sorption and diffusion of methyl substituted benzenes through cross-linked nitrile...

Journal of Membrane Science 220 (2003) 13–30

Sorption and diffusion of methyl substituted benzenes throughcross-linked nitrile rubber/poly(ethylene co-vinyl acetate)

blend membranes

Aji Joseph, Asha Elizabeth Mathai, Sabu Thomas∗School of Chemical Sciences, Mahatma Gandhi University, Priyadarshini Hills P.O., Kottayam, Kerala 686560, India

Received 14 October 2002; accepted 3 April 2003

Abstract

The diffusion and sorption of methyl substituted benzenes through cross-linked nitrile rubber/poly(ethylene co-vinyl acetate)(NBR/EVA) blend membranes has been studied. The influence of blend composition, cross-linking systems, temperature andsize of penetrants on the transport behaviour has been analysed. It was observed that as the EVA content increases in the blends,the solvent uptake decreases. An increase in the penetrant size also decreases the solvent uptake. The diffusion experimentswere carried out in the temperature range 23–75◦C. As temperature increases the equilibrium uptake also increases. Thetransport coefficients namely diffusion coefficient, sorption coefficient and permeation coefficient have been calculated. Thesorption data has been used to estimate the activation energies for permeation and diffusion. The van’t Hoff relationshipwas used to determine the thermodynamic parameters. The affine and phantom models for chemical cross-links were used topredict the nature of cross-links. Models for permeability were used and the theoretical values compared with the experimentalresults.© 2003 Elsevier Science B.V. All rights reserved.

Keywords: Acrylonitrile butadiene rubber; Poly(ethylene co-vinyl acetate); Transport; Diffusion; Permeation

1. Introduction

The most important attraction of polymer blendsresides in the potential to tailor material propertiesfor specific applications[1,2]. The knowledge of thepermeation property of polymer blends is essential forpractical applications such as separation process, per-vaporation, controlled drug release, microelectronicsand also to investigate the morphology of the blend bythe permeation of small molecules into the structure

∗ Corresponding author. Tel.:+91-481-2730-003;fax: +91-481-561-190/800.E-mail addresses: [email protected],[email protected] (S. Thomas).

[3]. The transport behaviour in polymer blends wasfirst report by Cates and White[4–6]. The most ex-tensive study of the permeability of rubber blends wasthe early works of Barrer[7] Siddaramaiah et al.[8]have reported the sorption and diffusion of aldehydesand ketones into natural rubber blends of bromobutyl,chlorobutyl, neoprene, EPDM, polybutadiene andSBR at 25, 40 and 60◦C. Transport properties areaffected by the nature of the interaction of solventmolecule, size and also the structural variation. Thetransport of small molecules through polymer blendshas been studied extensively by our research group[9–13]. Solvent sorption effects on the structureand properties of polypropylene and thermotropicliquid crystal polymer (Rodrun) blends have been

0376-7388/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0376-7388(03)00175-3

14 A. Joseph et al. / Journal of Membrane Science 220 (2003) 13–30

investigated by Guerrica-Echevarria et al.[14]. Therate of sorption and desorption and the solvent con-tent at the equilibrium were higher in the blends thanin pure polypropylene (PP). This was attributed to mi-crocracking in the PP matrix induced by the presenceof Rodrun.

Aminabhavi and Phayde[15] have investigated themolecular transport of alkanes through thermoplas-tic blends of ethylene–propylene random co-polymerand isotactic polypropylene. For all liquids, equi-librium penetrant uptake and degree of penetrantovershoot have been influenced by factors such aspenetrant size and shape, polymer morphology andtemperature. Dilorenzo et al.[16] have reported thetransport and mechanical properties of polypropy-lene/polyamide (PA) 6 blends. The results show thatthe barrier performance of polyamide was not reducedeven at high percentages (30%) of PP in the blend.The transport characteristics of poly(styreneN-phenylmaleimide)/poly(2,6-dimethyl-1,4-phenylene oxide)blends were studied by Lokaj et al.[17]. The syn-thesis and properties of ion-selective membranesprepared from a polyelectrolyte compound and anuncharged second polymeric component has beenextensively studied by Gregor et al.[18] and Gre-gor and Wetstone[19,20]. These studies includethe blends of poly(styrene sulphonic acid) and aco-polymer of acrylonitrile and vinyl chloride. Aninvestigation of the gasoline permeation resistanceof the as-blow-moulded and annealed polyethylene,polyethylene/polyamide and polyethylene/modifiedpolyamide (MPA) bottles is reported by Yeh et al.[21]. The gasoline permeation resistance improveddramatically after blending PA and MPA barrierresins in PE matrices during blow moulding. Thebarrier mechanisms and properties of PE, PE/PA andPE/MPA bottles against paint solvent has also beenstudied [22]. GonzalezNunez et al.[23] have in-vestigated the toluene diffusivity through polyamide6/ high-density polyethylene blends with and with-out compatibilizer and found that the presence ofpolyamide 6 in the blend results in a decrease of thetoluene diffusivity. This reduction is even larger in thecase of the interfacial modified system. The perme-ability of different solvents through the blends showsthat the permeability decreases with increasing size ofthe penetrant molecules. However, till date no detailedanalysis has been made in the correlation between

