# Microwave Dielectric Properties of CCTO/PVA Composites

Authors: M. P. F. Graça; K. D. A. Sabóia; F. Amaral; L. C. Costa
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

The CaCu3Ti4O12 (CCTO) ceramic powder was inserted in the polyvinyl alcohol (PVA) polymeric matrix, with an increasing weight fraction of the filler, to form a flexible and high dielectric constant composite at the GHz region. The structural characterization of the samples was performed using X-ray diffraction and scanning electron microscopy (SEM). The complex permittivity was calculated by the small perturbation theory using two resonant cavities (2.7 GHz and 5.0 GHz). Several classical models (Maxwell Garnett, Lichtenecker, effective medium theory (EMT), and Yamada) were used to fit the real part of the complex permittivity of the composite as a function of the weight fraction of CCTO powder inserted in the PVA matrix. The best predictions for the dielectric behavior of these samples were obtained with the EMT and Yamada models.


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## Body

## 1. Introduction

Materials with excellent dielectric properties, such as a high-dielectric constant, low dissipation factor, and good stability over a broad frequency and temperature ranges, are required for some of modern electronic applications. In the last few years, it has emerged an increasing interest in size reduction and performance enhancement of embedded passive components, especially for embedded capacitors [1–3]. Materials for such kind of applications must present (beyond the already mentioned properties) good dielectric and thermal stability over a broad frequency and temperature ranges. Furthermore, the final piece should be manufactured in a simple way, with low production costs. To achieve this goal, many trials were performed with ceramic-polymer composites with high-dielectric constant [4–7].Generally, ceramics with high-dielectric constant values are very promising for capacitive applications in microelectronics and microwave devices (like dielectric resonators for cell mobile phones, for example) where miniaturization is crucial. However, it is well known that, for some applications, they are too brittle which becomes a critical factor. On the contrary, polymers that have normally lower dielectric constant, but present a much lower dielectric loss, are flexible, easy to process, and traditionally used in low-leakage capacitors. The association of high-dielectric constant ceramics with a polymer results in composites with acceptable dielectric constant and loss factor values, with lower dependence on frequency and temperature and, simultaneously, more flexible than ceramics [5–7].In this work, the polyvinyl alcohol (PVA) was used as a polymeric matrix, and CaCu3Ti4O12 (CCTO) ceramic particles were used as a filler. PVA is a water-soluble polymer widely applied in adhesives, sealants, coatings, paints, plastics, textiles, etc. It is also a polymer of great interest because of its characteristics, for various pharmaceutical and biomedical applications. PVA is produced by polymerization of vinyl acetate to polyvinyl acetate (PVAc), followed by hydrolysis of PVAc to PVA. Because the hydrolysis reaction does not go to completion, the final result of the polymerization process is a copolymer of PVA and PVAc. The PVA is normally supplied in powder form, and several grades are available with varying viscosity and solubility characteristics [8]. Besides the simplicity associated with the PVA synthesis process, we have chosen this polymer matrix because of its high thermal and chemical stabilities and nontoxicity. PVA also presents a high-dielectric strength and good charge storage capacity, which makes it usable as the polymer matrix in composite-based electronic components [9, 10].On the contrary, CaCu3Ti4O12 (CCTO) is a known oxide of the ACu3M4O12 family. Subramanian et al. have been the first to report the exceptional dielectric properties of CCTO [11], and since then, a significant effort has been devoted to understand the polarization mechanisms that justify the colossal dielectric constant (ε′ > 105) observed for poly- [12, 13] and single-crystalline ceramics [14]. The CCTO is a perovskite-like compound that, depending on the synthesis and sintering process, can present a dielectric constant (at 1 kHz and room temperature) as high as 105 and such dielectric properties are almost temperature- and frequency-independent for large ranges [15–17]. The CCTO has a high potential for technological applications, like memory devices based on capacitive components [18].Many CCTO/polymer composites have been investigated in the last years [6, 19, 20]. Some of them, CCTO/epoxy and CCTO/polyvinylidene fluoride, for instance, are very promising to be used as new embedded capacitors [19, 21–23]. The dielectric properties of such composites are, however, very dependent on temperature, and the dissipation factor is high. Besides, their preparation process is complex and harsh thermal environments are necessary to improve their thermal properties.Rarely the dielectric response of CCTO/polymers at the microwave frequency region has been reported. Considering this lack, this paper is focused on the development of a new kind of CCTO/polymer composite prepared by a simple method and with desirable dielectric properties, particularly at the microwave frequency region, such as a high-dielectric constant and low dissipation factor. The complex permittivity of the composites was calculated by the small perturbation theory using two resonant cavities, at 2.7 GHz and 5.0 GHz. Several classical models (Maxwell Garnett, Lichtenecker, effective medium theory (EMT), and Yamada) were used to fit the real part of the complex permittivity of the composite as a function of the weight of CCTO powder inserted in the PVA matrix.


