The dielectric property relations of a series of BaTiO3–polymer composites with a uniquely high-volume fraction of ceramic [(1 − x)BaTiO3x polytetrafluoroethylene (PTFE), with volume fractions x = 0.025, 0.05, 0.1, and 0.2] are studied. Such high-volume fraction of the BaTiO3 phase is achieved by using the cold sintering process, as it enables a single-step densification of oxides at an extremely low temperature; typically, the volume fractions from other processing methods are limited to ceramic filler volume fractions of ∼0.6. Microstructural and resistivity analyses suggest that the optimal range of the polymer content to effectively enhance the functions is x = 0.05, as higher volume fractions of the polymer hinder the densification of the ceramic. The composite exhibits improved properties such as lower loss tangent, higher resistivity, and high permittivity that vary systematically with x following an empirical mixing law. Here, we consider the composite mixing law trends and the changes to properties, which indicate that size effects are also being induced in the dielectric response, including shift of Tc, broadening of transition, and reduction of permittivity with respect to volume fraction of the PTFE. Our findings provide a new and simple strategy for the fabrication of ceramic–polymer composites with extremely high relative permittivities and resistivities, and these observations all point to a route that can allow us to engineer new types of advanced dielectric materials.

High permittivity ceramic–polymer composites typically are fabricated with high-volume fractions of the polymer.1–5 The permittivity is dominated by the polymers and often leads to a limited enhancement of relative permittivity; some examples are listed in Table I in considering composite trends in regard to relative permittivity and the volume fraction of the composite constituent phases.6–10Figure 1 shows the basic trend of a low permittivity polymer with high permittivity fillers. The general weighting of permittivity varies in accordance to the mixing law,

ε¯rn=i=1Nfiεin,
(1)

where ɛi is the relative permittivity, ε¯r is the average composite relative permittivity, fi is the volume fraction of the ith phase, ifi=1.0, n is an exponent ranging between −1 ≤ n ≤ +1, and N is the number constituent of phases making up the composite.

FIG. 1.

Effective permittivity of the polymer high permittivity ceramic composite as a function of volume fraction of the ceramic fillers calculated using mixing low with different exponent n. Schematic illustration of connectivity patterns at given n is shown on the right side.

FIG. 1.

Effective permittivity of the polymer high permittivity ceramic composite as a function of volume fraction of the ceramic fillers calculated using mixing low with different exponent n. Schematic illustration of connectivity patterns at given n is shown on the right side.

Close modal
TABLE I.

Effective permittivity of ceramic–polymer composites. All of the data are taken using BaTiO3 particles as the fillers and measured at 1 kHz. The references are listed in the last column.

Polymer (matrix)Filler/sizefBT (vol. %)ɛcomtan δReference
Epoxy BaTiO3, ∼100 nm 30 23 ∼0.03 6  
Polyetheretherketone (PEEK) BaTiO3, ∼900 nm 67 48 … 7  
Polyvinylidene fluoride (PVDF) BaTiO3, ∼100 nm 60 95 ∼0.04 8  
Poly(vinylidene fluoride-co-hexafluoro propylene) (PVDF-HFP) BaTiO3, 6.9 nm 70 35 ∼0.05 9  
Polyimide BaTiO3, 240 nm 90 125 ∼0.1 10  
Polymer (matrix)Filler/sizefBT (vol. %)ɛcomtan δReference
Epoxy BaTiO3, ∼100 nm 30 23 ∼0.03 6  
Polyetheretherketone (PEEK) BaTiO3, ∼900 nm 67 48 … 7  
Polyvinylidene fluoride (PVDF) BaTiO3, ∼100 nm 60 95 ∼0.04 8  
Poly(vinylidene fluoride-co-hexafluoro propylene) (PVDF-HFP) BaTiO3, 6.9 nm 70 35 ∼0.05 9  
Polyimide BaTiO3, 240 nm 90 125 ∼0.1 10  

The exponent, n, is influenced by the spatial connectivity of each of the phases, as at the extremes, n = +1 is parallel connectivity, n = −1 is serial connectivity, and n = 0 is an equal weighted mixture of parallel and serial connectivities.

