Effects of Sub-Micro Sized BaTiO3 Blocking Particles and Ag-Deposited Nano-Sized BaTiO3 Hybrid Particles on Dielectric Properties of Poly(vinylidene-fluoride) Polymer

This work provided an alternative route to balance the significantly increased dielectric permittivity (ε′) and effectively retained tanδ using an effective two-step concept. Ag-deposited nano-sized BaTiO3 (Ag-nBT) hybrid particle was used as the first filler to increase the ε′ of the poly(vinylidene-fluoride) (PVDF) polymer via the strong interfacial polarization and a high permittivity of nBT and suppress the increased loss tangent (tanδ) owing to the discrete growth of Ag nanoparticles on the surface of nBT, preventing a continuous percolating path. The ε′ and tanδ values at 103 Hz of the Ag-nBT/PVDF composite with fAg-nBT~0.29 were 61.7 and 0.036. The sub-micron-sized BaTiO3 (μBT) particle was selected as the blocking particles to doubly reduce the tanδ with simultaneously enhanced ε′ due to the presence of the tetragonal BT phase. The μBT blocking particles can effectively further inhibit the formation of conducting network and hence further reducing tanδ. By incorporation of μBT clocking particles with fμBT = 0.2, the ε′ value of the Ag-nBT/PVDF-μBT composite (fAg-nBT = 0.30) can significantly increase to 161.4, while the tanδ was reduced to 0.026. Furthermore, the tanδ was lower than 0.09 in the temperature range of −60–150 °C due to the blocking effect of μBT particles.

In addition to dielectric oxides, metal nanoparticles and conductive carbons have widely been used as a filler in the PVDF and other polymer composites such as (AgNO3) (RCI Labscan, 99.8% purity). First, 5 g of AgNO3 was dissolved in 300 mL of ethylene glycol, and 5 g of nBT was added to the solution later. The mixture solution was stirred for 2 h at room temperature (RT). Secondly, the temperature increased to 140 °C and kept stirring for 25 min. Next, the mixture solution was centrifuged with ethanol to obtain the mixture powder. Finally, the mixture powder was dried in an oven at 100 °C for 24 h. A schematic figure of the synthesis of Ag-nBT hybrid particles is demonstrated in Figure 1.

Synthesis of Ag-nBT/PVDF-μBT Composites
The BT with a particle size of <1 μm (μBT) (Sigma-Aldrich) was used as blocking particles to prevent the formation of conducting network between Ag-nBT hybrid particles. Therefore, PVDF-μBT was considered a matrix in this composites system. A homemade ball-milling machine was used to mix the starting powders, consisting of two rotating horizontal axles and a rotating horizontal polyethylene jar that is partly filled with ZrO2 balls with 2.0 mm in diameter and particles to be mixed. The volume fraction ratio of ZrO2 balls to total starting powders and ethanol was 0.4:0.4. First, the PVDF and μBT particles with a volume fraction ratio of 0.8:0.2 were mixed by ball-milling method in ethanol for 3 h. The speed of rotation was ~150 rpm. Second, the mixture was dried at 100 °C for 24 h to remove ethanol. Next, the mixed PVDF-μBT powder was further mixed with Ag-nBT hybrid particles using a ball-milling method in ethanol. Then, ethanol was evaporated. Finally, the polymer composites powder of each volume fraction was molded by the hot-pressing method at 200 °C for 0.5 h. The nanocomposite disks with a thickness of ~0.6-1.0 mm and a diameter of ~12 mm were achieved.

