Copolyimides Containing Alicyclic and FluorinatedGroups: Solubility and Gas Separation Properties

CORINE BAS,1 REGIS MERCIER,2 JOSE SANCHEZ-MARCANO,3 SYLVIE NEYERTZ,1

N. DOMINIQUE ALBEROLA,1 ELIETTE PINEL1,2

1Laboratoire Materiaux Organiques a Proprietes Specifiques (LMOPS), UMR 5041, Universite de Savoie,Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France

2Laboratoire Materiaux Organiques a Proprietes Specifiques (LMOPS), UMR 5041, Universite de Savoie,BP 24, 69390 Vernaison, France

3Institut Europeen des Membranes (IEM), UMR 5635—cc047, Universite de Montpellier II, 2 Place Bataillon,34095 Montpellier, France

Received 29 October 2004; revised 6 May 2005; accepted 30 May 2005DOI: 10.1002/polb.20534Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: A series of polyimides with alicyclic and fluorinated moieties previouslysynthesized were studied for gas separation applications. The solubility behavior ofpolyimides in various solvents was analyzed through the solubility parameterapproach. Permeability coefficients and ideal selectivities were determined for commongases, that is, He, H2, O2, and N2. Polyimide permeabilities were correlated to animprovement of the soluble character and were increased by the introduction of bothalicyclic and fluorinated structures. The effect of the casting solvent on gas separationproperties was also pointed out. It was found that it is enhanced with increasing dia-meters for the gas molecules. Finally, some correlations between permeability coeffi-cients and microstructural parameters were discussed. The probability of correlationappears to be also dependent on the diameter and on the polarizability of the gas mole-cule. VVC 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2413–2426, 2005.

Keywords: polyimides; solution properties; free volume; gas permeation; subglassrelaxation

INTRODUCTION

Aromatic polyimides display interesting gas se-paration properties.1 By modifying the chemicalstructures of precursor monomers, polyimidescan be tailored for the optimization of both per-meability (P) and selectivity (a) coefficients.Nevertheless, the development of new polyimidesrequires not only an improvement of the gas se-paration properties but also elaboration anddurability criteria. In other words, new poly-

imides need to have a good solubility in solventsand to be mechanically and chemically resistant.

Fluorinated polyimides are often considered aspromising membrane materials, since the pre-sence of trifluoromethyl entities in polyimidesincreases the permeability without decreasingthe permselectivity.1–3 Such a behavior has beenattributed to various factors, that is, the sterichindrance of CF3-groups and, for polyimides con-taining hexafluoroisopropylidene groups, thereduction of the charge transfer complex (CTC),helical conformations of the chains, and a restric-tion of mobility due to the bridge.2–6 In addition,Chun has underlined that the substitution ofthe 4,40-hexafluoroisopropylidene diphtalic anhy-

Correspondence to: Corine Bas (E-mail: corine.bas@univ-savoie.fr)

Journal of Polymer Science: Part B: Polymer Physics, Vol. 43, 2413–2426 (2005)VVC 2005 Wiley Periodicals, Inc.

2413

dride (6FDA) by the bicyclo[2.2.2]-oct-7-ene-2,3,5,6-tetracarboxylic dianhydride (BCDA) indu-ces either an increase in the permeability of COwithout any change in the CO/CH4 selectivity oran increase in this selectivity coefficient withoutany reduction of the CO permeability coefficient.7

For these reasons, BCDA groups and trifluo-romethyl subtituents were considered for thedesign of a series of copolyimides based on the4,40-oxydiphthalic anhydride (ODPA) and the4,40-oxydianiline (ODA). The properties of thesepolyimides are thus investigated in this paper.Their solubility and gas permeability characterare especially detailed. These properties arethen analyzed and correlated with the micro-structure of the membrane.

EXPERIMENTAL

The film properties of 10 copolyimides basedeither on the ODA diamine or on the 2-trifluoro-methyl-4,40-diaminodiphenyl ether (ODACF3)with various ODPA/BCDA ratios were analyzed.Molecular weight-controlled copolyimides weresynthesized using a one-pot two-step polycon-densation method to disperse BCDA entitieswithin the chains.8 Membranes were preparedusing a solvent cast method with two solvents,m-cresol and N-methyl pyrrolidinone (NMP).The solvent evaporation occurred during theheating step program at 80, 150, and 280 8C for1 h at each temperature, with cooling and heat-ing rates between each step controlled at 1 8C/min. Their microstructure was then character-ized. Full details of the synthesis procedure aswell as chemical and structural characteriza-tions are reported elsewhere.8,9 For clarification,films were numbered and some characteristicsof their microstructure are recalled in Table 1.The microstructure of these polyimide mem-branes was characterized in terms of FractionalFree Volume (FFV), intersegmental chain dis-tance (dspacing), c-relaxation temperature (Tc),color index (k50), low- and high-momentum elec-tron–positron pairs, S and W respectively.

Solubility

The solubility of polyimides was evaluated visuallyfor 1-wt % solutions, based on 14 solvents. Thebehavior of each polymer was marked according tothe following classification: insoluble (0 pt), parti-ally soluble or swelling (1 pt), soluble upon heating(2 pts), and soluble at room temperature (3 pts).

