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Effect of the ceramic grain size and concentration on the dynamical mechanical and dielectric behavi_图文

Appl Phys A (2009) 96: 899–908 DOI 10.1007/s00339-009-5141-2

Effect of the ceramic grain size and concentration on the dynamical mechanical and dielectric behavior of poly(vinilidene ?uoride)/Pb(Zr0.53 Ti0.47)O3 composites
S. Firmino Mendes · C.M. Costa · V. Sencadas · J. Serrado Nunes · P. Costa · R. Gregorio Jr. · S. Lanceros-Méndez

Received: 1 July 2008 / Accepted: 5 February 2009 / Published online: 4 March 2009 ? Springer-Verlag 2009

Abstract In this work, poly(vinilidene ?uoride)/Pb(Zr0.53 Ti0.47 )O3 ([PVDF]1?x /[PZT]x ) composites of volumetric fractions x and (0–3) type connectivity were prepared in the form of thin ?lms. PZT powder of crystallite size of 0.84, 1.68, and 2.35 ?m in different amounts of PZT (10, 20, 30, and 40%) was mixed with the polymeric matrix. The crystalline phase of the polymeric matrix was the nonpolar α-phase and the polar β-phase. Dielectric and dynamic mechanical (DMA) measurements were performed to these composites in order to evaluate the in?uence of particle size and the amount of PZT ?ller with respect to the PVDF matrix. The inclusion of ceramic particles in the PVDF polymer matrix increases the complex dielectric constant and dynamical mechanical response of the composites. A similar behavior is observed for the α- or β-phase of the polymeric matrix indicating that the PVDF polymer matrix is not particularly relevant for the composite behavior. On the other hand, ceramic size and especially content play the major role in the increase of the dielectric response and the room temperature storage modulus. In particular, the storage modulus increases with
S. Firmino Mendes · C.M. Costa · V. Sencadas · J. Serrado Nunes · P. Costa · S. Lanceros-Méndez ( ) Department of Physics, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal e-mail: lanceros@?sica.uminho.pt Fax: +351-253-604061 C.M. Costa CeNTI—Centre for Nanotechnology and Smart Materials, Rua Fernando Mesquita 2785, 4760-034 Vila Nova de Famalic?o, Portugal R. Gregorio Jr. Department of Materials Engineering, Universidade Federal de S?o Carlos, C.P. 676 13.565-905 S?o Carlos, SP, Brasil

increasing PZT concentration, but this increase is more pronounced, in terms of maximum value, for the sample with 2.35 ?m particle size; DMA reveals two main relaxations in the analyzed samples. A low-temperature process maximum at ca. ?40°C, usually labeled by β or αa associated to the Tg of the polymer and the α-relaxation at temperatures above 30°C. The β-relaxation is also observed in the dielectric measurements. The models used to asses the dielectric behavior of the samples with increasing PZT concentration indicate that the particle–matrix interaction plays a relevant role, as well as the particle asymmetry and relative orientation, being the Yamada model the most appropriate to describe the composite behavior. PACS 77.22.-d · 77.84.Lf · 81.70.-q · 82.35.Jk

1 Introduction “Smart Materials” are materials that show reproducible and stable responses through signi?cant variations of at least one property when subjected to external stimuli [1, 2]. Responses given by the materials must be controlled, reproducible, stable, and expectable regarding the speci?c stimuli that are being applied to the material. Material responses and stimuli may be: electric, magnetic, mechanical, chemical, thermal, optical, etc. Among the smart materials there are the ones classi?ed showing piezo- and pyroelectric properties. One of the best piezo- and pyroelectric polymers is the semicrystalline polymer poly(vinilidene ?uoride) (PVDF) [3]. The processed ceramic-polymer PVDF/PZT composites consist of a ceramic ferroelectric phase soaked in a polymeric insulating dielectric matrix. These composite materi-


