Thermally stimulated depolarization current and dielectric spectroscopy used to study dipolar relaxations and trap level distribution in PMMA polymer

Journal of Non-Crystalline Solids 427 (2015) 76–82

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Thermally stimulated depolarization current and dielectric spectroscopy used to study dipolar relaxations and trap level distribution in PMMA polymer Fatma Namouchi ⁎, Wissal Jilani, Hajer Guermazi Research Unit Physics of Insulators and Semi-insulator Materials, Faculty of Sciences of Sfax, University of Sfax, Soukra Road, BP 1171, 3000 Sfax, Tunisia

a r t i c l e

i n f o

Article history: Received 5 May 2015 Received in revised form 27 June 2015 Accepted 2 July 2015 Available online xxxx Keywords: PMMA; Dielectric relaxations; DRS; Windowing polarization; TSDC

a b s t r a c t In this work, thermally stimulated depolarization current (TSDC) and dielectric relaxation spectroscopy (DRS) techniques were performed in complementarities to characterize the dielectric relaxation processes in poly(methylmethacrylate) (PMMA) polymer. Three relaxations were highlighted. Based on correlation between TSDC and DRS data, they were attributed respectively to dipolar β and α relaxations as well as interfacial ρ relaxation. New experimental procedure of fractional polarization was used to investigate space charge trap depth distribution within the band-gap of PMMA. Then the individual peaks were fitted to Bucci–Fieschi model, to evaluate the relaxation parameters. The obtained values were discussed in correlation to those evaluated from DRS data fitted to Havriliak–Negami and Arrhenius models. The various observed peaks in the thermograms are discussed on the basis of space charge polarization. The trap energies were evaluated from the fit to the Bucci–Fuschi model. Similarly other parameters such as relaxation time and charge release are evaluated. © 2015 Published by Elsevier B.V.

1. Introduction Electrical properties of insulating polymers are complicated because of their dependency on structure, impurities, polarizing conditions etc. [1,2]. Poly(methyl methacrylate) (PMMA) which is a polar thermoplastic polymer, is one of the most important engineering materials. It forms an important category of polymeric insulating materials, used in a wide range of electric power insulations and equipment [3,4]. The presence of space charge in this material considerably affects its properties. Indeed, the submission of polymer to several external conditions such as electric field and heating, leads to relaxation of space charge. Consequently, the study of charge relaxation phenomena in polymers is crucial. Several techniques have been used for this purpose [5–8]. Thermally stimulated discharge current (TSDC) has been shown to be a very sensitive tool in polymer investigations, especially if combined with DRS [9]. It is widely used for the study of main and secondary dipolar relaxations as well as the release of trapped charges in polymeric materials [10–14]. Numerous works have already been done on the TSDC method of polymers in order to gain insight into the mechanism of relaxation processes, charge carrier generation, trapping, and other related processes involved in the material. The TSDC is recorded as a function of temperature, and the relaxation processes can be seen as current peaks in TSDC ⁎ Corresponding author at: Research Unit Physics of Insulators and Semi-insulator Materials, Faculty of Sciences of Sfax, University of Sfax, Soukra Road, km 3.5, BP 1171, 3000 Sfax, Tunisia. E-mail address: [email protected] (F. Namouchi).

http://dx.doi.org/10.1016/j.jnoncrysol.2015.07.004 0022-3093/© 2015 Published by Elsevier B.V.