## 2. Experimental Methods

### 2.1. Sample Preparation

The CCTO powder was prepared by the solid-state method using stoichiometric quantities of calcium carbonate (CaCO3) (Aldrich, 99%), titanium oxide (TiO2) (Aldrich, 99%), and copper (II) oxide (CuO) (Merck). The powders were mixed in a Fritsch 7.0 planetary mill for 30 min at 370 rpm. Milling was performed in agate vials and balls, under air, with a powder/balls weight fraction of 1 : 9. Therefore, the milling was used to guarantee the homogeneity of the powder. Then, the mixed powder was submitted to calcination in air at about 1,320 K for 24 h [24, 25]. The PVA (polyvinyl alcohol [-CH2CHOH-]n, from Merck) flakes were milled in a Fritsch 7.0 planetary mill to obtain a powder with granulometry lower than 200 µm. The X-ray analysis confirmed the presence of CCTO as the major phase. The CCTO powder was added to PVA, to obtain composites with weight fraction between 0 and 70% to study the dielectric response in the microwave region. The mix of CCTO and PVA was milled for 100 min, and the resulting material was uniaxially pressed into small cylinders, with 15 mm in height and 2 mm in diameter, applying 4.0 MPa during 20 min. These cylindrical samples were submitted to a heat treatment of about 420 K for two hours.Composites with a weight fraction higher than 70% produced brittle samples; thereafter, their use as an electronic component would be compromised. We also point out that the preparation method used in this work to produce the CCTO/PVA composites presents some advantages compared to the wet techniques. In particular, the maximum weight fraction that is admitted for CCTO/PVA composites prepared by the wet techniques is about 30%, which, along with a more complex procedure, makes our method suitable for future industrial applications [26, 27].The adopted nomenclature to point the weight fraction of the composites is CCTO(x), where x stands for the percentage of CCTO in the sample. For instance, CCTO(30) represents a sample with 70% (weight) of PVA and 30% (weight) of CCTO.


### 2.2. Structural and Morphological Characterization

The structure of the obtained samples was examined by X-ray diffraction using a X’Pert MPD Philips diffractometer (CuKα radiation, λ = 1.54056 Å) at 40 kV, and 30 mA, with a curved graphite monochromator, an automatic divergence slit, a progressive receiving slit, and a flat plane sample holder in a Bragg–Brentano parafocusing configuration with a step of 0.04° in 1 s, in the 2θ angle range of 10–60°. The samples morphology was characterized by scanning electron microscopy (SEM) using a Hitachi S4100. To perform this analysis, all the samples were covered with carbon.


