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Eur. Polym. J. Vol. 34, No. 10, pp. 1405±1413, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0014-3057/98 $ - see front matter S0014-3057(97)00285-1

CARBON DIOXIDE TRANSPORT PROPERTIES OF COMPOSITE MEMBRANES OF A POLYETHERIMIDE AND A LIQUID CRYSTAL POLYMER C. URIARTE,* J. ALFAGEME and J. J. IRUIN Departamento de Ciencia y Tecnologia de Polimeros, Facultad de Quimica, Universidad del Pais Vasco, P.O. Box 1072, 20080 San Sebastian, Spain (Received 8 July 1997; accepted in ®nal form 23 July 1997) AbstractÐThe e€ect of the addition of a liquid crystal polymer (Rodrun) on the gas sorption and transport properties of a polyetherimide (PEI, Ultem 1000) was investigated. CO2 permeation and sorption measurements were made with ®lms of PEI, Rodrun and heterogeneous PEI/Rodrun blends at di€erent pressures and temperatures. In all cases, permeability, di€usion and sorption coecients decreased when the amount of Rodrun increased. A good agreement was found when permeability data obtained using both a permeability cell and a Cahn electrobalance were compared. Permeabilities of the binary composite material were calculated on the basis of those of the pure components and some theoretical assumptions concerning blend morphology. Results were consistent with a Rodrun structure in the composite intermediate between a ®brillar and a laminar morphology, as electron microscopy evidenced experimentally. # 1998 Elsevier Science Ltd. All rights reserved

INTRODUCTION

The transport of a permanent gas through a dense, nonporous glassy polymeric membrane can be basically described in terms of a ``solution±di€usion'' mechanism. The gas is sorbed at the entering face, dissolving there, with equilibrium rapidly being established between the two faces. The dissolved penetrant molecules then di€use through the membrane, desorbing at the exit face. According to this mechanism, gas permeation is a complex process controlled by both di€usion and solution of the penetrant gas molecules in the membrane matrix. At the steady state and when di€usion coecient is independent of the penetrant concentration, permeability coecient of amorphous polymers can be written as the product of the e€ective di€usion, D, and solubility, S, coecients. PˆDS

…1†

Solubility is a thermodynamic parameter and gives a measure of the amount of penetrant sorbed by the membrane under equilibrium conditions. In contrast, the di€usivity is a kinetic parameter which indicates how fast a penetrant is transported through the membrane. These properties are sensitive to changes in membrane structure which, at its turn, can provide the adequate keys to develop new polymeric membranes mainly based on glassy polymers. Among these changes in structure, changes in crystallinity [1], degree of crosslinking [2±4], the use of additives [5], other variations of polymer morphology [6], preparation of ``composite'' membranes [7] or poly*To whom all correspondence should be addressed.

mer blends [8] can be used to modify the transport properties of a selected membrane. For instance, it has been found that orientation and crystallization of polymers generally improve the barrier properties of the material as a result of the increased packing eciency of the polymer chains. Liquid crystal polymers (LCP) have a unique morphology with a high degree of molecular order. These relatively new materials have been found to exhibit excellent barrier properties. To the date, few reports of investigations on the gas transport properties of main chain liquid crystalline polymers have appeared. Chiou and Paul [9] have brie¯y described the transport properties of an extruded ®lm of an LCP having a similar structure to the commercial product denoted as Vectra. More recently, permeation properties for some gases through laminated side-chain LC polymer-based membranes were measured using a gas-chromatographic method [10]. Finally, Weinkauf and Paul [11±15] have studied gas transport properties of thermotropic liquid-crystalline copolyesters and liquid crystalline poly(p-phenyleneterephthalamide). Among polyimides, polyetherimide (PEI) is a high-performance thermoplastic which has been investigated by several authors. Besides transport properties [6, 16±18], its miscibility with other polymers [19±21] has been studied as well as the improvement of mechanical properties when it is used in ``in situ'' composites with liquid crystalline polymers [22±30]. The dimensional order exhibited by the nematic LCP melts supposes a low viscosity in the melt allowing the use of these materials as potential processing aids. But, in the subsequent solidi®cation, the liquid crystal ®brillar morphology improves the modulus of elasticity, the tensile