thermogram [15]. The characteristic peaks due to dipolar reorientation or detrapping of charge carriers observed in a TSDC thermogram, provide information about the activation energy, relaxation time, and trap distribution [16]. In general, the TSDC thermograms are complex for two main reasons. The first one is that the charge activated during polarization can be due to several microscopic processes [17,18]. The second reason is that relaxation processes were distributed. Therefore, they cannot be described in terms of a single relaxation time. In such processes, the behavior can be adequately defined by a set of elementary modes and thus described by a distribution of relaxation times and/or activation energies. In polymers, this idea is approved by the lack of order and the existence of different conformations of the macromolecules in addition to the interactions between the relaxing entities [18,19]. Many attempts have been made in order to elucidate the origin of complex TSDC peaks. They are based on the behavior of the TSDC peaks as a function of the polarization parameters [8,20,21]. Several methods were used to decompose the experimental complex bands into limited number of elementary peaks [18,22]. The first suggestion is to decompose the complex experimental thermogram obtained with conventional polarization into elementary peaks using the theoretical equation of TSDC current describing one relaxation process (so called Debye relaxation) [18]. The second suggestion is to change experimental conditions and include a large number of experimental protocols like the peak cleaning technique [14,18,23,24] and the fractional polarization usually named windowing polarization (WP) technique [25,26]. In previous works [25–27] we have studied the relaxation processes in polymers using conventional and WP TSDC measurements. Among several methods

F. Namouchi et al. / Journal of Non-Crystalline Solids 427 (2015) 76–82

used in literature to determine activation energy of trap from experimental TSC curves, we have chose to use the initial rise [15,26,28] and curve fitting methods [26]. The obtained parameters don't converge in all cases and sometimes unrealistic values were found. Thermally stimulated depolarization currents (TSDC), were often used in complementarity with Dielectric relaxation spectroscopy (DRS), to reach a most complete knowledge of the relaxation mechanisms in various materials [29–31]. The present paper studied the dipolar and space charge relaxations in PMMA by a combined use of TSDC and DRS measurements. The purpose of our present work is to obtain further details regarding deep and shallow traps in PMMA polymer using a new fractional polarization method prior to TSDC measurements. We propose a new experimental protocol for TSDC measurements (fractional polarization) to investigate space charge trap depth distribution within the band-gap of PMMA polymer. In contrast with all previous TSDC measurements on polymers [32–34], we for the first time employ this new method, which allows us to check for the possibility of evaluating the dipolar and trap states. We report on the activation energy, and the traps level distribution in PMMA. The related relaxation times were also investigated. DRS measurement over wide ranges of frequency and temperature was used as a complementary method to assist the TSDC results. DRS results are fitted by theoretical model of Havriliak–Negami and characteristic parameters were deduced using the Arrhenius model. TSDC and DRS data were correlated and compared to the literature.

77

(a) EP

TP T0

tS

tP

(b) EP

2. Experimental TP

2.1. Thermally stimulated discharge current TSDC To perform TSDC measurements (50 × 50 × 2) mm3 samples used in this work are from commercially available PMMA (MADREPELA) (density: 1.19 g/cm3) were coated with 3 cm diameter silver electrodes. The TSDC experiments were carried out using a programmed air-forced Memmert oven (ULE500) controlled by a Celsius program, and a Keithley 6487 electrometer for current measurements. Prior to the TSDC measurements, the samples were poled using either the conventional polarization or the fractional polarization methods. The fractional polarization was carried out by the thermal sampling (TS) technique, in which a new protocol of windowing polarization (WP) was applied. In the conventional TSDC method (Fig. 1a), the sample in a sandwich configuration, was heated at a constant rate until the polarization temperature TP = 70 °C. At this temperature an electric field (EP = 3 kV/ mm) was applied during a time tP = 1 h. Afterward, the sample is cooled to room temperature under electric field to freeze the orientation of dipoles. Then the applied electric field was removed and the sample was short-circuited between aluminum sheets for an enough time ts = 30 min, in order to remove eventual surface charges and stabilize the sample temperature. Finally, sample is short-circuited through an electrometer and heated at a constant rate. The resulting current is a function of temperature, and the recorded TSDC thermograms present several peaks, indicating that several processes are operative including mainly the depolarization of permanent dipoles and the release of charges from traps. Nevertheless, conventional TSDC spectrum is complex; it is the superposition of several elementary peaks because the charge activated during the polarization can be due to several microscopic processes. The study of this spectrum is difficult. So it is necessary to decompose it into elementary peaks; each of them is characterized by a single relaxation time and activation energy. In this order, we applied both theoretical and experimental methods. The theoretical decomposition method was carried out using a fit program based on Bucci–Fieschi Eq. (1). The experimental one consisted of the new fractional polarization protocol (Fig. 1b). It consists of an isothermal depolarization (ID) at the temperature TP for a given time td, next to the isothermal polarization (WP) stage, before the cooling step. So the charges activated by this process are related to TP.

