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Polymer Testing 28 (2009) 315–323

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Polymer Testing

journal homepage: www.elsevier .com/locate/polytest

Test Method

Non-Fickian diffusion of amyl acetate in polypropylene packaging:Experiments and modelling

Oussama Zaki a, Boussad Abbes b,*, Laurent Safa b

a ENSIB/LEES, Ecole Nationale Superieure d’Ingenieurs de Bourges, Laboratoire Energetique Explosions Structures, 88 boulevard Lahitolle 18020 Bourges cedex,Franceb URCA/GRESPI/LMN, Universite de Reims Champagne-Ardenne, Groupe de Recherche en Sciences Pour l’Ingenieur (EA 4301), Laboratoire de ModelisationNumerique, Faculte des Sciences, Moulin de la Housse, BP 1039, F51687 Reims cedex 2, France

a r t i c l e i n f o

Article history:Received 28 November 2008Accepted 8 January 2009

Keywords:SorptionNon-Fickian diffusionPolypropyleneAmyl acetate

* Corresponding author. Fax: þ33 3 26913803.E-mail address: boussad.abbes@univ-reims.fr (B.

0142-9418/$ – see front matter � 2009 Elsevier Ltddoi:10.1016/j.polymertesting.2009.01.002

a b s t r a c t

In this paper, we present the methodology and the results obtained by the gravimetric andthe FTIR methods to study the sorption of amyl acetate in polypropylene packaging. Theinfluence of the concentration of amyl acetate and the temperature of aging on thesorption is discussed. A non-Fickian model is used to determine the diffusion coefficientand the surface mass transfer coefficient and their evolution with the amyl acetateconcentration and the temperature of aging. The effect of the diffusion of amyl acetate onthe polypropylene is studied by means of thermal properties.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Diffusion in polymeric materials is of fundamentalimportance in many applications and is the subject ofconsiderable scientific interest. The ingress of chemicals intopolymers can have a critical effect on the service perfor-mance of a component or structure. The diffusion of chem-icals in a polymer component may affect the mechanicalperformance of the material, degrade the material orproduct that the polymer should protect (e.g. spoiling ofpackaged foodstuffs, cosmetics or pharmaceuticals),damage the interface between the polymer and anothermaterial (e.g. adhesive joints) or pollute the environment.

Diffusion is the concentration gradient driven processwhereby the absorbed molecules are transported withinthe polymer, and diffusion properties are characterised viadiffusion coefficients. There is an extensive body of liter-ature on diffusion in plastics and other polymers, e.g. [1–12], reflecting a strong industrial need for reliable test

Abbes).

. All rights reserved.

methods to measure the diffusion of gases and liquids inpolymers.

In thick sections, such as sheets, pipes and containers,since the time taken to reach equilibrium moisture contentis proportional to the square of the thickness, it may takevery long periods for equilibrium conditions to be reached.In many applications, the material will see variations in theenvironment to which it is exposed (e.g. temperature,chemical concentrations) and the mass transport is likely tobe a transient problem rather than steady state. It is difficultto test such thick sections reliably since only the early stagesof the absorption and permeation curves will be achievablein realistic experimental timescales. Extrapolation ofbehaviour is necessary to predict long-term behaviour. Theoptions available include: extrapolation of short-term datato long-term behaviour, testing reduced size samples andscaling results to full size through modelling or acceleratingmass transport mechanisms through, e.g. higher concen-trations or increased temperatures. The study of masstransport in thick sections often involves modelling,requiring good quality data and appropriate models.

There are many measurement methods and severalstandard techniques for determining mass transport in

O. Zaki et al. / Polymer Testing 28 (2009) 315–323316

polymers such as: nuclear magnetic resonance (NMR)[13,14], laser interferometry [15–17], gravimetric methods[18–27] and Fourier Transform Infra-Red spectroscopy(FTIR) [28–32]. The most suitable method will depend onthe type of sample, the diffusing chemical species and thelikely rate of diffusion.

