Slow relaxations in semicrystalline poly(butylene succinate) below and above [T.sub.g].
Poly(butylene succinate) (PBS) is an aliphatic polyester that has similar processability as conventional resins like polyethylene, being one of the most suitable materials for processing into films. Furthermore, it is a pioneer of green plastic materials due to its good biodegradability, which gave rise to wide range of applications [l]. As biodegradable polyester with balanced mechanical properties and processability, PBS has attracted intensive attention in both academic and industrial areas for applications for agricultural purposes (garden films and compostable bags), shopping bags, eco-friendly dielectric polymeric materials for drug delivery, artificial implants, tissue engineering, as well as green materials.
Biodegradable polymeric materials are one kind of good materials showing ecological advantages over other nondegradable plastics and offering alternative solutions for global waste problems. In fact, the use of petroleum for plastics production contributes to problems such as global warming and depletion of petroleum reserves. To reduce the amount of petroleum used for plastics production, various biomass-based plastics have been developed. Another environmental problem caused by plastics is plastics waste. To solve the environmental problems caused by this waste, new biorecycling waste treatment systems such as composting or methane fermentation have been developed. PBS is one of these biodegradable materials, and the chemical synthesis of fully biomass-based PBS has been described .
The features of the molecular mobility determine many physical properties, and the relaxation processes present, including the secondary, have influence in the glassy state stability (crystallization and aging) [3-5], during storage and in the utilization conditions. Among the techniques suitable to study molecular mobility in very viscous systems, dynamic mechanical spectroscopy, NMR spectroscopy, dielectric relaxation spectroscopy (DRS), and thermally stimulated depolarization currents (TSDC) are the most frequently used. The studies on the kinetics of the relaxation processes present in pure PBS are relatively scarce. Two dynamical mechanical studies just provide the temperature location of the loss tangent peak [6, 7], A detailed study based on the DRS technique  covers the glass transition and the sub-[T.sub.g] relaxations. No TSDC studies on the slow relaxations in PBS are available in the literature.
In this work, we use the dielectric TSDC technique to obtain insight on the slow molecular mobility in the amorphous part of semicrystalline PBS. DRS and TSDC are dielectric related techniques: in DRS the sample is submitted to a ac electric field and the real and imaginary parts of the permittivity are measured as a function of the frequency; in TSDC the sample is submitted to a dc electric field, the polarization is frozen by cooling, and the depolarization current is recorded on heating allowing the calculation of the kinetic parameters of the relaxation modes , We will carefully explore the orientational and space charge relaxations, looking at the local and cooperative processes, and eventually at some chain diffusion process. The obtained results will be discussed and compared to those provided by DRS .
PBS, trade name "Bionolle," was a gift from Showa Denko K. K. (grade 1001MD), mean molecular weight ~240,000 g [mol.sup.-1], water content 0.026%. The repeating unit of PBS is --O-- [(C[H.sub.2]).sub.4]--O--CO--[(C[H.sub.2]).sub.2]--CO--, with a molecular weight of 172.1785 g [mol.sup.-1]. PBS shows a good thermal stability; the initial decomposition temperature is 396[degrees]C, and the temperature ascribed to the maximum rate of thermal degradation is 455[degrees]C (onset 396[degrees]C, endset 455[degrees]C, and weight loss 98.2%). At 400[degrees]C, the weight loss is reported to be 5% .
Pellets of PBS were compressed between two stainless steel plates heated at T = 145[degrees]C, during 30 min under a pressure of 10 ton. After cooling to room temperature, cylindrical slices (diameter 8 mm) were produced from the created film (thickness of ca. 0.1 mm). The slices were dried overnight in a vacuum oven at T = 100[degrees]C and P = [10.sup.-3] mbar. For the TSDC measurements each slice of PBS used was previously submitted, inside the apparatus cell, to three cycles of vacuum/inert gas. Finally, and during all the measurements, the sample remained under an inert atmosphere of helium (P = 1.1 bar) that, simultaneously, allowed a better temperature control due to the higher helium thermal conductivity value compared with that of nitrogen. For DSC measurements, a small portion of the film or of a slice was used.