T0

tP

td

tS

Fig. 1. TSDC experiments using (a) conventional polarization and (b) windowing polarization/ isothermal discharge.

All TSDC measurements were performed with a heating rate of 2 °C/ min. 2.2. Dielectric spectroscopy Dielectric relaxation spectroscopy (DRS) is a technique that gives valuable information on the thermal and frequency behavior of polymer. When an electrical field is applied across a parallel-plate capacitor containing a dielectric material, the various atomic and molecular charges present in the dielectric are displaced from their equilibrium positions and the material is said to be polarized. Different polarization mechanisms can occur, including dipole orientation, extrinsic free charges or intrinsic charge migration and electrode polarization [35]. In this work, dielectric measurements were carried out using a Novocontrol High Resolution Impedance Analyzer under inert gas, in the temperature range from −80 to 160 °C and in the frequency interval 10−2106 Hz. The temperature was controlled with a Linkam TMS 94

Fig. 2. Structural formula of PMMA.

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where A = P0/τ0, τ0 is the relaxation time at temperature T0. P0 is the total polarization at the initial temperature T0. While the current due to release of charge from traps is given by the following expression (2):

-8

2,5x10

-8

2

J(A/m )

2,0x10


  Ea 1 T Ea dT0 : JðTÞ ¼ B exp − − ∫ T0 exp − 0 KB T ϑτ0 KB T

-8

1,5x10

-8

1,0x10

-9

5,0x10

0,0 20

40

60

80

100

120

140

160

T(°C) Fig. 3. Experimental TSDC thermogram obtained by conventional polarization (TP = 70 °C, EP = 3 kV/mm, tP = 1 h, ts = 30 min) (black solid line), elementary β and α peaks resulting from the decomposition by Eq. (1), ρ peak from Eq. (2), and red solid line represents the global theoretical TSDC thermogram. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

instrument. The applied ac voltage was 1 V rms. Before measurements, 40 nm thick gold electrodes were pulverized on both sides of each sample with a guard ring pattern. The low (current sense) guarded electrode is 3 mm diameter. The sample's thickness was 2 mm. 3. Results and discussion 3.1. Thermally stimulated discharge current TSDC PMMA polymer was conventionally polarized under electric field EP = 3 kV/mm at TP = 70 °C for tP = 1 h and ts = 30 min. The measured TSDC current is shown in Fig. 2. It can be easily noticed that the thermogram contains shoulder at high temperature and two broad and partially separated relaxation peaks. In the temperature range considered in this study (25–160 °C), the proposed relaxation mechanisms are the depolarization of permanent dipoles and the release of charges from traps [9]. Thus, the experimental I(T) data can be decomposed into elementary peaks [11], in order to extract the individual relaxation parameters from the experimental profile. There are several methods in literature to determine activation energy of traps and the related relaxation time from experimental TSDC curves. In our case, the elementary processes involved in these broad peaks were separated by application of theoretical and experimental methods. Firstly, we used theoretical decomposition of TSDC thermogram of PMMA polymer on its elementary peaks, each of them was well fitted to the theoretical expression of Bucci– Fieschi model, in which the current due to dipole disorientation is given by the following expression [11,29,36]: 
  Ea 1 T Ea dT0 − ∫ T0 exp − JðTÞ ¼ A exp − 0 KB T ϑτ0 KB T