The main objective of this work was to study the sorp-tion of amyl acetate in polypropylene packaging usinggravimetric and FTIR methods. In addition, the effect ofamyl acetate concentration and temperature of aging wereevaluated. A non-Fickian model was used to determine theevolution of the diffusion coefficient and the surface masstransfer coefficient. The effect of the sorption of amylacetate on the thermal properties of polypropylene wasalso studied.

Fig. 1. Relative mass uptake in polypropylene samples for differentconcentrations of amyl acetate at: (a) 23 �C and (b) 40 �C.

2. Experimental

2.1. Samples preparation and contact conditions

In this study, we have used samples from commercialextruded blown polypropylene bottles (PP, 0.9–1 mmthick) cut into strips. This polymer is commonly used asa food or cosmetic packaging because of its low weight,flexibility, strength, good moisture barrier and low cost. Wehad no information about the polypropylene structure andforming conditions. FTIR analysis showed that the polymeris a copolymer polypropylene (CPP) containing 83% ofpropylene and 17% of methylene monomers.

The amyl acetate (n-pentyl acetate) used is an analyticalgrade reagent obtained from Aldrich Chemical Company(Lyon, France), with about 99% purity. The product

Fig. 2. Gravimetric sorption kinetic curves of amyl acetate into poly-propylene samples for different concentrations at: (a) 23 �C and (b) 40 �C.

Fig. 3. FTIR spectra after contact with 5000 ppm amyl acetate solution at23 �C of: (a) reference polypropylene sample and (b) polypropylene sample.

Fig. 4. Evolution of the integrated intensity ratio Ar during diffusion of amylacetate into PP for different concentrations at: (a) 23 �C and (b) 40 �C.

O. Zaki et al. / Polymer Testing 28 (2009) 315–323 317

properties are as follows: molar weight, 130.2 g/mol;density at 20 �C, 0.876 g/cm3; boiling point, 146 �C; andfusion point, �71 �C. The enthalpy of vaporization of amylacetate calculated from data in the Handbook of Chemistryand Physics is 41.9 kJ/mol. This molecule is used as a foodaroma and as a test odorant in studies of olfactory function.

From pure amyl acetate, we prepared aqueous solutionsof 5000 ppm, 10 000 ppm, 20 000 ppm and 50 000 ppm.These solutions were prepared from pure amyl acetatesolution with 2.5% ethanol to improve solubilisation insome cases.

Samples were cut in rectangular shape (9 cm� 1 cm)using a warm scalpel. All of the samples had an aspect ratio(length over thickness) greater than 10, which ensuredapplication of a one-dimensional diffusion equation foranalysis of the transport data.

2.2. Gravimetric diffusion measurements

The gravimetric method is one of the most widely usedmethods for the study of sorption of liquids in solidmaterials. It consists in following the evolution of the massof a sample immersed in the solution. This method can beused only when one compound is studied, but it isuniversally applicable whatever the product tested.

The polymer samples were soaked in screw-tight testglass vials containing 15 ml of aqueous solutions of amylacetate. The immersion experiments were conducted at23 �C and 40 �C. The contact times varied from 1 min to 21

days. These samples were removed periodically, the solventdrops adhering to the surface were wiped off using softfilter paper wraps and samples were weighed immediatelyon a digital analytical balance model AG 204 (MettlerToledo, Switzerland) with accuracy of �0.01 mg. Weightgain versus time data was collected, and all experimentswere conducted at 23 �C.

2.3. FTIR diffusion measurements

The Fast Transform Infra-Red spectroscopy (FTIR) tech-nique is a valuable method for investigating the kinetics ofsorption of organic molecules in polymers. In other studies[2,32], we have developed such a method to study the

Fig. 5. FTIR sorption kinetic curves of amyl acetate into polypropylenesamples for different concentrations at: (a) 23 �C and (b) 40 �C.

