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Origin of dielectric response and conductivity of some alicyclic polyimides.

INTRODUCTION

Among the heterocyclic polymers recognized as high performance systems, aromatic polyimides (PIs) are the most studied polymers possessing excellent properties, including high thermal and chemical stability, high radiation resistance, high mechanical and insulating properties, and in particular, a high inherent refractive index (1). The superior properties of the aromatic polyimides come from the strong intramolecular and intermolecular charge--transfer complexes (CTCs) formed between the electron-donating diamine and the electron-accepting dianhydride moieties, which give their color and establish their dielectric constant, and make most of them insoluble and intractable in full imidized form (2-4). In this context, literature data indicate few main structural modifications of the backbone (5), such as incorporation of flexible linkages (6), introduction of twisted (7) or unsymmetrical (8) structures, bulky substituents (9), incorporation of aliphatic or alicyclic monomers (10) (organic compounds that are both aliphatic and cyclic), and copolymerization (11), which may improve solubility.

Polyimides-containing alicyclic structures have attracted much attention in recent years, due to their potential applications in opto-electronics and as low dielectric materials (12-16), because of their solubility, negligible birefringence, low refractive index, lack of color, and thermal stability. These characteristics come from their low molecular density and polarity, low probability of undergoing intermolecular CT, and even lower probability of main chain scission, because of the presence of multibonds which increase main chain rigidity (16). According to this literature review, one of the methods for designing of soluble and transparent polyimide is the incorporation of alicyclic groups and flexible linkages for the control of chain flexibility and segmental mobility, so that to reduce the intermolecular interactions, by disrupting co-planarity and conjugation, reducing symmetry, separating electronic segment (17) inhibiting packing, and reducing the intensity of the yellow color (18).

More than that, two major polarization mechanisms in polymeric materials are studied by dielectric spectroscopy, namely polarization due to charges migration which gives rise to conductivity and polarization created by orientation of permanent dipoles. The origin of conductivity in polymer networks is due especially to intrinsic migrating charges which can follow a more complex pattern. Unlike the electronic and atomic polarizations which are considered instantaneous by dielectric spectroscopy, the permanent dipoles, dipole orientation or dipoles polarization, are results of the dipoles alignment in the direction of the applied field, involving cooperative motions of molecular segments with time-scale measurable by dielectric spectroscopy. Thus, the time-dependent loss of dipole orientations upon removal of the electric field is defined by dipole relaxation. In this context, this is a great interest concerning the fundamental aspects of dielectric spectroscopy of polyimide materials (19), (20) for knowledge of various molecular motions and relaxation processes, and also the applicability domain in electronic interconnected devices, optoelectronic switches, printed board circuitry, etc.

In previous investigations (21-23), we have synthesized different polyimide structures based on cycloaliphatic dianhydrides, such as homo- and co-polyimides. We have also studied some special properties of various polyimide-based blend systems, related to morphological and structural-rheological aspects (24), blood compatibility (25), or different novel approaches for patterning such type of polymers (26).

This article discusses the dielectric spectroscopy and some optical properties of semi-alicyclic polyimide thin films obtained from 5-(2,5-dioxotetrahydrofurfuryl)-3-methyl-3-cyclohexene-1,2-dicarboxylic acid anhydride (DOCDA) and bicyclo[2.2.2]oct-7-ene-2,3,5,6- tetracar-boxylic dianhydride (BOCA) and two aromatic diamines: 4,4'-oxydianiline (ODA) and bis[4-4-(aminophenoxy) phe-nyl]sulfone (p-BAPS). The changes in the chemical structure, correlated to the effect on the dielectric spectra behavior and optical properties, should provide information on the molecular processes involving different relaxation and AC-conductivity.

EXPERIMENTAL

Materials

High purity chemicals: DOCDA dianhydride (Merk, 98% purity), BOCA dianhydride (Aldrich, >99% purity), ODA diamine (Aldrich, 99 % purity), and 1-methyl-2-pyrrolidone (NMP, Sigma-Aldrich 99.5 %, anhydrous) were used as received. p-BAPS diamine (TCI Europe, >97% purity) was recrystallized from ethylic alcohol.

Polymer Synthesis

The pure polyimides, poly(DOCDA-ODA), poly(-DOCDA-p-BAPS), poly(BOCA-ODA), and poly(BOCA-p-BAPS), were obtained from the alicyclic dianhydrides, DOCDA or BOCA, and two aromatic diamines, ODA and p-BAPS, by a two-step polycondensation reaction. A typical example for the synthesis of poly(DOCDA-ODA) is described in the following: in a 100 mL three-necked flask equipped with mechanical stirrer and nitrogen inlet and outlet, 2.64 g (10 mmol) of DOCDA were added at the same time with stirring, over a solution of 2 g (10 mmol) of ODA dissolved in 27 mL anhydrous NMP (19). The relative amounts of monomers and NMP were adjusted to maintain a solid content of 15%. After stirring for 12 h at room temperature, a viscous poly(amic acid) (PAA) solution was obtained. In the next step, the PAA solution was converted into polyimide (PI) by thermal imidization at 185[degrees]C for 6 h (Scheme 1).

