clay nanocomposites

Materials Chemistry and Physics 232 (2019) 99–108

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Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Thermal and dielectric behavior of polyamide-6/clay nanocomposites Imen Hammami a, *, Helmi Hammami a, J�er�emie Soulestin b, Mourad Arous a, Ali Kallel a a b

LaMaCoP, Faculty of Sciences of Sfax, Department of Physic, University of Sfax, 3018, Sfax, Tunisia TPCIM, IMT Lille Douai, Department of Polymers and Composites Technology and Mechanical Engineering, University of Lille, 59500, Douai, France

H I G H L I G H T S

G R A P H I C A L A B S T R A C T

� Adding C30B nanocharge to PA6 matrix led to the increase of the RAF. � Quantitative knowledge on the crystal­ lization and nucleation kinetics of PA6 and its nanocomposites is investigated. � Dipolar relaxation and interfacial po­ larization are modelled. � The nanocomposites fragility parame­ ters and activated energy for different process are estimated.

A R T I C L E I N F O

A B S T R A C T

Keywords: Polymer Composite Interface

In this work, the influence of the incorporation of nanoparticles (organo-modified montmorillonite Cloisite 30B) in polyamide 6 (PA6) on rigid amorphous fraction (RAF) formation had been explored employing Differential Scanning Calorimetry (DSC), Flash Differential Scanning Calorimetry (Flash DSC) and Broadband Dielectric Spectroscopy (BDS) techniques. The existence of a RAF in PA6-montmorillonite nanocomposite films is available from specific heat capacity measurement at the glass transition region of the nanocomposites. It was shown that at high C30B content, this fraction becomes larger. Using Flash DSC, it was possible not only to measure the heat capacity step at the glass transition of the materials, but also to provide quantitative knowledge on the kinetics of crystallization and nucleation of PA6-based nanocomposites. The dielectric relaxation spectroscopy measure­ ment was investigated, in the frequency range 0.1–106 Hz and varying temperature from 20 to 200 � C, which highlight different relaxation phenomena: the α dipolar relaxation, the αc relaxation and Max­ well–Wagner–Sillars (MWS) interfacial polarizations. As C30B content increases, a MWS relaxation emerges in the nanocomposites, thus revealing the increase of RAF in the nanocomposite with high C30B content.

1. Introduction Polymer nanocomposites have attracted a great deal of attention in recent years due to their exceptional properties. Indeed, filling polymers with nanoparticles, particularly those containing high aspect ratio nanofillers, is used to enhance physical characteristics, such as increased

mechanical strength, resistance to dielectric breakdown, and improved thermal behavior [1]. Among the Numerous types of nanosized fillers, clay and layered silicates are the most commonly used nanofiller because of their natural abundance, their low cost and their high aspect ratio (greater than 100). To optimize and to control the montmorillonite (MMT) filled

* Corresponding author. E-mail address: [email protected] (I. Hammami). https://doi.org/10.1016/j.matchemphys.2019.04.048 Received 23 January 2019; Received in revised form 3 April 2019; Accepted 16 April 2019 Available online 20 April 2019 0254-0584/© 2019 Elsevier B.V. All rights reserved.

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Materials Chemistry and Physics 232 (2019) 99–108

