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Mechanical behaviour of a plasticized PVC subjected to ethanol exposure Q. Yu, A.P.S. Selvadurai * Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, QC, Canada H3A 2K6 Received 28 October 2004; received in revised form 29 December 2004; accepted 11 January 2005 Available online 3 March 2005 Abstract This paper presents the results of a series of experimental investigations conducted to assess the influence of ethanol exposure at different concentrations on the mechanical properties of a plasticized PVC membrane. Exposure to pure ethanol resulted in a reduction in flexibility, or embrittlement, and the transformation of the PVC membrane from a flexible material capable of undergoing large strain hyperelastic behaviour to a stiffer material with pronounced yield behaviour. Results of X-ray fluorescence measurements indicate the loss of the plasticizer from the PVC membrane as a contributing factor for the alteration in the mechanical properties of the PVC membrane. The experiments also indicate a slower rate of plasticizer leaching during exposure to lower concentrations of ethanol. Exposure of the PVC membranes to 80% and 50% concentrations of ethanol and pure water has a reduced influence on the loss of large strain deformability of the PVC membrane, even after more than one year of exposure. The PVC membranes exposed to a mixture of ethanol and pure water in equal volume proportions indicate that, after longer period, the PVC membranes became softer and exhibit greater deformation under the same external load. This phenomenon can be attributed to the swelling of the PVC membrane. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Plasticized PVC; Uniaxial testing; Chemical exposure; Strain-rate effects; Embrittlement; Geosynthetic liners 1. Introduction Plasticized PVC is used extensively in geo-environ- mental applications, particularly as engineered barrier systems for landfills and for containment of other forms of hazardous and toxic wastes [1]. The plasticized PVC membrane constitutes an important component in a multi-barrier containment system that includes alter- nate layers of impermeable clay and serves as the collector system [1,2]. While the clay layers are intended to provide the main barrier against contaminant migra- tion, on occasions, particularly those involving thermal desiccation of the clay liners, the effluents from the retained waste can come into direct contact with the PVC membrane. The possibility of direct contact of the PVC membrane with waste leachate is therefore of major concern for the engineering usage of such PVC membrane barriers. In adverse environmental condi- tions in a landfill, the exposure of the PVC membrane to chemicals can lead to leaching of the plasticizer from the PVC membrane [3]. The evidence of leaching of the plasticizer from plasticized PVCs is also documented in other literatures [4e6]. The plasticizer contributes to a significant increase in the flexibility of an otherwise brittle PVC polymer [7e9]. The work of Pita et al. [10] shows that a monotonically increasing relationship exists between the stress and strain for plasticized PVC with high plasticizer content. When the plasticizer content is lowered, a clear yield-type stressestrain behaviour is observed (Fig. 1). The addition of plasti- cizers also lowers the glass transition temperature (T g ) of * Corresponding author. William Scott Professor. Tel.: C1 514 398 6672; fax: C1 514 398 7361. E-mail address: [email protected] (A.P.S. Selvadurai). 0141-3910/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymdegradstab.2005.01.007 Polymer Degradation and Stability 89 (2005) 109e124 www.elsevier.com/locate/polydegstab

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Polymer Degradation and Stability 89 (2005) 109e124

www.elsevier.com/locate/polydegstab

Mechanical behaviour of a plasticized PVCsubjected to ethanol exposure

Q. Yu, A.P.S. Selvadurai*

Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, QC, Canada H3A 2K6

Received 28 October 2004; received in revised form 29 December 2004; accepted 11 January 2005

Available online 3 March 2005

Abstract

This paper presents the results of a series of experimental investigations conducted to assess the influence of ethanol exposure atdifferent concentrations on the mechanical properties of a plasticized PVC membrane. Exposure to pure ethanol resulted ina reduction in flexibility, or embrittlement, and the transformation of the PVC membrane from a flexible material capable of

undergoing large strain hyperelastic behaviour to a stiffer material with pronounced yield behaviour. Results of X-ray fluorescencemeasurements indicate the loss of the plasticizer from the PVC membrane as a contributing factor for the alteration in themechanical properties of the PVC membrane. The experiments also indicate a slower rate of plasticizer leaching during exposure to

lower concentrations of ethanol. Exposure of the PVC membranes to 80% and 50% concentrations of ethanol and pure water hasa reduced influence on the loss of large strain deformability of the PVC membrane, even after more than one year of exposure. ThePVC membranes exposed to a mixture of ethanol and pure water in equal volume proportions indicate that, after longer period, the

PVC membranes became softer and exhibit greater deformation under the same external load. This phenomenon can be attributedto the swelling of the PVC membrane.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Plasticized PVC; Uniaxial testing; Chemical exposure; Strain-rate effects; Embrittlement; Geosynthetic liners

1. Introduction

Plasticized PVC is used extensively in geo-environ-mental applications, particularly as engineered barriersystems for landfills and for containment of other formsof hazardous and toxic wastes [1]. The plasticized PVCmembrane constitutes an important component ina multi-barrier containment system that includes alter-nate layers of impermeable clay and serves as thecollector system [1,2]. While the clay layers are intendedto provide the main barrier against contaminant migra-tion, on occasions, particularly those involving thermaldesiccation of the clay liners, the effluents from the

* Corresponding author. William Scott Professor. Tel.: C1 514 398

6672; fax: C1 514 398 7361.

E-mail address: [email protected] (A.P.S. Selvadurai).

0141-3910/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.polymdegradstab.2005.01.007

retained waste can come into direct contact with thePVC membrane. The possibility of direct contact of thePVC membrane with waste leachate is therefore ofmajor concern for the engineering usage of such PVCmembrane barriers. In adverse environmental condi-tions in a landfill, the exposure of the PVC membrane tochemicals can lead to leaching of the plasticizer from thePVC membrane [3]. The evidence of leaching of theplasticizer from plasticized PVCs is also documented inother literatures [4e6]. The plasticizer contributes toa significant increase in the flexibility of an otherwisebrittle PVC polymer [7e9]. The work of Pita et al. [10]shows that a monotonically increasing relationshipexists between the stress and strain for plasticized PVCwith high plasticizer content. When the plasticizercontent is lowered, a clear yield-type stressestrainbehaviour is observed (Fig. 1). The addition of plasti-cizers also lowers the glass transition temperature (Tg) of

110 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

Fig. 1. Stressestrain curve of plasticized PVC with different amounts of DOP plasticizer (in phr) [10].

a rigid PVC polymer, making it more flexible [8,11,12].The mechanism of the action of a plasticizer in PVC is,however, quite complex [7e9]. Results of spectroscopicexaminations presented by Dubault et al. [12] show thatthe lowering of the glass transition temperature can beattributed to the interaction between the plasticizer andthe backbone of the PVC chain. These authors alsoconclude that changes to the mechanical behaviour(including plastic and yielding behaviour at varioustemperatures), due to the presence of plasticizer, can beattributed to such interactions.

