Dielectric relaxation of near-percolated carbon nanofiber polypropylene composites

Physica B 516 (2017) 41–47

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Dielectric relaxation of near-percolated carbon nanofiber polypropylene composites

MARK

⁎

A.J. Paleoa, , A. Zillea, F.W. Van Hattumb, A. Ares-Pernasc, J. Agostinho Moreirad 2C2T – Centro de Ciência e Tecnologia Têxtil, Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal Saxion University of Applied Sciences, Research Center Design and Technology, M.H. Tromplaan 28, Postbus 70.000, 7500 KB Enschede, Netherlands c Universidade da Coruña, Grupo de Polímeros, Centro de Investigacións Tecnolóxicas, Campus de Ferrol, 15471 Ferrol, Spain d IFIMUP and IN—Institute of Nanoscience and Nanotechnology, Department of Physics and Astronomy, Faculty of Science, University of Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal a

b

A R T I C L E I N F O

A BS T RAC T

Keywords: Carbon nanofiber Percolated materials Dielectric properties Cole-Cole analysis

In this work, the morphological, structural and dielectric analysis of near-percolated polypropylene (PP) composites containing carbon nanofibers (CNF) processing by melt-mixing are investigated. Whereas the morphological analysis shows that CNF exhibit some tendency to agglomerate within the PP matrix, the structural analysis showed first a general decrease in the intensity of the IR bands as a consequence of the interaction between carbon nanofibers and PP matrix and second an increase of the crystallinity degree of the PP/CNF composites when compared to the pure PP. The dielectric analysis demonstrates enhanced dielectric constants (from 2.97 for neat polymer to 9.7 for 1.9 vol% loaded composites at 200 Hz) and low dielectric losses. Furthermore, the dielectric relaxation for composites with concentrations in the vicinity of percolation is evidenced and well described by the generalized polydispersive Cole-Cole model from which the values of static dielectric constant (εs ), high frequency dielectric constant (ε∞), distribution of relaxation time (α) and mean relaxation time (τo), are determined, suggesting that this latter analysis constitutes a strong tool for understanding the relationships between microstructure and dielectric properties in this type of polymer composites.

1. Introduction Nanostructures composed of graphitic layers, including graphene and their derivatives, carbon nanotubes (CNT) and carbon nanofibers (CNF), are currently the focus of intense investigation [1]. In particular, CNF have a unique morphology in which exposed graphene edge planes are placed on the outer surface of the fiber [2]. Their outer and inner diameters ranging from 50 to 200 nm, and 30–90 nm, respectively, are slightly larger than CNT, while their lengths have average dimensions ranging from 50 to 100 µm [3,4]. Furthermore, their excellent electrical (σ~104 S/m) and thermal (τ~1950 W/mK) [5] conductivities along with their excellent mechanical properties, with an elastic modulus around 300 GPa and approximately 2.5 GPa in tensile strength [6], have converted CNF into an object of study in several fields of materials science [5,7,8]. For instance, an important area of application of CNF is the field of polymer composites. By incorporating different CNF loadings in a polymer matrix, important mechanical reinforcement [9], as well as, the enhancement of thermal, electrical and dielectric properties can be achieved [10,11]. In parti-

⁎

Corresponding author. E-mail address: [email protected] (A.J. Paleo).

http://dx.doi.org/10.1016/j.physb.2017.04.027 Received 12 February 2017; Received in revised form 24 April 2017; Accepted 25 April 2017 Available online 26 April 2017 0921-4526/ © 2017 Elsevier B.V. All rights reserved.

cular, it is known that CNF distributed in a polymer matrix can form into a large number of minicapacitors in a way that the final polymer composites can be used in applications which demands high electric permittivity such as electromagnetic radiation shielding [12], energy storage capacitors [13], actuators and sensors [14]. Accordingly, CNF/ CNT have been used to fabricate polymer composites with improved dielectric constant due to their high electrical conductivity and aspect ratio [15–17]. On one hand, it is well known that for conducting polymer composites a percolation transition is established when connected networks formed by CNF/CNT fillers span the sample and several critical exponents associated with critical composition fluctuations have been determined [18]. On the other hand, it is commonly accepted that two relaxations processes are the main responsible factors for the enhancement of the dielectric properties in nearpercolated materials: the interfacial polarization, associated with the charge trapping at the interface between the polymer and the filler and the space charge polarization at interfaces between the sample and the deposited electrodes [19]. However, the use of CNF/CNT fillers in dielectric polymer composites has been limited by several crucial

