Enhancement of dielectric performance upto GHz of the composites with polymer encapsulated hybrid BaTiO₃–Cu as fillers: multiple interfacial polarizations playing a key role

Abstract

Cu nanoparticles with diameters of 15–25 nm were grown discretely on the surface of BaTiO₃ (about 100 nm) via a hydrothermal method, and a polyethylene glycol 4000 layer was coated on the surface of the obtained BT–Cu hybrid particles. The PEG layer will serve as a robust interface layer to suppress the mobilization of charge carriers and protect Cu from oxidation. The BT–Cu particles were loaded as fillers in the matrix of polyvinylidene fluoride (PVDF) to fabricate the BT–Cu/PVDF composites. Microstructure and dielectric performance have been investigated. The results showed that the relative permittivity (ε_r) of the composites increased prominently with the loading amount and meanwhile the dielectric loss tangent was suppressed at a low level. For instance, the permittivity of BT–Cu/PVDF with the volume fraction of 53.7% reached 150 with a low loss of 0.16 at 1 kHz. The permittivities maintained high values of over 55 and the dielectric loss was less than 0.05 upto 1 GHz. Investigation on the polarization mechanisms has been conducted and the interfacial polarization between different phases should account for the high dielectric permittivity upto GHz. The energy storage characteristics were also studied.

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1. Introduction

Polymer based nanocomposites with high permittivity offer the promise of flexible, scalable and low-cost devices, and have attracted much interest in energy storage, electronic and electrical applications.^1–15 Meanwhile, with the development of high-frequency communication in cellular, radio navigation, base station and collision avoidance system, composites with high dielectric performance up to gigahertz (GHz) are highly desired, which however, have been rarely investigated.^16–18

In the polymer based composites, it has been deemed that interfacial polarization plays the primary mechanism for the enhanced dielectric permittivity and never could be neglected. In a composite system with poor dispersion of the inorganic fillers, however, high permittivity can only be obtained at low frequency (e.g.<1 kHz) accompanied with an interfacial relaxation, which is caused by the accumulated free charges in the hetero system. For example, in Fan's report,² the dielectric permittivity of graphene/poly(vinylidene fluoride) composite decayed from ∼7500 at 100 Hz to ∼35 at 10⁷ Hz with a reduction of 99.5%. On the other hand, if the fillers could disperse uniformly and a robust interface form in-between different phases, the charge carriers would be immobilized and the effects of interfacial polarization can be expected to extend to high frequency range.^1,9,10

In our recent work, a strategy was proposed to combine the advantages of ceramic, conductor and polymer matrix to obtain the three-phase composites with prominently enhanced dielectric properties, in which nano Ag was deposited on the surface of BaTiO₃ grains to form BT–Ag hybrids and used as fillers.^8,32 It turned out that the dielectric permittivity did not drop quickly with the increase of frequency. A high permittivity of 127.3 was obtained at 100 kHz, which is much higher than that of the two-phase BaTiO₃/PVDF (usually <50) and the dielectric loss was only 0.06. Inspired by these preliminary results, we believe that the interfacial polarization plays a key role in enhancing the dielectric performance and the high-frequency properties need be further investigated. Therefore in this study, the polarization mechanism of the three-phase composites upto gigahertz was explored by employing Cu deposited BaTiO₃ hetero-structure as fillers. In order to prevent the Cu nano particles from oxidization, a polymer layer was coated on the surface of the BT–Cu hybrids, which simultaneously will act as a robust interfacial layer to suppress the mobilization of charge carriers. As a result, the leakage current could be suppressed and the interfacial polarization could occur over a broad frequency band.

Herein, hybrid ceramic–metal particles were synthesized through a simple hydrothermal method by depositing Cu on the surface of BaTiO₃ particles (with an average diameter of 100 nm), which were subsequently coated with polyethylene glycol 4000 (PEG-4000). In the obtained BT–Cu hybrids, the Cu nanoparticles are discretely grown and bond tightly to the BT grains. As a result, homogeneous dispersion of both BT and Cu particles are guaranteed when the hybrids are used as fillers to prepare the polymeric composites. Our results demonstrated that the permittivity of the BT–Cu filled polyvinylidene fluoride (PVDF) composites reached a high value of 55, with a loss of only 0.05 at 1 GHz. The permittivity value at the gigahertz is almost the highest one ever reported for the polymer composites.^16,17,33 A systematic analysis on the dielectric performance, the energy storage characteristics and polarization mechanism of the BT–Cu/PVDF composites were investigated based on Maxwell–Wagner polarization theory, effective medium theory percolation (EMPT) model and analysis on electric modulus.^23,24