As an approximation, in the mathematical limit n0,

logε¯r=i=1Nfilogεi.
(2)

On the basis of Eq. (2), even with high permittivity ceramic fillers (ɛf > 1000), the composite had relatively low permittivity in the effective volume fraction range (mostly <60 vol. %) of fillers7,11–14 since the effective properties are dominated by the low permittivity matrix except for the extreme case of n = +1, as shown in Fig. 1. Some examples of typical composites with BaTiO3 and various polymers are shown in Table I. In the high-volume fraction composites (mostly >60 vol. %), the permittivity substantially shifts downward from Eq. (2) because of the formation of voids or pores in composites.15–17 Consequently, excess fillers lead to lower permittivity, as well as lower reliability, including resistivity and breakdown strength.9,18,19 However, with the introduction of the cold sintering process (CSP), it is found possible to co-sinter polymer and ceramic materials into a composite in the high-volume fraction range of ceramics (≫60 vol. %).20–23 The CSP allows for extremely low temperatures to densify ceramic and metal powders with the assistance of the uniaxial pressure and the sintering flux.24–26 Very recently, Tsuji et al. have used the NaOH–KOH flux as a method to sinter the high permittivity ceramic, such as BaTiO3, in a single step.27 This concept has been extended to other fluxes, such as Ba(OH)2 · 8H2O, and this has allowed the densification of BaTiO3–polymer composites to high theoretical densities of ≥ 93% at low sintering temperatures of ≥150 °C.28 The objective of this paper is to explore the dielectric property relations of these unique high permittivity composites, with the unusually high-volume fraction of the BaTiO3 phase, where polytetrafluoroethylene (PTFE) polymer is added up to 20% volume fraction relative to the BaTiO3 content.

BaTiO3 nanoparticles (average particle size: 100 nm, BET surface area: 10.07 m2 g−1) synthesized by a typical oxalate method were used in this study. The as-received BaTiO3 powder was first calcined at 700 °C for 1 h to completely remove organic residues. The calcined BaTiO3 powder (4.0 g) was mixed with a 1M acetic acid aqueous solution (20 ml) at 80 °C for 1 h for further BaTiO3 surface preparation to form a thin amorphous layer,29 which facilitates densification.28 After the treatment, the powder was collected by filtration (EZFlow PES membrane, 0.22 μm), washed with de-ionized water, and dried at 120 °C for 24 h. Barium hydroxide octahydrate [Ba(OH)2 ⋅ 8H2O, >98%] was purchased from Alfa Aesar. Micro-fine polytetrafluoroethylene (PTFE) was obtained from Howard P. Industries. These powders were used as received.

0.75 g of BaTiO3 and PTFE were homogeneously mixed in ethanol using a pestle and mortar until ethanol was evaporated. The volume fraction of PTFE was 2.5, 5, 10, and 20 vol%. After drying completely, 0.15 g of Ba(OH)2 ⋅ 8H2O was added to the mixture and homogeneously ground and mixed using a pestle and mortar prior to sintering. The mixture was loaded into a 12.7 mm diameter die and uniaxially pressed under 350 MPa. Since the melting point of Ba(OH)2 ⋅ 8H2O is 78 °C, a pre-heating step was conducted at 80 °C for 0.5 h to allow its homogeneous distribution in the BaTiO3 powder. Then, the set temperature was increased to 225 °C using both a heater jacket and a press equipped with hot plates and held for 2 h under 350 MPa. The pressure was applied before ramping up and released immediately after the dwell time. Samples were cooled down to room temperature. The as-prepared samples after cold sintering were dried and stored in an oven at 200 °C.

Bulk densities (ρb) were obtained by the Archimedes method, performed using ethanol. Theoretical densities were calculated using a volumetric mixing law from contributing compounds BaTiO3 (6.03 g cm−1) and PTFE (2.2 g cm−1). The relative density was then calculated from the ρb/ρth ratio. X-ray diffraction (XRD) was measured using Empyrean (Malvern Panalytical) operating at 45 kV and 40 mA. Scanning electron microscopy (SEM) images of the microstructure with sputtered iridium were observed using Apreo SEM (Thermo Fisher Scientific) operating at an accelerating voltage of 5 kV. The presence of PTFE after CSP was evaluated by Fourier Transformed Infrared Spectroscopy by Attenuated Total Reflectance (FTIR-ATR), using a Vertex 70 FTIR spectrometer (Bruker). Spectra were collected at room temperature.