The resulting water was removed with a gentle nitrogen flow which allows moving of the reaction balance for poly imide formation. The reaction mixture was cooled to room temperature. Part of the resulting polyimide solution was poured onto glass plates for the preparation of thin films, and the rest was poured into water, to precipitate the solid polymer. The powder product was filtered, washed twice with water and methanol and dried for 5 h in at 100[degrees]C in a vacuum oven. Molecular weight of structural units, [M.sub.0], and number average molecular weight, [M.sub.n], of these polyimides are presented in Table 1.

TABLE 1. Molecular weight of structural units, [M.sub.0],
number average molecular weight, [M.sub.n], glass
transition temperature,  [T.sub.g]([degrees]C), and
energies corresponding to four repeating units
((kcal [mol.sup.-1]) of the studied polymers,
calculated by the computational method: potential
energies at 0 K, [E.sub.pot.sup.0], and at 300 K,
[E.sub.pot.sup.300]. kinetic energies at 300 K,
[E.sub.kin.sup.300]; total energies at 300
K, [E.sub.tot.sup.300].

Polyimides          [M.sub.0]  [M.sub.n]  [T.sub.g]  [E.sub.pot.sup.0]

Poly(DOCDA-ODA)           428      20998        238             165.62
Poly(DOCDA-p-BAPS)        660      29419        191             335.51
Poly(BOCA-ODA)            412      53104        390             116.60
Poly(BOCA-p-BAPS)         644      43664        320             287.35

Polyimides          [E.sub.pot.sup.300]  [E.sub.kin.sup.300]

Poly(DOCDA-ODA)                  260.84                96.32
Poly(DOCDA-p-BAPS)               472.91              1,41.56
Poly(BOCA-ODA)                   203.52                86.74
Poly(BOCA-p-BAPS)                416.99               130.53

Polyimides          [E.sub.tot.sup.300]

Poly(DOCDA-ODA)                  357.16
Poly(DOCDA-p-BAPS)               614.47
Poly(BOCA-ODA)                   290.26
Poly(BOCA-p-BAPS)                547.52


Measurements

Polyirnide thin films, prepared by casting NMP polyimide solutions onto a glass substrate, were placed in a preheated oven at 80[degrees]C, to remove most of the solvent, and then dried by heating at 100, 150, 200, and 250[degrees]C for 1 h at each temperature. After stripping the films in hot water, the resulting samples were dried at 105[degrees]C in an oven.

Spatial molecular conformations and energy evaluations were performed with the HyperChem 8.07 professional program (Demo Version) (27), using the molecular mechanics (MM+) force field approximation method with the Polak-Ribiere algorithm for conjugate gradient--a graphic professional program that allows for rapid structure building, geometry optimization, and molecular display. For molecular dynamics, temperature was set to 300 K, time to 5 ps, and the time step was [10.sup.-3] ps.

Attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) was carried to characterize polyimide films. ATR-FTIR measurements were performed with a Nicolet-6700 ATR-FTIR spectrometer (Thermo Electron Corporation). ATR spectra were obtained in the 500-4000 [cm.sup.-1] range.

Dielectric spectroscopy measurements over the I Hz to 1 MHz frequency range were carried out using a Novocon-trol Concept 40 broadband dielectric spectrometer. Temperature was controlled with a 0.1[degrees]C device by the Novocontrol Quatro Cryosystem, in dry nitrogen atmosphere. The samples, around 25 [micro]m thick, with slightly larger diameters than those of the upper electrode (20 mm), were sandwiched between two gold-coated brass electrodes and then tested. Dielectric constant, [epsilon]', dielectric loss, [epsilon]'', and AC-conductivity, [sigma], of polyimides were determined by sweeping the frequency between 1 Hz and 1 MHz at fixed temperatures, at 4[degrees]C intervals, over a temperature domain between -150 and + 250[degrees]C, at an increasing temperature rate of 2[degrees]C [min.sup.-1]. This temperature range does not exceed the thermal decomposition temperatures. Measurements were performed in nitrogen atmosphere, thus avoiding water adsorption. According to literature data (28), one can observe that some polar molecules, such as water, influence the dielectric spectra. To eliminate this inconvenient in present investigation, a second heating cycle was performed for the polyimide samples.

The glass transition temperature ([T.sub.g]) of the investigated polymers was determined with a Mettler differential scanning calorimeter 12E (DSC), at a heating rate of 10[degrees]C [min.sup.-1] under nitrogen atmosphere.

Transmittance of the polyimides here under study was recorded at 300-1100 nm wavelengths, on a SPECORD 200 Analitik-Jena spectrophotometer.

Wide-angle X-ray diffraction measurements (WAXD) were performed on a D8 Advance Bruker AXS darn-tometer, with a Bragg--Brentano parafocusing goniometer. The X-rays were generated using a Ni-filtered Cu [K.sub.[alpha]] source with an emission current of 30 mA and a voltage of 36 kV. Scans were collected at room temperature, over the scattering angle 2[theta] = l[degrees] - 40[degrees], using a step size of 0.02[degrees]. Bruker AXS computer soft "DIFFRAC-plus EVA" was used to plot and process the data.