While additives, such as plasticizers, are favored forthe modification of the mechanical properties of a PVC,issues related to the durability of a plasticized PVC canarise from either the loss of additives such as plasticizerfrom the polymer matrix, or the alteration in chemicalcomposition of the additives or, more adversely, due tothe scission of the polymeric chain from within thepolymer structure. Polymeric chain scission representsthe chemical alteration of the polymer molecule back-bone, which directly affects its integrity and subsequentlycontributes to the failure of the material. Polymer chainscission can materialize more prominently under low-level radiation. The loss of plasticizers is believed to bethe dominant process contributing to the aging ofplasticized PVC [13,14]. In some cases, while the loss ofadditives such as the plasticizer may alter the propertiesof the material, it does not change the integrity of thepolymer structure. Plasticizer loss can either take theform of extraction during contact with chemicallyincompatible media, or migration or volatilization[15e18]. Migration refers to the situation where theplasticizer transfers from one polymer to another(usually an unplasticized one) during contact [17].Volatilization occurs when the plasticizer is releasedinto surrounding gas usually at high temperatures[13,14,16]. In contrast to the volatilization process athigh temperature, the loss of plasticizers in a liquid at

low temperature is considered to be an extractionprocess [4e6,19]. The extraction of plasticizers froma solid takes place through diffusion [13]. The diffusionprocess is related to the type of surrounding media, thenature and concentration of the plasticizer, molecularweight of the polymer, the plasticization process andtemperature [20]. The diffusive nature of the transport ofthe plasticizer from within a plasticized PVC createsa non-uniform distribution of its concentration acrossthe thickness of the PVC membrane, with the highestconcentration at the center [21,22]. Loss of plasticizercan also be induced by other processes such as biologicalaction [15,23,24], thermal degradation [13] and weath-ering [25]. Chemical alteration of a plasticizer can alsooccur when a proper chemical reaction is enhancedunder UV dosage [26]. In connection with the use ofplasticized PVC membranes as landfill liners, theadverse environments can include exposure to heat,ultra-violet light, bacteria and chemicals [27]. Thelongevity of the containment provided by a PVC mem-brane can thus be influenced by any of these actions.Previous investigations have recognized the importanceof the loss of additives in determining the longevity andserviceability of the PVC membrane barrier [28]. Thealterations manifest in the form of the loss of physicalproperties of the PVC membrane including its totalweight and thickness, and an alteration in the mechan-ical properties such as an increase in elastic modulus, anincrease in tensile strength and the loss of flexibilitywhich results in a reduction in the strain to failure.

In this paper the performance of a plasticized PVCmembrane as a landfill liner subjected to chemicalexposure will be discussed. While the range and com-plexity of the contaminants in a waste disposal endeav-our can be diverse, this research is directed to theexamination of the behaviour of the PVC membranewhen exposed to commonplace contaminants such asethanol and acetone. Previous preliminary experimental

111Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

investigations conducted by Haedrich [29] and Con-tamin and Debeauvais [30] point to a significant loss ofelasticity of the PVC membrane during exposure toacetone and ethanol, respectively. The research reportedin this paper is an effort to examine the influence of theexposure of a PVC membrane to concentrations ofethanol, in terms of alteration in the mechanicalresponse of the material. The volumetric concentrationswere 100%, 80%, 50% and 0% of ethanol in a watereethanol mixture. The focus of the experimental inves-tigations was to assess the effects of exposure on the lossof flexibility of the PVC membrane and to correlate suchfindings with the loss of plasticizer from the PVCmembrane.

2. Experimental investigations

2.1. Materials and sample preparation

The PVC membrane tested (Solmax 220, manufac-tured by Canadian General Tower, Inc., ON, Canada)was supplied from Groupe Solmax Inc., QC, Canada.The PVC membrane has a nominal thickness of 0.5 mmand contains PVC resin (50e70% weight content) asa major component along with several types ofadditives, such as plasticizer, lubricant, pigment andfillers to alter its mechanical behaviour [31]. Thechemical composition of a typical PVC polymer is(CH2CHCl)n. The plasticizer comprises the major partof the additives, and amounts between 25 and 35% ofthe total weight. The PVC membrane samples subjected

to chemical exposure were cut from a larger sheetmeasuring 250 mm!180 mm [Fig. 2(aeb)].

2.2. Chemical exposure facility

In the current experimental program, the samplesof the PVC membrane were subjected to ethanolexposure at various concentrations through immersion[Fig. 3(a)]. The samples of the PVC membrane mea-suring 250 mm!180 mm were separated by layers ofa highly permeable and inert polypropylene geotextile,and placed in a stainless container. The stack of PVCmembranes was then dosed with appropriate chemicalconcentrations. The stainless container was then coveredby a stainless cover. To further reduce the possibleleakage of the ethanol, a thin strip of silicone glue wasused between the cover and the container. When a stackof PVC membranes that were separated by geotextilelayers was immersed in a watereethanol mixture, thegeotextile layer allowed the mixture to come into contactwith both faces of the PVC membrane. In view of thehighly volatile nature of ethanol, the entire exposurefacility was stored in a ventilated chamber that wasmaintained at a relatively constant room temperature.In the exposure facility the samples were kept un-disturbed except during situations where the PVCmembranes had to be removed manually, which inducedsome mixing of the watereethanol mixture inside thecontainer. There is a likelihood that such disturbancescan also alter the contact condition between the watereethanol mixture and the PVC membrane during animmersion sequence; such effects are, however, not

25.4mm

l0 = 50.0mm

200mm 200mm

180mm

18 0 mm

(a) Cut across the machine direction (b) Cut along the machine direction

(c) Samples prepared for tensile testing

Unused Unused

Fig. 2. PVC membrane prepared for the immersion test and the tensile test.