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strength and the dimensional stability. Finally, the LCP's morphology gives excellent barrier properties that could improve the transport properties of a second polymer when they are mixed together. All these characteristics seem to be well established in spite of one of the more relevant features of these composites: the immiscibility between the blend components. In this paper and to further investigate the question of polymer structure±permeability relationships, the sorption and transport properties of a polyetherimide (PEI), commercially known as Ultem-1000, have been measured in order to see the changes induced by the addition of small quantities of a liquid crystal polymer (Rodrun). This study has been carried out using carbon dioxide and two di€erent experimental techniques. Permeability data in the steady state have been obtained using a Linde cell. We have also determined CO2 solubility, di€usion and permeability coecients from sorption measurements using a electromicrobalance. Results obtained using both techniques have been compared. Finally, the paper also includes an analysis of the transport properties of the mixtures using an approach which takes into account the relationship between the permeability of binary composite polymeric materials and their heterogeneous morphologies. EXPERIMENTAL

Materials The polyetherimide ULTEM-1000 was supplied by General Electric. Its molecular weight was 20,000. The liquid crystal polymer RODRUN LC-5000 is a random copolyester of ethylene terephthalate and p-hydroxybenzoic acid in a 18/82 molar composition, as determined by 1 H-NMR2 [31]. It was provided by UNITIKA, Tokyo, Japan. PEI and PEI/Rodrun ®lms were extruded in a Brabender extruder. Materials were mixed at 3308C with a static mixer composed of ®ve Kenics elements. The die temperature was 3708C. Drawing of the extruder ribbon was carried out in the melt state by means of an Axon three roll drawing unit. The average thickness of the membrane samples used for the permeability and sorption measurements was 50 mm, determined with a Duo-Check ST-10 apparatus with a thickness variation of 21 mm. The same samples were used for each set of measurements. In the case of the Rodrun, it was impossible to prepare ®lms with adequate diameter size for permeability cell experiments. Smaller ®lms for sorption measurements were obtained by compression molding in a Schwabenthan press, Polystat 200T model, with a maximum temperature of 3008C. A description of the ®lms used in this study is given in Table 1. CO2 was provided by SEO (Sociedad EspanÄola de Oxigeno) and was stated to have a minimum purity of 99.9%. It was used without further puri®cation.

Apparatus and procedure The phase behavior of the mixtures was characterized by di€erential scanning calorimetry (DSC). A PerkinElmer DSC-7 calorimeter was used at a heating rate of 208C/min in a nitrogen atmosphere. Two scans were carried out from 50 to 3208C. Cooling between scans was carried out at the maximum speed available for the calorimeter. The thermal transitions of the blends were

Table 1. Description of the ®lms used in this study Film

Thickness (mm)