Density was measured by the Pycnometer Method.

RESULTS AND DISCUSSION

Molecular Modeling

Generally, conformational sampling necessary to efficiently explore the multidimensional potential energy surface of large molecules (and to find the global minimum) can be performed by simulation methods using a professional software. Molecular dynamics are used to calculate the potential, kinetic, and total energy at a temperature over 0[degrees]K. However, this method has time restrictions, as only short periods of time can be simulated, on the order of picoseconds. The molecular dynamics technique has been chosen for the present study, because it allows subsequent variation of geometry, being known as a very powerful technique for the evaluation of energy barriers between different stable or metastable conformations. Conformational changes in polyimides depend upon rotations around single bonds.

As a consequence of the chemical structure of the studies polyimides (alicyclic dianhydrides--DOCDA or BOCA--linked together by single bonds with aromatic diamines ODA or p-BAPS) (see Scheme 2), the torsion angle [PHI] along the linkages between the aromatic and imides rings (both planar), or between the aromatic rings linked with an ether bridge expresses the main degree of freedom that describes the general shape of the polymers. Furthermore, DOCDA contains a supplementary single bond that offers an additional degree of freedom. For each of the so-generated conformations, the energy was minimised and the structure was geometrically optimized with the HyperChem 8.07 professional program. Scheme 2 plots chemical structures of polyimides and spatial molecular conformations calculated for four structural units. Energies thus obtained are presented in Table 1; they suggest a more rigidity of polyimides with BOCA dianhydride than those with DOCDA dianhydride, while the two diamines influence is weaker. Therefore, an optimized characteristic adjusting rigidity and flexibility could be achieved by structural modification of polyimides.

Finally, computational evaluation shows that two assumption must be considered in the following sections of paper: primarily, the polyimide properties are more influenced by changes in dianhydride structure comparatively with changes in diamine structure of the main chain and secondly, the glass transition temperature is an important factor in interpretations of the structure--properties relationship, a high [T.sub.g] being associated with high rigidity (29). Moreover, energies calculated in this section (Table 1) confirm on the one hand the most rigid structure of BOCA moieties (with small, symmetrical, rigid, and non-planar bicycle-system), leading to highest glassy transition temperature than DOCDA moieties (with a large, non-symmetrical, and flexible molecule). On the other hand, the steric hindrance induced by the S[O.sub.2] groups from p-BAPS increases the free volume of polyimide chain and generates different limited motions, such as phenyl ring oscillations, in comparison with ODA diamine. Therefore, different structural features of these two dianhydrides and diamines significantly influence macromolecular conformation and physico-chemical properties of the synthesized polymers.

General Properties of Polyitnides

Polymers have been synthesized by the classical two-step method (Scheme 1), involving a PAA precursor subsequently cyclized into PI form (24). The chemical structure of the resulted PIs is presented in Scheme 2. According to Fig. 1, the FTIR spectra recorded for the studied film samples show characteristic imides absorption bands around: 1777-1770 [cm.sup.-1] and 1710-1703 [cm.sup.-1] (assigned to the C=0 asymmetrical and symmetrical stretching vibrations of imide rings), 1384-1382 [cm.sup.-1], and also at 784-769 [cm.sup.-1] (assigned to C-N stretching and C-N bending, respectively, in imide groups). The absorptions bands at 29272925 and 3068-3035 cm' should be assigned to the CH2 vibration of the aliphatic units and to the C-H linkage of the aromatic rings, respectively. Special bands at 1239-1232 [cm.sup.-1] are attributed to the ether bridge from ODA and p-BAPS diamine moieties, while those around 1320 or 1166 [cm.sup.-1] are assigned to the -S[O.sub.2] asymmetrical and symmetrical stretching vibrations in the p-BAPS diamine moities corresponding to poly(DOCDA-p-BAPS) and poly(BOCA-p-BAPS). The broad absorption band at 3350-3450 [cm.sup.-1] and the narrow absorption peak at 1650-1660 [cm.sup.-1], specific to amidic NH and C=0 group from the amide linkage, have disappeared entirely, indicating the completion of thermal imidization of the intermediate poly(amic acid) into final polyimide.

At room temperature, the investigated polyimides are soluble in test solvents, including N-methyl-2-pyrrolidone, N,N-dimethylacetamide, N,N-dimethylformamide, and tetrahydrofuran. This fact is due to the chain flexibility promoted by the flexible linkage and cycloaliphatic moieties with greater rotational freedom. Thus, takes place a decrease in close packing--by decreasing the entropy energy of internal rotation (30), a lighter solvent diffusion among macromolecules, and an increased solubility.

AC-dielectric Measurements at afferent Frequencies and Temperatures

The dielectric properties of polyimides, such as dielectrical constant, [epsilon]', and dielectric loss, [epsilon]", were measured over a wide temperature and frequency range.