Hildebrand’s parameter based on cohesiveenergy density was computed by using theFedors’ method.10,11 The cohesive energy wasestimated using the additive group contributionfor the energy of vaporization, while the molarvolume was derived from the density measure-ments9 based on the flotation method. The threedimensional solubility parameters defined byHansen were evaluated by both Hoy and Hof-tyzer–van Krevelen approaches.11 The method ofHoftyzer and van Krevelen contains three energyfunctions estimated from the addition of thegroup contributions and the experimental molarvolume. Hoy’s calculation is quite different fromthat of Hoftyzer–van Krevelen. It is based onfour additive functions: the molar attractionfunction, the polar component, the molar volume,and the Lyderson correction.12 The details of thecalculations were reported elsewhere.11,13

Gas Permeation

Steady-state gas permeation measurements wereperformed at 25 8C by using a pressure-rise typepermeation cell. All the gases under study, He,H2, O2, and N2, were pure (99.99%). To ensurethat equilibrium conditions were achieved for thepolyimide film, secondary vacuum was pulled onboth faces of the membranes during at least 12 hbefore any measurement and then, for 1 hbetween each gas application. An upstream pres-sure of 3 bars was then applied on the membrane.The pressure in the downstream compartmentwas measured using an MKS baratron pressuretransducer (pressure range, 0.01–100 mbar).Each permeability coefficients (Pi) of pure gas iwas calculated from the slope of the pressure riseas a function of time. The errors in the Pi valueswere estimated to be of the order of 0.5 Barrer forhelium and hydrogen and of 0.01 Barrer for bothnitrogen and oxygen. The ideal permselectivities(aij) are given by eq 1.

aij ¼ Pi

Pjð1Þ

According to Fick’s second law, the gasdiffusivities (D) were determined by the timelag method through the following equation:

D ¼ e2

6hð2Þ

where e is the thickness of the membrane and h isthe time lag, that is, the extrapolation on thetime axis of the linear steady-state permeationportion.

2414 BAS ET AL.

For checking the values of D coefficient, sorp-tion experiments have been performed. Itresults that the gas sorption in our samples islower than the limit of detection of our equip-ment. Thus, no experimental values of D can bedone for comparison. Nevertheless, we can esti-mate an error of 20% for the diffusion coefficientdetermined from the time lag method.

RESULTS AND DISCUSSION

Solubility Analyses

The solubility of polymers was evaluated using14 solvents, which exhibit quite different Hilde-brand parameters.11 Table 2 reports the behav-ior of each polyimide with respect to these sol-vents. As reported in a previous paper,8 solubil-ity tends to be improved either by increasingthe BCDA content or by replacing the ODA di-amine with the ODACF3 diamine. To quantifythese improvements, the respective marks for all14 solvents were added and the resulting sum isdrawn in Figure 1 as a function of the BCDA con-tent. Such a plot confirms the favorable effect ofthe alicyclic group on the solubility. Nevertheless,Figure 1 underlines that the effect of the BCDAunit is already optimized at 20 mol %. In addition,

according to our solubility marks related to thetested solvents and on an overall point of view,the improvement of solubility by trifluoromethylsubstitution of the diamine seems to be twice aseffective as that by the incorporation of the ali-cyclic dianhydride.

Table 2. Solubility Behavior for the Copolyimides

Solvents

CODA SeriesF3 ODACF3 Series

0a 5 10 20 100 0 5 10 20 100

Acetone 0 0 0 0 0 0 0 0 0 3Ethyl acetate 0 0 0 0 0 0 0 0 0 1DMF 1 2 2 3 3 3 3 3 3 3c-Butyrolactone 1 1 1 3 3 3 3 3 3 3m-Cresol 3 3 3 3 3 3 3 3 3 3Methanol 0 0 0 0 0 0 0 0 0 1Chloroform 1 1 1 1 0 3 3 3 3 2DMSO 0 0 0 1 3 1 3 3 3 3NMP 1 3 3 3 3 3 3 3 3 3Toluene 0 0 0 0 0 0 1 0 3 0DMAc 1 1 1 1 3 3 3 3 3 3THF 0 0 0 0 0 3 3 3 3 3Dioxane 0 1 3 3 0 3 3 3 3 3Chlorobenzene 0 0 0 0 0 1 1 1 1 1

Insoluble (0), partially soluble or swelling (1), solubleupon heating (2), and soluble at room temperature (3).

a 0, 5, 10, 20, and 100 are BCDA mol%.

Table 1. Characteristic Parameters for the Copolyimide Films

Film No. PolymerMolar Ratio ofODPA/BCDA FFV k50 (nm) Tg (8C) S

ODA–cresol series1 ODA-0 100/0 0.134 454 244 0.4422 ODA-5 95/5 0.134 454 248 0.4433 ODA-10 90/10 0.135 – 262 0.4434 ODA-20 80/20 0.136 457 266 0.4445 ODA-100 0/100 0.149 430 384 0.466

ODACF3–cresol series6 ODACF3–0 100/0 0.153 422 251 0.4417 ODACF3–5 95/5 0.152 422 248 0.4428 ODACF3–10 90/10 0.136 432 255 0.4439 ODACF3–20 80/20 0.147 423 261 0.445

