properties ofpermeates) [8–11].

Fig. 1. Structural units of (a) Nafion, (b) polyethylene membranes. Theindex m is usually equal unity, so that the value of n determines the ratioof polar to non-polar material in the membrane and varies from 5 to 11.

2896 A. Randová et al. / European Polymer Journal 45 (2009) 2895–2901

2. Theory

The sorption of a binary liquid mixture (components 1and 2) in a polymer (component 3) is characterised bytwo parameters: the swelling degree and the preferentialsorption [12–25].

2.1. The swelling degree

On immersion into a liquid the polymer imbibes certainamount of liquid. This process can be quantified by theswelling degree, i.e., the relative mass increase:

Q ¼ m3 �m3;0

m3;0ð1Þ

where m3 is the mass of the swollen polymer membraneand m3,0 is the mass of the dry membrane.

2.2. The preferential sorption and the composition of binarymixture sorbed in the polymer

When a polymer is in contact with a binary liquid mix-ture, in most cases one of the mixture components is moresorbed into the polymer. The extent of this phenomenon ischaracterised by the preferential sorption, i.e., by the ex-cess number of moles of certain component sorbed in thepolymer compared to its number in the bulk solution hav-ing the same total number of moles of liquid mixture ns themixture sorbed in the polymer. If, for example, the compo-nent 2 is preferentially sorbed, the preferential sorption X2

related to unit of mass of dry polymer (in mol g�1) is givenby the relation

X2 ¼ nsðxs2 � xb

2Þ ð2Þ

where xs2 is the molar fraction of the component 2 in liquid

sorbed in the polymer, xb2 the molar fraction of this compo-

nent in the bulk binary liquid surrounding the polymer.The total number of moles of substances sorbed in onegram of polymer ns from Eq. (2) can be expressed as

ns ¼ QMs¼ Q

xs2M2 þ ð1� xs

2ÞM1ð3Þ

where M1 and M2 are the molar masses of pure compo-nents 1 and 2, and Ms is the average molar mass of binarysorbed liquid. Preferential sorption X2 is available fromexperimental data using equation

X2 ¼N0

m3;0� ðxb

2;0 � xb2Þ ð4Þ

where N0 ¼ m0=ðxb1;0 �M1 þ xb

2;0 �M2Þ is the initial molenumber in m0 grams of the binary solution brought in con-tact with m3,0 grams of polymer, xb

i;0 and xbi are the molar

fractions of the component i (i = 1 for benzene and i = 2for methanol) in bulk initial and equilibrium solutions,respectively.

The dependence of the preferential sorption on the bulksolution composition at constant temperature is called theisotherm of concentration change or composite isotherm.

The combination of Eqs. (2) and (3) allows determina-tion of the molar fraction of the preferentially sorbed com-ponent in the polymer phase from experimental data onpreferential and total sorptions (Eqs. (1) and (4))

xs2 ¼

Qxb2 þX2M1

X2ðM1 �M2Þ þ Qð5Þ

2.3. The individual isotherms

In many applications it is necessary to have informationnot only on the total sorbed amount (ns) but also on theamounts of single components sorbed in the polymer (socalled individual sorptions ns

1 and ns2) at different bulk

solution compositions. Knowing the composition of thesorbed liquid as a function of bulk solution composition(Eq. (5)) and the total sorbed amount ns (Eq. (3)), the indi-vidual isotherms can be gainedns

1 ¼ xs1 � ns ð6Þ

ns2 ¼ xs

2 � ns ð7Þ

2.4. The separation factors

The effectiveness of the separation processes can be ex-pressed by the separation factors

asb21 ¼

xs2=xs

1

xb2=xb

1

ð8Þ

for the sorption equilibrium and

ag‘21 ¼

y2=y1

x2=x1ð9Þ

for the vapour–liquid equilibrium (xi and yi are the molarfractions of the component i in the liquid and vapourphases, respectively).

2.5. The composition of the swollen polymer

The composition of the ternary phase, i.e., swollen poly-mer, is expressed in weight fractions, because the molarmass of the polymer is not known. The weight fraction ofpolymer (component 3) in the ternary system (superscriptter) is given by the equilibrium swelling degree as

wter3 ¼

11þ Q

ð10Þ

and weight fractions of components 1 and 2 are calculatedfrom the individual sorptions:

wter1 ¼

ns1 �M1

1þ Qð11Þ

A. Randová et al. / European Polymer Journal 45 (2009) 2895–2901 2897

wter2 ¼ 1�wter

1 �wter3 ð12Þ

(the base for all the above mentioned quantities is 1 g ofdry polymer membrane).

