Diffusivity of ethylene and propylene in atactic and isotactic polypropylene: Morphology effects and free-volume simulations

Diffusivity of Ethylene and Propylene in Atacticand Isotactic Polypropylene: Morphology Effectsand Free-Volume Simulations

A. Gonzalez, S. Eceolaza, A. Etxeberria, J. J. Iruin

Polymer Science and Technology Department and Institute for Polymer Materials (POLYMAT), University ofthe Basque Country, 20080 San Sebastian, Spain

Received 11 January 2006; accepted 16 December 2006DOI 10.1002/app.26000Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: Diffusion coefficients of propylene andethylene through particles and films of isotactic polypro-pylene (iPP) as well as through films of atactic, com-pletely amorphous, polypropylene have been measuredby gravimetric experiments. iPP particles with relativelysimilar crystallinities but with different particle size dis-tributions (PSD), and different origins have been used.They exhibited very different diffusion coefficients whenthe average radius of the PSD was used as the dimen-sional parameter of the diffusion process. However, filmsprepared with these particles and having similar crystal-linities provided similar diffusion coefficients. The resultsare consistent with the idea of a multigrain structure in

the particles, where the apparent (or experimental) diffu-sion coefficient is a consequence of the complex systemformed by internal and external areas. The diffusioncoefficient of the films, taken as the real diffusion mag-nitude, can be used in the calculation of the true diffu-sional radius of these multigrain particles. Experimentalresults of the diffusion coefficients have been reasonablywell reproduced with the aid of the Vrentas-Duda freevolume model. � 2007 Wiley Periodicals, Inc. J Appl PolymSci 104: 3871–3878, 2007

Key words: poly(propylene); monomer diffusion; Vrentas-Duda model

INTRODUCTION

Although isotactic polypropylene (iPP) is one of themost important commercial polymers available, insome applications such as automotive components, thepure polymer is too brittle and requires some kind ofmodification to impart toughness to its relativelybrittle character. Ethylene-propylene rubber domainsare added to iPP to improve its impact resistance. Thefinal product is denoted as high impact polypropylene(HIPP).1 This material is usually produced in a hybridprocess consisting of propylene polymerization in theliquid phase followed by copolymerization of ethyleneand propylene in the gas phase.

In preparing particles of HIPP, ethylene and pro-pylene monomers should diffuse through previouslyobtained iPP particles. The copolymerization takesplace at temperatures in the interval 310–350 K andin a pressure range between 1.5 and 3 MPa. It isclear that properties, such as solubility and diffusiv-ity of monomer, in the polymer are important in

modeling such type of processes. Although the avail-able experimental methods seem to be well founded,the complexity of the polyolefin particles (speciallyin terms of porosity, size distribution, crystallinity,and crystalline morphology) has given rise to someunsolved problems.

In the experimental determination of the diffusioncoefficients, the second Fick’s law is the usual equa-tion to reduce the experimental data. But the applica-tion of this equation requires the knowledge of thegeometric shape of the sample (flat films, spheres, cy-lindrical bars, etc.) and their characteristic dimen-sions. In the case of the iPP particles, it could beassumed that they are spherical, an assumption that,in some cases, TEM micrographs support.2 But TEMmicrographs also clearly show that these particleshave a complex structure. They can be seen as aggre-gates of smaller particles, generated as a consequenceof the presence of different catalyst points, with im-portant pores among them. In fact, Floyd et al.3 pro-posed some years ago a model for propylene and eth-ylene polymerizations in which they took intoaccount such type of structure. Consequently, the av-erage radius of the whole particle does not representthe true diffusional dimension of the process and, if itis used to calculate diffusion coefficients, these shoulddepend on the particle size distribution (PSD) and theinternal morphology of the sample.

Correspondence to: A. Etxeberria ([email protected]).Contract grant sponsor: University of the Basque Coun-

try (UPV/EHU), San Sebastian, Spain.

Journal of Applied Polymer Science, Vol. 104, 3871–3878 (2007)VVC 2007 Wiley Periodicals, Inc.

In this article, we have used iPP particles with dif-ferent morphologies and different PSD. We have con-firmed that the diffusion coefficient is not characteris-tic of the polymer but depends on the particle size ifthe average radius is used as characteristic dimensionof the material. We have hypothesized that polymerfilms with controlled thickness, obtained after meltingthe particles, have a well-defined geometry that canprovide reliable diffusion coefficients. With these dif-fusion coefficients of the films, the apparent valuesobtained with the particles can be used to calculatethe true diffusional radius of each type of particles,giving an idea of the multigrain characteristics of theparticles in a specific sample.