10 ODACF3–100 0/100 0.147 – 330 –

ODACF3–NMP series11 ODACF3–0 100/0 0.160 435 252 0.44212 ODACF3–5 95/5 0.161 441 249 0.44013 ODACF3–10 90/10 0.162 428 252 0.44314 ODACF3–20 80/20 0.164 415 261 0.44415 ODACF3–100 0/100 0.168 – 330 –

POLYIMIDES WITH ALICYCLIC AND FLOURINATED GROUPS 2415

To explain these results, the components ofthe solubility-parameter for each polyimide weredetermined according to both Hoy and Hof-tyzer–van Krevelen methods11 and are reportedin Table 3. The total solubility parameter, dtotal,was also estimated by two other methods,Fedors’ method based on the group contributionapproach11 and a Molecular Dynamics (MD)method14 (Table 3). Both approaches are basedon the evaluation of the total cohesive energy.According to the chosen approach, dtotal valuesare quite different for the polymers in contrastto the solvent molecules. The parameters esti-mated by Hoy and Fedors calculations wereoverestimated compared to MD values14 and, toa less extent, to Hoftyzer–van Krevelen’s esti-

mations. In spite of these discrepancies, thesemethods are quite consistent. Indeed, they showa decrease in dtotal induced by the presence ofthe BCDA group. A same trend can be observedfor the substitution of the aromatic ring by a tri-fluoromethyl group, except for the Hoy method.However, both these reductions of the Hilde-brand parameters have different origins accord-ing to our calculations and to molecular model-ing.14 The introduction of the CF3-substituentresults in an expansion of the molar volumewithout any significant change in the cohesiveenergies. In contrast, the BCDA moiety inducesa decrease in the molar volume balanced out byan increase in the intermolecular energies (or adecrease in the cohesive energies).14

Due to its good solvent character for the over-all series of polyimide, m-cresol was used for thecomparison of solubility parameter calculations.Hoy’s method gives the highest discrepancy onthe global solubility parameters between thecopolyimides and m-cresol, while Fedors’ estima-tion exhibits the lowest gap. However, the changein dtotal values is not large enough to predict thesolubility behavior in all these solvents.11 Thepolar, hydrogen, and dispersion components haveto be taken into account. The solubility data ofsolvents and homopolyimides were then plottedin a dpolar–dhydrogen–ddispersion diagram (Fig. 2). Incontrast to Hoftyzer–van Krevelen results, thedata of polymers obtained from Hoy’s approachare quite far from those of the solvents thatdisplay a good solvent behavior. The three solubi-

Figure 1. Marks of solubility versus chemical com-position for (�) ODA- and (*) ODACF3-based copoly-imides. The solid line is a eye-line guide.

Table 3. Hildebrand and Hansen Parameters (J1/2 cm�3/2) Determined by Hoy’s, Fedor’s, Hoftyzer–vanKrevelen’s,11 and MD14 Methods

Hoy Fedors Hoftyzer–van Krevelen MD

dpolar dhydrogen ddispersion dtotal dtotal dpolar dhydrogen ddispersion dtotal dtotal

ODA-0 15.5 15.6 17.3 27.9 25.8 5.8 8.3 18.9 21.4 21.2ODA-5 15.5 15.5 17.2 27.9 25.7 5.8 8.3 18.8 21.4ODA-10 15.5 15.2 17.1 27.6 25.7 5.8 8.3 18.8 21.3ODA-20 15.4 14.8 17.0 27.3 25.6 5.9 8.3 18.7 21.2 20.5ODA-100 14.9 10.8 15.6 24.1 24.8 6.3 8.2 17.6 20.5 18.9

ODACF3-0 16.3 17.1 21.3 31.8 24.7 5.2 7.9 18.1 20.4ODACF3-5 16.3 16.9 21.3 31.7 24.6 5.2 7.9 18.1 20.4ODACF3-10 16.3 16.7 21.3 31.5 24.6 5.3 7.9 18.1 20.4ODACF3-20 16.2 16.2 21.2 31.2 24.5 5.3 7.9 17.9 20.3 19.2ODACF3-100 16.0 12.5 20.7 29.0 23.6 5.7 7.8 17.2 20.0

m–Cresol 5.1 12.9 18.8 23.3 25.2 4.9 13.8 18.1 23.3 18.6NMP 12.3 7.2 17.9 22.9 22.9 11.5 8.5 18.0 23.0

2416 BAS ET AL.

lity components appear to be overestimated byHoy’s method, as suggested by the dtotal parame-ter. Hoftyzer–van Krevelen’s approach gives quitesimilar solubility components for all the poly-imides. The solubility criterion, Dd (eq 3) shouldbe less than 5 J1/2 cm�3/2. It should be noticedthat, even for Hoftyzer–van Krevelen’s calcula-tions, this criterion cannot explain all the changesin the solubility behavior of the polyimides.

�d¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½dp;P � dp;S�2 þ ½dd;P � dd;S�2 þ ½dh;P � dh;S�2

q

ð3Þ

where dp, dd, and dh are the polar force, the disper-sive force and the hydrogen bonding componentsof the polymer (index P) and the solvent (index S),respectively.

Nevertheless, such an analysis can explainthe nonsolvent character of some solvents understudy for our polyimides. The insoluble behaviorof the copolyimides under study can be relatedto the low hydrogen-bonding component of tol-uene and chlorobenzene. Moreover, for metha-nol, acetone, and ethyl acetate, it can originatefrom the low dispersion parameter (Fig. 2).

