Dielectric losses in polyethylene/neodymium composites Cristina STANCU1, Petru V. NOTINGHER1, Denis PANAITESCU2, Virgil MARINESCU3 1University POLITEHNICA of Bucharest, ROMANIA 2ICECHIM, Bucharest, ROMANIA 3INCDIE ICPE CA, Bucharest, ROMANIA Email:
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[email protected] Abstract- Polymer/metal composite materials have good rheological properties due to the polymer matrix and superior electrical or magnetic properties through the conductive or magnetic filler. For this reason, they can be used in a number of industrial applications as electromagnetic shields or permanent magnets. This paper deals with the results of an experimental study regarding the manufacturing and characterization of composite materials containing low density polyethylene (LDPE) as matrix and neodymium (Nd) as filler, obtained by melt processing. The structure of composites, the loss factor measured in harmonic fields at frequencies between 1 mHz and 1 MHz and temperature between 30 and 80 oC and the relative and specific losses are presented and discussed in this paper. Both loss factor and specific losses vary with the frequency of the electric field, temperature and filler content. For certain values of the frequency, the loss factor and relative losses show maximum values which increase of the temperature and filler content. The specific losses decrease with temperature but increase with the filler content and frequency of the electric field. For frequency values close to 1 MHz the specific losses overlap the ones in copper conductors. I. INTRODUCTION Composite polymer materials with conductive or magnetic fillers have electrical, magnetic and thermal properties superior to those of polymers, easy processability and low cost [1]. For their manufacture, polyethylene, polyvinylchloride, polycarbonate, epoxy resin, acrylonitrile- butadiene-styrene, polystyrene, nylon 6,6 etc can be used as matrix and aluminum [2] carbon and graphite [3,4], copper [5], steel [6], aluminum nitrides [7], nickel or silver particles [9], polyacrylonitrile [9], barium titanate [10] etc – as filler. Such composite materials were used for encapsulation, thin film coating, packaging for electronic circuits [4], electromagnetic and radio-frequency interference shielding for electronic devices and electrostatic dissipation [9], [11]. Properties of composites materials depend, on one hand, on the matrix and filler characteristics, and on the other hand, on the technological processes parameters and environmental action [12-14]. The influence of nature, concentration and filler dimensions on the properties of polymer composites with conductive [15-18] or magnetic [14], [19-20] fillers was studied in several papers. It is shown that there is a critical concentration for that the percolation process occurs, leading to important variations of the electrical conductivity, permittivity and dielectric losses [14], [21-22] and magnetic properties [20]. An experimental study concerning the electrical conductivity – measured in DC and AC regime – of some polymer composites from polyethylene and neodymium particles is presented in [14]. Experimental and theoretical determination of the permittivity using the dielectric response function is presented in [23]. It is shown that for certain values of the frequency the calculated values of the permittivity are very close to those experimentally determined. In this paper results concerning the dielectric losses that occur in composites containing low density polyethylene and neodymium magnetic particles (of micron sizes) subjected to harmonic electric fields are presented. The loss factor and volume density of losses and of relative losses values are determined. The dependencies of these quantities on the filler content, temperature and frequency of the electric field are analyzed. II. DIELECTRIC LOSSES If a dielectric is subjected to harmonic electric field of effective value E and frequency f, conduction losses (due to the charge movement) and polarization losses (due to the electric dipoles rotations, induced or permanent) occur [24]: 2σEpc = (1) 2"0εεπ2 Efp rp = , (2) where pc and pp represents the volume density of losses in time unit, by conduction and polarization, respectively, ε0 = 8.85x10-12 F/m - permittivity of vacuum, σ – DC conductivity and "ε r - imaginary part of complex permittivity. The volume density of total active power dissipated in dielectric p ( pc ppp += ) is: tgδεεπ2 20 Efp ' r= (3) 223978-1-4799-5183-3/14/$31.00 ' 2014 IEEE ' 0 ' " εεπ2 σ ε εtgδ rr r f += (4) where 'ε r represents the real part of complex permittivity and tgδ – the dielectric loss factor [24]. It results, thus, that the specific