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Composites based on HDPE filled with BaTiO3 submicrometric particles. Morphology, structure and dielectric properties
Accepted Manuscript Composites based on HDPE filled with BaTiO3 Submicrometric Particles. Morphology, Structure and Dielectric Properties J. Gonzalez-Benito, J. Martinez-Tarifa, M.E. Sepúlveda-García, R.A. Portillo, G. Gonzalez-Gaitano PII:
S0142-9418(13)00170-0
DOI:
10.1016/j.polymertesting.2013.08.012
Reference:
POTE 4108
To appear in:
Polymer Testing
Received Date: 1 July 2013 Accepted Date: 16 August 2013
Please cite this article as: J. Gonzalez-Benito, J. Martinez-Tarifa, M.E. Sepúlveda-García, R.A. Portillo, G. Gonzalez-Gaitano, Composites based on HDPE filled with BaTiO3 Submicrometric Particles. Morphology, Structure and Dielectric Properties, Polymer Testing (2013), doi: 10.1016/ j.polymertesting.2013.08.012. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Material Properties Composites based on HDPE filled with BaTiO3 Submicrometric Particles. Morphology, Structure and Dielectric Properties J. Gonzalez-Benito1*, J. Martinez-Tarifa2, M.E. Sepúlveda-García2, R.A. Portillo1, G. Gonzalez-Gaitano3 1
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Dpt. Materials Science and Engineering and chemical engineering and IQMAAB, Universidad Carlos III de Madrid. Av. Universidad 30, 28911 Leganés (Spain). [email protected] 2 Departamento de Ingeniería Eléctrica. Universidad Carlos III de Madrid. Av. Universidad 30, 28911 Leganés (Spain). [email protected] 3 Departamento de Química y Edafología. Universidad de Navarra. [email protected]
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*Corresponding author Address: Av. Universidad 30, 28911 Leganés (Madrid – Spain) Phone: +34 916248870 Fax: +34 916249430 e-mail: [email protected]
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Abstract
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Composites of high density polyethylene, HDPE, filled with submicrometric particles of BaTiO3, BT, have been prepared. Uniform dispersion of the particles was achieved by high energy ball milling and subsequent hot pressing. Using SEM, FTIR, TGA-DTA and stress-strain tests, studies of the structural, morphological and mechanical features of the composites have been carried out. Frequency response analysis, dielectric strength and resistivity measurements were also performed to evaluate the final electrical properties as a function of the processing and the amount of BaTiO3 particles. From the analysis of the microscopic structure, it can be deduced that any change in the properties of the materials must be solely ascribed to the presence of the BT particles. A balance between an enhancement of space charge polarization with the presence of BT and the existence of permanent dipoles associated to them might explain an initial increase in the dielectric losses with the BT content, and its later decrease at higher BT content. The observed decrease in resistivity and breakdown voltage when increasing the amount of BaTiO3 can be explained by the lower resistivity of BT particles at room temperature and the growing accumulation of space charge.
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Keywords: High density polyethylene (HDPE), barium titanate nanocomposites, high energy ball milling (HEBM), dielectric strength.
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1.
Introduction
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Polymer matrix composites are usually prepared looking for synergy between the advantages of the polymers and the special characteristics of the fillers, leading to unique properties. It is the case of high density polyethylene (HDPE), a thermoplastic polymer, its features such as regular structure of macromolecular chains, low cost and energy requirements for its processing, excellent biocompatibility and good mechanical properties result in continuous expansion of its applications. Also, thermoplastic polymers as HDPE are considered electrical insulating materials with good processability and easily controlled electric properties [1]. However, their low dielectric constant (usually below 5) sometimes makes it necessary to add other materials with high permitivity in order to reach higher density of energy storage [2]. Sometimes, certain kinds of filler are added in order to modify other properties, such as mechanical and optical, but this can change the main properties required for a specific application (i.e. resistivity, dielectric strength, etc.). Thus, in order to understand the influence of those additives, it seems essential to firstly study those properties and correlate them with possible structural and morphological changes in the polymer. Barium titanate (BaTiO3, BT) is a ceramic material with high permittivity and ferroelectric properties in its tetragonal structure, but difficult to process. This makes composite materials based on HDPE filled with BaTiO3 particles very appealing in the manufacture of electric and electronic systems such as integrated circuits, insulators for cables, electrical switches and high voltage capacitors [2,3].
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To date, it has been shown that nanocomposites based on polymethylmetacrylate and polystyrene filled with BT particles produce significant improvements on the electrical properties only when the amount of filler is very high [4,5]. Also, some authors claim that the incorporation of certain inorganic particles can suppress the formation of space charge [6]. For example M. Salah Khalil [6] stated that the incorporation of BaTiO3 seems to be beneficial from the point of view of space charge formation. However, more detailed information about the possible structural and morphological changes induced by the presence of filler particles is required in order to properly assign the real origin of the final properties of the composites.
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Furthermore, it is necessary to take into account that one of the main prerequisites to achieve the best performance of these composites is to ensure uniform dispersion of the particles within the polymer matrix, since the formation of aggregates or even agglomerates of particles may lead to non-desired properties. For instance, microscopic variations of permittivity may lead to local increase of electrical field in small volumes that might create partial discharges [7]. The challenge of obtaining uniform dispersion in nanocomposites has been an object of many researches, and different methods of processing have been evaluated [8]. However, these are usually based on material processing in solution or molten state and, when the particle diameter is smaller than 500 nm, a uniform blend is difficult to obtain if the amount of filler is higher than 5% by weight or if the polymer presents high viscosity. Recently, by using high energy ball milling, HEBM, Gonzalez-Benito et al. have prepared nanocomposites based on thermoplastic polymers filled with inorganic nanoparticles [8-10] and demonstrated that it is possible to achieve a real dispersion of 3
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nanoparticles within the polymer [8-10]. HEBM can also be applied under cryogenic conditions, which reduces potential polymer degradation and cross-contamination coming from the milling tools [11, 12].
Materials and methods
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The aim of this work has been to prepare new composites based on the mixture of HDPE with submicrometric particles of BaTiO3. HEBM has been used to uniformly disperse the particles within the polymer matrix to subsequently obtain composites in the form of films by hot pressing. Structural, morphological and mechanical characterization of the films prepared has been done. Frequency response analysis (FRA), dielectric strength and resistivity measurements have been carried out to evaluate the final electrical properties as a function of the amount of BaTiO3 particles. A discussion relating structure, morphology or the sole presence of BaTiO3 particles with different properties (structural, mechanical and electrical) is presented to understand the possible mechanisms which may permit improving the electrical performance of the materials under consideration.
