JOURNAL OF APPLIED PHYSICS 107, 124115 共2010兲
Low loss high dielectric permittivity of polyvinylidene fluoride and KxTiyNi1−x−yO „x = 0.05, y = 0.02… composites Debabrata Bhadra,1 A. Biswas,1 S. Sarkar,1 B. K. Chaudhuri,1,a兲 K. F. Tseng,2 and H. D. Yang2 1
Department of Solid State Physics, Indian Association for the Cultivation of Science, Kolkata, West Bengal 700032, India 2 Department of Physics, National Sun Yat Sen University, Kaohsiung, Taiwan 804, Republic of China
共Received 8 February 2010; accepted 2 May 2010; published online 25 June 2010兲 Homogeneous thick film 共⬃0.10 mm兲 of high dielectric K0.05Ti0.02Ni0.93O; abbreviated as KTNO/ polyvinylidene fluoride 共PVDF兲 composite has been prepared by hot-molding technique. The frequency and temperature dependent dielectric behavior of this composite has been studied by varying the KTNO volume fraction 共f KTNO兲. Near the percolation threshold 共f KTNO = 0.40兲, a large enhancement of effective dielectric permittivity 共eff ⬃ 400 which is 40 times higher than that of pure PVDF兲 with low loss 共⬃0.20 at 1 kHz兲 is observed. The experimental eff data have been fitted with different theoretical models and found to follow percolation theory successfully. Such a high eff and low loss flexible dielectric material appears to be suitable for technological applications. © 2010 American Institute of Physics. 关doi:10.1063/1.3437633兴 I. INTRODUCTION
Flexible composites of electroactive ceramics and ferroelectric polymers with high dielectric permittivity 共high-兲 and low dielectric loss have recently been investigated for many application including device miniaturizations. For instance, polymer composites could find applications as gate dielectric for ICs, embedded capacitors in microelectronics, artificial muscles, “smart skins” for drag reduction and in microfluidic systems for drug delivery.1–3 Though polymers offer good mechanical flexibility and high electrical breakdown strength, they suffer from low dielectric permittivity. Novel ferroelectric polyvinylidene fluoride 共PVDF兲 共Ref. 4兲 stands out among other polymers due to its extraordinary pyroelectric and piezoelectric properties. It is highly desirable to enhance the dielectric permittivity of this polymer substantially by dispersing high- ceramic powder, such as Pb共Mg1/3Nb2/3兲O – PbTiO3共PMN– PT兲, Pb共Zr, Ti兲O3共PZT兲, and BaTiO3共BT兲 into the polymer matrix to form 0–3 composites.3–5 But most of the ferroelectric fillers used in the composites are lead-based ceramics, which are not environment friendly. So synthesis of lead-free polymer composites with high- has become a focus of current interest. During the last decade colossal dielectric permittivity 共 ⬃ 104兲 has been displayed by several nonferroelectric materials such as CaCu3Ti4O12 共CCTO兲, 共Ref. 6兲 doped NiO systems, viz., AxTiyNi1−x−yO 共A = Li, K, and Na兲 共Ref. 7兲, CuO 共Ref. 8兲, etc., and most importantly, the high- value of these materials is almost independent over a wide range of temperature. However, loss factors of such oxides are quite high. Dang et al.9,10 have studied dielectric properties of PVDF based PVDF/LixTiyNi1−x−yO 共LTNO兲 and PVDF/ Bi2S3 composites with enhanced effective dielectric permittivity 共eff兲 but sharply drop in high frequency region. Intera兲
Author to whom correspondence should be addressed. Electronic mail:
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estingly, among the doped NiO family, KTNO 共Refs. 7 and 11兲 is found to show high- 共⬃104兲 with lowest loss 共⬃0.2 for x = 0.05兲 near ambient temperature and also lead-free material. Therefore, KTNO can be chosen as filler of PVDF for a suitable polymer composite. By changing f KTNO, it could be possible to adjust the dielectric properties of the composites which motivate us to make the simple combination of PVDF ferroelectric polymer and KTNO semiconducting11 powder at different volumetric fractions by standard hot blending procedure.10,12 It is known that percolation is a promising way to improve eff of polymers, because it improves eff dramatically as the concentration of the filler approaches the percolation threshold.13–16 However, experimental study on dielectric dispersion of the electroactive polymer composites is still rather fragmentary and it is hard to tailor the composites with low dielectric loss. Hence our aim in this study was to fabricate low loss K0.05Ti0.02Ni0.93O / PVDF composite films with different concentration of KTNO and to investigate how effective dielectric permittivity and ac conductivity responded to changes in f KTNO within broad frequency and temperature ranges. To observe the percolation behavior, we made composites with different f KTNO and the experimental dielectric permittivity data have been explained using well the established theoretical models. The high eff and low dielectric loss of the prepared composite films make them attractive as an alternative lead-free dielectric material for device fabrication. II. EXPERIMENTAL DETAILS