According to Figs. 2 and 3, the dielectric constants increase slightly with temperature for all samples, due to the increase of total polarization arising from dipole orientation and trapped charge carriers, and decrease with increasing frequency, due to dielectric dispersion, as a result of the lag of molecules behind the alternation of the electric field at higher frequency (31). In this context, one can mention that the dielectric constants depend on the chemical structures of polyimides. Incorporation in the molecular structure of polyimides of asymmetric alicyclic DOCDA or symmetric alicyclic BOCA moieties, together with aromatic diamine units containing ether and/or sulfonic linkages, reduces electronic conjugation along the macromolecular chain to different extents.

First, involvement of a flexible co-monomer DOCDA reduces the polyimide chain--chain interaction and disrupts the interaction with the aromatic moieties of ODA or p-BAPS diamines. In addition, the presence of ether linkages in the diamine component disturbs the close packing of the polymer chains, increases the free volume, and reduces interchain electronic interactions. On the other hand, the presence of -S[O.sub.2] groups determines a decrease of the free volume due to competition between the increase of interchain interactions and the steric effects--with opposite contributions, and causes an increase in electronic conjugation chains for poly(DOCDA-p-BAPS). As a consequence, the dielectric constant of the polyimide containing only ether linkages is lower than that of the polyimide which contains both ether and sulfonic linkages. Thus, Fig. 3 shows that increasing frequency in the analyzed domain leads to dielectric constants in the ranges of 2.90-2.84, and of 3.33-3.29, respectively, for poly(DOCDA-ODA) and poly-(DOCDA-p-BAPS), at 25[degrees]C.

Secondly, the values of the dielectric constants for pair of BOCA--based polyimides are equal to or lower than those of the related polyimides which contain DOCDA dianhydride moieties. The lower values obtained for poly-(BOCA-p-BAPS) could be the result of a synergetic steric hindrance effect induced by the bicyclic non-coplanar group of BOCA moieties and the -S[O.sub.2] group from diamine. This cumulative effect increases the free volume, decreasing the close packing of the chains, thus decreasing the number of polarizable groups per volume units, lowering polarization (32). In this context, according to Fig. 3, with increasing of frequency, the values of dielectric constant at 25[degrees]C decrease from 2.90-2.84 for poly(BOCA-ODA) to 2.80-2.73, respectively, for poly(BOCA-p-BAPS). The rapid increase of [epsilon]' at higher temperature was attributed to the increase in chaotic thermal oscillations of the molecules and to the diminishing order degree of dipole orientation, near the glass transition temperature.

Variation of Dielectric Loss with Frequency and Temperature

Figure 4 plots the tridimensional variation of dielectric loss, [epsilon]', with frequency and temperature, for the studied sample, where two types of relaxation, [gamma] and [beta], appear. In addition, Fig. 5 presents this variation for the prime heating cycle, where the intensity of [gamma] relaxation is more pronounced. Note that the [gamma] transition is very sensitive to the presence of residual moisture and that drying leads to change (decrease) its intensity.

According to literature data, [gamma] and [beta] processes are initiated by localized motions of groups of atoms or molecular segments (33). The local regions containing the smallest group capable of reorientation should produce the [gamma] relaxation peak, while the local regions containing larger groups should produce the [beta] relaxation peak. Polyimide structures from this work can have a polarization degree caused, on the one hand, by polar structures of imide cycles and, on the other hand, by the existence of a minimum number of polar carboxylic side groups from the polyamic acid remained uncyclized into the final polyimide form. In addition, polymers containing p-BAPS shows a polarity-induced supplementary by the polar sulfone groups of this diamine. These small polymer segments absorb water from the atmosphere, having a strong effect on the dielectric measurements. Moreover, the decreasing of relaxation after drying in the second heating process can be observed by comparison between Figs. 4 and 5.

Detailed spectrum of dielectric loss in the frequency domain of [gamma] relaxation are exemplified in Fig. 6 for poly-(BOCA-ODA) and poly(BOCA-p-BAPS) for second heating measurements. This relaxation is observed at lower temperatures and for different frequencies. In addition, the main contribution to dielectric relaxation arises in the low frequency range, and this dielectric relaxation becomes faster with increasing temperature at higher frequencies.

On the other hand, [beta] relaxation appears at higher temperatures for different frequencies (Fig. 7).

