Achieving Excellent Dielectric and Energy Storage Performance in Core-Double-Shell-Structured Polyetherimide Nanocomposites

The development of pulse power systems and electric power transmission systems urgently require the innovation of dielectric materials possessing high-temperature durability, high energy storage density, and efficient charge–discharge performance. This study introduces a core-double-shell-structured iron(II,III) oxide@barium titanate@silicon dioxide/polyetherimide (Fe3O4@BaTiO3@SiO2/PEI) nanocomposite, where the highly conductive Fe3O4 core provides the foundation for the formation of microcapacitor structures within the material. The inclusion of the ferroelectric ceramic BaTiO3 shell enhances the composite’s polarization and interfacial polarization strength while impeding free charge transfer. The outer insulating SiO2 shell contributes excellent interface compatibility and charge isolation effects. With a filler content of 9 wt%, the Fe3O4@BaTiO3@SiO2/PEI nanocomposite achieves a dielectric constant of 10.6, a dielectric loss of 0.017, a high energy density of 5.82 J cm−3, and a charge–discharge efficiency (η) of 72%. The innovative aspect of this research is the design of nanoparticles with a core-double-shell structure and their PEI-based nanocomposites, effectively enhancing the dielectric and energy storage performance. This study provides new insights and experimental evidence for the design and development of high-performance dielectric materials, offering significant implications for the fields of electronic devices and energy storage.


Introduction
Dielectric capacitors play a pivotal role as energy storage components in domains such as pulse power systems and electric power transmissions, owing to their exceptional attributes of ultra-fast charging and discharging rates and high power density [1][2][3]. However, the practical application of these capacitors is currently hindered by the limited energy storage density of polymer dielectrics [4]. With the growing demand for high-temperature applications, such as electric vehicles and aerospace systems, the urgent need for dielectric materials exhibiting exceptional thermal resistance has become increasingly apparent [2,[5][6][7][8][9]. Therefore, the development of dielectric materials that exhibit high-temperature durability, high energy storage density, and efficient charge-discharge performance is of paramount importance. The utilization of composite materials, which amalgamate the advantages of inorganic and organic constituents, has attracted considerable attention and holds promising prospects in the electrical and electronic industries [10][11][12]. Two primary methodologies are employed in the fabrication of high-performance dielectric composites. The first approach involves the incorporation of ferroelectric ceramics possessing high dielectric constants, such as barium titanate (BaTiO 3 ) [13,14], strontium titanate (SrTiO 3 ) [15][16][17], titanium dioxide (TiO 2 ) [18,19], and copper calcium titanate (CCTO) [20,21] into polymers. However, this method often necessitates a substantial filler content, thereby potentially compromising the mechanical properties of the composite. The second approach involves the addition of conductive fillers, such as ferroelectric oxide (Fe 3 O 4 ) [22,23], graphene (GNs) [24][25][26], carbon nanotubes (CNTs) [27], MXene [28,29], etc. Among these alternatives, Fe 3 O 4 exhibits more promising characteristics as a filler. Nevertheless, the practical application of Fe 3 O 4 encounters certain limitations, including nanoparticle agglomeration, poor compatibility with organic matrix, and the possibility to form conductive pathways [30].
To address these challenges, coating is regarded as an effective solution that enables better filler dispersion by introducing various functional layers and thus effectively modulating the dielectric properties of composite materials. Numerous studies have confirmed the effectiveness of coating techniques [22,[30][31][32][33], such as the coating of silicon dioxide (SiO 2 ) on the surface of ultrafine barium titanate (BaTiO 3 ) nanoparticles [34] or the coating of Fe 3 O 4 with functionalized carbon layers and organic polyaniline (PANI) using high-temperature-resistant polymers [23]. Simultaneously, due to the limited operating temperature of commercial biaxially oriented polypropylene (BOPP) films, they fail to meet the requirements of high-temperature electrical systems [35][36][37]. Consequently, there is a compelling need to develop a dielectric material that exhibits both high energy storage density and temperature stability. Polyetherimide (PEI) holds immense promise due to its intrinsically high glass transition temperature (T g = 217 • C) and a maximum operating temperature of 200 • C, thereby satisfactorily meeting the demands of high-temperature applications [38]. By incorporating suitable fillers, the dielectric performance and energy storage density of PEI can be further enhanced while maintaining its high-temperature stability. As a result, PEI exhibits significant potential for widespread applications in high-temperature electrical systems.