For the preparation of KTNO/PVDF composite films, KTNO powder was first prepared by conventional sol-gel method. A stoichiometric amount of Ni 共NO3兲26H2O 共99.9% purity of Merck兲, K2CO3 共Merck, 99.9%兲 and citric acid 关C6H8O7兴 共Merck, 99.9%兲 were mixed and dissolved into an appropriate amount of distilled water. Tetrabutyltitanate 共关CH3共CH2兲3O兴4Ti兲 共Aldrich, 99.5%兲 was then added slowly
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FIG. 1. 共Color online兲 共a兲 SEM image of KTNO powder. 共b兲 XRD patterns of pure KTNO powder and 共PVDF+ 0.4KTNO兲 composite. 共c兲 SEM micrographs of the polished surface of KTNO/PVDF composites with volume fraction f KTNO = 0.10 and 共d兲 same as 共c兲 with f KTNO = f c = 0.40.
and the solution was heated and stirred continuously to form the gel, which was carefully dried in the oven at 120 ° C. The dried gel was finally calcinated at 800 ° C for 1 h in air. Thus KTNO powder 共average grain size ⬃0.5 m兲 was obtained. The preparation of the KTNO/PVDF composite was described as following. The PVDF powder 共Aldrich, 99.9%兲 was initially dissolved in dimethylformamide 共DMF兲 共Merck, 99.5%兲. After the solution was stirred for 8 h at 70 ° C, the KTNO ceramic powder was poured into the solution. The mixed solution was sonicated for about 20 min and stirred for an additional 8 h to disperse KTNO particles into PVDF homogenously. The final solution was poured onto a glass plate to form a cast film at 70 ° C in an oven for 8 h. The ultimate result was a flexible KTNO/PVDF film. To improve the uniformity of the composite,17,18 the solutioncast film19 was then hot-pressed at 200 ° C under 10 MPa for 15 min 共prepressing was conducted for 5 min under the same conditions, after which the pressure was released for a while and the sample was then repressed for 20 min, followed by cooling to room temperature while maintaining the same pressure兲. The films with different f KTNO 共=0.10– 0.50兲 were prepared each having 12 mm in diameter and 0.10 mm in thickness. For electrical measurement, electrodes were painted on both sides using good quality silver paste. An impedance/gain-phase analyzer 共HP 4192A, 100 Hz–13 MHz兲 was used for the measurements of capacitance and ac impedance at different frequencies and temperatures. The size of the KTNO powder and grain morphology and EDX of polished surface of the polymer composites 共KTNO/ PVDF兲 were examined by field emission scanning electron microscopy 共FESEM Model No: JEOL JSM 6700 F兲. Elemental analysis and distribution of different elements, e.g., Ni, Ti, etc. in PVDF matrix were studied, respectively, by energy dispersive x-ray 共EDX兲 and electron probe microanalyzer 共EPMA兲 equipped with another scanning electron mi-
croscope 共Carl Zeiss, EVO-MA10兲. X-ray diffraction 共XRD兲 pattern of KTNO sample and composites are also performed with SEIFERT XRD 3000P diffractometer by using Cu K␣ radiation. III. RESULTS AND DISCUSSION
Figure 1共a兲 shows the typical microstructure of asderived KTNO powders where the grains are nearly spherical in shape with an average size of about 0.5 m. As shown in Fig. 1共b兲, the XRD peaks of NiO can be well detected in the original KTNO powder as well as in 共PVDF+ 0.4KTNO兲 composite and the samples were found to be free from any impurity peak. The average particle size as calculated from the XRD data was found to be ⬃0.55 m which matches quite well with our SEM micrographs. The microstructure of the polished surface of the composites depicts that for low KTNO concentration 共f KTNO ⬃ 0.10兲, the KTNO particles are randomly dispersed in the PVDF matrix 关Fig. 1共c兲兴 and for higher f KTNO, as high as 0.40, the particles are dispersed uniformly in the PVDF polymer, in which the polymer is self connected into a continuous network as shown in Fig. 1共d兲. With increasing f KTNO, the KTNO particles aggregate to form large particle clusters and become self connected as a continuous percolation cluster at the percolation threshold 共f KTNO = 0.40兲 which is responsible for the divergence of dielectric permittivity. Figure 2共a兲 displays EDX spectra of 共PVDF + 0.4KTNO兲 composite. The area on which the above study has been done is shown in the corresponding SEM image in Fig. 2共b兲. The EDX study successfully detects the presence of C, O, F, Ni, Ti, and K peaks. The weight percentages of the mentioned elements in the composite have also been tabulated 共see Table I兲. EPMA studies have been done 共Fig. 3兲 with the aim of showing the distribution of individual
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FIG. 2. 共Color online兲 共a兲 EDX spectroscopy of 共PVDF+ 0.4KTNO兲 composite and 共b兲 the SEM image of the corresponding area on which EDX has been done.