112 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

considered significant from the point of view of theexperiment. It has also been noted that direct contactbetween the solid polypropylene geotextile and PVCmembrane can induce plasticizer migration between twomedia [17]. The quantitative analysis of such migrationprocesses is rare due to the absence of the definition ofcontact conditions between two materials. In the currentexperimentation, it was assumed that the contact areabetween the PVC membranes and highly porous geo-textile was small (with an area ratio corresponding tothe porosity of the geotextile) and that entire surfaces ofthe PVC membrane were therefore subjected to expo-sure to the watereethanol mixture, enabling freediffusion of the plasticizer from the PVC membrane.Furthermore, the chemical interactions between thewatereethanol mixture and the polypropylene wereconsidered not to be important to the examination ofthe interaction between the PVC membrane and theethanol.

The process governing the migration of the plasticizerfrom a PVC membrane subjected to ethanol exposurewas considered to be diffusive. The process involvesboth ethanol migration into the PVC membrane andmigration of plasticizer from the PVC membrane [32e36]. Once a chemical comes into contact with the surfaceof a PVC membrane, the transport of the chemical tothe interior of the PVC membrane will take placethrough a concentration-gradient-dependent transportprocess. The classical diffusion process was identified by

PP geotextile

PVC membrane

Water-ethanol mixture

Stainless cover

A thin layer of silicone glue

(a) Immersion tank

C(−H / 2,t)=C0

C(−H / 2,t)=C0

PVC membrane

H

(b) Boundary conditions during immersion

Fig. 3. Immersion test for PVC membranes subjected to chemical

exposure.

Fick [37] and the equations governing chemical diffusionwithin the medium can be obtained through consider-ation of mass transport [38]. In view of the large lateraldimensions of the chemical dosage area in comparisonto the thickness of the PVC membrane, the chemicaldiffusion within the membrane can be modelled asa one-dimensional process [Fig. 3(b)]. The one-dimen-sional diffusion of the chemical through the thickness ofa membrane is obtained from the solution of thegoverning partial differential equation

Dv2C

vz2Z

vC

vt; tR0; z˛

h�H=2;H=2

ið1Þ

subject to the initial condition

Cðz;0ÞZ0; z˛½ �H=2;H=2� ð2Þ

and the boundary conditions

CðH=2; tÞZC0; Cð �H=2; tÞZC0; tR0 ð3Þ

where H is the thickness of the PVC membrane. In Eq.(1), Cðz; tÞ is the through-thickness chemical concentra-tion; z is the spatial coordinate; D is a diffusioncoefficient and t is time. The linearized form of thediffusion Eq. (1) is simplification of a much morecomplicated non-linear process where the diffusioncoefficient can be altered during the chemical migrationprocess. A further assumption is that the chemical influxis directly related to the loss of plasticizer from the PVCmembrane. In practice, when a PVC membrane is usedin a waste isolation endeavour, chemical migration tothe membrane will take place only through one of itssurfaces. In relation to the experimental research thatwill be conducted, however, it is assumed that theimmersed PVC membrane will allow chemical migrationto take place from both lateral surfaces as described bythe boundary condition (Eq. (3)). The solution to theinitial boundary value problem is elementary [38,39] andthe through-thickness chemical concentration in themembrane is given by

C

C0

Z1� 4

p

XNnZ0

ð � 1Þn

ð2nC1Þ exp��ð2nC1Þ2p2Dt

H2

!coshð2nC1Þp z

H

ið4Þ

The objective of a diffusion analysis is mainly toascertain the time required for chemical diffusion to takeplace over a significant portion of the 0.5 mm thick PVCmembrane. Theoretically, the elementary diffusion pro-cess requires an infinite time for the chemical tocompletely occupy the membrane. In contrast, onlya finite time is required to saturate roughly 90%e95%of the thickness of the membrane. For example, the

113Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

time required to achieve 90% saturation of the chemi-cal concentration at the central plane of the membraneis

t90%ZH 2

4Dð5Þ

The critical parameter needed for the estimation ofmigration time is the diffusion parameter D. Messadiand Vergnaud [22] conducted tests to determine thediffusion parameters for both pure ethanol and an 80%concentration of ethanol in an ethanolewater mixture.Their results indicated that a plasticized PVC with 38%weight content of DOP plasticizer had a diffusioncoefficient DZ1:0!10�8 cm2=s for pure ethanol at30 �C. Considering Eqs. (4), (5) and this value of D,the time required to dose in excess of 90% of the centralplane of a 0.5 mm-thick PVC membrane will be

t90%ZH2

4DZ

ð0:05 cmÞ2

4!10�8 cm2=sz0:7 days ð6Þ

Similarly, considering the value for the diffusioncoefficient for 80% ethanol, DZ0:21!10�8 cm2=s at45 �C (also given by Messadi and Vergnaud [22]), thetime required to saturate in excess of 90% of the centralplane of the 0.5 mm-thick PVC membrane will be

t90%ZH2

4DZ

ð0:05 cmÞ2

0:21!10�8 cm2=sz13:8 days ð7Þ

For immersion tests conducted at room temperatureand on a PVC membrane containing plasticizers otherthan DOP, the time taken for the ethanol to fullypenetrate the PVC membrane is considered to be slightlylonger. Considering these results, it is reasonable toassume that the effective migration will occur afterseveral weeks. Such a short saturation time can allow fora reasonably complete distribution of the watereethanolmixture within the PVC membrane and this distributionwas observed to be almost uniform within a 1-monthimmersion period [30]. Results of fast saturation ofa PVC membrane by other organic liquids are alsoavailable in the literature; for example, in the experi-ments conducted by Messadi and Vergnaud [22],a 3.5 mm-thick PVC membrane is almost fully saturatedby pure ethanol within 5 days of exposure at a temper-ature of 45 �C. Liquids such as paraffin oil and whitespirit can also fully migrate into a 0.5 mm-thick PVCmembrane within about 20 days of exposure ata temperature of 37 �C [40]. These experimentalinvestigations enable the choice of the duration ofimmersion test for the purposes of achieving a satisfac-tory chemical exposure of the PVC membrane. Thecriterion for the selection of the exposure period wasbasically to allow the alteration in the mechanical