### 2.3. Dielectric Measurements

To study the dielectric response of the composites in the high-frequency region, we used the resonant cavity method. The measurement of the complex permittivity was performed using two resonant cavities (2.7 GHz and 5.0 GHz) [28]. When the sample is introduced inside the cavity, a perturbation of the electromagnetic field is induced. As a consequence, there is a change in the transmission in the cavity, shifting the resonance frequency, and degrading the quality factor. The shift in the cavity resonant frequency, Δf (Figure 1), is related to the real part of the complex permittivity, ε′, while the change on the inverse of the quality factor of the cavity, Δ1/Q, is related to the imaginary part of the complex permittivity, ε″. It is possible to obtain a simple expression when we consider only the first-order perturbation in the electric field caused by the sample [29]:(1)Δff0+iΔ12Q=ε0ε∗−1∫VsEi∗E0dV∫Vε0E02dV,where f0 is the resonance frequency of the cavity, ε∗=ε′−iε″ is the complex permittivity of the material, and Ei and E0 are the electric fields inside and outside the material, respectively. The integration is performed in the volume of the sample, VS, and in the volume of the cavity, V. Splitting the real and imaginary parts, we can obtain the expressions for ε′ and ε″:(2)ε′=KΔff0VVS+1,(3)ε″=K2Δ1QVVS,where K is a constant related to the depolarization factor, which depends upon the geometric parameters. This parameter can be determined using a sample of known dielectric constant. In our case, we used a polytetrafluorethylene (PTFE) sample with the same size and shape of the studied samples. In these measurements, were used rectangular cavities operating in the TE1,0,5 and TE1,0,11 modes with the resonant frequencies of 2.7 GHz and 5.0 GHz, respectively. The transmission of the cavities was measured using a HP 8753D Network Analyzer, at room temperature.Figure 1
Transmission of the cavity with and without PTFE samples, showing the two resonances separated by∆f.


## 2.1. Sample Preparation

The CCTO powder was prepared by the solid-state method using stoichiometric quantities of calcium carbonate (CaCO3) (Aldrich, 99%), titanium oxide (TiO2) (Aldrich, 99%), and copper (II) oxide (CuO) (Merck). The powders were mixed in a Fritsch 7.0 planetary mill for 30 min at 370 rpm. Milling was performed in agate vials and balls, under air, with a powder/balls weight fraction of 1 : 9. Therefore, the milling was used to guarantee the homogeneity of the powder. Then, the mixed powder was submitted to calcination in air at about 1,320 K for 24 h [24, 25]. The PVA (polyvinyl alcohol [-CH2CHOH-]n, from Merck) flakes were milled in a Fritsch 7.0 planetary mill to obtain a powder with granulometry lower than 200 µm. The X-ray analysis confirmed the presence of CCTO as the major phase. The CCTO powder was added to PVA, to obtain composites with weight fraction between 0 and 70% to study the dielectric response in the microwave region. The mix of CCTO and PVA was milled for 100 min, and the resulting material was uniaxially pressed into small cylinders, with 15 mm in height and 2 mm in diameter, applying 4.0 MPa during 20 min. These cylindrical samples were submitted to a heat treatment of about 420 K for two hours.Composites with a weight fraction higher than 70% produced brittle samples; thereafter, their use as an electronic component would be compromised. We also point out that the preparation method used in this work to produce the CCTO/PVA composites presents some advantages compared to the wet techniques. In particular, the maximum weight fraction that is admitted for CCTO/PVA composites prepared by the wet techniques is about 30%, which, along with a more complex procedure, makes our method suitable for future industrial applications [26, 27].The adopted nomenclature to point the weight fraction of the composites is CCTO(x), where x stands for the percentage of CCTO in the sample. For instance, CCTO(30) represents a sample with 70% (weight) of PVA and 30% (weight) of CCTO.