elements in the composite. The EPMA performed on the area shown in Fig. 3共a兲 of the percolation 共PVDF+ 0.4KTNO兲 composite. The typical distributions of Ni and Ti over one percolation cluster of the composite have been shown, respectively, in Figs. 3共b兲 and 3共c兲. It is evident that Ni and Ti are distributed homogeneously and uniformly over composite film can be revealed by the help of EPMA. The dependence of eff on filler concentration of the ceramic particles for this two-phase KTNO/PVDF composite is shown in Fig. 4. As expected, eff increases with the volume fraction of KTNO, viz., f KTNO. We tried to fit the present experimental eff data with different relevant models17–20 with the aim of finding the best fit model. Bruggeman20 self consistent effective medium approximation 共EMA兲 describes eff by the relation: 共1 − f KTNO兲
1 − eff 2 − eff + f KTNO = 0, 1 − 2eff 2 − 2eff
共1兲
where 1 = 10.41 and 2 ⬇ 104 共at 1 kHz兲 are room temperature 共RT兲 dielectric permittivity of PVDF and KTNO, respectively. As seen from the Fig. 4, the above model fails to explain the present experimental data of linear composite. Bruggeman’s idea is primarily applied to random composite media. Although EMA describes the macroscopic properties of a medium based on the properties and relative fraction of its components, but do not relate directly to the percolating systems. This theory assumes that the macroscopic system is homogeneous and failed to predict the properties of the multiphase medium close to the percolation threshold due to long range correlation. Thus, it deviates from for the present system as percolation is approached.
Another model for the effective permittivity of composite was proposed by Yamada21 which is described by the relation
再
eff = 1 1 +
冎
nf KTNO共2 − 1兲 , n1 + 共2 − 1兲共1 − f KTNO兲
where n is the parameter related to the geometry of the ceramic particle and n = 4 / m 共m is a phenomenological constant兲 having typical numerical value of 10.6 considered to be applicable for our present system of linear composites. According to this model, the value of the arbitrary parameter n is related to the shape, specially takes the typical value of the ellipsoidal particle and varies so much from our nearly spherical KTNO particles and hence not suitable for the present composites. Lichtenecker22 proposed a model for composite system having the form log eff = log 1 + 共1 − k兲f KTNO log
2 , 1
wt %
共3兲
which illustrates that the effective dielectric function of a composite consisting of two distinct phases and k in Eq. 共3兲 is specified by the system microgeometry. It has been found that for the special case, trivial solution for k = 0 can be presented for spheroid particles. But for the present KTNO particles which are not in absolute spherical microgeometry, as the model assumes, the experimental eff value deviates from the Lichtenecker’s equation 共Fig. 4兲. Eventually, it is found that the power law23–25 expression fitted the present experimental data quite well 共see in inset of Fig. 4兲 for f KTNO ⬍ f c 共below percolation concentration兲
TABLE I. The weight percentages of the individual elements in the KTNO/PVDF composite obtained from EDX study for f KTNO = 0.40. Elements
共2兲
C
O
F
K
Ti
Ni
21.61
5.68
35.76
0.08
0.86
36.01
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FIG. 3. 共a兲 SEM image of PVDF+ 0.4KTNO composite on which EPMA has been done. Distribution of 共b兲 Ti and 共c兲 Ni from EPMA 共white dots兲 showing both Ni and Ti are homogeneously and uniformly distributed in the composite.
