On the dynamic mechanical behavior of polyimides based on aromatic and alicyclic dianhydrides.

INTRODUCTION

In recent years, there has been increasing interest in the understanding of macroscopic properties of polymers such as ductility, dielectric behavior, gas permeation character, and so on. In the field of amorphous polymers, works have shown that some specific properties appear to be dependent on chain mobility. For instance, the mechanical behavior is likely to be controlled by the cooperative character of main-chain motion. For PEEK (1) and for polycarbonate (2), it has been shown that the brittle-to-ductile transition temperature is dependent on the subglass relaxation temperature. Recently for polyimides, Chauvin et al. (3) pointed out that the [beta] subglass transition temperature coincides with the temperature at which oriented chromophores starts to disorient. Accordingly, it is of interest to understand which parameters govern the polymer relaxation.

Polyimides exhibit several temperature (or frequency) regions where relaxation processes occur. Each may be associated with specific molecular motions. The molecular motions of polyimides have been examined by different techniques including dielectric relaxation (4-6), nuclear magnetic resonance spectroscopy (4, 7) and dynamic mechanical analysis (DMA). Three relaxations, designed by [alpha], [beta] and [gamma], have been detected by DMA. Some controversy still remains concerning the molecular mechanisms at the origin of the two subglass transitions.

The [gamma] mechanical relaxation has been observed at about -100[degrees]C at 1 Hz (8-11) This transition obeys an Arrhenius law and the activation energy is about 50 kJ/mol (4, 9, 10). It was proposed a motion relaxation of water molecules linked to the polar group in polyimides (4, 11-13). Supported by NMR studies, dielectric loss measurements conducted by Greenbaun et al (4, 14) have shown the presence of a second [gamma] relaxation related to small clusters of water molecules. By contrast, based on 0-13 NMR experiments, Cheng et al (10) have associated the [gamma] relaxation to oscillation and [pi] flipping motions of the phenoxy group in the diamine sequence. This hypothesis was supported by Habas et al (11) analysis.

Above room temperature, polyimides display the [beta] relaxation at 1 Hz located in a large temperature range i.e. 100-200[degrees]C (1 Hz). The activation energy of this transition is about of 100-200 kJ/mol (9-11, 15, 16). Ikeda has attributed this relaxation to interplane slippage of crystalline region (17). Because this transition is also detected in amorphous polyimides, more recent works have attributed it to motions in the polyimide chain backbone. Based on 0-13 NMR studies, Cheng et a!. conclude that the molecular motion is mainly connected to the dianhydride moiety (10). Other investigators have ascribed this relaxation to oscillations or rotations of the para-phenylene moieties In the diarnine part (12, 13, 18). The hypothesis of Sun et al. has related the [beta] relaxation to the rotation of rigid segment of p-phenylene and imide groups (11, 16). More recently, Li et al. (19) and Vora et al. (6) have distinguished two [beta] processes. At low temperatures, the [[beta].sub.1] relaxation was associated w ith noncooperative motions of the diamine while the [[beta].sub.2] component is caused by motion of the dianhydride sequence. The cooperative character of this last process depends on the chemical structure (19).

In this paper, we propose to investigate the microstructural parameters, which are susceptible to govern the viscoelastic behavior of polyimides. In this aim, based on preliminary study (20, 21). the dynamic mechanical behavior of aromatic and semi-aromatic polyimides have been studied. The semi-aromatic polyimide is based on bicyclo[2.2.2]oct-7-ene-2,3,5,6-tetracarboxylic. This dianhydride is of interest because of its high rigidity and its alicyclie character which gives rise to a soluble product (22, 23). The changes in the chemical structure correlated to the effect on the viscoelastic behavior of polyimides should also give information on the molecular processes, which are involved in the different relaxations.