power values p depend not only on the strength and frequency of the electric field but also on the real part of complex permittivity ( 'ε r ) and loss factor (tgδ) values. In order to understand much easier the variations of p with the temperature T and frequency f, the volume density of the relative power pr is used: tgδε επ2 ' 2 0 rr Ef pp == . (5) The quantity pr shows the direct influence of the material characteristics (respectively, the real part of complex permittivity and the loss factor) on the losses inside a dielectric. For the volume density of the dissipated power inside a dielectric p, it results the equation: rpEfp 2 02 επ= . (6) III. EXPERIMENTS Experiments were performed on flat samples of composites prepared from low density polyethylene LDPE with a melt flow index (190 oC, 2.16 kg) of 0.3 g/10 min, a density of 0.920 kg/dm3 at 23 ºC and an electrical conductivity of 5⋅10-17 S/m. As filler, particles of Neodymium of 75-100 μm length and 30-50 μm width (Fig. 1), density of 7 kg/dm3 and electrical conductivity of 1.56⋅106 S/m were used. Maleic anhydride-grafted polyethylene (MA-PE), with a density of 0.925 g/cm3 and a melting point of 105 °C, was used as compatibility agent. Fig.1. Neodymium particles (Optical microscopy, 200 X). TABLE I SAMPLES Sample Nd mass concentration cm (%) E0 0 E1 5 E2 10 E3 15 A 50 cm3 mixing chamber of a Brabender Plasti-Corder LabStation was used for mixing and homogenizing Neodymium powder with the polymer matrix and the compatibility agent (5 wt % MA-PE). Metal powders (concentration of 5, 10 and 15 wt %) were slowly added (~ 2 minutes) to the mixture of PE and MA-PE and mixed at 160 0C, for 8 min (the speed of the rotors being 100 rpm) [14]. By hot pressing at 170 °C for 5 min., with a force of 50 kN, square plates of 100x100x0.5 mm3 of composite materials have been obtained. After pressing, the samples were cooled to room temperature under a pressure of 5 bars. The structure of samples and the dispersion of neodymium particles in polyethylene matrix were analyzed using the optical microscopy (with a NIKOV TI-e microscope) and Scanning Electron Microscopy SEM (with a workstation Karl Zeiss SMT-model AURIGA and detector type EVERHART- THORNLEY) [14]. The loss factor values were measured (on samples of 40 mm square) with a Novocontrol Impedance Analyzer. The applied voltage was 1 V and the frequency between 1 mHz and 1 MHz [14]. For each type of material (E0, E1, E2 and E3, see Table 1), 3 samples were manufactured. All measurements were performed 3 times on each sample and the average values were calculated. IV. RESULTS AND DISCUSSIONS In order to calculate the relative power values pr, the loss factor was experimentally determined on samples E0, E1, E2 and E3 for frequencies between 1 mHz and 1 MHz. Using the values of the real part of complex permittivity 'ε r presented in [23], the specific losses p and relative losses pr was calculated and their variations with filler content, temperature and frequency of the electric field were analyzed. 4.1. Microscopic investigation SEM analysis reveals a small (almost negligible) porosity in both surface and volume of the samples (P, Fig. 2). LDPE shows a lamellar structure and neodymium particles form clusters (metal “islands” [14]) (Fig. 2) of variable dimensions, between 30.4 μm and 174 μm (Fig. 3). These clusters are uniform distributed in the samples and the distance d between them decreases with the increase of the filler content. Thus, for E1 samples the distance d varies between 99.5 ÷ 275 μm and for E3 varies between 67.5 ÷ 211 μm. On the other hand, the dimensions of the clusters increase with the filler content (Fig. 4). 224 Fig. 2. Neodymium particles cluster in LDPE matrix (SEM, 1000 X). a) b) Fig. 3. Neodymium particles clusters (metal “island”) in E2 (a) and E3 (b) samples (Optical microscopy, 200 X). a) b) Fig. 4. Dimensions (a) and distances between neodymium particles clusters (b) in E3 samples (Optical Microscopy, 200X). 4.2. Loss factor The values of loss factor tgδ depend on filler content, temperature and frequency. In Figure 5 variations of the loss factor with mass filler content at 1 mHz and 1 kHz for 80 oC are presented. For both frequencies, the loss factor values increase with filler content, in accordance with other results obtained for polymer composites with fillers of copper and steel wire [26], iron and nickel-iron powders having the dimensions of 44-149 μm [27], nickel and cobalt ferrite powders [29-30] or nickel particles [31] etc. This is due to the increase of the LDPE/Nd interface area, number of chain ends which are fixed on neodymium particles, and, therefore, the required energy to rotate the polar entities. Dependency of