Differential Scanning Calorimetry (DSC)
The calorimetric measurements were performed with a 2920 MDSC system from TA Instruments (USA). The samples of ~5-10 mg were introduced in aluminum pans. The measuring cell was continuously purged with dry high purity helium gas at a flow rate of 30 mL [min.sup.-1]. An empty aluminum pan, identical to that used for the sample, was used as the reference. Cooling was achieved with a liquid nitrogen cooling accessory, which permits automatic and continuous programmed sample cooling down to -150[degrees]C (123 K). The baseline was calibrated by scanning the temperature domain of the experiments with an empty pan. Additional details on the calibration procedures, including temperature and enthalpy, are given elsewhere ,
TSDC and TSPC
Thermally stimulated current experiments were carried out with a TSC/RMA spectrometer (TherMold) covering the range from -170 to +400[degrees]C. For these measurements the sample was placed between the disc-shaped electrodes (7 mm diameter) of a parallel plate capacitor. TSDC is a dielectric technique in the time domain, adequate to probe slow molecular motions (1 to 3000 s). The fact that the relaxation times of the motional processes are temperature dependent, and become longer as temperature decreases, allows to make them exceedingly long (freezing process) compared with the timescale of the experiment.
We believe that the degree of crystallinity of the sample was a constant during all the TSC experiments. In fact, the pellets have been prepared at 145[degrees]C (above the melting temperature), dried under vacuum at 100[degrees]C (above the crystallization temperature), and cooled very slowly inside the vacuum oven down to room temperature, so that the crystallization temperature region was crossed at rates <1[degrees]C min-1. The crystallization was thus complete, as the article by Bikiaris et al.  stated that PBS crystallizes rapidly on cooling from the melt, which is confirmed by our thermogram shown below in Figure 2. Furthermore, the TSDC experiments covered the temperature interval between - 130 and 25[degrees]C, well below the crystallization temperature.
In a TSDC experiment, the sample under study is placed between the electrodes of a parallel plate capacitor, and is polarized with a dc electric field at a given temperature (the polarization temperature, [T.sub.P]), for a given period of time (the polarization time, [t.sub.P]; see Fig. 1a, step 1). Two important parameters in a TSDC experiment are the polarization temperature, [T.sub.P], at which the polarizing electric field is turned on, and the temperature [T.sub.P] < [T.sub.P] at which the field is turned off.
In a second step (2), the sample was cooled down to a temperature [T.sub.P] = [T.sub.P] - [DELTA]T in the presence of the electric field (see Fig. 1a). This freezes-in the dipolar orientations, retaining (at least partially) the polarization created by the electric field applied in the temperature window [DELTA]T = [T.sub.P] - [T.sub.P']. At the end of this step, often called the freezing-in step, with the sample at the temperature [T.sub.P'], the polarizing electric field is removed [step (3)]. Part of the polarization created by the polarizing electric field will disappear including the induced polarization, but part of the orientational polarization will be preserved by the subsequent cooling process [step (4) in Fig. 1a]. The sample so obtained is thus a stable electret, that is, a sample presenting a given amount of permanent orientational polarization [step (5)]. Finally, the polarized sample is submitted to a constant rate heating process in step (6). This is the thermally stimulated depolarization step of a TSDC experiment, in which the sample returns to the equilibrium state. The depolarization process gives rise to a measurable current intensity, I, the depolarization current, which is recorded as a function of temperature.