behaviour of the PVC membrane. In view of the shortduration required for saturation of the PVC membraneby both pure and 80% ethanol, in the current experi-mental investigations, the exposure time was chosen as 1week, 2 weeks, 1 month, 2 months, 7 months, and 9months. In cases where there is a faster migrationprocess, shorter exposure periods of 2 h and 1 day werechosen. At each exposure stage, three exposed PVCmembranes measuring 250 mm!180 mm were pre-pared; these membranes provided adequate samplesfor mechanical testing. In cases where no significantalterations in the mechanical behaviour of the PVCmembrane were observed during testing further 12 PVCmembranes were subjected to ethanol exposure toexamine the change in the mechanical behaviour withprolonged exposure. For ethanol concentrations lessthan 80%, the information concerning the diffusivitycharacteristics is not readily available in the literature; inthese cases, a longer period of exposure was attempted.A stack of 12 PVC membranes was prepared for eachethanol concentration (at 50% and 0%). The choice ofthe time interval between tests was based on observa-tions concerning the alteration in the mechanicalproperties of the PVC membrane. For purposes ofcomparison, tests were also conducted on PVC mem-branes which were exposed to air. In these tests, a stackof 12 alternate layers of PVC membranes and geotextileswas placed in an open container located in a darkstorage area maintained at room temperature. The PVCmembranes were kept isolated except when the contain-er was opened for sample removal for testing.

2.3. X-ray fluorescence analysis

A liquid form of the phthalate monomer has beenused as the plasticizer in the manufacturing of the PVCmembrane used in this experimental research program[31]. The loss of the plasticizer content in the exposedmembrane was identified through X-ray fluorescencetechniques. The sample of the PVC membrane used forthis purpose had a circular shape with a radius of20 mm. The weight ratio of the oxygen element tothe chloride element in the PVC membrane, definedby RO=Cl, can be used as an indicator to assess theplasticizer content at any stage of exposure of the PVCmembrane to ethanol. Table 1 shows the value of RO=Cl

Table 1

The value of RO=Cl for PVC membranes subjected to ethanol exposure

Specimen RO=Cl

PVC membrane as supplied 6.47%

2-month pure ethanol exposure 5.33%

5-month pure ethanol exposure 5.20%

16-month 50% ethanol exposure 5.44%

18-month water exposure 5.55%

114 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

determined at different stages of exposure to pureethanol. The continuous decrease in this ratio is indica-tive of the loss of plasticizer in the PVC membrane. Theexposure resulted in an appreciable loss of plasticizerduring the first 2 months. The results of the X-rayfluorescence experiments, however, indicate that the rateof extraction was significantly reduced after a 2-monthexposure. The evidence of loss of plasticizer fromplasticized PVC exposed to low concentrations ofethanol was also observed in other studies [4e6]. TheX-ray fluorescence technique was also applied toexamine PVC membranes exposed to 50% ethanol andpure water after 16 months and 18 months, respectively.Both cases, however, reveal noticeable alterations in theRO=Cl value when compared with the correspondingvalues for the untreated PVC membrane. The PVCmembrane exposed to 50% ethanol mixture showsslightly lower value for RO=Cl indicating faster leachingrate of plasticizer.

2.4. Measurement of mechanical properties

The alteration in the mechanical properties of thePVC membrane subjected to various durations ofexposure to ethanol was examined through conventionaluniaxial tensile testing. The testing facility consists ofa servo-controlled MTS Machine with a load capacityof 44,000 N (10,000 lbs). The conventional grips formaterial testing were considered to be inadequate forproviding fixity at the ends of the PVC membrane.Special grips were therefore fabricated for purposes ofthe current experimental research program. The detailsof the grips consisting of an upper and a lower set areshown in Fig. 4. During testing, the lower set of gripswas fixed and the upper one was moved by the MTSmachine in a displacement-controlled mode. The PVCmembrane was clamped between the grips and subjectedto extension. The rigid connections between the gripsand MTS Testing Machine were achieved through theprovision of two adaptors. Holes inside the upper andlower connectors of the adaptors fit the grips to theMTS frame. The grips that were originally designed fortesting PVC membrane strips of width 200 mm, wereused to test strips of width 25.4 mm. In comparison tothe peak load capacity of the MTS machine, the forcesinvolved in the uniaxial testing of the PVC membraneswere extremely small. Therefore a lower capacity loadcell [4400 N (1000 lbs)] was used to measure the appliedloads. The steel grips were fabricated in such a way thatthe PVC membrane could be stretched without de-velopment of either an eccentricity or a tilt. The detailsof the grips are shown in Fig. 5(aeb). The sides of thealuminum plates that come into contact with thePVC membranes were roughed to generate adequatefrictional forces. The aluminum plates could slide freelyon three steel rods within a steel box and five adjustable

screws were used for alignment. To further prevent slipbetween the PVC membrane and the roughed sectionsof aluminum plates, an additional layer of the PVCmembrane strip was bonded to each end of the PVCmembrane, using a non-reactive LOCTITE� 404 instantadhesive [Fig. 2(c)], which increased the thickness of theends of the PVC membrane. The ends were then tightlyclamped between two faces of the aluminum grips. Itwas found that without the provision of this additionallayer, there was insufficient frictional resistance betweenthe surfaces of the membrane and the grips, whichresulted in slippage. If the additional layer was notbonded to the PVC membrane, the slippage wasrestricted to a limited extent at small strains but becameappreciable at large strains, largely due to the pro-gressive loss of friction between layers of membrane asthe PVC membrane contracts in the thickness direction.There is the possibility of chemical reactions between theadhesive and the PVC membrane during prolongedtests. The time-scale of such chemical reactions,however, is expected to be much greater than thoseassociated with the duration the tests. Therefore, theinfluence of the reactivity of the adhesive was notconsidered in the examination of the experimentalresults. All PVC membranes used had an initial cross-section area of 25:4 mm!0:5 mm. The experiments wereconducted in a Material Testing Laboratory maintainedat a room temperature of approximately 24 �C. Thesedurations of tensile tests were restricted to about 1 h.The temperature variation in the laboratory during thisperiod was less than 1 �C. The duration of the chemicalexposure lasted up to 13 months. During this period, thetemperature in the storage area varied between 20 �Cand 26 �C. The influence of these temperature fluctua-tions on either the rate of chemical reaction or on themechanical properties of the PVC membrane was notconsidered in this study. During uniaxial testing, thedisplacement of the PVC membrane was initiallymeasured using two LVDTs located on either side ofthe PVC membrane. Since the PVC membrane washighly deformable in comparison to the rigid steel gripsand test frame, a machine stiffness correction to themeasured deformations was not considered to benecessary; the relative extension of the grips was foundto be quite close to the average of the LVDT valueswhen the displacement was smaller than 30 mm. Atlarger extensions, the accuracy of the LVDT issignificantly reduced. For simplicity and for accuracy,the movement of the grips was therefore taken as thechange in the current gauge length l. The initial gaugelength was taken as the distance between two edges ofthe PVC membrane ðl0Z50 mmÞ as indicated inFig. 2(c). The stress s0 was defined as the magnitudeof applied load divided by initial cross-sectional area ofthe PVC membrane. The strain was calculated as thepercentage change of the initial gauge length. All tests

115Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

(a) Grip with a wide-strip PVC membrane

(b) Grip with a narrow-strip PVC membrane

Load cell

Upper set of the grips

Lower set of the grips

Samples of PVC membrane

Connector on MTS machine

Steel bar

Load cell

A

A

Connector on the gripper

Upper adaptor to MTS machine

Lower adaptor to MTS machine

(c) General layout

Fig. 4. Tensile testing facility.

were performed at a constant strain rate _30, which wasdefined as

_30Zd

dt

�l� l0l0

�ð8Þ

The ASTM Standard D4885-1988 [41] advocatesstrain rates in the range 1%=mine100%=min. Theexperiments on the PVC membrane were conducted atthree strain rates 4%=min, 40%=min and 160%=min.

PVC membranes are manufactured through calen-dering techniques [1,31,42]. The objective of a calender-ing process is either to eliminate or to reduce thedevelopment of anisotropy in the deformability andstrength characteristics [43]. The development of anisot-ropy can be minimized through heat treatment andcuring processes, which induces thermal relaxation. Todetermine the possible influences of the calenderingprocess on the mechanical behaviour, uniaxial tests werealso performed on PVC membranes, the axes of whichwere oriented normal to the calendering direction.

116 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

229mm

178mm

Roughed regions

Load cell

Aluminum grip

Steel box

Upper adaptor to MTS machine

Side plate

(a) Upper set of the grips

Aluminum grip

Steel box

Screw

Side plateLower adaptor toMTS machine

(b) Lower set of the grips

(c) A pair of aluminum grips

Fig. 5. Design of a set of grips.

Test specimens of PVC membranes were prepared bothalong the machine direction and across the machinedirection [see Fig. 2(aeb)].

3. Experimental results

3.1. PVC membrane as supplied

The results of the uniaxial tests conducted on intactPVC membranes are shown in Figs. 6e8. The untreated

PVC membrane undergoes significant large strainsduring a tensile test. The PVC membrane exhibits failureat a strain in the range 150%e250%. By examining thecontinuous stressestrain curve shown in Fig. 6, it isfound that the PVC membrane exhibited significantcreep during these tests. Experiments were also con-ducted to identify the unloading behaviour of theuntreated PVC membrane. Unlike the typical behaviourof hyperelastic rubber-like materials without fillers,where unloading behaviour closely follows the loadingcurve, the untreated PVC membrane exhibits significant

117Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

σ0 (MPa)

σ0 (MPa)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10 12 14 16 18 20

Unloading at “small” strain

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100 120 140 160

Fracture

ε0 = 0.4 / min

ε0 = 4.0 / min

(a) Unloading at “small” strain

(b) Unloading at various strains

ε0 = (l − l0) / l0 × 100

ε0 = (l − l0) / l0 × 100

Fig. 6. A continuous stressestrain curve of a PVC membrane as supplied.

irreversible deformations. Fig. 6(b) shows the responsesof the untreated PVC membrane, which is loaded todifferent levels of maximum strain, followed by unload-ing. It may be observed that, irreversible strain is presentover a large range of the strain experienced by the PVCmembrane. In order to examine the possibility of theexistence of fully reversible behaviour similar to that ofa typical rubber-like material, a test was also conductedat a lower strain rate of _30Z0:4%=min and up toa maximum strain level of 10%. The results are shown inFig. 6(a). The existence of an irreversible strain is stillnoticeable; the amount of the irreversible component is,however, greatly reduced. This indicates the possibilityof fully reversible behaviour of the untreated PVCmembrane in situations where the loading rate andmaximum strain are considerably restricted. Furtherresults obtained by extracting data from several selectivepoints on a continuous stressestrain curve are shown inFig. 7(a). The inset figures shown in Fig. 7(a) indicate

that the grips, while providing no slippage at the ends,also restricted the lateral contraction at the grippedboundary during uniaxial stretching. This violates thecondition necessary for straining PVC membrane toproduce a homogeneous deformation, which is requiredfor any theoretical treatments particularly related to thedevelopment of constitutive relationships. To observethe extent to which the end constraints influence thedevelopment of homogeneous straining, a grid wasmarked on the surface of an undeformed PVC mem-brane with a spacing of 5 mm between the grid lines. Asdeformation progressed, the horizontal grid lines wereused to calculate the real physical gauge lengths fordifferent sections on the PVC membrane [Fig. 7(b)].These distances were averaged over the width of thePVC membrane. The deformed configurations of thePVC membrane were recorded using a digital camera.The distances were first measured in image pixels andthen calibrated against the value of image pixels

118 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

(a) Stress-strain curves

(b) Deformed shapes (with strain measured at different sections of the specimen)

0

2

4

6

8

10

12

14

0 50 100 150 200 250

Undeformed specimen

25.4mm

50mm

σ0 (MPa)

ε0 = (l − l0) / l0 × 100

ε0 = 160 min

ε0 = 40 min

ε0 = 4 min

Fig. 7. Tensile behaviour of a PVC membrane as supplied loading at different strain rates.

corresponding to a known physical distance. The knownphysical distance is chosen as the distance between twogrips. The distance between the two grips is directlymeasured in a displacement-controlled experiment. Thestrains measured by considering different original gaugelengths are presented in Fig. 7(b). Test results indicatethat the effects of the fixity constraints result in an errorof 6.8% over an average strain range of 30Z44% and anerror of 2.4% at a larger strain, in the range of30Z162%. Tests were performed at three different strainrates, 4%=min, 40%=min and 160%=min. To establishthe influence of any anisotropy in the deformability ofthe PVC membrane, tests were conducted on PVC

membranes cut from, both along and perpendicular tothe calendering direction. Fig. 8 shows the correspondingstressestrain curves derived from uniaxial tests con-ducted at three different strain rates. There is someevidence of the influence of manufacturing process onthe stressestrain behaviour, but the results are consid-ered to be within the range of experimental error.

