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0022-3697/$ - se

doi:10.1016/j.jp

�Correspondifax: +00216 74

E-mail addre

ines.benamor@

zouheir.fakhfak

(G. Perrier).

Journal of Physics and Chemistry of Solids 68 (2007) 1405–1414

www.elsevier.com/locate/jpcs

Crystallinity and dielectric relaxations in semi-crystallinepoly(ether ether ketone)

M. Arousa,�, I. Ben Amora, A. Kallela, Z. Fakhfakha, G. Perrierb

aLaboratoire des Materiaux Composites, Ceramiques et Polymeres, Faculte des Sciences de Sfax, 3018 Sfax, TunisiebLaboratoire d’Optimisation de la Conception et d’Ingenierie de l’Environnement, (LOCIE-ESIGEC)-Universite de Savoie, 73376 Le Bourget du Lac, France

Received 21 August 2006; received in revised form 23 February 2007; accepted 26 February 2007

Abstract

The Maxwell–Wagner–Sillars (MWS) relaxation is studied for semi-crystalline polymers poly (ether ether ketone) (PEEK), in the range

20Hz–1MHz and temperature varying from 80 to 330 1C. The parameter is the crystallization condition in the case of PEEK, which is a

semi-crystalline polymer considered as a particulate composite. The relaxation found in the semi-crystalline polymers above the arelaxation of the PEEK is ascribed to the trapping of conductive carriers at the interface between crystalline lamellae and the amorphous

matrix. The study of PEEK microstructure is based on differential calorimetry and X-rays diffraction. Two lamellae populations have

been detected, that depends on the crystallization temperature and its duration. The crystallinity rate is increasing with crystallization

temperature and duration. In dielectric studies, the use of the electric modulus instead of permittivity allows us to minimize the ionic

conduction and then leads to the appearance of the interfacial relaxation. According to our measurements, the crystallinity rate is not the

main factor of the interfacial relaxation intensity, which also depends on the nature and degree of perfection of the lamellae.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: A. Polymers; C. DSC; D. Dielectric properties; D. Microstructure

1. Introduction

The poly(ether ether ketone) or PEEK is a highperformance thermoplastic thermostable, which can beobtained both in amorphous form as well as in semi-crystalline form depending on process conditions. Themolecular formula of PEEK is

O C

O

O

n

e front matter r 2007 Elsevier Ltd. All rights reserved.

cs.2007.02.046

ng author. Tel.: +00216 98 68 71 45;

27 44 37.

sses: Mourad.arous@fss.rnu.tn (M. Arous),

fss.rnu.tn (I.B. Amor), ali.kallel@fss.rnu.tn (A. Kallel),

h@fss.rnu.tn (Z. Fakhfakh), gerard.perrier@univ-savoie.fr

The combination of high performance properties ofPEEK such as thermal and chemical stability, excellentmechanical properties, high glass transition temperature(Tg) and extremely large temperature interval of crystal-lization, is outstanding. From the scientific point of view,the properties of PEEK have attached significant attentionsince its early introduction to researches [1]. Indeed, theseproperties allow the creation of a great variety of semi-crystalline morphologies and thus pave the way for thestudy of a wide range of structure/property relationships.Many reports have been devoted to the microstructure ofsemi-crystalline PEEK using various methods such asdifferential scanning calorimetry (DSC), infrared spectro-scopy, wide angle X-ray diffraction (WAXS), and electronmicroscopy [2–15]. It was shown that the microstructuredisplayed by semi-crystalline PEEK specimen is complexand strongly depends on the thermal history undergone bysamples. According to the crystallization conditions, semi-crystalline PEEK could exhibit one or more melting peaks.The dynamic relaxation behaviour of PEEK has beeninvestigated by both dielectric [16–27] and dynamic

ARTICLE IN PRESSM. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–14141406

mechanical methods [16,20,25–30]. PEEK displays abroad, sub-glass relaxation at low temperatures in additionto its glass-rubber (a) relaxation.