The appearance of a TSDC peak can be rather complex, and this complexity depends on the temperature interval, AT, where the polarizing field acts, often referred to as polarization window. If [DELTA]T is wide ([T.sub.P] >> [T.sub.P']), the retained polarization arises from the orientation by the electric field of a wide variety of dipolar motions, and these different dipolar motions are depolarized in such a way that less hindered motions depolarize at lower temperatures, while the most hindered motions depolarize at higher temperatures. In contrast, if [DELTA]T is small, the retained polarization arises from a narrow variety of dipolar motions. Such an experiment with a narrow [DELTA]T is often called fractional polarization or partial polarization (PP) TSDC experiment, and a typical value of the polarization window is 2[degrees]C. The PP experiment allows probing more narrowly distributed relaxation modes and, in the conceptual limit of a very narrow polarization window, the experimental depolarization current peak is supposed to correspond to a single mode of relaxation , We used polarization windows two degrees wide, and we tacitly assumed that this window isolated single relaxation processes. This assumption is based on the observation that similar PP experiments with polarization windows of 0.5, 1, or 2[degrees] led to the same results.
The analysis of the PP results is based on the hypothesis that the depolarization process obeys a first order rate kinetics, that is
dP(t)/dt = J(T) = P(T)/[tau](T), (1)
where P(t) is the polarization stored by the sample at time I, J(T) the depolarization current density at temperature T, and [tau] (T) is a temperature dependent relaxation time, characteristic of the elementary mode of motion under consideration. This assumption was the subject of controversy, and its correctness was discussed in detail elsewhere [14--16). In Eq. /, temperature and time are related by dT = r.dt, where r is the heating rate of the linear heating ramp. The temperature dependent relaxation time can be obtained by rewriting Eq. ! as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where I denotes the current intensity, whereas J denotes the current density (the current intensity per unit area). Equation 2 allows the calculation of the relaxation time at each temperature T of the depolarization process given that J(T) is the output of a PP experiment, and P(T) can be obtained from the area of the PP peak above the temperature T . This capability of directly calculating the temperature dependent relaxation time from the results of a single PP experiment constitutes the essential quantitative feature of the TSDC technique.
Thermally stimulated currents can also be originated working in the so-called polarization mode (Thermally Stimulated Polarization Currents, TSPC). In a TSPC experiment, the sample is also polarized with a dc electric field at a given temperature (the polarization temperature, TP), for a given period of time (the polarization time, [t.sub.P]), but now, in the following step, it is submitted to a constant rate heating process in the presence of the polarizing field (see Fig. 1b). In a TSPC experiment, the current is recorded while the sample is under short-circuit during heating. The charging current has two contributions: the dipolar orientation and the motion of space charges. These contributions behave differently as a function of temperature.
A dipolar reorientation is a transient process giving rise to a current peak, J(T), whose equation is well known in depolarization, [J.sub.D](T) as well as in polarization [J.sub.P](T). The similarity between [J.sub.D](7') and [J.sub.P](T) implies that a TSPC peak should be characterized by the same position, height and shape as the corresponding TSDC peak, the only difference being that the polarization current is of opposite sign. Oppositely, the mobility of free charge carriers is a conduction process which gives rise to a current that exponentially increases with temperature, in TSDC as well as in TSPC. However, in disordered solids there are charge carriers (homo and hetero-charges) that move by a hopping mechanism, and can give rise to space charge peaks. If the charge carrier mobility has low activation energy, it can behave as a conduction process in TSPC. In some more complex cases, the space charge peaks can also be distinguished from the dipolar peaks by comparing the TSDC and TSPC results .