eff ⬀ 共f c − f KTNO兲−q ,
共4兲
where f c is the percolation threshold and q is a critical exponent. As seen from the inset of Fig. 4, the experimental values of the eff are in good agreement with Eq. 共4兲, with f c 500
@ 1 kHz
-q
400
400
eff=PVDF(fc-fKTNO)
300 200
fc=0.40 q=1.60+0.07
100
300
Experimental data Non-linear fitting
0 0.0
0.1
0.2
0.3
0.4
0.5
eff 200 Yamada model Lichtenecker model
100
Bruggeman model Experimental result
0 0.0
0.1
0.2
0.3
fKTNO
0.4
0.5
FIG. 4. 共Color online兲 Variation in the effective dielectric permittivity 共eff兲 of the KTNO/PVDF composites with the volume fraction of KTNO particles fitted with different theoretical model. The power law 关Eq. 共4兲兴 fits the experimental result. Inset shows the variation in eff in the neighborhood of the percolation threshold.
⬇ 0.40 and q = 1.60⫾ 0.07. The homogeneous dispersion of the KTNO particles in the PVDF 关see Fig. 1共d兲兴 could lead to a high threshold. There is a giant increase in eff of the composites especially with f KTNO ⬃ 0.40. The eff values of the composites can reach as high as 400, which is about 40 times higher than that of PVDF matrix and the variation in the dielectric permittivity in the neighborhood of the percolation threshold can be described by the above mentioned power law 关Eq. 共4兲兴. In Fig. 5, we showed the dependence of the effective conductivity 共eff兲 and eff on f KTNO, for different KTNO/ PVDF composites. The eff and eff of the composites increase slowly with the KTNO volume fraction and then drastically at a particular volume fraction 共f c兲 suggesting the percolation nature of the KTNO/PVDF composite system. It is seen from this figure that below the percolation limit, the dielectric permittivity increases slowly with an increase in volume fraction of the KTNO filler due to the formation of microcapacitor network.10,12 We have also estimated the critical volume fraction of KTNO fillers by fitting the experimental conductivity to the equation
eff ⬀ 共f c − f KTNO兲−q⬘ ,
共5兲
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400
3
10 (b)
2.4
1.2
eff
=1kHz
0.8
-6
fc=0.40 q=1.60+0.07
1.5x10
-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3
log(fc-fKTNO)
-6
1.0x10 -7
1.5x10
Experimental Data Linear fitting
-7
1.0x10
log
100
0.0
0.1
0.2
0.3
1
10
fKTNO =0.0
-7
5.0x10
-8
5.0x10
0 0.0
(a)
2
10
eff
1.6
200
2.0x10
2.0
log
300
(a)
-6
Experimental Data Linear fitting
(S/m)
2.8
0.1 0.2 0.3 0.4 0.5
fc=0.40 q'=1.96+0.06
-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 log(fc-fKTNO)
0.4
0.0 0.5
fKTNO
0
10 3 10
4
5
10
10
/Hz
-3
10
-3
10
6
7
10
10 (b)
-4
-4
10
fKTNO=0.4 u=0.88+0.003
-5
10
-6
10
-5
10
(S/m)
FIG. 5. 共Color online兲 Dependence of effective dielectric permittivity 共eff兲 and conductivity 共eff兲 on the volume fraction of KTNO fillers at 1 kHz. Inset 共a兲 shows critical exponent fitting of the eff and 共b兲 eff, below percolation threshold 共f KTNO = 0.4兲.