The Maxwell–Wagner–Sillars (MWS) [31–33] relaxationis an interfacial relaxation, which can be seen in hetero-geneous materials subjected to a periodic electrical field. Inpolymers and composites, it arises from the fact that thematerial contains impurities or catalyst residues from theprocessing stage; such molecules behave as free chargesthat can migrate in the external bias, if the material israised to a temperature high enough to ensure someconductivity of the medium. These free carriers are thenblocked at the interface between the two media of differentconductivities and permittivities, leading to an interfacialor MWS polarization. The frequency at which the MWSrelaxation appears is relative to the respective values of theconductivities and the permittivities of the conductive partand of the insulating part of the composite, and on thegeneral structure of the heterogeneous system (multilayer,loaded composite, etc.).

In the previous Work, we have studied the interfacialrelaxation found in model composite constituted ofamorphous thermoplastic polymer matrices, filled withspherical glass particles. The effect of the diameter, thevolume fraction and the surface coating of glass beads onthe interfacial relaxation characteristics have been studied[34–36]. A very good agreement was found betweenexperiments and calculations embedded in an insulatingmatrix [37].

In fact, a semi-crystalline polymer can be considered as acomposite constituted of crystalline inclusions (lamellae,spherulites) dispersed in amorphous matrix of the samechemical nature. Then, MWS relaxations that are to beseen in such materials provided the permittivity andconductivity of the crystalline region are different enoughfrom those of the amorphous matrix.

We reported here MWS relaxations in PEEK. The aimof this paper is to show that the study of the interfacialrelaxation is an investigation method that could giveinformation on the nature of the interface in semi-crystal-line polymers. The intensity of the MWS relaxations is putin relation to the annealing-dependent morphologicalcharacteristics of the crystalline inclusions in PEEK.

2. Experimental

2.1. Materials

The semi-crystalline polymer used is the poly(ether-ether-ketone) (PEEK) Stabar K200 supplied by ICI Filmsin the form of amorphous sheets whose thickness is about250 mm. Semi-crystalline PEEK samples were obtained byannealing as-received films at temperatures of 160 or320 1C for times varying from 30min to 25 h. Thedegradation mechanism is noticeable at prolonged heatingabove 400 1C [3,38].

2.2. Differential scanning calorimetry (DSC)

DSC was used as a guide in assessing the annealingconditions that would produce the widest range of crystal-linity. DSC curves were carried out from 50 to 400 1C usinga Perkin Elmer DSC-7 instrument for a heating rate of10 1C/min under nitrogen atmosphere. Thermograms werecalibrated by scanning melting-point substances, i.e.indium and zinc, at the same heating rate. This allowedtwo corrections to the ordinate, both of which are essentialfor details comparisons to be made. One of these is thecorrection for thermal lag in the differential control loopobtained from the leadings edge slop of indium and zincendotherms. The other is for thermal lag in the averagecontrol loop, which adds directly to any error in thecalibration. Baselines were determined by running anempty can at the same rate of the analyzed samples, givinga curve that was subtracted from the specimen thermo-grams.

2.3. X-ray diffraction

X-ray diffraction of the as-received and annealedsamples were recorded at room temperature with 0.021(2y) scan increments. The crystallinity ratio was obtainedfrom the area of crystalline X-ray diffraction peaks aftersubtracting the contribution of the amorphous phase. Thehalf-height of the diffraction peak Dx located at about 191(2y) is chosen as a reliable parameter to evaluated both sizeand perfection degree of crystallinity; i.e., Dx decreaseswith increasing size and/or the degree of perfection.

2.4. Dielectric relaxation spectroscopy

Dielectric measurements were performed on a DRSRheometric Scientific spectrometer in the range 80–320 1Cand at scan speed of 2 1C/min. A circular gold electrode(1 cm-diameter) was sputtered on both surfaces of thesample in order to insure good electrical contacts with thegold-plated measuring electrodes. When the isothermalstep method was used, data were collected isothermically atseveral frequencies increasing temperature following 10 1Csteps.A dielectric measurement, which consists of the measure

of a material’s response to an applied alternating voltage,provides an excellent means of characterizing the electricalproperties of polymeric materials. Dielectric relaxationspectroscopy allows one to study the two fundamentalelectrical characteristics of a material, capacitance andconductance, as function of temperature and frequency.The capacitance C and conductance G results were thentransformed to the apparent complex dielectric constant,e* ¼ e0�je00. The real part of the dielectric constant, e0, isdetermined by

C ¼ �0�0A

d

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Fig. 2. DSC curves at 10 1C/min for annealed PEEK crystallized

isothermally at (A) 160 1C for 30min, (B) 160 1C for 1 h, (C) 160 1C for

25 h, (D) 320 1C for 30min, (E) 320 1C for 1 h, and (F) 320 1C for 25 h.

M. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–1414 1407

where A is the area of circles electrode with a diameterapproximately 1 cm and d the thickness of sample.

The imaginary part of the dielectric constant at otherfrequencies and temperature was then calculated using thedefinition:

�00 ¼ �0G

oC

with o, angular frequency.

3. Results and discussion

3.1. Morphology studies

3.1.1. Differential scanning calorimetry

The DSC curve (Fig. 1) for the as-received amorphousPEEK shows its behaviour as the temperature is raisedfrom 100 1C through its melting temperature. An en-dotherm is observed in the region of 143 1C defining theglass transition temperature Tg of PEEK. With increasingtemperature, a crystallization exotherm is observed at172 1C. As the temperature increases further, a point isreached where the crystalline material melts, as shown bythe endotherm peaking at 343 1C.

By thermal annealing the sample for different lengths oftime at selected temperatures, amorphous PEEK can beconverted into a material with varying degrees of crystal-linity. The behaviour of the material resulting from sixdifferent annealing processing conditions is given in theDSC scans in Fig. 2. They are representative of the changethat occurs to PEEK film during the annealing process andindicate the extent of formation of crystalline region.

In these examples, the material has been isothermallycrystallized at 160 and 320 1C and then cooled to roomtemperature. All scans in Fig. 2 exhibit a similar Tg at143 1C as that seen in Fig. 1. In scans A through F, inaddition to the melt endotherm at 343 1C, a lower

Fig. 1. DSC curve at 10 1C/min of amorphous PEEK.

temperature endotherm is also observed and representsmelting of crystals formed during the annealing process. Ineach instance, the lower melting endotherm occurs at atemperature slightly higher than the annealing tempera-ture. As the isothermal annealing temperature is increased,it appears that the crystalline perfection is improved andleads to the higher melting endotherm [2,4]. Curve F doesnot show any crystallization process, a fact indicating thatthese samples already have the highest degree of crystal-linity.A study of the size distribution and of the perfection of

crystal lamellae in PEEK showed that crystallizationtemperature above 320 1C give layer lamellae, due to thefact that the growth rate is higher than the germination rate[5]. The mobility of the macromolecular chains taking partin the formation of new crystallites is then reduced by thepresence of the first lamellae population. Small lamellaeresult from crystallization temperatures lower than 175 1C,due to the fact that germination of new crystalline isimproved compared to the growth.A high crystallization temperature would lead to a

thickening and better stability of the crystallites. Theseeffects are related to the shift of the first peak towards hightemperatures (Fig. 2). The 320 1C treatment transformslow-perfection crystallites into thicker lamellae with ahigher degree of perfection, comparing to the 160 1Ctreatment.

3.1.2. X-ray diffraction

Fig. 3 shows the X-ray data for the as-received PEEK. Itpresents a wide strip characteristic of a non-crystallinestructure. This is in agreement with the amorphous natureof the material. X-ray crystallographic studies were alsoperformed on the annealed PEEK samples in order todetermine their crystallinity values. X-ray diffraction

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Fig. 3. X-ray data for amorphous PEEK.

Fig. 4. X-ray data for annealed PEEK crystallized isothermally at

(A) 160 1C for 30min, (B) 160 1C for 1 h, (C) 160 1C for 25 h, (D) 320 1C

for 30min, (E) 320 1C for 1 h, and (F) 320 1C for 25 h.

Table 1

Characteristics of samples issued from X-ray data. Dx is the half height of

the diffraction peak

Annealing T (1C) Time h Crystallinity (%) Dx

160 0.5 — —

160 1 7.70 0.761

160 25 10.6 0.652

320 0.5 26.1 0.578

320 1 27.6 0.545

320 25 31.3 0.564

Fig. 5. Isochronal runs of (a) the dielectric permittivity e0 and (b) the

dielectric loss factor e00 as a function of temperature for the amorphous

PEEK.

M. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–14141408

curves of annealed PEEK samples are shown in Fig. 4, withincreasing annealing temperature and duration of crystal-lization, weight crystallinity ratio increases. Moreover, thehalf height of the diffraction peak (Dx) located at about 191(2y) decreases with increasing the annealing temperature.This indicates an increase in size and/or perfection degreeof crystallinity (Table 1). We confirm the studies obtainedby DSC and conclude that the crystallized samples with160 1C present lamellae smaller and less perfect than thosecrystallized at 320 1C.

3.2. Dielectric studies

In Figs. 5 and 6, for amorphous PEEK and crystallizedPEEK at 320 1C during 30min respectively, we show thevariation of the real permittivity e0 and the loss factor e00 as

a function of temperature. The spectra can be divided intotwo temperature regions: The first one (100–180 1C) dealswith dipolar relaxation, whereas the second (180–300 1C)shows evidence for ionic conduction.In the first temperature region, two distinct phenomena can

be considered. The first peak is related to the dipolarrelaxation associated with glass transition of the amorphous

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Fig. 6. Isochronal runs of (a) the dielectric permittivity e0 and (b) the

dielectric loss factor e00 as a function of temperature for the annealed

PEEK crystallized isothermally at 320 1C for 30min.

Fig. 7. Isochronal runs of (a) the real modulus M0 and (b) the imaginary

modulus M00 as a function of temperature for the amorphous PEEK.

M. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–1414 1409

PEEK. This is the so-called a relaxation that appears at atemperature around 150 1C for the reported frequencies. Thesample is now at a temperature above its glass transition. Anincrease of the dissipation factor (ac) is seen in the 165–180 1Crange, just following the a relaxation. The second peak hasalready been reported [17,18] and assigned to the relaxationof the just-crystallized sample whose amorphous part motionsare now restricted by the presence of crystals.

In the higher temperature regions, the increase ofpermittivity due to ionic conduction is so dramatic that itmasks the interfacial relaxation. To overcome this diffi-culty, it has been decided to introduce the electric modulusthat has been proposed for the description of systems withionic conductivity [39–41].

The electric modulus are defined by the following equations:

Mn ¼1

�nM 0 ¼

�0

�02 þ �002M 00 ¼

�00

�02 þ �002,

where M0 is the real and M00 the imaginary electricmodulus, and e0 the real and e00 the imaginary permittivity.The modifications of the real part M0 and imaginary

parts M00 of the electric modulus according to thetemperature are quite visible in Figs. 7 and 8 comparedto Figs. 5 and 6. There is no difference in e00 or M00 spectrafor the a and ac relaxation. For high temperature, anotherrelaxation appears in M00 spectra, as well for amorphousand crystallized samples. This relaxation is attributed tothe trapping of ionic charges at the interface between theamorphous and the crystalline regions of the polymer(interfacial relaxation). Space-charge effects [42] as de-tected by Thermally Stimulated Current technique arerelated to this interfacial polarization mechanism. Asimilar aspect of the plots of M0 and M00 versus temperaturewas found for amorphous poly(ethylene terephthalate)(PET).Interfacial relaxation results from the fact that a difference

exists in the values of permittivity and conductivity of at

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Fig. 8. Isochronal runs of (a) the real modulus M0 and (b) the imaginary

modulus M00 as a function of temperature for the annealed PEEK

crystallized isothermally at 320 1C for 30min.

Fig. 9. Isothermal runs of (a) the real modulus M0 and (b) the imaginary

modulus M00 versus frequency for the PEEK crystallized isothermally at

160 1C for 25 h.

M. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–14141410

least two distinct phases. In our case, we can suppose thatthe electric characteristics of the mobile amorphous phaseand rigid amorphous phase are not different enough to allowthe charge carriers to be trapped with the rigid phase/mobilephase interface. In fact, the measured density is 1.225 for anamorphous sample and 1.281 for a sample crystallized at320 1C during 2h (320 1C/2 h), the values of the literaturebeing 1.260–1.267 for amorphous PEEK and 1.384–1.401for the PEEK crystal [43,44] (for the sample 320 1C/2 h with27.6% of crystalline phase, the calculated density liesbetween 1.350 and 1.364). One can conclude that thetrapping of the electric charges rather lies at the interfacebetween the amorphous phase and the crystalline areas ofpolymer, because of the differences in the organizations ofthe macromolecules between crystallites and the amorphouszones of polymer.