2.1. Materials
2.2. Sample preparation
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Pellets of high density polyethylene (HDPE) supplied by Sigma-Aldrich were used as the polymer matrix of the composites (density = 0.96 g/cm3, melt index = 2.2 g/10 min at 190ºC and Vicat transition temperature 123ºC). Barium titanate, (BaTiO3) submicrometric particles supplied by Nanostructured and Amorphous Materials Inc. were used as the filler in the composites (mean diameter 200 nm, 99.9 % by weight of purity and density 6.02 g/cm3).
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In order to facilitate the blending process with the barium titanate particles, HDPE pellets are firstly ground in a 1 kW Moulinex grinder (grinding time was from 5 to 10 min to avoid polymer melting due to the increase of temperature associated with the process). Powder mixtures of HDPE with different weight percentages (0%, 1%, 5%, 10% and 20%) of BaTiO3 were prepared using high energy ball milling at room temperature. A mixture of a particular weight percent of BaTiO3 in HDPE was subjected to HEBM in a planetary miller Fritsch Planetary Mono Mill (Pulverisette 6). A vessel of 250 mL of capacity and 6 balls of 20 mm of diameter made of stainless steel were used. The process was carried out according to the following protocol: 2 hours of active milling divided into cycles of 5 minutes of milling at 400 rpm and 15 min of resting at room temperature. Films of composite materials were prepared using a universal testing machine pEM1/FR Microtest with temperature controlled steel plates to exert pressure over the milled powder. An aluminium frame was used to finally obtain films of 10×10 cm. Films of Kapton were used between the steel plates and the powders to avoid their adhesion and help the film extraction. A pressure of 10 kN was exerted for 10 min at a temperature of 150ºC. The samples were then left under pressure until room temperature was reached to finally extract films with thicknesses of about 200-250 µm. 2.3. Techniques 4
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A Philips XL30 scanning electron microscope, SEM, with the signal coming from secondary electrons, SE, was used to inspect the topography of the samples; while, the morphology associated to the distribution of domains with different elemental composition was imaged using backscattered electrons, BSE. Also, microanalysis at specific sites of the surfaces was performed with a DX4i coupled energy-dispersive Xray spectroscopy, EDAX, detector. Samples were gold coated by sputtering to avoid charge accumulation on the sample surfaces. The samples in the form of films were studied by attenuated total reflectance, FTIRATR using an FTIR-ATR Nicolette Avatar 360 spectrometer, with a resolution of 4 cm1 and collecting 32 scans per spectrum.
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Thermogravimetric analysis was carried out in a Mettler TGA/SDTA851e. The samples were heated from 25ºC to 800ºC at 10ºC/min under a N2 atmosphere.
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Mechanical tensile tests were performed on specimens cut from the films. Dimensions of the specimens were chosen according to the requirements given in ISO 3167:2002. The long axis of the specimens were taken from two perpendicular directions in the films in order to study whether there is a preferential flow direction of particles during the hot pressing process, and if that is reflected in the mechanical properties. A Shimadzu universal testing machine Autograph series was used to carry out the stressstrain tests.
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Frequency response analyses, FRA, were performed with an impedance analyzer Solatron Mobrey SI 1260. A sinusoidal voltage of 3 V was applied to the films in between circular electrodes. A frequency scan from 0.5 Hz to 15 kHz was carried out in every case. Making use of the MultiStat Software (Zview 2), the data necessary to build the Bode diagram were obtained. The impedance data were fitted using an equivalent RC circuit to obtain the capacitance and losses associated with the specimen under test. The permittivity was estimated using the following equation:
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(1)
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where εr is the relative permittivity, Cp the measured capacitance, d the thickness of the film, A the surface of the circular electrodes and εo the permittivity of the vacuum. The volumetric resistivity tests were carried out in a Keithley 6517A electrometer after applying a DC voltage of 1000V to the sample for 10 minutes. These measurements required samples with a thickness less than 100 µm in order to avoid high resistance values out of range for this equipment (0.125% rgd of electrometer accuracy). A high voltage transformer was used for the voltage breakdown tests. A voltage ramp below 1kVrms/s was applied to the specimens until breakdown was detected. The specimens in the form of films were located between two electrodes and immersed in mineral oil to avoid electrical arcing through the air. In order to characterize the dielectric strength, sample thickness was measured three times near the failure point, and the average was considered for calculation. The dispersion of the data in such tests is usually very wide, since dielectric breakdown is a probabilistic phenomenon that 5
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depends on environmental conditions and the molecular structure of the weakest point. Therefore, several specimens were tested for all samples, and the data were statistically treated using a Weibull accumulated distribution function (Equation 2):
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where Pf is the failure accumulated probability, Eb the dielectric strength (MV/cm), Eγ the characteristic dielectric strength (whose accumulated probability is Pf = 63.2%), the scale parameter, and β is the shape parameter which determines the measurement variability (the higher this value, the narrower the distribution). Coppard et al. [13] demonstrated that β is related to the distribution of the defects present in the dielectric. Commonly, the parameter Eγ is used to compare differences in dielectric strength determined in the breakdown tests.
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The parameters β and Eγ are calculated from the linear regression of equation (2) when linearized by means of logarithms: (3)
where Pf,i can be expressed as follows:
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in which i is the i-th result when the values of Eb are sorted in ascending order and n is the number of points; for this study, n = 5.
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All the electrical measurements were carried out at 24ºC and 29.5% of relative humidity.
Results and discussion
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The SEM images obtained from the BSE signal are shown in Figure 1 for the composites under study. In every case, a dark matrix with uniformly dispersed small bright domains is observed. The BSE signal provides information about the compositional distribution in the area of observation, showing brighter regions at those locations composed by atoms of higher atomic number elements. Therefore, the dark matrix can be associated with the polymer while the bright spots are the BaTiO3 particles. The microanalysis made by X-ray spectroscopy on the bright domains confirms a high concentration of Ba and Ti. Also, the mean diameter of the bright domains is nearly coincident (250 nm) with the diameter of the BT particles given by the supplier. Figure 1
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The presence of BT particles may affect the degree of crystallinity (a factor that can influence the dielectric strength results). Two infrared bands corresponding to the CH2 bending mode, one at 1474 cm-1 due to the crystalline phase and the other at 1464 cm-1 due to the amorphous phase, are usually used to calculate the crystalline fraction [14] in polyethylene samples. In particular, the empirical formula given below has been used to obtain the amorphous content [15]:
(5)
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where Ic and Ia are the intensities of the bands at 1474 and 1464 cm-1, respectively. The constant 1.233 represents the intensity ratios of these bands in the spectrum of a 100% crystalline polyethylene, and was derived using the factor group splitting applied to a single polyethylene crystal [16] (this phenomenon can be predicted using group theory and is used to calculate crystallinity content in polyethylene because it causes certain fundamental vibrational modes of the chain to split only in the crystals). The FTIR spectra of the neat HDPE and HDPE/BT composites are shown in Figure 2. There are no significant differences except, as expected, those associated with the increase of the absorbance at the short wavenumber limit as the BaTiO3 content increases. Figure 2
Table 1
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The relative values of amorphous content, obtained from the analysis of FTIR-ATR spectra using Eq.5 are shown in Table 1. These results show that the incorporation of BaTiO3 does not modify the HDPE crystallinity. On the other hand, no extra IR bands were found in the composite samples compared to those of the neat HDPE (Figure 2), which indicates the absence of degradation and, hence, chemical changes in the matrix during processing which could influence electrical properties such as the dielectric breakdown strength (e.g., oxidation of the polymer).