O. Zaki et al. / Polymer Testing 28 (2009) 315–323318

sorption rate of different esters by PP. The ester function ischaracterized by absorption band in regions where the PPdoes not absorb. The sorption can be evaluated by the ratioof the carbonyl ester (CO) band area at 1747 cm�1 to thearea of a reference band (characteristic peak) of the PP at841 cm�1.

For this study, we have used a FTIR spectroscope MB-100 from Michelson Bomem Company (Quebec, Canada).The samples were scanned between 4000 cm�1 and700 cm�1. This method allows the direct comparison ofpenetration speeds, the time to reach the maximumpenetration and the rate of equilibrium.

Before beginning the spectroscopic study, we cut thesamples in the form of plates of 50 mm thickness usinga microtome. These plates were then placed on a rectan-gular support adapted for the spectroscopic analysis.

2.4. Thermal properties

Differential scanning calorimetry (DSC) was used forthermal analysis of the packaging polymers. Themeasurements were conducted on a modulated DSC 2920(TA Instruments Inc., France). Samples of 10 mg averageweight were cut from virgin and contaminated PP. Thereference was an empty aluminium pan. The samples wereheated from �50 �C to 250 �C at a rate of 10 �C/min. Allexperiments were carried out under a purge of nitrogen.The samples were stored at room temperature (23 �C)before the analysis, and DSC measurements were per-formed in triplicate.

Fusion temperature (Tf), crystallinity temperature (Tc),heat of fusion enthalpy (DHf) and heat of crystallizationenthalpy (DHc) were measured.

3. Results and discussion

3.1. Gravimetric sorption results

After contact with amyl acetate at different concentra-tions and temperatures, the mass of the PP samples wasdetermined immediately. Equation (1) was used tocompute the relative mass uptake of the PP samples attime t:

DM ¼ Mt �M0

M0� 100 (1)

where M0 is the initial mass of the sample and Mt is themass of the sample after a contact time t.

Fig. 1(a) shows the kinetics of sorption of amyl acetate inPP at 23 �C. We have observed that the sorption equilibriumwas reached after 10 days. The largest sorption wasobserved with the solution containing 50 000 ppm of amylacetate and the order of sorption is50 000 ppm> 20 000 ppm> 10 000 ppm> 5000 ppm. Thesorption curves at 40 �C (Fig. 1(b)) show that the equilib-rium is reached after 7 days whatever the concentration ofamyl acetate. When the contact temperature increases, theamount of the ester sorbed into the PP samples increasesand the time to reach the equilibrium state decreases.These effects are essentially due to the increase in themobility of the macromolecules in the amorphous phase ofthe polypropylene, accompanied by the increase in thepolymer free volume.

To identify the type of sorption, we have adopteda better representation which consists in plotting theevolution of Mt/MN against the square root of the time ofcontact (Fig. 2). This figure shows that the kinetics ofsorption of the amyl acetate in polypropylene is of sigmoidtype for the two temperatures of ageing. In these cases,there is a limitation of the kinetics of sorption at theinterface of the polymer. That means during the transfer ofthe molecules towards the polymer they are slowed downby the interface before diffusing inside the polymer. Theabsence of strong interactions between amyl acetate andpolypropylene can then suggest a weak sorption at thebeginning followed by diffusion in the material.

Fig. 6. Comparison of experimental sorption kinetic data with sigmoid-shape fitted curves at 23 �C for: (a) 5000 ppm, (b) 10000 ppm, (c) 20000 ppm and(d) 50000 ppm.

O. Zaki et al. / Polymer Testing 28 (2009) 315–323 319

3.2. FTIR sorption results

The FTIR spectrum of virgin polypropylene is repre-sented on Fig. 3(a). This spectrum is taken as a referenceduring this study. This spectrum presents a characteristicpeak of polypropylene located at 841 cm�1. Fig. 1(b) showsa FTIR spectrum of a polypropylene sample after contactwith 5000 ppm of amyl acetate solution at 23 �C at theequilibrium stage, where the absorption characteristicband of esters at 1747 cm�1 is clearly observed.