PEI PEI/Rodrun 95/5 (w/w) PEI/Rodrun 90/10 (w/w) PEI/Rodrun 85/15 (w/w) Rodrun

50 50 50 49 103

Density (g/cm3) 1.270 1.276 1.283 1.289 1.410

determined in the usual way, using the second calorimetric scan. The fracture surfaces of some blend samples were examined, after gold coating, using a scanning electron microscope (SEM, Hitachi S2700), operated at 15 kV. The permeability measurements were based on the variable-volume method. The design and operation of the permeability equipment used in this work have been described in detail elsewhere [32, 33]. The Permeability Cell CS-135, from Custom Scienti®c Instruments Inc., was immersed in a constant-temperature bath maintained to within 20.18C. The permeated gas was allowed to expand on the low-pressure side of the membrane into a precision capillary containing a short column of colored methyl isobutyl ketone. The permeation ¯ux was measured by monitoring the displacement of the column as a function of time by means of a cathetometer. Permeability is reported herein in Barrer (10ÿ10cm3 (STP)cm/(cm2scmHg)). The permeability of PEI and PEI/Rodrum mixtures to CO2 was measured. The data presented in this work cover a temperature range from 25 to 508C and a pressure range from 0.5 to 4.5 atm. CO2 sorption±desorption measurements in PEI, Rodrun and PEI/Rodrun mixtures were determined using integral gravimetric sorption experiments performed on a Cahn D200 electrobalance enclosed in a constant temperature chamber. The sorption system was serviced by a high vacuum line for sample degassing and penetrant removal. The ®lm under study was conditioned at 1208C in a vacuum oven for 24 h. After this process, the ®lm was maintained at 608C in a vacuum oven for a week, then suspended in the glass chamber of the electrobalance and exposed to vacuum again for at least 24 h to remove air gases. CO2 was then introduced into the chamber at a ®xed pressure and temperature, the subsequent increase in sample weight being recorded as a function of time. When the sample attained equilibrium saturation, no more weight gain was observed. Then the sample was totally degassed and a new pressure of CO2 was introduced in the chamber to do a new experiment. The sorption experiments cover a pressure range from 0 to 1 atm and a temperature range from 30 to 508C.

Computations The equilibrium concentration, C0, of a penetrant gas dissolved in a polymer is given by the equation: C0 ˆ

22141  m Mgas  Vpol

…2†

where m is the penetrant equilibrium mass in mg, Mgas the penetrant molecular mass and Vpol the polymer volume in cm3. The equilibrium concentration can be related to the pressure of the penetrant, p, by the isothermal relation [34] C0 ˆ p  S

…3†

where S is the solubility coecient. When the concentration of the penetrant in the polymer is very low, equation (3) reduces to the form of the Henry's law; the solubility coecient is then independent of pressure. Substituting Equation (3) into Fick's ®rst law J = ÿ D dc/dx and integrating across the membrane leads to:

Polyetherimide/liquid crystal polymer composite membranes Jˆ

SD P … p1 ÿ p2 † ˆ … p1 ÿ p2 † l l

…4†

p1 being the pressure on the feed side, p2 the pressure on the permeate side and l the membrane thickness. In the permeability cell experiments and when steady state is established, the permeability coecient determination is immediate. Using sorption±desorption experiments and if the concentrations just within the surfaces of a plane sheet are maintained constant, the amount of di€usant, Mt, taken up by the sheet in a time, t, is given by the equation [35, 36]:   1 Mt 8X 1 D…2n ‡ 1†2  p2  t ˆ1ÿ 2 exp ÿ …5† p nˆ0 …2n ‡ 1†2 l2 M1 where Mt is the absorbed mass at t time, M1 the total absorbed mass at equilibrium, l the ®lm thickness and D the di€usion coecient (cm2/s). For long times, Equation (5) may be approximated by:   Mt 8 D  p2  t …6† ˆ 1 ÿ 2 exp ÿ 2 p l M1 and D can be calculated from an adequate plot of sorption data.

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sition temperature was detected. This slight decrease in the Tg of the PEI phase in the composites could indicate some degree of miscibility of the LCP and PEI. However, such a decrease could also be attributed [23] to a more active movement of the LCP chains in the blends. Since calorimetric measurements can not clearly prove the miscibility or immiscibility of the mixtures, the morphology of the extruded ®lms were analyzed by EM at the fracture surfaces of tensile specimens with the testing direction parallel to the processing direction. Figure 2 show selected photomicrographs obtained from PEI/Rodrun ®lms. As can be observed, the ®brillar structures characteristic of oriented LCP's are present showing a high aspect ratio near the surfaces of the ®lm. The adhesion level seems to be fairly low as the particle surfaces appeared clean and regular. This is consistent with a nearly full immiscibility of both blend components. When the percentage of Rodrun increases in the mixture, the ®brils come together forming lamellae that are immersed in the holes of the polymer matrix (PEI), as it can be seen in the micrograph of the 85/15 PEI/Rodrun ®lm. Transport properties