nanocomposites performance, it is essential to increase as much as possible the degree of nanoparticles exfoliation and dispersion within polymer matrix for creating large interaction surfaces promoting the formation of interphase. These interphases are formed due to the exis­ tence of an amorphous polymer fraction immobilized around the nanoparticles. Several parameters influence the state of dispersion and exfoliation such as the matrix type, the clay treatment and the pro­ cessing conditions. Polyamide 6 (PA6), also called Nylon 6, have been widely used in packaging applications due to their good mechanical resistance, the high barrier against gas and water, the fire resistance and the excellent bal­ ance cost/performance [2]. The presence of clay nanoparticles in the polyamide 6 induces an improvement in its properties and in particular those related to barrier against water and gases. In this work, the interfacial effects in polymer PA6/MMT nano­ composites were investigated by several techniques. Differential Scan­ ning Calorimetry (DSC) is such a technique, and it is used to study the interfacial effects in polymer nanocomposites by focusing on glass transition region. Indeed, Privalko et al. [3,4] recognized the impor­ tance of specific heat capacity measurements for the identification of a fraction of reduced mobility in nanocomposites. Following these ideas, the existence of a rigid amorphous fraction (RAF) in poly(methyl methacrylate) (PMMA)/SiO2 nanocomposites was shown by applying heat capacity measurements at the glass transition of the polymer as described by Wunderlich et al. [5,6]. Then, a ‘3-phase-model’ was established for semicrystalline polymers where the polymer matrix consists of the mobile amorphous fraction (MAF), the crystalline fraction (CF), and the RAF. Complementary to thermal analysis, Broadband Dielectric spectros­ copy (BDS) is one of the most powerful methods used to evaluate the different molecular mobilities of complex nanostructured systems and provide an experimental access to the interfacial effects. The paper aims, using the correlation between thermal and dielectric analysis, to char­ acterize the RAF induced by clay nanoparticles.

2.3. Experimental procedure 2.3.1. Transmission electron microscopy (TEM) The morphologies of the nanocomposite films were analyzed by transmission electron microscopy (TEM). The specimens of 70 nm nominal thickness were cut with a diamond knife on an ultracut microtome (Leica UCT, Switzerland), at cryo tem­ perature ( 120 � C). Bright-field TEM images of nanocomposites were obtained at 300 kV under low dose conditions with an electronic microscope (Philips CM30), using a Gatan CCD camera (Gatan, USA). 2.3.2. Differential scanning calorimetry (DSC) Differential Scanning Calorimetry (DSC) was performed to study the effect of C30B incorporation on PA6 melting and crystallization behavior, hence the percentage of RAF. The DSC experiments were realized on a Mettler Toledo DSC-1 in­ strument under a nitrogen atmosphere at heating and cooling rate of 50 � C min-1 and 10 � C min-1 respectively. In all cases, the samples, with a mass ranging between 2 and 4 mg, were heated from 90 � C to 250 � C, cooled from 250 � C to 90 � C, then followed by a second heating step from 90 � C to 250 � C. The crystallinity index can be calculated from melting enthalpy by the following relation: XC ¼

ðΔHm ΔHc Þ ΔHmo ð1 ϕÞ

(1)

where ΔHm is the melting enthalpy, ΔHc is the cold crystallization enthalpy, ΔHm0 is the theoretical melting enthalpy of 100% crystalline PA6 (ΔHm0 ¼ 190 J/g [8]) and ϕ is the mass fraction of C30B intro­ duced into PA6. Temperature Modulated Differential Scanning Calorimetry (TMDSC) is a method that allows a separation of reversing and non-reversing processes. Hence, this technique provides more information about the dynamics of the processes involved. In this study, stochastic TMDSC runs were carried out on a Mettler-Toledo DSC1 instrument. The measure­ ments were made using samples with a mass of about 20 mg, at under­ lying heating rate of 1 � Cmin-1 between 60 � C and 250 � C. The amplitude of the temperature pulse was set at � 0.5 � C and the switching time range from 25 to 50 s.

2. Experimental section 2.1. Materials A commercially available polyamide 6 (Akulon, F132E1, DSM, NL) with a molecular weight of 66000 g/mol and density of 1.13 g/cm3, was used in this study. As reinforcement, the cloisite 30B (C30B) organomodified, contains the cation methyl tallow bis-2-hydroxyethyl, seems to be a good choice. In fact, the cloisite 30B, as already shown before, leads to a high exfoliation degree in PA6 [7]. The presence of hydrogen bond between the hydroxyl groups and the amide groups of the polymer chains facilitates the delamination.