To study this interfacial relaxation, we carried outisothermal spectra according to the frequency. Fig. 9

represents an example characteristic of the variation of thereal part and the imaginary part of the electric modulus fora crystallized polymer.The increase in the values of M0 with the frequency and

the displacement of the peak of the maximum of M00 withthe temperature are behaviours characteristic of dielectricdispersion. The evolution towards a constant value of M0

high frequency is due to the fact that interfacial polariza-tion is ineffective at high frequency, since the pairs ofcharges developed with the interfaces cannot follow theelectric field applied when the frequency is very high.The reduction in the values of M0 (increase in e0) at

increasing temperature in the zone low frequency resultsfrom the increase in the mobility of the molecular chain inpolymer with the temperature. The orientation of the pairsof charges to the interface becomes easier and the aptitudeto be polarized becomes more significant, which result in anincrease of the permittivity.

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Table 2

Activation energies Ea and relaxation times t0 for annealed PEEK

crystallized isothermally

Annealed PEEK Ea (kJ/mol) t0 (s)

1601C for 30min — —

1601C for 1 h 103 10�13.8

1601C for 25 h 128 10�16.1

3201C for 30min 112 10�14.7

3201C for 1 h 90 10�12.6

3201C for 25 h 111 10�14.6

Fig. 11. Cole–Cole plots of the electric modulus, M* of the PEEK

M. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–1414 1411

3.2.1. Arrhenius analysis

Fig. 10 shows the Arrhenius plots for MWS relaxation ofthe examined semi-crystalline polymers. These plots areobtained with M00 frequency maximum position fortemperatures varying from 250 to 310 1C. The data inFig. 10 can be described by straight lines, indicating thatthe temperature dependence of the MWS relaxationprocess for all the samples is described by the Arrheniusequation:

f ¼ f 0exp �Ea

kBT

� �,

where f0 ¼ 1/2pt0, f being the frequency and kB theBoltzmann constant, Ea and t0 are extracted, respectively,from the slopes and the intercepts of the plots of thefrequency at which appears the M00 maximum versusthe reciprocal of the temperature (Fig. 10). The data of theactivation energies and the relaxation times are listed inTable 2 give mean values of 108.8 kJ/mol for Ea and10�14.4 s for t0 for the all semi-crystalline polymers. TheMWS relaxation had an activation energy of 75, 131.83,and 139 kJmol�1 observed in polymer-glass-bead compo-sites [34–36], in composites with 0.5 or 1.5 p.h.r in Kevlarfibres and 25 p.h.r in aluminium [45] and in polymer-PZTcomposites [46], respectively. The mean relaxation timebeing very close to the characteristic time of Debye(10�13 s), it shows that the MWS effect in our samples isa thermo-activated phenomenon related to elementaryrelaxation of dipoles.

crystallized at 320 1C for 1 h. The dotted lines are produced by best-fitting

the experimental points to the Havrilik–Negami approach.

3.2.2. Argand analysis

A typical curve in the complex plane is reported in Fig.11 for semi-crystalline PEEK at 280 1C. The curves areshaped as skewed arcs that can be fitted by theHavriliak–Negami equation [47]:

Fig. 10. Arrhenius plots of the frequency of the M00 maximum versus the

reciprocal temperature for the annealed PEEK crystallized isothermally at

320 1C for 1 h, 320 1C for 25 h, 160 1C for 1 h and 160 1C for 25 h.