3.2. PVC membranes subjected to concentrationsof ethanol exposure

Fig. 9 illustrates the typical stressestrain curves forPVC membranes subjected to a 7-month exposure to

119Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

pure ethanol. The experiments were conducted ata loading rate of _30Z4%=min. During the exposure topure ethanol, the stressestrain behaviour experiencesa significant change; PVC membrane has developeda pronounced yield point, and both strain-softening andstrain-hardening regions can be observed. The experi-ments also show that the PVC membrane can continueto sustain appreciable post-yield large strains withoutfailure. When unloading is performed, it is evident thatsignificant irreversible strain is present when the stressesexceed the initial ‘‘yield point’’ or ‘‘yield strain’’ of thePVC membrane. Unloading tests were also conductedup to maximum strains that did not exceed the yieldstrain. It is assumed that within this small strain range,the unloading behaviour closely follows the loadingpath. The PVC membrane exposed to pure ethanolbasically exhibits an initial linear elastic responsefollowed by a distinct yield point, a noticeable softeningbehaviour and appreciable post-yield hardening. Inorder to examine the influence of the rate-dependencyon the stressestrain responses, experiments were alsoconducted at loading rates of _30Z40%=min and_30Z160%=min. The influence of the loading rate onthe stressestrain response is also noticeable (Fig. 10).

Fig. 11 shows the results of the tensile tests conductedon samples of the PVC membrane subjected to different

Fig. 8. Tensile behaviour of a PVC membrane as supplied loading at

different strain rates in two orthogonal directions (filled symbols

represent PVC membrane tested along machine direction, while

unfilled symbols represent PVC membrane tested across machine

direction).

periods of exposure to pure ethanol. These results aretypical and indicate a significant continued alteration inthe mechanical behaviour of PVC membrane. It isobserved that the PVC membrane experiences continuedalteration in its mechanical response. The influences ofthe ethanol exposure, include, loss of the hyperelasticcharacteristics or embrittlement and development of aninitial linear modulus and a distinct yield point. Theintact PVC membrane exhibits a monotonically in-creasing hyperelastic behaviour with path dependentpartial recoverability of the strain. The PVC membranessubjected to pure ethanol, on the other hand, showedthe development of a distinct failure threshold withappreciable irrecoverable deformations. The initiallinear modulus and yield stress of the PVC membraneexhibits a continuous increase up to an exposure periodof 2 months after which, there is a slight decrease in thepeak yield value, which is influenced by furtherexposure. The rapid alterations in the mechanicalbehaviour of the PVC membrane within the first 2months correlate well with the results of the X-rayfluorescence analysis. The rate of alteration of themechanical response of the PVC membrane tends tostabilize after a 2-month exposure period. This corre-lates with the reduction in the rate of loss of theplasticizer itself. The experimental results also point tothe slight reduction in the initial modulus and yieldstress in the stressestrain response between a 2-monthand a 7-month exposure period. The reasons for thereduction in the initial linear modulus and yield stress instressestrain response are not entirely clear. A likelyreason could be the swelling-induced alteration in themechanical response, as the PVC membrane experiencesmoisture absorption. While there is no conclusiveobservation of the reduction in the failure strains duringthe first 9 months exposure, the PVC membranesubjected to 13-month exposure shows significant lossin its ability to experience large strain deformability; thePVC membrane breaks at a strain that just exceeds theyield strain without exhibiting any post-yield hardening.This possibly indicates the significant chemical alter-ation in the polymer molecule backbone in the last 4months of exposure period, which directly affects itsintegrity, and subsequently contributes to the failure ofthe PVC membrane.

The experiments also investigated the alteration inthe mechanical properties of the PVC material subjectedto exposure at volumetric concentrations of 80% and50% [Fig. 12(a)]. The influence of exposure at lowerconcentrations of ethanol tends to be much lesssignificant than that observed in cases involvingexposure to pure ethanol. For this reason, the resultsof stressestrain data derived from PVC membranesubjected to 80% and 50% ethanol are presented forlonger exposure times. The stressestrain curve of thePVC membrane subjected to exposure to an 80%

120 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

0

5

10

15

20

25

0 50 100 150 200

Fracture

σ0 (MPa)

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30

Linear initial elastic response

(a) Unloading prior to yield strain

(b) Unloading at various strains that exceed yield strain

σ0 (MPa)

ε0 = (l − l0) / l0 × 100

ε0 = (l − l0) / l0 × 100

Fig. 9. Continuous stressestrain curves of a PVC membrane subjected to 7-month exposure to pure ethanol ð3_0Z4%=minÞ.

concentration of ethanol indicates a slight ‘‘hardening’’response after a 7-month period, which results in lessdeformation under a same external load. A slightincrease in the failure strength is also observed in thiscase. The repeatability of the experiments was alsoexamined [Fig. 12(beg)]. The PVC membranes that hadbeen subjected to exposure to 80% ethanol were loadedto maximum strains of 60% and 100%, which wasfurther followed by an unloading [Fig. 12(c)]. Theexperimental results indicate a variability of approxi-mately 3%. It is inferred that the alteration in thestressestrain behaviour of the membrane was primarilydue to exposure. The ‘‘hardening’’ response in thestressestrain curve is absent after exposure to 50%ethanol; instead the PVC membrane became softer after13-month exposure, which can be attributed to theswelling of the PVC membrane indicated previously.For the purpose of comparison, experiments were alsoconducted on PVC membranes exposed to pure water

and air. The stressestrain curve for the PVC membranesubjected to exposure to pure water after period of 15months closely follows the response of the PVCmembrane subjected to exposure to 50% ethanol, whichindicates that similar chemical and physical mechanismswould contribute to the ‘‘softening’’ of the PVCmembrane. The results of tests conducted on PVCmembranes exposed to air for a period of 21 monthsindicate no observable changes. The possible influencesof the exposure to air (in the absence of ultra-violetlight) can be neglected for the purpose of currentexperimental investigations.