For electrical property measurements, 100 nm-thick Ag electrodes were deposited by sputtering (Q150R Plus, Quorum) on polished surfaces. Dielectric properties were measured at 1 kHz using an HA 4980A LCR meter. Transmission electron microscopy (TEM) for high-resolution microstructure analysis was measured using FEI TALOS F200X TEM (Thermo Fisher Scientific) operated at 200 kV, while the TEM specimen was prepared using an FEI Helios 660 focused ion beam (FIB) system. Scanning transmission electron microscopy–energy dispersive spectroscopy (STEM–EDS) was performed using the SuperX EDS system to collect elemental maps in the composite.

Relative densities of cold sintered (1 − x) BaTiO3x PTFE composites with x = 0.025, 0.05, 0.1, and 0.2 are shown in Fig. 2(a). To aid the comparison, the same CSP conditions (225 °C, 350 MPa, and 2 h) were used. The relative density gradually decreases with the amount of polymer but remains high and above 90%. In Fig. 2(b), x-ray diffraction (XRD) patterns show sharp diffraction peaks and good phase purity for the starting BaTiO3 powder (black line) and the cold sintered composites. Small peaks corresponding to PTFE are observed in the composites with a high polymer content (x > 0.1).30 Since the presence of PTFE is clearly confirmed for the composite with x = 0.05 by FTIR, it can be confirmed that the polymer did not undergo thermochemical decomposition under the applied processing conditions (see Fig. S1 in the supplementary material). It is also noted that we did not observe XRD peaks of PTFE, so we suspect that it is highly disordered and/or difficult to detect at low volume fraction within the diffractometer used here. Figures 2(c)2(f) show SEM images of fractured surfaces of (1 − x) BaTiO3x PTFE composites with x = 0.025, 0.05, 0.1, and 0.2, respectively. High-magnification images are shown under their corresponding low-magnification ones. Dense microstructures with polygonal facets are clearly observed, especially at the low polymer content, which is consistent with effective sintering. The low-magnification TEM image also confirms the high dense microstructures without obvious pores and voids (see Fig. S2 in the supplementary material). In contrast, as the polymer content increased, the polymer segregation became noticeable, as shown in low-magnification images, and the grain tends to have rounder shapes, with similar grain sizes around 90 nm (see Fig. S3 in the supplementary material). A similar trend of segregation was observed in ZnO–PTFE composites using SEM, where it was confirmed for the samples with >10 vol. % PTFE loading.21 From the viewpoint of the CSP mechanisms, the excess amount of polymer would prevent densification and result in the formation of pores. It is recognized that successive reactions in CSP take place at the solid-flux interface. If the hydrophobic polymer covered the powder surfaces, it would lead to surface passivation for the interface reaction. Therefore, it is reasonable that there is an optimal range of polymer addition that does not hinder densification. Judging from the microstructures shown in Figs. 2(c)2(f), it suggests that the optimal amount of PTFE is less than 10 vol. % under our processing conditions. For further investigation and verification of the polymer distribution, high-resolution TEM observation and the corresponding STEM–EDS were conducted for the composite with x = 0.05 [Figs. 2(g)2(j)]. In addition to areas showing polymer segregation, we clearly observe a continuous region that contains elements such as carbon, coming from the polymer located at a nanometer length scale in the grain boundary [Figs. 2(g) and 2(h)] and the triple point [Figs. 2(i) and 2(j)]. There are some regions where BaTiO3/BaTiO3 grain boundaries are without polymers (data not shown). There are also variations in the polymer thickness throughout the grain boundary microstructure, and those detected are between 1 nm and 12 nm. These forms of inhomogeneity are to be expected as the polymers that are dispersed as powders among the BaTiO3 powders, and then, there can be plastic flows around the sintering BaTiO3 particles under the applied stress driving the cold sintering of the composite. These results suggest that the optimal amount of the polymers helps to engineer grain boundaries and triple points, without hindering densification.

FIG. 2.

(a) Relative density of cold sintered (1 − x)BaTiO3x PTFE composites with x = 0.025, 0.05, 0.1, and 0.2. (b) XRD patterns of BaTiO3 powder and the composites with the given volume fraction of PTFE. The peaks associated with PTFE are magnified. SEM images of the composites with x = (c) 0.025, (d) 0.05, (e) 0.1, and (f) 0.2. Arrows point out smaller particles; note there are also small particles in (e) and (f), and also the grain morphology is more rounded at higher PTFE content. TEM and corresponding EDS mapping images of the [(g) and (h)] grain boundary, and [(i) and (j)] triple point for the composite with x = 0.05. Titanium (green) and carbon (red) are shown in mapping.