The quantification of the sorbed product is achieved bycomparing the ratio Ar of the area of the absorption band ofamyl acetate At at 1747 cm�1 and the area of the charac-teristic band of polypropylene App at 841 cm�1:

Ar ¼At

App(2)

In Fig. 4, we have presented a comparison of theevolution of the ratio Ar for all the concentrations(5000 ppm, 10 000 ppm, 20 000 ppm and 50 000 ppm)

according to the time of ageing and for the temperaturesof 23 �C and 40 �C.

In Fig. 5, we have presented the kinetics of sorption byplotting the ratio of areas at time t and the ratio of areas atequilibrium according to the square root of time of contactfor the ageing temperatures 23 �C and 40 �C. The resultsobtained with the FTIR technique are coherent with thoseobtained by the gravimetric method. The shape of thecurves also confirms that the kinetics of sorption is ofsigmoid type.

3.3. Sigmoid diffusion model

The experimental results of sorption obtained by thegravimetric technique and FTIR showed that the kinetics ofsorption is non-Fickean. Such results have been observedexperimentally in many systems [33]. The sorption curves aresigmoid in shape (S-shape) with a single point of inflexion.

In this case, the Fickean model cannot be used. Verg-naud [34] has proposed a model where the total amount of

Fig. 7. Comparison of experimental sorption kinetic data with sigmoid-shape fitted curves at 40 �C for: (a) 5000 ppm, (b) 10000 ppm, (c) 20000 ppm and(d) 50000 ppm.

Table 1Values of D and H for the sigmoid model identified by SiDoLo.

Concentration(ppm)

T¼ 23 �C T¼ 40 �C

H (cm/s)� 10�7

D (cm2/s)� 10�7

H (cm/s)� 10�7

D (cm2/s)� 10�7

5000 1.94 1.50 3.49 6.7310000 1.98 1.50 3.81 6.7320000 2.08 1.50 4.22 6.7350000 2.13 1.50 4.33 6.73

O. Zaki et al. / Polymer Testing 28 (2009) 315–323320

diffusing substance Mt entering the sample up to time t canbe expressed as a fraction of MN, the correspondingquantity after infinite time, by:

Mt

MN

¼ 1�XNn¼1

2R2

b2n

�b

2n þ R2 þ R

� exp

� b

2nDtL2

!(3)

where bn are positive roots of:

btanðbÞ ¼ R (4)

and R¼ LH/D is a dimensionless parameter. L is the thick-ness of the sample, H is the surface mass transfer coefficientat the interface and D is the diffusion coefficient.

The coefficient of diffusion D and the surface masstransfer coefficient H are the two unknown parameterswhich we will try to identify using SiDoLo software [35].

Figs. 6 and 7 show a comparison of experimentalsorption kinetic data with sigmoid-shape fitted curves atrespectively 23 �C and 40 �C for all the concentrationsstudied. These figures show that sigmoid sorption model

fits well the experimental results obtained by gravi-metric and FTIR techniques. The identified values for Dand H are reported in Table 1 for the two contacttemperatures.

In Fig. 8, we have plotted the evolution of the coeffi-cients D and H according to the amyl acetate concentrationat the temperatures of 23 �C and 40 �C respectively. Theyshow that the surface mass transfer coefficient at theinterface H increases according to the concentration ofthe solution. This confirms that for high concentrations, themolecules of ester are blocked on the surface and cannot

Fig. 8. Evolution of the identified H and D coefficients with the concentra-tion of amyl acetate at: (a) 23 �C and (b) 40 �C.

Fig. 10. Variation of (a) fusion temperature and (b) crystallisation temper-ature with the concentration of amyl acetate at 23 �C and 40 �C.