ð1Þ

ð2Þ

Ea is the activation energy, KB is the Boltzmann constant, ϑ is the rate of heating, and τo is the relaxation time at To. The pre-exponential factor A is related to the dipole moment and B is related to charge traps. Results revealed that only with three peaks, we get successfully fitting. Fig. 2 shows experimental and theoretical thermograms. The peak which appears at approximately 85 °C is assigned to β dipolar relaxation associated with the orientation of polar side groups [27,37]. The more intense peak around 115 °C was ascribed to the α relaxation (at the glass rubber transition). Indeed, the glass transition temperature was already detected, by calorimetric measurements, at 110 °C in previous works [33]. This transition is related to the cooperative motions of polymer main chain segments. The structural formula of PMMA is shown in Fig. 3. The relaxation parameters were evaluated from the best fit to experimental data using Eq. (1) for dipolar modes β and α. The obtained values were summarized in Table 1. The TSDC thermogram shows also ρ peak, at temperature above the glass transition (around 135 °C). It was assigned to the release of trapped charges, associated with interfacial Maxwell–Wagner–Sillar (MWS) polarization. The study of this peak results in information about the charge trapping properties of the polymer. As it is not observed in dielectric measurements, it may originate from free chare relaxation. The fit by Eq. (2) for ρ mode leads to the characteristic parameters τ0 = 4.52 × 10−25 s and activation energy Ea = 2.10 eV (see Table 1). To experimentally resolve the complex TSDC thermogram into its elementary peaks, the fractional polarization (WP) is an optimal technique [27]. The polarization temperatures were thus chosen based on the above results: TP = 50 °C, 80 °C and 120 °C, to isolate respectively β, α and ρ processes. Fig. 4 shows the related experimental TSDC peaks, obtained for the different polarization temperatures (Tp). It can be seen that for polarization temperature at 50 °C, only β process is activated. For polarization temperature around 80 °C, only α relaxation peak is observed and isolated. When poling samples at 120 °C the MWS process (ρ) is activated. In order to extract the relaxation characteristics the experimental peaks were fitted by Eqs. (1) and (2) for dipolar modes and charge release respectively. The inset of Fig. 4 shows that the isolated ρ mode was fitted by two peaks. The obtained values of fit parameters were added in Table 1. The values of τ0 for α and ρ processes were found to be smaller than the lower limit of (~ 10−13 s). It has been reported in literature that the lower limit of τ0 value (~10−13 s) was obtained in the ideal situation when the measured quantity (TSDC current) is determined only by dipoles [20]. However, in several TSDC studies with the use of the thermal sampling technique (such as WP) much smaller values for τ0 were reported [37,38]. These low values can be explained by a correlation with a distribution in the activation energy values, determined by the

Table 1 Fit parameters of relaxation processes in PMMA from TSDC and DRS data. Relaxation process

γ

TSDC

τ0(s) – –

Ea(eV) – –

τ0(s) 1.07 × 10−7 5.65 × 10−7

Ea(eV) 0.680 ± 0.02 0.65 ± 0.01

τ0(s) 8.52 × 10−15 6.31 × 10−15

Ea(eV) 1.28 ± 0.01 1.30 ± 0.01

– – – – 6.75 × 10−8

– – – – 0.140 ± 0.005

1.19 × 10−8 2.04 × 10−10 2.26 × 10−11 2.24 × 10−15 7.79 × 10−17

0.78 ± 0.03 0.88 ± 0.04 0.552 ± 0.009 0.780 ± 0.062 0.870 ± 0.050

6.08 × 10−20 1.05 × 10−24 – – –

1.70 ± 0.02 2.05 ± 0.02 – – –

Relaxation parameters Conventional polarization WP procedure ID procedure

DRS

T = 120–160 °C T = 20–100 °C T = −80–20 °C

td = 30 min td = 1 h

β

α

ρ τ0(s) 4.52 × 10−25 2.5 × 10−25 8.05 × 10−30 6.07 × 10−28 1.85 × 10−30 – – –

Ea(eV) 2.10 ± 0.03 2.26 ± 0.06 2.19 ± 0.03 2.40 ± 0.02 2.58 ± 0.09 – – –

F. Namouchi et al. / Journal of Non-Crystalline Solids 427 (2015) 76–82

(a)