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polymer matrix. One type of stacked-cup CNF used in this study (PR 25 PS XT), commercially known as Pyrograf III, were supplied by Applied Sciences, Inc. (ASI, Cedarville, OH, USA). PR 25 PS XT fibers have an average bulk density ranging from 0.0192 to 0.0480 g/cm3 and an outer layer consisting on a disordered pyrolytically stripped layer. They have an average diameter of 120 nm and they have been heat-treated at temperatures of 1100 °C. They have shown to have lengths ranging from 50 to 100 µm [28]. Compared to other grades PR 24 and PR 19 produced by this company, the PR 25 grade has lower iron content and a larger number of graphitic edge sites available along the length [29].

challenges. The most important of them is that though dielectric constants can increase with the number of CNF/CNT present, mainly due to the two relaxation processes mentioned above, percolative composites have shown at the same time quite high dielectric losses due to the insulator–conductor transition near and beyond the percolation threshold [20]. To solve this problem, different strategies have been investigated. One approach is by preparing an insulating coating on the surface of carbon-based nanomaterials to avoid the composites become electrically conductive. For instance, Yang et. al prepared flexible dielectric polystyrene (PS) composites containing core-shell nanostructures consisting of polypyrrole (PPy) shell on core multiwall carbon nanotubes. By using this strategy, composites with dielectric constants up to 44 and low losses ( < 0.07) at 1 MHz for 10 wt % of CNT, were reported [21]. Other approach is to design composites with special structures, such as sandwich-like, layered and gradient structures. One example of this latter approach reports the processing of double-layer materials with one layer consisting of cyanate ester (CE) loaded with carbon nanotubes and other layer consisting of CE loaded with expanded graphite (EG) through two-step curing procedure [22]. A dielectric constant of 486 without dramatic high dielectric losses were reported for 0.5CNT/CE-5EG/CE systems with 0.5 wt% CNT and 5 wt% EG at 1 Hz. A disadvantage of both strategies is that they require the use of various materials, and additional physical and/ or chemical processes which makes more costly and energy-consuming the final product. In this study, a simple strategy based on the effect that poor dispersion of low aspect ratio CNF in polypropylene (PP) has on the final dielectric properties, is proposed. The basic principle is that if percolation threshold is decreased with well-dispersed CNF, then the opposite (i. e. an increase of percolation threshold) must be true for worse dispersed systems, this latter effect would allow that larger amounts of CNF below percolation threshold can be incorporated in the matrix, and as consequence, an enhancement in the dielectric constant, without strong damage in dielectric losses of conducting nature, can be observed. Furthermore, though extensive research has been done regarding the effects of contents of different kind of carbon structures in the final dielectric constant and dielectric loss of polymer composites by using percolation theory [21,23], few reports have been focused on the analysis of their dielectric processes by phenomenological models which would enable to accurately determine the main characteristics of relaxation mechanisms over a broad frequency range [24]. For instance, Belattar et. al. found that the Cole-Cole equation of dielectric relaxation, quantitatively described the experimental data in percolated carbon black (CB) filled ethylene butylacrylate (EBA) copolymer with nominal CB volume fractions between 0% and 22%, from which the relaxation time τo (4.1 ms for 13 vol% of CB) and the parameter α, associated with the distribution of relaxation time, with values from 0.06 to 0.10, were calculated [25]. The Cole-Cole formulism was used as well to calculate a relaxation time of 0.16 μs in PECNT/CE double-layer materials consisting of 0.5 wt% filled CNT [26]. In summary, the principal aims of this work are: firstly, to demonstrate that near-percolated carbon based polymer composites processing by meltmixing can be a very effective route to produce materials with enhanced dielectric constants and moderate low dielectric losses without damaging in mechanical enhanced properties, (associated with the increase of the elastic modulus and strength ascribed to the larger amount of CNF in the polymer, as it was discussed in our previous work [27]); and secondly, thanks to the quantitative determination of values of dielectric strength, relaxation time and distribution of relaxation time by using the Cole-Cole model, to contribute for the discussion of the origin of the relaxation mechanisms in the field of near-percolated carbon based polymer composites.