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The mechanical properties obtained after analyzing the stress-strain tests results are gathered in Table 2.
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As can be seen, no important differences were obtained for the σ values either as a function of BT content or as a function of the direction of specimen preparation. As expected, only a reduction of ductility is observed (maximum deformation at break, εmax) when the BT content is increased. The presence of hard inclusions within the polymer increases the probability of the occurrence of points of accumulation of stress favoring local failure. In Figure 3, the thermogravimetric curves and their corresponding derivatives are represented for the HDPE neat polymer and HDPE/BT composites. A slight 7
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improvement in the thermostability as the BT content increases is observed since the onset of the thermodegradation process slightly increases. However, the temperature for which the thermo degradation rate is maximum is the same regardless of the BT content. Figure 3
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These results, together with those obtained by FTIR, indicate that the presence of BT particles does not exert any influence on the structure of the HDPE. Also, it seems that BT is not varying the HDPE morphology either, since no changes are perceived in its melting peak (Figure 4). On the other hand, the endothermic region (from 250 to 530 ºC) observed in the DTA curves shows that all samples display the same behavior, indicating again that there is not any particular effect of the BT particles on the thermodegradation of HDPE. All these results confirm that any change in the properties of the composites should be exclusively due to the presence of the BT submicrometric particles.
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Regarding the frequency response of the composites, in Figure 5 the Nyquist (left) and Bode (right) diagrams are represented for all the samples under study. By considering a parallel RC equivalent circuit model, the resistance and the capacitance of the composites can be calculated from these results (Table 1). Figure 5
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It is possible to get the loss factor, tan δ, of the materials at every frequency by introducing the values of Table 1 in Eq. 6 The values of the dissipation factor for each sample at different frequencies are shown in Table 3.
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It can be observed that, regardless of the composition, the loss factor (Table 3) lay within the typical range of values found in the literature for unprocessed HDPE. Therefore, these materials keep behaving as a dielectric with low losses. It is interesting to highlight that at low concentration of BT particles there is an increase of the loss factor (at least up to 5% by weight of BT); however, for higher contents of BaTiO3 (from 5% to 20%) the loss factor decreases, indicating that the dielectric losses are improved when considerable amounts of BaTiO3 particles (up to 10%) are incorporated in the HDPE. There are other systems for which a continuous increase of loss factor is observed as the filler content increases [17, 18]. It is known that the dielectric loss depends on electronic, ionic, dipole-orientation and space-charge polarizations; among them, this last effect (known as the Maxwell-Wagner effect) arises from heterogeneities in the sample. This involves masses larger than low-molecular-weight dipoles and should exert its influence more considerably at lower frequencies. The present systems are composites formed by the mixture of two dielectrically different materials, where BaTiO3 is ionic, crystalline and ferroelectric while HDPE is partially crystalline but 8
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non-polar. Assuming enhancement of space charge polarization with the presence of BT particles, a continuous increase of dielectric losses would be expected. However, it seems reasonable to think that the permanent dipoles associated with the BT particles may be neutralizing them. Therefore, a balance between these two effects could explain the results obtained (Table 2).
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On the other hand, the dielectric permittivity can be estimated from equation 1 if the surface area of the electrodes, A, and the thickness, d, of the films (Table 1) are known.
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Basically, there are no significant variations in the relative permittivity when the BaTiO3 content varies from 0% to 20% by weight, apart from a slight increase for the composition of 20%. This result is in accordance with most of the experimental and theoretical results obtained for systems formed by a polymer filled with high dielectric permittivity particles [12]. For this kind of system, there is only a clear increase of permittivity from a composition of about 10% by volume or about 40% by weight [19].
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The values of resistivity are gathered in Table 4 for the composites in the form of film (all thicknesses smaller than 100 µm). Table 4
The values are similar to those obtained for HDPE by other authors [19, 20]. In general, it is observed that the resistivity decreases when the amount of BaTiO3 increases, since BT particles have lower resistivity at room temperature (about 108 Ω·cm [21]), allowing composites to be less resistive.
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Finally, the data of the dielectric strength are shown in Table 5. As can be seen, the dielectric strength shows a relatively low dispersion of data represented by values of β higher than 2 and a correlation coefficient, r, close to 1, suggesting that the Eb values are statistically significant and the Weibull distribution fit is reliable. Table 5
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The value obtained for the neat HDPE is coincident with data from the literature: 59.0 kV/mm [22] or 62.3 kV/mm [23]. On the other hand, in general it is observed that the dielectric strength decreases as the amount of BaTiO3 particles increases, regardless of the probability of failure chosen (Figure 6). Figure 6
These results are also in accordance with those of Khalil et al. [6]. For instance, it was shown that the addition of BaTiO3 to low-density polyethylene (LDPE) reduced the short-term DC breakdown strength of the doped material by ∼16% and increased the dispersion of the breakdown data [6]. This decrease of breakdown strength can be due to accumulation of space charge, mainly under DC conditions. With the addition of titanium dioxide particles [24], a similar behavior in the breakdown strength was observed. The step DC breakdown of LDPE with 1% of titanium dioxide showed a loss of 10% in the dielectric strength of doped LDPE (65 kV/mm) compared with pure LDPE (71 kV/mm). This was related to the changes in space charge distribution in the doped LDPE, passing from balanced homocharges in the pure polyethylene (PE) to a 9
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distribution dominated by negative charges in the PE with TiO2. This provides an increase in the electric field in one of the electrodes causing the material to break at lower voltages. However, it is usually accepted that the filler particles decrease the breakdown strength because they create electrical defect centers that distort and locally enhance the electrical field. The field distortion is due to the difference in permittivity between the filler particles and the polymer matrix under alternating current (AC) conditions, and the difference in conductivity under direct current (DCDC) conditions [6, 25, 26].