-8 3.0x10

-8

2.5x10

-8

2.0x10

-8

1.5x10

-8

1.0x10

-8

5.0x10

-9

1,2x10

-8

1,0x10

-8

8,0x10

-9

6,0x10

-9

4,0x10

-9

2,0x10

-9

(1)

2

J(A/m )

4,0x10

79

3,0x10

-8

100

2,0x10

1,0x10

110

-8

120

130

140

150

160

170

T(°C)

2 J (A/m )

2 J(A/m )

0.0

-8

(2) (3)

0,0

0,0 20

40

60

80

100

120

140

160

180

20

T(°C)

40

60

80

100

120

140

160

180

140

160

180

T (°C)

P¼

1 ∞ ∫ J ðT ÞdT : v T0

2 J (A/m )

different environments in which the relaxing units are moving in the bulk of the polymer. Indeed, the existence of different conformations of the macromolecules in polymers, together with the interactions between the relaxing units can lead to a distribution in activation energy, which results in a broad experimental TSDC peaks as observed in Figs. 2 and 3. In order to analyze the charge trap depth distribution within the band gap of polymer, we applied an isothermal depolarization (ID) phase next to WP procedure (an extended WP polarization method). This new process consists in keeping the Tp temperature after the polarization field is shut down for a time td (Fig. 1b). This time td permits some entities to relax before TSDC measurements. Fig. 5 shows the experimentally isolated (ID/WP) TSDC peaks at several discharge time td. Fig. 6 shows the variations of the relaxed charges Q (which is proportional to the TSDC peak area), according to the ID time td. The decrease in the current intensity and the charge decay observed versus the time td, confirm that the charges are trapped in distributed energetic levels [39]. Thus, a distribution of trap levels in PMMA, were filled in the poling stage, the charges in shallow traps levels released during ID time td before TSDC measurements, and deeper ones were activated and released during TSDC measurements. Then we can conclude that as the td increases, the relaxed charges were located in traps associated to deeper energetic levels within the polymer. In fact, the disorientation of dipoles involves the rotation of polar groups and requires certain activation energy per dipole. The activation energy is not the same for all the dipoles. The distribution of activation energy values can be due to different environments (resulting from inter and intra-molecular interactions) in which the relaxing entities moved within the polymer structure. Polarization values were calculated from Eq. (3):

(b) 4,0x10

-8

3,0x10

-8

2,0x10

-8

1,0x10

-8

(1)

(2)

(3)

0,0 20

40

60

80

100

120

T (°C)

(c) (1)

-8

3,0x10

(2) -8

2,0x10

2 J(A/m )

Fig. 4. Experimentally isolated WP/TSDC peaks. The inset shows theoretical decomposition of the isolated ρ peak using Eq. (2).

(3) -8

1,0x10

0,0

ð3Þ

The obtained values are given in Table 2. In order to evaluate the traps energies, TSDC peaks in Fig. 5 were fitted to theoretical models (Eqs. (1) and (2)). We presented in Fig. 7, the best fit to experimental data obtained with Tp = 80 °C, td = 0 h as an example. The fit parameters values were gathered in Table 1. Thus, we can confirm that poling samples with the ID/WP method for Tp = 50 °C, 80 °C and 120 °C make possible the individual peak separation and the evaluation of trap level distribution. From Table 1, it can be seen that the values of the activation energy increase with increasing td according to the experimental of TSDC. Furthermore, it can be observed that the energies of each relaxation peak are very close suggesting that the broad relaxations in PMMA were characterized by a narrow

100

110

120

130

140

150

160

170

T°(C) Fig. 5. Experimentally isolated (ID/WP) TSDC β peak: (a), α peak: (b), and ρ peak: (c). (1) td = 0 h, (2) td = 30 min and (3) td = 1 h.