morphology and transport of cross-linked polymerblends.

Blending of nitrile rubber, NBR with poly(ethyleneco-vinyl acetate) EVA gives rise to a novel class of ma-terials which combines the excellent oil resistance ofNBR and the ozone resistance and mechanical proper-ties of EVA. The morphology, mechanical properties,viscoelastic behaviour, failure mechanism and repro-cessability of nitrile rubber/poly(ethylene co-vinyl ac-etate) (NBR/EVA) blends have been reported[24,25].The diffusion and transport of aliphatic organic sol-vents through cross-linked nitrile rubber/poly(ethyleneco-vinyl acetate) blends has been reported[26]. Theuse of these blends in practical applications like perva-poration, gas separation, oil seals, gaskets, etc. makesit necessary to understand how these blends behave inthe presence of aggressive aromatic solvents. The aimof this work is to investigate the diffusion and sorptionof methyl substituted benzenes through cross-linkedNBR, cross-linked EVA and NBR/EVA blends. Thesorption behaviour of the blends has been related tothe morphology of the system. The effect of blendcomposition, cross-linking systems, temperature andsize of penetrants on the diffusion process has beeninvestigated.

2. Experimental

2.1. Materials

NBR (Aparene N553 NS) with a bound acryloni-trile content of 34% was supplied gratis by GujaratApar Polymers Ltd., Mumbai, India. EVA (Pilene1802) with vinyl acetate content of 18% was procuredfrom Polyolefins Industries Ltd., Chennai, India. Thebasic characteristics of NBR and EVA are given inTable 1. The rubber chemicals such as dicumyl per-oxide, zinc oxide, stearic acid, mercaptobenzothiazyldisulfide (MBTS) and sulfur used were of commer-cial grade. Solvents (laboratory reagent grade) usedwere toluene,p-xylene and mesitylene, which weredistilled twice before use.

2.2. Sample preparation

The mixing was done on a two-roll mixing millof friction ratio 1:1.4 and vulcanising agents were

A. Joseph et al. / Journal of Membrane Science 220 (2003) 13–30 15

Table 1Details of materials used

Materials Characteristics Source

Nitrile rubber (Aparene N553 NS) Volatile matter (%) 0.13 Gujarat Apar Polymers Ltd., MumbaiAntioxidant (%) 1.40Organic acid (%) 0.25Soap (%) 4× 10−3

Mooney viscosity (ML1+4 100◦C) 40.00Bound acrylonitrile (%) 34.00Intrinsic viscosity (dl g−1) 1.53

Poly(ethylene co-vinyl acetate)Pilene 1802

Melt flow index (g/10 min) 2.00 Polyolefins Industries Ltd., Chennai

Density (g cm−3) 0.94Vicat softening point◦C 59.00Vinyl acetate (%) 18.00Intrinsic viscosity (dl g−1) 0.17

incorporated as per ASTM procedure D15-72. Thecompounding recipes are given inTable 2. Nitrile rub-ber/ethylene vinylacetate blends were prepared by themaster batch technique[27].