the loss factor values tgδ with the frequency of the electric field f, measured on samples E0, E1 and E3 at 50 oC, is presented in Figure 6. It can be seen that tgδ(f) curves present 2 peaks whose frequencies fmax and amplitudes tgδmax depend on the neodymium content. For T = 50 oC, the first peak (corresponding to α transitions of some polar entities with higher molecular weight [23]) is located in the frequency range (0.02, 0.4) Hz (Fig. 6). Increasing the filler content, this peak moves to lower values of the frequency (respectively, the values of fmax decrease) and their amplitudes (tgδmax) increase to a maximum value for cm = 10 %. The increase of tgδmax values is smaller for temperatures close to ambient (30-40 oC) and large close to 80 oC, especially for higher filler content (Fig. 7). The second peak occurs for frequencies higher than 1 MHz [24] and corresponds to polar entities with smaller molecular weight [23], [25]. Dependency of the loss factor with the frequency and temperature, for samples E0…E4 is presented in Figures 6- 11. Increasing the temperature, a movement of both peaks to higher values of the frequency may be seen, for all samples (Figs. 8…11) [32]. For example, if the temperature rises from 30 to 80 oC the values of fmax for the first peak increases from 0.03 Hz to 4.8 Hz. On the other hand, the amplitudes of this peak increase with the temperature. 225 Fig. 5. Variations of the loss factor with filler content (T = 80 oC). Fig. 6. Variations of the loss factor with frequency for E0, E1 and E3 samples (T = 50 oC). Fig. 7. Variations of maximum loss factor values tgδmax with filler content. Fig. 8. Variations of the loss factor with frequency and temperature for E0 samples. Fig. 9. Variations of the loss factor with frequency and temperature for E1 samples. Fig. 10. Variations of the loss factor with frequency and temperature for E2 samples. 226 Fig. 11. Variations of the loss factor with frequency and temperature for E3 samples. Increasing the temperature, loss factor tgδ values increase for frequency values higher than 100 Hz as it can be observed in Figures 12 (curves 1, 2 and 3) and 13. For low frequency values (below 0.5 Hz), the variations of tgδ with the temperature present a peak (corresponding to α relaxation) (Fig. 12, curves 4, 5 and 6). For all samples, the values of the first peak of the curves tgδ(f) (respectively, tgδmax) increase with the temperature (Figs. 8-11 and 14). These values are more significant for higher filler content, due to the increased number of the polar bonds which are attached to neodymium clusters (Fig. 13, blue curve). One can expect that the specific relative power pr will have higher values for the frequency and temperature values for which the loss factor shows maxima. Fig. 12. Variations of the loss factor with temperature for samples E0 (1, 4), E1 (2, 5) and E3 (3, 6) at f = 50 Hz (curves 1, 2, 3) and f = 0.1 Hz (4, 5, 6). Fig. 13. Variations of the loss factor with temperature for E0, E1, E2 and E3 samples (f = 1 kHz). Fig. 14. Variations of maximum loss factor values tgδmax with temperature for E0, E1 and E3 samples. Fig.15. Variations of the real part of complex permittivity 'ε r with frequency and temperature for E2 samples. 227 4.3. Relative permittivity An experimental study concerning the influence of the filler content, frequency and temperature on the complex permittivity components for LDPE/Nd composites is presented by the authors in [23]. Values of 'ε r increase with the neodymium content (in accordance with the results presented in [27-28]). Dependency of the real part of complex permittivity 'ε r with the frequency and temperature for E2 is presented in Figure 15 [23]. Increasing the frequency (from 1 mHz to 1 MHz) and temperature (from 30 to 80 oC) the values of 'ε r decrease (according to [32]). 4.4. Relative specific losses Knowing the values of 'ε r and tgδ, the volume density of relative power pr was calculated. Their variations with the filler content, frequency and temperature are presented in Figures 16-18. Important increases of the relative specific losses pr with the neodymium content cm can be seen in Figures 16 and 17. For example, if the neodymium content increases from 5 % to 15 %, pr increases almost three times (from 0.01 to 0.0275). These increases are more significant especially for loss frequencies (50 – 100 Hz) (Fig. 16, red curve) and less important for higher frequencies (1 MHz) (Fig. 16, blue curve). Moreover, with increasing of the frequency the differences between the relative specific powers values pr measured at high and low frequency decrease, the nonlinearity of pr (cm) curves reduces and, for values close to 1 MHz, these become straights (Fig. 16, blue curve). Increasing the temperature, the relative power density pr decreases, for all samples (Fig. 17). This is probably due to the increase with the temperature of the own (thermal) energies of all polar species which oscillate under the action of the electric field. Fig. 16. Variations of the relative power density with filler content at 50 Hz, 1 kHz and 1 MHz (T = 50 °C). Fig. 17. Variations of the relative power density with temperature for E0, E1, E2 and E3 samples (f = 1 kHz). Fig. 18. Variations of the relative power density with frequency for E0, E1 and E3 samples (T = 50 °C). Variations of the relative power density with the frequency of the electric field for samples E0, E1 and E3 are presented in Figure 18. It comes out that pr has two maxima, one in the low frequency range (0.1…0.5 Hz) and the other one in the high frequency range (above 1 MHz). These maxima correspond to resonance phenomena related with the inhomogeneous (at low frequencies) and orientation polarization (at high frequencies) [24]. For samples without or with low neodymium content (E0 and E1) a minimum occurs in the pr(f) curves, that corresponds to frequency range 100 - 1000 Hz (Fig. 18, black and red curves). 4.5. Specific losses Knowing the relative power density values pr and using the equation (6), the volume density of dissipated power p was calculated for all types of samples. For this, it was considered that the samples (of thickness d = 0.5 mm) are situated between the plates of a condenser, having applied a 228 voltage U = 220 V, that correspond to an effective electric field E = 0.44 MV/m. The calculus has been done for different temperature, frequency and electric field values. Some results, for the samples E0, E1 and E3, are presented, in Figures 19 and 20. It comes out that the power density increases with frequency. For low frequencies (f = 1 mHz) the values of p are relative small (p < 0.25 mW/m3, Fig. 19). For high frequencies (close to 1 MHz) these values increase with 9 orders of magnitude (0.3 MW/m3) overlapping the common losses in copper conductors pCu = 0.14 MW/m3 (passed by current densities J = 3 A/mm2). Considering that the sample E3 has the temperature T = 50 oC and DC conductivity σDC = 10-16 S/m [14], the Joule component of the volume power density (calculated with relation (1)) was obtained pc = 4.44 μW/m3. As, for f = 1 mHz, the total power density has the value p = 0.242 mW/m3, it results that the volume density of losses by polarization is pp = 0.24156 mW/m3, being practically equal with the total power p. Fig. 19. Variation of the power volume density with frequency for E0, E1 and E3 samples at T = 50 °C and E = 0.44 MV/m. Fig. 20. Variations of the power volume density with temperature for E0, E1, E2 and E3 samples (f = 1 kHz, E = 0.44 MV/m). Therefore, for LDPE/Nd composites with neodymium mass content lower than 15 %, the dielectric losses are due only to the inhomogeneous and orientation polarization processes. The specific losses increase with the neodymium content and are dependent on the frequency of the electric field. For example, by using a neodymium content cm = 15 % the specific losses increase from 1.26 W/m3 to 33.25 W/m3 – for f = 100 Hz and from 27.44 W/m3 to 304.51 W/m3 – for f = 1 kHz. These differences are smaller for low (1 mHz) and very high (1 MHz) frequencies (Fig. 19). Variations of the power volume density with temperature for samples E0...E3 subjected to an effective electric field E = 0.44 MV/m and frequency f = 1 kHz are presented in Figure 20. It comes out that the increase of the temperature leads to the reduction of the specific dielectric losses for all samples type. This is probably due to the own energy of the electric dipoles and therefore to the reduction of the necessary energy to rotate them in the polarized electric field direction. V. CONCLUSIONS In LDPE/Nd composites, neodymium particles are grouped inside the samples giving rise of metallic islands where macromolecular chains are attached. At the LDPE/Nd interfaces true electric charge is separated leading to the creation of the inhomogeneous polarization and to increase of permittivity components and dielectric losses. For LDPE/Nd composites, the real component of complex permittivity increases with the filler content and decreases with temperature and frequency. The values of loss factor tgδ increase with the filler content, temperature and with frequency. tgδ(f) curves present two peaks: the first one for frequencies in the range 40 – 100 Hz and the second one for frequencies above 1 MHz. The relative specific losses pr increase with filler content and decrease with temperature. 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