EXPERIMENTAL

Materials and Samples

The dianhydrides and the diamines used in this study are commercially available, except for the 2,6-bis-(3'aminophenox)-benzonitrile (BACN), which was synthesized according to a previously reported procedure (24). The solvents and commercial monomers were purified prior to use. m-Oresol was distilled at 140[degrees]C under reduced pressure. The pyromellitic dianhydride (PMDA), the bicyclo(2.2.2)oct-7-ene-2,3,5,6-tetracarboxylic dianhydride (BCDA) and the 3,3',4,4'-benzophenonetetracarboxylic (BTDA) were recrystallized from acetic anhydride. acetonitrile and acetic anhydride/xylene (35/65). respectively. 9,9-bis(4'-aminophenyl)fluorene (FDA) was recrystallized twice from a mixture of anisole/xylene (60/40) while 4,4' aminodiphenyl-ether (DDE) was purified by sublimation at 200[degrees]C under reduced pressure. Bis[4-(4'-ammophenoxy)phenyl]sulfone (BAPS) was purified through a column chromatography on silica gel with the cyclohexan/ethyl acetate (50/50) as eluent.

The chemical structures of investigated polyimides are shown in Fig. 1. Polyimides based on BCDA dianhydride were synthesized in m-cresol while N-methyl pyrrolidinone (NMP) was used for the synthesis of BTDA- and PMDA-based polyimides. The polyimides were obtained via a two-step process by thermal imidization method as shown in Scheme 1. Excepted for PMDA-DDE, the poly(amic acids) were not isolated and all the polymers were synthesized by thermal imidization method in solution. In a thoroughly dried 250 ml three-necked round bottom flask equipped with a mechanical stirrer, a nitrogen inlet tube and a reflux condenser with a drying tube, the diamine was dissolved in the anhydrous solvent. A slow nitrogen flow through the flask was continuously employed throughout the reaction. A solution of the dianhydride In anhydrous solvent was rapidly added. The mixture was stirred at room temperature, then at 160-180[degrees]C for at least 5 hours and finally cooled down. Approximately 20% of the polymer solution was remo ved, poured into an excess of methanol and homogenized with a laboratory mixer. The precipitate was filtered off and soaked in excess methanol during 2h. The precipitate was again filtered. The obtained powder was finally dried in an oven at 80[degrees]C under reduced pressure for 4h. Intrinsic viscosity of the polymers was measured using Ubbelhode viscosimeter at 30[degrees]C (Table 1) with 1% wt. solutions in NMP or m-cresol. These viscosities indicate that the molecular weights of our synthesized polymers were high enough to obtain polymeric films.

Typically, the polyimide films were prepared by casting 20 wt% polymer solution onto clean glass plate and then dried in an oven. Two thermal programs were used. For BCDA-polyimides, it was imposed 70[degrees]C for 4h, 100[degrees]C for 4h and 250[degrees]C for 7h. For BTDA-, and PMDA-polyimides, the thermal cycling is 100[degrees]C for 1h, 200[degrees]C for 1h and 300[degrees]C for 3h. Solvent content was determined by thermogravimetric analysis to be less than 1% (w/w). Completed imidization of all soluble polymers was confirmed by NMR analysis. Then, films were kept under room atmosphere before analysis.

Characterizations

Glass transition temperatures of polyimides were measured by differential scanning calorimetry using a Perkin Elmer DSC-7 instrument purged with nitrogen gas. DSC thermograms were recorded from +200[degrees]C + 500[degrees]C at 20[degrees]C/min. Densities of the film were measured by floating method. The density of n-hexane was adjusted by mixing with carbon tetrachloride until the films reached the flotation equilibrium at 20[degrees]C. This density method was validated by using calibrated density floats. The accuracy of the density measurement was of [+ or -]0.001. The Wide-angle X-ray scattering (WAXS) measurements were performed on a Siemens D500 X-ray diffractometer (CuK[alpha]l, Nickel-filtered radiation) with 0.02[degrees] (2[theta]) scan increments in reflexion mode. Film transmission spectra were measured at room temperature using a UV-visible spectrophotometer (Perkin-Elmer). The curves were then normalized to a 20 [micro]m thickness according to the Beer-Lambert Law. From these spectra, the [[lambda].sub.0] parameter was determined by the wavelength of transmission threshold. Water contents of films were estimated by weighing the sample at a heating rate of 50[degrees]C/min under air, using a TA2050 thermogravimetric analyzer.