The cross-linking systems used namely peroxidesystem and sulfur system are indicated using lettersP and S, respectively. Dicumyl peroxide can be usedfor cross-linking of both NBR and EVA; hence in theperoxide cured system both NBR and EVA phases arecross-linked and interwoven resulting in the forma-tion of a full interpenetrating network. But sulfur cancross-link only NBR and not EVA due to the saturatedbackbone structure of EVA. So in the sulfur-curedsystem only one phase, i.e. NBR is cross-linked andresults in the formation of a semi-interpenetrating net-work. The compounded blends are designated as N0P(pure EVA), N30P (30 NBR and 70 EVA), N50P (50NBR and 50 EVA) and so on. The subscript indicates

Table 2Compounding recipe for NBR/EVA blends

Ingredients (phr)a Peroxide system Sulphur system

Polymer 100 100Zinc oxide – 5.0Stearic acid – 1.5MBTSb – 1.5Sulphur – 1.5DCPc 4.0 –

a Parts per 100 rubber by weight.b Mercapto benzothiazyl disulphide.c Dicumyl peroxide.

the weight percentage of NBR in the blend. The lettersP and S indicate peroxide cured and sulfur-cured sys-tems, respectively. They were compression mouldedalong the mill grain direction in a hydraulic pressat 160◦C for optimum cure. Cure characteristics ofNBR/EVA blends at 160◦C are given inTable 3. Themaximum torque refers to the maximum viscosity ofthe polymer sample.

2.3. Diffusion experiments

Circular samples (diameter≈ 2 cm) were punchedout by means of a sharp edged steel die from themoulded sheets. Thickness measurements were madeat several points with an accuracy of±0.0001 cm byusing a micrometer screw gauge.

Table 3Cure characteristics of NBR/EVA blends at 160◦C (peroxide andsulphur systems)

Sample Cure time(min)

Scorch time(min)

Maximumtorque (dN m)

CRI

N0P 24 2.0 80.2 4.5N30P 20 3.0 70.1 5.8N50P 18.4 2.5 49.9 6.3N70P 17.2 2.2 35.1 6.7N100P 16.5 2.1 39.2 6.9N30S 32.0 20.0 61.9 8.3N50S 19.0 13.0 51.9 16.6N70S 19.4 11.0 38.1 11.9N100S 14.4 7.2 19.2 13.9


The cut polymer samples were weighed and sorp-tion experiments were performed by immersing themin solvents contained in test bottles with airtight stop-pers kept at constant temperature. The samples werewithdrawn periodically from the solvent; any solventadhering to the surface was rubbed off. The sampleswere weighed on a highly sensitive electronic balance(Schimadzu, Libror AEU-210, Japan) with an accu-racy of 0.001 g and immediately replaced in the testbottles. This process was continued till equilibriumwas reached. To minimise the error due to evapora-tion of solvent from sample, the time for weighingwas kept to a minimum of 30 s in all the experiments.For experiments above room temperature the sampleswere kept in a thermostatically controlled air oven.The mol uptake (Qt) for the solvent by 100 g of thepolymer was plotted against the square root of timeand the results were analysed. When equilibrium wasreachedQt was taken asQ∞, i.e. mol uptake at infinitetime:

Qt (mol)

= mass of solvent sorbed/molar mass of solvent

mass of polymer×100 (1)

3. Results and discussion

3.1. Blend composition

The results of the sorption experiments are pre-sented as the mol uptakeQt of the solvent by 100 gof the rubber as a function of square root of time. Theeffect of blend composition on the sorption behaviourof peroxide cross-linked blends in the solvent tolueneis shown inFig. 1. It is observed that pure NBR hasmaximum equilibrium uptake and pure EVA has thelowest equilibrium uptake. There is a decrease in equi-librium uptake with an increase in EVA content. Thiscan be related to the morphology of the system. Thescanning electron micrographs of NBR/EVA blendsare given inFig. 2.