2.6. The percentage relative specific volume increment

The volume changes of the membrane in contact withliquid medium are often attributed only to the sorbed li-quid. The specific volume of the swollen membrane is thencalculated under the assumption of additivity as

Vadd ¼ 1q3;0þ nsðxs

1 � Vm1 þ xs2 � Vm2 þ VEÞ ð13Þ

whereq3,0 is the density of dry polymer [g cm�3], ns the equi-librium mole number of liquid sorbed into 1 g of dry mem-brane [mol g�1], Vm1 and Vm2 the molar volumes of pureliquid penetrant 1 and 2 [cm3 mol�1], respectively, and VE

the excess volume of binary liquid mixture [cm3 mol�1].In numerous cases the real volume of the swollen mem-

brane (Vexp) is different from Vadd calculated from Eq. (13)as the simple sum of polymer and liquid volumes, i.e.,assuming zero mixing volume of polymer with binary li-quid solution. This difference can be attributed to theinteractions between the polymer and the liquid medium.To characterise the extent of these interactions, thequantity

b ¼ Vexp

Vadd � 1� �

� 100 ð14Þ

called the percentage relative specific volume increment(in further text only the volume increment) was proposed.

1 Other experiments (measurement of the dimensions of a membraneimmersed into the liquid [29–31]) confirmed that this time period is morethan sufficient for establishing the equilibrium.

3. Experiments

3.1. Chemicals and materials

High-pressure low-density polyethylene (LDPE) BRALENFB 2-30 (Slovnaft, Bratislava) in the form of foil (thickness0.046 mm – measured by an Inductive Dial Indicator,Mahr, Germany) was used. Its density, (q = 0.940 g cm�3),was determined by weighing of the sample of known areaand thickness. Prior to experiments, the foil was washedwith distilled water, dried in the drying box for 20 h at60 �C and then kept in a vacuum desiccator.

Nafion N-112 (thickness 0.051 mm – measured by anInductive Dial Indicator Mahr, density 1.925 g cm�3 –determined by weighing of the sample of known areaand thickness) was used as received (DuPont).

Methanol (M = 32.04 g mol�1, q = 0.78664 g cm�3) andbenzene (M = 78.12 g mol�1, q = 0.87370 g cm�3) were p.a.purity grade products of Sigma–Aldrich. Binary liquid mix-tures, used for experiments, were prepared by weight. TheTRC Tables [26] were used as the source of the cited den-sity values.

3.2. The sorption measurements

The swelling degree has been determined by the gravi-metric method [27,28]. A sample of the membrane (about

0.15 g) was immersed into about 40 g of binary liquid mix-ture benzene + methanol in a closely sealed bottle forapproximately 24 h.1 The swollen foil was then transferredinto a tightly closed weighing bottle inlaid by filter paper sothat only edges of the foil touched the paper. This arrange-ment enabled to drain off the excess liquid from the foil (in-stead of commonly used drying between two sheets of filterpaper which gave entirely unreliable results because of thesmall thickness of the sample). After approximately 3 h thebottle was weighed, the swollen foil taken out and the bottlewith the wet paper was weighed again. The difference rep-resented the weight of the swollen membrane. This proce-dure was found to be reproducible within 2%.

The preferential sorption has been determined from theconcentration change of the bulk solution brought aboutby contact with polymer. Exactly weighed amounts ofdry polymeric foil (m3,0), cut to small pieces, and of binaryliquid solution of known composition (m0; m0/m3,0 � 3) ina tightly sealed bottle were kept at constant temperaturefor 24 h. The difference in the initial and equilibrium solu-tions compositions was determined using the Rayleigh–Haber–Lowe differential interferometer (Carl Zeiss, Ger-many) with 0.5 cm double cell was used (with maximumdifference in molar fraction ± 0.02) [28]. This change inthe solution concentration, caused by the sorption, allowsthe calculation of the preferential sorption according toEq. (4).

3.3. Volume measurements

The volume of the swollen membrane, Vexp, was deter-mined from the dimensional changes of the square mem-brane samples cut off in parallel with the edges of asheet supplied by manufacturer. Two dimensions (in thedrawing direction, and in the perpendicular direction)were measured in situ by the optical method, describedin our previous papers [29–31]. Thickness was measuredimmediately after taking the membrane out of the liquidby an Inductive Dial Indicator Mahr. It was observed thatthe changes in thickness were the same as the changes inthe perpendicular direction. The experimental errors inthe percentage relative expansion were determined to be±1 for the optical measurements and ±2 for the thicknessdetermination.