10
Experimental Data Linear fit
-7
10
3
10
4
10
5
10
6
10
7
10
8
10
-6
10
where q⬘ is the critical exponent in the insulating region as previous Eq. 共4兲 for f KTNO ⬍ f c. The best fit to the conductivity data gives q⬘ = 1.96⫾ 0.06 关see 共a兲 in the inset of Fig. 5兴 from Eq. 共5兲. The f c 共=0.40兲 values obtained from both the fit 关see Figs. 5共a兲 and 5共b兲兴 agree very well. However, this percolation threshold value is higher than the corresponding universal value26 of f c = 0.16 for random continuum composites. Though universality of the percolation theory suggests a similar behavior for the conductivity and the dielectric permittivity with q = 1, this is not observed in a real continuum systems. A deviation from the universal value has been observed in the 0–3 composite systems based on the grain-size or the ceramic fillers.26,27 It is not only the size of the filler that affects; the shape of the filler particles 共nearly spherical in present case兲 might also influence both critical threshold value and the exponents. Such a high percolation threshold could be ascribed to the semi-conducting property11 of the KTNO powders and the microstructure of KTNO/PVDF composites. Xie et al.27 suggested a large deviation of f c and exponents q and q⬘ for filler particles that are nonspherical and low aspect ratio systems. As mentioned above, the percolation threshold is visible at volume concentration f c, where the dielectric permittivity abruptly increases. At this stage, the conduction behavior of the composites is controlled by the concentration of KTNO phase. The electrical property of the composites with composition near the percolation threshold follows a scaling law23–25 关see Eqs. 共4兲 and 共5兲兴. The f KTNO at the percolation threshold plays an important role in determining the conductivity of the composite. Moreover, it is seen that the dielectric loss rapidly increases for the above mentioned volume fraction 共f c兲 of the composites. Compared to the other PVDF composites with high concentration of CCTO 共Ref. 12兲 and BaTiO3,10 present two-phase KTNO/PVDF composites exhibit higher eff. The dielectric permittivity of the PVDF + 0.4KTNO composite at 1 kHz is as high as 400. Such a high- of the composite could be explained using the said percolation theory23–26,28,29 because of semiconducting11 behavior of KTNO. The variation in the dielectric permittivity with frequency for different f KTNO in the KTNO/PVDF system is
fKTNO =0.0 0.1 0.2 0.3 0.4 0.5
-7
10
-8
10
-9
10
3
10
4
10
5
10
/Hz
6
10
7
10
FIG. 6. 共Color online兲 共a兲 The effective dielectric permittivity and 共b兲 electrical conductivity of the KTNO/PVDF composites as a function of frequency at room temperature. Inset 共b兲 shows best fit of values for f KTNO = 0.40 to Eq. 共6兲.
shown in Fig. 6共a兲. The eff values exhibit weak frequency dependence over a wide range of frequency which contradicts the behavior of similar LTNO/PVDF 共Ref. 9兲 composites. eff is quite high even at higher frequency 共more than 200 at 1 MHz兲 regime. The PVDF has a characteristic relaxation drop in the dielectric permittivity at about 105 Hz which, however, disappears with f KTNO → f c in these composites. eff of the composites with f KTNO ⱕ f c increases almost linearly with frequency, a log–log plot shown in Fig. 6共b兲 demonstrates the power-law behavior. According to the percolation theory,23–26,28,29 as f KTNO → f c
eff ⬀ u,eff ⬀ u−1 ,
共6兲
where = 2 and u is a critical exponent. The data for the composite with f KTNO = 0.40 gives u = 0.88⫾ 0.003 which is little larger than the corresponding universal value26 共uun ⬃ 0.73兲 as shown in the inset of Fig. 6共b兲. Normally, higher value of u, approaching toward 1, implies that eff is weakly dependent on the applied frequency 关according to Eq. 共6兲兴. Beside the requirement of high eff, it is also essential for the ideal capacitor materials to maintain low dielectric loss. Figure 7共b兲 shows the increasing nature of dielectric losses of PVDF/KTNO composite with f KTNO. At f KTNO ⬍ 0.40, the dielectric loss remains below 0.12, while it increases sharply for f KTNO = 0.40 关inset of Fig. 7共a兲兴. It is important to note that the dielectric loss of the present composite is lower than those of other polymer composites which might be attributed to the microstructure of the polymer composite. It is also worth mentioning that the dielectric loss of this composite is ⬍0.2 in the wide frequency range which is much lower than
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(a)
400
0.25
350
o
30 C O 60 C O 90 C O 120 C
400
0.25
eff
tan
eff
0.15
250
0.10
0.20
200
300
200
tan
0.15 0.10
0.05
0.05 0.00 0.0
100 3 10 0.30
0.1
0.2
0.3
fKTNO
0.4
0.5
4
5
10
/Hz
6
10
7
10
0.00
500
(b)
fKTNO = 0.0
4
5
10
10
/Hz
6
7
10
10
5 kHz 10 kHz 100kHz
(b)
450
0.1 0.2 0.3 0.4 0.5
400
eff
0.20
100 3 10
0.6
10
0.25
tan
(a)
0.20
300
150
500
0.15
350 300
0.10
250 40
0.05 3
10
4
10
5
10
/Hz
6
10
7
10
FIG. 7. 共a兲 Frequency dependence of the relative effective permittivity and loss tangent 共tan ␦兲 of PVDF+ 0.4KTNO composite and 共b兲 tan ␦ of the KTNO/PVDF composites. Inset of 共a兲 shows variation in tan ␦ on f KTNO.