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In order to study how the breakdown mechanism in HDPE is affected by the BaTiO3 content, SEM images were taken of the broken samples precisely in the perforated region. As can be seen in Figures.7a and 7b, when BaTiO3 content is 1% or lower, a channel through the HDPE surface towards the failure point is formed in a well defined cylindrical shape. However, as the BaTiO3 content increases, the previous “conducting channel” disappears. Likewise, the insulation failure point loses its geometrical uniformity it had in the low BaTiO3 content samples, which could be explained by the higher interaction between filler particles; this leads to higher dipole moment in specific areas of the dielectric, where the electrical field is amplified. This phenomenon would be less probable for HDPE samples in which the distances between filler particles are higher, that is to say, with lower BT content . Figure 7 4.
Conclusions
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Good uniform dispersion of submicrometric BaTiO3 particles within HDPE is achieved from mixing by high energy ball milling and subsequent hot pressing. The processing and incorporation of BaTiO3 does not modify the crystallinity and morphology of the HDPE, nor induce chemical alterations in the polymer, thus changes in the properties of the composites can be solely ascribed to the presence of the BT submicrometric particles. A balance between enhancement of space charge polarization with the presence of BT particles and the existence of permanent dipoles associated with them might explain an initial increase in the dielectric losses with the BT content and a final decrease from high enough amount of BT particles. A decrease in resistivity is observed when the amount of BaTiO3 increases simply because BT particles have lower resistivity at room temperature than neat HDPE. Finally, a decrease of dielectric strength is observed at higher amounts of BT, probably due to accumulation of space charge within the polyethylene. Deep observations of the failure area confirm the existence of different breakdown mechanisms when a high concentration of BT particles is present. Acknowledgement
This research has been carried with the funding from the Ministerio de Ciencia e Innovación projects: MAT2010-16815 and AIB2010PT-00267. Electrical properties have been measured in the High Voltage Research and Tests Laboratory of Universidad Carlos III de Madrid (LINEALT).
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Figure captions Figure 1.- SEM images obtained from the BSE signal for the composites under study: a) HDPE-BT1%; b) HDPE-BT5%; c) HDPE-BT10% and d) HDPE-BT20%.
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Figure 2.- FTIR spectra of the HDPE neat polymer and HDPE/BT composites. The inset shows the region in which the bands used to estimate the crystalline fraction appear. Figure 3.- Thermogravimetric curves (top) and their corresponding derivatives (bottom) for neat HDPE and HDPE/BT composites.
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Figure 4.- DTA thermograms for the neat HDPE and HDPE/BT composites. Figure 5.- Nyquist and Bode diagrams for the composites at different amounts of BT. Figure 6.- Probability of failure as a function of the applied voltage.
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Figure 7.- SEM images of the perforations generated after the breakdown tests for all the samples under study: a) HDPE-0% BT; b) HDPE-1% BT; c) HDPE-5% BT; d) HDPE-10% BT and e) HDPE-20% BT.
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Tables Table 1.- Estimated values of the relative amorphous content, resistance, capacitance and permittivity of the composites under study. X Rp (MΩ Ω) Cp ×10-10 (F) 0.51 8,80 6.10 0.53 8,89 4.50 0.52 8,90 4.00 0.50 8,88 6.50 9,00 7.00
εr 3.06 2.99 1.80 3.15 3.19
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Sample % wt of BaTiO3 HDPE-0% BT 0 HDPE-1% BT 1 HDPE-5% BT 5 HDPE-10% BT 10 HDPE-20% BT 20
HDPE-10% BT
E ⊥ σmax (MPa) (MPa) 476±69 20±1 530±33 17±1 567±30 21±2 550±29 19±1 530±17
σmax ⊥ σyield σyield ⊥ (MPa) (MPa) (MPa) 19±3 19±1 17±1 19±1 17±1 19±1 19±1 20±1 19±1 19±1 19±1 19±1 18±2 18±2
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E (MPa) As received HDPE 503±63 HDPE-0% BT 449±51 HDPE-1% BT 582±23 HDPE-5% BT 558±27 Sample
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Table 2.- Mechanical properties obtained from the stress-strain tests. The symbols and ⊥ indicate the parallel and perpendicular directions of the long axis of the specimens respectively. εmax (%) 710±82 430±220 480±260 200±190
εmax ⊥ (%) 670±140 430±220 300±220 300±160 83±30
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HDPE0%BT 372.578 3.72578 1.86289 0.03726 0.01863 0.01242 0.00186 0.00019
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Frequency (Hz) 0.5 50 100 5000 10000 15000 100000 1000000
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Table 3.- Dissipation factor obtained at different frequencies for the composites under study.
HDPE1%BT 499.937 4.99938 2.49969 0.04999 0.02500 0.01666 0.00250 0.00025
Tan δ HDPE5%BT 561.797 5.61798 2.80899 0.05618 0.02809 0.01873 0.00281 0.00028
HDPE10%BT 346.500 3.46500 1.73250 0.03465 0.01733 0.01155 0.00173 0.00017
Table 4.- Resistivity values of the materials under study. Sample d (µ µm) Resistivity (× ×10-13 Ω·cm) HDPE-0% BT 84 1.155 HDPE-1% BT 66 0.937 HDPE-5% BT 65 1.726 HDPE-10% BT 71 0.710 14
HDPE20%BT 317.460 3.17460 1.58730 0.03175 0.01587 0.01058 0.00159 0.00016
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HDPE-20% BT 92 0.647 Table 5.- Parameters obtained after the Weibull fit of the data of the dielectric breakdown tests.