Herein, we present a high-temperature polyetherimide (PEI) nanocomposite material, incorporating a core-double-shell-structured nanofiller comprising Fe 3 O 4 nanoparticles as the core, ultrafine BaTiO 3 ceramic as the inner shell, and insulating SiO 2 as the outer shell. Fe 3 O 4 nanospheres as the highly conductive core serve as the foundation for the presence of microcapacitor structures within the material. The addition of the BaTiO 3 shell enhances the polarization and interfacial polarization strength of the composite while simultaneously acting as a barrier during the transfer of free charges. The SiO 2 shell possesses a wide bandgap, thereby providing excellent interface compatibility and charge isolation, resulting in heightened polarization intensity, reduced dielectric loss, and diminished leakage current. The remarkable comprehensive performance of the nanocomposite can be elucidated using the interfacial polarization theory and the innovative microcapacitor structure. Under the influence of an electric field, the interfaces between the core-double-shell-structured nanofillers in the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite accumulate a significant amount of charge, leading to a robust interfacial polarization effect and enhanced dielectric performance. Furthermore, the regular and uniformly distributed core-double-shell-structured nanoparticles within the thin film form numerous microcapacitor structures, which effectively isolate and store charges, thereby substantially improving the dielectric and energy storage performance of the material. With a filler content of 9 wt%, the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite exhibits a dielectric constant of 10.6, a low dielectric loss of 0.017, and a high energy density of 5.82 J cm −3 , with a charge-discharge efficiency (η) of 72%. The fabricated nanocomposite demonstrates outstanding dielectric performance, energy storage capability, and thermal stability. This innovative research provides novel insights and experimental evidence for the design and development of high-performance dielectric materials, thereby holding tremendous potential in various domains, including dielectric composites, wave-absorbing materials, energy storage materials, and supercapacitors [39][40][41][42][43][44].

Synthesis of Fe 3 O 4 with a Hydrothermal Method
Initially, 3.25 g of FeCl 3 ·6H 2 O, 1.3 g of trisodium citrate, and 6 g of sodium acetate were dissolved in 100 mL of ethylene glycol, stirring thoroughly to guarantee the complete dissolution of all compounds. Subsequently, the homogeneous solution was transferred to a 100 mL hydrothermal kettle and heated for 10 h at 200 • C. Following the reaction, the hydrothermal kettle was taken out and left to naturally cool down to room temperature. The resulting product was subsequently washed multiple times with deionized water and anhydrous ethanol to eliminate any remaining impurities and unreacted precursors. Finally, the collected sediment was placed into a vacuum oven and dried at 50 • C for 24 h, yielding Fe 3 O 4 black powder [22,23].

Preparation of Core-Shell-Structured Fe 3 O 4 @BaTiO 3 Nanospheres
The 0.35 g Fe 3 O 4 nanoparticles and 0.25 g CTAB powder were weighed and uniformly dispersed in a mixture containing 100 mL of n-butanol and 5 mL of deionized water. The suspension was then subjected to 1 h of vigorous mechanical stirring and ultrasonication to ensure stability. Concurrently, 1.2 g of tetrabutyl titanate (TBOT) was dissolved in 50 mL of n-butanol, with the precursor solution formed after 1 h of continuous stirring. This solution was then gradually added to the Fe 3 O 4 suspension under mechanical stirring and ultrasonication. Following a 24 h reaction, the products were collected, cleaned with deionized water and ethanol, and vacuum-dried to eliminate impurities and residues, resulting in Fe 3 O 4 @TiO 2 nanoparticles. Finally, the resulting Fe 3 O 4 @TiO 2 and 0.37 g of Ba(OH) 2 ·8H 2 O were dispersed in 60 mL of deionized water and mixed thoroughly. The mixture was transferred to a 100 mL hydrothermal kettle and reacted at 200 • C for 5 h. The powder was then washed with acetic acid to eliminate BaCO 3 impurities, and after multiple deionized water rinses and vacuum drying, Fe 3 O 4 @BaTiO 3 nanoparticles were obtained [45].