Permeation Properties

Depending on the casting conditions, the filmscan be broadly classified into two classes15:porous and dense membranes. To analyze theeffects of the chemical structure on the gastransport properties, only the results for densemembranes were retained, that is, those with aselectivity ratio for binary gas mixtures higher

Figure 2. Hansen parameters determined for solvents (closed symbol) and polymersusing Hoy’s (open symbols) and Hoftyzer–van Krevelen’s (gray circles) methods.

POLYIMIDES WITH ALICYCLIC AND FLOURINATED GROUPS 2417

than Knudsen’s criteria (Table 5). Pure gas per-meability and diffusion coefficients as well asselectivities for the gas pairs are reported inTable 4 and Table 5, respectively. For each poly-

imide film, the permeability coefficients decreasein the following order: PHe > PH2 > PO2 > PN2.In agreement with previous works,17–20 such anevolution is correlated with the kinetic diameter

Table 4. Pure Gas Permeability Properties for the Copolyimides

Film No.

Permeability Coefficient (Barrers) Diffusion Coefficient (10�8 cm2/s)

PHe PH2PO2

PN2DHe DH2

DO2DN2

ODA-cresol series1 2.3 1.8 0.07 0.09 50 20 0.2 0.42 5.2 4.7 0.49 0.39 60 40 0.6 0.23 4.8 4.6 0.46 0.41 –a 40 2.3 0.84 5.2 4.4 0.20 0.05 – 50 0.4 0.35 16.1 19.6 2.04 1.35 75 40 3.8 2.5

ODACF3–cresol series6 11.8 9.6 0.61 0.09 – 110 0.5 0.27 15.3 12.0 0.79 0.14 – – 1.7 2.58 11.7 9.3 0.60 0.08 – – 1.3 0.39 13.5 12.3 1.13 0.59 – – 2.0 3.1

ODACF3–NMP series11 12.7 10.4 0.84 0.35 – – 1.6 7.412 11.8 9.0 0.54 0.07 – 100 0.7 0.213 13.1 10.4 0.68 0.09 – 80 1.4 0.714 14.8 11.9 0.82 0.09 90 90 1.5 3.9

a Not accessible values because the time lag was too small.

Table 5. Ideal Selectivities for the Copolyimides

Film No. aHe/H2aHe/N2

aHe/O2aH2

/N2 aH2/O2 aO2

/N2

ODA-cresol series1 1.24 26.3 32.8 21.2 26.3 0.82 1.11 13.2 10.6 11.9 9.5 1.33 1.04 11.8 10.5 11.4 10.1 1.14 1.17 99.2 27.1 84.5 23.1 3.75 0.82 11.9 7.9 14.5 9.6 1.5

ODACF3–cresol series6 1.22 136.9 19.5 111.9 15.9 7.07 1.27 109.6 19.4 86.2 15.3 5.78 1.25 149.7 19.6 119.9 15.7 7.79 1.10 22.9 11.9 20.8 10.9 1.9

ODACF3–NMP series11 1.23 36.2 15.2 29.6 12.4 2.412 1.31 163.7 21.9 125.4 16.7 7.513 1.25 144.6 19.2 115.5 15.3 7.514 1.24 163.3 18.0 131.6 14.5 9.1

Knudsen constant 0.71 2.65 2.83 3.74 2.83 0.94ri � rj (A) 0.28 1.25 0.92 0.97 0.64 0.33di � dj (A) 0.29 1.04 0.86 0.75 0.57 0.18

The differences of kinetic diameters, d, and collision diameters, r, between gas pairs are reported.16

2418 BAS ET AL.

of the gas molecule.21 Moreover, a similar classi-fication can be observed for the coefficients of dif-fusion. The evolution of the permeability isstrongly dependent on the variation of the gasdiffusivities (Table 4). Considering as a firstapproximation that the permeability coefficientresults from the product of the diffusion and gassolubility coefficients, we can observe in Figure 3that the solubility coefficient of oxygen is quiteconstant, irrespective of the chemical structureof the polyimide. The correlation between thepermeability coefficient and the diffusion coeffi-cient displayed by ODA-based polyimides is thesame for nitrogen and oxygen gases (Fig. 3).Thus, the transport of O2 and N2 molecules isstrongly dependent on the diffusivity in ODA-based copolymers, as reported in the literaturefor other polyimides.17,22 In contrast, the depend-ence of N2 permeability with respect to diffusionvaries according to the fluorinated character ofthe polyimides. Fluorinated polyimides tend tohave a low N2 solubility coefficient in comparisonwith polyimides containing the ODA diamine.Consequently, it appears that N2 permeationdepends not only on the diffusion transport butalso on the sorption coefficient.

Except for the ODA-based homopolyimides,the permselectivities of pure gases vary in the

following order: aHe/H2� aO2/N2

> aH2/O2� aHe/O2

> aH2/N2� aHe/N2

Such a classification is confirmed by the anal-yses of polyimide data for permanent gases, thatis, O2, N2, and H2.

1,2,4–6,17,19,23–33 The differen-ces in the kinetic diameter of gas molecules donot explain such a classification. Indeed, a bet-ter correlation can be found between selectivityand differences in collision diameter (Table 5).