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β Correlation (r) Eγ (kV/mm) 4.0 0.99 61.6 2.2 0.89 68.6 2.7 0.93 60.4 2.0 0.94 57.6 4.3 0.94 51.1
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Sample Eb (kV) HDPE-0BT 14.2 HDPE-1BT 13.4 HDPE-5BT 12.8 HDPE-10BT 11.3 HDPE-20BT 11.5
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S0142-9418(13)00170-0
DOI:
10.1016/j.polymertesting.2013.08.012
Reference:
POTE 4108
To appear in:
Polymer Testing
Received Date: 1 July 2013 Accepted Date: 16 August 2013
Please cite this article as: J. Gonzalez-Benito, J. Martinez-Tarifa, M.E. Sepúlveda-García, R.A. Portillo, G. Gonzalez-Gaitano, Composites based on HDPE filled with BaTiO3 Submicrometric Particles. Morphology, Structure and Dielectric Properties, Polymer Testing (2013), doi: 10.1016/ j.polymertesting.2013.08.012. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Material Properties Composites based on HDPE filled with BaTiO3 Submicrometric Particles. Morphology, Structure and Dielectric Properties J. Gonzalez-Benito1*, J. Martinez-Tarifa2, M.E. Sepúlveda-García2, R.A. Portillo1, G. Gonzalez-Gaitano3 1
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Dpt. Materials Science and Engineering and chemical engineering and IQMAAB, Universidad Carlos III de Madrid. Av. Universidad 30, 28911 Leganés (Spain). [email protected] 2 Departamento de Ingeniería Eléctrica. Universidad Carlos III de Madrid. Av. Universidad 30, 28911 Leganés (Spain). [email protected] 3 Departamento de Química y Edafología. Universidad de Navarra. [email protected]
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*Corresponding author Address: Av. Universidad 30, 28911 Leganés (Madrid – Spain) Phone: +34 916248870 Fax: +34 916249430 e-mail: [email protected]
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Abstract
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Composites of high density polyethylene, HDPE, filled with submicrometric particles of BaTiO3, BT, have been prepared. Uniform dispersion of the particles was achieved by high energy ball milling and subsequent hot pressing. Using SEM, FTIR, TGA-DTA and stress-strain tests, studies of the structural, morphological and mechanical features of the composites have been carried out. Frequency response analysis, dielectric strength and resistivity measurements were also performed to evaluate the final electrical properties as a function of the processing and the amount of BaTiO3 particles. From the analysis of the microscopic structure, it can be deduced that any change in the properties of the materials must be solely ascribed to the presence of the BT particles. A balance between an enhancement of space charge polarization with the presence of BT and the existence of permanent dipoles associated to them might explain an initial increase in the dielectric losses with the BT content, and its later decrease at higher BT content. The observed decrease in resistivity and breakdown voltage when increasing the amount of BaTiO3 can be explained by the lower resistivity of BT particles at room temperature and the growing accumulation of space charge.
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Keywords: High density polyethylene (HDPE), barium titanate nanocomposites, high energy ball milling (HEBM), dielectric strength.
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(BaTiO3),
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1.
Introduction
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Polymer matrix composites are usually prepared looking for synergy between the advantages of the polymers and the special characteristics of the fillers, leading to unique properties. It is the case of high density polyethylene (HDPE), a thermoplastic polymer, its features such as regular structure of macromolecular chains, low cost and energy requirements for its processing, excellent biocompatibility and good mechanical properties result in continuous expansion of its applications. Also, thermoplastic polymers as HDPE are considered electrical insulating materials with good processability and easily controlled electric properties [1]. However, their low dielectric constant (usually below 5) sometimes makes it necessary to add other materials with high permitivity in order to reach higher density of energy storage [2]. Sometimes, certain kinds of filler are added in order to modify other properties, such as mechanical and optical, but this can change the main properties required for a specific application (i.e. resistivity, dielectric strength, etc.). Thus, in order to understand the influence of those additives, it seems essential to firstly study those properties and correlate them with possible structural and morphological changes in the polymer. Barium titanate (BaTiO3, BT) is a ceramic material with high permittivity and ferroelectric properties in its tetragonal structure, but difficult to process. This makes composite materials based on HDPE filled with BaTiO3 particles very appealing in the manufacture of electric and electronic systems such as integrated circuits, insulators for cables, electrical switches and high voltage capacitors [2,3].
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To date, it has been shown that nanocomposites based on polymethylmetacrylate and polystyrene filled with BT particles produce significant improvements on the electrical properties only when the amount of filler is very high [4,5]. Also, some authors claim that the incorporation of certain inorganic particles can suppress the formation of space charge [6]. For example M. Salah Khalil [6] stated that the incorporation of BaTiO3 seems to be beneficial from the point of view of space charge formation. However, more detailed information about the possible structural and morphological changes induced by the presence of filler particles is required in order to properly assign the real origin of the final properties of the composites.
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Furthermore, it is necessary to take into account that one of the main prerequisites to achieve the best performance of these composites is to ensure uniform dispersion of the particles within the polymer matrix, since the formation of aggregates or even agglomerates of particles may lead to non-desired properties. For instance, microscopic variations of permittivity may lead to local increase of electrical field in small volumes that might create partial discharges [7]. The challenge of obtaining uniform dispersion in nanocomposites has been an object of many researches, and different methods of processing have been evaluated [8]. However, these are usually based on material processing in solution or molten state and, when the particle diameter is smaller than 500 nm, a uniform blend is difficult to obtain if the amount of filler is higher than 5% by weight or if the polymer presents high viscosity. Recently, by using high energy ball milling, HEBM, Gonzalez-Benito et al. have prepared nanocomposites based on thermoplastic polymers filled with inorganic nanoparticles [8-10] and demonstrated that it is possible to achieve a real dispersion of 3
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nanoparticles within the polymer [8-10]. HEBM can also be applied under cryogenic conditions, which reduces potential polymer degradation and cross-contamination coming from the milling tools [11, 12].
Materials and methods
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The aim of this work has been to prepare new composites based on the mixture of HDPE with submicrometric particles of BaTiO3. HEBM has been used to uniformly disperse the particles within the polymer matrix to subsequently obtain composites in the form of films by hot pressing. Structural, morphological and mechanical characterization of the films prepared has been done. Frequency response analysis (FRA), dielectric strength and resistivity measurements have been carried out to evaluate the final electrical properties as a function of the amount of BaTiO3 particles. A discussion relating structure, morphology or the sole presence of BaTiO3 particles with different properties (structural, mechanical and electrical) is presented to understand the possible mechanisms which may permit improving the electrical performance of the materials under consideration.
2.1. Materials
2.2. Sample preparation
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Pellets of high density polyethylene (HDPE) supplied by Sigma-Aldrich were used as the polymer matrix of the composites (density = 0.96 g/cm3, melt index = 2.2 g/10 min at 190ºC and Vicat transition temperature 123ºC). Barium titanate, (BaTiO3) submicrometric particles supplied by Nanostructured and Amorphous Materials Inc. were used as the filler in the composites (mean diameter 200 nm, 99.9 % by weight of purity and density 6.02 g/cm3).