2.2. Fabrication of the CNF/PP composites PP/CNF composites were fabricated, under the same processing conditions, on a modular lab-scale intermeshing mini-co-rotating twinscrew extruder, with a screw diameter of 13 mm, barrel length of 31 cm and an approximate L/D ratio of 26, coupled to a cylindrical rod dye of approximate 2.85 mm of diameter. A detailed description of the melt extrusion conditions has been previously published [27]. The extruded PP/CNF composites were then pelletized and pressed into compression-molded specimens with the appropriate square-form geometries for AC electrical measurements. At the end, composites with five CNF concentrations in polypropylene matrix from 0.5 to 2.4 vol% were prepared. 2.3. Methods 2.3.1. Morphological characterization Morphological characterization and CNF dispersion of the composites were examined using a JEOL JSM-6400 scanning electron microscope (SEM) at an accelerating voltage of 20 kV. The samples were broken under cryogenic conditions and then sputter-coated with a thin layer of gold before testing. An analytical TEM (JEOL JEM 1010) was used to observe the morphology of CNF. Fiber samples was dispersed in isopropanol and a drop was placed in a grid for direct observation. 2.3.2. Structural characterization Infrared measurements (FTIR) were performed at room temperature with IRAffinity-1S (Shimadzu) in ATR mode from 4000 to 380 cm−1. FTIR spectra were collected with 40 scans and a resolution of 4 cm−1, at room temperature. The crystalline structure of the composites was evaluated from XRD patterns recorded at room temperature using a Rigaku smartlab diffractometer with a copper (Kα1;2 radiation λ=1.540593 and 1.544414 Å ) anode x-ray tube operated at 9 kW (40 kV e 200 mA). Samples were scanned using a θ/2θ mode in a range from 2° to 10° (corresponding to a lattice spacing range between 44.14 and 8.84 Å) with a 0.04 deg step size. The degree of crystallinity of the polypropylene matrix was estimated using the following equation: CI (%)=AC/AT where the AC is the sum of the all areas of deconvoluted crystalline peaks, and AT represents the total area of the XRD spectra. Deconvolution into subpeaks was performed by least-squares peak analysis software, XPSPEAK version 4.1, using the Gaussian/Lorenzian sum function and Shirley-type background subtraction. The components of the various spectra were mainly modeled as symmetrical Gaussian peaks for the best fit. 2.3.3. AC Electrical characterization Composites with CNF concentrations from 0.5 to 2.4 vol% and PP neat samples were compression molded into square films of dimensions 0.5×10×10 mm3. Au electrodes were deposited in both sides by thermal evaporation method. The capacity (C) and dissipation factor (tan δ) were measured at room temperature, in the 200 Hz to 20 MHz frequency range, with an AC applied signal of amplitude 0.5 V, using an automatic Quadtech 1929 Precision LCR meter. The real (ε´) and imaginary (ε´´) parts of the complex permittivity (ε*=ε´−iε´´) were then

2. Materials and methods 2.1. Materials A polypropylene (PP) powder, Borealis EE002AE, was used as 42

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calculated from the measurements, taking into account the geometrical factors, by means of the following equations:

d εoA

ε´´ = ε´ tan δ

1.9 vol %

(1) (2)

Transmittance / a.u

ε´ = C

where d is the thickness (0.5 mm) and A the surface area (10×10 mm2) of the samples. 3. Results and discussion 3.1. Morphological analysis