All experiments were carried out at the temperature of25 �C and at atmospheric pressure.

4. Results and discussion

It was shown on the basis of Flory–Huggins thermody-namics that the preferential sorption depends on the dif-ferences in molar volumes of the two penetrants, theaffinity of both components towards the membrane andthe mutual interaction between the two penetrants [32].As the liquid mixture in both systems under study is the

Fig. 2. The equilibrium swelling degree as a function of the molar fractionof methanol in the bulk solution in the equilibrium. h system Naf-ion + benzene (1) + methanol (2), s system LDPE + benzene (1) +methanol (2).

2898 A. Randová et al. / European Polymer Journal 45 (2009) 2895–2901

same, it is the interaction of polymer with the penetrantswhich has predominant influence on sorption behaviour.

The results are plotted in Fig. 2 as the swelling degreesQ and in Fig. 3 as composite isotherms. In both graphs theconcentration axis is in terms of xb

2, the mole fraction ofcomponent 2 (methanol) in the bulk liquid phase atequilibrium.

4.1. The equilibrium swelling degree

Both polymers show the liquid uptake extent of approx-imately same order – up to approximately Q ffi 0.3. Thecourses of the swelling curves are however reversed.

Methanol was found to be a weak swelling agent forLDPE. The swelling degree of LDPE in pure methanol is verysmall (Q ffi 0.01), but with even a little benzene in the bulksolution the total liquid uptake gets significantly larger.The presence of benzene enhances the sorption of metha-nol in the membrane. The swelling degree of LDPE in pure

Fig. 3. Composite isotherm – the preferential sorption as a function of themolar fraction of methanol in the bulk solution in the equilibrium. h

system Nafion + benzene (1) + methanol (2), s system LDPE + benzene (1)+ methanol (2).

benzene amounts to 0.25 and with increasing methanolcontent in the bulk solution the swelling curve goes upand passes through a gentle maximum (Q ffi 0.3).

The swelling degree of Nafion follows an inverse trend.Minimum swelling degree (Q = 0.008) is observed in purebenzene. The swelling curve is steadily rising, mildly S-shaped with an inflection around 60 mol.% of methanol.Maximum swelling (Q = 0.272) is observed in puremethanol.

4.2. The preferential sorption

The swelling degree (Fig. 2) gives no information aboutthe benzene + methanol mixture composition in the mem-brane, i.e., the occurrence of preferential sorption cannotbe deduced from the total sorption experiments alone.The results of preferential sorption determination are gi-ven in Fig. 3. The ordinate represents the preferential sorp-tion of methanol, X2, in millimoles sorbed in one gram ofpolymer.

No inversion has been found on either of the compositeisotherms. The preferential sorption of methanol in Nafionreaches its maximum value at xb

2 = 0.4 � 0.5. LDPE displaysan opposite behaviour: it is benzene, which is here prefer-entially sorbed, the maximum absolute value of benzenepreferential sorption being several times smaller thanmethanol sorption in Nafion.

The measurements with membranes in pure benzeneand pure methanol proved that no change in concentrationoccurs.

4.3. The individual isotherms

The individual isotherms calculated from experimentaldata on the total and preferential sorptions using Eqs.(5)–(7), are shown in Fig. 4a and b together with totalamounts of binary liquid mixture sorbed by the polymer(in millimoles per one gram of dry polymer).

The individual isotherm of methanol in Nafion is verynear to the curve of the total sorption; therefore the totalamount of the sorbed liquid consists mainly of methanol,especially at bulk solution concentrations higher than50 mol.% of methanol. The sorbed amount of benzene isnot greater than 1 mmol g�1 (at approximately xb

2 = 0.1).Both individual isotherms in the system LDPE + ben-

zene + methanol pass through a maximum; the isothermof benzene at about 80 mol.% of benzene in the bulk solu-tion (3.6 mmol g�1), the isotherm of methanol at about80 mol.% of methanol in the bulk solution (3.2 mmol g�1).

4.4. The sorption equilibrium in comparison with vapour–liquid equilibrium (VLE)

The separation factors calculated from Eqs. (8) and (9)are shown in Fig. 5. The content of the component 2 (meth-anol) in the sorbed liquid (xs

2) vs. that in the equilibriumbulk solution surrounding the swollen polymer (xb

2) forboth systems is plotted in Fig. 6. Both plots are here com-pared with vapour (y2) – liquid (x2) diagram representingthe vapour–liquid equilibrium [33].