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In order to facilitate the blending process with the barium titanate particles, HDPE pellets are firstly ground in a 1 kW Moulinex grinder (grinding time was from 5 to 10 min to avoid polymer melting due to the increase of temperature associated with the process). Powder mixtures of HDPE with different weight percentages (0%, 1%, 5%, 10% and 20%) of BaTiO3 were prepared using high energy ball milling at room temperature. A mixture of a particular weight percent of BaTiO3 in HDPE was subjected to HEBM in a planetary miller Fritsch Planetary Mono Mill (Pulverisette 6). A vessel of 250 mL of capacity and 6 balls of 20 mm of diameter made of stainless steel were used. The process was carried out according to the following protocol: 2 hours of active milling divided into cycles of 5 minutes of milling at 400 rpm and 15 min of resting at room temperature. Films of composite materials were prepared using a universal testing machine pEM1/FR Microtest with temperature controlled steel plates to exert pressure over the milled powder. An aluminium frame was used to finally obtain films of 10×10 cm. Films of Kapton were used between the steel plates and the powders to avoid their adhesion and help the film extraction. A pressure of 10 kN was exerted for 10 min at a temperature of 150ºC. The samples were then left under pressure until room temperature was reached to finally extract films with thicknesses of about 200-250 µm. 2.3. Techniques 4
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A Philips XL30 scanning electron microscope, SEM, with the signal coming from secondary electrons, SE, was used to inspect the topography of the samples; while, the morphology associated to the distribution of domains with different elemental composition was imaged using backscattered electrons, BSE. Also, microanalysis at specific sites of the surfaces was performed with a DX4i coupled energy-dispersive Xray spectroscopy, EDAX, detector. Samples were gold coated by sputtering to avoid charge accumulation on the sample surfaces. The samples in the form of films were studied by attenuated total reflectance, FTIRATR using an FTIR-ATR Nicolette Avatar 360 spectrometer, with a resolution of 4 cm1 and collecting 32 scans per spectrum.
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Thermogravimetric analysis was carried out in a Mettler TGA/SDTA851e. The samples were heated from 25ºC to 800ºC at 10ºC/min under a N2 atmosphere.
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Mechanical tensile tests were performed on specimens cut from the films. Dimensions of the specimens were chosen according to the requirements given in ISO 3167:2002. The long axis of the specimens were taken from two perpendicular directions in the films in order to study whether there is a preferential flow direction of particles during the hot pressing process, and if that is reflected in the mechanical properties. A Shimadzu universal testing machine Autograph series was used to carry out the stressstrain tests.
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Frequency response analyses, FRA, were performed with an impedance analyzer Solatron Mobrey SI 1260. A sinusoidal voltage of 3 V was applied to the films in between circular electrodes. A frequency scan from 0.5 Hz to 15 kHz was carried out in every case. Making use of the MultiStat Software (Zview 2), the data necessary to build the Bode diagram were obtained. The impedance data were fitted using an equivalent RC circuit to obtain the capacitance and losses associated with the specimen under test. The permittivity was estimated using the following equation:
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where εr is the relative permittivity, Cp the measured capacitance, d the thickness of the film, A the surface of the circular electrodes and εo the permittivity of the vacuum. The volumetric resistivity tests were carried out in a Keithley 6517A electrometer after applying a DC voltage of 1000V to the sample for 10 minutes. These measurements required samples with a thickness less than 100 µm in order to avoid high resistance values out of range for this equipment (0.125% rgd of electrometer accuracy). A high voltage transformer was used for the voltage breakdown tests. A voltage ramp below 1kVrms/s was applied to the specimens until breakdown was detected. The specimens in the form of films were located between two electrodes and immersed in mineral oil to avoid electrical arcing through the air. In order to characterize the dielectric strength, sample thickness was measured three times near the failure point, and the average was considered for calculation. The dispersion of the data in such tests is usually very wide, since dielectric breakdown is a probabilistic phenomenon that 5
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depends on environmental conditions and the molecular structure of the weakest point. Therefore, several specimens were tested for all samples, and the data were statistically treated using a Weibull accumulated distribution function (Equation 2):
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where Pf is the failure accumulated probability, Eb the dielectric strength (MV/cm), Eγ the characteristic dielectric strength (whose accumulated probability is Pf = 63.2%), the scale parameter, and β is the shape parameter which determines the measurement variability (the higher this value, the narrower the distribution). Coppard et al. [13] demonstrated that β is related to the distribution of the defects present in the dielectric. Commonly, the parameter Eγ is used to compare differences in dielectric strength determined in the breakdown tests.
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The parameters β and Eγ are calculated from the linear regression of equation (2) when linearized by means of logarithms: (3)
where Pf,i can be expressed as follows:
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in which i is the i-th result when the values of Eb are sorted in ascending order and n is the number of points; for this study, n = 5.
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All the electrical measurements were carried out at 24ºC and 29.5% of relative humidity.
Results and discussion
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The SEM images obtained from the BSE signal are shown in Figure 1 for the composites under study. In every case, a dark matrix with uniformly dispersed small bright domains is observed. The BSE signal provides information about the compositional distribution in the area of observation, showing brighter regions at those locations composed by atoms of higher atomic number elements. Therefore, the dark matrix can be associated with the polymer while the bright spots are the BaTiO3 particles. The microanalysis made by X-ray spectroscopy on the bright domains confirms a high concentration of Ba and Ti. Also, the mean diameter of the bright domains is nearly coincident (250 nm) with the diameter of the BT particles given by the supplier. Figure 1
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The presence of BT particles may affect the degree of crystallinity (a factor that can influence the dielectric strength results). Two infrared bands corresponding to the CH2 bending mode, one at 1474 cm-1 due to the crystalline phase and the other at 1464 cm-1 due to the amorphous phase, are usually used to calculate the crystalline fraction [14] in polyethylene samples. In particular, the empirical formula given below has been used to obtain the amorphous content [15]:
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where Ic and Ia are the intensities of the bands at 1474 and 1464 cm-1, respectively. The constant 1.233 represents the intensity ratios of these bands in the spectrum of a 100% crystalline polyethylene, and was derived using the factor group splitting applied to a single polyethylene crystal [16] (this phenomenon can be predicted using group theory and is used to calculate crystallinity content in polyethylene because it causes certain fundamental vibrational modes of the chain to split only in the crystals). The FTIR spectra of the neat HDPE and HDPE/BT composites are shown in Figure 2. There are no significant differences except, as expected, those associated with the increase of the absorbance at the short wavenumber limit as the BaTiO3 content increases. Figure 2
Table 1
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The relative values of amorphous content, obtained from the analysis of FTIR-ATR spectra using Eq.5 are shown in Table 1. These results show that the incorporation of BaTiO3 does not modify the HDPE crystallinity. On the other hand, no extra IR bands were found in the composite samples compared to those of the neat HDPE (Figure 2), which indicates the absence of degradation and, hence, chemical changes in the matrix during processing which could influence electrical properties such as the dielectric breakdown strength (e.g., oxidation of the polymer).
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The mechanical properties obtained after analyzing the stress-strain tests results are gathered in Table 2.