Our experimental results of diffusion coefficientson film samples have been compared with simulateddiffusion coefficients obtained using the so-calledVrentas and Duda4 model. Although this free-volume model has repeatedly shown its capacity toreproduce experimental results, it requires an impor-tant number of parameters, characteristic of the poly-mer and the penetrant. Fortunately, in the PP case,all these parameters, except one that remains as ad-justable, have been recently obtained, as we willdetail in the next paragraphs.

The results here summarized are not only impor-tant for understanding and modeling the diffusionprocess during the HIPP polymerization reaction butalso in the design of monomer removal equipments,where after the production of polymer particles inslurry or gas-phase reactors, significant amounts ofthe monomers or comonomers must be removed tomeet quality, safety, and environmental standards.

EXPERIMENTAL PART

Materials

Table I summarizes the different investigated sam-ples. H-171-II is a REPSOL-YPF (Mostoles, Madrid,Spain) sample of iPP. Received in form of particles,its molecular weight averages by SEC were Mn

¼ 71,800 and Mw ¼ 244,700. Crystallinity was 36%(as raw particles, determined by DSC on the basis of

a heat of melting of 190 J/g for a 100% crystallineiPP). Fractions of particles with different PSDs wereobtained by screening using testing sieves. Only thetwo extreme fractions have been used in this article,as Table I indicates. Crystallinities of these fractions,following the procedure earlier described, were inthe 35–39% interval.

Films of these particles were prepared after meltingthem at 2008C and keeping this temperature for twominutes. The melt was then transferred to anotherunit at room temperature to allow crystallization.

Using the same protocol, a different film was pre-pared from a randomly selected sample (in pelletform) of another REPSOL-YPF iPP (the one called PP070) to compare results from different films of com-mercial iPPs. According to the supplier, isotacticitywas 95% and the viscosity-average molecular weightMv was 164,700.

The atactic polypropylene (aPP) was also suppliedby REPSOL-YPF and denoted as aPP141. It wasobtained by polymerization in heterogeneous phaseusing metallocenic catalysts. It is a rubbery materialwith a glass transition near 280 K. The molecularweight distribution was characterized by SEC in chlo-roform at 258C. The weight average molecular weightwas 70,000 and the polydispersity 2.2. 13C-NMR in1,2,4-trichlorobenzene/deuterated benzene gives thefollowing dyad analysis: (mm) ¼ 14.1%; (rm)¼ 50.7%, and (rr) ¼ 35.2%. The film was prepared bymolding the sample at room temperature. Because ofthe rubbery character and to prevent some undesir-able flow during the gravimetric experiments, theaPP film was thicker than the iPP ones.

Finally, we have investigated iPP particles pro-vided by SABIC (Geleen, Holland). The weight aver-age molecular weight was 395,000 and the numberaverage molecular weight 80,000, as reported by thesupplier. Another film was prepared with these par-ticles following the earlier described methodology.

Ethylene (>99%) and propylene (>99%) were pro-vided by Air Liquide in the form of gas cylinders.They were used as received. Propylene was in theform of a pressurized liquid in equilibrium with itsvapor. Given that the cylinder was maintained at

TABLE ICharacteristics of the Different Samples of Polypropylene Used in the Gravimetric Experiments

Polymer Supplier Cryst. (%) MorphologyCharacteristic dimensions: average

diameter f, thickness ‘ (mm)

iPP H-171-II REPSOL-YPF 36 Original particles f ¼ 1800iPP H-171-II REPSOL-YPF 39 Particles after fractionation f ¼ 2900iPP H-171-II REPSOL-YPF 35 Particles after fractionation f ¼ 900iPP H-171-II REPSOL-YPF 44 Film ‘ ¼ 562iPP PP 070 REPSOL-YPF 40 Film ‘ ¼ 204aPP aPP 141 REPSOL-YPF 0 Film ‘ ¼ 701iPP SABIC 33 Original Particles f ¼ 693iPP SABIC 51 Film ‘ ¼ 224

3872 GONZALEZ ET AL.

Journal of Applied Polymer Science DOI 10.1002/app

room temperature, it was not possible to performgravimetric experiments at pressures above thevapor pressure of propylene in these conditions.