In N30 (30 NBR and 70 EVA) and N70 (70 NBRand 30 EVA) the major component tends to be thecontinuous phase. The N50 (50 NBR and 50 EVA)exhibits a co-continuous morphology. In the case ofcross-linked samples the extraction of the rubber phase

was not possible; therefore SEM analysis of the mor-phology of the system is difficult. The morphologyof the cross-linked system is speculated based on themorphology of uncross-linked system and is given inFig. 3. When N30 (Fig. 3a) is cross-linked a parti-cle size reduction is expected for the dispersed NBRphase. In N50 (Fig. 3b) when sulfur is the curing agent,only NBR is cross-linked and results in the formationof a semi-interpenetrating network. For the peroxidecured systems both phases are cross-linked resultingin the formation of a full interpenetrating network. InN70 (Fig. 3c) a particle size reduction is also expectedfor the dispersed phase. The sorption behaviour ofN70P where NBR is the continuous phase is similar tothat of NBR (N100P). Again the sorption of EVA richblend (N30P) is similar to that of pure EVA (N0P).The N50P where both phases are continuous exhibitsan intermediate sorption between those of the purecomponents. This clearly indicates that we can studythe phase continuity from transport studies. But N30P(30 NBR and 70 EVA) has higher uptake than N50P(50 NBR and 50 EVA). This can be explained on thebasis of cross-link density. The cross-link densities ofthe samples were calculated using the equation:

γ = 1

2Mc(2)

whereγ is the cross-link density andMc is the molec-ular mass between cross-links.

The molecular mass between cross-links has beenestimated from the equation[28]:

Mc = − ρpVsφ1/3

ln(1 − φ) + φ + χφ2(3)

where ρp is the density of polymer,Vs the molarvolume of solvent,φ the volume fraction of swollenrubber andχ is the polymer–penetrant interactionparameter.

χ is calculated from the equation[29]:

χ = β + Vs

RT(δs − δp)

2 (4)

whereβ is the lattice constant which had been assigneda value of 0.34 in the older literature, but since a valueof ‘0’ gives better correlation with other quantities thevalue ofβ is taken as 0[30], Vs the molar volume ofsolvent,R the universal gas content,T the temperaturein Kelvin, δs the solubility parameter of solvent andδp is the solubility parameter of polymer.


Fig. 1. Sorption curves of peroxide cured NBR/EVA blends in toluene at 23◦C.

The volume fraction of rubberφ in the solventswollen sample was calculated using the equation[31]:

φ = W1/ρ1

(W1/ρ1) + (W2/ρ2)(5)

whereW1 is the weight of rubber sample,ρ1 the den-sity of rubber,W2 the weight of solvent in the swollensample andρ2 is the density of solvent.

The calculated cross-link density (γ) and volumefraction of rubber (φ) in swollen blends is given inTable 4. The higher equilibrium uptake of N30P than

N50P is due to its lower cross-link density. A highvalue of φ is an indication of high cross-link den-sity. The φ value also supports the higher equilib-rium uptake of N30P. In the sulphur cured systemalso as the EVA content increases the equilibrium up-take decreases (Fig. 4). This is because EVA is crys-talline and crystalline areas offer more resistance tothe solvent uptake. As EVA content increases crys-tallinity increases and equilibrium uptake decreases.The cross-link density values also support the equilib-rium uptake.


Fig. 2. Scanning electron micrographs showing the morphologyof (a) N30 (b) N50 and (c) N70 samples.

Table 4Cross-link density (γ) and volume fraction of rubber (φ) in swollenmass of NBR/EVA blends in toluene at 23◦C

Samples φ γ (g mol cm−3) (×104)

N100P 0.34 4.10N70P 0.47 9.50N50P 0.56 14.60N30P 0.51 12.20N0P 0.62 20.40N100S 0.29 2.80N70S 0.35 4.80N50S 0.51 10.10N30S 0.59 17.40

3.2. Cross-linking systems

The two cross-linking systems used in this inves-tigation are sulphur and peroxide systems. The sorp-tion curves expressed as mol uptakeQt of the solventby 100 g of polymer versus square root of time wereplotted.Fig. 5 shows the mol uptake of N100 samples(sulphur cured and peroxide cured) in toluene.

It is evident that the mol uptake is more for thesulphur-cured system than for the peroxide curedsystem. This is because of the different types ofcross-links formed. In the case of sulphur system,the polysulfidic linkages are present which are longand flexible and imparts high chain mobility. So thesolvent molecules can penetrate through the poly-mer matrix easily and the solvent uptake is more.In the peroxide cured system rigid C–C linkages arepresent, which hinders the movement of chains andpenetration of solvent molecules through the polymermatrix becomes difficult; hence there is lesser sol-vent uptake. The equilibrium uptake values (Q∞) aregiven in Table 5. The lower cross-link density of the