Fig. 4. The individual isotherms. (a) j Individual isotherm of benzene inNafion (ns

1), h individual isotherm of methanol in Nafion (ns2). (b) d

Individual isotherm of benzene in LDPE (ns1), s individual isotherm of

methanol in LDPE (ns2)

Fig. 5. The separation factors. h system Nafion + benzene (1) + methanol(2), s system LDPE + benzene (1) + methanol (2) — vapour–liquidequilibrium in the system benzene (1) + methanol (2).

Fig. 6. Comparison of sorption and VLE equilibria. h Sorption equilibriumin the system Nafion + benzene (1) + methanol (2), s sorption equilib-rium in the system LDPE + benzene (1) + methanol (2) — vapour–liquidequilibrium in the system benzene (1) + methanol (2).

A. Randová et al. / European Polymer Journal 45 (2009) 2895–2901 2899

It is evident that the membrane separation eliminatesthe main disadvantage of distillation, because contrary toVLE there is no azeotropic point on either of the sorptionequilibrium curves. The separation factors in the systemNafion + benzene + methanol are markedly higher, espe-cially at concentrations between 60 and 80 mol.% of metha-nol in bulk liquid, than those in the system LDPE +benzene + methanol.

4.5. The composition of the ternary system

In order to sketch in the image of the two systems un-der study, the composition of the swollen polymers (inweight fractions) was calculated from Eqs. (10)–(12). It ispresented in ternary diagrams in Fig. 7. Both equilibriumphases, the swollen polymer and the binary bulk solution,are connected by tie-lines.

4.6. The volume of the swollen membrane

Our experiments confirmed that the assumption ofideal sorption behaviour cannot be used for the title sys-tems. The swollen membrane volumes, determined fromthe dimensional changes, Vexp, at various compositions ofthe bulk solution are shown in Fig. 8 (open points). Thesame graphs include also curves representing the concen-tration dependence of the swollen membrane volume cal-culated from Eq. (13) under the assumption of additivity,Vadd, considering the binary mixture non-ideality (usingexcess volume – Ref. [34]). It is evident, that both data sets,experimental and calculated ones, do not coincide. Thisdemonstrates clearly the existence of interactions poly-mer-binary liquid mixture. Both systems are comparedfrom this point of view by means of the volume incrementb (Eq. (14)) in Fig. 9.

Positive b-values mean that the real volume increase ofthe membrane immersed into a liquid is greater thenthat predicted by additive calculation from total and

Fig. 7. The composition of the swollen polymers. (a) h Swollen Nafion, j

binary bulk solution benzene + methanol in equilibrium with swollenNafion, — tie-lines. (b) s Swollen LDPE, d binary bulk solutionbenzene + methanol in equilibrium with swollen LDPE, — tie-lines.

Fig. 8. Comparison of the calculated and experimental volumes of theswollen membranes. h Vexp of the swollen Nafion, - - - connecting line, –– – Vadd of the swollen Nafion, s Vexp of the swollen LDPE, -�-�- connectingline, –�–�– Vadd of the swollen LDPE.

Fig. 9. The volume increment b. h System Nafion + benzene (1) +methanol (2), - - - connecting line, s system LDPE + benzene (1) +methanol (2), -�-�- connecting line.

2900 A. Randová et al. / European Polymer Journal 45 (2009) 2895–2901

preferential sorption data together with information on themixing data of binary liquid mixture.

Not taking this fact into account when designing a de-vice with an anchored membrane can lead to the worseperformance of the device, because the membrane swellsmore than the calculation suppose and it wriggles in itsmiddle parts.

Negative b-values indicate that the volume expansionof the membrane in liquid is not so large as that supposingthe additive calculation (in methanol the LDPE membraneeven contracts in the drawing direction instead of expand-ing). The membrane area usable for separation is thensmaller than calculated one and/or a tendency to contrac-tion causes unfavourable tension in membrane fastenedinto a device.

No similar data on these systems have been found inliterature.