1.4 vol %

0.9 vol %

PP

Transmission Electron Microscopy is a suitable technique for characterizing carbon nanofibers, as it provides information on the homogeneity, morphology, and microstructure (orientation of the walls and graphitic character) of the nanofibers [28]. Representative TEM image of two individual fibers is shown in Fig. 1(a). Overall, it can be seen a tubular core surrounded by two different structural layers. The main diameter is about 120 nm, whereas its outer two layers shows a total diameter of ~30 nm. The Scanning Electron Microscopy observations of 0.9 vol% CNF filled composites shown in Fig. 1(b) demonstrate that CNF exhibit some tendency to agglomerate within the PP matrix. Compared to other grades of Pyrograf III, the PR 25 PS XT grade has lower aspect ratio than other grades such as PR 24 LHT XT and PR 19 LHT XT

500

1000

1500

2000

2500

3000

3500

4000

-1

Wavenumber / cm

Fig. 2. Infrared spectra of PP and PP/PR 25 PS XT composites.

which would explain their worse dispersion when compared with them [27]. For this reason, the PR 25 PS XT grade was specifically selected for the current study, with the aim of allowing that larger amounts of CNF below percolation threshold can be incorporated in the PP and enhanced dielectric properties before conducting percolating behaviors can be obtained consequently.

3.2. Structural analysis Infrared spectroscopy is a widely used characterization technique to elucidate the structure and interactions in different materials, including polymer composites. Fig. 2 presents the spectra of PP in comparison with the samples filled with 0.9, 1.4 and 1.9 vol% of CNF. Neat PP spectrum shows the characteristic bands assigned to asymmetric and symmetric stretching vibrations of methyl and methylene groups in the 3000–2750 cm−1 region and to the CH3 asymmetric and symmetric bending between 1455 and 1375 cm−1 [30]. Other noticeable bands are located at 1166 cm−1 and 1044 cm−1 assigned to CH2 twisting and CH wagging vibration and to C-C chain stretching vibration, respectively. The bands at 998 cm−1 and 973 cm−1 are assigned to CH bending and wagging vibration and CH3 rocking vibration and to CH3 rocking, CH2 wagging and CH bending vibrations, respectively. Finally, the band at 898 cm−1 is assigned to C-C chain symmetric stretching vibration, the band at 840 cm−1 to CH2 rocking and C-CH3 stretching vibrations and the band at 809 cm−1 to C-C chain symmetric stretching vibration and CH2 rocking vibration [31]. After the addition of the CNF to the system several new peaks appeared between 1500 cm−1 and 2000 cm−1 attributed to the carbon skeleton of CNFs [32]. Moreover, a general decrease in the intensity of the IR bands can be noticed as a consequence of the interaction between carbon nanofibers and PP matrix. This behavior can be explained with the presence of a high number of hydrogen bonds arise from hydroxyl groups present at CNF surface. The presence of high amount of hydroxyl and oxygenated groups at the CNF surface produced by heat treatment it was previously reported [33]. The new peaks at 1400 cm−1 and 1420 cm−1 attributed to O-H bending deformation of carboxyl [34], the O-H out-of-plane bending at 670 cm−1 [35] and the peaks at 2350 cm−1 and 2380 cm−1 that can be attributed both to the presence of chemo-adsorbed CO2 [36] and to the O-H stretching within strongly hydrogen bonded -COOH groups confirm the surface oxidation of the CNF surface [37]. The deconvoluted XRD patterns of neat extruded PP samples and composites at 0.9, 1.4 and 1.9 vol% CNF loadings are shown in Fig. 3. In the 2θ range of 10°−30°, the X-ray diffraction peaks shows the

Fig. 1. TEM micrographs of PR 25 PS XT fibers (a) SEM micrographs of 0.9 vol% PP/PR 25 PS XT composites (b).

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10 a)

0 vol % 0.5 vol % 0.9 vol % 1.4 vol % 1.9 vol % 2.4 vol %

8

ε´

6

4

2 2

10

3

10

4

10

5

10

6

10

Freq. (Hz) 10

b)

0 vol % 0.5 vol % 0.9 vol % 1.4 vol % 1.9 vol % 2.4 vol %

8

Fig. 3. XRD patterns of PP and PP/PR 25 PS XT composites.