FIG. 2.

(a) Relative density of cold sintered (1 − x)BaTiO3x PTFE composites with x = 0.025, 0.05, 0.1, and 0.2. (b) XRD patterns of BaTiO3 powder and the composites with the given volume fraction of PTFE. The peaks associated with PTFE are magnified. SEM images of the composites with x = (c) 0.025, (d) 0.05, (e) 0.1, and (f) 0.2. Arrows point out smaller particles; note there are also small particles in (e) and (f), and also the grain morphology is more rounded at higher PTFE content. TEM and corresponding EDS mapping images of the [(g) and (h)] grain boundary, and [(i) and (j)] triple point for the composite with x = 0.05. Titanium (green) and carbon (red) are shown in mapping.

Close modal

Dielectric properties of cold sintered (1 − x) BaTiO3x PTFE composites with x = 0.025, 0.05, 0.1, and 0.2 were measured over a temperature range between 20 and 200 °C [Figs. 3(a) and 3(b)]. To clarify the polymer effect, the relationship between the room temperature permittivity at 1 kHz, along with the corresponding loss tangent at different values of x, is shown in Fig. 3(c). At room temperature, the permittivity is 1760 for the composite with x = 0.025. As the amount of polymer increased, it gradually declines to ∼850, 470, and 160 due to the increase in the volume fraction of low permittivity of the PTFE polymer (ɛp = 2.1). Concurrently, loss tangents are ∼0.09, 0.02, 0.005, and 0.006 for the composites with x = 0.025, 0.05, 0.1, and 0.2, respectively. It is noted that some fluxes remain in the form of Ba(OH)2·xH2O and/or Ti-complexes at the grain boundaries, while some are excluded from the sample. Therefore, the relatively high loss for the sample with lower polymer loading may be due to the residual flux complexes. However, the polymer with low loss tangent may improve such disadvantages of using flux chemistry; otherwise, a drying and hermetically sealing process would have to be applied for high quality humidity stable dielectrics. The temperature dependence of permittivity is strongly influenced by the polymer content. As shown in Fig. 3(a), there is a broadened and decreased maximum permittivity around at 125 °C, associated with the ferroelectric to the paraelectric phase transition of BaTiO3. To investigate and quantify the influence of polymers on the temperature dependence, a modified Curie–Weiss law was applied to the composites, which is given as31 

1ε1εm=(TTm)γC,
(3)

where C is a constant, T is the temperature, Tm is the temperature of maximum permittivity, ɛ is the permittivity, ɛm is the maximum permittivity, and γ is the dielectric critical exponent. γ gives information on the degree of deviation from the ideal Curie–Weiss law, where the value normally varies between 1 for a normal ferroelectric and 2 for a diffuse ferroelectric.32 The exponent γ can be obtained by the slope in the plots of ln(1/ɛ – 1/ɛm) as a function of ln(T – Tm). As shown in Fig. S4 in the supplementary material, a linear relationship is observed for all samples. At 1 kHz, γ increased as the PTFE amount increased, suggesting PTFE addition led to the diffuse character of phase transition [Fig. 3(d)]. In addition, the Curie-maximum temperature (Tm) obtained from the dielectric curves decreased with an increase in the amount of polymer, as shown in Fig. 3(e). According to the previous studies, dielectric properties, including Tc and diffusivity, are influenced by many factors;33 thus, the cause is difficult to identify. For instance, grain size,34 porosity,35 stresses,36 and charged defects37 have been recognized as the causes of the change in the nature of permittivity and the phase transition of BaTiO3. At this time, we favor the nature of the temperature dependence being influenced in the nanocomposites polymer BaTiO3, through a ferroelectric size effect, as there is systematic scaling of the decrease in the permittivity maxima, diffuseness, and the shift of transition.34 To emphasis these trends, we have considered a scaling law dependence between these indicators and the volume fraction of PTFE, fPTFE. We only consider a general scaling in the following forms in Eq. (4.1)(4.3):

εmfPTFEk,
(4.1)
TdifffPTFEm,
(4.2)
TcfPTFEp,
(4.3)

where k, m, and p are the unknown scaling parameters; but these can be determined in the form of a natural logarithm plot, as shown in Figs. 3(f)3(h). So the scaling trends are then identified, and the quantification of diffuseness temperature (Tdiff) is by considering the temperature broadening at 98% of peak permittivity, as indicated in the inset in Fig. 3(g). So although we do not have a physical model at this time, there is a route to later consider the meaning of critical exponents for these empirical trends.