2. Experimental section

2.1 Materials

Copper sulfate pentahydrate and ethylene glycol used as precursor of Cu and solvent were purchased from Aladdin Reagent Co., Ltd. The BaTiO₃ nanoparticles with an average diameter of 100 nm (BT: GC-BT-01) were used as base material for deposition and supplied by Shandong Sinocera Functional Materials Co. China. Polyethylene glycol 4000 (PEG-4000) (Guoyao Chemical Co. China) was used as surfactant. Polyvinylidene fluoride (PVDF) which was provided by Shanghai 3F Co. China was chosen as the polymer matrix. Absolute ethyl alcohol and ultrapurewater were used in all the experiments.

2.2 Preparation of Cu–BT hybrid structure fillers

PEG-4000 (3.0 g) was added into 300 mL ethylene glycol solution in a 500 mL beaker, stirred under ultrasonic condition until PEG-4000 was absolutely dissolved into ethylene glycol solution, followed by addition of 5.0 g of CuSO₄·5H₂O and 5.0 g BT and sonicated for about 30 min till the solution changed into blue suspension. The temperature of the mixture was raised from room temperature to 180 °C in the oil base and reaction kept for 2 hours. Then, the hybrid suspension was centrifuged and rinsed three times with ethyl alcohol. At last, the resulting BT–Cu nanoparticles were dried in a vacuum oven at 50 °C for 24 h.

2.3 Preparation of Cu–BT/PVDF ternary composites

The as prepared BT–Cu particles and PVDF powers were mixed according to a certain proportion in ethanol solution, and the suspension was stirred under ultrasonic treatment for 40 min to disperse the hybrid particles sufficiently. Then the suspension was dried at 70 °C for 12 h. The resultant mixer was shaped by hot pressing at 180 °C and 10 MPa for 20 min. The final samples with a discoid shape were about 1 mm in thickness and 12 mm in diameter. In the end, silver paste was painted as electrode for the electrical test.

2.4 Characterization

The characterizations of the samples were carried out by various techniques. The phase constituents of the BT–Cu particles were recorded on an X-ray diffractometer (XRD, D/max2500/PC, Rigaku Co.) with monochromatic Cu-Kα radiation (λ = 1.54 Å) and 40 kV of acceleration voltage applied. X-ray photoelectron spectroscopy (XPS) spectra were carried out by a PHI-5702 multifunctional spectrometer using an Al Kα X-ray excitation source. Fourier transform infrared (FT-IR) spectra were recorded with a Vertex70 FT-IR-Spektrometer Fourier transform infrared spectrophotometer between 4000 and 400 cm⁻¹. In order to measure the mass fraction of PEG-4000 which was coated on BT–Cu particles, TGA measurements were conducted with a METTLER TOLEDO STAR^e system thermogravimetric analyser, in N₂ atmosphere with the heating rate of 10 °C min⁻¹ from 30 °C to 800 °C. The morphology and size of the synthesized Cu microspheres depositing on nano BT were observed with field-emission scanning electric microscope (FE-SEM, FEI NovaNanoSEM450). Transmission electron microscopy (TEM) images were observed using a FEI Tecnai Spirit instrument operated at an accelerating voltage of 160 kV. The dielectric and electrical responses were measured using an impedance analyzer (Agilent 4294A) in the frequency range of 100 Hz to 10 MHz. Influence of temperature on the dielectric properties was obtained using Agilent 4294A connected with a T95-Linkpad Temperature programmer (Linkam Scientific Instruments) and a THMS 600 Temperature Controlled stage in a temperature ranging from −50 °C to 130 °C. The DC breakdown strength was tested using an Allwin dielectric strength tester (CS9912BX, Allwin Instrument Science and Technology co. Ltd, China).

3. Results and discussion

3.1 Microstructure of BT–Cu hybrid fillers and BT–Cu/PVDF composites

The schematic illustration (Fig. 1) reveals the fabrication process of BT–Cu core–satellite hybrid particles. Under a certain temperature, the reducing agent ethylene glycol turns to acetaldehyde to reduce Cu^II, and transforms to 2,3-buranedione finally. BT grains could reduce the nucleation energy and offer sites for the hetero-growth of Cu nanoparticles.³² The use of PEG-4000 as capping agent avoids agglomeration and prevents oxidation of Cu particles. PVDF is melted during hot-pressing process and binds the BT–Cu hybrids together, and PVDF as matrix material offers good mechanical strength.