As mentioned in literature (10), (30), [gamma] relaxation intensity of polyimides is reduced in the second heating cycle of dielectric loss vs. temperature measurements. Possibly, sonic polar molecules, such as water, are removed from the polyimide samples during heating. More than that, we can say that both [beta] and [gamma] relaxations of polyimides related to chain motions appear to be governed by different parameters. Thus, the [gamma] relaxation temperature related to bound-water molecules is very sensitive to changes in the chemical structure. A statistical correlation concluded that the [gamma] relaxation temperature of polyimides is dependent on the microstructural characteristics, such as inter-chain distance, fractional free volume, and color index. In this context, WAXD experiments show that the DOCDA-based polyimide films present no crystallinity. This can be explained taking into account the bulky, non-symmetrical, and flexible structure of DOCDA. These combined features are responsible for irregularity and non-linearity of the polymer chains, resulting in disturbance of the chain packing. On the other hand, the presence of the bridging oxygen atom in diamines ODA or p-BAPS, imparts additional flexibility, leading to decrease of chain packing regularity. Such synergistic effects were decisive for the amorphous character obtained for these samples. In the case of BOCA-based polyimide films, WAXD measurements (unpublished data) revealed broad peaks around 2[theta] = 15[degrees] - 16[degrees], assigned to the diffraction of intermolecular packing having some regularity, combined with amorphous halo (34). This fact is due to the geometrical constraints of the macromolecular chains induced by the BOCA moieties, which exhibit a noncoplanar configuration. Characteristics that quantify the intermolecular chain packing, such as the intersegmental distance (computed from the Bragg's equation), and the free volume fraction (calculated based on the density measurements ([rho]), according to the Eq. 1), are listed in the Table 2.

TABLE 2. Density of polyimides ([rho]), Bragg angle (2 [theta]),
intersegmental distance (d-spacing), and the free volume fraction
(FVF) of the poly(BOCA-ODA) and poly(BOBA-p-BAPS).

Polyimides         [rho] (g [cm.sup.-3])  2[theta]  d-spacing,  FVF, %
                                                    [Angstrom]

poly(BOCA-ODA)     1.347                    17.54         5.06   10.21

poly(BOCA-p-BAPS)  1.358                    16.32         5.43   10.86


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

where [M.sub.0] is the molar weight and [V.sub.0] is the volume occupied by chain (estimated in accordance with Bondi theory (35), (36)).

The obtained results are in agreement with those reported in literature (37) and support the explanation of the work concerning influence of inter-chain distance and fractional free volume.

From the experimental data, for each pair of polyimides having the same dianhydride segment, [gamma] transition temperature was lower for the polymers with p-BAPS moieties, comparatively with that of the polymers containing ODA moieties. It is possible that the steric hindrance effect induced by the S[O.sub.2] group should increase the free volume and, consequently, facilitate different limited motions such as phenyl ring oscillations or other fragments responsible for this transition.

Enthalpy and Entropy Contributions to the [gamma] and [beta] Processes Activation Energy

Taking into consideration that the strength and frequency of relaxation depend on the characteristic properties of dipolar and ionic relaxation, the present study can also provide some information on the modification of local relaxation (38). Thus, individual relaxations can be described using the Havriliak--Negami (HN) expression:

e* = [epsilon]' - i[epsilon]" = [[epsilon].sub.U] + [[[epsilon].sub.R] - [[epsilon].sub.U]] / [[1 + [(i[omega][[tau].sub.HN]).sup.a]].sup.b] (2)

where [[epsilon].sub.R] and [epsilon].sub.U] represent the relaxed and ([omega] [right arrow] 0) unrelaxed ([omega] [right arrow] [infinity]) values of the dielectric constant for each relaxation, [omega] = 2[pi]f is frequency [[tau].sub.HN], is the relaxation time for each process, and a and h represent the broadening and skewing parameters, respectively. When parameter a is much below 1, the distribution of the relaxation time is broader (39). Also, when parameter b is equal to or smaller than 1, dielectric dispersion is symmetrical or asymmetrical, respectively. The relaxation time, [[tau].sub.max] associated with the peak maxim, can be derived from the HN relaxation time, [[tau.sub.HN], at each temperature, according to expression:

[[tau].sub.max] = [[tau].sub.HN][[[sin([pi]ab/(2 + 2b))] / [sin([pi]a/(2 + 2b))]].sup.1/a] (3)

In this context, the relaxation time for [gamma] relaxation, [[tau].sub.max], resulting from HN curve fits, correlated with the maximum frequency for dielectric relaxation by the [f.sub.max] = [(2[pi][[tau].sub.max]).sup.-1] dependence, is plotted versus the reciprocal temperature (i.e., Arrhenius plots) in Fig. 8, according to the following equation, corresponding to the temperature domain of [gamma] and [beta] relaxations, respectively:

[[tau].sub.[gamma]or[beta]] = [[tau].sub.[gamma]or[beta]O]exp[[E.sub.[gamma]or[beta]]|RT] (4)

where [E.sub.[gamma]or[beta]]/RT express the apparent activation energies and [[tau].sub.[gamma]Oor[beta]O]--the pre-exponential factors of the [[tau].sub.[gamma]or[beta]] relaxation times, respectively.

The pre-exponential and apparent activation energy parameters provide information about the nature of the motions involved in relaxation processes.