Table 5Equilibrium uptake (Q∞) of NBR/EVA blends in solvents toluene,p-xylene and mesitylene at 23◦C

Samples Toluene p-Xylene Mesitylene

N100S 2.38 1.60 0.98N100P 1.80 1.28 0.82N70S 1.98 1.28 0.76N70P 1.07 0.76 0.53N50S 0.99 0.65 0.46N50P 0.77 0.55 0.43N30S 0.48 0.34 0.30N30P 0.95 0.62 0.54


Fig. 3. Schematic model for the morphology of cross-linked NBR/EVA blends.

sulphur cured system compared to the peroxide curedsystem (Table 4) also supports the higher equilibriumuptake of the sulphur cured system. The higherQ∞value for N30P sample than N30S sample is due tolower cross-link density of N30P sample.

3.3. Effect of penetrant size

There is a systematic trend in the sorption behaviourof liquids of different molecular size. With an increase

in the size of solvent molecules there is a decrease inthe value ofQt in all the systems (Fig. 6).

Among the solvents used in this work, mesity-lene shows the lowest uptake, while toluene showsthe maximum uptake andp-xylene occupies inter-mediate position. The decrease inQt uptake withincrease in penetrant size can be explained by con-sidering the interaction parameterχ between thesolvent and polymer. Theχ values calculated usingEq. (4) for solvents toluene,p-xylene and mesitylene


Fig. 4. Sorption curves of sulphur cured NBR/EVA blends inp-xylene at 23◦C.

are 0.0424, 0.0701 and 0.0804, respectively. The in-creasingχ values support the observed trend inQt

values.

3.4. Mechanism of transport

The results of the sorption experiments were anal-ysed by using the empirical relation[32,33]:

logQt

Q∞= logk + n log t (6)

whereQt is the mol sorption at timet andQ∞ is themol sorption at equilibrium. The value ofk dependson the structural features of polymer in addition to itsinteraction with the solvent. The value ofn indicatesthe mechanism of sorption. Ifn = 0.5 the mechanismof sorption is termed Fickian and this occurs whenthe rate of diffusion of permeant molecules is muchless than the polymer segment mobility. Ifn = 1 themechanism of sorption is termed as case II. This ariseswhen the rate of diffusion of permeant molecules ismuch greater than polymer segmental mobility. Ifn


Fig. 5. Sorption curves of sulphur cured and peroxide cured NBR in toluene at 23◦C.

lies between 1 and 0.5 then the mechanism of dif-fusion follows an anomalous trend. Then the perme-ant mobility and polymer segment relaxation rates aresimilar.

By regression analysis the values ofn and k areobtained as slope and intercept, respectively. It is ob-served that the value ofn ranges from 0.41 to 0.66.This suggests an anomalous mode of diffusion. Herethe polymer relaxation and rate of diffusion are com-parable. No systematic trend is observed for the valuesof k.

From the swelling data the diffusion coefficientDwas calculated using the equation[34,35]:

D = π

(hθ

4Q∞

)2

(7)

whereD is the diffusion coefficient,θ the slope of thesorption curve before attainment of 50% equilibriumand h is the initial thickness of the polymer sample.Diffusivity is a kinetic parameter, which depends onthe polymer segmental mobility. The estimated valuesof the diffusion coefficient are given inTable 6.


Fig. 6. Sorption curves of peroxide cured N50 samples in toluene,p-xylene and mesitylene at 23◦C.

In all the systems as the size of the penetrantmolecule increases, the diffusion coefficient de-creases. According to the free volume theory[36] forthe diffusion process in polymers, the diffusion rate ofa molecule depends primarily on the ease with whichpolymer chain segments exchange their position withpenetrant molecules. In addition to that the mobilityof the polymer depends on the amount of free volumein the matrix. As penetrant size increases, the ease ofexchange becomes less, leading to a decrease in thevalue of diffusion coefficient.

The permeation of a penetrant into a polymerdepends on the diffusivity as well as the solubilityor sorptivity of the penetrant. Hence the sorptioncoefficientS which is the maximum saturation sorp-tion value has been calculated using the equation[35,37]:

S = M∞M0

(8)

whereM∞ is the mass of solvent taken up at equilib-rium andM0 is the initial mass of polymer sample.