Dynamic mechanical experiments have been carried out using a Rheometrics MKIII analyzer. The instrument was operated in a tensile mode at three frequencies (1, 3 and 10 Hz). Dynamic strain amplitude of 10 [micro]m (0.1%) was superimposed on a static deformation. Isochronal scans for were recorded at 1[degrees]C/min from - 150[degrees]C to up to the glass transition under nitrogen gas. A storage modulus E', a loss modulus E" and tan[delta] were recorded. The relaxation temperature (T) is determined at the maximum of tan[delta] peak. The frequency (f) dependence of the relaxation temperature (T) of the subglass relaxation is assumed to obey to the Arrhenius law.

f = [f.sub.0] * exp (-[E.sub.a]/RT) (1)

where [E.sub.a] is the activation energy and [f.sub.0] is the preex-ponential factor.

RESULTS AND DISCUSSION

Physical Properties

All the studied polyimides form transparent and yellow films. Toughness of these films allows mechanical handling. The physical characteristics of the synthesized polyimide films derived from various analyses are listed In Table 2.

The wide-angle X-ray diffraction curves of all polyimide films exhibit a broad peak, which is consistent with an amorphous character. Nevertheless, some differences between the amorphous structures of the polyimide are detected as the comparison of the WAXS patterns suggests (Fig. 2 and 3). According to the literature, the top of broad peaks on each X-ray pattern for noncrystalline polymers Is attributed to intersegmental interference. It Is thus representative of the average intersegmental distance, called d-spacing and calculated from the Bragg's equation. The intermolecular chain packing can also be quantified by the free volume fraction (FVF) determined from density measurements ([rho]) according to the equation.

FVF = 1 - [rho]/M [V.sub.0] (2)

where M is the molar weight and [V.sub.0] is the occupied chain volume. Based the Bondi group contribution method (25, 26). [V.sub.0] was estimated to be 1.3 times the Van der Waals volume ([V.sub.w]). The d-spacing and FVF values are listed in Table 2. Excepted for PMDA-DDE, no comparison with literature value can be made for these microstructural parameters. For PMDA-DDE, the density value reported in the literature lies in the 1.395 (273-1.431 (28) g.[cm.sup.-3] range. Both density and d-spacing values are also consistent with those reported by Stern et al. (29). The d-spacing measured for BCDA-based polyimides is higher than that of other polyimides. Moreover, the highest FVF were observed for polyimides based either on BCDA dianhydride or on FDA diamine. These high values of both microstructural parameters relating to these BODA-based polyimides can be attributed to the alicyclic structure, which induces steric hindrance for chain packing.

The [[lambda].sub.0] parameter value is mainly attributed to charge transfer complex (CTC) formation (30, 31), i.e. charge-transfer between electron-acceptor diimide fragments and electron-donor aromatic units (32, 33). The polyimides based on BODA dianhydrides are colorless as [[lambda].sub.0] ranges from 275 to 315 nm. These results are consistent with Chun study (22), which indicates that BODA does not favor inter-molecular interaction on both steric and electronic point of view because of its non-planar and non-aromatic structure. Now, it is of interest to examine the correlation between [[lambda].sub.0] and FVF (Fig. 4) for our polyimides. No data from literature is available for comparison. Good correlation between FFV and [[lambda].sub.0] can be observed except for both FDA-based polyimides. This induces that a decrease in chain packing could be attributed to the reduction of intermolecular CTC Interaction, as the decrease of [[lambda].sub.0] value suggests. However, both BTDA-FDA and BCDA-FDA films seem to e xhibit free volume fraction higher than expected from transmission measurements. This could be due to a [V.sub.w] underestimation of fluorene bridge because of the additive group method (26). This hypothesis could explain why representative points for 9,9-fluorenylene bridge polyimides deviate from the logarithmic relationship of oxygen permeability versus FVF (34).