2.3.3. Flash differential scanning calorimetry (Flash-DSC) In order to evaluate the mobility of macromolecular chains in un­ filled films and composite films, Flash DSC experiments were performed using a Flash DSC 1 instrument provided by Mettler-Toledo [9]. Contrary to conventional DSC instrument, a tiny fragment of sample (with a mass in the order of nanograms) was placed onto a MultiSTAR UFS 1 chip sensor, based on MEMS (Micro-Electro-Mechanical Systems) sensor technology. Heating-cooling cycles in dry nitrogen gas are essential to ensure that the sample has established a good thermal contact to the sensor. Measuring the weight of such low masses is not feasible with a common balances. Therefore, the sample masses were estimated by applying an identical protocol on the sample placed on the conventional DSC and on another sample inserted in the Flash DSC. Finally, the evaluation of the samples masses can be easily done via the melt enthalpy determined from the two DSC curves. For the PA6 matrix, the mass was estimated at 106 ng, while for the filled PA6, it was estimated at 27 ng for PA6þ3%C30B, 131 ng for PA6þ5%C30B and 201 ng for PA6þ7%C30B. To study the kinetics of crystallization and nucleation, Flash DSC measurements were made in a temperature range of 90 � C to 250 � C using different heating and cooling rates (from 10 � Cs-1 to 1000 � Cs-1). After carrying out the calorimetric measurements of the nano­ composite films, the RAF can be determined by applying the method

2.2. Processing of PA6 nanocomposite films The nanocomposites PA6/C30B were obtained using a two-step treatment: the first step called masterbatch step, corresponded to the preparation of a mixture containing the PA6 with 12% by weight of C30B using a twin-screw extruder type Clextral BC45 at a rotation speed of 50 rpm and a temperature ranging from 240 � C to 270 � C. The second step was the dilution of this masterbatch into a Haake Buchler Rheocord 40 single-screw extruder at a temperature and screw speed of 230 � C and 50 rpm. Nanocomposites films of 200–250 μm in thickness with different clay content (3%, 5% and 7%) are finally obtained using single extrusion. Prior to processing into films, the PA6 polymer and the nano-fillers C30B are dried at 80 � C under vacuum overnight to remove residual water moisture.

100

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Fig. 1. TEM micrographs of (a, b) PA6 þ 3% C30B, (c, d) PA6 þ 5% C30B and (e, f) PA6 þ 7% C30B [14].

described by Xenopoulos and Wunderlich [10] for semi-crystalline polymers. From the heat capacity measurements at the glass transition region, they led to establish a model that makes it possible to distinguish between the crystalline fraction CF, the rigid amorphous fraction RAF and the mobile amorphous fraction MAF. This model is called a three-phase model. From the results obtained by the TMDSC and the DFSC, the RAF can be determined using the following equation: Xrað%Þ ¼ 1

ðXc þ xmaÞ

(2)

where Xc is the crystallinity degree, calculated using eqn (1), and Xma is the mobile amorphous phase fraction, deduced from eqn (3). Xmað%Þ ¼

ΔCp ΔCp ðamÞ

(3)

Δcp and Δcp(am) are the measured heat capacity increment at the glass transition region of the semi-crystalline and 100% amorphous polymer respectively. Δcp(am) can be determined experimentally by the Flash DSC measurements or taken theoretically from ATHAS database [11].

Fig. 2. DSC thermograms of PA6 matrix and PA6/C30B nanocomposites.

The measures dielectric permittivity data were collected and evaluated using a WinDETA impedance analysis software. The dielectric behavior is investigated with the complex dielectric constant ε* and the complex electric modulus M * expressed as [12,13]:

2.3.4. Dielectric Spectroscopy (DS) Dielectric Spectroscopy measurements were performed on a Novo­ control Impedance Spectrometer based on an Alpha analyzer and a Quatro temperature controller in the temperature ranged from to 20 � C–200 � C on heating at a rate of 5� Cmin-1 and in a broad frequency window from 0.1 Hz to 1 MHz. For the dielectric analysis, an alternating voltage with amplitude 1V was applied to a sample placed between two parallel plate electrodes.

ε* ¼ ε’

101

jε}

(4)

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Materials Chemistry and Physics 232 (2019) 99–108

Table 1 Crystallinity index of PA6 matrix and PA6/C30B nanocomposites. Samples

Xc (%)

PA6 PA6þ3% C30B PA6þ5% C30B PA6þ7% C30B

27.7% 30.9% 31.8% 31.4%

Fig. 4. Molar heat capacity of PA6 and PA6/C30B matrix in the glass transi­ tion region.