Table 6S, D and P values of NBR/EVA blends in different solvents at23◦C

System Solvent S D (cm2 s−1)(×107)

P (cm2 s−1)(×107)

N100S Toluene 2.19 4.79 10.49p-Xylene 1.70 2.87 4.88Mesitylene 1.18 1.43 1.70




The estimated sorption coefficient values are given inTable 6.

Out of N100S, N70S, N50S and N30S it is observedthat theS value is maximum for the N100S system.This indicates that the solvent molecules are best ac-commodated in the N100S system. This is because ofthe amorphous nature of the pure rubber sample. Theblends have varying proportion of EVA, which is crys-talline and offers resistance to the solvent uptake. Asthe size of the penetrant molecules increases theSvalue decreases as it is more difficult to accommodatelarger molecules in the polymer matrix.

The permeability coefficientP can be com-puted from the following mathematical expression[34,35]:

P = DS (9)

whereP is the permeability coefficient,D the diffu-sion coefficient andS is the sorption coefficient. Thecalculated permeability coefficient values are given inTable 6.

It is evident that the permeability coefficient valuedecreases with increase in EVA content in the blends.The presence of EVA hinders the movement of solventmolecules between the polymer chains. So a lowervalue forD as EVA content increases. TheS value alsoshows the same trend. Since the permeability coeffi-cient is the net effect ofD andS theP value decreaseswith increase in EVA content in the blends.

3.5. Effect of temperature

Sorption experiments were done at three differenttemperatures 23, 60 and 75◦C. Fig. 7 illustrates thesorption curves of peroxide cured N50 samples inp-xylene at different temperatures. The equilibriumuptake increases with increase in temperature. Thisbehaviour is attributed to the increase in free vol-ume and greater segmental mobility at higher tempe-rature.

The computed values of the diffusion coefficientD and permeability coefficientP at temperatures 23,60 and 75◦C are compiled inTable 7. The generaltrend is an increase in the value ofD andP with anincrease in temperature. This can be expected as athigher temperature the chains are more flexible andthe process of diffusion becomes much easier and soP also increases with an increase in temperature.

Table 7D and P values of NBR/EVA blends inp-xylene at 23, 60 and75◦C

System Temperature(◦C)

D (cm2 s−1)(×107)

P (cm2 s−1)(×107)

N100S 23 2.87 4.8960 5.33 8.6175 7.46 11.90

N70S 23 3.65 5.0060 9.05 11.9075 9.85 11.90

N50S 23 1.38 0.9560 3.77 3.3175 5.42 6.28

N30S 23 1.06 0.3860 5.06 2.9275 6.28 5.08

N100P 23 2.63 3.6560 4.74 6.0775 7.01 8.80

N70P 23 1.42 1.1460 3.62 3.4175 3.95 4.21

N50P 23 1.38 0.8260 3.47 2.9175 3.50 4.78

N30P 23 1.80 1.1960 3.07 4.3175 3.34 6.10


Fig. 7. Effect of temperature on the sorption curves of peroxide cured N50 samples inp-xylene.

From a consideration of the temperature variation oftransport coefficients (P, D andS), we have estimatedthe energy of activation for the diffusion and perme-ation process from the Arrhenius relationship[11]:

X = X0 exp−EX/RT (10)

whereX is P, D or S andX0 denotesP0, D0 or S0 whichis a constant. Arrhenius plots of logD or logP versusI/T were constructed (Fig. 8) and from the slopes ofthe curves, the values of the activation energy for dif-fusion, ED and the activation energy for permeation,

EP are estimated by linear regression analysis. Fromthe difference betweenEP and ED the heat of sorp-tion, �HS was estimated. The values ofEP, ED and�HS are complied inTable 8. TheEP andED valuesare found to increase with an increase in the EVA con-tent. As the EVA content increases the chains becomemore rigid as EVA is more crystalline. Hence activa-tion energy increases with increase in EVA content inthe blends.