Fig. 1 Schematic illustration of the fabrication process of the BT–Cu/PVDF composites.

The SEM and TEM images of BT–Cu hybrid particles (Fig. 2) show that the average diameter of BT particles is 100 nm (Fig. 2a). Cu particles are attached to the surface of BT discretely like satellites with the diameter of 15–25 nm (Fig. 2b), which is further confirmed by the TEM image, as shown in Fig. 2c. In comparison, the size and morphology of BT powders remain unchanged after reaction. Fig. 2d clearly shows that a PEG-4000 layer with a thickness of about 2.0–4.2 nm has been coated on the surface of BT–Cu hybrid particles. The polymer shell prevents the hybrids from exposing to oxygen at ambient environment, and as a result, oxidation of Cu nanoparticles could be avoided. The polymer layer could also suppress the mobilization of the charge carriers and reduce the leakage current under applied electrical field.

Fig. 2 SEM images of (a) pure BT, (b) Cu-deposited BT hybrid particles (c) TEM images of as-synthesized BT–Cu hybrid nanoparticles and (d) BT–Cu hybrid particle coated with PEG-4000. The Cu nanoparticles on BT and PEG-4000 on the surface of BT–Cu hybrid particles are indicated with arrows.

SEM images of BT–Cu/PVDF hybrid composites are shown in Fig. 3. The BT–Cu hybrid particles are encased randomly in the matrix of PVDF which is like a waterfall when the loading amount is 7.3 vol% (Fig. 3a). As the filler loading is increased to 17.9 vol%, the morphology of PVDF matrix changes to spherical particles, as shown in Fig. 2b. Fig. 3c shows that mesh-bonding network are formed, among which the groups of BT–Cu hybrid fillers are dispersed when the contents reaches 31.8%. For the composite containing 53.7 vol% hybrids, the PVDF matrix is in shape of fibers and the Cu particles can be clearly seen on the BT surface. The SEM images clearly show that the BT–Cu hybrids are distributed uniformly in the PVDF matrix. Meanwhile, the nano Cu particles are effectively isolated by BT grains and as a result, it is hard to form conductive path in the whole system.

Fig. 3 SEM images of BT–Cu/PVDF composites with different volume fractions of BT–Cu hybrid particles (a) f_BT–Cu = 7.3%, (b) f_BT–Cu = 17.9%, (c) f_BT–Cu = 32.3%, and (d) f_BT–Cu = 53.7%.

3.2 Study of the oxidation resistance

Fig. 4 presents the XRD patterns of pure Cu, BT powders and BT–Cu hybrids after storing for different time. The diffraction peaks of BT and Cu are distinguishable in the BT–Cu hybrids, both corresponding to the cubic (fcc) phase. The lattice parameters of BT and Cu are 3.95 Å and 3.61 Å respectively. The impurity phases including Cu₂O, CuO and Cu(OH)₂ are not detected in the as-prepared BT–Cu. For the BT–Cu samples after being placed for 30 and 60 days at room temperature in the ambient atmosphere, the XRD patterns of BT–Cu-30 and BT–Cu-60 exhibit almost the same characteristic peaks as that of BT–Cu-0 and no characteristic peaks of oxide impurities are found.³¹ The results indicate that this kind of BT–Cu hybrid particles coated with PEG-4000 have obtained good ability to resist oxidization.

Fig. 4 XRD patterns of (a) Cu (b) BaTiO₃ (c) BT–Cu-0 day (d) BT–Cu-30 days and (e) BT–Cu-60 days.

XPS results further confirmed the oxidation resistance of the Cu on BT surface with the PEG layer. As shown in Fig. 5, the XPS spectrums of the as prepared BT–Cu (BT–Cu-0) and that stored for 30 days (BT–Cu-30) both exhibit a single Cu 2p_3/2 peak at 932.3 eV (Fig. 5a and b). A shoulder peak appears at 934 eV for the BT–Cu stored for 60 days, which relates to the existence of Cu^II, as shown in Fig. 4c. The result indicates that slight oxidation of Cu nanoparticles on the BT surface occurs after being stored for 60 days. Therefore, the PEG-4000 coated BT–Cu hybrid particles could be stored for at least 30 days without any oxidation in the ambient atmosphere. FTIR spectra further confirm the existence of PEG layer on the surface of the BT–Cu hybrid particles (see ESI Fig. S1†).