S. Firmino Mendes et al.

als combine the best of the ceramic properties: high piezoelectric coef?cients, low dielectric and mechanical losses, good thermal properties, large range of dielectric constants, as well as the advantages of the polymer properties: low density, high resistivity, ?exibility [4, 5]. The properties of the ceramic-polymer composites will depend on how the ?ller and the matrix are related: the connectivity [6]. In 1979 Furukawa et al. [7] published a study on the effect of the ceramic particles in various polymer/PZT systems. For the PVDF/PZT composites the authors conclude that the piezoelectric effect is originated by the ceramic particles, unless the volume fraction of the PZT is very small. Later, Yamada et al. [8] developed expressions to predict the dielectric, piezoelectric constants, and elastic modulus of binary systems like PVDF/PZT composites. This work also concludes that the piezoelectricity of the binary system PVDF/PZT is originated by the piezoelectricity of PZT. The high dielectric constant of the ceramic allowed a high dielectric constant in the composite for moderate volume fractions of the ceramic ?ller and a strong piezoelectric effect. The elastic modulus of such composites increases with the increase of PVDF weight fraction on the PVDF/PZT composites. Theoretical work was also developed by Bhimasankaram et al. to predict the effect on dielectric and piezoelectric behavior of the piezoelectric ceramic particles in composites with 0–3 connectivity [9]. The results from Yamada et al. [8] were con?rmed and extended by S.P. Marra et al. [10]. It was found that the viscoelastic properties of the composite changes as a function of ceramic content, strain, and frequency. In general, as the amount of ceramic increases, the composites become stiffer, more brittle, and display larger nonlinear stress vs strain behavior. Both the storage and loss moduli also increase as the ceramic content increases. The interaction between the matrix and the ceramic particles is believed to play a large role in the overall viscoelastic properties of the composites. In the present study the polymeric material used in order to prepare the composites was the poly(vinilidene ?uoride) (PVDF) and the ceramic material was the lead zirconate titanate (PZT). Both materials are piezoelectric but with quite different characteristics. PVDF has low density (ρ = 1780 kg/m3 ) compared to the PZT (ρ = 7500 kg/m3 ); the PZT has high dielectric constant (ε = 810) compared to the β-PVDF (ε = 12) [3, 11]. PVDF is a semicrystalline polymer exhibiting four crystalline phases [12]. The β-phase gives the highest piezo-, pyro-, and ferroelectric properties. Films of α-phase can be converted to the β-phase by mechanical stretching at temperatures below 100°C and stretch ratios higher than 2 [13]. To optimize the electroactive properties of the β-PVDF a poling procedure of several kV is applied to the micrometerthick samples [13–15]. Unoriented ?lms exclusively in the β-phase can be obtained from the crystallization of PVDF from solution with

N ,N -dimethyl formamide (DMF) or dimethyl acetamide (DMA) at temperatures below 70°C. These ?lms show high degree of porosity what makes them opaque (milky) and fragile [16]. Furthermore, these pores cause a degradation of the electrical properties of the material (lower dielectric constant) and do not allow poling of the ?lms, which is essential for the applications involving the piezo-, pyro-, and ferroelectric effects [3, 16, 17]. Also, the mechanical properties are also affected by high porosity and the ?lms cannot be oriented by stretching due to high fragility. The PZT is a ceramic with the following chemical formula: Pb(Zrx Ti1?x )O3 and crystallizes in a perovskite structure [18].The phases diagram is complex, but one of the most interesting issues is the existence of the morphotropic phase boundary (MPB) dividing the ferroelectric region in two parts: a rhombohedral phase region rich in Zr atoms and a tetragonal phase region rich in Ti atoms. At room temperature the MPB is placed in the region of Zr/Ti = 52/48 [19, 20]. At the MPB the dielectric and piezoelectric response of the material is the largest. In this work, PVDF/PZT composites samples with different PZT particle size and content of PZT were prepared by solution in the nonpolar and polar phases of PVDF, α- and β-phase respectively. The dielectric and dynamical mechanical behavior of the samples was evaluated in order to provide information and investigate the origin of the in?uence of ceramic particle size and content on the dielectric and viscoelastic properties of such composite materials. This will be achieved by application of different theoretical models considering different interactions between the polymer matrix and the ceramic ?ller.