2.3. Preparation of Core-Shell-Structured Fe 3 O 4 @SiO 2 or Core-Double-Shell-Structured Fe 3 O 4 @BaTiO 3 @SiO 2 Nanospheres An aliquot of 0.15 g of Fe 3 O 4 @SiO 2 or Fe 3 O 4 powder was weighed and evenly dispensed into 210 mL of ethanol through ultrasonication and mechanical agitation, resulting in a stable suspension. Subsequently, 70 mL of deionized water and 4 mL of ammonia solution were introduced to the suspension and stirred at a high rate for 15 min. A precursor solution was prepared by dissolving 0.3 mL of TEOS in 10 mL of ethanol. The TEOS suspension was gradually introduced to the mixture at a pace of one drop every two seconds while maintaining continuous stirring for 12 h. Following centrifugation to collect the powder, it was rinsed multiple times with deionized water and anhydrous ethanol before being vacuum-dried to yield Fe 3 O 4 @BaTiO 3 @SiO 2 nanoparticles. In particular, for systems of Fe 3 O 4 @SiO 2 nanoparticles with a SiO 2 shell thicknesses of 5 nm and 50 nm, the particle mass-to-TEOS volume ratios were 1.5 g/mL and 0.3 g/mL, respectively. The ratios of other components to particle mass remain unchanged when preparing Fe 3 O 4 @BaTiO 3 @SiO 2 nanoparticles. Figure 1 is the schematic diagram of the preparation process of Fe 3 O 4 @BaTiO 3 @SiO 2 nanospheres [46]. particle mass-to-TEOS volume ratios were 1.5 g/mL and 0.3 g/mL, respectively. The ratios of other components to particle mass remain unchanged when preparing Fe3O4@Ba-TiO3@SiO2 nanoparticles. Figure 1 is the schematic diagram of the preparation process of Fe3O4@BaTiO3@SiO2 nanospheres [46].

Preparation of PEI-Based Nanocomposite Films
The solution-casting method was employed to yield nanocomposite films with various fillers: Fe3O4/PEI, Fe3O4@BaTiO3/PEI, Fe3O4@SiO2/PEI, and Fe3O4@BaTiO3@SiO2/PEI were fabricated. PEI pellets and the four types of nanoparticles obtained were individually dispersed into DMAc through sonication for ~60 min and mechanically stirred for 4 h. Subsequently, each blend solution was subsequently cast onto a glass plate and vacuumdried at 80 °C for 24 h in an oven, thus completely eliminating the solvent. The films were then delicately peeled from the glass plates, ultimately resulting in flexible PEI-based nanocomposite films.