Characterization Techniques
Transmission electron microscopy (Eindhoven, The Netherlands) (TEM, FEI, TEC-NAI G 2 20) was used to reveal the hybrid particles. X-ray diffractometry (Almelo, The Netherlands) (XRD, PANalytical, EMPYREAN) technique was used to examine the phase composition of the hybrid particles and composites. The microstructure of the polymer

Synthesis of Ag-nBT/PVDF-µBT Composites
The BT with a particle size of <1 µm (µBT) (Sigma-Aldrich) was used as blocking particles to prevent the formation of conducting network between Ag-nBT hybrid particles. Therefore, PVDF-µBT was considered a matrix in this composites system. A homemade ball-milling machine was used to mix the starting powders, consisting of two rotating horizontal axles and a rotating horizontal polyethylene jar that is partly filled with ZrO 2 balls with 2.0 mm in diameter and particles to be mixed. The volume fraction ratio of ZrO 2 balls to total starting powders and ethanol was 0.4:0.4. First, the PVDF and µBT particles with a volume fraction ratio of 0.8:0.2 were mixed by ball-milling method in ethanol for 3 h. The speed of rotation was~150 rpm. Second, the mixture was dried at 100 • C for 24 h to remove ethanol. Next, the mixed PVDF-µBT powder was further mixed with Ag-nBT hybrid particles using a ball-milling method in ethanol. Then, ethanol was evaporated. Finally, the polymer composites powder of each volume fraction was molded by the hot-pressing method at 200 • C for 0.5 h. The nanocomposite disks with a thickness of~0.6-1.0 mm and a diameter of~12 mm were achieved.

Characterization Techniques
Transmission electron microscopy (Eindhoven, The Netherlands) (TEM, FEI, TEC-NAI G 2 20) was used to reveal the hybrid particles. X-ray diffractometry (Almelo, The Netherlands) (XRD, PANalytical, EMPYREAN) technique was used to examine the phase composition of the hybrid particles and composites. The microstructure of the polymer composites was displayed using Field Emission Scanning Electron Microscopy (Hillsboro, OR, USA) (FESEM, FEI, Helios NanoLab G3 CX) with an energy dispersive X-ray spectrometer (EDS). Fourier transformed infrared spectroscopy (FTIR, Bruker, TENSOR27) was used to indicate the phase conformation of the polymer composites. Dielectric properties were measured at a frequency range of 10 2 -10 6 Hz, a temperature range of −60-150 • C and 500 mV of oscillation voltage using KEYSIGHT E4990A Impedance Analyzer (Santa Rosa, CA, USA). Figure 2 shows the XRD pattern of the µBT, nBT, and Ag-nBT hybrid particles, confirming the presence of BT and Ag phases. Both BT and Ag phases can be observed in the XRD pattern of Ag-nBT hybrid particles. Usually, the tetragonal phase structure of BT ceramics is observed below the curie temperature (~120 • C). As shown in inset (a), the characteristic peak at 2θ ≈ 45 • ((200) plane) of the nBT appears a single peak, indicating a cubic perovskite structure in the ABO 3 family for the nBT particles used [6,34]. On the other hand, double peaks at 2θ ≈ 45 • of the tetragonality structure were observed in the XRD pattern of µBT. It is expected that the ε value of the µBT particle is larger than that of the nBT owing to the ferroelectric phase in the µBT particle. The Ag diffraction planes (111), (200), (270), and (311) are located at 2θ around 38 • , 44 • , 65 • and 78 • , respectively [22,35]. The Ag-nBT hybrid particles have been successfully synthesized, and the phase structure of the nBT was unchanged. The inset (b) demonstrates the morphologies of the Ag-nBT hybrid particles, which were studied using the TEM technique. The TEM image shows the discretely deposited Ag particles on nBT surface. The particle sizes of the nBT and Ag nanoparticles are around 50-100 and <10 nm, respectively. composites was displayed using Field Emission Scanning Electron Microscopy (Hillsb OR, USA) (FESEM, FEI, Helios NanoLab G3 CX) with an energy dispersive X-ray s trometer (EDS). Fourier transformed infrared spectroscopy (FTIR, Bruker, TENSO was used to indicate the phase conformation of the polymer composites. Dielectric p erties were measured at a frequency range of 10 2 -10 6 Hz, a temperature range of −60 °C and 500 mV of oscillation voltage using KEYSIGHT E4990A Impedance Ana (Santa Rosa, CA, USA). Figure 2 shows the XRD pattern of the μBT, nBT, and Ag-nBT hybrid particles, firming the presence of BT and Ag phases. Both BT and Ag phases can be observed i XRD pattern of Ag-nBT hybrid particles. Usually, the tetragonal phase structure o ceramics is observed below the curie temperature (~120 °C). As shown in inset (a) characteristic peak at 2θ ≈ 45° ((200) plane) of the nBT appears a single peak, indicat cubic perovskite structure in the ABO3 family for the nBT particles used [6,34]. On other hand, double peaks at 2θ ≈ 45° of the tetragonality structure were observed in XRD pattern of μBT. It is expected that the ε′ value of the μBT particle is larger than of the nBT owing to the ferroelectric phase in the μBT particle. The Ag diffraction pl (111), (200), (270), and (311) are located at 2θ around 38°, 44°, 65° and 78°, respect [22,35]. The Ag-nBT hybrid particles have been successfully synthesized, and the p structure of the nBT was unchanged. The inset (b) demonstrates the morphologies o Ag-nBT hybrid particles, which were studied using the TEM technique. The TEM im shows the discretely deposited Ag particles on nBT surface. The particle sizes of the and Ag nanoparticles are around 50-100 and <10 nm, respectively.  ation of the µBT blocking particles disappeared. The µBT particles were well dispersed in the polymer matrix. As a result, the conducting network of Ag-nBT hybrid particles can be inhibited, which may lead to a reduction in tanδ values and conductivity of the polymer composites.