The basic description of the TSDC experiment, the discussion of the nature of the information it provides, and the methods for TSDC data treatment are presented elsewhere  in a detailed and comprehensive way, particularly in the Supporting Information of this reference. The physical background of the TSDC technique is presented in a variety of review articles [9, 18-21], A review on the diversity of TSDC applications is also available ,
RESULTS AND DISCUSSION
Melting and Ciystallization Behavior
PBS is a semicrystalline polymer, with a degree of crystallinity, [X.sub.c], reported by the manufacturer to be between 35 and 45%. To estimate [X.sub.c], the value of the melting enthalpy for 100% crystalline polymer, [[DELTA].sub.fus]/[H.sup.0], is needed. The value of [[DELTA].sub.fus]/[H.sup.0] = 110 J [g.sup.-1] was reported [10, 23], obtained from the crystallization enthalpy extrapolated to the cooling rate 0[degrees]C [min.sup.-1]. However, the infinite slowness of the cooling rate does not warrant the full crystallinity of the polymer. Different and more reliable values of the melting enthalpy of the fully crystalline polymer are reported in the literature. The value [[DELTA].sub.fus]/[H.sup.0] = 200 J [g.sup.-1] was obtained extrapolating to 0[degrees]C [min.sup.-1] the cooling rate and taking into account the density of the crystalline form calculated from transmission electron microscopy and X-ray Diffraction data ; [[DELTA].sub.fus]/[H.sup.0] = 210 J [g.sup.-1] was obtained by experimentally determining the crystallinities (by wide angle Xray diffraction) and the melting enthalpies (by DSC) of different samples prepared by different isothermal treatments [24, 25]. This latest procedure seems the most reliable and, based on this value, and on the melting enthalpy of our samples ([[DELTA].sub.fus]/[H.sup.0] = 67.4 J [g.sup.-1]), we obtain [X.sub.c] = 32%.
The crystallization and melting behavior of PBS was studied in detail [23, 24, 26], It is well know that many semicrystalline polymers, including flexible polymers (such as PBS) and semistiff polymers, display multiple endothermic peaks in the DSC thermogram [24, 26], Figure 2 shows the DSC results obtained in different cooling/heating cycles of our sample. The heat flow curves on heating confirm the complex nature of the melting process, and show that the maximum of the melting peak is at [T.sub.fus] = 113[degrees]C, independent of the heating rate, in good agreement with the literature values [8, 23, 24, 26-28].
It can also be observed that the melting peak shows a slow premelting, and presents a small peak in the lower temperature side, at 103 [degrees]C. It was argued that this complexity cannot be related to polymorphism, but rather to melting followed by cold crystallization and remelting, and to the melting of two different kinds of lamellae in the crystalline solid [24, 26, 29]. However, it is apparent from Fig. 2 that the maximum of the crystallization peak, which is [T.sub.cryst] = 81.5[degrees]C at 10[degrees]C [min.sup.-1], moves to lower temperatures (the metastability range increases) as the cooling rate increases. The crystallization on cooling begins sharply, but the final stage, after the maximum rate, is rather broad. Finally, the signature of the glass transition can be seen on cooling as well as on heating (see the arrow on Fig. 2); on heating at 10[degrees]C min-1 the onset is at [T.sub.g,on] = -34[degrees]C, in reasonable agreement with most literature values [23, 26-28, 30-32]. The observed heat capacity step was [DELTA][C.sub.P] = 0.20 J [g.sup.-1] [degrees][C.sup.-1].
A study of the slow mobility in PBS was published using the technique of dielectric relaxation spectroscopy, in the temperature range from -110 to 110[degrees]C and in the frequency range of 0.01-[10.sup.5] Hz , Both the dipolar [alpha] and [beta] processes have been identified at low temperatures. Notice that, we use here the usual nomenclature for relaxations in amorphous systems, but some authors use a different one in the case of semicrystalline and crystalline systems [33, 34]. The [beta] process obeys Arrhenius temperature dependence, typical of a subglass transition process, with an activation energy estimated to be 43 kJ [mol.sup.-1] . The [alpha] process is associated with the amorphous fraction, originated from the segmental motions, and the temperature dependent relaxation time follows the Vogel-Fulcher-Tammann form, with activation energies as high as 195 kJ [mol.sup.-1] at [T.sub.g]. The space charge effect was found to dominate the high temperature dielectric spectra, strongly interfering with the [alpha] relaxation. These nondipolar relaxations showed an Arrhenius nature, with activation energy of 112 kJ [mol.sup.-1] . The ion mobility in polymers is considered to be related with the segmental motion of the chains: the ions move from one site to a neighboring one, through the cooperative rearrangements of polymer segments. However, the Arrhenius behavior and the low activation energy (compared with that of the motional modes in the glass transition region), lead the author to suggest  that the motion of these impurity ions is somewhat independent of the chain rearrangements, that is, the ions move in a more independent and less correlated manner.