Thus, the activation energy, [E.sub.A], for [gamma] relaxation has approximately the same small values for all samples, being close to the values reported in the literature for similar polyimides, and [[tau].sub.0] is close to the Debye time [[tau].sub.D]) = [10.sup.-13]s = 2[pi]h/kT (at room temperature). In this situation, the motions associated with [gamma] relaxation may be considered, from present data, as to be localized and noncooperative. In this context, literature (39), (40) shows that, in the sub-glass relaxation domain, the activation energy associated with each relaxation is related to the relaxation temperature and to its corresponding activation entropy at a frequency of 1 Hz, according to the approach described by Starkweather equation (41):

E = RT[1 + ln(KT / 2[pi]hf)] + T[DELTA]S (5)

The first term in this equation is the enthalpy contribution of the activation energy, where k is the Boltzmann constant, h--the Planck constant, and T--the absolute temperature. The second term, [DELTA]S, is the entropy contribution of the activation energy of a thenno-activated motion.

Thus, for the [gamma] relaxation of the studied polyimides, entropy contribution is negligible (because the activation energy varies linearly with T) for the limiting low-temperature at a given frequency, while the activation energy is essentially due to an enthalpy contribution.

On the other hand, the [beta] relaxations are mainly considered to correspond to dipole-segmental motions. In this context, it is observed that the average apparent activation energies for [beta] relaxations increase for polyimides based on BOCA dianhydride, known as more rigid, comparatively with those containing DOCDA dianhydride (Fig. 8). The rigidity of some samples is confirmed by the higher values of their potential energy (Table 1). Simultaneously, the pre-exponential time, [[tau].sup.0[beta]], decreases.

In addition, the activation energy values for [beta] relaxations are higher than those found for [gamma] relaxations. The short pre-exponential time combined with the high apparent activation energy for [beta] relaxation can be analyzed using Starkweather equation as previously discussed. Thus, it can be considered that the entropy contribution, T[DELTA]S, for the [beta] process is not negligible compared to the enthalpy term, having a greater contribution to the activation energy for more flexible polymers. In addition, the origin of the activation entropy of [beta] relaxation is effect of cooperative contributions of intramolecular/intermolecular interactions.

HN parameters versus temperature for [gamma] and [beta] relaxations were presented in Fig. 9 for all studied samples.

For both samples with DOCDA dianhydride, the intensity of the [gamma] relaxation, [DELTA][epsilon] = [[epsilon].sub.R] - [[epsilon].sub.U], decreases with temperature, reflecting a decrease of dipolar correlation factor (41). In addition, [DELTA][epsilon] and consequently the net dipolar moment per volume unity for poly(DOCDA-ODA) are higher than poly(DOCDA-p-BAPS). On the other hand, the broadening, a, and skewing parameters, b, increase with temperature, reflecting the fact that the relaxation time distribution becomes tighter at higher temperature. Unlike these samples, the intensity of [gamma] relaxation increase with temperature and has the closest values for both poly(BOCA-ODA) and poly(BOCA-p-BAPS). Also, [gamma] relaxation for poly(BOCA-p-BAPS) expands as the temperature increases because the broadening parameter, a, decreases with increasing temperature.

For all studied samples containing DOCDA or BOCA dianhydrides, the [beta] relaxation occurring at higher temperature is found to be symmetric in the frequency domain, with the skewing b parameter equal to unity. The intensity of the [beta] relaxation is about the same for both samples with BOCA dianhydride and is higher than for samples with DOCDA dianhydride. Lowest intensity of [beta] relaxation is observed for poly(DOCDA-p-BAPS), suggesting a lower net dipol moment caused by the molecular groups that became less mobile during this transitions. For this sample, the broadening parameter increases with temperature, suggesting a narrowing of the relaxation times distribution with increasing temperature.

The [alpha] relaxation, near the glassy transition temperature, [T.sub.g], is caused by a rotatory diffusional motion of the molecules from one quasi-stable position to another one, around the skeletal bond, involving a large-scale conformational rearrangement of the main chain. For the polyimides based on DOCDA, which have lower glass transition temperature, [alpha] relaxation was not observed at low frequencies, where the losses caused by conduction are prevalent; this type of relaxation appears only close to glass transition at high frequencies. For polymers based on BOCA, this transition does not appear in the spectra, because [T.sub.g] exceeds the upper temperature developed in the experiments.

Electrical Modulus Analysis

Conductivity behavior in the frequency domain is more conveniently interpreted in terms of conductivity relaxation time, [tau], using the representation of electrical modulus, M* = 1 / [epsilon]*. The M* representation is now widely used to analyze ionic conductivities, by associating a conductivity relaxation time with the ionic process (42). Thus, the electric modulus, M*, is defined in terms of the reciprocal of the complex relative permittivity, [epsilon]*, as:

M* = 1 / [epsilon]* = M' + iM" (6)

where M' = [epsilon]'/[[[epsilon]'.sup.2] + [[epsilon]".sup.2]] and M" = [epsilon]"/[[[epsilon]'.sup.2] + [[epsilon]".sup.2]]

Tridimensional variation with frequency and temperature of the real, M', and imaginary part of the modulus, M", for polyimides, is shown in Figs. 10 and 11.