The required thickness of the different films (‘)was measured by a Duo Check gauge with an accu-racy of 1 mm. In the case of the particles, the averageradius was calculated assuming a spherical morphol-ogy and taking as average volume of the particlesthe maximum in the PSD. PSDs of the original sam-ples were provided by the suppliers.

Sorption experiments: Data reduction

Gravimetric sorption experiments have been carriedout in an electromagnetic balance sold under the tradename of IGA-2 by Hiden in United Kingdom. It oper-ates with gases and vapors in a wide range of temper-atures and up to 20 bars.5 It can be programmed bothin sorption and desorption experiments, where thepressure is increased or decreased in a step-by-stepmode. We have performed experiments at differenttemperatures. 608C and 808C were selected becausethey are close to the interval used in the HIPP poly-merization. But these temperatures are far from theaPP glass transition temperature, making difficult tokeep the dimensional stability of its films. Because ofthat, sorption experiments in the vicinity of 308 and 408were carried out with the aPP film, as well as someiPP particles and films provided by REPSOL-YPF (seenext paragraphs). At these temperatures, aPP and theiPP amorphous regions are above the glass transitiontemperature and, consequently, in a rubbery state.

During the gravimetric experiments, the weight gain(Mt) increases with time (t) up to an equilibrium value,M1. The Avrami’s semiempirical model, originallydeveloped to explain the kinetics of metal crystalliza-tion, can be used to describe the sorption kinetics of apenetrant in a polymer, according to eq. (1):

Mt ¼ M1 1� expð�ðt� t0Þx=kÞ½ � (1)

where x is an exponent allowing the fitting of non-fickian curves, k is a time constant related with thediffusional process and t0 is the actual origin fromwhich the trend is analyzed, after eliminating someweight readings affected by aerodynamic disturban-ces occurring during the pressurization of the bal-ance. All our sorption kinetics had an approximatelyfickian behavior (x ¼ 1). This simplifies eq. (1).

It is possible to demonstrate that this equation canbe derived from the so-called long-time approxima-tion of the general equation:6

Mt

M1¼ 1� A

p2X1n¼0

1

ð2nþ 1Þ2 exp�Dð2nþ 1Þ2p2

x2t

!

(2)

obtained by solving the differential equation corre-sponding to the second Fick’s law. The A constantequals to 8 and x ¼ ‘, where ‘ is the thickness, in thecase of a sample of rectangular geometry. In the caseof spherical particles A ¼ 6 and x ¼ r, where r is theaverage radius of the particle.

In our case, diffusivities have been calculated fromthe time constant k provided by a least squares anal-ysis of the experimental data, using eq. (1). In theparticle case and assuming a spherical geometry,6 kand D are related by:

D ¼ 1

kr2

p2(3)

If the sample is in the form of a film with rectan-gular geometry and a thickness ‘,

D ¼ 1

k‘2

p2(4)

RESULTS AND DISCUSSION

Experimental diffusion coefficients

As previously mentioned, iPP particles are aggregatesof smaller particles with extended pores amongthem.2 These pores are completely accessible to thepenetrant, and consequently, the use of the averageradius of the aggregate as representative diffusivitypath of the process could introduce some uncertaintyin the determination of the real diffusion coefficient.Our hypothesis was that the best way to determinethis diffusion coefficient (D) is to use dense films ofthe different samples. In using films, we have bulksamples with a completely controlled geometry. Thethickness, which is the dimensional value appearingin eq. (4), can be measured with high accuracy(61 mm). If the hypothesis is correct, we have to findsimilar diffusion coefficient with films prepared withdifferent iPP samples. The only condition is that thecrystallinity degree should be similar.

This final condition arises from the fact that it is gen-erally accepted that the penetration of small-moleculepenetrants in semicrystalline polymers is restrictedto the noncrystalline fraction. Consequently, becauseof the presence of the crystallites, the trajectory ofthe penetrant molecule is extended with respect tothat in the fully amorphous or rubbery polymer.This extension is usually quantified in terms of ageometrical impedance or tortuosity factor.7

On the other side, if our hypothesis is correct, thediffusion coefficients obtained using films would dif-fer from those of the particle samples, in which theuse of the average radius should lead to apparent

DIFFUSIVITY OF ETHYLENE AND PROPYLENE IN aPP AND iPP 3873


diffusion coefficients, depending on the PSD and theparticle morphology.