## 2.2. Structural and Morphological Characterization

The structure of the obtained samples was examined by X-ray diffraction using a X’Pert MPD Philips diffractometer (CuKα radiation, λ = 1.54056 Å) at 40 kV, and 30 mA, with a curved graphite monochromator, an automatic divergence slit, a progressive receiving slit, and a flat plane sample holder in a Bragg–Brentano parafocusing configuration with a step of 0.04° in 1 s, in the 2θ angle range of 10–60°. The samples morphology was characterized by scanning electron microscopy (SEM) using a Hitachi S4100. To perform this analysis, all the samples were covered with carbon.


## 2.3. Dielectric Measurements

To study the dielectric response of the composites in the high-frequency region, we used the resonant cavity method. The measurement of the complex permittivity was performed using two resonant cavities (2.7 GHz and 5.0 GHz) [28]. When the sample is introduced inside the cavity, a perturbation of the electromagnetic field is induced. As a consequence, there is a change in the transmission in the cavity, shifting the resonance frequency, and degrading the quality factor. The shift in the cavity resonant frequency, Δf (Figure 1), is related to the real part of the complex permittivity, ε′, while the change on the inverse of the quality factor of the cavity, Δ1/Q, is related to the imaginary part of the complex permittivity, ε″. It is possible to obtain a simple expression when we consider only the first-order perturbation in the electric field caused by the sample [29]:(1)Δff0+iΔ12Q=ε0ε∗−1∫VsEi∗E0dV∫Vε0E02dV,where f0 is the resonance frequency of the cavity, ε∗=ε′−iε″ is the complex permittivity of the material, and Ei and E0 are the electric fields inside and outside the material, respectively. The integration is performed in the volume of the sample, VS, and in the volume of the cavity, V. Splitting the real and imaginary parts, we can obtain the expressions for ε′ and ε″:(2)ε′=KΔff0VVS+1,(3)ε″=K2Δ1QVVS,where K is a constant related to the depolarization factor, which depends upon the geometric parameters. This parameter can be determined using a sample of known dielectric constant. In our case, we used a polytetrafluorethylene (PTFE) sample with the same size and shape of the studied samples. In these measurements, were used rectangular cavities operating in the TE1,0,5 and TE1,0,11 modes with the resonant frequencies of 2.7 GHz and 5.0 GHz, respectively. The transmission of the cavities was measured using a HP 8753D Network Analyzer, at room temperature.Figure 1
Transmission of the cavity with and without PTFE samples, showing the two resonances separated by∆f.


## 3. Results and Discussion

### 3.1. X-Ray Analysis

The XRD patterns were obtained at room temperature (300 K) by step scanning using powdered samples. Figure2 shows the XRD pattern of the base samples (CCTO and PVA) and of the CCTO(x) for x = 30 and x = 50. The pattern obtained from the database of Inorganic Crystal Structures Database (ICSD) confirms the presence of CCTO as a major phase, presenting a cubic structure, with space group 1 m–3 m and space group number 229. Using Celref program [30], the lattice parameters of the CCTO powders were obtained: a = b = c = 7.3998 ± 0.0027 Å and α = β = γ = 90.00°, which is in accordance with the ICSD data of CCTO (a = 7.3930 Å and α = β = γ = 90.0000°). From the patterns of the base samples, we could see in Figure 2 that the patterns of the samples with x = 30 and x = 50, for example, are formed by peaks that can only be associated with PVA and CCTO. Although it is not presented here, the samples with different values of x show the same pattern. This result was already expected, once the temperature that we used for the heat treatment of the cylindrical samples is too low to degrade the polymer or to initiate any chemical reaction between the CCTO and the polymer.Figure 2
XRD patterns of the CCTO, PVA, and CCTO(x) for x = 50 and 30.