2 Theory In order to better understand the nature of the dielectric response of the composite material with increasing ceramic concentration, several theoretical models will be used. The ?rst model developed to predict the dielectrical behavior of the composites was proposed by Maxwell and Garnett in 1904 [21]. This model is still widely used. In this model, the ceramic material of spherical geometry is randomly immersed in the polymeric matrix without any kind of interaction between the different materials. In this model, the dielectric response of the composite is given by: ε = ε1 1 + 3q[ε2 ? ε1 /ε2 + 2ε1 ] , 1 ? q[ε2 ? ε1 /ε2 + 2ε1 ] (1)

where ε1 is the dielectric constant of the polymer, ε2 is the dielectric constant of the ?ller, and q is the volume fraction of the ?ller. In 1979, Furukawa et al. [7] derived an expression for biphasic composites with 0–3 connectivity. This model also

Effect of the ceramic grain size and concentration on the dynamical mechanical and dielectric behavior


assumes that the ceramic particles are spherical and uniformly dispersed in the polymeric matrix. The entire system is dielectrically homogeneous and depends mainly on the dielectric constant of the matrix. The dielectric behaviour of the composites is predicted by: ε= 1 + 2q ε1 , 1?q (2)

work with spherical particles. The equation that describes the model of Yamada is the following [8]: ε = ε1 1 + n · q(ε2 ? ε1 ) . n · ε1 + (ε2 ? ε1 )(1 ? q) (6)

where ε1 is the dielectric constant of the matrix and q is the volume fraction of the spherical ceramic particles. Rayleigh developed a theory based on the Maxwell– Garnett and Furukawa models for biphasic composite materials containing minor spherical ?ller. In this model, the dielectric behavior is given by [9]: ε= 2ε1 + ε2 ? 2q(ε1 ? ε2 ) ε1 . 2ε1 + ε2 + q(ε1 ? ε2 ) (3)

As a conclusion, three families of approaches are used in order to describe the composite materials: Maxwell and Garnett [21], Furukawa et al. [7], and Rayleigh [9] created models based on spherical ?llers randomly immersed at the polymeric matrix; Bhimasankaram et al. [9] and Kerner and Paletto [22] created models also based on randomly distributed spherical ?llers but took into account the polarization of the materials, the local variations of the electric ?eld and the interaction with the applied electric ?eld. Finally, the model by Yamada et al. [8] takes into account also the shape and the relative orientation of the ?llers.

Bhimasankaram et al. also presented a theory that considers a composite material of connectivity 0–3 in which the system is composed of spherical piezoelectric material randomly dispersed in a continuous medium (BSP model) [9]. The main difference with the previously described models is that each dielectric sphere is polarized and the dipoles get aligned in the direction of the applied electric ?eld. These dipoles locally modify the ?eld in the neighboring region. The effect of the local dipolar ?elds becomes more important for composites with a larger fraction of piezoelectric particles. The effective dielectric function is given by [9]:
ε= ε1 (1 ? q) + ε2 q[3ε1 /(ε2 + 2ε1 )][1 + 3q(ε2 ? ε1 )/(ε2 + 2ε1 )] , (1 ? q) + q(3ε1 )/(ε2 + 2ε1 )[1 + 3q(ε2 ? ε1 )/(ε2 + 2ε1 )]