Fig. 5 XPS spectra of synthesized BT–Cu hybrid nanoparticles (a) BT–Cu-0 day (b) BT–Cu-30 days and (c) BT–Cu-60 days.

Fig. 6 shows the thermal decomposition behavior of the BT–Cu hybrid nanoparticles. The weight loss and heat flow curves of the thermal decomposition process in Fig. 6 can be divided into two parts. Part I from 30 °C to 100 °C is attributed to the evaporation of a small amount of water adsorbed on the surface of BT–Cu nanoparticles. The weight percentage drops to about 96.8% and the heat flow hits the peak at 70 °C. Part II from 100 °C to 800 °C corresponds to the pyrolysis of PEG-4000 and the left weight loss is about 2.04%. Through TG analysis we could see that the small amount of PEG-4000 as a kind of protective agent has increased the ability of BT–Cu hybrid particles to resist oxidization to a great extent.

Fig. 6 TG result of PEG4000-coated BT–Cu hybrid nanoparticles.

3.3 Dielectric properties of BT–Cu/PVDF composites

a. Filler loading dependence. The volume fraction dependence of the dielectric property of the BT–Cu/PVDF composites measured at 1 kHz and room temperature is shown in Fig. 7. Both permittivity and loss tangent increase continuously with the BT–Cu filler loading. When the volume fraction is 53.7 vol%, the permittivity increases to 150.6 (4 times larger than that of BaTiO₃/PVDF with 50 vol% filler content) and the dielectric loss tangent rises to 0.16 which is smaller than that of BaTiO₃/PVDF composites as reported in Lin's work.⁴³ The composite with f_BT–Cu = 42.3 vol% is the most acceptable, of which the loss tangent is suppressed at 0.09 and the permittivity reaches 88.8 which is about 9 times higher than the ε_r of pure PVDF matrix (ε_r of PVDF is about 10 at 1 KHz). As is stated in the percolation theory,^2,6,8 high ε_r can be reached by padding the conductive elements into polymer matrix. The improved permittivity is partially owing to the deposition of nano Cu particles and substantially increased interface area in the whole system. It has been suggested that the charges will move and get accumulated at the interfaces between the dielectric media under applied field. This accumulated charges at the interfaces would produce interfacial polarization and polarize the surrounding polymer.²² As a result, an interfacial electric double layer was generated surrounding the fillers. The increasing loading amount of Cu particles would cause the augment of the amount of this electric double layer, which get overlapped and leading to the improvement of ε_r. Besides, the hetero-interface between BT–Cu could also be polarized under applied electric field and contribute to the increase of ε_r.

Fig. 7 (a) Volume fraction of BT–Cu hybrid particles dependence of the dielectric property and (b) EMPT fitting values of the BT–Cu/PVDF composites at 1 kHz and room temperature.

The effective medium percolative theory (EMPT) model has been proved very helpful to predict the permittivity of metal/ceramic/polymer composite.^23,24,28 As shown in Fig. 7b, the variation tendency of permittivity was simulated by EMPT model (according to the equation below) with the increase of the volume fraction of BT–Cu loading.

where ε_r, ε₁ and ε₂ are respectively the relative permittivities of the BT–Cu/PVDF composite, polymer and ceramic, respectively. f_c, f_cer and f_m stand for the percolation threshold of the metal filler, the volume fraction of the ceramic filler and metallic filler. n is the ceramic morphology fitting factor which is related to the ceramic fillers, and the higher value of n indicates the lower sphericity of the ceramic fillers. And q is a critical exponent. If the value of diverges from the typical value 1.0, it means that in the composites there are more than one mechanisms of charge movement. The results indicate that the EMPT curve is consistent with the experimental value in the filler loading range from 7.3% to 53.7%. The best fitting parameters of f_c, n, q are 0.079, 0.069 and 0.0052. That is to say, on the basis of EMPT model, the percolation threshold of this composites is f_Cu = 7.9%, the ceramic morphology fitting factor (n) is 0.069 and the critical exponent (q) is 0.0052. As mentioned before, f_Cu is 7.5% when the volume fraction of BT–Cu fillers reaches 53.7%, which is near the percolation threshold, consistent with the relatively fast increase of permittivity from f_Cu = 42.3% to 53.7%. q = 0.0052 approaching the value of 0 reveals that the BT–Cu hybrid fillers are not real conducting phase in the composites because of the discrete distribution of nano Cu on the BT surface. It is because of this discretely fixed Cu on BT surface, there is little chance for the nano Cu particles to get together and form the conductive pathway, leading to the slow growth of loss tangent.