RESULTS AND DISCUSSION

Films characterization Di€erential scanning calorimetry (DSC) thermograms of PEI, Rodrun and PEI/Rodrun ®lms are shown in Fig. 1. Pure PEI shows a glass transition temperature at 2198C and Rodrun only exhibits a melting point detected at 2678C. DSC is not sensitive to observe the glass transition of the Rodrun. In analyzing the di€erent compositions of the mixture, only a small decreasing of the PEI glass tran-

As we have mentioned above, the permeability of a polymer depends on both di€usion and solubility characteristics. The main parameter that determines the solubility of a gas is its ease of condensation, with molecules becoming more condensable with increasing diameter. Gas solubility in polymers generally increases with increasing gas condensability [37]. The critical temperature, Tc, is a measure of the ease of condensation. Because of this and in most polymers, CO2 (Tc=318C) is more soluble than other permanent gases such as O2

Fig. 1. DSC thermograms of di€erent ®lms: (A) PEI (Tg=2198C); (B) 5/95 Rodrun/PEI (Tg=214.38C); (C) 10/90 Rodrun/PEI (Tg=214.48C); (D) 15/85 Rodrun/PEI (Tg=2168C); (E) Rodrun (TM=267.28C).

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Fig. 2. SEM photomicrographs of fractured surfaces of Rodrun/PEI ®lms of di€erent compositions: (A) 5/95 Rodrun/PEI; (B) 10/90 Rodrun/PEI; (C) 15/85 Rodrun/PEI.

Polyetherimide/liquid crystal polymer composite membranes

Fig. 3. CO2 permeability coecients at 308C as a function of pressure for the di€erent ®lms: (.) PEI; (q) 5/95 Rodrun/PEI; (R) 10/90 Rodrun/PEI; (w) 15/85 Rodrun/ PEI.

(Tc= ÿ 118.48C) and N2 (Tc= ÿ 1478C) [35]. Typically, CO2 is used as a probe of gas-induced plasticization since CO2 is often the most soluble gas examined in a gas transport study, and the propensity of a penetrant to plasticize a polymer increases as the amount of penetrant dissolved in the polymer increases [38]. This is a consequence of the interactions between CO2 and most of the polymers. Figure 3 shows the CO2 experimental permeability coecients as determined by the permeability cell at 308C in ®lms of PEI and its mixtures with Rodrun. CO2 permeability decreases monotonically with increasing pressure as predicted by the dual model [39]. Barbari et al. [16] have obtained PEI permeability data using a manometric method. If we compare their values obtained for CO2 at 358C with our values at the same temperature the agreement is excellent. Figure 3 also shows that permeability decreases when the amount of Rodrun in the mixture increases. This can be explained in terms of the e€ects of the LCP addition on the two processes involved in the permeation. The addition of a LCP like Rodrun to PEI generates the creation of ®brillarlike structures of the nematic mesophase into the matrix of the polymer as a consequence of the increased elongation during processing. This ordered microstructure of the nematic mesophase acts as crystalline regions in semicrystalline polymers that typically preclude penetrant solubility. On the other side, impermeable ``crystallites'' act to increase the tortuosity of the path taken by penetrant molecules through a polymer. Moreover, gas di€usion in polymers depends on a complex relation between chain mobility and free volume and is typically understood to be limited by the polymer segment motion which results in the formation of a hole of sucient size to accommodate a penetrant molecule. This process is hindered, however, by a decrease in polymer chain mobility in the amorphous regions of the polymer motivated by the presence of the LCP nematic regions. If both solubility and di€usion are restricted by the presence of the LCP, permeability will decrease when LCP content increases.

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Fig. 4. CO2 sorption isotherms for PEI at di€erent temperatures: (.) 308C; (q) 358C; (R) 408C; (w) 458C; (Q) 508C.