3 Experimental details Composites of PVDF with PZT [Pb(Zr0.53 Ti0.47 )O3 ] were prepared by dispersing the ceramic powder in a solution of PVDF in dimethylacetamide (DMA). The initial concentration of the solution was 0.2 g PVDF (Fora?on F4000— Atochem) per milliliter of DMA. The average size of the ceramic particles used in this work was 0.84, 1.68 and 2.35 ?m. Flexible ?lms with ?30 ?m were obtained by spreading the suspension on a glass plate which was then maintained at 65°C for 1 h. This period of time is suf?cient for total evaporation of the solvent. The temperature of 65°C was chosen in order to allow crystallization of the electroactive β-phase of PVDF [17]. Next, the samples were heated in an oven at 80°C for 12 h in order to remove any remaining traces of solvent. The volume percentage of the ceramic varied from 10–40%. Percentages higher than 40% were not used in order to guarantee 0–3 connectivity and to maintain the ?exibility of the ?lms. Scanning electron microscopy (Leica Cambridge apparatus at room temperature) was performed in order to evaluate the composites microstructure and the dispersion of the ceramic powder within the polymer matrix. All the specimens were coated with a conductive layer of sputtered gold. Dielectric measurements were performed with a General Radio 1693 digital RLC bridge. The real (ε ) and imaginary (ε ) parts of the permittivity were obtained in the frequency range from 100 Hz to 100 kHz at a temperature rate at 1°C min?1 from ?60 to 140°C for the sample α-PVDF with 40% PZT and 0.84 ?m particle size. For the other samples a frequency scan from 100 Hz to 100 kHz was performed at room temperature in order to evaluate the effect of the particle size and concentration in the dielectric response of the

(4) where ε1 is the dielectric constant of the polymer, ε2 is the dielectric constant of the ?ller, and q is the volume fraction of the ?ller. Kerner and Paletto developed an expression for the effective dielectric constant of composites materials. These authors propose a relationship between the average electric ?eld E1 and E2 of the individual materials over the total applied electric ?eld E [22]: ε=q [(1 ? q)ε1 (3ε2 /ε1 + 2ε2 )2 + qε2 ] [1 + (1 ? q)((3ε2 /ε1 + 2ε2 ) ? 1)]2 [(1 ? q)ε1 + qε2 (3ε1 /2ε1 + ε2 )2 ] . [(1 ? q) + q(3ε1 /2ε1 + ε2 )]2 (5)

+ (1 ? q)

One of the most general attempts of describing the dielectric behaviour of composites was the one by Yamada et al. [8]. It is based on the properties of the individual materials and also considers a factor (n = 4π/m) related with the shape and relative orientation of the ?ller, while others authors only


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composite. Circular aluminum electrodes of 5 mm in radius were vacuum evaporated onto both sides of each sample. Mechanical measurements were performed in a Seiko DMS210 apparatus at 1 Hz in the tensile mode. The temperature dependence of the storage modulus and loss tangent was measured in the temperature range from ?90 to 120°C at 2°C/min for the α-PVDF with 40% PZT and 0.84 ?m particle-sized sample, the same in which temperature dependent dielectric measurements were performed. In the remaining samples a frequency scan from 0.05 to 20 Hz was performed at room temperature. The samples for these experiments were rectangular (10 × 5 × 0.3 mm3 , typically).

and 1c); the β-phase composite samples reduce its characteristic porosity [12] with respect to the pure β-phase sample (compare Figs. 1b and 1d). 4.2 Dielectric response 4.2.1 Temperature behavior Determination of the dielectric constant and its variation with temperature and frequency are among the most important characterization procedures to be performed in dielectric materials, especially when these materials can be used for applications involving its electroactive properties. Moreover, differences detected in different samples may re?ect morphological variations occurring due to physical changes induced by the processing conditions and interactions between the different materials. Figure 2 shows the variation of ε and tan(δ) for the α-PVDF/PZT sample with 40% of piezoelectric ceramic particles and with 0.84 ?m size as a function of the temperature for several frequencies. Measurements for the complex dielectric constant were performed in the composite samples in order to evaluate the effect of the ceramic particles in the polymeric matrix both on the overall response of dielectric permittivity with temperature and frequency, and, in particular, on the different relaxation observed in these composite materials. In the present study the temperature evolution of the dielectric and mechanical response of the composites is shown just for the α-PVDF with 40% PZT particles with 0.84 ?m, as it is representative of the main effects observed for the other samples. It corresponds to one of the samples with the highest ceramic concentration so the observed effects on the