Figure 1 summarizes diffusion coefficients of pro-pylene at 408C in films and particles of differentREPSOL-YPF samples. It shows that the particles asreceived from the supplier have a significantly higherdiffusion coefficient than those of the films. Thisresult confirms our original hypothesis, according towhich, this would be the consequence of using theaverage radius as characteristic dimension of the par-ticles to calculate D. The diffusion coefficient of theparticles so calculated is, in average, 50 times higherthan D of the corresponding film. Taking into accountthat the radius appears in eq. (3) as a square, thiswould imply that the effective diffusion radius isseven times smaller than the average one.

The second interesting but intriguing result in Fig-ure 1 is that the two films of iPP and the film of aPPexhibit similar diffusion coefficients. Although in thecase of the two iPP films the result could be under-stood in terms of their similar geometries and crys-tallinities, the case of aPP is certainly surprising ifwe consider the usual concepts7 about the tortuosityinduced by the crystalline regions.

In the experimental section we have described thedifficulties in performing sorption experiments withaPP at 408C. The whole sample is above its Tg and,eventually, it can flow during the gravimetric experi-ment, changing the original thickness, as a visualinspection at the end of the tests has revealed. How-ever, no special changes were observed in the sorptionprofiles of the different experiments. The thicknesschanges during the experiments do not seem to be inthe origin of the similar diffusion coefficients observedwith the iPP and aPP samples: when the aPP filmreduces its thickness during the experiment the corre-

sponding diffusion coefficient should be overestimated,leading to actual D values lower than the ones of thecrystalline samples, a result difficult to explain.

It is also true that, for the reasons explained in theexperimental part, the aPP film was thicker than theiPP films. This is important because in calculating Dusing the equations of the precedent sections, it isimplicitly assumed that the thickness dimension isnegligible with respect to the other two dimensionsof the film. When the sample is progressivelythicker, its specific surface decreases and the diffu-sion process slows. For instance, when the thicknessincreases one order of magnitude (100 mm–1 mm)the specific surface of a rectangular sample decreasesin a factor between two and three. This will be inthe origin of a D value of aPP lower than expectedand similar to the D values of the iPPs. In fact, thedifferences between the two iPPs could be caused, inpart, by the different thickness of the two samples.

The effect of the particle size (and of the averageradius used in calculating D) is more clearly evi-denced in Figure 2. Here, we are including diffusioncoefficients (at 408C) of the original particles andthose of two fractions of particles having the extremeparticle average radii of the original PSD, fromwhich they were obtained. In comparing the diffu-sion coefficients of these two fractions, the smallestparticles exhibit a lower diffusion coefficient. This isconsistent with our hypothesis. When the particlesare becoming smaller, the aggregation is less impor-tant and the average radius tends to the true diffu-sional dimension. Even in the case of these smallparticles, there are differences of about a factor of 10between the experimental D results and the valuesof the atactic PP (selected as a reference, given thesimilarities between its diffusion coefficient and

Figure 1 Diffusion coefficients of propylene (408C) in dif-ferent REPSOL-YPF samples.

Figure 2 Diffusion coefficient of propylene (408C) inREPSOL-YPF particles of different sizes.



those of the films included in Fig. 1). This wouldimply that, in the case of the smallest particles, theeffective diffusion radius is about 3 times the aver-age one. A similar situation has been found at 608C.

An interesting result, which confirms the depend-ence of the diffusion coefficient on the average radiusused in calculating D, is summarized in Figure 3. Par-ticles provided by SABIC are smaller (693 mm as aver-age diameter) than the REPSOL-YPF ones (1800 mm).Consequently, the diffusion coefficients calculatedwith these dimensions are different and smaller inthe case of the small particles. However, the diffusioncoefficients in the films prepared with these particlesare in reasonable agreement (they have similar crys-tallinity degrees). These films have D coefficientssmaller than those of their corresponding particles.

Similar results have been obtained in the case ofethylene. As an example, Figure 4 shows results at608C with the H-171-II REPSOL-YPF original particlesand the film prepared with them. A close comparisonof Figures 3 and 4 clearly shows that the differencebetween the diffusion coefficient of the particles andfilms is higher in the case of the propylene penetrant.This could be related with the different size of thepenetrant molecules and/or with the higher pro-pylene activities used in the experiments.