Characterization
The nanoscale morphology of the nanoparticles was observed and analyzed using a JEOL JEM-2100 high-resolution transmission electron microscope (HR-TEM, Tokyo, Japan) and a Gemini SEM 500 energy-dispersive X-ray spectroscopy (EDS, Zeiss, Oberkochen, Germany). X-ray diffraction (XRD) analysis was conducted using a D/MAX 2550 VB/PC rotating anode X-ray diffractometer (Rigaku, Tokyo, Japan) equipped with a Cu Kα radiation source and a Ni filter (operating at 100 mA and 40 kV). Fourier-transform infrared spectroscopy (FT-IR) was performed using a Nicolet 6700 spectrometer (Thermo Fisher, Waltham, MA, USA) with the potassium bromide pellet method. Thermal gravimetric analysis (TGA) was carried out using a Ne sch TG 209 F3 Tarsus instrument from Weimar, Germany under an inert nitrogen atmosphere, with a testing range from room temperature to 800 °C. The cross-sectional images of the films were observed using a Hitachi S-4800 field emission scanning electron microscope (FESEM, Tokyo, Japan). The dielectric impedance spectra of the films were measured using a Novocontrol Concept 80 broadband dielectric impedance spectrometer in the frequency range of 10 0 to 10 6 Hz and a temperature range of 25-100 °C (Montabaur, Germany). According to the ASTM D149 standard [47], the dielectric breakdown strength of the films was determined using a CS2674AX high-voltage tester from Allwin Instrument Co., Nanjing, China. The polarization hysteresis loop and leakage current density were obtained using a ferroelectric polarization tester from Radiant, Inc. at a frequency of 10 Hz and at room temperature. For all electrical tests, a spu er coating technique was employed to deposit 3 mm diameter gold electrodes on both surfaces of the thin film samples.

Preparation of PEI-Based Nanocomposite Films
The solution-casting method was employed to yield nanocomposite films with various fillers: Fe 3 O 4 /PEI, Fe 3 O 4 @BaTiO 3 /PEI, Fe 3 O 4 @SiO 2 /PEI, and Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI were fabricated. PEI pellets and the four types of nanoparticles obtained were individually dispersed into DMAc through sonication for~60 min and mechanically stirred for 4 h. Subsequently, each blend solution was subsequently cast onto a glass plate and vacuumdried at 80 • C for 24 h in an oven, thus completely eliminating the solvent. The films were then delicately peeled from the glass plates, ultimately resulting in flexible PEI-based nanocomposite films.

Characterization
The nanoscale morphology of the nanoparticles was observed and analyzed using a JEOL JEM-2100 high-resolution transmission electron microscope (HR-TEM, Tokyo, Japan) and a Gemini SEM 500 energy-dispersive X-ray spectroscopy (EDS, Zeiss, Oberkochen, Germany). X-ray diffraction (XRD) analysis was conducted using a D/MAX 2550 VB/PC rotating anode X-ray diffractometer (Rigaku, Tokyo, Japan) equipped with a Cu Kα radiation source and a Ni filter (operating at 100 mA and 40 kV). Fourier-transform infrared spectroscopy (FT-IR) was performed using a Nicolet 6700 spectrometer (Thermo Fisher, Waltham, MA, USA) with the potassium bromide pellet method. Thermal gravimetric analysis (TGA) was carried out using a Netzsch TG 209 F3 Tarsus instrument from Weimar, Germany under an inert nitrogen atmosphere, with a testing range from room temperature to 800 • C. The cross-sectional images of the films were observed using a Hitachi S-4800 field emission scanning electron microscope (FESEM, Tokyo, Japan). The dielectric impedance spectra of the films were measured using a Novocontrol Concept 80 broadband dielectric impedance spectrometer in the frequency range of 10 0 to 10 6 Hz and a temperature range of 25-100 • C (Montabaur, Germany). According to the ASTM D149 standard [47], the dielectric breakdown strength of the films was determined using a CS2674AX high-voltage tester from Allwin Instrument Co., Nanjing, China. The polarization hysteresis loop and leakage current density were obtained using a ferroelectric polarization tester from Radiant, Inc. at a frequency of 10 Hz and at room temperature. For all electrical tests, a sputter coating technique was employed to deposit 3 mm diameter gold electrodes on both surfaces of the thin film samples. while the nanoscale barium titanate shell thickness in Fe 3 O 4 @BaTiO 3 is approximately 50 nm. In Fe 3 O 4 @BaTiO 3 @SiO 2 , the respective shell thicknesses of the nanoscale barium titanate and silica are 50 nm and 5 nm. All shell thickness measurements were conducted based on Fe 3 O 4 cores with diameters close to the average particle size (230 nm). We then used the software Digital Micrograph V3.2 to obtain a statistical average thickness.