### 3.2. SEM Analysis

Figure3 shows the micrographs of some of the prepared composites. In Figure 3(a), we present the micrograph of the PVA sample. From the micrograph of the surface of PVA polymer sample, we can identify large polymer platelets. Between these structures, it is possible to identify many holes uniformly distributed throughout the sample. Figure 3(b) shows the micrograph of the CCTO particles. From this micrograph, it is possible to assume that the CCTO grains have dimensions ranging between 3 μm and 15 μm, presenting a spherical-like shape.Figure 3
SEM micrographs of (a) PVA sample (100x), (b) CCTO powders (2000x), (c) CCTO(20) (100x), (d) CCTO(50) (100x), (e) CCTO(20) (1000x), and (f) CCTO(50) (1000x).Figure3(c) shows the micrograph of the CCTO(20) sample, and Figure 3(d) shows the micrograph of the CCTO(50) sample, both with an amplification of 100 times. From the analysis of Figures 3(c) and 3(d), we can point that the porosity is low, particularly for the higher CCTO percentage (CCTO(50)). Combining these micrographs with those with higher amplification (x1k), we can state that, in both cases, the polymeric phase completely enfolds the ceramic particles, which means that a good affinity between these two phases is expected. The polymer is responsible for the aggregation of the ceramic powder and for the stiffness of the final composite, keeping the piece with enough mechanical strength for technological applications.


### 3.3. Dielectric Analysis

Figure4 presents the signal transmission along the 2.7 GHz resonant cavity for the following samples: PVA, CCTO(x) (for x = 10, 20, 30, 40), PTFE, and empty cavity. The observed curves of the transmission for the samples with x = 50, 60, and 70 are very close to the values found for x = 40. These are not presented to avoid overlapping of the curves. Increasing the weight fraction of CCTO powder of the composite implies a larger perturbation in the electromagnetic field configuration, leading to a frequency shift to the lower frequencies (red shift) and a pronounced attenuation of the intensity of the transmission signal.Figure 4
Transmission of the 2.7 GHz resonant cavity for PVA, CCTO(x) (for x = 10, 20, 30, 40), PTFE, and empty cavity.Figure5 shows the dielectric constant, as a function of the weight fraction of CCTO in the composites, for 2.7 GHz and 5.0 GHz cavities, measured at room temperature. It also shows the imaginary part of the complex permittivity (εʺ) as a function of the weight fraction of CCTO for the 5.0 GHz cavity. The values of εʺ in the cavity of 2.7 GHz were the same for all the samples which means that εʺ is too low to be measured by this method. As expected, the dielectric constant (ε′) increases with the weight fraction of CCTO, for each of the analyzed frequencies, and a similar behavior is observed for εʺ. The real part of the complex permittivity for the pure PVA samples was 5.5 at 2.7 GHz and 5.3 at 5.0 GHz (and εʺ = 0.11). For the sample CCTO(10), it was measured 7.4 at 2.7 GHz cavity and 6.7 at 5.0 GHZ (εʺ = 0.11). The dielectric constants for the sample CCTO(70) were 17.4 at 2.7 GHz and 16.2 at 5.0 GHZ (εʺ = 0.31).Figure 5
Real and imaginary parts of complex permittivity measured in 2.7 GHz and 5 GHz resonant cavity, for different weight fractions of CCTO.Several models were used in order to predict the dielectric constant of the composite material. Figure6 shows the experimental dielectric constant at 5.0 GHz, and, for comparison, the dielectric constants predicted by the Maxwell Garnett, Lichtenecker, EMT, and Yamada models are also included. The Maxwell Garnett [31] and the Lichtenecker [32, 33] models describe the dielectric property of a biphasic dielectric mixture comprising spherical crystallites, with high-dielectric constant, dispersed in a matrix of low-dielectric constant. According to the Maxwell Garnett model, the effective dielectric constant of the composite is given by(4)ε′=ε11+3Vfβ1−Vfβ,β=ε2−ε1ε2+2ε1,where ε1 and ε2 are the permittivities of the polymer matrix and of the CCTO, respectively. Vf is the volume fraction of the ceramic fillers. The Lichtenecker model is expressed by(5)lnε′=Vflnε2+1−Vflnε1.Figure 6
Real part of complex permittivity of the composite samples, as a function of the weight fraction of CCTO, obtained for the 5 GHz cavity, and respective fitting using four classic mixing models.From Figure6, one can see that the predicted values for ε′, for both Maxwell Garnett and Lichtenecker models, deviate too much from that of the measured experimental values, only correctly fitting for the samples with lower (10%) and higher (70%) weight fractions of CCTO. The micrograph images (Figure 3(b)) show that the CCTO grains do not present a perfect spherical geometry, and the discrepancy between experimental and predicted values could be directly related to this fact.Since CCTO particles dispersed in the matrix have no spherical shape, as could be evidenced by SEM, the models that take into account different morphologies for the particles are more suitable. One example of this is the effective medium theory (EMT) model. The real part of the dielectric constant for the composite in the EMT model is given as follows [34]:(6)ε′=ε11+Vfε2−ε1ε1−n1−Vfε2−ε1,where n is a ceramic morphology fitting factor. Small values of n indicate the filler particles have a shape nearly spherical, while high values of n indicate that the shape of the particles is very irregular. The better value for the shape parameter obtained for the experimental results was n = 0.1. Although this model is suitable for particles with dimensions less than 1 μm, Figure 6 shows a good approximation between the values predicted by the EMT model and the experimental data obtained for the composites with a weight fraction up to 50%. However, for higher weight fractions, the model begins to deviate, which should be related to an increasing aggregation of the CCTO particles as the polymer matrix becomes less significant.From Figure3(b), it can be seen that the CCTO grain morphology and granulometry are not homogenous for all the particle distribution, presenting differences in size and shape. In addition, from Figure 3(d), one can note that some irregular dispersion of the CCTO particles in the polymeric matrix is present. Thereby, another model was used to try a better agreement with the experimental curve: the Yamada model. The Yamada model [35] predicts the following values for real part of the dielectric constant of a biphasic composite:(7)ε′=ε11+γVfε2−ε1γε1−1−Vfε2−ε1,where γ is also a fitting factor associated with the ceramic grain morphology. The best fitting was obtained for γ = 14.309. Globally, the fitting performed with the EMT model presents a better approximation to the experimental data. However, both Yamada and EMT models fail to predict the dielectric behavior of these CCTO/PVA composites for weight fractions higher than 50%. Once again, this discrepancy should be related to a deficient dispersion of the minor phase.