b. Frequency dependence up to GHz. The permittivity and loss tangent of the BT–Cu/PVDF composites with different volume fractions of BT–Cu hybrid particles as a function of frequency ranging from 100 Hz to 1 GHz at room temperature are presented in Fig. 8. As f_BT–Cu < 17.9 vol%, the permittivity of the composites shows weak dependence in the frequency range of 100 Hz to 10 MHz, as shown in Fig. 8a. For the composites containing BT–Cu filler content of 17.9 vol% or above, the permittivity declines at low frequencies of 100 Hz to 10 kHz, which is prominent as f_BT–Cu reaches 53.7 vol%. This phenomenon is attributed to the interfacial relaxation or called Maxwell–Wagner (M–W) relaxation, which is associated with the entrapment of free charges based on the great difference in electrical properties between the fillers and matrix.^9,11 The permittivity of all the BT–Cu/PVDF composites show slight decrease with increasing frequency in the range of 10 MHz to 1 GHz. And the permittivities increase with the f_BT–Cu at a fixed frequency. For example, the permittivity increases from 9.13 as f_BT–Cu = 7.3% to 57.1 as f_BT–Cu = 53.7% at the fixed frequency of 1 GHz. It is particularly important that the permittivity maintains much higher values, compared with the CCTO–epoxy and PVDF/RGO composites reported by Qing et al.¹⁶ and Zhang et al.³³ respectively.

Fig. 8 Frequency dependence of (a) dielectric permittivity from 100 Hz to 10 MHz, (b) dielectric permittivity from 10 MHz to 1 GHz (c) dielectric loss tangent from 100 Hz to 10 MHz, (d) dielectric loss tangent from 10 MHz to 1 GHz.

The detailed volume fraction and dielectric properties of each component in BT–Cu/PVDF composites are listed in Table 1. The volume fraction of each component was calculated according to the corresponding equations in ESI.†⁸ As shown in the table, PVDF has a low dielectric permittivity of only 2.63 at 1 GHz. In our previous report on the BaTiO₃/epoxy system, the dielectric permittivity is only about 10.8 as f_{BT(100 nm)} = 0.4 (in vol) in the frequency range of GHz.¹⁷ Considering that the permittivities of PVDF and epoxy are both in the range of 2–3 at GHz, the permittivity of BT–Cu/PVDF system with steadily introduced Cu nano particles obtained in this study is significantly high.

Table 1 Contents of each component in the BT–Cu/PVDF composites and dielectric properties at 1 kHz, 100 kHz and 1 GHz

Samples	BT–Cu (wt%)	BT–Cu (vol%)	BT (vol%)	Cu^a (vol%)	εr/δ (1 kHz)	εr/δ (100 kHz)	εr/δ (1 GHz)
a The calculated mass fraction of Cu in the BT–Cu hybrid fillers was 21.6 wt%.
PVDF	0	0	0	0	10.1/0.03	9.61/0.05	2.62/0.083
	5%	1.81%	1.55%	0.26%	12.8/0.024	11.9/0.065	—
	10%	4.1%	3.5%	0.6%	18.3/0.023	16.7/0.064	—
	20%	7.3%	6.3%	1.0%	24.2/0.025	22.3/0.061	9.13/0.091
BT–Cu/PVDF	40%	17.9%	15.3%	2.6%	47.7/0.038	36.6/0.063	19.8/0.090
	60%	32.3%	27.6%	4.7%	66.6/0.067	60.5/0.074	25.7/0.084
	70%	42.3%	36.1%	6.2%	88.1/0.091	66.1/0.079	35.8/0.08
	80%	53.7%	45.8%	7.5%	150.6/0.16	97.0/0.084	57.1/0.064