215 � C, associated with the fusion of the α-form crystals of PA6. We also observe a second peak at 175 � C for the neat PA6 while it is centered at 195 � C for the nanocomposites. This peak is due to the fusion of γ-form crystals. In fact, according to the literature [15–17], the PA6 exhibits a polymorphic structure that presents two major crystal forms: the α-form and the γ-form. This polymorphic behavior is dependent on the pro­ cessing conditions, thermal history, crystallization conditions and me­ chanical stress. The most thermodynamically stable phase is the α-form. This phase has a monoclinic structure, in which the anti parallel polymer chains are linked by hydrogen bonding. The γ-form crystal structure is monoclinic or pseudo-hexagonal, in which hydrogen bonds are formed between parallel polymer chains. Furthermore, the α and γ structures coexist in the presence of MMTs in which the γ structure occurs near the interfaces of the nanolayers. For the α structure, it develops where the nanoplates do not affect the conformation of the chain and the folding of the PA6. The cause of this is that MMT hampers the displacement of the Hydrogen bonds associated with the transformation from γ structure to α structure. Therefore, the difference in melting temperatures of the γ-form crystal between the pure PA6 and the nanocomposites may be due to a growth in formation of crystal nuclei caused by the presence of MMT in the nanocomposites. From the two endothermic peaks associated with the fusion of the α-form crystals and the fusion of the γ-form observed in the DSC ther­ mograms (Fig. 2) and using the equation (1), the crystallinity index Xc of the samples could be deduced. These values are reported in Table 1.We notice a slight increase in crystallinity index following the introduction of MMT. This increase confirms the formation of new crystal nuclei caused by the presence of MMT.

Fig. 3. Molar heat capacity of PA6 in the glass transition region: measured curve for the semi-crystalline PA6; amorph (Cp am) and cristal (Cp cr) reference curves from ATHAS database; expected molar heat capacity from a 2-phase model; molar heat capacity calculated from a 3-phase model; the tangent on the measured curve above the glass transition region.

M* ¼

1

ε*

¼ M’ þ iM} ¼

ε’ ε’2 þ ε}2

(5)

where ε ’ is the real and ε ’’ is the imaginary parts of the dielectric constant, M’ and M00 are, respectively, the real and imaginary parts of the electric modulus. 3. Results and discussion 3.1. Morphological analysis Fig. 1 shows TEM images of PA6 matrix and PA6/C30B nano­ composites taken at two magnifications (100 n.m. and 200 n.m.) The TEM observation reveal that the PA6/C30B nanocomposites contained individual nanoplatelets with more or less associated platelets observed at law filler content. Therefore, PA6/C30B films present a high degree of exfoliation of C30B nanoplatelets for the law and hight C30B content. Moreover, the TEM images show a high degree of orientation of the nanoclay with an orientation parallel to the surface of the film. This effect is associated to the processing condition, in other word to the shearing forces induced in during the extrusion. These result are more exploited in alix et al. research work [14].

3.3. Determination of the rigid amorphous fraction For semi-crystalline polymers, a RAF is broadly discussed [5]. This fraction is defined as the polymer, which behaves liquid like, e.g., vitrified or devitrified in the common glass transition region (Tg) and contributes therefore to the heat capacity step at Tg. According to the DSC measurements, the RAF is considered completely rigid and does not contribute to the glass transition. In order to determine the RAF, precise measurements of heat capacity performed by the TMDSC technique in the temperature range of the glass transition of the polymer nano­ composite are required. Fig. 3 shows the evolution of the specific heat capacity of the PA6 determined by TMDSC (TOPEM) measurement. The standard method evaluates the glass transition by using tangents