## 3.1. X-Ray Analysis

The XRD patterns were obtained at room temperature (300 K) by step scanning using powdered samples. Figure2 shows the XRD pattern of the base samples (CCTO and PVA) and of the CCTO(x) for x = 30 and x = 50. The pattern obtained from the database of Inorganic Crystal Structures Database (ICSD) confirms the presence of CCTO as a major phase, presenting a cubic structure, with space group 1 m–3 m and space group number 229. Using Celref program [30], the lattice parameters of the CCTO powders were obtained: a = b = c = 7.3998 ± 0.0027 Å and α = β = γ = 90.00°, which is in accordance with the ICSD data of CCTO (a = 7.3930 Å and α = β = γ = 90.0000°). From the patterns of the base samples, we could see in Figure 2 that the patterns of the samples with x = 30 and x = 50, for example, are formed by peaks that can only be associated with PVA and CCTO. Although it is not presented here, the samples with different values of x show the same pattern. This result was already expected, once the temperature that we used for the heat treatment of the cylindrical samples is too low to degrade the polymer or to initiate any chemical reaction between the CCTO and the polymer.Figure 2
XRD patterns of the CCTO, PVA, and CCTO(x) for x = 50 and 30.


## 3.2. SEM Analysis

Figure3 shows the micrographs of some of the prepared composites. In Figure 3(a), we present the micrograph of the PVA sample. From the micrograph of the surface of PVA polymer sample, we can identify large polymer platelets. Between these structures, it is possible to identify many holes uniformly distributed throughout the sample. Figure 3(b) shows the micrograph of the CCTO particles. From this micrograph, it is possible to assume that the CCTO grains have dimensions ranging between 3 μm and 15 μm, presenting a spherical-like shape.Figure 3
SEM micrographs of (a) PVA sample (100x), (b) CCTO powders (2000x), (c) CCTO(20) (100x), (d) CCTO(50) (100x), (e) CCTO(20) (1000x), and (f) CCTO(50) (1000x).Figure3(c) shows the micrograph of the CCTO(20) sample, and Figure 3(d) shows the micrograph of the CCTO(50) sample, both with an amplification of 100 times. From the analysis of Figures 3(c) and 3(d), we can point that the porosity is low, particularly for the higher CCTO percentage (CCTO(50)). Combining these micrographs with those with higher amplification (x1k), we can state that, in both cases, the polymeric phase completely enfolds the ceramic particles, which means that a good affinity between these two phases is expected. The polymer is responsible for the aggregation of the ceramic powder and for the stiffness of the final composite, keeping the piece with enough mechanical strength for technological applications.


## 3.3. Dielectric Analysis

Figure4 presents the signal transmission along the 2.7 GHz resonant cavity for the following samples: PVA, CCTO(x) (for x = 10, 20, 30, 40), PTFE, and empty cavity. The observed curves of the transmission for the samples with x = 50, 60, and 70 are very close to the values found for x = 40. These are not presented to avoid overlapping of the curves. Increasing the weight fraction of CCTO powder of the composite implies a larger perturbation in the electromagnetic field configuration, leading to a frequency shift to the lower frequencies (red shift) and a pronounced attenuation of the intensity of the transmission signal.Figure 4
Transmission of the 2.7 GHz resonant cavity for PVA, CCTO(x) (for x = 10, 20, 30, 40), PTFE, and empty cavity.Figure5 shows the dielectric constant, as a function of the weight fraction of CCTO in the composites, for 2.7 GHz and 5.0 GHz cavities, measured at room temperature. It also shows the imaginary part of the complex permittivity (εʺ) as a function of the weight fraction of CCTO for the 5.0 GHz cavity. The values of εʺ in the cavity of 2.7 GHz were the same for all the samples which means that εʺ is too low to be measured by this method. As expected, the dielectric constant (ε′) increases with the weight fraction of CCTO, for each of the analyzed frequencies, and a similar behavior is observed for εʺ. The real part of the complex permittivity for the pure PVA samples was 5.5 at 2.7 GHz and 5.3 at 5.0 GHz (and εʺ = 0.11). For the sample CCTO(10), it was measured 7.4 at 2.7 GHz cavity and 6.7 at 5.0 GHZ (εʺ = 0.11). The dielectric constants for the sample CCTO(70) were 17.4 at 2.7 GHz and 16.2 at 5.0 GHZ (εʺ = 0.31).Figure 5