O. Zaki et al. / Polymer Testing 28 (2009) 315–323 321

penetrate at the same time in the polymer. These figuresalso show that the values obtained for D remain constantand do not depend on the concentration. On the otherhand, the coefficient of diffusion values increase accordingto the temperature of ageing.

Fig. 9. DSC thermogram of virgin polypropylene.

3.4. Thermal properties results

A typical thermogram is presented in Fig. 9 for thevirgin polypropylene used in this study. From this ther-mogram, we can determine temperature of fusion Tf

(endothermic peak) and the temperature of crystalliza-tion Tc (exothermic peak), as well as the enthalpy offusion DHf and the enthalpy of crystallization DHc of thepolymer.

This thermogram shows that the peak of fusion isnarrow and does not present a double peak: the crystallitesmelt at the same fusion temperature Tf.

The knowledge of the enthalpy of fusion allows us toobtain the rate of crystallinity (in %) of the polymer usingthe following equation:

Xcð%Þ ¼DHf � DHc

DH0� 100 (5)

where DH0¼ 209 J/g is the enthalpy of fusion of the poly-mer counterpart 100% crystalline [36].

Fig. 11. Variation of the crystallinity with the concentration of amyl acetateat 23 �C and 40 �C.

O. Zaki et al. / Polymer Testing 28 (2009) 315–323322

In Fig. 10, an increase in the temperature of fusion anda decrease in the temperature of crystallization wereobserved on the aged polypropylene samples in contactwith amyl acetate aqueous solutions at temperatures of23 �C and 40 �C. These variations can be explained on theone hand by the increase in the concentration of ester inpolymer, and on the other hand by the effect of plastici-zation, which induces migration of the additives from thepolymer into the solution.

In Fig. 11, we have plotted the variation of the crystal-linity rate versus the concentration of amyl acetate aqueoussolutions at temperatures of 23 �C and 40 �C. We canobserve that the crystallinity rate decreases according tothe concentration of the amyl acetate in the solution. Oncethe amyl acetate is sorbed in the polymer, it plays a role ofplasticizer which will reduce the intermolecular interac-tions [37] by decreasing the physical barriers of the poly-mer [38].

The decrease in the rate of crystallization of the agedpolymer at 40 �C is more important than at 23 �C. Thiseffect of the temperature of ageing is due to the quantity ofamyl acetate sorbed in the polypropylene which is moreimportant when the temperature increases.

4. Conclusions

The sorption results obtained with the FTIR techniqueand the gravimetric method are very close. When the agingtemperature increases, the amount of the ester sorbed inthe PP samples increases and the time to reach the equi-librium state decreases. The results showed that thekinetics of sorption is non-Fickean and the shape of thesorption curves are of sigmoid type. A two coefficientmodel is identified and showed that the coefficient ofdiffusion D remains constant and the surface mass transfercoefficient at the interface H increases according to theconcentration of the solution. However, the two coefficients

increase according to the temperature of aging. An increasein the temperature of fusion and a decrease in the temper-ature of crystallization were observed on the aged poly-propylene. The crystallinity rate decreases according to theconcentration of the amyl acetate in the solution, and thedecrease in the rate of crystallization of the aged polymer at40 �C is more important than at 23 �C.

Acknowledgements

The authors thank Professor Philippe PILVIN of Uni-versite de Bretagne-Sud who has gracefully allowed us touse the SiDoLo software.

References

[1] A.M. Riquet, N. Wolff, S. Laoubi, J.M. Vergnaud, A. Feigenbaum, Foodand packaging interactions: determination of the kinetic parametersof olive oil diffusion in polypropylene using concentration profiles,Food Addit. Contam. 15 (6) (1998) 690.

[2] L. Safa, B. Abbes, O. Zaki, Effect of amyl acetate sorption onmechanical and thermal properties of polypropylene packaging,Packag. Technol. Sci. 20 (2007) 403.