In gravimetric sorption experiments at di€erent pressures and temperatures both solubility and diffusion coecients were evaluated. Sorption and diffusion isotherms for gases in glassy polymers are typically concave to pressure axis at low pressures as it can be seen, for example, in Figs 4 and 5 for pure PEI. Similar isotherms were obtained with Rodrun and PEI/Rodrun blends. In these Figs., the dependence on temperature of both PEI coecients at constant pressure can be also observed. This dependence is also observed in mixtures which result of the addition of small quantities of Rodrun to PEI. As an example, in Fig. 6, the opposite dependence of the solubility and di€usion coecients on temperature is illustrated for pure PEI and for the PEI/Rodrun 5% mixture. In this Fig., the in¯uence of the addition of Rodrun in the solubility and di€usion coecients is also clear. Following a similar behavior to that described in the permeability experiments, the solubility and the di€usion coecients decreased when the amount of Rodrun in the ®lms increased, a consistent result with the direct observations of the permeability coecient. The di€usion of small penetrant molecules in polymers is a thermally activated process that follows an Arrhenius relationship, and di€usion coe-

Fig. 5. CO2 di€usion coecients as a function of pressure for PEI at di€erent temperatures: (.) 308C; (q) 358C; (R) 408C; (w) 458C; (Q) 508C.

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Fig. 6. Temperature dependence of the CO2 sorption parameter at 1 atm in di€erent ®lms: (w) PEI; (q) 5/95 Rodrun/PEI. And temperature dependence of the CO2 diffusion parameter at 1 atm in di€erent ®lms: (.) PEI; (Q) 5/95 Rodrun/PEI.

cient is, therefore, expressed as [39]   ED D ˆ D0 exp ÿ RT

…7†

where ED is the activation energy of di€usion and D0 is a constant. The gas di€usion coecients increase appreciably with increasing temperature. From Equation (7) and the slope of ®gures such as Fig. 6 the activation energy for di€usion was calculated in each case, as can be seen in Table 2 for pure PEI, Rodrun and PEI/Rodrun ®lms. The solubility dependence on temperature in polymers is typically written in terms of the van't Ho€ relationship:   DHs S ˆ S0 exp ÿ …8† RT where S0 is a constant and DHs is the partial molar enthalpy of sorption. The dissolution of a penetrant molecule into a polymer can be expressed as a twostep thermodynamic process: the condensation of the gaseous penetrant to a condensed density, and the formation of a molecular hole in the polymer of sucient size to accommodate the penetrant molecule [40]. As a result, the enthalpy of sorption can be written as DHs ˆ DHcondensation ‡ DHmixing

…9†

where DHcondensation and DHmixing are the enthalpy changes associated with the ®rst and second thermodynamic processes, respectively. For permanent gases such as N2, DHcondensation is very small and interactions between polymers and these permanent gases tend to be weak. Therefore, DHs is governed by DHmixing and since DHmixing is positive, penetrant solubility increases with increasing temperature. For

more condensable gases, such as CO2, DHs may be negative due to the large contribution of DHcondensation to DHs, and the solubility, in turn, decreases with increasing temperature. This behavior is observed for the CO2 and our membranes in Fig. 6 and as it could be expected, a negative DHs was obtained from the slope (Table 2). Combining Equations (7) and (8), the temperature dependence of the permeation coecient can be expressed as     ED ‡ DHs Ep P ˆ …D0  S0 †exp ÿ ˆ P0 exp ÿ RT RT …10† where P0 is a constant, equal to S0D0, and Ep is the activation energy of permeation, which is equal to the algebraic sum of ED and DHs. From Equation (10) we have calculated the activation energy for the permeation process (Table 2). Given that the di€usivity is generally a stronger function of temperature than the solubility coecient, the gas permeability usually increases with temperature. CO2 permeability coecients, at 1 atm and di€erent temperatures, calculated from Equation (1) as the product of di€usion and sorption coecients and obtained from sorption measurements for pure PEI and Rodrun and for PEI/Rodrun ®lms, are summarized in Table 3. This Table 3 also includes PEI permeability data obtained using the permeability cell at 1 atm and di€erent temperatures. As it can be seen, the agreement between the techniques is reasonable if we take into consideration the di€erent conditions involved in these experiments. While in sorption experiments both sides of the membrane are subjected to the same penetrant pressure, conditions are completely di€erent in permeation experiments. Furthermore, the data also agree with the PEI values obtained by other authors [10] as we have mentioned above. A similar agreement is observed in Table 4 where we compare data at the same temperature and pressure (308C and 1 atm) but di€erent compositions. The permeability data at 1 atm from permeation measurements were calculated from plots of permeability vs pressure. Permeability and morphology: two-phases model One of the problems in studying the transport properties of composite polymeric materials is the diculty in predicting such properties. Several approaches leading to what are the best partial solutions of the problem have been developed in various ®elds. Most of the equations which have been applied to permeability are included in a review by Barrer [41]. The so-called two phase model attempts