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As can be seen, no important differences were obtained for the σ values either as a function of BT content or as a function of the direction of specimen preparation. As expected, only a reduction of ductility is observed (maximum deformation at break, εmax) when the BT content is increased. The presence of hard inclusions within the polymer increases the probability of the occurrence of points of accumulation of stress favoring local failure. In Figure 3, the thermogravimetric curves and their corresponding derivatives are represented for the HDPE neat polymer and HDPE/BT composites. A slight 7
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improvement in the thermostability as the BT content increases is observed since the onset of the thermodegradation process slightly increases. However, the temperature for which the thermo degradation rate is maximum is the same regardless of the BT content. Figure 3
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These results, together with those obtained by FTIR, indicate that the presence of BT particles does not exert any influence on the structure of the HDPE. Also, it seems that BT is not varying the HDPE morphology either, since no changes are perceived in its melting peak (Figure 4). On the other hand, the endothermic region (from 250 to 530 ºC) observed in the DTA curves shows that all samples display the same behavior, indicating again that there is not any particular effect of the BT particles on the thermodegradation of HDPE. All these results confirm that any change in the properties of the composites should be exclusively due to the presence of the BT submicrometric particles.
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Regarding the frequency response of the composites, in Figure 5 the Nyquist (left) and Bode (right) diagrams are represented for all the samples under study. By considering a parallel RC equivalent circuit model, the resistance and the capacitance of the composites can be calculated from these results (Table 1). Figure 5
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It is possible to get the loss factor, tan δ, of the materials at every frequency by introducing the values of Table 1 in Eq. 6 The values of the dissipation factor for each sample at different frequencies are shown in Table 3.
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It can be observed that, regardless of the composition, the loss factor (Table 3) lay within the typical range of values found in the literature for unprocessed HDPE. Therefore, these materials keep behaving as a dielectric with low losses. It is interesting to highlight that at low concentration of BT particles there is an increase of the loss factor (at least up to 5% by weight of BT); however, for higher contents of BaTiO3 (from 5% to 20%) the loss factor decreases, indicating that the dielectric losses are improved when considerable amounts of BaTiO3 particles (up to 10%) are incorporated in the HDPE. There are other systems for which a continuous increase of loss factor is observed as the filler content increases [17, 18]. It is known that the dielectric loss depends on electronic, ionic, dipole-orientation and space-charge polarizations; among them, this last effect (known as the Maxwell-Wagner effect) arises from heterogeneities in the sample. This involves masses larger than low-molecular-weight dipoles and should exert its influence more considerably at lower frequencies. The present systems are composites formed by the mixture of two dielectrically different materials, where BaTiO3 is ionic, crystalline and ferroelectric while HDPE is partially crystalline but 8
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non-polar. Assuming enhancement of space charge polarization with the presence of BT particles, a continuous increase of dielectric losses would be expected. However, it seems reasonable to think that the permanent dipoles associated with the BT particles may be neutralizing them. Therefore, a balance between these two effects could explain the results obtained (Table 2).
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On the other hand, the dielectric permittivity can be estimated from equation 1 if the surface area of the electrodes, A, and the thickness, d, of the films (Table 1) are known.
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Basically, there are no significant variations in the relative permittivity when the BaTiO3 content varies from 0% to 20% by weight, apart from a slight increase for the composition of 20%. This result is in accordance with most of the experimental and theoretical results obtained for systems formed by a polymer filled with high dielectric permittivity particles [12]. For this kind of system, there is only a clear increase of permittivity from a composition of about 10% by volume or about 40% by weight [19].
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The values of resistivity are gathered in Table 4 for the composites in the form of film (all thicknesses smaller than 100 µm). Table 4
The values are similar to those obtained for HDPE by other authors [19, 20]. In general, it is observed that the resistivity decreases when the amount of BaTiO3 increases, since BT particles have lower resistivity at room temperature (about 108 Ω·cm [21]), allowing composites to be less resistive.
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Finally, the data of the dielectric strength are shown in Table 5. As can be seen, the dielectric strength shows a relatively low dispersion of data represented by values of β higher than 2 and a correlation coefficient, r, close to 1, suggesting that the Eb values are statistically significant and the Weibull distribution fit is reliable. Table 5
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The value obtained for the neat HDPE is coincident with data from the literature: 59.0 kV/mm [22] or 62.3 kV/mm [23]. On the other hand, in general it is observed that the dielectric strength decreases as the amount of BaTiO3 particles increases, regardless of the probability of failure chosen (Figure 6). Figure 6
These results are also in accordance with those of Khalil et al. [6]. For instance, it was shown that the addition of BaTiO3 to low-density polyethylene (LDPE) reduced the short-term DC breakdown strength of the doped material by ∼16% and increased the dispersion of the breakdown data [6]. This decrease of breakdown strength can be due to accumulation of space charge, mainly under DC conditions. With the addition of titanium dioxide particles [24], a similar behavior in the breakdown strength was observed. The step DC breakdown of LDPE with 1% of titanium dioxide showed a loss of 10% in the dielectric strength of doped LDPE (65 kV/mm) compared with pure LDPE (71 kV/mm). This was related to the changes in space charge distribution in the doped LDPE, passing from balanced homocharges in the pure polyethylene (PE) to a 9
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distribution dominated by negative charges in the PE with TiO2. This provides an increase in the electric field in one of the electrodes causing the material to break at lower voltages. However, it is usually accepted that the filler particles decrease the breakdown strength because they create electrical defect centers that distort and locally enhance the electrical field. The field distortion is due to the difference in permittivity between the filler particles and the polymer matrix under alternating current (AC) conditions, and the difference in conductivity under direct current (DCDC) conditions [6, 25, 26].
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In order to study how the breakdown mechanism in HDPE is affected by the BaTiO3 content, SEM images were taken of the broken samples precisely in the perforated region. As can be seen in Figures.7a and 7b, when BaTiO3 content is 1% or lower, a channel through the HDPE surface towards the failure point is formed in a well defined cylindrical shape. However, as the BaTiO3 content increases, the previous “conducting channel” disappears. Likewise, the insulation failure point loses its geometrical uniformity it had in the low BaTiO3 content samples, which could be explained by the higher interaction between filler particles; this leads to higher dipole moment in specific areas of the dielectric, where the electrical field is amplified. This phenomenon would be less probable for HDPE samples in which the distances between filler particles are higher, that is to say, with lower BT content . Figure 7 4.