distribution of the activation energies. This observation is supported by the results reported in different papers from TSDC, DRS and dynamicmechanical relaxation measurements [40,41]. The ID/WP procedure can be of particular interest for the study of dielectric relaxations in PMMA based nanocomposites, since it permits evaluation of the localized states distribution in the band gap. As it has been demonstrated by G. Lach and al [42] and V. Kapustianyk and al [43], the interfaces created in PMMA by adding TEA-CBC nanocrystals,

80

F. Namouchi et al. / Journal of Non-Crystalline Solids 427 (2015) 76–82 -6

1,0x10

3

(x10 ) -7

Q( C)

8,0x10

-7

6,0x10

-7

4,0x10

-7

2,0x10

0,0

0

10

20

30

40

50

60

td(mn) Fig. 7. An example of the fit to TSDC experimental data obtained with Tp = 80 °C, td = 0 h, using Eq. (1).

Fig. 6. Evolution of released charge from traps versus the td.

take a major role in modifying the physical properties of PMMA mainly in the resonance type dielectric relaxation. 3.2. Dielectric investigation The temperature dependence of dielectric loss was plotted at different frequencies in Fig. 7. The dielectric loss exhibits two clear peaks. The first at low temperatures was assigned to secondary dipolar relaxations γ which was not observed in TSDC. In fact, in the conventional TSDC experiment, the sample was cooled to ambient temperature under applied field, then the discharge current was measured with increasing temperature at a constant rate of 2 °C/min from ambient temperature to final temperature (160 °C) above Tp. As a result, the TSDC global thermogram includes only dielectrically active relaxation processes taking place at temperature above ambient temperature. So, γ relaxation appears only in dielectric measurements. The second peak in Fig. 7, observed at higher temperature, was assigned to β mode. The frequencies chosen here (0.1–103Hz) were higher than the equivalent frequencies of the TSDC measurements (10−2–10−4Hz) [18], so the peaks are shifted to higher temperatures with respect to TSDC. Moreover, it is interesting to note that no peak corresponding to the TSDC MWS (ρ) peak is observed, and that even the α relaxation peak can be masked by conductivity signal. Owing to the large conductive effects it is preferable to express the dielectric results in terms of the complex electric modulus via the following equation [44]: M ¼

0

00

00 0 1 1 ε ε ¼ þ j 02 ¼ M þ jM 00 ¼ ε ε0 −jε ε0 2 þ ε0 0 2 ε þ ε0 0 2

ð3Þ

Where ε′, M′ are the real parts and ε″, M″ are the imaginary parts of the dielectric permittivity and electric modulus respectively. Isothermal plots of M″ versus frequency for various temperatures are given in Fig. 8. For low temperatures ranging from (− 80 °C) to 0 °C, two local dipolar relaxation processes were observed designated as β and γ in order of increasing frequency at a constant temperature [9]. γ relaxation was observed only for the low temperatures (− 80– 0 °C) in the high frequency edge of the spectra. It is associated to the rotation of methyl groups attached to either the main chain or to the ester

side group, whereas the β relaxation is related to the hindered rotation of the ester side groups attached to the main chain [45]. As seen in Fig. 8, for high temperatures above Tg (120 and 160 °C), α relaxation peak is evident in the low frequency side of the spectra. The main α relaxation is associated to the segmental motion of the polymer main chains. The MWS relaxation observed in TSDC response is not observed in dielectric measurements, thus it may originate from free charge relaxation. The Havriliak–Negami (H–N) model can be used to describe the dielectric behavior of PMMA. The experimental M″ data were fitted to the H–N approach according to the Eq. (4) [22,44]: ½ðM ∞ −Ms Þsin b∅Ab