Results and Discussion
The FESEM technique was used to reveal the microstructure of the Ag-nBT/PVDF-μBT polymer composites. The outer surface of the composites was removed by focus ion, as shown in Figure 3a Figure  3c,d, respectively. showing the dispersion of μBT and Ag-nBT hybrid particles. The agglomeration of the μBT blocking particles disappeared. The μBT particles were well dispersed in the polymer matrix. As a result, the conducting network of Ag-nBT hybrid particles can be inhibited, which may lead to a reduction in tanδ values and conductivity of the polymer composites. The SEM-EDS elemental mapping technique was used to show the dispersion of fillers, especially for the Ag nanoparticles, in the polymer composites. Figure 4 shows the SEM-EDX elemental mapping of all elements in the (0.3)[Ag-nBT]/PVDF-(0.2)μBT composite. Barium (Ba), Titanium (Ti), and Oxygen (O), which are the elements of BT particles, were distributed throughout the PVDF matrix. Moreover, the elemental mapping of Ag nanoparticles was also revealed. There were some small clusters of Ag nanoparticles, which can be observed as a bright spot in the SEM-EDS mapping image of Ag. However, the clusters of Ag particles were not enough to create the conductive pathways. The Ag element disappeared in the μBT areas. The presence of all elements for BT and Ag particles confirmed that the PVDF matrix was filled with the Ag-nBT hybrid particles and μBT particles. In addition, Carbon (C) and Fluorine (F) represented the composition of the PVDF polymer. It is worth noting that for practical application in capacitors, the dielectric layer The SEM-EDS elemental mapping technique was used to show the dispersion of fillers, especially for the Ag nanoparticles, in the polymer composites. Figure 4 shows the SEM-EDX elemental mapping of all elements in the (0.3)[Ag-nBT]/PVDF-(0.2)µBT composite. Barium (Ba), Titanium (Ti), and Oxygen (O), which are the elements of BT particles, were distributed throughout the PVDF matrix. Moreover, the elemental mapping of Ag nanoparticles was also revealed. There were some small clusters of Ag nanoparticles, which can be observed as a bright spot in the SEM-EDS mapping image of Ag. However, the clusters of Ag particles were not enough to create the conductive pathways. The Ag element disappeared in the µBT areas. The presence of all elements for BT and Ag particles confirmed that the PVDF matrix was filled with the Ag-nBT hybrid particles and µBT particles. In addition, Carbon (C) and Fluorine (F) represented the composition of the PVDF polymer. It is worth noting that for practical application in capacitors, the dielectric layer was sandwiched by two metal electrodes. The electrode and dielectric layers are usually encapsulated by an insulating polymer to prevent the hydration of a dielectric layer. Furthermore, the perovskite-BT particles were embedded in the PVDF polymer matrix; thus, the effect of humidity on the dielectric properties of BT was double protected. was sandwiched by two metal electrodes. The electrode and dielectric layers are usually encapsulated by an insulating polymer to prevent the hydration of a dielectric layer. Furthermore, the perovskite-BT particles were embedded in the PVDF polymer matrix; thus, the effect of humidity on the dielectric properties of BT was double protected. The phase conformation of the PVDF matrix in the polymer composites was restudied again with FTIR spectroscopy. As displayed in Figure 5a, the α-phase located at wavenumber around 614, 766, 795, and 976 cm −1 [36][37][38]. Furthermore, the peak at wavenumber about 840 cm −1 was representative of both the γ-and β-phases [37,38]. The β-phase also appeared