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The enhanced permittivity at GHz should be mainly attributed to the following polarization mechanism. (i) Under applied electric field, Ti ions get deviated from the centre of oxygen octahedral in BT and produced polarization;²⁷ (ii) nano Cu particles could get polarized under applied electric field; (iii) interfacial polarization exists between BT and PVDF, and Cu and PVDF, both are isolated by the robust PEG barrier layer, which could impede motions of electrical charges under applied electric field;⁴² and (iv) the interfacial polarization between BT and nano Cu particles, which is bridged by a hetero-structure could also take effect upto GHz; without (ii)–(iv), we can see that in Yang's report,¹⁷ permittivity of 100 nm BT–epoxy composites could only reach ∼10.8 in the range of 2–20 GHz. The property over 1 GHz in this study was not measured yet, but the variation of permittivity is usually slight in the whole gigahertz frequency range. For comparison, BT–Cu without PEG coating was used to fill PVDF. The dielectric properties of the resulted composites are shown in Fig. 9. In general, dielectric permittivities of the composites with BT–Cu (no PEG) as filler are lower than that with BT–Cu (coated with PEG) with the same filler loading. Besides, ε_r of the former ones reduces faster with the increase of frequency. For example, ε_r decreases from 55 to 32 in the frequency range of 10 MHz to 1 GHz, while for the composite with PEG coated BT–Cu as filler, ε_r is from 70 to 60, both with the fill loading of 53.7 vol%. This phenomenon further confirms that the robust PEG layer acts as an electron barrier, which isolates Cu and enhances the interfacial interaction. Huang⁴¹ also reported that a shell layer coated on the nanoparticles surface could result in a strong nanoparticle/matrix interface. The PEG layer immobilizes electrons from the nano particles and as a result, the electronic polarization could be enhanced, leading to relatively high permittivity in the GHz frequency range. This phenomenon was also studied in Bowler's report.⁴⁴ Interfaces between two phases can be divided into two types, the loose one and robust one. The loose layer mainly contributes interfacial polarization in the low frequency range (<1 kHz) while the robust can keep interfacial polarization up to very high frequency (10¹¹ Hz). This theory was also confirmed in Lin's report, in which the relaxation frequency of Ag@C–epoxy composite was far over 10⁷ Hz.⁴² Therefore, the enhanced permittivity upto GHz in this study is related to the enhanced interface areas and interactions between BT–PVDF and Cu–PVDF through the robust PEG layer, and BT–Cu through the hetero-structure. The results suggest that with a stable interface layer between different phases, the interfacial polarization can take effect upto high frequency and the dielectric property can be manipulated.

Fig. 9 Frequency dependence of (a) dielectric permittivity and (b) dielectric loss tangent from 10 MHz to 1 GHz BT–Cu/PVDF (no PEG) composites.

The dielectric loss tangents display a similar dielectric relaxation to that of the PVDF matrix and remains at a low level (tan δ < 0.27) in the whole frequency range of 100 Hz to 1 GHz as shown in Fig. 8. In the low frequency range (100 Hz to 1 KHz), the interfacial relaxation between BT–Cu hybrid particles and PVDF matrix plays a dominant role. The interfacial polarization in BT–Cu/PVDF composites with higher filler contents (higher-filler composites) is stronger than that of composites with lower filler contents (lower-filler composites). So, the interfacial polarization influences more obviously for the composites with higher volume fraction of the BT–Cu filler. In the high frequency range (1–100 MHz), the relaxation process of PVDF matrix should be mainly responsible for the loss change, which was caused by the reorientation of electric moment of PVDF matrix under alternating current field. The polarization of PVDF in lower-filler composites was larger than that of higher-filler composite. So, the losses of composites with lower filler contents were larger than that of composites with higher contents. It has also been proved that the loss peak at ∼10 MHz should be related to the micro-Brownian cooperative motions of the main chain backbone and is the dielectric manifestation of the glass transition temperature of PVDF.¹¹ Besides, over the high frequency range, the loss tangent of BT–Cu/PVDF composite decreases with the volume fraction. As listed in Table 1, the dielectric losses of all the composites were less than 0.01 at 1 GHz, which is mostly desired in the electronic application.