The homopolyimide ODA-0 exhibits the low-est permeability coefficient, irrespective of thegas. It can be correlated with its lowest FFV, itshighest k50 (Table 1), and its nonamorphouscharacter compared to the other polyimidesunder study.9 In the opposite direction, both thehighest permeability and the lowest selectivityare obtained for the ODA-100 membrane,although this homopolyimide does not exhibitthe highest FFV. This suggests that the distribu-tion of the free volume sizes in ODA-100 is nar-row and does not allow for any gas selection.

For the ODA-cresol series, the permeabilitycoefficient increases with increasing BCDA con-tent, while the selectivity slightly decreasesexcept for the ODA-20 membrane. The increasein the permeability coefficient with the BCDAcontent is in agreement with the increase in thefree volume fraction reported in Table 1. Theimprovement of the permeability by the intro-duction of the BCDA unit is consistent with theincrease in low-momentum electron–positronpairs (S) and with the decrease in both colorindices (k50%) and c-relaxation temperatures.9

Figure 4. Dependence of Fi on the kinetic diameterof gases for ODACF3-0 (n), ODACF3-10 (*), andODACF3-20 (�).

Figure 3. Dependence of the permeability coefficienton the diffusion coefficient of oxygen (�,*) or nitro-gen (þ,l) for nonfluorinated (�) and fluorinated(circles) copolyimides. The dotted lines show the bestfits for oxygen permeation in all the copolyimides (a)and the nitrogen behavior in the fluorinated poly-imides (b).

POLYIMIDES WITH ALICYCLIC AND FLOURINATED GROUPS 2419

The permeability coefficients of the three copo-lyimides are quite close and significantly differ-ent from those of their homopolyimides, exceptfor the O2 and N2 permeation through theODA-20 membrane.

The trifluoromethyl substitution of the ODAdiamine induces an increase in the permeabilitycoefficient for H2, He, and O2. This result agreeswith the increase in the FFV and the decrease

in the color index reported in Table 1. Moreover,the ODACF3-based polyimides exhibit a higherseparation factor than the polyimides containingthe ODA diamine.

Table 4 and Table 5 show that the casting sol-vent affects both permeability and selectivitycoefficients.34 As no residual solvent wasdetected using both ATG and NMR experi-ments,9 the difference in permeability coefficient

Figure 5. Selectivity versus permeability for binary gas mixtures O2/N2 (a) and H2/O2 (b), for published results on polyimides (�),1,2,4–6,17,19,23–33 ODA-cresol (u),ODACF3-cresol (*), and ODACF3-NMP (l) series. The line is the upper bounddetermined by Robeson et al.22 [Color figure can be viewed in the online issue, whichis available at www.interscience.wiley.com.]

2420 BAS ET AL.

(Pi) of the gas i correlated to the casting solventcan only be attributed to some microstructuralchanges. Such a dependence of the permeationon the casting solvent can be quantified by thefunction Fi described as follows (eq 4).

Fi ¼ PiðcresolÞ � PiðNMPÞPiðcresolÞþPiðNMPÞ

2

� � ð4Þ

The difference in F between ODACF3–cresoland ODACF3–NMP series increases with in-crease in the kinetic diameter of the gas mole-cules (Fig. 4). Furthermore, the increase in theBCDA content results in a significant increasein the F function for N2. In addition, theincrease in the BCDA content tends to decreasethe selectivity for the ODACF3–cresol series,while it involves an increase in the selectivityfor the ODACF3–NMP series. It implies that thegas separation properties of most of the mem-branes based on ODACF3 diamine are quiteclose to Robeson’s limit (Fig. 5). Changes in Ffor nitrogen versus BCDA content are not con-sistent with variations in free volume fraction.Thus, we can suppose that the gas permeabilityis not only dependent on the free volume frac-tion but also on the distribution of the free vol-ume sizes35 resulting from changes in the chainconformations.

m-Cresol and NMP solvents have quite simi-lar properties (Table 6), such as boiling tempera-tures, total solubility parameters, and densities.The effects of the casting solvent on the permea-tion properties cannot originate from a discrep-ancy in the boiling temperature as suggested byKhulbe et al.38 or from the residual solvent con-tent as suggested by Joly et al.39

Thus, these differences induced by the castingsolvent originate from other causes such as the

kinetic rate of the solvent evaporation shown ina previous work,34 the inherent viscosity of thepolyimide solutions,9 and the Hildebrand para-meters (Table 3). On another hand, NMP isknown to be a very hygroscopic solvent, whilewater is a nonsolvent for polyimides. So it canbe assumed that the presence of water mole-cules in NMP can induce either aggregation ofpolyimide chains40 or a similar effect as forasymmetric membrane to a lesser extent. Inturn, it could contribute to an increase in theselectivity. Unfortunately, such a phenomenoncannot be confirmed by Doppler broadeningspectrometry results coupled to a positron beam,as the fluorine atoms mask the microstructuralanalysis.9

Permeability Correlation

To assess the degree of correlation between per-meability coefficients and both microstructuraland solubility parameters, the linear correlationcoefficients (r) were calculated based on N meas-urements. According to both r and N values, the

Table 6. Physical Constants for the Solvents at 20 8C as well as for the Gas Molecules Under Study36,37

q (g/cm3) Tboiling (8C) Vm (cm3/mol) g ((mN s)/m2) c (mN/m) r (A) a (A3)

m-Cresol 1.03 203 104.6 20.8 38NMP 1.03 202 96.4 1.67 41.8

He 2.55 0.205H2 2.83 0.805O2 3.47 1.581N2 3.80 1.740

q: specific volume; Vm: molar volume; g: viscosity; c: surface tension; a: static polarizability.