Finally, Table II summarizes the average diffusioncoefficients of ethylene and propylene at the threeinvestigated temperatures. These averages were cal-culated using all the investigated films.

Theoretical approach to the experimentaldiffusion coefficients

As a final conclusion of the previous section, thetrue diffusion coefficients of ethylene and propylene

through the iPP particles and films are thoseobtained using films with a well-known geometryand a measurable thickness. As an additional test ofthe validity of this conclusion, we have calculateddiffusion coefficients with the aid of one of the mod-els that has been proposed for describing diffusionof low molecular weight gases or vapors in amor-phous polymers above the glass transition.

The most successful models for describing the dif-fussional process are based on free volume conceptsin which the components of the system are envi-sioned to migrate by jumping into the free-volumeholes formed by natural thermal fluctuations. Thesebasic free-volume concepts were first proposed byCohen and Turnbull,8 modified by Fujita9 for thecase of diffusion in amorphous, rubbery polymersand refined by Vrentas and Duda10,11 for both selfand mutual diffusion in polymer-solvent systems.

According to Vrentas and Duda the diffusion of apenetrant will depend on the probability to create ahole sufficiently big near of the penetrant moleculeand on the probability that this molecule gets energyenough to jump into the hole. The basic assumptionsmade in that model:

Figure 3 Diffusion coefficient of propylene (608C) inREPSOL-YPF and SABIC particles and in the films pre-pared with them.

Figure 4 Diffusion coefficient of ethylene (608C) inREPSOL-YPF particles and in the films prepared withthem. Note that with this penetrant pressure goes up to 20bars.

TABLE IIAverage Values of Propylene and Ethylene Diffusion

Coefficients at the Three Investigated Temperatures. Allthe Samples were Tested in the Film Morphology

D40 � 107

(cm2/s)D60 � 107

(cm2/s)D80 � 107

(cm2s)

Propylene 0.9 (60.2) 1.8 (61.0) 3.5 (61.1)Ethylene 2.9 (61.0) 3.0 (61.0) 6.7 (62.1)



• Thermal expansion coefficients necessary to cal-culate different volumes are considered not tochange in the temperature range of work.

• The partial specific volumes of the solvent andpolymer are considered to remain constant atdifferent concentrations.

• The chemical potential of the solvent is calculatedby the Flory–Huggins equation, where the poly-mer/solvent interaction parameter will be constantat different concentrations and temperatures.

The original formulation has had several modifica-tions to be adapted to different systems.12,13

Although, the original model is not totally predic-tive, the authors have recently proposed14 the possi-bility of obtaining all the parameters without usingexperimental data of diffusion coefficients.

In this theory the self-diffusion coefficient for thesolvent is calculated as:

D1 ¼ D0 exp�E�

RT

� �exp

�ðw1V̂�1 þ xw2V̂�

2ÞV̂FH=g

!(5)

where D0 is a preexponential factor, E* the activationenergy required for a molecule to overcome theattractive forces holding it to its neighbors, V̂�

i is thecritical local hole free volume required for a i unit tojump, wi is the weight fraction of i component, and gis an overlap factor (between 1/2 and 1) introducedto correct for overlapping free volume. The x param-eter is the ratio of polymer and solvent molar jump-ing units, defined by the following equation:

x ¼ V̂01ð0ÞV̂�

2j

¼ Mj1V̂�1

Mj2V̂�2

(6)

where Mji is the molecular weight of a jumping unitof component i.

Finally, V̂FH is the critical free volume of the sys-tem and is calculated by:

V̂FH

g¼ w1

k11g1

ðk21 � Tg1 þ TÞ þ w2k12g2

ðk22 � Tg2 þ TÞ(7)

where k1i and k2i are free volume parameters, withdimensions of temperature, that can be calculatedusing viscosity-temperature data of the componentand the Vogel empirical equation adapted to theVrentas and Duda nomenclature.15

The critical volumes V̂�i can be estimated from

group contribution correlations. D0,k11g , and k21 � Tg1

can be determined by correlating viscosity and spe-cific volumes of the penetrant at different tempera-tures. k21

g and k22 � Tg2 can be adjusted using viscos-ity-temperature data of the polymer.