at wavenumber around 1279 cm −1 [36,37]. There were α-, γ-and β-phases in the PVDF polymer and polymer composites. As well known, the β-phase has the highest polarity among all phase conformation of PVDF [37]. The β-phase can affect the dielectric properties of the PVDF polymer composites. The Lambert-Beer equation was used to calculate the content of β-phase (F(β)), assuming that there are only α-and β-phases in the polymer composites [37]. The equation can be presented as follows, where Aα and Aβ represent the absorbance of α-, β-phases at wavenumber = 766 cm −1 and 840 cm −1 , respectively. Kα  The phase conformation of the PVDF matrix in the polymer composites was restudied again with FTIR spectroscopy. As displayed in Figure 5a, the α-phase located at wavenumber around 614, 766, 795, and 976 cm −1 [36][37][38]. Furthermore, the peak at wavenumber about 840 cm −1 was representative of both the γ-and β-phases [37,38]. The β-phase also appeared at wavenumber around 1279 cm −1 [36,37]. There were α-, γ-and β-phases in the PVDF polymer and polymer composites. As well known, the β-phase has the highest polarity among all phase conformation of PVDF [37]. The β-phase can affect the dielectric properties of the PVDF polymer composites. The Lambert-Beer equation was used to calculate the content of β-phase (F(β)), assuming that there are only α-and β-phases in the polymer composites [37]. The equation can be presented as follows, where A α and A β represent the absorbance of α-, β-phases at wavenumber = 766 cm −1 and 840 cm −1 , respectively. K α (6.1 × 10 4 cm 2 mol −1 ) is the absorbance coefficient of α-phase. and 52% for the polymer composites, respectively. The F(β) increased with increasing f Ag-nBT from 0.06 to 0.25, which was attributed to the negatively charged of filler induced the formation of β-phase (all trans, TTT) [37]. However, the β-phase conformation was inhibited in the case of f Ag-nBT = 0.3, leading to low value of F(β) [39].
(a) (b) nBT]/PVDF composite was slightly higher than those of the PVDF polymer and (0.2)μBT/PVDF composite over the measured frequency range, whereas the ε′ of the (0.29)[Ag-nBT]/PVDF composite was much larger. This result indicated that the ε′ of the PVDF polymer can be significantly increased by incorporating with Ag-nBT hybrid particles due to the strong interfacial polarization (i.e., Ag-nBT and Ag-PVDF interfaces) and a relatively high permittivity of nBT particles compared to that of the PVDF polymer.
Generally, the tanδ of PVDF polymer composites filled with conductive nanoparticles is largely increased as the filler loading increases. The suppressed tanδ in the creased by factors of 6 and 12 compared to that of the (0.2)µBT/PVDF composite and PVDF polymer, respectively, while the tanδ values of these three samples are nearly the same in value. This result indicated the essential role of Ag-nBT hybrid particles for increasing the dielectric response without any effect on the tanδ. The important role of the µBT blocking particles is to efficiently obstruct the conductive pathways with simultaneously increasing the ε due to the tetragonal ferroelectric phase of the µBT. Therefore, the µBT blocking particles were the key factor in low tanδ values of the Ag-nBT/PVDF-(0.2)µBT composites. Typically, polymer nanocomposites can provide a high tanδ values. This is because of high surface energy, which may contribute to the agglomeration of nanoparticles [13]. Therefore, the addition of µBT can also inhibit the agglomeration of the Ag-nBT hybrid particles. The ε and tanδ values are better than our previous work [32], which PVDF incorporated with the Ag-µBT hybrid particles and nBT blocking particles.