The heat of sorption,�HS, is a composite param-eter involving both Henry’s law and Langmuir type


Fig. 8. Arrhenius plot of sulphur cured NBR/EVA blends.

sorption. The negative values suggest that the Lang-muir type sorption mechanism predominate in whichthe solvent molecules fill the holes already existingwithin the polymer matrix. It gives rise to an exother-mic process. The positive values suggest Henry’s typesorption mechanism in which the molecules have to

Table 8Activation parameters of diffusion (ED), permeation (EP) and heatof sorption (�HS) for NBR/EVA blends inp-xylene

System ED (kJ mol−1) EP (kJ mol−1) �HS (kJ mol−1)

N100S 15.28 14.17 −1.10N70S 15.82 15.38 −0.44N50S 22.47 30.3 7.84N30S 30.50 43.03 12.53

make room for themselves in the polymer matrix. It isan endothermic process.

The molar equilibrium sorption coefficientKS isdefined as[38]:

KS = number of moles of solvent sorbed at equilibrium

mass of polymer(11)

From the values ofKS at temperatures 23, 60 and75◦C, the heat of sorption (�HS) and entropy of sorp-tion (�S) were calculated using the van’t Hoff relation[34]:

logKS = �S

2.303R− �HS

2.303RT(12)


Table 9van’t Hoff parameters, enthalpy (�HS) and entropy (�S) of sorp-tion in p-xylene

System �HS (kJ mol−1) �S (J mol−1 K−1)

N100S −1.12 −38.13N70S −0.43 −37.68N50S 7.80 −15.70N30S 12.58 −4.89

A plot of logKS versusI/T was plotted for the vari-ous blends and the computed values of�HS and�Sare given inTable 9. The value of�S ranges from−38.13 to−4.89 J mol−1 and is negative in all thecases. This suggests that there is retainment of liq-uid structure in the sorbed state within the polymermatrix. It is interesting to note that the�HS valuesare in close agreement with those calculated from thedifferenceEP − ED. It again supports the fact thatmolecular transport of aromatic hydrocarbons throughcross-linked NBR/EVA blends is a net effect of sorp-tion and diffusion processes.

3.6. Theoretical modelling

In the case of heterogeneous blends, the permeabil-ity can be interpreted in terms of various theoreticalmodels. Robeson’s two limiting models (i.e. series andparallel models) are generally used in the case of poly-mer blends.

According to the parallel model:

Pc = P1φ1 + P2φ2 (13)

and by the series model:

Pc = P1P2

φ1P2 + φ2P1(14)

wherePc is the permeation coefficient of blend,P1the permeation coefficient of component I,P2 the per-meation coefficient of component II,φ1 the volumefraction of component I andφ2 is the volume fractionof component II.

Further, for conducting spherical filler, the over-all composite permeation coefficient is given byMaxwell’s equation as[39,40]:

Pc = Pm

[Pd + 2Pm − 2φd(Pm − Pd)

Pd + 2Pm + φd(Pm − Pd)

](15)

where the subscripts d and m correspond to dispersedphase and the matrix, respectively.

Robeson[40] extended Maxwell’s analysis to in-clude the continuous and discontinuous characteristicsof both phases at intermediate compositions and ex-pressed the equation:

Pc = xaP1

[P2 + 2P1 − 2φ2(P1 − P2)

P2 + 2P1 + φ2(P1 − P2)

]

+ xbP2

[P1 + 2P2 − 2φ1(P2 − P1)

P1 + 2P2 + φ1(P2 − P1)

](16)

where xa and xb are the fractional contributions tocontinuous phase so thatxa + xb = 1.

Fig. 9shows the variation of permeation coefficientwith volume fraction of NBR. The experimental valuesare close to the Robeson Model up toφNBR = 0.3 andbeyond that it is close to the series model.

3.7. Network analysis

The investigation of swelling equilibrium can helpto elucidate the structure of the polymer network.Flory [41] developed the affine model for a networkdeforming affinely where the components of eachchain vector transform linearly with macroscopic de-formation and the junction points are assumed to beembedded in the network without fluctuations. Thenthe molecular weight between cross-links (Mc) forthe affine limit of the model [Mc(aff)] was calculatedby the formula[41,42]:

Mc(aff) = ρVsγ2/32c γ

1/32m (1 − (µγ

1/32m /γ))

−(ln(1 − γ2m) + γ2m + χγ22m)

(17)

whereVs is the molar volume of the solvent,µ andγ are called the number of effective chains and junc-tions, γ2m the polymer volume fraction at swellingequilibrium,γ2c the polymer volume fraction duringcross-linking andρ is the polymer density.