4 Results and discussion 4.1 Microstructure The microstructure of the prepared samples was analyzed by scanning electron microscopy (SEM) in order to evaluate the dispersion of the ceramic and understand how the composites may in?uence the polymer crystallization microstructure [13]. Figure 1 shows the SEM images of the pure αand β-phase of the PVDF and for composites with different amounts of PZT particles and in different crystalline polymer matrix (α- and β-PVDF, respectively). The main relevant microstructural feature of the composites is the following: In both, α- and β-phase composites the ceramic particles distribute randomly (Figs. 1c and 1d). The large spherulites characteristic of the α-phase materials [3, 12] disappear with increasing ceramic content (compare Figs. 1a
Fig. 1 SEM images of: (a) α-PVDF, (b) β-PVDF, (c) PZT/PVDF (α-PVDF with 10% PZT and Φ = 0.84 ?m), and (d) PZT/PVDF (β-PVDF with 40% PZT and Φ = 2.35 ?m)

Effect of the ceramic grain size and concentration on the dynamical mechanical and dielectric behavior


Table 1 Vogel–Tammann–Fulcher and fragility parameters for the β-relaxation α-PVDF and for the composite α-PVDF/PZT with 40% of ceramic particles and with 0.84 ?m size EVTF (eV) TVTF (K) τ0 (s) α-PVDF/PZT (40%) 0.085 α-PVDF 0.129 191 168 Tg (K) m 83 67

2.51 × 10?11 225 5.96 × 10?13 213

where EVTF is the VTF energy, kB is the Boltzmann constant, and TVTF is the critical temperature at which molecular motions in the material become in?nitely slow. The ?tting parameters obtained for the ?ttings are summarized in Table 1, in comparison with the results obtained for pure α-PVDF. Table 1 reveals that the inclusion of electroactive ceramic particles in the PVDF affects the characteristics parameters of the β-relaxation of the polymer. The activation energy (EVTF ) decreases with the inclusion of PZT. On the other hand, the TVTF is high for the composite sample, just like the cut-off time. The difference of TVTF is intimately related with the Tg value of the samples. A consequence of the values of the ?tting parameters of the VTF relaxation plot is the calculation of the fragility parameter [14]: m=
Fig. 2 ε and tan(δ) vs temperature for α-PVDF with 40% PZT particles with 0.84 ?m ?lms measured at several frequencies between 100 Hz and 100 kHz

EVF /kB Tg , (ln 10)(1 ? TVF /Tg )2


different parameters are also larger. The rest of the samples show the same general features. A detailed account of the effect of the ceramic size and content on the observed dielectric and mechanical relaxation parameters will be subject of a separate discussion. Figure 2 reveals that the real part of complex dielectric permittivity of the composites at room temperature increases almost 10 times when compared with the pure polymer (ε ? 7) [3]. On the other hand, when compared to the = pure PZT ceramic (ε ? 810) [12] the ε is almost 10 times = lower. The low-temperature β-relaxation assigned to the glass transition dynamics of the polymer matrix is still present. This process is mainly probing the cooperative segmental motions within the amorphous phase. The dynamics of the β-relaxation were analyzed by the Vogel–Fulcher–Tammann (VFT) relaxation formalism (Fig. 3). τ = τ0 exp ? ? ?EVTF , kB (T ? TVTF ) (7)

where m is an indication of the steepness of the variation of the material properties (viscosity, relaxation time, etc.) as Tg is reached. A high m value de?nes a fragile material whereas a strong material will be characterized by small m values. The m(Tg ) value calculated with the VTF parameters is determined at the glass transition temperature (Tg ) where the relaxation time is equal to 100 s. The fragility parameter of α-PVDF is lower than the one calculated for the PZT/PVDF composite. This demonstrates that the inclusions of micro ceramic particles has an effect on the relaxation process and affects in a signi?cant way the amorphous part of the polymer. In fact, it is possible to observe from the m value that the ceramic particles immersed in the polymeric matrix make the composites more fragile (the m factor of the composite is higher than the pure polymer sample). The m value found for PVDF and for the composite are in the range of the values of several glass-forming amorphous polymers (m ? 46 = for polyiso-butylene to 191 for poly[vinyl chloride]) [14]. At T ≥ 70°C conductivity-like effects appear in the sample. The frequency dependence of the real and imaginary parts of complex permittivity of PVDF at constant temperature (Fig. 3a) can be ?tted by (9) [10, 15]: ε = ε∞ + Aω?n , (9)