cles are 161 and 0.026, respectively. Obviously, the μBT blocking particles can further improve the dielectric properties of the (0.30)[Ag-nBT]/PVDF-(0.2)μBT composite, resulting in a further significantly increased ε′ with simultaneously reducing the tanδ to the initial value of the PVDF polymer. As shown in Figure 6a, the ε′ of the (0.30)[Ag-nBT]/PVDF-(0.2)μBT composite increased by factors of 6 and 12 compared to that of the (0.2)μBT/PVDF composite and PVDF polymer, respectively, while the tanδ values of these three samples are nearly the same in value. This result indicated the essential role of Ag-nBT hybrid particles for increasing the dielectric response without any effect on the tanδ. The important role of the μBT blocking particles is to efficiently obstruct the conductive pathways with simultaneously increasing the ε′ due to the tetragonal ferroelectric phase of the μBT. Therefore, the μBT blocking particles were the key factor in low tanδ values of the Ag-nBT/PVDF-(0.2)μBT composites. Typically, polymer nanocomposites can provide a high tanδ values. This is because of high surface energy, which may contribute to the agglomeration of nanoparticles [13]. Therefore, the addition of μBT can also inhibit the agglomeration of the Ag-nBT hybrid particles. The ε′ and tanδ values are better than our previous work [32], which PVDF incorporated with the Ag-μBT hybrid particles and nBT blocking particles. The frequency-dependence behavior of dielectric properties of the Ag-nBT/PVDF-(0.2)μBT composites with different fAg-nBT is displayed in Figure 7a. The ε′ increases with increasing fAg-nBT in the frequency range of 10 2 -10 6 Hz, which is attributed to the significantly increased interfacial polarization and the increase in a high-permittivity nBT phase. Moreover, the ε′ is nearly independent of the frequency. However, the ε′ drops at a frequency range of 10 6 Hz, which is noticeable at high fAg-nBT. The frequency-dependence behavior of the ε′ value in a high-frequency range is usually ascribed by the dielectric relaxation of the PVDF matrix. The dipole polarization relaxation of the PVDF matrix was prominent at this frequency range [6]. Figure 7b demonstrates the variation in the tanδ in the frequency of 10 2 -10 6 Hz. The low-frequency tanδ values of all composites are lower than 0.09. Notably, the tanδ value of the (0.30)[Ag-nBT]/PVDF-(0.2)μBT is lower than 0.1 over the measured frequency range. In a high-frequency range, the increased tanδ value is usually due to the dielectric relaxation of the PVDF matrix, corresponding to the decreased ε′ value at high frequencies. The frequency-dependence behavior of dielectric properties of the Ag-nBT/PVDF-(0.2)µBT composites with different f Ag-nBT is displayed in Figure 7a. The ε increases with increasing f Ag-nBT in the frequency range of 10 2 -10 6 Hz, which is attributed to the significantly increased interfacial polarization and the increase in a high-permittivity nBT phase. Moreover, the ε is nearly independent of the frequency. However, the ε drops at a frequency range of 10 6 Hz, which is noticeable at high f Ag-nBT . The frequency-dependence behavior of the ε value in a high-frequency range is usually ascribed by the dielectric relaxation of the PVDF matrix. The dipole polarization relaxation of the PVDF matrix was prominent at this frequency range [6]. Figure 7b demonstrates the variation in the tanδ in the frequency of 10 2 -10 6 Hz. The low-frequency tanδ values of all composites are lower than 0.09. Notably, the tanδ value of the (0.30)[Ag-nBT]/PVDF-(0.2)µBT is lower than 0.1 over the measured frequency range. In a high-frequency range, the increased tanδ value is usually due to the dielectric relaxation of the PVDF matrix, corresponding to the decreased ε value at high frequencies.