other related LTNO/PVDF 共⬃2兲 共Ref. 9兲 and BaTiO3 / PVDF 共⬃1兲 共Ref. 10兲 composites. Near percolation, the semiconducting KTNO particles are separated by thin polymer layer that enhances the entrapment of charge carriers between the polymer-semiconductor interfaces, resulting in a high eff and low loss factors. A low loss observed in the present system may suggest the formation of a thin polymer layer on the KTNO particles that prevents the particle to particle contact both below and above the percolation. Conduction mechanism through small polaron hopping in KTNO 共Refs. 11 and 30兲 might also influence the loss in the composite. The temperature dependence of the dielectric behavior of the composite for f KTNO = 0.40 is shown in Fig. 8. The eff increases obviously with the rise in temperature at low frequencies 关Fig. 8共a兲兴. The increase in eff could be due to the increase in conductivity of semiconducting KTNO particles with temperature. At low frequency, the dipoles have enough time for polarization. However, at high frequency, the polarization of molecules does not have enough time to catch up with the change in electrical field frequency, which leads to the weak dependence of eff with temperature. In the temperature range of 40– 160 ° C as shown in Fig. 8共b兲, the dielectric permittivity slowly increases with temperature, while an anomaly is observed at 135 ° C. Slow increase in dielectric permittivity with temperature between 40 and 100 ° C is due to an increase in conductivity of the semiconducting KTNO particles. This anomaly might be attributed to the thermal expansion of the PVDF polymer and subsequent softening of the composites at high temperatures.9,10 The di-
60
80
100 O
T/ C
120
140
160
FIG. 8. Dependence of the effective dielectric permittivity of the 共PVDF + 0.4KTNO兲 composite on frequency 共a兲 and temperature 共b兲.
electric permittivity drops gradually when the temperature further increases up to 135 ° C above which the composite becomes enough flexible and the movement of the molecules increases. Namely, the percolation in the 共PVDF + 0.4KTNO兲 composite disappears at high temperature 共above 135 ° C兲 and the percolation path is destroyed due to a large thermal expansion. A similar phenomenon was observed for CCTO/PVDF 共Ref. 12兲 and composites BaTiO3 / PVDF.10 For the sake of completeness, we should mention that the samples showed banana like polarizationelectric field 共P-E兲 loops 共for f KTNO ⱕ 0.4, not shown in this paper兲 which do not indicate real ferroelectric hysteresis behavior of the composite samples but due to change in conductivity. IV. CONCLUSIONS
In summary, we have prepared a novel two-phase 共KTNO/PVDF兲 composite system with a semiconducting KTNO particles dispersed in the ferroelectric PVDF matrix that exhibits high effective dielectric permittivity with low loss. At higher temperature, effective dielectric permittivity 共eff兲 shows a peak around 135 ° C and then decreases due softening of the polymer and destruction of the percolation pathways above this temperature. The dielectric behavior of the composites is dominated by the dynamics of the polymer matrix and the inorganic contents. Within the frequency range of our investigation 共1 kHz–13 MHz兲, the main role of KTNO filler is to enhance the static dielectric permittivity of the polymer composite compared to that of pure PVDF and at the same time exhibit a percolation threshold for f KTNO = 0.40. The eff value of the composite at the percolation limit 共f KTNO → f c兲 reaches as high as 400 共almost 40 times to
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that of pure PVDF兲 and possesses weak frequency dependence. Such a flexible high dielectric low loss material might be very suitable for applications in devices. ACKNOWLEDGMENTS
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