6

ε´´

characteristic crystalline bands of the PP (Table 1). The strong intensity peaks at 14.2°, 17.0°, 18.6°, 21.3°, and 22.0° 2θ correspond to (110), (040), (130), (111), and (041) planes of the α-phase PP crystallites, respectively [38]. The other two low intensity bands at 25.6° and 28.9° 2θ are assigned to the (060) and (220) crystallographic planes, respectively [30]. No significant difference in 2θ reflection positions was observed in the PP/CNF composites compared to the pure PP. However, as it was observed in our previous study, an increase of the crystallinity degree of the PP/CNF composites was observed compared to the pure PP [27]. The inclusion of CNF in the PP matrix display an increase in CI proportional to the added amount of CNF (Table 1). This effect could be related to the more heterogeneous crystallization promoted by the introduction of CNF forming new crystalline zones in the amorphous regions of PP [39,40].

2 0 2

10

1.4 vol%

1.9 vol%

110 040 030 111 041 060 220 CI (%)

14.2 17.0 18.6 21.3 22.0 25.6 28.8 40.3

14.3 17.1 18.7 21.4 22.1 25.6 28.9 45.8

14.2 17.0 18.7 21.3 22.0 25.6 28.8 45.3

14.3 17.1 18.7 21.4 22.1 25.6 28.9 48.0

5

10

6

10

function of the CNF concentrations; for instance at 200 Hz (Fig. 4a), the composites with the highest CNF concentrations 1.9 and 2.4 vol% show the largest values of ε´´, with values of 1.7 and 8.6 respectively, compared with the values of 0.014 and 0.22 found for the neat PP and composites with 1.4 vol% of CNF, respectively. The increased dielectric loss for all composites is due to the effect of the electrically conductive nature of CNF, in particular dielectric losses increase significantly from 1.9 vol% due to the conduction losses associated with the percolative character of 1.9 and 2.4 vol% composites [26]. However, for frequencies above 3 kHz, ε´´ shows the maximum value for intermediate CNF concentrations; for instance, at 100 kHz, the maximum value of ε´´ (2.61) is reached in the sample with 1.9 vol% of CNF, while for 1 MHz, ε´´ is maximum for the 1.4 vol% CNF´ samples (1.05). Furthermore, a ω−1 dependence of ε´´ at low frequencies is shown in composites with 1.9 and 2.4 vol% of CNF, which is typically observed in conductive composites [43]. Fig. 5a shows the real (ε´) and imaginary (ε´´) parts of the complex electric permittivity at 200 Hz for all contents of CNF measured at room temperature. Overall, as the CNF loading increases up to 1.9%, the ε´ gradually increases, reaching the value 9.7, and then, on further increase of CNF loading, ε´ remains almost constant. These results show that ε´ can be described in the framework of the percolation theory according to that ε´ would obey the power law relationship ε´α(ϕc −ϕ)−t , for ϕ<ϕc where t is a critical exponent, which is between 0.7 and 1.0 for a 3D system, ϕc is the critical volume fraction, and ϕ is the filler volume fraction [44]. For these particular composites, for a critical volume fraction of ϕ=1.9 , a value of t = 0.98 ± 0.28 was c obtained (Fig. 5b), which is in agreement with the percolation theory

Table 1 Crystallographic planes positions and crystalline degree of PP and PP/CNF composites. 0.9 vol%

4

10

Feq. (Hz)