The phantom network model was proposed byJames and Guth[43], where the chains may movefreely through one another. The junction points fluc-tuate over time around their mean positions withoutbeing hindered by the presence of the neighbour-ing chains and are independent of deformation. Themolecular weight between cross-links for the phan-tom limit of the model [Mc(ph)] was calculated


Fig. 9. Theoretical modelling for the permeation coefficient of NBR/EVA blends.

by [42,44]:

Mc(ph) = (1 − (2/φ))ρVsγ2/32c γ

1/32m

−(ln(1 − γ2m) + γ2m + χγ22m)

(18)

whereφ is the junction functionality.

Table 10Comparison ofMc values

System Mc(chem)(g mol−1)

Mc(aff)(g mol−1)

Mc(ph)(g mol−1)

N100P 1218 1187 594N70P 525 512 256N50P 343 334 167N30P 411 400 200N0P 244 238 119

Mc(aff) andMc(ph) were compared withMc(chem)and the values are given inTable 10. It is observedthatMc(chem) values are close toMc(aff) values. Thissuggests that in the highly swollen state, the chainsin the blends and in the component polymers deformaffinely, i.e. the chains in the network are freely mov-ing without fluctuating the junction points.

4. Conclusion

The variations in blend composition, cross-linkingsystems, temperature and size of penetrants on the dif-fusion process through NBR/EVA has been analysed.It was seen that as the EVA content increases in theblends the solvent uptake decreases. This has been


attributed to the crystalline nature of EVA. Also an in-crease in the penetrant size decreases the solvent up-take, as larger solvent molecules find it difficult to beaccommodated in the polymer matrix.

The variations in the equilibrium uptake values areexplained on the basis of blend morphology, volumefraction of polymer in the swollen mass, cross-linkdensity and crystallinity. The value ofn shows a slightdeviation from Fickian behaviour and the mechanismis anomalous. The effect of different cross-linking sys-tems on the sorption was also investigated. The per-oxide cured system has lower solvent uptake than thesulphur cured system as the peroxide cured sampleshave rigid C–C bonds and higher cross-link densitywhile the sulphur cured samples have more flexibleand long S–S bonds and lower cross-link density.

The effect of temperature was studied by carryingout the sorption experiments at 23, 60 and 75◦C. Astemperature increases the equilibrium uptake also in-creases. This is because of the greater chain mobilityat higher temperatures. It is found that temperatureactivates the diffusion process. The activation ener-gies for the process of diffusion,ED and permeation,EP were estimated. The thermodynamic parameters,heat of sorption (�HS) and heat of entropy (�S) weredetermined using van’t Hoff relationship. Theoreti-cal models like parallel, series, Maxwell and Robesonwere used to fit the experimental data. The affine andphantom models for chemical cross-links were usedto predict the nature of cross-links. The experimentalvalues are close to the affine model. This indicates thatthe chains in the network are freely moving withoutfluctuating the junction points. These results are use-ful for the design of high performance membranes.

Nomenclature

CRI cure rate index (min−1)D diffusion coefficient (cm2 s−1)ED activation energy for diffusion

(kJ mol−1)Ep activation energy for permeation

(kJ mol−1)h initial thickness of the polymer

membrane (cm)�HS enthalpy of sorption (kJ mol−1)M mass (g)

Mc molecular weight between cross-links(g mol−1)

M0 mass of polymer sample (g)M∞ mass of solvent taken up at

equilibrium (g)P permeability coefficient (cm2 s−1)Qt moles of solvent sorbed by 100 g

of polymer at timetQ∞ moles of solvent sorbed by 100 g

of polymer at equilibriumR universal gas constant (J K−1 mol−1)S sorption coefficient�S entropy of sorption (J mol K−1)T absolute temperature (K)V molar volume (cm3 mol−1)W weight (g)

Greek lettersβ lattice constantδ solubility parameter (J cm−3)1/2

µ number of effective chainsν number of effective junctionsν2c polymer volume fraction during

cross-linkingν2m polymer volume fraction at swelling

equilibriumθ slope of the initial linear portion of the

sorption curveρ density (g cm−3)φ volume fraction of polymer in the

solvent swollen sampleχ polymer–solvent interaction parameter

Subscriptsp polymer (membrane)s solvent

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sorption and diffusion of methyl substituted benzenes through cross-linked nitrile...

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