Table 7. Probability of a Lack of CorrelationBetween the Following Solubility Probes andPermeability Coefficients

PHe PH2PO2

PN2

dt (Fedors) <0.05 0.1 5 75dt (Hoy) 19 92 40 2dt (HVKa) <0.05 0.4 6 82dpolar (HVK) 15 51 46 50dhydrogen (HVK) 0.2 8 45 38ddispersive (HVK) <0.05 <0.05 <0.1 20Solubility mark <0.1 4 35 50

a Hoftyzer–van Krevelen.

POLYIMIDES WITH ALICYCLIC AND FLOURINATED GROUPS 2421

probability of a lack in linear correlation wasdetermined (Tables 7 and 8).

As suggested by Matsumoto et al. for CO2,41

the negative correlation between the permeabil-ity and the solubility parameters based on Fedorsand Hoftyzer–van Krevelen calculations appearsto be highly possible for He, H2, and O2. This cor-relation can be attributed to the dispersion com-ponent whose decrease enhances the permeationof small gas molecules (Table 7 and Fig. 6a). Theabsence of correlation between permeability coef-ficient and d parameter calculated using Hoy’smethod confirms that this calculation of solubilityparameters does not describe the behavior of ourpolyimides. Moreover, Figure 6b emphasizes therelationship between the permeability coefficientand the improvement of the solubility characterfor the polyimides under study.

No correlation was found between the inter-chain distances determined from X-ray experi-ments and the permeability properties of films.This is not a surprising conclusion. Indeed, wehave previously underlined that WAXS resultsare quite sensitive to fluorine atoms, whichmask microstructural contribution.9 In contrast,a correlation may exist between the color indexand permeabilities, especially for the small gasmolecules. This could indicate that the chainability to form CTCs induces a decrease in thepermeability coefficient (Fig. 7a). To our knowl-edge, no published data are available to checksuch a correlation.

It is likely that the permeability coefficientand the c-relaxation temperature are correlatedwith a probability of at least 92%, except for N2.The results from the studies of Hirayamaet al.24,42 also confirm this tendency even for N2

(Fig. 7c). This plot suggests that the shift of thec-relaxation temperature toward higher temper-atures involves a decrease in the permeabilitycoefficient. This tendency is in agreement withprevious conclusions on the c-relaxation temper-ature in polyimides acting as a microstructuralprobe.44,45 Singla et al.43 have found similar cor-relations for polysulfones and polyarylates,while Houde et al.46 have reported an increasein the permeability coefficient with an increasein the subglass relaxation temperature for poly-arylates. Such conflicting conclusions can beattributed to differences in the molecularmotions giving rise to the c-relaxation. For poly-imides, the considered c-subglass relaxation isrelated to motions of water molecules linked tothe macromolecular chain,45 while the so-calledc-relaxation displayed by polyarylates and poly-sulfones can also originate from the motion ofthe phenyl rings in the backbone chain.47,48

According to Singla’s work,43 the best-fit correla-tion can be described by eq 5 and is plotted inFigures 7b and 7c.

P ¼ Ac e�TcBc ð5Þ

where Ac and Bc display logarithm dependenceon the square of the gas kinetic diameter. Inaddition, Ac also depends on the polymer struc-ture and, especially, on the dianhydride moietiesfor polyimides.

Figures 7b and 7c show that our data aresuperimposed with the Hirayama et al. data,24,42

although Tc was not recorded at the same fre-quency. To compare data at the same frequency,Arrhenius law has to be applied with an activa-tion energy of 50 kJ/mol, as previously deter-

Table 8. Probability of a Lack of Correlation Between the Microstructural Parameters and (a) the PermeabilityCoefficients or (b) the Logarithm of the Permeability Coefficients

(a) Permeability Coefficients PHe PH2PO2

PN2

dspacing 100 41 19 5k50 0 0.6 6 51S 25 1.3 0.03 0.01W 1.4 25 100 13

(b) Logarithm of Permeability Coefficients logPHe logPH2logPO2

logPN2

dspacing 93 80 42 8k50 0.05 0.1 0.8 63Tc 8 3 7 251/FFV 0.4 0.9 5.6 831/FFVi 0.8 0.1 0.6 18

2422 BAS ET AL.

mined.44 The results for the c-relaxation temper-ature at 1 Hz are lower by about 10 8C than theTc recorded at 10 Hz. Thus, for comparison, thelogP versus Tc curve for our polyimides based onthe BCDA and the OPDA dianhydrides has tobe shifted toward the lower temperatures. Thisshift confirms that Ac is slightly dependent onthe dianhydride chemical group. The Bc slopesfor He and O2 are the same as those publishedand the value found for H2 is consistent withSingla’s estimation, that is, 0.07 8C�1.

Table 8 also confirms that the dependence oflogPi on the reciprocal FFV reported ineq. 618,49,50 is quite valid for polyimides even if a

better correlation can be found with 1/FFVi, whereFFVi estimated by Park and Paul’s method49 isthe FFV for the specific gas i (Fig. 7d).