Table 2. Activation energies of di€usion and permeation and the partial molar enthalpy of sorption for the di€erent ®lms to the CO2 at 1 atm Film PEI PEI/Rodrun 95/5 (w/w) PEI/Rodrun 90/10 (w/w) PEI/Rodrun 85/15 (w/w) Rodrun

ED (kJ/mol)

DHS (kJ/mol)

EP (kJ/mol)

24.87 27.35 26.67 27.35 44.85

ÿ17.07 ÿ23.07 ÿ23.22 ÿ23.12 ÿ16.56

7.80 4.28 3.45 4.23 28.29

Polyetherimide/liquid crystal polymer composite membranes

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Table 3. Permeability to CO2 at 1 atm and di€erent temperatures determined by sorptiona and permeabilityb methods P(308C) (Barrer)

Film a

1.717 1.425 1.178 0.789 0.016 1.56

PEI PEI/Rodruna 95/5 PEI/Rodruna 90/10 PEI/Rodruna 85/15 Rodruna PEIb

P(358C) (Barrer) 1.886 1.463 1.232 0.815 0.019 1.65

1.995 1.519 1.253 0.848 0.022 1.75

to predict the permeability coecient of composite polymeric membranes on the basis of the permeabilities of the components and the morphology of the membrane [42]. In this approach, membranes are considered to be composed by distinct domains of non-interacting components A and B, usually of microscopic size, but characterized by permeability coecients PA and PB not appreciably di€erent from those of the corresponding bulk phases. The problem is to determine the dependence of the composite permeability, P, on the pure components permeabilities (PA and PB are assumed to be independent of the concentration of the permeant), the composition (expressed in terms of the volume fractions, vA and vB=1 ÿ vA), and the structural characteristics of the composite medium. The simplest composite medium structures are those giving rise to strictly unidimensional permeation ¯ow, as is the case of a laminate of A and B oriented so that the lamination is parallel or normal to the direction of ¯ow. In the former case, the expression is the arithmetic mean permeability, P ˆ PA vA ‡ PB vB

…11†

whereas the armonic mean permeability is adequate for the latter case, 1 vA vB ˆ ‡ P PA PB

…12†

Other types of more complex structures require a di€erent treatment. Most approaches developed for this purpose suppose a system of a microparticulate dispersion of one component (A) in a continuous matrix of the other (B). In this case, the dispersed phase can be de®ned in terms of particle shape, size, orientation, and mode of packing [41, 43, 44]. Most of the developed equations are referred to dispersions of spheres or long cylindrical rods. De®ning the relation between the permeabilities of the same penetrant in both components, a, as, aˆ

PA PB

P(408C) (Barrer)