Preparation and Structure of the Nanoparticles
TEM and SEM images presented in Figures 2 and S1 illustrate the structural evolut from the Fe3O4 core to the Fe3O4@SiO2 and Fe3O4@BaTiO3 core-shell structures, as wel the intermediate Fe3O4@TiO2, and further to the core-double-shell structure of Fe3O4@ TiO3@SiO2. All of these nanoparticles maintain a highly spherical and uniform size. T average diameters of Fe3O4, Fe3O4@BaTiO3, Fe3O4@SiO2, and Fe3O4@BaTiO3@SiO2 are proximately 230 nm, 235/285 nm, 285 nm, and 290 nm, respectively. The silica shell thi ness in Fe3O4@SiO2 is estimated to be around 5 nm and 50 nm (corresponding to Fig  2c,d), while the nanoscale barium titanate shell thickness in Fe3O4@BaTiO3 is appro mately 50 nm. In Fe3O4@BaTiO3@SiO2, the respective shell thicknesses of the nanosc barium titanate and silica are 50 nm and 5 nm. All shell thickness measurements w conducted based on Fe3O4 cores with diameters close to the average particle size (230 n We then used the software Digital Micrograph V3.2 to obtain a statistical average thi ness. The EDS images shown in Figure 2(l-1-l-5) confirm the core-double-shell structure the nanoparticles through the spatial distribution of elemental signals. The Fe elemen signal is primarily concentrated at the center of the nanoparticles, indicating the prese of the Fe3O4 core. The Ba and Ti elemental signals are predominantly concentrated arou The EDS images shown in Figure 2(l-1-l-5) confirm the core-double-shell structure of the nanoparticles through the spatial distribution of elemental signals. The Fe elemental signal is primarily concentrated at the center of the nanoparticles, indicating the presence of the Fe 3 O 4 core. The Ba and Ti elemental signals are predominantly concentrated around the Fe 3 O 4 core, indicating the distribution of the BaTiO 3 shell. Lastly, the Si elemental signal is mainly distributed on the outer surface of the BaTiO 3 shell, indicating the presence of the SiO 2 coating. Overlaying the Fe and Si elements provides a clearer view of the core-shell features. The elemental detection report shown in Figure S2 successfully identifies the presence of Fe, Ba, Ti, and Si in the nanoparticles.
In the XRD spectrum of  [45]. These diffraction peaks align precisely with the crystallographic data provided by JCPDS card number 00-075-0213. Due to the amorphous nature of the encapsulated silica, lacking a long-range ordered crystal structure, the XRD spectra do not display distinct sharp peaks. Hence, the XRD patterns of Fe 3 O 4 @SiO 2 and Fe 3 O 4 @BaTiO 3 @SiO 2 resemble those of nanostructured Fe 3 O 4 and Fe 3 O 4 @BaTiO 3 , respectively. The FTIR spectra of the nanoparticles shown in Figure 3c reveal a prominent absorption peak at 570 cm −1 , corresponding to the Fe-O bond in Fe 3 O 4 . This characteristic peak is observed in all four types of nanoparticles. However, when Fe 3 O 4 is encapsulated by the BaTiO 3 shell and the silica shell, this feature becomes significantly weaker. The broad peak around 3410 cm −1 is attributed to the stretching vibration of hydroxyl groups on the nanoparticle surfaces or the absorbed water molecules. Compared to Fe 3 O 4 , Fe 3 O 4 @BaTiO 3 exhibits a more pronounced peak at 3410 cm −1 . This can be attributed to the smaller size and larger surface area of the synthesized barium titanate, which allows for a greater amount of hydroxyl groups and easier adsorption of water molecules.