5. Conclusions

The sorption experiments and dimensional measure-ment were carried out to obtain more complex informationon the separation processes. The total and preferentialsorption characteristics of benzene + methanol liquid mix-tures in Nafion and low-density polyethylene (LDPE) mem-branes were studied as a function of the binary liquidmixture composition. Nafion films were found to be selec-tive toward methanol in the whole concentration range(maximum preferential sorption of methanol isX2 = 3.1 � 10�3 mol g�1), LDPE films to benzene (maxi-mum preferential sorption of benzene is X1 = 0.58 �10�3 mol g�1) and it means that no inversion occurs oneither of the xs

2 � x‘2 curves (Fig. 6). This implies a markedadvantage of the first step of membrane processes (i.e.,sorption of the binary mixture in the membrane) overthe distillation separation considering the existence ofazeotrope on the vapour–liquid equilibrium curve. How-ever, to be able to make an overall comparison betweenthe membrane separation using Nafion or LDPE and

A. Randová et al. / European Polymer Journal 45 (2009) 2895–2901 2901

distillation, it would be necessary to have information onrate of mass transport through membrane.

Another interesting aspect which can be deduced fromour dimensional experiments is that the assumption ofideal sorption behaviour cannot be used nor for systemNafion + benzene + methanol nor for system LDPE +benzene + methanol. The change in the membrane volumecaused by contact with liquid medium calculated underthe assumption of ideal mixing of polymer with binary li-quid mixture is not the same as that obtained from thedimensional changes of the membrane on swelling. Thedifference, attributed to the interactions polymer–liquidmedium, is expressed as percentage of the additively cal-culated volume in the dependence on the bulk solutioncomposition.

Acknowledgements

This research was supported partially by Grant No. 104/08/0600 from Czech Science Foundation. Co-authors fromInstitute of Chemical Technology acknowledge the finan-cial support from the grant from Ministry of Education ofthe Czech Republic (MSM 6046137307).

References

[1] Heitner-Wirguin C. Recent advances in perfluorosulphonatedionomer membranes: structure, properties and application. JMembr Sci 1996;120:1–33.

[2] Mauritz KA, Moore RB. State of Understanding of Nafion. Chem Rev2004;104:4535–85.

[3] Perma-pure: dryers and humidifiers. Available from: http://www.permapure.com/PDF%20Files/Nafion.pdf.

[4] Pintauro PN, Wycisk R. Polymeric Membranes for fuel cells:overview and future outlook, workshop on membrane science,advanced photon source, August 17–18. Argonne, Illinois; 2004.

[5] Subramanian K, Asokan K, Jeevarathinam D, Chandrasekaran M.Electrochemical membrane reactor for the reduction of carbondioxide to formate. J Appl Electrochem 2007;37:255–60.

[6] Benziger JB, Chia EJ, Karnas E, Moxley J, Teuscher C, Kevrekidis IG.The stirred tank reactor polymer electrolyte membrane fuel cell.AIChE J 2004;50:1889–900.

[7] Jörissen J. Electrochemical processes based on ion exchangemembranes, Universität Dortmund. Available from: http://www.mv.chemietechnik.uni-dortmund.de/tca/web/de/textonly/con-tent/mitarb/akad_oberrat/akad_oberrat.html.

[8] Saito M, Tsuzuki S, Hayamizu K, Okada T. Alcohol and protontransport in perfluorinated ionomer membranes for fuel cells. J PhysChem B 2006;110:24410–7.

[9] Yeo SC, Eisenberg A. Physical properties and supermolecularstructure of perfluorinated ion-containing (Nafion) polymers. JAppl Polym Sci 1977;21:875–98.

[10] Yeo RS, McBreen J, Kissel G, Kulesa F, Srinivasan S.Perfluorosulphonic acid (Nafion) membrane as a separator for anadvanced alkaline water electrolyser. J Appl Electrochem1980;10:741–7.

[11] Walsby N, Hietala S, Maunu SL, Sundholm F, Kallio T, Sundholm G.Water in different poly(styrene sulfonic acid)-grafted fluoropol-ymers. J Appl Polym Sci 2002;86:33–42.

[12] Yuzhong Z, Keda Z, Jiping X. Preferential sorption of modified PVAmembrane in pervaporation. J Membr Sci 1993;80:297–308.

[13] Katime I, Anasagasti M, Rivas I, Valenciano R. Preferential sorption ofpolyvinylpyrrolidone (PVP) in the binary solvent mixture water/DMF. Polym Bull 1991;26:587–94.

[14] Manito Pereira AM, Lopes MC, Timmer JMK, Keurentjes JTF. Solventsorption measurements in polymeric membranes with ATR–IRspectroscopy. J Membr Sci 2005;260:174–80.