3.2. Crystalline structure and crystallinity In semi-crystalline polymers, the formation of the RAF can be affected by a change in the crystalline state of the material due to the presence of the nanoclay reinforcements. Therefore, it is necessary to determine the effect of the incorporation of these MMT nanolayers on the crystallinity degree. Fig. 2 shows thermograms obtained from ther­ mal analysis using differential scanning calorimetry (DSC). We note that all the samples display an endothermic peak located in the region of 102

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Table 2 The thermal parameters of PA6 and its nanocomposites: glass transition tem­ perature (Tg), heat capacity step (ΔCp), crystalline fraction (CF), mobile amorphous fraction (MAF) and rigid amorphous fraction (RAF). Sample

Tg (� C)

ΔCp (J mol 1K 1)

CF (%)

MAF (%)

RAF (%)

PA6 PA6þ3 wt% C30B PA6þ5 wt% C30B PA6þ7 wt% C30B

52 51

18.35 15.63

27.7 30.9

34.1 29.1

38.2 40.0

52

14.78

31.8

27.5

40.7

53

14.07

31.4

26.2

42.4

Table 3 The thermal parameters of PA6 and its nanocomposites determined from Flash DSC measurements at a heating rate of 1000 � C.s-1: glass transition temperature (Tg), heat capacity step (ΔCp), crystalline fraction (CF), mobile amorphous fraction (MAF) and rigid amorphous fraction (RAF). Sample

Tg (� C)

ΔCp (J mol 1K 1)

CF (%)

MAF (%)

RAF (%)

PA6 PA6þ3 wt% C30B PA6þ5 wt% C30B PA6þ7 wt% C30B

60.5 61.5

36.93 32.7

21.8 28.1

68.7 60.8

9.5 11.1

59.5

31.68

30.0

59.0

11.0

60.5

28.14

33.6

52.4

14.0

Fig. 6. Diagram of time-temperature profile of the Flash DSC experiments used to investigate the nucleation and crystallization in PA6 and PA6/C30B films.

capacity shows a non-negligible contribution added to the measured thermal capacity. This contribution can be either an excess heat ca­ pacity, or a continued extension of the glass transition to higher tem­ peratures (successive devitrification of the RAF) [19]. The same formalism can be applied for nanocomposites taking into account the crystalline fraction from MMT incorporation [20]. To determine the RAF, the heat capacity measurements, using the TOPEM method, in the temperature range of the glass transition were performed for the different samples of PA6/C30B. The results are shown in Fig. 4. As shown in Fig. 4, the heat capacity curves are shifted towards lower values by increasing filler concentration. The lowering is due to a part of the polymer immobilized by the C30B which does not contribute to the glass transition. From the obtained curves, the heat capacity step at Tg of PA6 and its nanocomposites can be determined. Eventually, the MAF and the RAF can be deducted. The value of ΔCp(am) used for the calculation of the MAF is determined from the ATHAS database. This value corresponds to 53.7 J.K-1.mol. The ΔCp, MAF, CF and MAF are available and given in Table 2. From the Table 2, it can be noticed that ΔCp is directly related to MAF. This result means that MAF decreases in the presence of MMT. Therefore, the increase in the percentage of MMT introduced in the PA6 causes the increase of the RAF. The incorporation of the nanoparticles in the matrix affects the polymer layer adjacent to these additives by stopping the movement of this layer. Consequently, this reduction in molecular mobility tends to increase RAF. In addition, the RAF is related to the degree of dispersion of C30B in the matrix [21]. In fact, the per­ centage of RAF increases for nanocomposites with a higher degree of dispersion and higher clay content. This is the case of PA6þ7 wt% C30B nanocomposite which is exfoliated and has the higest clay content [7]. It can be expected that the RAF will increase with increasing the filler content. However, at a high filler content, it is known that the C30B tended to aggregate and that will lead to the decrease of the RAF [22, 23]. To confirm the results obtained by the TMDSC technique, the Flash

Fig. 5. Flash DSC thermograms of PA6 matrix and PA6/C30B nanocomposites.