In general, through the strategy of depositing copper on BT fillers and coating a PEG protective layer, the permittivity of the PVDF composites maintains high values (e.g. ε_r = 57 when f_BT–Cu = 53.7%) at 1 GHz. As reported in Qing's study¹⁶ and Zhang's work,³³ CaCu₃Ti₄O₁₂ (CCTO)–epoxy composite consisting both 40 wt% CCTO particles and 40 wt% Fe–Si–Al particles, and PVDF/RGO composite with 7 wt% RGO filler loading, exhibited permittivities of ∼18 and ∼8 at 2–18 GHz respectively. In our previous work,¹⁷ permittivity of ∼11 (at 3–18 GHz) of 100 nm BaTiO₃/epoxy with 40 vol% filler loading was reported, which was much lower than that obtained in this study. It is also worth noting that the loss keeps at an acceptable level (tan δ < 0.3) in the whole measure frequency range in the view point of application during the increase of frequency up to 1 GHz.

c. Conductivity and electric modulus. The frequency dependence of conductivity (σ) and imaginary electric modulus formulism of different contents of BT–Cu fillers are employed for analyzing the relaxation process in Fig. 10.^8,34–36

Fig. 10 Frequency dependence of (a) conductivity and (b) imaginary electric modulus of the BT–Cu/PVDF composites with different volume fraction of BT–Cu hybrid filler.

The conductivity of the composites increases with the frequency in the range of 100 Hz to 10 MHz. For example, as the BT–Cu filler loading is 53.7%, σ increases from 10⁻⁶ (Sm⁻¹) at 100 Hz to 0.01 Sm⁻¹ at 10 MHz. The phenomenon result indicates that Cu particles disperse well and no conductive network has been developed in the composites, corresponding to the low dielectric loss in Fig. 8. There are two relaxation regions in the M′′ curves circled by imaginary line in Fig. 10b. The relaxation peaks at low frequency are caused by the interfacial polarization.^8,23 The valley bottom of M′′ moves towards to high frequency with the increase of BT–Cu fillers, indicating the interfacial polarization was enhanced, which is consistent with the increment of permittivity. The obvious relaxation peaks at high frequency are attributed to the dipole polarization of PVDF matrix. The β-phase dipoles in PVDF matrix are arranged in order, making free charges in composite move smoothly along the PVDF molecular chains.²³ One can see that the change of the peak values at high frequency tends to smaller with the increase of BT–Cu hybrid fillers, which further proves the relaxation peaks was mainly concerned with the relaxation process of PVDF matrix and not the BT–Cu fillers.

d. Temperature dependence. Having demonstrated the frequency dependence of conductivity (σ) and imaginary electric modulus, we then examined the temperature dependence of the dielectric properties of the BT–Cu/PVDF composites measured at 100 kHz.

Fig. 11a shows that the permittivities increase with the temperature for all composites. Particularly, an increase step was observed around 0 °C in the pure PVDF and composites. This phenomenon should be related to the rotational motions of dipolar groups in the amorphous regions of PVDF matrix.³⁹ The motions will be unfrozen over glass-transition temperature which cause the increase of ε_r. ε_r of the composites with f_BT–Cu less than 53.7% tends to be steady with the temperature over 20 °C. It is noted that ε_r of the f_BT–Cu = 53.7% composite experiences a much higher climbing speed over 20 °C. This feature could be interpreted by the increased interfacial polarization density relating to more entrapped charges in the composite.⁸ Fig. 10b shows that a loss peak appears around −25 °C in the dielectric loss curve for PVDF and all composites, which is similar to the report by Rahimabady et al.²² The possible reason for this behaviour is the dipolar polarization of PVDF matrix, and the good mobility of main polymeric chains in combination with the diploes leads to the variation of dielectric loss. Then the loss tangents increase with the temperature. The increase of loss tangents realizes that the relaxation loss plays the dominant role. It is also worth noting that both the permittivity and loss tangent display a relaxation at ∼130 °C. This so-called α relaxation of PVDF was associated with the annealing process in the crystalline regions in the hot pressing process. Dipolar units in the crystalline regions are unfrozen and they can move unimpededly. They prefer alter the dipole direction only along the applied electrical field.³⁹ Another phenomenon should be pointed out that the loss tangent of higher-filler composite increases much faster than that of lower-filler composite. As the temperature increases, there are much more electric charges excited onto the interface areas of higher-filler composites, resulting in the higher climbing rate of the loss.^25,30

Fig. 11 Temperature dependence of the (a) dielectric permittivity and (b) loss tangent of the BT–Cu/PVDF composites measured at 100 kHz.