4. Conclusions

The exposure of a PVC membrane to an organicliquid chemical results in two synchronized processes:the first being a fast through-thickness diffusion of the

121Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

liquid into the PVC membrane and second is a relativelyslower loss of plasticizer in a diffusive manner. Theexperiments reported here deal with the examination ofthe alteration in the mechanical behaviour of a 0.5 mm-thick PVC membrane subjected to exposure to ethanol

Fig. 10. Rate dependency of the stressestrain curves of a PVC

membrane subjected to 7-month exposure to pure ethanol.

at different concentrations. The alteration in themechanical properties of the PVC membrane subjectedto exposure to pure ethanol was a continuing process.These alterations included a progressive loss in the largestrain hyperelastic deformability response, the develop-ment of embrittlement with an observable initial linearmodulus and a distinct yield point. The exposure to pureethanol up to 13 months results in a complete loss in thelarge strain deformability capacity of the PVC mem-brane. The rapid alterations in the mechanical proper-ties of the treated PVC membranes in the first 2 monthscorrelated well with the loss of plasticizer from the PVCmembrane, as inferred from the results of X-rayfluorescence techniques. The rate of loss of plasticizerdiminished after 2 months, with the resulting reductionin the rate of alteration in the mechanical behaviour.Although the exposure to other concentrations ofethanol reveals leaching of the plasticizer from thePVC membrane over long period, such exposureproduced a less significant alteration in the mechanicalbehaviour. After 7-month period, the PVC membraneexposed to 80% ethanol exhibited a slight ‘‘hardening’’behaviour. After 13-month period, however, the PVCmembrane subjected to exposure to 50% ethanolbecame softer. The same phenomenon is observed inPVC membranes exposed to pure water for a 15-monthperiod. Both the causes of the ‘‘softening’’ behaviourcould be attributed to the swelling of the PVCmembrane by moisture migration. In a practical context

Fig. 11. Tensile behaviours of a PVC membrane subjected to different periods of pure ethanol exposure.

122 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300 350

PVC membrane as supplied

15-month water exposure

21-month air exposure

1-week 100 ethanol exposure

7-month 80 ethanol exposure

13-month 50 ethanol exposure

0

2

4

6

8

10

12

14

16

0 100 200 300 0 100 200 300

0

2

4

6

8

10

12

14

16

0 100 200 300 4000

2

4

6

8

10

12

14

0 100 200 300 400

0

2

4

6

8

10

12

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250

0

2

4

6

8

10

12

0 50 100 150 200

(a) Response of PVC membrane subjected to exposure to concentrations of ethanol

(b) Exposure to pure ethanol (c) Exposure to 80 ethanol (d) Exposure to 50 ethanol

(e) PVC membrane as supplied (f) Exposure to air (g) Exposure to pure water

ε0 = 40 min−1

σ0 (MPa)

σ0 (MPa)

σ0 (MPa)σ0 (MPa) σ0 (MPa)

σ0 (MPa)

σ0 (MPa)

ε0 = (l − l0) / l0 × 100

ε0 = (l − l0) / l0 × 100

ε0 = (l − l0) / l0 × 100 ε0 = (l − l0) / l0 × 100 ε0 = (l − l0) / l0 × 100

ε0 = (l − l0) / l0 × 100 ε0 = (l − l0) / l0 × 100

Fig. 12. Tensile behaviours of a PVC membrane subjected to concentrations of ethanol exposure.

123Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

involving landfill application of PVC membranes, theconcentration of ethanol can reach a maximum2e3%[44]. The durability of the PVC membrane barrierresulting from the leaching of plasticizer can posea problem over the long-term especially when thelandfill is subjected to wetting and drying cycles wherethe leaching of the plasticizer will occur due toprolonged contact with chemicals, whereas swelling islimited due to temperature increases in the landfillassociated with its decay.

Acknowledgements

The authors are grateful to the reviewers for theirconstitutive comments. The work reported in the paperwas supported by an NSERC eDiscovery Grantawarded to A.P.S. Selvadurai.

References

[1] Koerner EM. Designing with geosynthetics. 3rd ed. Upper Saddle

River, NJ: Prentice Hall; 1994.

[2] Qian X, Koerner RM, Gray DH. Geotechnical aspects of landfill

design and construction. Upper Saddle River, NJ: Prentice Hall;

2002.

[3] Kamykowski GW. Durability consideration for PVC formula-

tions used in geosynthetics: a review. Polym Plast Technol Eng

1994;33:281e93.

[4] Kawamura Y, Maehara T, Wakui C, Yamada T. Migration of

plasticizers and nonylphenol from polyvinyl chloride gloves.

J Food Hyg Soc Jpn 2000;41:330e4.

[5] Tsumura Y, Ishimitsu S, Kaihara A, Yoshii K, Nakamura Y,

Tonogai Y. Di(2-ethylhexyl) phthalate contamination of retail

packed lunches caused by PVC gloves used in the preparation of

foods. Food Addit Contam 2001;18:569e79.

[6] Kim JH, Kim SH, Lee CH, Nah J-W, Hahn A. DEHP migration

behavior from excessively plasticized PVC sheets. Bull Korean

Chem Soc 2003;24:345e9.

[7] Bruins PF. Plasticizer technology, vol. 1. New York: Reinhold

Publishing; 1965.

[8] Wilson AS. Plasticizers: principles and practice. London: Institute

of Material; 1995.

[9] Matthews G. PVC: production, properties and uses. London: The

Institute of Materials; 1996.

[10] Pita VJRR, Sampaio EEM, Monteiro EEC. Mechanical proper-

ties evaluation of PVC/plasticizers and PVC/thermoplastic poly-

urethane blends from extrusion processing. Polym Test 2002;

21:545e50.[11] Elicegui A, del Val JJ, Bellenger V, Verdu J. A study of

plasticization effects in poly(vinyl chloride). Polymer 1997;

38(7):1647e57.