FIG. 3.

Temperature dependence of (a) the dielectric constant and (b) the loss tangent, measured at 1 kHz, of the cold sintered (1 − x)BaTiO3x PTFE composites with x = 0.025, 0.05, 0.1, and 0.2. Change in (c) dielectric constant, loss tangent at room temperature, (d) dielectric critical exponent (γ) in the modified Curie–Weiss law, and (e) Curie-temperature (Tc) as a function of volume fraction of PTFE. Scaling law dependence of (f) the permittivity maxima, (g) diffuseness, and (h) the shift of Tc with respect to volume fraction of PTFE. (i) Resistivity of the composites as a function of volume fraction of PTFE. The resistivity of the cold sintered BaTiO3 without PTFE is shown as a white circle in (i).

FIG. 3.

Temperature dependence of (a) the dielectric constant and (b) the loss tangent, measured at 1 kHz, of the cold sintered (1 − x)BaTiO3x PTFE composites with x = 0.025, 0.05, 0.1, and 0.2. Change in (c) dielectric constant, loss tangent at room temperature, (d) dielectric critical exponent (γ) in the modified Curie–Weiss law, and (e) Curie-temperature (Tc) as a function of volume fraction of PTFE. Scaling law dependence of (f) the permittivity maxima, (g) diffuseness, and (h) the shift of Tc with respect to volume fraction of PTFE. (i) Resistivity of the composites as a function of volume fraction of PTFE. The resistivity of the cold sintered BaTiO3 without PTFE is shown as a white circle in (i).

Close modal

The size effect could be associated with the interface of high permittivity grain and high resistivity polymers that provide unique boundary conditions at the grain boundaries of the 90 nm BaTiO3 grains, but it could be through the precipitation of a smaller population of ∼10 nm BaTiO3 particles (see Fig. S5 in the supplementary material) that then coexist with the larger grains and also contribute to the observed experimental trends. The ferroelectric spontaneous polarization has less possibilities of interfacial space charge screening at the grain boundaries in these ferroelectric–polymer nanocomposites. Therefore, the polarization gradients inside the BaTiO3 grains will be influenced by these polymers and their volume fractions, thereby inducing effective additional contributions to the size effect phenomenon. It is important to recall that in ferroelectric materials, depolarization fields, Ed, are controlling the spatial distribution of spontaneous polarization. This, in turn, is influenced by the domain configurations, surface charge, and polarization gradients. For small grains <100 nm, domain configurations become difficult, and the compensation for Ed is possible via polarization gradients and/or surface charges. The depolarization field in a ferroelectric at an interface is given by

Ed(z)=ε0(P(z)+σ),
(5)

where Ed(z) is the spatial variation of the depolarization field, P(z) is the spatial polarization in a distance z normal from the grain boundary interface, σ is the surface charge density, and ɛ0 is the permittivity of free space.38 So, for highly insulating polymer grain boundaries, σ = 0. Then, the polarization gradients within the BaTiO3 grains are now expected to dominate to accommodate the continuity of the displacement field and minimize the depolarization field. In a one-dimensional approximation, the spatial distribution of polarization in a ferroelectric layer is described by the Landau–Ginzburg–Devonshire (LGD) and provides an analytic solution to the spatial polarization, viz.,

P(z)=Pmax×(1cosh(αz)cosh(αh/2)),
(6)