at the heat capacity curve above and below the glass transition region. The glass transition temperature (Tg) is the temperature at which the measured curve is equidistant between tangents. Then, the step height at the glass transition Δcp is specified as the difference between the upper and lower tangents at Tg. In Fig. 3, the tangent below the glass transition coincides with the heat capacity of the crystal (obtained from ATHAS database), while the tangent traced above the glass transition is shown in dashed lines. In order to fit the measured curve above Tg, a 2-phase model was applied using the following equation: Cpsc(2-phase model) ¼ Cpam � (1 CF)þCpcr � CF

(6)

We note that the heat capacity measured just above the Tg is lower than that expected from the 2-phase model. Consequently, a 3-phase model, taking into account the RAF, has to be applied according to Equation (7). Cpsc(3-phase model) ¼ Cpam � MAF þ Cpcr � CF þ Cpra � RAF

(7)

It is highlighted that for semi-crystalline polymers, two glass tran­ sitions can be detected. The first transition results from the MAF and the second transition arises from the RAF [18]. Above the glass transition of the MAF, the RAF is still in the vitreous state and it can be considered as solid and subsequently its heat capacity is equal to the solid Cp. Equation (7) can be described as follows: Cpsc (3-phase model) ¼ Cpam � MAF þ Cpcr � SF

(8)

Where SF ¼ CF þ RAF: solid fraction. The comparison between the slope of the tangent traced above the glass transition (dashed line) and the slope of the semi-crystalline heat 103

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Fig. 8. Temperature dependence of real (a) and imaginary (b) parts of the dielectric permittivity for the PA6 matrix.

DSC was used in this study. To calculate the RAF, the same approach described previously was used. The results were calculated and shown in Table 3. The values of ΔCp and ΔHf are determined from the Flash DSC curves (Fig. 5). Subsequently, a correction of these values with respect to the masses of the samples was made. The results observed in Table 3 confirm that obtained from the TMDSC measurements despite the remarkable difference in the per­ centages of MAF and RAF. This difference is due to the fact that in these two techniques we did not use the same heating and cooling rates. 3.4. Nucleation and crystallization kinetics As known, Flash DSC is the ideal technique for studying nucleation and crystallization kinetics in PA6 and PA6/C30B nanocomposites during cooling. A simple analysis protocol is schematized in Fig. 6. The advantage of this analysis is its ability to acquire additional in­ formation on the crystallization, nucleation and stability of objects formed by controlled cooling. In fact, information on the interaction of the growing objects and the surrounding melt can be determined from changes in the increase in thermal capacity at Tg. Then, the available mobile and crystallizable material is given by the analysis of the cold crystallization peak. In addition, in noncrystalline samples, the cold crystallization enthalpy appears to be a good measure of the number of available nuclei, and the temperature of the cold crystallization range is related to changes in the type of nuclei present. Finally, the melting temperature of the different species can be related to the stability of the objects and the change of total enthalpy at heating provides information

Fig. 7. Apparent heat capacity of: (a) PA6, b) PA6þ3%C30B, c) PA6þ5%C30B, d) PA6þ7%C30Bfrom Flash DSC on heating with 1000 � C/s after cooling with rates between 50 and 1000 � C/s.

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Fig. 10. The dielectric loss data ε" and the corresponding derivative data ε00 deriv at 150 � C for the PA6 matrix.

Fig. 9. Frequency dependence of imaginary of the dielectric permittivity (a) and imaginary (b) for the PA6 matrix.

the total crystallinity present in the sample before the heating scan [24]. A set of heating curves after cooling at different rates is shown in Fig. 7. For PA6, the melting peak decreases and becomes zero at cooling rates above 500 � C.s-1. Then, no crystallization occurs in this case. At low cooling rates, the nanocomposites show at the glass transition range a relatively small and broadened increment, no cold crystalliza­ tion and a large melting peak. While for higher cooling rates, the increment in the glass transition increases and becomes more noticeable due to the onset of a cold crystallization peak. This peak develops and its intensity increases for high cooling rates. This increase is explained by a growth in the formation of crystalline nuclei. In addition, the melting peak decreases as a result of low crystallinity developed during cooling. It can be deduced that, depending on the cooling rates, different states of the materials can be detected allowing modeling of their thermal histories. Indeed, a slow cooling leads to a thickening and better stability of the crystallites. This thickening occurred through homoge­ neous and heterogeneous nucleation followed by growth, i.e., the transformation of low-perfection crystallites into thicker crystalline lamellae with a higher degree of perfection. By increasing the cooling rate, the sample cannot complete its crystallization during cooling. Initially, a homogeneous and heterogeneous nucleation occurs but fewer crystals grow. The remaining nuclei induce cold crystallization.at higher rates of cooling the homogeneous and heterogeneous nuclei in their growth do not reach a perfect size, i.e., the amount of crystals continues to decrease, which causes the decrease of the melting peak. On the other hand, the amount of nuclei continues to increase causing the increase of