To complement this dielectric work and to improve our knowledge on the molecular dynamics in PBS, we carried out a study by thermally stimulated currents. Figure 3 shows different single motional modes (PP peaks) of the three relaxation processes observed in PBS by TSDC.
The analysis of these peaks allows the determination of the temperature dependent relaxation time, [tau] (T), associated to each peak (see experimental section), that is, to each mode of motion. The insert in Fig. 4 shows the [tau] (T) lines corresponding to the PP peaks in the main Fig. 3. Furthermore, the fitting of a [tau] (T) line with an appropriate equation enables the estimation of the kinetic parameters of the corresponding motional mode. It is to be noted that the In [tau] (T) versus 1 IT lines in the insert of Fig. 4 are linear, meaning that the temperature dependent relaxation time follows an Arrhenius-type temperature dependence for all the observed relaxations. Figure 4 displays the activation enthalpy of the motional modes in Fig. 3, as a function of their temperature location (temperature of maximum intensity, [T.sub.m], of the corresponding peak).
This representation synthesizes the relaxation map of the studied system, and is often called Starkweather plot [35-37], The dotted line in Fig. 4 is the zero activation entropy line (or Starkweather line) that depicts the behavior of the local and noncooperative relaxations (see Appendix C of Ref. ).
The [alpha] and [beta] Relaxations Viewed by TSDC
The points between -130 and -65[degrees]C in Fig. 4 refer to the motional modes of the secondary relaxations shown in the insert of Fig. 3 (peaks below -65[degrees]C), and the corresponding Log z (T) versus 1/T lines are displayed on the insert of this figure (more spaced lines in the right-hand side). We see from the main Fig. 4 that the components of this mobility obey to the zero entropy line, that is, they are narrowly distributed in enthalpy (from 30 to 55 kJ [mol.sup.-1]) but not in entropy. Note that the value of 43 kJ [mol.sup.-1] reported before , and obtained by DRS, is compatible with our TSDC results, and corresponds to the mean value of the energy distribution. It is clear that TSDC provides more detailed information regarding the distribution of relaxation times in these secondary relaxations, when compared with DRS.
The fact that these relaxations obey to the Starkweather line indicates that they correspond to the secondary relaxations: the faster one (or [gamma]-relaxation) at lower temperatures, and the Johari-Goldstein (JG or slow [beta]-relaxation) in the vicinity of the glass transition relaxation. The fast secondary relaxations correspond to a cage mobility arising from local motions of groups of atoms or small chain segments, in a cage delimited by the repulsive forces of the neighboring chains and segments. This is often a complex relaxation due to the variety of internal rotations that originate different dielectrically active local motions. In the case of aliphatic polyesters, as is the case for PBS, we can consider the polar bonds between the ether oxygen and the aliphatic carbon (CO), and the aliphatic C--C bond where one of the carbons is linked to oxygen or to the ester carbon. The internal rotations, that is, conformational transitions, in the chain that originate reorientations of those polar bonds will give rise to fast secondary relaxations. In aromatic polyesters, the reorientations of the aliphatic C--C bonds are believed to appear at lower frequencies compared with the reorientations of the C--O bonds (39, 40]. In aliphatic polyesters, however, the two relaxations probably coalesce.