[3] H. Siddaramaia, P. Mallu, Sorption and diffusion of aldehydes andketones through aastor oil-based interpenetrating polymernetworks of PU–PS, J. Appl. Polym. Sci. 67 (1998) 2047.

[4] T.M. Aminabhavi, H.T.S. Phayde, Molecular transport characteristicsof Santoprene thermoplastic rubber in the presence of aliphaticalkanes over the temperature interval of 25–70 �C, Eur. Polym. J. 36(5) (1995) 1023.

[5] S. Al-Malaika, M.D. Goonetileka, G. Scott, Migration of 4-substituted2-hydroxy benzophenones in low density polyethylene: part I –diffusion characteristics, Polym. Degrad. Stab. 32 (1991) 231.

[6] Z.N. Charara, J.W. Williams, R.H. Schmidt, M.R. Marshall, Orangeflavor absorption into various polymeric packaging materials, J. FoodSci. 57 (1992) 963.

[7] S.N. Dhoot, B.D. Freeman, M.E. Stewart, A.J. Hill, Sorption andtransport of linear alkane hydrocarbons in biaxially oriented poly-ethylene terephthalate, J. Polym. Sci. Part B: Polym. Phys. 39 (11)(2001) 1160.

[8] I.J. Chiang, C.C. Chau, S. Lee, The mass transport of ethyl acetate insyndiotactic polystyrene, Polym. Eng. Sci. 42 (4) (2002) 724.

[9] S.B. Kulkami, M.Y. Kariduraganavar, T.M. Aminabhavi, Molecularmigration of aromatic liquids into a commercial fluoroelastomericmembrane at 30, 40, and 50 �C, J. Appl. Polym. Sci. 90 (2003) 3100.

[10] M. Patzlaff, A. Wittebrock, K.H. Reichert, Sorption studies ofpropylene in polypropylene. Diffusivity in polymer particles formedby different polymerization processes, J. Appl. Polym. Sci. 100 (2006)2642.

[11] A. Escobal, C. Iriondo, I. Katimed, Organic solvents adsorbed inpolymeric films used in food packaging: determination by head-space gas chromatography, Polym. Test. 18 (1999) 249.

[12] P. Hernandez-Munoz, R. Catala, R.J. Hernandez, R. Gavara, Foodaroma mass transport in metallocene ethylene-based copolymersfor packaging applications, J. Agric. Food Chem. 46 (1998) 5238.

[13] W.P. Rothwell, D.R. Holecek, A. Kershaw, NMR imaging: study offluid absorption by polymer composites, J. Polym. Sci: Polym. Lett.Ed. 22 (5) (1984) 241.

[14] L.A. Weisenberger, J.L. Koenig, NMR imaging of case II diffusion inglassy polymers, J. Polym. Sci. Part C: Polym. Lett. 27 (2) (1989) 55.

[15] K.L. Saenger, H.M. Tong, Laser interferometry: a measurementtechnique for diffusion studies in thin polymer films, Polym. Eng.Sci. 31 (6) (2004) 432.

[16] K.L. Saenger, H.M. Tong, Bending-beam study of water sorption bythin poly(methyl methacrylate) films, J. Appl. Polym. Sci. 38 (5)(2003) 937.

[17] C.J. Durning, M.M. Hassan, H.M. Tong, K.W. Lee, A study of case IItransport by laser interferometry, Macromolecules 28 (1995) 4234.

[18] H. Kumara, B. Siddaramaiah, A study of sorption/desorption anddiffusion of substituted aromatic probe molecules into semi inter-penetrating polymer network of polyurethane/polymethyl methac-rylate, Polymer 46 (2005) 7140.

[19] I.O. Igwe, C.M. Ewulonu, I. Igbuanugo, Studies on the diffusioncharacteristics of some aromatic solvents into polypropylene film, J.Appl. Polym. Sci. 102 (2006) 1985.