P(458C) (Barrer) 20.86 1.543 1.271 0.859 0.029 1.89

P(508C) (Barrer) 2.112 1.583 1.289 0.875 ÿ 1.96

cases. In this way, for a dilute dispersion of spheres, in which interparticle distances are suciently large to ensure that the ¯ow around any sphere is practically undisturbed by the presence of the others, the following relation, ®rst derived by Maxwell [41, 43], describes the permeability of the composite,   ÿ1  a‡2 ÿ vA …14† P ˆ PB 1 ‡ 3vA aÿ1 On the other hand, in the case of long cylinders oriented at right angles to the direction of the ¯ow, a similar expression has been developed. All these equations can be included in a more general relation [43, 44],   ÿ1  a‡A P ˆ PB 1 ‡ …1 ‡ A†vA ÿ vA …15† aÿ1 where A is a parameter which describes di€erent morphologies depending on its value. When A 4 1 or A = 0 Equation (15) leads to Equation (11) or Equation (12) respectively; if A = 2 yields the Maxwell equation for spheres (Equation (14)) and, ®nally, when A = 1, Equation (15) describes the case of long transverse cylinders,   ÿ1  a‡1 P ˆ PB 1 ‡ 2vA ÿ vA …16† aÿ1 In the case of eciently packed particles of appropriate shape, the proposed expression is, ÿ1 P ˆ PB ‰1 ‡ …vÿ1 ‡ vÿ1=2 ÿ 1†ÿ1 Š A …a ÿ 1† A

…17†

…13†

it is possible to obtain simple expressions for these Table 4. Comparison of permeabilities to CO2 (in Barrers) of the di€erent ®lms at 1 atm and 308C obtained using sorption and permeation techniques Film PEI PEI 95%-Rodrun 5% PEI 90%-Rodrun 10% PEI 85%-Rodrun 15%

P (sorption) 1.717 1.425 1.178 0.789

P (permeation) 1.56 1.30 0.95 0.53

Fig. 7. Permeability vs composition plots calculated from equation (15) with di€erent values of A parameter: (1) A = 1; (2) A = 1; (3) A = 0.16; (4) A = 0. Figure also includes permeability average data from sorption and permeation experiments of pure PEI and PEI/Rodrun ®lms (.).

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which in the case that a = 0, it yields simply, P ˆ PB …1 ÿ

v1=2 A †

…18†

These last two equations might be applicable at still higher vA. Figure 7 shows permeabilities of pure PEI and PEI/Rodrun ®lms from sorption and permeation experiments as well as theoretical simulations using Equation (15) with di€erent values of A parameter. None of the simpli®ed models (A = 0 which describes a composite laminated perpendicular to the direction of the ¯ow or A = 1 which corresponds to a composite with ®brillar morphology or A 4 1) is adequate to describe the observed experimental behavior. The deviation in the permeability coecient for the ®lm with a 15% of Rodrun is even more marked. As EM photomicrographs have demonstrated, whereas the ®lms with a 5% and a 10% of Rodrun showed a ®brillar structure, the ®lm with a 15% of Rodrun is basically laminate. Then, our ®lm structure is a mixture between ®bers and lamination and the proportion of lamination increase with the Rodrun amount in the mixture. That could be the reason why our experimental data do not ®t the equations properly. However, we could ®t our experimental data to an expression based on Equation (15), varying A between 0 and 1, which are the limiting values which describe the morphologies of our system. The best ®t is achieved with an A value of 0.16, although it should be taken into account that the morphology varies with the composition of the mixture and it is dicult to explain the meaning of a single parameter for all the investigated samples. Nevertheless, it provides a useful point of reference. In conclusion, the above analysis appears to be useful, at least for practical purposes, for this kind of immiscible materials forming composite membranes. If we know the morphology of the samples it is possible to predict the permeability coecient at di€erent compositions. Conversely, from experimental data of transport properties it is possible to extract some previous conclusions about membrane morphology. AcknowledgementsÐThis work has been supported by the CICYT (Project number MAT 92-0826) and the University of the Basque Country (Project number 203.215-EB173/95). J. A. also thanks the Spanish Ministerio de EducacioÂn (MEC) for the Ph.D. grant supporting this work. REFERENCES

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carbon dioxide transport properties of composite ...

Vasco, P.O. Box 1072, 20080 San Sebastian, Spain. (Received 8 July 1997; .... using a scanning electron micro- scope (SEM, Hitachi S2700), operated at 15 kV.

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