Fig. 4 shows the frequency dependence of ε´ and ε´´ for all composites at room temperature. The ε´ of the neat PP and composites with 0.5 vol% of CNF exhibits a frequency independent behavior with similar values of ε´, whereas for higher CNF concentrations, ε´ becomes frequency dependent and dispersion is observed. The improvement of ε´ in dielectric polymer composites is usually considered to be a result of the interfacial polarization, also known as Maxwell-Wagner-Sillars effect [41,42], which appears in heterogeneous materials due to the charge accumulation at the interface of the different constituents, though contact regions between Au deposited electrodes and bulk samples are expected to have lower conductivity and higher capacitance (space charge polarization) and its effect in increasing ε´ cannot be neglected. On the other hand, the frequency behavior of ε´´ is rather complex. In fact, for frequencies below 3 kHz, ε´´ is an increasing

PP

3

10

Fig. 4. (a) Real (ε´) and (b) imaginary parts of the complex permittivity (ε´´) measured at room conditions, in the frequency range from 20 Hz to 20 MHz, for all loadings in PP/ PR 25 PS XT composites.

3.3. Dielectric properties

2θ

4

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ε´ ε´´

10

8

8

6

6

4

6

ε´

8

ε´

10

a)

ε´´

10

2

4

4

0

2

2 0,0

0,5

1,0

1,5

2,0

2,5

2

10

3

10

vol %

5

10

6

10

Freq. (Hz)

0,2

Fig. 6. Cole-Cole plots ε´ and ε´´ (inset) for 0.9, 1.4 and 1.9 vol% loadings in PP/PR 25 PS XT composites. The solid lines where determined by the best fit of Eq. (3) to the ε´ and ε´´.

b)

0,1

Linear Fit

0,0 Log(ε´)

4

10

Table 2 Parameters result of the fitting with Cole-Cole Eq. (3).

-0,1 -0,2 -0,3 -0,3

-0,2

-0,1

0,0

0,1

Parameters

0.9 vol%

1.4 vol%

1.9 vol%

εs ε∞ τo (μs) α εs−ε∞

4.71 ± 0.01 3.45 ± 0.04 0.84 ± 0.06 0.09 ± 0.04 1.26 ± 0.05

6.38 ± 0.08 2.55 ± 0.22 1.40 ± 0.26 0.37 ± 0.05 3.83 ± 0.30

9.26 ± 0.99 1.28 ± 0.33 13.22 ± 2.24 0.49 ± 0.05 7.98 ± 0.05

0,2

Log (φc-φ )

can be observed that the experimental curves in Fig. 6 are well described by the Cole-Cole model with exception of ε´´ for composites with 1.9 vol% (Fig. 6 inset), where the ω−1 dependence of ε´´ discussed above at low frequencies prevents a reliable fitting. From the fitting procedure, the values of εs, ε∞, the dielectric strength (εs−ε∞), the mean relaxation time τ0, and the parameter describing the symmetric broadening of the relaxation time distribution α, were calculated and shown in Table 1. From this table, it is possible to observe that the local electrostatic interactions represented by the dielectric strength are increasing significantly as the CNF concentration increases. In particular, the sample with 1.9 vol% of CNF concentration exhibits the largest dielectric strength with a value of ~8 (compared with 1.26 for composites with 0.9 vol% of CNF) and a mean relaxation frequency of 75.5 kHz. In addition, the values of α and the mean relaxation time τo , closely related with the polydispersive character of the dielectric relaxation, become broader with increasing the CNF content. This increase of α and τo is associated with the growing local disorder present that relax according to the random distribution of higher amounts of CNF within the composites [46]. This leads, at the end, to a large multiplicity of local interactions which, by its turn influence the relaxation mechanisms, namely the width of the distribution of relaxation times. The effect of such interactions, which is generally modeled by a drag-like force in the phenomenological models for dielectric relaxation [47], slows the relaxation process and, as consequence, increases the mean relaxation time as function of CNF contents from 0.84 μs (0.9 vol%) to 13.22 μs (1.9 vol%), as it is observed in Table 2. In summary, the origin of the relaxation mechanisms in these nearpercolated carbon based polymer composites can be discussed by using the Cole-Cole model from which an overall increase of the distribution of relaxation time, α, dielectric strength εs − ε∞, and mean relaxation time τo is observed with the increase of the amount of CNF in the composites.