O. Zaki et al. / Polymer Testing 28 (2009) 315–323 323

[20] C.R. Moylan, M.E. Best, M. Ree, Solubility of water in polyimides.Quartz crystal microbalance measurements, J. Polym. Sci. Part B:Polym. Phys. 29 (1) (1991) 87.

[21] N. Lutzow, A. Tihminlioglu, R.P. Danner, J.L. Duda, A. De Haan, G.Warnier, J.M. Zielinski, Diffusion of toluene and n-heptane in poly-ethylenes of different crystallinity, Polymer 40 (7) (1999) 2797.

[22] K.M. Kruger, G. Sadowski, Fickian and non-Fickian sorption kinetics oftoluene in glassy polystyrene, Macromolecules 38 (20) (2005) 8407.

[23] A.R. Berens, Sorption of organic liquids and vapors by rigid PVC, J.Appl. Polym. Sci. 37 (1989) 901.

[24] C.C. McDowell, B.D. Freeman, G.W. McNeely, Acetone sorption anduptake kinetic in poly(ethylene terephthalate), Polymer 40 (1999) 3487.

[25] N.S. Oliveira, J. Oliveira, T. Gomes, A. Ferreira, J. Dorgan, I.M. Mar-rucho, Gas sorption in poly(lactic acid) and packaging materials,Fluid Phase Equilib. 222–223 (2004) 317.

[26] C. Kiparissides, V. Dimos, T. Boultouka, A. Anastasiadis, A. Chasiotis,Experimental and theoretical investigation of solubility and diffu-sion of ethylene in semicrystalline PE at elevated pressures andtemperatures, J. Appl. Polym. Sci. 87 (2003) 953.

[27] Y. Qin, M. Rubino, R. Auras, L.T. Lim, Use of a magnetic suspensionmicrobalance to measure organic vapor sorption for evaluatingthe impact of polymer converting process, Polym. Test. 26 (8) (2007)1082.

[28] S. Cotugno, D. Larobina, G. Mensitieri, P. Musto, G. Ragosta, A novelspectroscopic approach to investigate transport processes in poly-mers: the case of water–epoxy system, Polymer 42 (15) (2001) 6431.

[29] K. Ichikawa, T. Mori, H. Kitano, M. Fukuda, A. Mochizuki, M. Tanaka,Fourier transform infrared study on the sorption of water tovarious kinds of polymer thin films, J. Polym. Sci. Part B: Polym.Phys. 39 (18) (2001) 2175.

[30] A. Lasagabaster, M.J. Abad, L. Barral, A. Ares, FTIR study on the natureof water sorbed in polypropylene (PP)/ethylene alcohol vinyl(EVOH) films, Eur. Polym. J. 42 (2006) 3121.

[31] L.M. Doppers, S. Sammon, C. Breen, J. Yarwood, FTIR–ATR studies ofthe sorption and diffusion of acetone/water mixtures in poly(vinylalcohol), Polymer 47 (2006) 2714.

[32] L. Safa, B. Abbes, Experimental and numerical study of sorption/diffusion of esters into polypropylene packaging films, Packag.Technol. Sci. 15 (2) (2002) 55.

[33] G.S. Park, J. Crank, Diffusion in Polymers, Academic Press, 1968.[34] J.M. Vergnaud, Liquid Transport Processes in Polymeric

Materials: Modelling and Industrial Applications, Prentice Hall,1991.

[35] P. Pilvin, SiDoLo Users Guide, University of Bretagne-Sud, 2003.[36] H. Belofsky, Plastics: Product Design and Process Engineering,

Hanser Publisher, 1995.[37] J.K. Sears, J.R. Darby, The Technology of Plasticizers, Willey &

Sons, 1982.[38] J.W. Rhim, A.K. Mohanty, S.P. Singh, K.W.N. Perry, Effect of the

processing methods on the performance of polylactide films: ther-mocompression versus solvent casting, J. Appl. Polym. Sci. 101(2006) 3736.