Using the Flory–Huggins theory, the self diffusioncoefficient of the solvent (D1) can be related to the

binary mutual diffusion coefficient (D) as:

D ¼ D1ð1� f1Þ2ð1� 2wf1Þ (8)

where w is the Flory–Huggins interaction parameterthat accounts for the influence of the polymer/penetrant interactions in the diffusion process. f1 isthe penetrant volume fraction. These data are acces-sible from our sorption experiments given that M1in eq. (1) is the equilibrium penetrant mass absorbedin the polymer mass originally hanged in the bal-ance. With these two masses and the densities of thepolymer and the penetrant, f1 can be easily calcu-lated. In the case of the polymer, we have used thedensity of the amorphous polymer16 assuming thatonly these regions are available to the penetrant.

The interaction parameter, w, can be calculatedwith the aid of the Flory–Huggins expression:

ln a1 ¼ ln f1ð1� f1Þ þ wð1� f1Þ2 (9)

where the activity of the penetrant is calculated by,

a1 ¼ p1

p01(10)

using the vapor pressure of the pure penetrant atthe experimental temperature and the vapor pres-sure of the penetrant in equilibrium with the solu-tion obtained during the gravimetric sorptions.

Consequently, the parameters we need for calcu-lating D1 are: D0, E*, V̂

�i , x, k11/g, k21, Tg1, k21/g, k22,

and Tg2. Fortunately, the majority of these parame-ters have been reported in different papers of theauthors of the model and are resumed in the follow-ing Tables III and IV. The critical volumes V̂�

i can beestimated from group contribution correlations. xhas been calculated using eq. (6) and a correlationgiven by Hong17 for calculating V̂�

2j in amorphouspolymers above the glass transition temperature:

V̂�2jðcm3=molÞ ¼ 0:0925� Tg2ðKÞ þ 69:47 (11)

Using for Tg2ðKÞ a value of 253, as resumed in Ta-ble I, V̂�

2j ¼ 92.87 and the corresponding values for xare:

xðPP=propyleneÞ¼0:554xðPP=ethyleneÞ¼0:404

Figure 5 summarizes experimental results ofFlory–Huggins interaction parameters of propylene

TABLE IIIFree-Volume Parameters for Atactic Polypropylene as

given by Vrentas and Duda11

V̂�2ðcm3=gÞ K12=gð Þ �104ðcm3=gKÞ K22–Tg2 (K) Tg2 (K)

1.005 5.02 �205 253



and ethylene at 408C in aPP, an additional parameternecessary for the model calculations. In the propyl-ene case, an average value of 0.55 seems representa-tive. However, in the next paragraphs, we will showthat, in the concentration range we are involved, thevalue of the interaction parameter is irrelevant in thecalculation of the D coefficient.

Consequently the only adjustable parameter is E*.To adjust its value, Figure 6 contains experimentaldata of different aPP films at 303 and 310 K as wellas the best fitting using an E* value of 3800 cal/mol.This value is not very different from the 3210 valueused by Palamara.18

Using all the required parameters, the self-diffu-sion coefficient D1 can be calculated using eq. (5).With these values, using eq. (8) and the interactionparameters calculated from solubility data, the mu-tual binary diffusion coefficient can be estimated asa function of the weight fraction of the penetrant inthe polymer. This weight fraction has been calcu-lated on an amorphous basis.

Figure 7 shows the results of this type of calculationfor propylene. As expected, according to eq. (8), bothcoefficients (D1 and D) are similar at low penetrantconcentrations, whereas at higher concentration, theterm containing the interaction parameter in this equa-tion has a more pronounced effect in its evolutionwith the penetrant concentration. Given the limitedsolubilities of the two penetrants, our experimental

results are in a restricted interval of concentrationswhere the value of the interaction does not affect thecalculation of the mutual binary diffusion coefficients.

Figure 8 contains a comparison between experi-mental and calculated diffusion coefficients of pro-pylene in polypropylene at 333 K. In this figure, theexperimental data correspond to the two differentiPP samples provided by Repsol.

Diffusion coefficients of ethylene in polypropylenehave been similarly reproduced (Fig. 9) with an E*value of 2300 cal/mol and without considering theeffect of the term containing the interaction parame-ter, given that the concentration of the penetrant iseven lower than in the case of propylene.

CONCLUSIONS

Gravimetric sorption experiments are reliable, rela-tively nontime consuming methods for a simultane-ous determination of the solubility and the diffusiv-ity of gases and vapors in polymers. In this article,gravimetric experiments have been used to study thediffusivities of ethylene and propylene monomersthrough previously prepared particles of iPP.