[12] Dubault A, Bokobza L, Gandin E, Halary JL. Effect of molecular

interactions on the viscoelastic and plastic behaviour of plasti-

cized poly(vinyl chloride). Polym Int 2003;52:1108e18.

[13] Gumargalieva KZ, Ivanov VB, Zaikov GE, Moiseev, Ju V,

Pokholok TV. Problems of aging and stabilization of poly(vinyl

chloride). Polym Degrad Stab 1996;52:73e9.

[14] Jakubowicz I, Yarahmadi N, Gevert T. Effects of accelerated and

natural ageing on plasticized polyvinyl chloride (PVC). Polym

Degrad Stab 1999;66:415e21.

[15] Buszard DI. Properties of plasticized PVC. In: Titow WV, editor.

PVC technology. London: Elsevier; 1984. p. 181e214.

[16] Kovacic T, Mrklic Z. The kinetic parameters for the evaporation

of plasticizers from plasticized poly(vinyl chloride). Thermochim

Acta 2002;381:49e60.

[17] Marcilla A, Garcia S, Garcia-Quesada JC. Study of the migration

of PVC plasticizers. J Anal Appl Pyrolysis 2004;71:457e63.

[18] Frissell WJ. Volatility of vinyl plasticizers. Ind Eng Chem

1956;48:1096e9.

[19] Shin SM, Jeon HS, Kim YH, Yoshioka T, Okuwaki A. Plasticizer

leaching from flexible PVC in low temperature caustic solution.

Polym Degrad Stab 2002;78:511e7.[20] Kampouris EM. The migration of plasticizers into petroleum oils.

Eur Polym J 1975;11:705e10.

[21] Messadi D, Vergnaud JM, Hivert M. A new approach to the

study of plasticizer migration from PVC into methanol. J Appl

Polym Sci 1981;26:667e77.

[22] Messadi D, Vergnaud JM. Plasticizer transfer from plasticized PVC

into ethanolewater mixtures. J Appl Polym Sci 1982;27:3945e55.[23] Bessems E. The biodeterioration of plasticized PVC and its

prevention. J Vinyl Technol 1988;10(1):3e6.

[24] Gumargalieva KZ, Zaikov GE, Semenov SA, Zhdanova OA. The

influence of biodegradation on the loss of a plasticizer from

poly(vinyl chloride). Polym Degrad Stab 1999;63:111e2.

[25] Fayoux D. Durability of PVC geomembranes and resistance

to mechanical puncturing. In: Hoedt GD, editor. Geotextiles,

geomembranes and related products, vol. II. Brookfield: A.A.

Balkema; 1990. p. 561e5.

[26] Hollande S, Laurent JL. Study of discolouring change in PVC,

plasticizer and plasticized PVC films. Polym Degrad Stab

1997;55:141e5.

[27] Haxo HE, Haxo PD. Environmental conditions encountered

by geosynthetics in waste containment applications. In:

Koerner RM, editor. Durability and aging of geosynthetics.

London and New York: Elsevier; 1989.

[28] Mueller W, Jakob I. Oxidative resistance of high-density poly-

ethylene geomembranes. Polym Degrad Stab 2003;79:161e72.

[29] Haedrich T. The effect of chemical exposure on the burst strength

of a geomembrane. Master thesis. Ottawa: Carleton University;

1995.

[30] Contamin B, Debeauvais V. The effect of ethanol exposure

on burst strength of a geomembrane. Research report. McGill

University; 1998.

[31] Diebel P. Formulation, manufacturing and physical properties of

PVC geomembranes. In: PVC geomembrane institute technology

program: constructing with PVC geomembrane: video series,

Lecture 1. PVC Geomembrane Institute, University of Illinois at

Urbana e Champaign; 2002.

[32] Kampouris EM, Regas F, Rokotas S, Polychronakis S,

Pantazoglou M. Migration of PVC plasticizers into alcohols.

Polymer 1975;16:840e4.

[33] Frisch HL. Simultaneous nonlinear diffusion of a solvent and

organic penetrant in a polymer. J Polym Sci Polym Phys

1978;16:1651e64.

[34] Taverdet JL, Vergnaud JM. Study of transfer process of liquid

into and plasticizer out of the plasticized PVC by using short tests.

J Appl Polym Sci 1984;29:3391e400.

[35] Papaspyrides CD, Duvis T. Plasticizer transfer from plasticized

poly(vinyl chloride) sheets to petroleum oils. J Appl Polym Sci

1989;38:1573e80.

[36] Kondyli E, Demertzis PG, Kontominas MG. Migration of

dioctylphthalate and dioctyladipate plasticizer from polyvinyl-

chloride films into olive oil. Food chem 1990;36:1e10.

[37] Fick A. Ueber diffusion. Ann Phys 1855;170:59e86.[38] Selvadurai APS. Partial differential equations in mechanics.

Fundamentals, Laplace’s equation, diffusion equation, wave

equation, vol. 1. Berlin: Springer-Verlag; 2000.

124 Q. Yu, A.P.S. Selvadurai / Polymer Degradation and Stability 89 (2005) 109e124

[39] Seferis JC, Chung K, Buehler FU, Takatoya T. Heat and water

mass transfer modeling in polyamide based advanced composites.

Polym Degrad Stab 2000;68:43e51.

[40] Papaspyrides CD. Transport phenomena into and out of

plasticized PVC sheet: the influence of sample history. J Appl

Polym Sci 1992;44:1145e52.

[41] American Society for Testing and Materials (ASTM). Annual

book of ASTM standards, vol. 04.09, Soil and Rock (II): D4943-

latest; Geosynthetics. Philadelphia, PA: ASTM; 1999.

[42] Penn WS. PVC technology. 2nd ed. London and New York:

Elsevier; 1966.

[43] Alfrey T, Wiederhorn N, Stein R, Tobolsky A. Plasticized

polyvinyl chloride: structure and mechanical behaviour. Indust

Eng Chem 1949;41:701e3.

[44] USEPA. Summary of data on municipal solid waste landfill

characteristics e criteria for municipal solid waste landfills

(40CFR Part 258), OSWER.U.S. Environmental Protection

Agency, EPA/530 e SW-88-038; 1988.