[15] Aithal US, Aminabhavi TM. Sorption and diffusion of organic solventsin polyurethane elastomers. Polymer 1990;31:1757–62.

[16] Mateo JL, Bosch P, Serrano J, Calvo M. Sorption and diffusion oforganic solvents through photo-crosslinked SBS block copolymers.Eur Polym J 2000;36:1903–10.

[17] Ajithkumar S, Patel NK, Kansara SS. Sorption and diffusion of organicsolvents through interpenetrating polymer networks (IPNs) basedon polyurethane and unsaturated polyester. Eur Polym J2000;36:2387–93.

[18] Aminabhavi TM, Munk P. Preferential adsorption onto polystyrene inmixed solvent systems. Macromolecules 1979;12:607–13.

[19] Harogoppad AB, Aminabhavi TM. Diffusion and sorption of organicliquids through polymer membranes. 5. Neoprene, S tyrene–butadiene–rubber, ethylene–propylene–diene terpolymer, andnatural rubber versus hydrocarbons (C8–C16). Macromolecules1991;24:2598–605.

[20] Bristow GM. The swelling of rubber networks in binary solventmixtures. Trans Farad Soc 1959;55:1246–53.

[21] Wang H, Ugomori T, Tanaka K, Kita H, Okamoto K-I, Suma Y. Sorptionand pervaporation properties of sulfonyl-containing polyimidemembrane to aromatic/non-aromatic hydrocarbon mixtures. JPolym Sci B Polym Phys 2000;38:2954–64.

[22] Lue SJ, Wei YS. Sorption of organic solvents in poly(dimethylsiloxane) membrane. I. Permeant states quantification usingdifferential scanning calorimetry. J Macromol Sci B Phys2005;44:711–25.

[23] Enneking L, Heintz A, Lichtenthaler RN. Sorption equilibria of theternary mixture benzene/cyclohexene/cyclohexane in polyurethane-and PEBA-membrane polymers. J Membr Sci 1996;115:l61–170.

[24] Okuno H, Nishida T, Uragami T. Preferential sorption and permeationof binary liquid mixtures in poly (vinyl chloride) membrane bypervaporation. J Polym Sci B Polym Phys 1995;33:299–307.

[25] Ritums JE, Hedenqvist MS, Bergman G, Prodan T, Emri I. Sorptionbehavior in polymers above Tg: relations between mechanicalproperties and swelling in limonene. Polym Eng Sci2005;45:1194–202.

[26] Frenkel M, editor. TRC Thermodynamic Tables – Hydrocarbons.Publication Series NSRDSNIST-75, Non-Hydrocarbons, PublicationSeries NSRDS-NIST-74. Gaithersburg, MD: National Institute ofStandards and Technology, Boulder, CO, Standard Reference DataProgram; 2008.

[27] Izák P, Bartovská L, Friess K, Šípek M, Uchytil P. Description of binaryliquid mixtures transport through non-porous membrane bymodified Maxwell–Stefan equations. J Membr Sci2003;214:293–309.

[28] Izák P, Bartovská L, Friess K, Šípek M, Uchytil P. Comparison ofvarious models for transport of binary mixtures through densepolymer membrane. Polymer 2003;44:2679–87.

[29] Izák P, Hovorka Š, Bartovsky T, Bartovská L, Crespo JG. Swellingkinetics of polymeric membranes in room temperature ionic liquids.J Membr Sci 2007;296:131–8.

[30] Randová A, Hovorka Š, Izák P, Bartovská L. Swelling of Nafion inmethanol–water–inorganic salt ternary mixtures. J ElectroanalChem 2008;616:117–21.

[31] Randová A, Bartovská L, Hovorka Š, Poloncarzová M, Kolská Z, Izák P.Application of the group contribution approach to Nafion swelling. JAppl Polym Sci 2009;111:1745–50.

[32] Kargupta K, Datta S, Sanyal SK. Quantitative approach for theprediction of preferential sorption in the case of pervaporation of aphysico-chemically similar binary mixture. J Membr Sci1997;124:253–62.

[33] Gmehling U et al. Vapor–liquid equlibrium data collection,Dechema; 1998.

[34] Šerbanovic SP, Kijevcanin ML, Radovic IR, Djordjevic BD. Effect oftemperature on the excess molar volumes of somealcohol + aromatic mixtures and modelling by cubic EOS mixingrules. Fluid Phase Equil 2006;239:69–82.