�nðoÞ ¼ �1 þ�s � �1

ð1þ ðiotÞaÞb,

where es and eN are the dielectric constants on the low- andhigh-frequency sides of the relaxation, a is the symmetricand b the asymmetric broadening parameters, t is thecentral relaxation time and o is the radial frequency. Thisequation is a combination of the formula of Cole–Cole fora ¼ 1, Cole–Davidson for b ¼ 1 and Debye for a ¼ 1 andb ¼ 1.In the electric modulus formalism, the Havriliak–Nega-

mi equations have the following forms [45]:

M 0 ¼�0

�02 þ �002¼M1Ms

MsD21 þD1D2 cos bj

M2sD

21 þD2½D2 þ 2MsD1 cos bj�

M 00 ¼�00

�02 þ �002¼M1Ms

D1D2 sin bjM2

sD21 þD2½D2 þ 2MsD1 cos bj�

where Ms ¼ 1/es, MN ¼ 1/eN,

D1 ¼ ðcos jÞb 1þ ðotÞ2a þ 2ðotÞa sin

ap2

h ib,

D2 ¼ ðM1 �MsÞ 1þ ðotÞa sin

ap2

h ib,

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Fig. 12. Cole–Cole plots of the electric modulus, M* of the PEEK

crystallized at 320 1C for 25 h at different temperatures.

M. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–14141412

ðotÞa ¼tan 1

b arctanM1M 00

M1M 0�M 002�M 02

h ih i

cos ap2� sin ap

2tan 1

b arctanM1M 00

M1M 0�M 002�M 02

h ih i .

It is impossible to pass the Havriliak–Negami modelwith all the experimental points in the case of the semi-crystalline PEEK. It should be noted, in addition, that theexperimental points pass by the origin of the axes for allPEEK curves. This behaviour is a clear sign that in the caseof the semi-crystalline PEEK, another phenomenon ispresent in addition to the interfacial relaxation. Thisphenomenon could be the appearance of a significant ionicconduction in the material at high temperatures with smallvalues of electric modulus or high values of permittivityalready noticed in such materials, for example polyvinyl-pyrrolidone [48].

A half-circle passing by the origin in the complex planhad been regarded as being a characteristic of a conductionphenomenon in PET [49] and PBT [50]. Besides, con-ductivity relaxation can be present in more conductingcomposite materials like polyethylene-carbon black [51] orin polystyrene with a significant content of glass beads [34]leading to percolation phenomenon. The data at lowfrequencies (low M0) fit the semicircle quite well (a ¼ 1 andb ¼ 1). They are only related to ionic characterization. Itshould be emphasized that this ‘‘conductivity relaxation’’ isa result of algebraic properties of conductivity and does notprovide information about interfacial relaxation in PEEK.Since known interfacial relaxation in composites are alwaysbroader than the Debye model, these tests tell us that thispeak in M00 (at low frequencies) does not probably belongto that category. Cole–Cole plots of the PEEK crystallizedat 320 1C for 25 h at 250, 270, 290, 310 and 330 1C areshown in Fig. 12. When the temperature increase, thecurves were more complete, their beginnings movedtowards the origin (low values of M0 and M00) and themaximum values of M00 is increased. This behaviour isrelated to the considerable effects of conduction. When thetemperature is increased, the electrical properties arefrequently dominated by conduction. The rise in conduc-tivity must be attributed to the increasing mobility of thecarriers. The same behaviour was found in all the examinedcrystallized PEEK.

At higher frequencies, interfacial relaxation effects makeadditional contribution to M00. Table 3 presents theparameters characteristic of the Havriliak–Negami equa-tion as well as the values of the frequency at the maximumof interfacial relaxation in permittivity fmax,e00 mode, for thevarious crystallized PEEK samples. The frequency of themaximum of the relaxation in the electric modulus isobtained from the isothermal spectra of the imaginarypart of the electric modulus M00. The following relationgives the frequency of the maximum in the permittivitymode [45]:

f max;�00 ¼Ms

M1

f max;M 00 .

From Table 3, we note that the frequency of themaximum of the interfacial relaxation is always lower than500Hz. With these frequencies, the ionic conductionphenomenon is very significant and then masking theMWS relaxation, justifying the use of the electric modulusin this study.For a given sample and in general, a rise in the

temperature leads to an increase in the intensity ofrelaxation and to a shift of the maximum of relaxationtowards the high frequencies. That suggests that theaptitude of the ions to be polarized at the interface ismore significant at high temperature, a phenomenon thatcan be due to the greatest number of charges, whichmigrate towards the interface and block themselves there,and to the greatest mobility of these charges.The ratio of crystallinity does not seem to be an essential