where α is the correlation parameter in the LGD exchange energy term and h is the grain size.39 Collectively, these create a boundary condition that effectively reduces the average grain size from h to heff = h − 2hd, if hd is a characteristic distance that is under the polarization gradient or the dead layer (the nonferroelectric layer). Although no significant difference was observed in the major population of grain size (see Fig. S3 in the supplementary material), the presence of smaller precipitated BaTiO3 cannot be denied, which may increase with the volume fraction of PTFE. Given the dissolution–precipitation process in the CSP, polymer addition might influence the nucleation reaction during CSP, leading to the formation of small particles, as shown in Fig. S5 in the supplementary material. Indeed, using TEM, Zhao et al. observed the formation of small ZnO with the diameter of a few nm in the polymer grain boundaries as a result of the CSP of ZnO with PTFE.21 These particle sizes, observed and shown in Fig. S5 in the supplementary material, are within the intrinsic size effect regime and, therefore, would also influence the overall dielectric behavior in these new complexed nanocomposites. The TiO2-rich amorphous layers that would be on BaTiO3 powders following the treatment with acetic acid are believed to be removed from the surfaces and not play a significant role in the change to dielectric data.40 The Ba(OH)2 ⋅ 8H2O as a flux dissolves and removes these amorphous TiO2 layers completely in pure cold sintered BaTiO3, and high permittivities are noted. In the TEM image [Figs. 2(g) and 2(i)], we did not see evidence for any residual amorphous phase in BaTiO3-PTFE composites. However, the precise control of the perovskite Ba/Ti ratio may be non-stoichiometric, but these stoichiometric fluctuations would be below the ability to detect with differences with EDS. As the volume fraction of PTFE increases, it is possible that the polymer can kinetically limit some areas of dissolution and the remaining amorphous layers may increase the thickness in the dead layer (hd), but we do not consider the amorphous TiO2 to be a contributor to the observed property scaling with PTFE vol fraction. Currently, the overall contributions of the size effect mechanism in these new ferroelectric polymer nanocomposites are not known, but it is prudent to qualitatively point to these possible mechanisms. In the future, we can see that nanocomposites with different grain sizes of BaTiO3 can be fabricated to investigate these scientific details, and detailed particle size distributions can be determined with modeling to better note the size effect phenomena. Under such an investigation, the respective temperature dependence affects with size could be systematically decoupled. It will also be important to consider the ferroelectric low and high field behavior, and in considering the high field, we would need to note the resistivity changes with polymer volume fractions. Here, we observed an increase in resistivity and reached ∼1012 Ω cm for the composite with x = 0.05, which is four orders of magnitude higher than that of cold sintered BaTiO3 (∼108 Ω cm), as shown in Fig. 3(i). The further addition of polymer results in the reduction of resistivity, probably because of incomplete sintering with undeveloped grain boundaries and pores that are observed in Figs. 2(e) and 2(f).

To design and understand these ferroelectric composites, it is significant to predict the permittivity of materials for various volume fractions for a given BaTiO3 grain size. Therefore, a number of theoretical models have been proposed to describe dielectric properties of two component systems, typically comprised of a low permittivity polymer and a high permittivity ceramic filler.41–45 Up to now, these models have been mainly applied to the polymer composites with a low amount of fillers because of difficulties in the introduction of high-volume fraction of them without pores. As we could fabricate the polymer composites with a high-volume fraction of BaTiO3, the volume fraction trend in room temperature permittivity for the CSP ferroelectric composite is investigated in Fig. 4(a). We selected room temperature permittivity to minimize the complexities of the size effects that are discussed above. To compare with previous reports, the permittivity obtained in this study was replotted in terms of the volume fraction of BaTiO3. For correlation with the typical mixing law, Eq. (1) is plotted as dashed lines using ɛBT = 2000 and ɛp = 2.1, where ɛBT and ɛp are the permittivities of BaTiO3 and PTFE, respectively. We limit our analysis to a diphasic composite mixing and ignore porosity effects that are small and any consideration to amorphous TiO2 phases, as rationalized above. Typically, n in Eq. (1) is influenced by spatial connectivity of each phase and varies from −1 to 1. As shown in Fig. 1, when BaTiO3 and PTFE are connected in parallel to the direction of the applied field, n value is +1, while n = −1 in the case of serial connectivity. For the random mixture, n value gets close to 0, which is expressed by the logarithmic mixing law, as shown in Eq. (2). According to reports on cold sintered low permittivity composites, the volume fraction trend in permittivity was well described by the logarithmic mixing law, n = 0; this corresponds to a 50/50 mixed case of serial and parallel.22 For high permittivity composites shown in this study, the experimental values showed a good agreement with Eq. (1) when n value is approximately −0.24, while there was not such good fitting with other mixing rules, such as Bruggeman, Jaysundere–Smith, and Maxwell–Garnett (see Fig. S6 in the supplementary material).46 If we consider equal serial and parallel weighting in the limiting case when n approaches 0, and 100% serial with n = −1, then n = −0.24 would represent 62% serial and 38% parallel, which might be due to the polymer flow under applied uniaxial compression pressure.23 In other words, the distribution and connectivity of both polymers and ceramics may be affected by pressure, resulting in an increase in both polymer-filled grain boundaries perpendicular to the force direction and ceramic–ceramic boundaries parallel to the force. It is noteworthy to reconsider that typical composites are reported with much low relative permittivity, as shown in Fig. 4(b) and Table I, despite addition of high permittivity fillers (>1000).7,15,16 To take advantage of high permittivity fillers, until this report, only artificial nanostructures with high parallel connectivity, n = +1, have been proposed,47,48 but it is not favorable for reliability since it easily forms the weakest path for a breakdown. With the introduction of CSP, we confirmed that the polymer composite with a high-volume fraction of ceramic can be fabricated with high density, leading to high permittivity in accordance with the predicted model and high resistivity. Our results would provide a new and realistic design of fabricating high permittivity ceramic–polymer composites. Considering the advantages of the interfacial design of grain boundaries with high resistive grain boundary and low permittivity polymers in the composites introduced in this paper, we can envision future studies focused on breakdown strength, mobility of oxygen vacancies, as well as reliability tests. This permits unique advantages in the dielectric design, and the ability to control the local field in such a composite cannot be overstated as a major advantage in materials engineering of such high permittivity dielectrics. At the same time, these new composites provide a unique structure and dielectric boundary conditions that can further the scientific understanding of size effects with the dead layer-grain size ratio (d/h) and mixtures of grain sizes with the precipitated nanoparticles. We hope that in introducing these new nanocomposites with their excellent electrical properties, it will inspire many future investigations.