3.4 Energy storage characteristics

The stored energy density U_e in a capacitor can be described as below:^{19–21,26,38}

From which we can see U_e is proportional to the permittivity and the square of the breakdown voltage. So in order to enhance the energy density, both the breakdown strength and the permittivity should be improved. The energy density and energy efficiency discharge (energy/charge energy)³ of BT–Cu/PVDF bulk samples (the thickness is 1.0 mm and the diameter is 12.0 mm respectively) with different filler contents were shown in Fig. 12. The energy storage density U_e in the samples is the shaded area in Fig. 12:^{11,19–21,37}

U_e = ∫EdD (4)

where E and D are the electric field and displacement, respectively. For bulk samples, the thickness value is several orders of magnitude higher than that of thin films, and defects appear at a much higher probability. Therefore, compared with thin films, the materials in bulk usually possess lower breakdown strength, which reduces the energy density. As shown in Fig. 12, The charging density of the BT–Cu/PVDF increases from 0.2 J cm⁻³ to 0.8 J cm⁻³ with the increase of volume fraction from f_BT–Cu = 7.3% to f_BT–Cu = 53.7%. The enhanced energy density in the composite is mainly attributed to the increased permittivity. The climbing speed becomes more rapid with the increase of loading of BT–Cu hybrid fillers when f_BT–Cu = 42.3%, corresponding to the significant increase of permittivity at the same loading amount. Meanwhile, energy efficiency declines with the filler loading as the content is raised from 7.3% to 42.3% and then rises to 60% as the loading reaches 53.7%. The BT–Cu/PVDF bulk samples with filler loading 42.3% or less exhibit a small leakage of less than 10⁻⁶ amps measured at the applied voltage of 3.8 kV, and only the composite with 53.7% BT–Cu fillers possesses a current density around 1 × 10⁻⁶ amps. The reason should be that in the composite with high CT–Cu loading, there is a higher probability for more charges to escape and form electric current under a high applied voltage.

Fig. 12 (a) Electric displacement–electric field (D–E) loops (b) energy storage properties (c) leakage current and (d) breakdown strength, E_brk (at 10 V s⁻¹), of the BT–Cu/PVDF composites as a function of Cu volume fraction at room temperature.

Fig. 12d presents the breakdown strength of BT–Cu/PVDF composite based on different loading amounts of BT–Cu fillers. As shown in the figure, there is a slight rise of breakdown strength with a small amount of Cu particles introduced. For example, the E_brk value of the composite with f_Cu = 0.6% is increased to 35.1 MV m⁻¹, which is improved about 8% compared with the pure PVDF matrix. The reason has been indicated in Liu's and Hu's reports.^3,18 There are two aspects for the improvement of breakdown strength. One is that the coating agent (PEG-4000) isolates Cu nanoparticles effectively and forms a robust interfacial layer. Another one is that such small amount of BT–Cu fillers with coating agent are easily distributed uniformly. The two aspects lead to the reduction of the percolation pathways for charge transfer and the mobility of polymer chain, resulting in the slightly improvement of breakdown strength. This phenomenon has also been found in Xie's and Yang's studies,^36,40 and the enhanced breakdown strength was attributed to the coulomb blockade. In our work, the diameter of some of the Cu particles could be smaller than a critical level, the coulomb blockade effect on the nano Cu particles prevents the charges passing through, playing a barrier role in the transport process, which results in the slightly enhanced breakdown strength.²⁹ As the filler loading increases, the breakdown strength value decreases gradually, which is caused by the increased content of conductive Cu particles and more free charges in the system.

4. Conclusion

In conclusion, BT–Cu hybrid nanoparticles were successfully fabricated by a simple hydrothermal method. Cu particles with the diameter of 15–25 nm were deposited on BT powders discretely and subsequently a PEG-4000 protective polymer layer was coated on this hybrid structure. This kind of core–satellite structured BT–Cu particle with the protective shell of PEG-4000 possessed good anti-oxidative stability. We also demonstrated that the PVDF composite with BT–Cu hybrid particles as fillers exhibited significantly improved dielectric properties up to GHz. Concretely, permittivities and dielectric losses of 150/0.16 at 1 kHz, and 57.1/0.064 at 1 kHz and 1 GHz were achieved respectively when the BT–Cu loading is 53.7 vol%. The multiple interfacial polarizations assured by the enhanced interface areas and interactions between BT–PVDF and Cu–PVDF through the robust PEG layer, and BT–Cu through the hetero-structure playing a key role in enhancing the permittivity up to GHz. Besides, copper comes with a great advantage over other noble metals in cost. And the easy processing of the BT–Cu hybrids renders the composites promising applications in the next generation electronic and electric devices.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 51377157), Guangdong Innovative Research Team Program (No. 2011D052), and the Key Laboratory of Guangdong Province (2014B030301014).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra03469a

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