P ¼ A e�ðB=FFVÞ ð6Þ

The correlation between permeability andparameters extracted from positron annihilationspectroscopy was also studied. In spite of thelow probability reported in Table 8, the correla-tion between PHe and W or S cannot really bedefined. Indeed, the lack of correlation for Sstrongly depends on the ODA-100 polyimide,which displays a very high S value as shown inFigure 7e. For the W parameter, the lack of cor-relation can be explained by the high sensitivityof such a parameter to the chemical structure.

The probabilities of a lack of correlationreported in Tables 7 and 8 for the FFV, Tc, k50parameters and solubility marks and in a lesserextent for the FFVi increase with the diameterof the four gas molecules. This behavior impliesthat those microstructural parameters cannotcharacterize the polyimide structure detected bylarge gas molecules. It will be thus quite inter-esting to perform positron lifetime spectroscopyto evaluate free volume sizes. In contrast, theprobability for dspacing increases from He to N2.This tendency can be related to the change inthe size of the gas molecule and also to theincrease in the static polarizability of the gasmolecules (Table 6). This last hypothesis can bementioned because of the chemical dependenceof the intersegmental distance.

CONCLUSIONS

Gas separation and solubility properties of aro-matic polyimide membranes were improved bythe introduction of alicyclic and fluorinatedgroups in the synthesis of ODPA/ODA copoly-imides, without any strong effect on the thermalproperties (Tg). In addition, the fluorinated sub-stituent is more effective than the BCDA one forboth solubility and permeation properties. Suchimprovements cannot be related to any changesin the solubility parameters of the polymers,while the Hansen’s parameters for solvents canexplain their nonsolvent character. The He, H2,and O2 permeability coefficients of copolyimidesare not correlated to the dspacing and the W

Figure 6. Gas permeation coefficients versus solu-bility parameters based on Hoftyzer–van Krevelencalculations (a) and on solubility experiments (b). Thesolid line represents the best-fit curve for polyimidesunder study.

POLYIMIDES WITH ALICYCLIC AND FLOURINATED GROUPS 2423

Figure 7. Permeability coefficients of gas versus color index (a), c-relaxation tem-perature at 10 Hz (b, c), fractional free volume for O2 (d), and S parameter (e) forour samples (l). The data recorded at 1 Hz from Hirayama et al. are added for poly-imides based on 6FDA (u), BPDA (þ), and PMDA (^).24,42 The continuous line rep-resents the best-fit curve. The dotted lines are the Singla’s fits.43

parameter because of their high sensitivity tothe chemical composition of polyimides. On theother hand, some relationships between perme-ability of He, H2, and O2 gases and microstruc-tural parameters such as color index, Tc, FFV,and solubility marks do exist. For N2, it seemsthat the permeability coefficient is not only con-trolled by the microstructure but also by thechemical interactions due to the polarizability ofthe gas molecule.

The authors are grateful to the French Research Min-istry for financial support.

REFERENCES AND NOTES

1. Langsam, M. In Polyimides: Fundamentals andApplications; Marcel Dekker: New York, 1996;Ch. 22, pp 697–741.

2. Kim, T. H.; Koros, W. J.; Husk, G. R.; O’Brien, K. C.J Membr Sci 1988, 37, 45–62.

3. Matsumoto, K.; Xu, P. J Appl Polym Sci 1993, 47,1961–1972.

4. Stern, S. A.; Mi, Y.; Yamamoto, H.; St Clair, A.J Polym Sci 1989, 27, 1887–1909.

5. Tanaka, K.; Kita, H.; Okano, M.; Okamoto, K. I.Polymer 1992, 33, 585–592.

6. Tanaka, K.; Okano, M.; Kita, H.; Okamoto, K. I.;Nishi, S. Polym J 1994, 26, 1186–1189.

7. Chun, B.-W. J Polym Sci Polym Phys Ed 1995,33, 731–737.

8. Pinel, E.; Bas, C.; Neyertz, S.; Alberola, N. D.;Petiaud, R.; Mercier, R. Polymer 2002, 43, 1983–1992.

9. Pinel, E.; Barthe, M.-F.; De Baerdemaeker, J.;Mercier, R.; Neyertz, S.; Alberola, N. D.; Bas, C.J Polym Sci Part B: Polym Phys 2003, 41, 2998–3010.

10. Fedors, R. F. Polym Eng Sci 1974, 14, 147–154.11. van Krevelen, D. W. In Properties of Polymers:

Their Estimation and Correlation with ChemicalStructure; Elsevier Science B.V.: Amsterdam,1997; Ch. 7, pp 189–225.

12. Hoy, K. C. J. Paint Technol 1970, 41, 76–118.13. Pinel, E. doctorat, Universite de Savoie, 2001.14. Pinel, E.; Brown, D.; Bas, C.; Mercier, R.; Alberola,

N. D.; Neyertz, S. Macromolecules 2002, 35, 10198–10209.

15. Pandey, P., Chauhan, R. S. Prog Polym Sci 2001,26, 853–893.

16. van Krevelen, D. W. In Properties of Polymers:Their Estimation and Correlation with ChemicalStructure; Elsevier Science B.V.: Amsterdam,1997; Ch. 18, pp 535–583.