Viscoelsatic Properties

Viscoelastic spectra of the BTDA-DDE polyimide are shown in Fig. 5. The BTDA-DDE polyimide exhibits three relaxations. The low-temperature process, designed as [gamma] relaxation, is observed at -95[degrees]C for 1 Hz. The activation energy of this subglass transition determined according the Arrhenius law is about 50 kJ/mol. The pre-exponential factor is about [10.sup.+14] Hz, characteristic of transition related to non-cooperative localized motions. The second subglass transition ([beta] relaxation) located at 118[degrees]C (1 Hz) displays higher activation energy and pre-exponential factor, respectively of about 130 kJ/mol and [10.sup.+18] Hz, respectively. The high-temperature transition ([alpha] relaxation) observed at 290[degrees]C (1 Hz) is related to the glass transition.

The changes of these three relaxations depending on the polyimide chemical structure are now being explored. Therefore the tensile tan[delta] profile for the different polymers are shown in Fig. 6-8. Table 3 summarizes the [alpha], [beta] and [gamma] relaxation temperatures. The activation energy and preexponential factor are also reported for subglass transitions.

The [alpha] Relaxation

The [alpha] relaxation temperature of theses polyimides ranges from 305 to 420[degrees]C. The Tg have been also determined from DSC thermograms. Nevertheless, the characteristic gap in heat capacity is not detected for PMDA-DDE and BCDA-FDE owing to the beginning of thermal degradation. A good correlation is found for Tg and T[alpha]. It is interesting to note that polyimides based on BACN have the lowest T[alpha]. This could be related to both the ether flexible bond and the meta link (33). The fluorene group gives rise to the highest T[alpha] whatever the dianhydride group is. This result can be attributed to steric hindrance of the fluorene linkage. Moreover, for flexible diamine as DDE and BACN, the T[alpha] of BTDA-based polyimides is the lowest. Thus, T[alpha] can not be related to the chain packing but it is mainly controlled by the monomer rigidity.

The [beta] Relaxation

As can be seen in Fig. 6-8, the [beta] relaxation is quite broad compared with both of the other mechanical relaxations. For BTDA-based polyimides, this relaxation is quite well defined from -50[degrees]C to the beginning of the glass transition temperature. The activation energy is of the same order as those reported in the literature (15). The activation energy calculated from Starkweather theory (9, 35, 36) for the lower limit of Ea for non-cooperative motion is of about 95 kJ/mol. As this value is close to the experimental activation energy and considering the preexponential factor of [10.sup.19] Hz, the [beta] relaxation would originate from quite local motions. It is worth noting that cooperative motions in poly(aryl ether ether ketone) is associated to a preexponential factor of [10.sup.30] Hz (37). No [beta] relaxation can be detected for PMDA- and BCDA-based polyimides, excepted for BCDA-BACN. Nevertheless, the tan[delta] value in 0 to 250[degrees]C-temperature range is of about 0.02. This value can not result from to the apparatus contribution. This could be attributed a very broad [beta] relaxation located from at least--150[degrees]C to the beginning of the glass transition temperature. Thus no characteristic parameter of this transition can be determined for these polyimides. These observations are consistent with the results of Sun et al. (16). Indeed, they have concluded that the [beta] relaxation is related to rotations of rigid segment of para-phenylene and imide rings due to phenyl-nitrogen conjugation.

However, this hypothesis does not explain why [beta] viscoelastic behavior of BCDA-BACN is the same as that of displayed by BTDA-BACN and differs from those exhibited by other BCDA-based polyimides (Fig. 6 and 8). No difference in microstructural parameters listed in Table 2 can be found to explain such a difference. However, the BACN unit differs from other diamine groups in that it is a meta diamine. Based on [N.sup.15] NMR chemical shift, Ando et al. (30, 38) have pointed out that the meta-linked diamines exhibit lower electron-donating property than para-linked one. Thus, the intra-molecular charge transfer in BACN-based polyimides can be strongly decreased in comparison to those of polyimides based on para-diamme. In these conditions, the [beta] relaxation of BACN-based polyimides likely arises from both oscillations of the imide ring and motions of the phenyl ring in the diamine moieties.