At lower frequencies, the real and imaginary parts of the modulus approach zero, indicating that the electrode polarization phenomenon makes a negligible contribution; the long tail that appears is due to the large capacitance associated with the electrodes (43). The presence of a peak in the imaginary modulus formalism at higher frequency suggests that ionic conduction is predominant in the structure of the studied polyimides. As temperature increases, the peak maximum shifts to higher frequencies, indicating that the conductivity of the charge carrier has been thermally activated.

AC-conductivity

Variation of AC-conductivity, [sigma], with frequency, at different temperatures, in the range of -150 / + 250[degrees]C, is shown in Fig. 12. It can be noticed that the conductivity of many materials, particularly of the amorphous ones, such as polyimides, is governed by the following dependence (44):

[sigma](f) = [[sigma].sub.DC] + A[f.sup.n] (7)

where [[sigma].sub.DC]: is DC-conductivity, A is the pre-exponential factor and n is the fractional exponent ranging between 0 and 1.

In the present study, n exponent, calculated from the frequency dependent conductivity, decreases for all samples with increasing temperature and the frequency domain, being generally [less than or equal to] 1 (see the values of n given in Fig. 12), for a temperature close to room temperature. The plateau region of conductivity corresponds to the DC conductivity, according to Eq. 7. The n value in region of higher frequency characterizes electronic conduction via a hopping process (45), (46). On the other hand, for temperatures exceeding 150[degrees]C, the AC-conductivity is nearly independent on frequency in the low frequency domain. Deviation from linearity at higher frequencies may be due to the dispersion of charge carriers produced by dipolar relaxation.

The thermal activation energies of AC-conductivity at frequency of 1000 Hz, in 5[degrees]C-85[degrees]C range of temperature, were evaluated from Eq. 8 (47), (48) and Fig. 13.

[sigma] = [[sigma].sub.0] exp(-[E.sub.[sigma]] / kT) (8)

where [E.usb.[sigma]] denotes the thermal activation energy of electrical conduction, [sigma] is a parameter depending on the polymer nature, k is Boltzmann's constant (k = 8.617343 * [10.sup.-5] eV [K.sup.-1]), and T represents the absolute temperature.

According to literature data (49), the higher slopes correspond to intrinsic electrical conduction, while decreasing slopes at lower temperatures indicates a reduction in the impurity concentration of the samples. In present investigations, for poly(DOCDA-ODA). poly(DOCDA-p-BAPS), poly(BOCA-ODA), and poly(BOCA-p-BAPS), at higher temperatures and 1000 Hz, the values of activation energy for AC-conductivity are 0.0898 eV, 0.0842 eV, 0.1010 eV, and 0.1033 eV, respectively. These obtained values (< 1 eV) can be explained in terms of a band conduction mechanism, through bandgap representation.

Transmittance and Optical Gap Energies

The values of the thermal activation energy of electrical conduction are different from those obtained from the optical bandgap energy--evaluated via transmission spectra.

Typical transmission spectra of the investigated polyimide films, over the whole measured range of 300-1200 nm wavelengths, are initiated in the ultraviolet domain, above 450 nm showing values of about 90 % transparency. To obtain the absorption coefficient, [alpha], from transmittance data, the following equation was used:

[alpha] = (1/d) ln(l/transmittance) (9)

where d is film thickness.

Generally, for a typical amorphous semiconductor, three domains are evident in the variation of the absorption coefficient versus photon energy. In the first region, the absorption coefficient, due to the inter-band transition near the band gap, describes the optical gap energy [E.sub.G] in amorphous semiconductors; in the second region, absorption at photon energy below the optical gap depends exponentially on photon energy, which defines the Urbach edge energy, [E.sub.U], according to the idea that the sharp absorption edge is enlarged by the electric fields produced by charged impurities; the third region describes the optical absorption generated by defects appearing at an energy lower than the optical gap; it is sensitive to the structural properties of the materials, being defined as the so-called Urbach tail, [E.sub.T]. This absorption tail lies below the exponential part of the absorption edge (the second region), and its strength and shape were found to depend on the preparation, purity, and thermal history of the material, varying only slightly with its thickness. The approach, typical for amorphous semiconductors, has been applied to the studied polymer films.

From the obtained data, the absorption coefficient was plotted in Fig. 14 for the studied film, as a function of photon energy, according to:

[alpha] = [[alpha].sub.0] exp(E/A) (10)

where [[alpha].sub.0] is a constant and E is photon energy.

The shape of the curve is very similar to the behavior proposed by Tauc for a typical amorphous semiconductor (50), although the absorption level is lower than for amorphous, inorganic thin films. These results agree with other literature data, which assume that a lower absorption in polymer materials is due to a lower degree of bonding delocalization (49). An absorption edge is a sharp discontinuity in the absorption spectrum by an element appearing when the energy of the photon corresponds to the energy of an atom shell. Each of the absorption edges in Fig. 14 exhibits two different slopes. Parameter A becomes either [E.sub.U], in the high-energy region, or [E.sub.T] in the low-energy region of the absorption coefficient. The values of Urbach energy in the 212-290 meV range agree with the specific values for transparent polymers. Also, the [E.sub.T] energies are related to the localized state induced by the polymeric atomic structures. Possible structural defects, such as breaks, configurationally imperfections, torsions, and kinks introduced by different linkages, -0-, or -S[O.sub.2] in diamine segments, or different special molecular configurations of dianhydride moieties in the polymer chains seem to be responsible for the higher values of Urbach tail energy, [E.sub.T]. Moreover, larger structural disorder and charged impurities may cause an increase in Urbach energy, [E.sub.U].