00

M ¼ M∞ Ms

M 2s A2b þ 2Ab ðM∞ −M s ÞM s cos b∅ þ ðM ∞ −M s Þ2

where M s ¼ ε1s ; M∞ ¼ ε1∞ h i12 πc A ¼ 1 þ 2ðωτÞ1−c sin þ ðωτ Þ2ð1−cÞ 2 2 3 πc ðωτÞ1−c cos 6 2 7 ∅ ¼ arctg4 πc5 1 þ ðωτÞ1−c sin 2 εs and ε∝ are the dielectric constants for the low and high frequency sides of relaxation respectively, τ is the relaxation time and ω is the angular frequency. The best fit of modulus data to HN Eq. (4) is presented with solid lines in Fig. 9(a) for β mode and in Fig. 9(b) for γ relaxation. Then the f=0.1Hz f=1Hz f=1KHz

1

relaxation relaxation

0.1

Table 2 Polarization values of relaxation processes in PMMA from TSDC data. Pβ(C/m2)

Relaxation process ID procedure

td = 0 min td = 30 min td = 1 h

Pα(C/m2) −10

1.01 × 10 6.05 × 10−11 5.62 × 10−11

3.30 × 10−10 2.35 × 10−10 1.13 × 10−10

ð4Þ

-80

-60

-40

-20

0

20

40

60

80

100 120 140 160

T(°C) Fig. 8. Isochronal plots of dielectric loss (ε″) versus temperature.

F. Namouchi et al. / Journal of Non-Crystalline Solids 427 (2015) 76–82

10

related Ln(τ) is plotted versus 1000/T for each relaxation as seen in Fig. 10. The plots show a linear behavior which can be fitted according to the Arrhenius equation [9]:

8 6

linear Fit Ea( )=0.87 eV

4

ð5Þ

(s)

where the pre-exponential factor τ0 is the relaxation time at very high temperatures, Ea is the activation energy of the relaxation process, kB is the Boltzmann constant, and T is the absolute temperature. The Arrhenius fit parameters were added in Table 1. The obtained values are in good agreement with those reported in other investigations [9]. For the β relaxation, the activation energies Ea show a good agreement between DRS and TSDC techniques.

2 0

ln


 Ea τ ¼ τ0 exp KBT

81

-2 -4 -6

Ea( )=0.78 eV

-10 2.0

2.4

4. Conclusion In this paper, TSDC and DRS methods were used as a tool to monitor and analyze the complex relaxations occurring in PMMA polymer. The various observed peaks in the TSDC thermograms were discussed on the basis of space charge polarization. The conventional TSDC complex

(a)

Ea( )=0.140 eV

-8 Ea( )=0.552eV

2.8

3.2

3.6

4.0

4.4

4.8

5.2

5.6

1000/T(K-1) Fig. 10. Relaxation times of secondary dipolar relaxation processes as a function of reciprocal temperature. The solid lines are fits of relaxation times using the Arrhenius model.

feature was theoretically then experimentally decomposed using a new polarization protocol derived from windowing polarization one. This new procedure allowed investigating space charge trap depth distribution within the band-gap of PMMA. In fact, the energy levels for β, α and ρ peaks are in the ranges of 0.65–0.88 eV, 1.28–2.05 eV and 2.1– 2.58 eV, respectively, as determined by curve fitting method. The distribution of activation energy is due to different environments (resulting from inter and intra-molecular interactions) in which the relaxing entities moved within the polymer structure. The activation energies of β relaxation mode, evaluated also using DRS data fitted to HN and Arrhenius methods, are in agreement with those from TSDC data. Moreover, the secondary γ relaxation appears only in dielectric measurements in the low temperature range (−80 °C–20 °C). The observed activation energy at low temperatures and high frequencies, for γ peak is 0.14 eV. Our results compared to the literature show a good agreement.

Acknowledgments The authors acknowledge the financial support of the Ministry of High Education and Scientific Research in Tunisia, and ICTP through TWAS Grant no. 00-043 RG/PHYS/AF/AC.

(b) References

Fig. 9. Isothermal M″(f) plots of PMMA fitted to HN model (Eq. (4)). The fit is presented by solid lines for of β peak (a) and γ peak.

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