S. Firmino Mendes et al.

Fig. 3 (a): Higher temperature dielectric constant as a function of frequency for α-PVDF with 40% PZT and an average grain size of 0.84 ?m. (b): log–log plot of the conductivity as a function of frequency for α-PVDF with 40% PZT and an average grain size of 0.84 ?m

Fig. 4 Fitting parameters n (a) and A (b) as a function of temperature

Table 2 Fitting parameters from (9) α-PVDF:PZT (40%) ε∞ 82 81 71 66 A 453 635 575 805 n 0.37 0.38 0.30 0.31

where ε∞ is the high-frequency limit of the real part of dielectric permittivity, A and n are constants. The results are presented in Table 2 and graphically represented in Fig. 4. Similarly, the high-temperature behavior was also analyzed in terms of the conductivity (Fig. 3b), as calculated from equation: σ = ωε0 ε , (10)

343 K 353 K 363 K 373 K

ε∞ decreases and A increases linearly with increasing temperature (Fig. 4). On the other hand, the value of n is relatively independent of temperature which indicates that the conduction mechanism does not change with temperature. Furthermore, the obtained values (0.31 < n < 0.37) are higher than the values found for PVDF (0.10 < n < 0.25 [15]) and they are typical of hopping conduction, just like for the pure polymer [23].

It is interesting to note in Fig. 3b, that the AC conductivity of the composites as a function of frequency does not show both the frequency independent low-frequency region and the high-frequency dispersive region characteristic of many disordered systems. In our case, just the dispersive region is measured for the frequencies under consideration. As the frequency independent conductivity results from the macroscopic conductivity and from the charge ?ow along paths, which are larger than v/ω, where v is some typical value for the mean velocity of the transferring charge car-

Effect of the ceramic grain size and concentration on the dynamical mechanical and dielectric behavior


Fig. 5 Conductivity ?tting for (a) α-PVDF/PZT composite (Φ = 0.84 ?m and 40% PZT) and (b) pure α-PVDF

Fig. 6 Variation of ε with ν for the PVDF/PZT samples with different volume fractions of ceramic particles: (a) β-PVDF/PZT with Φ = 0.84 ?m and (b) β-PVDF/PZT with Φ = 2.35 ?m

riers, this means that the paths for hopping conductivity are shortened due to the existence of polymer/ceramic interfaces blocking the charge carriers. This will also give rise to the Maxwell–Wagner–Sillars polarization [24]. From the calculation of the conductivity by (10) at different temperatures and frequencies, the variation of conductivity as a function of the temperature was analyzed by the following equation: σ T = B exp ?Ea , kB T (11)

Table 3 Best ?tting results for the conductivity model for the PVDF and for the α-PVDF/PZT Φ = 0.84 ?m and 40% PZT composite Frequency Composite α-PVDF B Ea (eV) B Ea (eV) 500 Hz 47.47 0.375 8.49 0.572 1 kHz 81.45 0.379 8.17 0.554 5 kHz 772.78 0.418 7.14 0.500 10 kHz 2472.54 0.439 7.01 0.486

where B is the pre-exponential factor, Ea the activation energy of the process, T is the temperature, and kB is the Boltzman constant. This ?tting is analogous to the Arrhenius Law for a thermically activated process. The results are shown in Fig. 5. The results obtained from Fig. 5, and presented in Table 3, reveal that the pre-exponential factor is higher for the composite sample and the activation energy of the process

is of the same magnitude for both materials but relatively higher for the α-PVDF when compared to the composite. The destruction of the spherulite structure of the pure α-PVDF due to the presence of ceramic particles may explain this behavior and also due to the fact that the PZT particles are somehow bonded to the matrix having an interface that responds to the applied electrical ?eld. Therefore, the polymer–ceramic interface of the composites should play an important role to the conductivity. Just like it was observed before for the fragility parameter and VTF parameters, the