The PP peaks between -30 and -65[degrees]C (lower intensity relaxation in the main Fig. 3) correspond to modes of the glass transition relaxation. The points between -65 and -30[degrees]C in Fig. 4 thus concern the glass transition relaxation (closer Arrhenius lines in the insert at 1000/7 = 4.5, beyond those of the secondary relaxations). The component peak with higher intensity of this relaxation (PP peak obtained with a polarization temperature [T.sub.p] = -42[degrees]C) has its maximum at [T.sub.m] = -40[degrees]C, which is the [T.sub.g] value provided by the TSDC technique. Note that this value is somewhat lower than the value of the calorimetric [T.sub.g] reported before (-34[degrees]C), but it is in good agreement with other values published in the literature [10, 23, 24, 41]. The fitting to the Arrhenius equation of the log [tau] (7) versus 1/T line corresponding to this higher intensity peak provides the value of the activation energy at [T.sub.g], [E.sub.a] ([T.sub.g]) = 191 kJ [mol.sup.-1] (close to the value 195 kJ [mol.sup.-1] reported before and obtained from DRS data). From the main Fig. 4, we see that the values of the activation enthalpy display a strong deviation from the zero entropy line, meaning that the distribution of relaxation times is now very wide in enthalpy (or energy), as well as in entropy (or in prefactor). This behavior, which is the signature of cooperativity, is an important feature of the so-called [alpha]-process as studied by TSDC. The motional modes involved are associated with the amorphous fraction, and originate from the segmental motions of the polymer chains. Let us underline that the TSDC results reported before confirms the published DRS results , and adds important specific information regarding the distribution of relaxation times in the glass transition relaxation.
The Fragility Index of PBS
The glass transition in polymers is viewed as a transition from a rubbery state to a glassy state on cooling, accompanied by drastic modifications of the physical properties in a narrow temperature range, namely by a slowing down of the relaxation time by many orders of magnitude on approaching [T.sub.g]. The fragility index, m, quantifies the steepness of the temperature dependence of the relaxation time, [[tau].sub.x], close to [T.sub.g], and is defined as [42-44],
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
It can be estimated from the TSDC data as :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where [E.sub.a] ([T.sub.g]), r, and [tau] ([T.sub.g]) are respectively the Arrhenius activation energy at the glass transition temperature, the heating rate of the TSDC experiment, and the relaxation time at the glass transition temperature. The estimated value is m = 43 (in close agreement with the value m = 42 calculated with data from ), meaning that PBS behaves as a relatively strong glass-forming system.
Effect of Aging on the Secondary and Glass Transition Modes
In recent publications [16, 46, 47] we showed that TSDC appears as a useful technique to discriminate, on the basis of aging studies, between the relaxations with different properties or motional mechanisms. Figure 5 shows the results of two TSDC experiments designed to evaluate the aging effect on a widely distributed relaxation of PBS. Both curves in Fig. 5 are broad and correspond to results of wide polarization window experiments where the electric field polarizes a broad relaxation that includes motional modes of the secondary and main processes. Both curves were obtained using the same experimental protocol (see caption of Fig. 5), but the higher intensity one was performed on the nonaged sample, while the lower one was obtained after aging the sample for [t.sub.ag] = 60 min at [T.sub.ag] =--50[degrees]C. From the results in Fig. 5, we conclude that some motional modes, the faster ones because they appear at lower temperatures, were not affected by aging (motional modes corresponding to the lower temperature part of the curves). Since the density increases on aging, it is reasonable to consider that these motional modes have a local origin given that they are independent of the molar volume and thus of intermolecular distances. PBS is a flexible polymer where all possible internal rotations occur about covalent bonds in the main chain, so that the local motions probably consist, as explained before, of internal rotations in very small and independent segments of the main chain, or some crankshaft-like rotations about two colinear chain bonds.
Other motional modes shown in Fig. 5, the slower ones since they appear at higher temperatures (motional modes corresponding to the higher temperature parts of the curves), are affected by aging in such a way that the corresponding intensity (the dielectric strength) decreases with aging. It seems acceptable to consider that these motional modes that are influenced by aging have segmental rather than a local nature, that is, they involve larger chain segments than for the lower temperature modes. Considering Figs. 3 and 4, we can reasonably conclude that the motional modes appearing between -145 and -100[degrees]C, that are aging independent and obey to the zero entropy line, belong to the fast secondary relaxations. However, the modes appearing above--70[degrees]C, that are strongly aging dependent and deviate from the zero entropy line, belong to the main (or alpha) relaxation. Furthermore, and in line with the reasons presented elsewhere [47, 48], the motional modes appearing between -100 and --70[degrees]C in Fig. 5 that are aging dependent but obey to the zero entropy line (have zero activation entropy) are the manifestation of the slow [beta] or JG relaxation [49, 50], The behavior of the secondary relaxations is thus complex, exhibiting a local character at lower temperatures and a JG at higher temperatures. As stated before, the fast secondary relaxation is a cage mobility arising from local motions of groups of atoms or small chain segments. The slow [beta] or JG-relaxation (affected by aging) involves larger chain segments, but smaller than those involved in the segmental mobility, and is believed to play an important role on the glass transition.