17. Yamamoto, H.; Mi, Y.; Stern, S. A.; St. Clair, A. K.J Polym Sci Polym Phys Ed 1990, 28, 2291–2304.

18. Stern, S. A. J. Membr Sci 1994, 94, 1–65.19. Li, Y.; Ding, M.; Xu, J. Macromol Chem Phys

1997, 198, 2769–2778.20. Ayala, D.; Lozano, A. E.; de Abajo, J.; Garcia-

Perez, C.; de la Campa, J. G.; Peinemann, K.-V.;Freeman, B. D.; Prabhakar, R. J Membr Sci 2003,5548, 1–13.

21. Jia, L., Xu, J. Polym J 1991, 23, 417–425.22. Robeson, L. M.; Burgoyne, W. F.; Langsam, M.;

Savoca, A. C.; Tien, C. F. Polymer 1994, 35, 4970–4978.

23. Kim, T. H.; Koros, W. J.; Husk, G. R. Sep Sci Tech1988, 23, 1611–1626.

24. Hirayama, Y.; Yoshinaga, T.; Kusuki, Y.; Nino-miya, K.; Sakakibara, T.; Tamari, T. J Membr Sci1996, 111, 183–192.

25. Tanaka, K.; Kita, H.; Okamoto, K. I.; Nakamura,A.; Kusuki, Y. Polym J 1989, 21, 127–135.

26. Tanaka, K.; Okano, M.; Toshino, H.; Kita, H.;Okamoto, K. I. J Polym Sci Part B: Polym Phys1992, 30, 907–914.

27. Tanaka, K.; Osada, Y.; Kita, H.; Okamoto, K. I. J.Polym Sci Part B: Polym Phys 1995, 33, 1907–1915.

28. Kawakami, H.; Mikawa, M.; Nagaoka, S. JMembr Sci 1996, 118, 223–230.

29. Langsam, M.; Burgoyne, W. F. J Polym Sci PartA: Polym Chem 1993, 31, 909–921.

30. Smith, C. D.; Langsam, M.; Robeson, L. M. In 4thEuropean Technical Symposium on Polyimides

and High Performance Polymers, Montpellier,1996, Agenda Communications, pp 400–406.

31. Matsumoto, K.; Xu, P. J Membr Sci 1993, 81, 23–30.

32. Okamoto, K. I.; Tanaka, K.; Kita, H.; Ishida, M.;Kakimoto, M.; Imai, Y. Polym J 1992, 24, 451–457.

33. Coleman, M. R.; Koros, W. J. J Membr Sci 1990,50, 285–297.

34. Pinel, E.; Mercier, R.; Sanchez-Marcano, J. G.;Neyertz, S.; Alberola, N. D.; Bas, C. C R Acad Sci2003, 6, 493–499.

35. Bi, J.; Wang, C. L.; Kobayashi, Y.; Ogasawara, K.;Yamasaki, A. J Appl Polym Sci 2003, 87, 497–501.

36. van Krevelen, D. W. In Properties of Polymers:Their Estimation and Correlation with ChemicalStructure; Elsevier Science B.V.: Amsterdam,1997; Part VII, pp 761–845.

37. Lide, D. R. In CRC Handbook of Chemistry andPhysics, 76th ed.; CRC Press: Boca Raton, FL,1995.

38. Khulbe, K. C.; Matsuura, T.; Lamarche, G.;Lamarche, A.-M. J Membr Sci 1997, 135, 211–223.

39. Joly, C.; Le Cerf, D.; Chappey, C.; Langevin, D.;Muller, G. Sep purif technol 1999, 16, 47–54.

40. Joly, C.; Le Cerf, D.; Chappey, C.; Langevin, D.;Muller, G. Polym Int 1997, 44, 497–502.

POLYIMIDES WITH ALICYCLIC AND FLOURINATED GROUPS 2425

41. Matsumoto, K.; Xu, P.; Nishikimi, T. J Membr Sci1993, 81, 15–22.

42. Hirayama, Y.; Yoshinga, T.; Kusuki, Y.; Ninomiya,K.; Sakakibara, T.; Tamari, T. J Membr Sci 1996,111, 169–182.

43. Singla, S.; Beckham, H. W.; Rezac, M. E. JMembr Sci 2002, 208, 257–267.

44. Bas, C. Macromolecular Symposium 2002, 184,193–201.

45. Bas, C.; Tamagna, C.; Pascal, T.; Alberola, N. D.Polym Eng Sci 2003, 43, 344–355.

46. Houde, A. Y.; Kulkarni, U. K.; Charati, S. G.;Kulkarni, M. G. J Membr Sci 1995, 103, 167–174.

47. Robeson, L. M.; Farnhan, A. G.; McGrath, J. E.In Molecular Basis of Transitions and Relaxations;Gordon and Breach, New York, 1978; pp 405–425.

48. Aitken, C. L.; McHattie, J. S.; Paul, D. R. Macro-molecules 1992, 25, 2910–2922.

49. Park, J. Y.; Paul, D. R. J Membr Sci 1997, 125,23–39.

50. Pixton, M. R.; Paul, D. R. J Polym Sci Part B:Polym Phys 1995, 33, 1135–1149.

2426 BAS ET AL.