S. Firmino Mendes et al.

Fig. 8 DMA spectra (storage modulus and loss factor) for the α-PVDF and α-PVDF/PZT (Φ = 0.84 ?m and 40% PZT) composite sample. The experiments were carried out at 2°C min?1 and at frequency of 1 Hz Table 4 The value attributed to the shape adjusted with Yamada Model Medium Grain Size (?m) 0.84 n α-phase β-phase 2.9 3.9 2.80 5.8 5.20 6.5 1.68 2.35

Fig. 7 Variation of ε as a function of the PZT concentration and particle size in the (a) α-PVDF and (b) β-PVDF matrix. The points are the experimental results and all ?ttings were realized for room temperature and 1 kHz. Open triangles: 0.84 ?m grain size; open circles: 1.68 ?m grain size; open squares: 2.35 ?m grain size

ceramic strongly in?uences the electric behavior of the composites. 4.2.2 Concentration behavior The inclusion of ceramic particles in the PVDF polymer matrix increases the complex dielectric constant of the composites (Fig. 6). A similar behavior is observed for the αor β-phase of the polymeric matrix clearly indicating that the PVDF polymer matrix is not particularly relevant for the composite behavior. On the other hand, ceramic size and especially content play the major role in the increase of the dielectric response. The behavior of the complex dielectric constant was evaluated according to the theoretical models presented previously. The results obtained for α-PVDF/PZT and β-PVDF/PZT composites are exposed in Fig. 7.

In order to apply the mathematical expressions, the ε value for the α- and β-phase of PVDF was 6.6 and 12, respectively, and for the PZT was 811. The models presented in [8, 9], and [22] that consider interactions beyond the simple homogeneous dispersion of particles in a dielectric media (models presented in [7, 9], and [21]) give better ?tting results indicating the relevance of these interactions. Nevertheless, best ?ts are obtained with the Yamada model [8], which together with those interactions enters with a shape parameter taken into account particle shape and relative orientation. The values obtained for the shape parameter, n, resulting from the best ?ts are shown in Table 4, for several PZT particle size and for the two crystalline phases of the PVDF (α and β). Gregorio et al. found an n value of 3.5 for a PZT particle size of 1.5 ?m [12]. The shape parameters give an indication of the asymmetry, orientation, and distribution of the ceramic particles. In both cases the n parameter increases with increasing particle size, which reproduced a larger particle asymmetry with larger size. The shape parameter, on the other hand, is lower for the α-phase material. As the n value increases as the distribution of particles in the polymeric matrix decreases, the obtained values for both polymeric matrixes suggest that the PZT distribution is more ef?cient for the β-phase. The β-PVDF crystallize in a porous structure (Fig. 1b) [12, 16], and for this crystalline phase of

Effect of the ceramic grain size and concentration on the dynamical mechanical and dielectric behavior


Fig. 9 E variation with frequency for the α-PVDF/PZT (a) Φ = 0.84 ?m and (b) 2.35 ?m composite samples. The experiments were carried out at room temperature and at frequency of 1 Hz

the polymer the PZT particles will probably ?ll the pores at low particle concentrations, This will lead to small microscopic agglomerates within the pores that can lead to an overall lower dispersion, higher effective particle sizes, and, therefore, higher n values [22]. 4.3 Dynamical–mechanical response 4.3.1 Temperature behavior The effect of the inclusion of ceramic particles into the PVDF matrix may have in?uence on the polymeric chain dynamics within the composite structure. A suitable method to evaluate the molecular mobility and microscopic viscoelastic behavior in polymer systems is by employing the dynamical mechanical analysis—DMA. Figure 8 shows the dependence of the storage modulus (E ) and loss factor (tan δ) at 1 Hz for the α-PVDF/PZT composite with 40% of 0.84 ?m PZT.