The Current Peak Above [T.sub.g]: Dipolar or Space Charge Relaxation?
Another relaxation process is observed in the TSDC thermogram, with PP peaks between -20 and 20[degrees]C (higher intensity or higher dielectric strength relaxation in the main Fig. 3). It is worth to point out that this relaxation is well separated from the a-relaxation in the TSDC spectra, while it was strongly interfering with the a relaxation in the dielectric relaxation spectra , The [tau] (7) lines of the components of this relaxation are located in the insert of Fig. 4 at 1000/T~3.8 (lines very close to each other in the left-hand side). From the main Fig. 4, we see that the components of this relaxation (points between -1 and + 10[degrees]C) have activation enthalpies deviating from the zero entropy line, narrowly distributed between 110 and 130 kJ [mol.sup.-1]; this corresponds to non-zero activation entropies distributed between 130 and 230 J/([degrees]C [mol.sup.-1]).
In the case of the TSDC technique, the appearance of relaxation peaks above [T.sub.g] (i.e., at lower frequencies) is a frequent occurrence, but the elucidation of the nature of these relaxations at the molecular level is difficult, has been the subject of a large amount of studies, and there has been considerable discussion and controversy about it. Since PBS is a semicrystalline polymer, we can be in the presence of dipolar mobility in the crystalline fraction of the sample. However, some authors believe at the existence of dipolar reorientations in the supercooled liquid (or rubbery) state of glass forming systems, and often call them liquid-liquid transitions [51, 52]. Others consider this as artifacts arising from field induced motions of intrinsic charge carriers or of extrinsic charges injected from the electrodes, or from the trapping of those charges carriers at the phase boundaries [53, 54]. Several methods have been proposed in the literature to discriminate between dipolar and space-charge relaxations [9, 55]. One of them is based on the comparison between TSC results obtained in the depolarization mode (TSDC) and in the polarization mode (TSPC), as explained in the experimental section.
The results are displayed in Fig. 6a, where the upper curve is the result of a wide polarization window TSDC experiment with [T.sub.p] = 20[degrees]C, [E.sub.p] = 3500 V [mm.sup.-1], while the lower curve is the result of a TSPC experiment with [T.sub.p]=--100[degrees]C, E = 800 V [mm.sup.-1]. The asymmetry between the TSDC and TSPC curves (see experimental section), suggests that the relaxation above [T.sub.g] is not originated by dipole reorientations but rather by space charge effects.
Another method to discriminate between dipolar and spacecharge relaxations is through the analysis of the influence of the applied field strength on the polarization of the relaxations. The TSDC peaks arising from dipolar reorientational motions are characterized by field-independent maximum temperatures, [T.sub.max], and polarizations (amplitudes or areas) that are strictly proportional to the polarizing field strength, while a more complex behavior is observed for space-charge processes. In fact, the buildup, release and equilibrium spatial distribution of the charge generally depend on the applied field, E, in a complex way. Figure 6b shows the plot of the polarization (area of the peak), [P.sub.E], (normalized to that of the peak at 1000 V [mm.sup.-1], [P.sub.E]/ [P.sub.1000]) as a function of the ratio E/1000, for the glass transition relaxation and for the relaxation above [T.sub.g]. The dot-dash line describes the strict proportionality between the two quantities. The triangles correspond to a PP component of the glass transition relaxation ([T.sub.P] = -44[degrees]C) and the diamonds to a PP component of the relaxation above [T.sub.g] ([T.sub.P] = -4[degrees]C); the maximum electric field strength used was E = 4000 V [mm.sup.-1]. A good linear relationship exists for the glass transition relaxation (triangles); oppositely, significant deviations from the straight-line with slope one and intercept zero are observed for the relaxation above [T.sub.g] (diamonds). Consequently, the result of this test also works in favor of the space charge hypothesis.