The [gamma] Relaxation

The temperature and the magnitude of the [gamma] relaxation are strongly dependent on the chemical structure of polyimide (Fig. 6-8). Nevertheless, after drying polyimide films in the dynamic mechanical setup, the magnitude of the [gamma] relaxation sharply decreases and it seems that it disappears as it is shown in Fig. 9. Furthermore, the height of the [gamma] relaxation tan[delta] peak ([H[gamma]) tends to increase when increasing the water content (Tables 2 and 3). Thus, unlike 13 and a relaxations, the [gamma] relaxation seems not to be only related to motions of the macromolecular backbone.

The comparison of the viscoelastic behavior for DDE-based polyimides in the -150[degrees]C to 0[degrees]C-temperature range is shown in Fig. 6. As reported in Table 3, the [gamma] relaxation temperature ([T.sub.[gamma]]) strongly depends on the dianhydride part. Nevertheless, the activation energy and the preexponential factor of this relaxation are in the same value range for all these polyimides. The [gamma] relaxation occurs 20[degrees]C lower for BTDA-DDE than for PDMA-DDE and it is located 35[degrees] higher than for BCDA-DDE. The [gamma] transition of the BTDA-based polyimides is located at higher temperature than those of the BCDA-based polyimides (Fig. 8). The tan[delta] spectra for BTDA-based polyimides are shown as a function of temperature at 1 Hz in Fig. 7. A small difference between [T.sub.[gamma]] for polyimide based on the same dianhydride part can be observed when changing the diamine structure. Such differences do not exceed 10[degrees]C (Table 3). Nevertheless, polyimides based on FDA diamine exhibit the lowest [T.sub.[gamma]] whatever the dianhydride group can be.

For the studied chemical structures, the [gamma] relaxation temperature seems to be more sensitive to the dianhydride moieties than to the diamine chemical structure. The comparison of the [gamma] process at 1 Hz induces the following classifications:

[T.sub.[gamma]]-BCDA [less than or equal to] [T.sub.[gamma]]-BTDA [less than or equal to] T-PMDA

[T.sub.[gamma]]-FDA [less than or equal to] [T.sub.[gamma]]-DDE [less than or equal to] [T.sub.[gamma]]-BACN

Replacement of BTDA dianhydride that can be considered as flexible groups by rigid dianhydride as BCDA and PDMA structure does not induce a systematic change on the [gamma] relaxation. Such a result is not consistent with conclusion reported by Hirayama et al. (39).

Xu et al. (4) have observed that the [gamma] relaxation temperature of PMDA-DDE is not dependent on the water content. It results that the modifications in the [gamma] relaxation temperature with chemical structure cannot be attributed to the differences in water content. To point out parameters, which govern the [gamma] relaxation temperature, dianhydride structures can be first compared. PMDA displays a planar and conjugated structure. Moreover, PMDA diimide has a high electron affinity (33). Thus PMDA-ODA film for which [gamma] relaxation is located at the highest temperature exhibits the lowest FVF and the highest [[lambda].sub.0]. In contrast, the presence of the cyclohexene in BCDA dianhydride avoids the interaction by conjugation and, thus, reduces the electron affinity of the diimide. In addition, BCDA displays a non-planar structure. Thus, the replacement of PDMA unit by the BCDA element could weaken the interaction between the polyimide chains as the decrease of [[lambda].sub.0] and the increase in both FVF and d-spacing suggest (Table 2). This decrease in the interchain interaction makes the packing chain state looser and promotes the molecular process at the origin of the [gamma] relaxation. Then, this induces a shift of the [gamma] relaxation towards lower temperatures (Table 3).