By mechanical measurements, two main relaxations are detected in both samples. In the low-temperature region a process is found with a maximum at ca. ?40°C assigned to the segmental motions of the amorphous regions and usually labeled by β or αa [23, 25]. The dielectric relaxation spectroscopy study (Fig. 2) for the same samples reveals that the central relaxation time of these depends upon the temperature according to the Vogel–Tammann–Fulcher equation, as it corresponds to a cooperative relaxation assigned to the dynamic glass transition in amorphous and other semicrystalline polymers. When comparing the effect of ceramic particles on the polymeric matrix, the pure α-PVDF samples show higher peak loss than the composite sample, being for the composites broader and occurring at slightly lower temperature (? ?42°C) than the one found for the pure polymer = (? ?38°C). This can be ascribed to the less restricted mo= bility of the chains for the α-PVDF. The inclusion of PZT particles on the polymer affects the dynamic of the relaxation, as indicated by the temperature shift of the tan(δ) peak. In pure PVDF samples, the chains in the amorphous samples are relatively free to rotate helping neighbor crystallites to minimize the overall energy of the sample. With the inclusion of ceramic particles, the movement of the chains are somewhat frozen reducing the intensity of the cooperative motions within the amorphous phase. The interphase between polymer and PZT particles may also contribute to the decrease of the macroscopic dissipation of the mechanical energy, decreasing the tan(δ). Above 30°C a new relaxation process emerges in both samples (Fig. 8) that in contrast with the β-relaxation is badly de?ned in the tan(δ) plot. This process labelled α or αa is associated with motions within the crystalline fraction and was also found in a variety of other semicrystalline polymers like polyethylene, poly(methylene oxide), or poly(methylene oxide), β-PVDF, among others [23, 26– 28] and its origin should be similar to the one observed in PVDF. This relaxation is not observed in the dielectric experiments due to the increase of the conductivity for temperatures above the room temperature. At low temperatures, higher values of the storage modulus are found for the α-PVDF samples. However, after the β-relaxation the E becomes higher for the composite samples, it seems that the increase of the stiffness takes place during the glass transition. In this context it should be noticed that the values of E are of same order of magnitude as the elastic modulus found in quasistatic mechanical experiments [14]. 4.3.2 Concentration behavior Figure 9 shows the behavior of the storage modulus for α-PVDF with different amounts of PZT particles.


S. Firmino Mendes et al.

As expected, the storage modulus increases with the increase of the PZT concentration but this increase is more pronounced, in terms of maximum value, for the sample with 2.35 ?m particle size. The β-PVDF/PZT has a similar behavior as the one described for the α-PVDF/PZT composites.

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5 Conclusions Thin and highly ?exible ?lms of PVDF/PZT composites with PVDF in the α- and β-phase have been produced by solution casting of PVDF with DMA. The inclusion of ceramic particles does not affect the PVDF crystalline phase, the processing conditions being the main responsible for the appearance of the α- or β-phase. The spherulitic structure of the pure α-PVDF is destroyed for the higher volume fraction of PZT. The same occurs with the characteristic porosity of the β-phase material. The dielectric properties of the composites are mainly affected by the amount of the ceramic particles. The ε value increases with increasing volume fraction of the PZT particles. The polymeric crystalline phase and the average size of the particles play a minor role in the dielectric response of the samples. The increase of the dielectric constant is better described by models that take into account polymer–ceramic interaction. The temperature behaviour of the dielectric response is affected both the low-temperature relaxation and the high-temperature conductivity. The polymer–ceramic interface plays the major role in the aforementioned effects. The introduction of ceramic ?ller also affects the mechanical response. DMA results reveal the same two main relaxations in the composites samples as in the pure polymers: A low-temperature process with maximum at ca. ?40°C associated to the Tg of the polymer (β-relaxation) and the α-relaxation at temperatures above 30°C. At room temperature the storage modulus increases with increasing the PZT concentration.
Acknowledgements The authors thank the Portuguese Foundation for Science and Technology (FCT) Grant POCI/CTM/59425/2004, PTDC/CTM/69316/2006, FAPESP and CNPq for ?nancial aid. V. Sencadas and S. Firmino Mendes thank to FCT grants SFRH/BD/16543/ 2004 and SFRH/BD/22506/2005, respectively.

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