The influence of the electrode/dielectric contact was also studied. First of all we compared the results obtained with our most frequently used stainless steel electrode with those obtained with a gold electrode. Changing the metal electrode does not affect a dipolar polarization, but may lead important variations in the formation and release of excess charges both of external and internal origin, owing to the differences in work function and blocking factor of the different metals. Our results show (see Fig. 6c, curves 1 and 2) that the size and shape of the glass transition peak is independent of the electrode's metal, while the intensity of the peak above [T.sub.g] is significantly lower with the gold (curve 2) compared with the stainless steel electrode (curve 1); the test of the effect of the electrode's metal reinforces the conclusions of the previous tests.
Comparing curves 2 (gold electrodes without spacer) and 3 (gold electrode with a spacer) in Fig. 6c allows looking at the effect of placing a Teflon spacer (0.1 mm thick) between the sample's surface, and the cathode gold electrode. When insulating Teflon spacers are used, there is an increase of the blocking degree of the electrode, preventing the injection of homocharges to the surface of the sample and reducing the heterocharge mobility. The comparison of curves 2 and 3 in Fig. 6c shows that the decrease in intensity of the higher-temperature peak is stronger compared with that of the glass transition peak, suggesting once more that it is most probably related to the transport of charge through the thickness of the sample. Note also the drastic reduction of the current intensity at the higher temperatures. Finally, let us say that the relaxation peak above [T.sub.g] showed a low reproducibility: it presented different positions, amplitudes, and shapes, in similar experiments done in different days, with the same sample submitted to different previous thermal treatments. This behavior is often found for the space charge mobility.
The TSDC thermogram of PBS exhibits a complex set of dielectric relaxations. The secondary relaxations are broad, extending from -135 to -70[degrees]C, with motional modes distributed in energy but not in entropy. A physical aging analysis shows two different kinds of behavior among the motional modes of the secondary relaxations: some of them, the faster ones, are not sensitive to aging ([gamma], [delta],... relaxations), while others, the slower ones, are aging dependent ([beta] or JG relaxation).
The glass transition relaxation displays relaxation times widely distributed in energy as well as in entropy, and is characterized by a steepness index of m = 43, meaning that PBS behaves as a relatively strong glass-former. A careful analysis of the current peak observed above the glass transition temperature indicated that it corresponds to a space charge rather to reorientational dipolar motions. It was also observed that the space charge peak was well separated from the glass transition peak in the TSDC thermogram, contrarily to what was observed in dielectric relaxation spectroscopy where a strong interference existed between both relaxations.
Authors gratefully acknowledge Dr. Mikihiko Ono (Showa Denko, Tokyo), for the kind gift of the PBS samples.
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Joaquim J. Moura Ramos, (1) Herminio P. Diogo (2)
(1) CQFM-Centro de Quimica-Fi'sica Molecular and IN-Institute of Nanoscience and Nanotechnology, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001, Portugal
(2) CQE--Centro de Qui'mica Estrutural, Complexo I, 1ST, Universidade de Lisboa, 1049-001, Portugal
Correspondence to: H. P. Diogo; e-mail: email@example.com
Contract grant sponsor: Fundaqao para a Ciencia e a Tecnologia (FCT), Portugal, projects PEst-OE/CTM/LA0024/2013 and PEst-OE/QUI/UIOIOO/2013.
Published online in Wiley Online Library (wileyonlinelibrary.com).
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|Author:||Ramos, Joaquim J. Moura; Diogo, Herminio P.|
|Publication:||Polymer Engineering and Science|
|Date:||Aug 1, 2015|
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