Real and imaginary parts of complex permittivity measured in 2.7 GHz and 5 GHz resonant cavity, for different weight fractions of CCTO.Several models were used in order to predict the dielectric constant of the composite material. Figure6 shows the experimental dielectric constant at 5.0 GHz, and, for comparison, the dielectric constants predicted by the Maxwell Garnett, Lichtenecker, EMT, and Yamada models are also included. The Maxwell Garnett [31] and the Lichtenecker [32, 33] models describe the dielectric property of a biphasic dielectric mixture comprising spherical crystallites, with high-dielectric constant, dispersed in a matrix of low-dielectric constant. According to the Maxwell Garnett model, the effective dielectric constant of the composite is given by(4)ε′=ε11+3Vfβ1−Vfβ,β=ε2−ε1ε2+2ε1,where ε1 and ε2 are the permittivities of the polymer matrix and of the CCTO, respectively. Vf is the volume fraction of the ceramic fillers. The Lichtenecker model is expressed by(5)lnε′=Vflnε2+1−Vflnε1.Figure 6
Real part of complex permittivity of the composite samples, as a function of the weight fraction of CCTO, obtained for the 5 GHz cavity, and respective fitting using four classic mixing models.From Figure6, one can see that the predicted values for ε′, for both Maxwell Garnett and Lichtenecker models, deviate too much from that of the measured experimental values, only correctly fitting for the samples with lower (10%) and higher (70%) weight fractions of CCTO. The micrograph images (Figure 3(b)) show that the CCTO grains do not present a perfect spherical geometry, and the discrepancy between experimental and predicted values could be directly related to this fact.Since CCTO particles dispersed in the matrix have no spherical shape, as could be evidenced by SEM, the models that take into account different morphologies for the particles are more suitable. One example of this is the effective medium theory (EMT) model. The real part of the dielectric constant for the composite in the EMT model is given as follows [34]:(6)ε′=ε11+Vfε2−ε1ε1−n1−Vfε2−ε1,where n is a ceramic morphology fitting factor. Small values of n indicate the filler particles have a shape nearly spherical, while high values of n indicate that the shape of the particles is very irregular. The better value for the shape parameter obtained for the experimental results was n = 0.1. Although this model is suitable for particles with dimensions less than 1 μm, Figure 6 shows a good approximation between the values predicted by the EMT model and the experimental data obtained for the composites with a weight fraction up to 50%. However, for higher weight fractions, the model begins to deviate, which should be related to an increasing aggregation of the CCTO particles as the polymer matrix becomes less significant.From Figure3(b), it can be seen that the CCTO grain morphology and granulometry are not homogenous for all the particle distribution, presenting differences in size and shape. In addition, from Figure 3(d), one can note that some irregular dispersion of the CCTO particles in the polymeric matrix is present. Thereby, another model was used to try a better agreement with the experimental curve: the Yamada model. The Yamada model [35] predicts the following values for real part of the dielectric constant of a biphasic composite:(7)ε′=ε11+γVfε2−ε1γε1−1−Vfε2−ε1,where γ is also a fitting factor associated with the ceramic grain morphology. The best fitting was obtained for γ = 14.309. Globally, the fitting performed with the EMT model presents a better approximation to the experimental data. However, both Yamada and EMT models fail to predict the dielectric behavior of these CCTO/PVA composites for weight fractions higher than 50%. Once again, this discrepancy should be related to a deficient dispersion of the minor phase.