A similar argument can be proposed for the comparison of BTDA-based polyimides with PMDA-DDE. The BTDA diimine has a lower electron affinity than the PMDA moieties. i.e. 1.55eV (38)-1.64eV (40) for BTDA and 1.90eV (40) for PMDA. These differences arise from the introduction of carbonyl group in the dianhydride, which isolates the powerful electron withdrawing effect of imide groups from each other (33). Moreover, the carbonyl group induces a torsion angle between the imide group. Therefore the charge transfer interaction and, thus, the [T.sub.[gamma]] of BTDA-DDE are lower than those exhibited by PMDA-DDE. The comparison with polyimides based on 2,2-bis(3,4-decarboxyphenyl) hexafluoropropane dianhydrides (6FDA) agrees with this interpretation. As a matter of fact, the perfluorinated group breaks up the electron conjugation between the imide groups (22, 41), then distorts the linearity of the polyimide chain and induces steric hindrance for chain interactions. These effects produce a weak CTC formation. In suc h conditions, it is not surprising that Hirayama et al. have observed the [gamma] relaxation of 6FDA-DDE at -116[degrees]C for 1 Hz (39).

The effect of the diamine part on the [gamma] relaxation temperature can also be explained according to intermolecular considerations. Like 6FDA, the FDA diamine induces steric hindrance, which limits the interchain CTC formation (34). The increase in the free volume fraction for the polyimides based on 9,9-bis(4'-aminophenyl)fluorene (FDA) compared to the DDE-based polyimides (Table 2) seems to induce a shift of the [T.sub.[gamma]] towards the lower temperature.

In order to give evidence for the intermolecular contributions to the [gamma] relaxation temperature variation, [T.sub.[gamma]] was plotted versus microstructural parameters (Figs. 10 and 11). In Fig. 10, the points 1 and 2 represent data of FDA-based polyimides, which FFV is likely overestimated. As shown in Fig. 10, [T.sub.[gamma]] increases when the free volume fraction decreases. In spite of the fact that this correlation cannot be confirmed by the result of Hirayama et al. (39, 42, 43), this tendency was consistent with previous [T.sub.[gamma]]/FVF relationship reported by Aitken et al. (44) for polysulfone (Fig. 10). Such an evolution is in agreement with the increase of the [gamma] relaxation temperature when the average interchain distance decreases (Fig. 11). In addition, the gamma relaxation appears at higher temperature when the wavelength of transmission threshold increases. Thus, the improvement of inter-molecular charge transfer which results in an increase of macromolecular chain packing makes the molecular process at the origin of the [gamma] relaxation more difficult and implies a shift of this relaxation towards the higher temperatures.

The linear correlation coefficients ([r.sup.2]) between the microstructural parameters and the [gamma] relaxation temperature are calculated based on N measurements. According to both [r.sup.2] and N values, the probability of linear correlation (P) is determined (Table 4). Based on the P values, statistical correlation can be discussed. Thus, it is likely that [T.sub.[gamma]] and [[lambda].sub.0] are correlated with a probability of 99%. In addition, the chance that free volume fraction and polyimide [T.sub.[gamma]] dependence is high (94%). Nevertheless, the probability for correlation between FVF and [T.sub.[gamma]] is lower than that of [T.sub.[gamma]] and [[lambda].sub.0] because of the additive group method for the Van der Waals volume of cyclic chemical function. In addition, correlation between [T.sub.[gamma]] and d can be assumed In spite of the fact that the statistical value is the lowest.

CONCLUSION

Relationships between the dynamic mechanical behavior of polyimides and the chemical structure as well as the microstructure were investigated by studying film specimens. Polyimides were synthesized with aromatic and non-aromatic dianhydride monomers. Both [beta] and [alpha] relaxations of polyimides related to chain motions appear to be governed by different parameters. Thus, the [alpha] relaxation temperature related to the glass transition is controlled by the monomer rigidity while the broadness of the [beta] relaxation is mainly governed by the intensity of the intramolecular charge transfer between diamine and diimide fragments. Moreover, the [gamma] relaxation temperature related to bound-water molecules is very sensitive to changes in the chemical structure. A statistical correlation concludes that the gamma relaxation temperature of polyimides is dependent on the microstructural characteristics such as the interchain distance, fractional free volume and color index. Therefore the location of gamma re laxation could be considered as a microstructural probe.