The effects of temperature on the dielectric properties of the Ag-nBT/PVDF-(0.2)µBT composites were also investigated. Figure 8a,b show the ε and tanδ values (at 10 3 Hz) of the Ag-nBT/PVDF-(0.2)µBT composites with various f Ag-nBT in the temperature range of −60-150 • C, respectively. The rapid increase in ε is observed when the temperature increased from −60 to 0 • C. Then, it slightly increased as the temperature increased from 0 to 150 • C. The rapid increase in ε in a low-temperature range correlates to the β relaxation of the PVDF polymer [22,40,41]. The β relaxation corresponds to the dipolar group motions and the glass transition [40,41]. Furthermore, the ε at high temperatures is dominant by the interfacial polarization and molecular motions of PVDF [22,41,42]. The relaxation peak Polymers 2021, 13, 3641 9 of 11 of tanδ in a low-temperature range is related to β relaxation, corresponding to the observed rapid change in the ε . The tanδ value increases with increasing the temperature. The tanδ value in a high-temperature range of the composites with high f Ag-nBT is lower than that of the composites with low f Ag-nBT , which is because the high fillers inhibited the movement of the PVDF chains, resulting in the lower tanδ [43]. The effects of temperature on the dielectric properties of the Ag-nBT/PVDF-(0.2)μBT composites were also investigated. Figure 8a,b show the ε′ and tanδ values (at 10 3 Hz) of the Ag-nBT/PVDF-(0.2)μBT composites with various fAg-nBT in the temperature range of −60-150 °C, respectively. The rapid increase in ε′ is observed when the temperature increased from −60 to 0 °C. Then, it slightly increased as the temperature increased from 0 to 150 °C. The rapid increase in ε′ in a low-temperature range correlates to the β relaxation of the PVDF polymer [22,40,41]. The β relaxation corresponds to the dipolar group motions and the glass transition [40,41]. Furthermore, the ε′ at high temperatures is dominant by the interfacial polarization and molecular motions of PVDF [22,41,42]. The relaxation peak of tanδ in a low-temperature range is related to β relaxation, corresponding to the observed rapid change in the ε′. The tanδ value increases with increasing the temperature. The tanδ value in a high-temperature range of the composites with high fAg-nBT is lower than that of the composites with low fAg-nBT, which is because the high fillers inhibited the movement of the PVDF chains, resulting in the lower tanδ [43].   The effects of temperature on the dielectric properties of the Ag-nBT/PVDF-(0.2)μBT composites were also investigated. Figure 8a,b show the ε′ and tanδ values (at 10 3 Hz) of the Ag-nBT/PVDF-(0.2)μBT composites with various fAg-nBT in the temperature range of −60-150 °C, respectively. The rapid increase in ε′ is observed when the temperature increased from −60 to 0 °C. Then, it slightly increased as the temperature increased from 0 to 150 °C. The rapid increase in ε′ in a low-temperature range correlates to the β relaxation of the PVDF polymer [22,40,41]. The β relaxation corresponds to the dipolar group motions and the glass transition [40,41]. Furthermore, the ε′ at high temperatures is dominant by the interfacial polarization and molecular motions of PVDF [22,41,42]. The relaxation peak of tanδ in a low-temperature range is related to β relaxation, corresponding to the observed rapid change in the ε′. The tanδ value increases with increasing the temperature. The tanδ value in a high-temperature range of the composites with high fAg-nBT is lower than that of the composites with low fAg-nBT, which is because the high fillers inhibited the movement of the PVDF chains, resulting in the lower tanδ [43].

Conclusions
The PVDF polymer composites filled with the Ag-nBT hybrid and µBT particles were fabricated as the 3-phase Ag-nBT/PVDF-(0.2)µBT composites. The µBT particles were used as blocking particles to inhibit the formation of conducting network. The microstructure analysis revealed a homogeneous distribution of fillers in the PVDF matrix. The significantly improved dielectric properties of the Ag-nBT/PVDF-(0.2)µBT composites were obtained. The ε values increased from 51.1 to 161.4, while the tanδ remained at a low value of <0.03. It was demonstrated that the addition of Ag-nBT hybrid particles could cause an increase in the ε of the polymer composites through interfacial polarization between filler-matrix and filler-filler. Moreover, the observed low tanδ and σ values indicated that there was no formation of the conducting network in the insulative PVDF polymer matrix. The µBT particles played an essential role in suppressing the formation of the conductive pathways. Therefore, the results of microstructure, dielectric properties, including electrical properties indicated that the Ag-nBT/PVDF-(0.2)µBT composites is a promising dielectric polymer composite, which has a potential for application in in electronic devices.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.