## 4. Conclusions

Two resonant cavities with 2.7 GHz and 5.0 GHz resonant frequencies were used to measure the complex permittivity of polymer matrix composites, prepared by the dispersion of CCTO (CaCu3Ti4O12) powders, prepared by the solid-state method, in a polyvinyl alcohol (PVA) matrix. Different weight fractions of the filler were used to form a flexible and high-dielectric constant composite at GHz region. PVA was chosen as the polymeric matrix because of its high thermal and chemical stability, nontoxicity, and for presenting a high-dielectric strength and good charge storage capacity, which makes it usable as the polymer matrix in composite-based electronic components. Within this study, we were able to prepare, by a simple method, a ceramic/polymer composite with desirable dielectric properties, particularly at the microwave frequency region, such as a high-dielectric constant and low dissipation factor. As expected, the dielectric constant increased with the weight fraction of CCTO for both analyzed frequencies, and a similar behavior is observed for εʺ. In an attempt to predict the dielectric constant of the CCTO/PVA composites as a function of the weight fraction of the filler, several classical mixing models were used. This way, the EMT (with n = 0.1) and Yamada (with γ = 14.309) models were identified as the most suitable to fit the experimental data. Best fitting results, using EMT and Yamada models, were obtained for weight fractions lower than 50%. Both EMT and Yamada models are more associated with nonspherical shape particles dispersed in a matrix, a fact that could be evidenced by the SEM.



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*Source: 6067519-2018-12-02.xml*