factor controlling the intensity of interfacial relaxation.Indeed, if the samples are differing by crystallinity ratio,they are also characterized by the distribution of crystallinelamellae. Let us recall, for example, that only the sample320 1C/25 h presents one crystallites population, whereasthe other semi-crystalline systems present a distributionthickness and/or degree of perfection of crystallites.For 160 1C-samples with crystallinity around 10%, the

relaxation intensity seems to weakly increase with theweakly increasing crystallinity ratio. For 320 1C-sampleswith crystallinity around 30%, the relaxation intensityseems to weakly decrease with the weakly increasingcrystallinity ratio.In the case of the 160 1C crystallization, the major

process is germination, the increase of crystallinity issupposed to result from the creation of new crystallites.The crystal/amorphous contact zone increases, leading to agreat number of relaxing dipole and to an increase of theintensity of relaxation.In the case of the 320 1C crystallization, the major

process is growth, with a thickening of the crystal lamellae.

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Table 3

Crystalline volumic fractions and parameters evaluated by fitting data according to the Havriliak-Negami equation for the PEEK with various annealing

conditions

Annealed PEEK Cryst. (%) T (1C) a b Ms MND� ¼ �s � �1

¼1

Ms�

1

M1

fmax,e00 (Hz)

160 1C for 30min — 270 0.89 0.73 0.036 0.234 23.50 154

280 0.85 0.73 0.024 0.240 37.50 160

290 0.80 0.80 0.020 0.240 45.83 217

160 1C for 1 h 7.7 270 0.89 0.67 0.040 0.279 21.42 230

280 0.99 0.64 0.034 0.230 25.06 296

290 0.94 0.76 0.026 0.218 33.87 358

160 1C for 25 h 10.6 270 0.80 0.81 0.027 0.234 32.76 115

280 0.79 0.82 0.025 0.236 35.76 170

290 0.80 0.79 0.019 0.240 48.46 206

320 1C for 30min 26.1 270 0.79 0.79 0.024 0.246 37.60 156

280 0.74 0.85 0.017 0.243 54.71 182

290 — — — — — —

320 1C for 1 h 29.5 270 0.75 0.82 0.024 0.246 37.60 156

280 0.92 0.66 0.027 0.250 33.04 281

290 0.79 0.80 0.030 0.249 29.32 425

320 1C for 25 h 31.3 270 0.97 0.61 0.038 0.236 22.08 210

280 0.69 0.93 0.028 0.258 31.84 217

290 0.84 0.73 0.026 0.238 34.26 437

M. Arous et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1405–1414 1413

For the 320 1C-25 h sample, the lamellae are less numerousand smaller than those resulting from 160 1C crystallizationand 320 1C crystallization with shorter times. The improve-ment of lamellae perfection, can lead to the improvementof the boundary between crystal and amorphous regions,and then to a weaker mobility of electric charge at theinterface. It is then concluded that the interface is a perfectone, accounting to Lestriez et al. [52], based on the decreaseof the intensity of relaxation. A previous study by Cebeand Huo [17] showed that, when the crystallizationtemperature increases, the volume fraction of the rigidamorphous phase decreases and the crystallinity rationincreases, making the system to more towards a two-phasessystem, and giving a ‘‘perfect’’ interface.

Therefore, the presence of a single lamellae population,with large sizes and having a high degree of perfection,leads to a weaker intensity compared to systems having alarge distribution of crystallites sizes.

4. Conclusion

The electric modulus is a useful computational tool forinvestigation of polymers in the region of the glasstransition and above where the electrical properties arefrequently dominated by conduction.

A MWS relaxation is seen in PEEK in addition todipolar relaxations and ionic conduction. This relaxation isattributed to the trapping of ionic charges between thecrystalline lamellae and the amorphous matrix. Theintensity of the relaxation is shown to be sensitive to the

annealing conditions and is related to morphologicalfeatures. It is shown that the crystallinity rate is not themain factor of the interfacial relaxation intensity, whichalso depends on the nature and degree of perfection of thelamellae.This approach pointed out the influence of the quality of

the interface in the interfacial relaxation characteristics,and showed that the study of this interfacial relaxation canbe an interesting tool for the analysis of interface indielectric spectrometry.

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