FIG. 4.

(a) Summary of the dielectric constant obtained in this study and previous studies on polymer composites with BaTiO3 particles. (b) The low dielectric constant range between 0 and 200 is magnified. The dashed lines are theoretically predicted values using the mixing law with different n.

FIG. 4.

(a) Summary of the dielectric constant obtained in this study and previous studies on polymer composites with BaTiO3 particles. (b) The low dielectric constant range between 0 and 200 is magnified. The dashed lines are theoretically predicted values using the mixing law with different n.

Close modal

BaTiO3 composites containing 2.5–20 vol. % PTFE were successfully fabricated by CSP at 225 °C for 1 h under uniaxial pressure of 350 MPa in assistance with a transient chemical flux of Ba(OH)2 ⋅ 8H2O. We clearly observed the dense microstructures of the BaTiO3 matrix with the presence of PTFE additive using SEM. The permittivity was found to be 1760, 850, 470, and 160 for the composites with 2.5, 5, 10, and 20 vol. % PTFE, respectively, which is in good agreement with the mixing law when the exponent n was approximately −0.24. In addition, the polymer addition led to a significant improvement in the function of composites. Specifically, the loss tangents were ∼0.09, 0.02, 0.005, and 0.006 for composites with 2.5, 5, 10, and 20 vol. % PTFE, respectively, while the value for BaTiO3 without polymer was ∼0.1 relatively high at 1 kHz. The dielectric temperature behavior was investigated, and it was found that systematically the magnitude of permittivity drops, Tm shifts, and the diffuseness of the dielectric anomaly transitions from a Curie–Weiss law to diffuse phase transition with the critical exponent changing from 1 to 2. These changes in the dielectric behavior were all consistent with a size effect phenomenon, and it was hypothesized that the high resistivity of the nanoscale polymer in the grain boundary drives dead layers in the BaTiO3 as well as a precipitated nanoparticle population. For composite resistivity, the value was >1012 Ω cm for the composites with 5 vol. % polymer loading, four orders of magnitude higher than that of cold sintered BaTiO3. These results confirm that CSP enables new and realistic designs to fabricate high permittivity ceramic–polymer composites through a straightforward interfacial design of highly resistive grain boundaries.

See the supplementary material for FTIR of BaTiO3 powder, cold sintered BaTiO3-PTFE composite, and PTFE; the TEM image of the composite with 5 vol. % PTFE; change in grain size; plots of ln(1/ɛ − 1/ɛm) as a function of ln(T − Tm) for the composites; SEM images of the composites with 5 and 10 vol. % PTFE; and theoretical predictions and experimental values of the dielectric constant of the composites.

T.S. would like to thank the Kyocera Corporation for funding his fellowship, enabling his time as a visiting scientist at the Pennsylvania State University. A.N., Z.F., and C.A.R. were partially supported by the AFOSR (Grant No. FA9550-19-1-0372). The authors also wish to thank the staffs of the MCL for aid in sample preparation and in maintaining electrical measurement facilities. They also thank Joanne Aller for helping in proof reading and formatting this publication.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
Prateek
,
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Supplementary Material