However, in calculating diffusion coefficientsusing this technique with iPP particles, the averageparticle radius of the polymer is not the correctdiffusional dimension. The bigger is the particle, the

TABLE IVFree-Volume Parameters for Propylene and Ethylene as given by Palamara16

V̂�1ðcm3=gÞ K11=gð Þ �103ðcm3=gKÞ K21–Tg1 (K) D0 (cm

2/s)

Propylene 1.225 2.91 �8.657 7.65 � 10�2

Ethylene 1.341 1.97 42.38 2.96 � 10�3

Figure 5 Flory–Huggins interaction parameters at 408 forethylene and propylene in atactic polypropylene.

Figure 6 Adjusting the E* parameter (3800 cal/mol) usingexperimental propylene D data through atactic PP at twotemperatures.



higher is the apparent diffusion coefficient. Thisseems to be a consequence of the multi-grain struc-ture of the particles. Effective diffusion radius ofthese particles can only be calculated after knowingthe diffusion coefficient obtained with films of well-characterized thickness. Using this morphology, sim-ilar diffusion coefficients are obtained with samplesprovided by two different suppliers.

Diffusion coefficients can be reasonably repro-duced with the aid of the Vrentas-Duda model.Although the model requires an important numberof parameters they are known in the case of the sys-tems considered in this article.

The experimental and theoretical results here sum-marized may be of interest in understanding theprocesses involved in the preparation of HighImpact Poly (propylene) (HIPP) particles.

This work has been supported by the POLYPROP project(GROWTH GSRD-CT-2001-00,597).

References

1. Karian H. G., Ed. Handbook of Polypropylene and Polypro-pylene Composites; Marcel Dekker: New York, 1999.

2. Urdampilleta, I.; Gonzalez, A.; Iruin, J. J.; de la Cal, J. C.;Asua, J. M. Macromolecules 2005, 38, 2795.

3. Floyd, S.; Choi, K. Y.; Taylor, T. W.; Ray, W. H. J Appl PolymSci 1986, 32, 2935.

4. Vrentas, J. S.; Duda, J. L.; Ling, C. J Polym Sci Polym Phys Ed1985, 23, 275.

5. Etxeberria, A.; Garcia, A.; Iriarte, M.; Iruin, J. J.; Uriarte, C. JAppl Polym Sci 2006, 102, 2034.

6. Crank, J. The Mathematics of Diffusion, 2nd ed.; ClarendonPress; Oxford, 1975.

7. Michaels, A. S.; Bixler, H. J.; Fein, H. L. J Appl Phys 1964, 35,3165.

8. Cohen, M. H.; Turbull, D. J Chem Phys 1959, 31, 1164.9. Fujita, H. Fortschr Hochpolym Forsch 1961, 3, 1.10. Vrentas, J. S.; Duda J. L. J Polym Sci Polym Phys Ed 1977, 15,

403.11. Vrentas, J. S.; Duda J. L. J Polym Sci Polym Phys Ed 1977, 15,

417.12. Vrentas, J. S.; Vrentas, C. M. Macromolecules 1994, 27, 5570.13. Vrentas, J. S.; Vrentas, C. M. Macromolecules 1996, 29, 4391.14. Zielinski, J. M.; Duda, J. L. AIChE J 1992, 38, 405.15. Hong, S. U. Ind Eng Chem Res 1997, 36, 501.16. Sato, Y.; Iketani, T.; Takishima, S.; Masuoko, H. Polym Eng Sci

2000, 40, 1369.17. Hong, S. U. J Appl Polym Sci 1996, 61, 833.18. Palamara, J. E. Ph.D. Dissertation, PennState University, Au-

gust, 2003.

Figure 7 The self and the mutual binary diffusion coeffi-cients at 310 K as a function of the weight fraction of pro-pylene in atactic polypropylene.

Figure 8 Experimental and calculated (Vrentas-Dudamodel) diffusion coefficients of propylene in isotactic poly-propylene at 608C.

Figure 9 Experimental and calculated (Vrentas-Dudamodel) diffusion coefficients of ethylene in isotactic poly-propylene at 608C.



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Diffusivity of ethylene and propylene in atactic and isotactic polypropylene: Morphology effects and free-volume simulations