Conclusions
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Good uniform dispersion of submicrometric BaTiO3 particles within HDPE is achieved from mixing by high energy ball milling and subsequent hot pressing. The processing and incorporation of BaTiO3 does not modify the crystallinity and morphology of the HDPE, nor induce chemical alterations in the polymer, thus changes in the properties of the composites can be solely ascribed to the presence of the BT submicrometric particles. A balance between enhancement of space charge polarization with the presence of BT particles and the existence of permanent dipoles associated with them might explain an initial increase in the dielectric losses with the BT content and a final decrease from high enough amount of BT particles. A decrease in resistivity is observed when the amount of BaTiO3 increases simply because BT particles have lower resistivity at room temperature than neat HDPE. Finally, a decrease of dielectric strength is observed at higher amounts of BT, probably due to accumulation of space charge within the polyethylene. Deep observations of the failure area confirm the existence of different breakdown mechanisms when a high concentration of BT particles is present. Acknowledgement
This research has been carried with the funding from the Ministerio de Ciencia e Innovación projects: MAT2010-16815 and AIB2010PT-00267. Electrical properties have been measured in the High Voltage Research and Tests Laboratory of Universidad Carlos III de Madrid (LINEALT).
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19. K.S. Shah, R.C. Jain, V. Shrinet, A.K. Singh. High Density Polyethylene (HDPE) Clay Nanocomposite for Dielectric Applications. IEEE Trans Dielectr Electr Insu 2009;16:853-861. 20. J. Du, L. Zhao, Y. Zeng, L. Zhang, F. Li, P. Liu, C. Liu. Comparison of electrical properties between multi-walled carbon nanotube and graphene nanosheet/high density polyethylene composites with a segregated network structure. Carbon 2011;49:1094-1100. 21. S. Panteny, C.R. Bowen, R. Stevens. Characterisation of barium titanate-silver composites part II: Electrical properties. J Mater Sci 2006;41:3845-3851. 22. M.M. Ueki, M. Zanin. Influence of additives on the dielectric strength of highdensity polyethylene. IEEE Trans Dielectr Electr Insu 1999;6:876-881. 23. S.A. Cruz, M. Zanin. Dielectric Strength of the Blends of Virgin and Recycled HDPE. J App Polym Sci 2004;91:1730-1735. 24. M.S. Khalil, 0. Henk, M. Henriksen. The Influence of Titanium dioxide Additive on the Short-term DC Breakdown Strength of Polyethylene. Conference Record of the 1990 IEEE International Symposium on Electrical Insulation.Canada 1990;268271. 25. G. Chen, A.E. Davies. The influence of defects on the short-term breakdown characteristics and long-term DC performance of LDPE insulation. IEEE Trans Dielectr Electr Insul 2000;7:401-407. 26. S. Fujita, M. Ruike, M. Baba. Annual Report of the Conf. on Electrical Insulation and Dielectric Phenomena. Millbrae 1996;738-741. 27. Von Hippel A.R. et al, “Dielectric Materials and Applications”, Cambridge: Technology Press MIT, 1995.
Figure captions Figure 1.- SEM images obtained from the BSE signal for the composites under study: a) HDPE-BT1%; b) HDPE-BT5%; c) HDPE-BT10% and d) HDPE-BT20%.
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Figure 2.- FTIR spectra of the HDPE neat polymer and HDPE/BT composites. The inset shows the region in which the bands used to estimate the crystalline fraction appear. Figure 3.- Thermogravimetric curves (top) and their corresponding derivatives (bottom) for neat HDPE and HDPE/BT composites.
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Figure 4.- DTA thermograms for the neat HDPE and HDPE/BT composites. Figure 5.- Nyquist and Bode diagrams for the composites at different amounts of BT. Figure 6.- Probability of failure as a function of the applied voltage.
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Figure 7.- SEM images of the perforations generated after the breakdown tests for all the samples under study: a) HDPE-0% BT; b) HDPE-1% BT; c) HDPE-5% BT; d) HDPE-10% BT and e) HDPE-20% BT.
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Tables Table 1.- Estimated values of the relative amorphous content, resistance, capacitance and permittivity of the composites under study. X Rp (MΩ Ω) Cp ×10-10 (F) 0.51 8,80 6.10 0.53 8,89 4.50 0.52 8,90 4.00 0.50 8,88 6.50 9,00 7.00
εr 3.06 2.99 1.80 3.15 3.19
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Sample % wt of BaTiO3 HDPE-0% BT 0 HDPE-1% BT 1 HDPE-5% BT 5 HDPE-10% BT 10 HDPE-20% BT 20
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E ⊥ σmax (MPa) (MPa) 476±69 20±1 530±33 17±1 567±30 21±2 550±29 19±1 530±17
σmax ⊥ σyield σyield ⊥ (MPa) (MPa) (MPa) 19±3 19±1 17±1 19±1 17±1 19±1 19±1 20±1 19±1 19±1 19±1 19±1 18±2 18±2
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E (MPa) As received HDPE 503±63 HDPE-0% BT 449±51 HDPE-1% BT 582±23 HDPE-5% BT 558±27 Sample
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Table 2.- Mechanical properties obtained from the stress-strain tests. The symbols and ⊥ indicate the parallel and perpendicular directions of the long axis of the specimens respectively. εmax (%) 710±82 430±220 480±260 200±190
εmax ⊥ (%) 670±140 430±220 300±220 300±160 83±30
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HDPE0%BT 372.578 3.72578 1.86289 0.03726 0.01863 0.01242 0.00186 0.00019
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Frequency (Hz) 0.5 50 100 5000 10000 15000 100000 1000000
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Table 3.- Dissipation factor obtained at different frequencies for the composites under study.
HDPE1%BT 499.937 4.99938 2.49969 0.04999 0.02500 0.01666 0.00250 0.00025
Tan δ HDPE5%BT 561.797 5.61798 2.80899 0.05618 0.02809 0.01873 0.00281 0.00028
HDPE10%BT 346.500 3.46500 1.73250 0.03465 0.01733 0.01155 0.00173 0.00017
Table 4.- Resistivity values of the materials under study. Sample d (µ µm) Resistivity (× ×10-13 Ω·cm) HDPE-0% BT 84 1.155 HDPE-1% BT 66 0.937 HDPE-5% BT 65 1.726 HDPE-10% BT 71 0.710 14
HDPE20%BT 317.460 3.17460 1.58730 0.03175 0.01587 0.01058 0.00159 0.00016
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HDPE-20% BT 92 0.647 Table 5.- Parameters obtained after the Weibull fit of the data of the dielectric breakdown tests.
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β Correlation (r) Eγ (kV/mm) 4.0 0.99 61.6 2.2 0.89 68.6 2.7 0.93 60.4 2.0 0.94 57.6 4.3 0.94 51.1
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Sample Eb (kV) HDPE-0BT 14.2 HDPE-1BT 13.4 HDPE-5BT 12.8 HDPE-10BT 11.3 HDPE-20BT 11.5
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