Fig. 11. Imaginary part of the dielectric modulus M00 versus frequency, at 70 � C (a) and at 150 � C (b), for the PA6 matrix and PA6/C30B nanocomposites.

the peak of cold crystallization. Furthermore, the Fig. 7 can provide information regarding the enthalpy relaxation of the polymer, which is also characteristic of a physical aging. It is known that the rate at which you cool through Tg has a considerable effect on the resulting ageing kinetics [25,26]. A slower cooling rate gives more time for the molecular chains to find 105

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Fig. 13. Relaxation map corresponding to the temperature dependence of the relaxation time for α, αcand MWS processes for PA6 matrix and PA6/C30B nanocomposites.

large increase in both the real and imaginary parts of the dielectric function [33]. In the same way, the variations of the loss factor ε ’’ can be presented, in isothermal conditions (Fig. 9a). These variations show a linear in­ crease of ε ’’ especially for the high temperatures and the low fre­ quencies. In these domains the slope of ε ’’ is close to 1, which indicates the presence of DC conductivity effect [34,35]. This phenomenon can be detected by presenting the frequency dependence of the AC conductivity. As it can be seen from Fig. 9.b, the presence of a horizontal plateau at low frequencies corresponds to the DC conductivity effect. Moreover, we notice a slight decrease of AC conductivity at low frequencies. This behavior is related to the elec­ trodes polarization mechanism [36,37]. To further investigate the phenomena that occur at low frequencies region, we use the first derivative of the real part of the dielectric permittivity [38]:

Fig. 12. Imaginary part of the electric modulus M00 versus frequency for the PA6þ7%C30B nanocomposites. at 70 � C (a) and at 150 � C (b).

energetically favorable orientations. For the PA6, it can be observed a peak of enthalpic relaxation at the glass transition region, which is more remarkable for the slowest cooling rate. In factthe PA6 has the time to undergo a physical aging at and below the Tg. The shorter the time (fast speed) the less physical aging. For the nanocomposites this phenomenon is less observable when the C30B content introduced in PA6 increases until disappearing at 7% of C30B content. This could be related to the increase of RAF with increasing the filler content. Indeed, the presence the RAF will affect the behavior of the mobile amorphous phase. Consequently, the phenome­ non of enthalpy relaxation decreases with the increase of the rigid amorphous phase [27,28].

ε’’deriv ¼

π ∂ε’ 2 ∂lnω

(9)

The ε’’deriv method is useful for systems that exhibit low frequency relaxations with appreciable ohmic conductivity, since the values of ε 0 (ω) are unaffected by ohmic conductivity, and according to KramersKroning relationships its derivative is proportional to the loss factor ε ’’ (ω). Indeed, in the derivative formalism, the relaxation processes that take place in the dielectric loss variations appear as sharper peaks and without contribution of conductivity [39]. In the Fig. 10, we compare the dielectric loss data ε’’ , ε’’deriv at 150 � C. From the variations of ε’’deriv , and as it can be seen, we note the presence of three relaxation phenomena: relaxation αc, interfacial polarization MWS that appears due to the differences in conductivity values of the crystalline and amorphous phases and the electrodes polarization PE. The frequency dependence of M00 for PA6 and the nanocomposites at two different temperatures is display in Fig. 11. At low temperature (70 � C) the α relaxation is observed for the four samples (Fig. 11a). The αc relaxation and interfacial polarization appear in the frequency win­ dows at higher temperatures (Fig. 11b at 150 � C). The effect of clay-nanoparticles on the segmental mobility is further analyzed by performing an analysis based on fitting appropriate model functions. The electric modulus spectra were fitted by a sum of Havriliak-Negami (HN) model function terms of the form. The equation is an approximation of the HN equation [40]:

3.5. Dielectric study Fig. 8 depicts the temperature dependence of the dielectric permit­ tivity ε0 and the loss factor ε00 , respectively, for the PA6 matrix. As it can be seen, three relaxations are observed: - The primary relaxation, α-relaxation, appears for temperatures be­ tween 40 and 140 � C and frequencies between 102 and 106 Hz. It is associated to the glass transition of PA6 matrix [29–31]. - The αc-relaxation occurs between 60 and 200 � C (between 10–1 and 104 Hz). According to Laredo et al. [32], in the case of PA6, this kind of relaxation may be related to the presence of crystalline phases or to the diffusion of carriers such as protons and other impurities. - The ionic conduction process observed at high temperature and a low-frequency ranges, which appears from the increase in the elec­ tric charges mobility in the polymer with temperature, resulting a 106

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value reflects the strong interactions between clay nanoparticles and PA6 matrix.

Table 4 Calculated activation energies EA and strength parameter D. α-Relaxation

αc-Relaxation

Interfacial polarization MWS

Samples

EA (eV)

D

PA6 PA6-3%C30B PA6-5%C30B PA6-7%C30B PA6 PA6-3%C30B PA6-5%C30B PA6-7%C30B PA6-7%C30B

– – – – – – – – 1.209

3.85 5.56 5.64 5.76 10.05 10.51 12.61 14.32 –

2 3 n X Msi M∞i 6 7 M * ðωÞ ¼ 4M∞i þ h �αi iβi 5 i¼1 1 þ ð jðωτi Þ 1

4. Conclusions In summary, thermal and dielectric properties of PA6/MMT nano­ composites were investigated. DSC analyzes allowed to highlight the existence of an immobilized fraction through measurements of the thermal capacity during the glass transition. At higher C30B content incorporated in the PA6 matrix, this fraction becomes larger. This means that two different parts of the RAF must be considered by analyzing the heat capacity of the semi-crystalline nanocomposites, one immobilized at the interface between the crystallites and the amorphous polymer and the other at the interface between the filler and the polymer. In addition, the Flash DSC analyzes provide new quantitative knowledge on the kinetics of crystallization and nucleation of PA6 and its nanocomposites. We have noticed that crystallization at high cooling rates may be related to an increase in nucleation density; while for low cooling rates the crystal growth rate is faster than the nucleation rate. Concerning the dielectric study, different relaxation processes have been detected for PA6 matrix and nanocomposites. These processes were mainly associated to the relaxation α associated with the glass transition of the amorphous mobile phase of polyamide 6 and the relaxation αc related to the interfaces created between the amorphous phase and the crystalline phase. Moreover, the incorporation of MMT into PA6 matrix gave rise to another relaxation associated to MWS interfacial polariza­ tion. This latter arises from the trapping of electric charges at the in­ terfaces between the MMT nanoparticles and the PA6 matrix. This later is well defined for the nanocomposite with 7% reinforcement. Thus, lead to the same results obtained by the TMDSC analysis.

(10)

where ω ¼ 2πf the angular pulsation, τ the relaxation time and α and β the symmetric and asymmetric broadening factor. To better distinguish the different mechanisms observed, a separa­ tion of overlapping relaxation regions via the deconvolution of the imaginary part of the electric modulus M00 is presented in the Fig. 12. We note a good agreement between the experimental data and the obtained modelizations. From the data obtained by the adjustment, the maximum relaxation times versus the reciprocal of the temperature can be traced as can be seen in Fig. 13. The temperature dependence of the relaxation rate for the MWSrelaxations were described by the Arrhenius equation [41]: � � Ea τ ¼ τ0 exp (11) kB T

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