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Table 1

Characterization of Polyimide

           Intrinsic viscosity
            (dL.[g.sup-1] in
              NMP (a) or in
Polyimide     m-cresol (b)      Tg([degrees]C)  % [H.sub.2]O

PMDA-DDE        0.91 (a) *         >390             0.3
BTDA-DDE        1.02 (a)            280             0.2
BTDA-FDA        0.98 (a)            370             0.4
BTDA-BACN       0.77 (a)            240             0.0
BCDA-DDE        0.89 (b)            390             3.0
BCDA-FDA        0.63 (b)           >390             3.1
BCDA-BACN       0.72 (b)            270             0.2
BCDA-BAPS       0.41 (b)            320             2.3

* Measured for poly (amic acide) solution.

Table 2

Microstructural Parameters of Polyimide Films

Polyimide  P (g.[cm.sup.-3])  FVF (%)  d-spacing (A)

PMDA-DDE         1.417         11.3         4.2
BTDA-DDE         1.373         12.2         4.0
BTDA-FDA         1.280         14.6         4.0
BTDA-BACN        1.359         12.1         4.2
BCDA-DDE         1.339         13.6         4.6
BCDA.FDA         1.251         15.7         6.3
BCDA-BACN        1.329         13.2         5.3
BCDA-BAPS        1.350         14.3         5.2

Polyimide  [[lambda].sub.0](nm)

PMDA-DDE           449
BTDA-DDE           439
BTDA-FDA           413
BTDA-BACN          407
BCDA-DDE           275
BCDA.FDA           310
BCDA-BACN          315
BCDA-BAPS          298

Table 3

                         [gamma] relaxation

           [T.sub.[gamma]] ([degrees]C)  [H.sub.[gamma]]
Polyimide            at 1 Hz             (x [10.sup.3])

PMDA-DDE                -78                    13
BTDA-DDE                -95                     9
BTDA-FDA               -100                     5
BTDA-BACN               -90                     7
BCDA-DDE               -122                    15
BCDA-FDA               -130                    19
BCDA-BACN              -115                    11
BODA-BAPS              -120                    18

                  [gamma] relaxation              [beta] relaxation

                  Ea (a)       [f.sub.0]   [T.sub.[beta]]([degrees]C)
Polyimide  (kJ.[mol.sup.-1])   (Hz) (b)             at 1 Hz

PMDA-DDE          54          [10.sup.14]
BTDA-DDE          49          [10.sup.14]             118
BTDA-FDA          38          [10.sup.12]             111
BTDA-BACN         54          [10.sup.15]             131
BCDA-DDE          55          [10.sup.19]
BCDA-FDA          60          [10.sup.22]
BCDA-BACN         47          [10.sup.18]             123
BODA-BAPS         74          [10.sup.25]

                   [beta] relaxation           [alpha] relaxation

                  Ea                         [T.sub.[alpha]]([degrees]C)
Polyimide  (kJ.[mol.sup.-1])  [f.sub.0](Hz)            at 1 Hz

PMDA-DDE          --                                     380
BTDA-DDE          132          [10.sup.18]               295
BTDA-FDA          135          [10.sup.18]               420
BTDA-BACN         139          [10.sup.18]               245
BCDA-DDE          --                                     370
BCDA-FDA          --                                     415
BCDA-BACN         143          [10.sup.19]               305
BODA-BAPS         --                                     335 *

(a)[+ or -] 4

(b)[+ or -] [10.sup.2]

* Determined at the E" maximum.

Table 4

Probability (%), P, That Both Parameters Are Non-Correlated

                                           Polyimides (39, 42)

          FVF       [rho]     [[lambda].sub.0]  FVF           [rho]

T[gamma]  6          10              1          95             13
FVF       *          28              33          *             28
p         *           *              21          *              *

          Polysulfones (44)

                 FVF

T[gamma]         <1
FVF               *
p                -**

** Data not available.

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Corine Bas *

Thierry Pascal #

* Corresponding author. Tel: [phone]; Fax: [phone] E-mail address: [e-mail]

# Present address. Elf Atochem-Centre de recherche Rhode-Alpes-BP63-69493 Pierre-Benite (France)