Fig. 5. (a) Real (ε´) and imaginary (ε´´) parts of the complex electric permittivity, measured at 200 Hz at room temperature for all loadings in PP/PR 25 PS XT composites and (b) fitting of experimental data with percolation theory for ε´.

for 3D systems. On the other hand, Fig. 5a shows that the lowest values of ε´´ are for composites with CNF loadings between 0 vol% (0.014) and 0.9 vol% (0.053). 3.4. Dielectric relaxation Dielectric relaxation behavior is generally described by the monodispersive Debye theory of relaxation [45]. However, polymers and their composites generally do not follow this theory and significantly broader dispersion processes without one single relaxation time are observed. In particular, the experimental data of the complex electric permittivity concerning these intermediary concentrations has been analyzed in the framework of the Cole-Cole model [24]:

ε*(ω) = ε´(ω) − iε´´(ω) = ε∞ +

(εs − ε∞) 1 + (iωτ0 )1− α

(3)

where α is associated with the distribution of relaxation time (α=0 corresponds to a monodispersive mechanism with a single relaxation time and 0 < α < 1 is due to the polydispersive nature of the bulk samples), εs − ε∞ is the dielectric strength, εs and ε∞ are the static and high frequency dielectric constant, respectively with εs = limωτ≪1ε′(ω) and ε∞ = limω ≫1ε′(ω), ω is the angular frequency, and τo is the mean relaxation time. The frequency dependence of ε´ and ε´´ of composites with 0.9, 1.4 and 1.9 vol% CNF concentrations in the 200 Hz-1 MHz frequency range, is shown in Fig. 6. The solid lines were determined by the simultaneous fit of Eq. (3) to the experimental ε´ and ε´´ values. It

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4. Conclusions [12]

Carbon nanofibers with low aspect ratio were incorporated in polypropylene matrix by twin-screw extrusion and their morphologic, structural and dielectric properties analyzed. The morphological analysis showed that CNF exhibit some tendency to agglomerate within the polypropylene, on the other hand, the structural analysis showed first a general decrease in the intensity of the IR bands as a consequence of the interaction between CNF and PP matrix and second an increase of the crystallinity degree of the PP/CNF composites when compared to the pure PP. The dielectric analysis in the vicinity of the percolation threshold showed improved dielectric constants without the high dielectric losses typically observed in electrically conducting composites. In particular, composites with loadings of 0.9, 1.4 and 1.9 vol% showed a gradual enhancement of ε´ at 200 Hz from 2.47 (neat PP) to 4.75 (0.9 vol%), 6.45 (1.4 vol%) and 9.7 (1.9 vol%), respectively, whilst their ε´´ at 200 Hz increased from 0.014 (neat PP) to 0.053 (0.9 vol%), 0.22 (1.4 vol%) and 1.71 (1.9 vol%), accordingly. Additionally, ε´ and ε´´ values experimentally obtained for the same concentrations of 0.9, 1.4 and 1.9 vol% as function of frequency have been analyzed by means of the generalized polydispersive Cole-Cole model in order to understand the mechanisms of their relaxation processes. It has been found that this model is capable of describing the experimental data from which an increase of values of dielectric strength εs−ε∞, relaxation time τo , and distribution of relaxation time α, as function of CNF´ contents in the polypropylene, were determined. In conclusion, this particular type of carbon nanofiber in combination with melt-mixing processing demonstrated to be a very effective route to produce potential polymer composites with enhanced dielectric permittivity and unwanted high dielectric losses useful in electronic applications such as energy storage, energy harvesting, sensors and actuators.

[13] [14]

[15]

[16]

[17]

[18] [19]

[20] [21]

[22]

[23]

[24] [25]

[26]

Acknowledgments

[27]

This work was partly financed by FEDER funds through the Competitivity Factors Operational Programme - COMPETE and by national funds through FCT – Foundation for Science and Technology within the scope of the project POCI-01–0145-FEDER-007136. A. Ares-Pernas acknowledge the financial support to Xunta de GaliciaFEDER (Program of Consolidation and structuring competitive research units (GRC2014/036).

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