The small plots introduced in Fig. 14 were used to obtain the optical gap energy, [E.sub.G], according to Tauc power law:

[([alpha] * E).sup.1/2] = B(E - [E.sub.G]) (11)

where B is a constant.

The obtained energy gap values of all polyimides in the 3.51-3.73 meV range correspond to transparent films. As the intermolecular and intramolecular CTC is reduced when using aliphatic monomers, the interaction between aromatic diamine and aliphatic dianhydride moieties is disrupted, transparency increases, and polymer color intensity decreases. Also, in the 207-222 meV and 830-976 meV ranges, respectively, the [E.sub.U] and [E.sub.T] values correspond to transparent films. All these values are in agreement with other results concerning the aliphatic--aromatic polyimides with different ratio of aliphatic to aromatic parts and different types of aliphatic diamine (51).

The optical bandgap energies, [E.sub.G], presented in Fig. 14 are different from those obtained from the values of thermal activation energy of AC-electrical conduction, [E.sub.[sigma]]. Generally, [E.sub.G] = 2[E.sub.[sigma]] (52). Considering that light emission in the semiconductor is a photon-creating process, by annihilation of an electron-hole pair, the gap energy obtained from optical measurements should be higher than the EG value given by conductivity analysis. Furthermore, the differences between optical and electrical gap energy can be explained if assuming that the band gap optical energy of the system is related to the photon energy intensity of the photoluminescence spectra, and that band gap electrical energy is a consequence of the relaxation process appearing when temperature is modified.

CONCLUSIONS

The dielectric and optical behavior-chemical structure relationship of semi-alicyclic polyimides were investigated. The polymers have been obtained by a polycondensation reactions between DOCDA and BOCA dianhydrides and the flexible aromatic diamines ODA or p-BAPS. At the applied frequencies, the studied polyimides exhibit low dielectric constant values, in the 2.73-3.33 range, at 25[degrees]C. For all samples, due to dielectric dispersion, the dielectric constant decreases with increasing frequency and increases with temperature--being influenced by total polarization arising from dipole orientation and trapped charge carriers.

Both [beta] and [gamma] relaxations in polyimide films, related to chain motions, appear to be governed by different parameters. It can be concluded that [gamma] relaxation corresponds to the isolated motions occurring without cooperative contributions and that the main activation energy process is enthalpy. In this context, for each pair of polyimides having the same dianhydride segment, [gamma] transition temperature, occurring at low temperatures, is lower for the polymers with p-BAPS moieties, due to steric hindrance effect induced by the S[O.sub.2] group which increase the free volume and facilitate different limited motions such as phenyl ring oscillations or other fragments responsible for this transition, comparatively with that of the polymers containing ODA moieties.

On the other hand, the [beta] relaxations are considered to correspond to dipole-segmental motions, where the average apparent activation energies increase for polyimides based on BOCA dianhydride, known as more rigid, comparatively with those containing DOCDA dianhydride. The entropy contribution, T[DELTA]S, for the [beta] process is not negligible, having a greater contribution to the activation energy for more flexible polymers. Thus, for [beta] dielectric relaxation, a specific cooperative contribution between intramolecular and intermolecular contributions appears, in correlation with the chemical structure of polyimides. In addition, a relatively broad distribution of the relaxation times and an asymmetrical dielectric dispersion are evidenced.

Finally, modification in AC-conductivity with temperature and frequency is dependent on the structural parameters of polyimides. At the same time, a model based on energy bandgap representation was established for explaining the influence of temperature on electrical conductivity. The values of thermal activation energy of electrical conduction are different from the results provided by absorption spectra, being first a consequence of the electronic transfer mechanism appearing when changing temperature and, secondly, of the absorbed photons, electrons, and holes generators.

The findings of this study demonstrate that semi-alicyclic polyimides, with a suitable macromolecular design, may potentially offer important advantages for microelectronic applications.

Correspondence to: Silvia loan; e-mail: ioan_silvia@yahoo.com

Contract grant sponsor: Romanian National Authority for Scientific Research, CNCS--UEFISCDI; contract grant number: PN-II-ID-PCE-2011-3-0937, 2012 phase.

DOI 10.1002/pen.23409

Published online in Wiley Online Library (wileyonlinelibrary.com).

[c] 2012 Society of Plastics Engineers

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Silvia loan, Camelia Hulubei, Dumitru Popovici, Valentina Elena Musteata

'Petru Poni' Institute of Macromolecular Chemistry, Iasi, Romania
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Author:Ioan, Silvia; Hulubei, Camelia; Popovici, Dumitru; Musteata, Valentina Elena
Publication:Polymer Engineering and Science
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Date:Jul 1, 2013
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