In the XRD spectrum of Fe3O4 (Figure 3a), there are seven prominent diffraction peaks, corresponding to the crystal planes, (220), (311), (400), (422), (511), (440), and (533), of Fe3O4, which are in accordance with the JCPDS card 01-088-0315. The X-ray diffraction (XRD) pa ern of Fe3O4@BaTiO3 exhibits multiple distinct diffraction peaks. In addition to the diffraction peaks a ributed to Fe3O4, the XRD pa ern also displays seven prominent diffraction peaks assigned to the crystal planes of barium titanate (BaTiO3), namely (100), (110), (111), (200), (210), (211), and (220) [45]. These diffraction peaks align precisely with the crystallographic data provided by JCPDS card number 00-075-0213. Due to the amorphous nature of the encapsulated silica, lacking a long-range ordered crystal structure, the XRD spectra do not display distinct sharp peaks. Hence, the XRD pa erns of Fe3O4@SiO2 and Fe3O4@BaTiO3@SiO2 resemble those of nanostructured Fe3O4 and Fe3O4@BaTiO3, respectively. The FTIR spectra of the nanoparticles shown in Figure 3c reveal a prominent absorption peak at 570 cm −1 , corresponding to the Fe-O bond in Fe3O4. This characteristic peak is observed in all four types of nanoparticles. However, when Fe3O4 is encapsulated by the BaTiO3 shell and the silica shell, this feature becomes significantly weaker. The broad peak around 3410 cm −1 is a ributed to the stretching vibration of hydroxyl groups on the nanoparticle surfaces or the absorbed water molecules. Compared to Fe3O4, Fe3O4@BaTiO3 exhibits a more pronounced peak at 3410 cm −1 . This can be a ributed to the smaller size and larger surface area of the synthesized barium titanate, which allows for a greater amount of hydroxyl groups and easier adsorption of water molecules. The FT-IR spectra of Fe 3 O 4 @SiO 2 and Fe 3 O 4 @BaTiO 3 @SiO 2 exhibit a strong absorption peak at 1086 cm −1 , which is associated with the stretching vibration of Si-O-Si bonds, further confirming the presence of SiO 2 ( Figure 3c). As depicted in Figure 3d, the four types of nanoparticles exhibited no evident thermal decomposition phenomena within the tested range. The loss in mass primarily originated from the desorption of surfaceadsorbed moisture or other volatile substances. Notably, all fillers displayed a residue weight exceeding 85% at 800 • C. This thermal stability serves as a fundamental prerequisite for fabricating high-temperature-resistant dielectric materials. The XPS spectrum shown in Figure S3 exhibits the elemental composition in the Fe 3 O 4 @BaTiO 3 @SiO 2 nanohybrid filler, with all peaks corresponding to known components.

Properties of the PEI-Based Nanocomposite Films
In this study, we initially embarked upon the fabrication of dielectric nanocomposites based on the principles of the percolation theory, utilizing conductive nanoparticles of Fe 3 O 4 as the filler. As illustrated in Figure S4 Figure S5). Although Fe 3 O 4 /PEI nanocomposite films exhibited an excellent dielectric constant, they did suffer from high losses and high electrical conductivity. These shortcomings could be mitigated by incorporating distinct functional shell layers to fabricate novel nanohybrid structures, thereby enabling precise modulation of the dielectric performance of the nanocomposite. Building upon the foundation of this study, we embarked on the synthesis of three distinct nanocomposites with core-shell and core-double-shell structures: Fe 3 O 4 @BaTiO 3 /PEI, Fe 3 O 4 @SiO 2 /PEI, and Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI. Our aim was to investigate the fundamental characteristics of these materials, such as their conductivity and polarization behavior, and thus the impact of each component on the dielectric performance. By doing so, we speculated to offer valuable guidance that will further advance the design of dielectric materials. Figure 4a-c illustrate the dielectric performance of the four nanocomposites at a filler content of 9 wt%. Fe 3 O 4 @BaTiO 3 /PEI exhibits a high dielectric constant of 14.9 at 1 kHz, which is 4.7 times higher than that of pristine PEI. The dielectric loss is reduced by 70% to 0.037 compared to the Fe 3 O 4 /PEI nanocomposite, and the AC conductivity is significantly decreased. The dielectric behavior of this nanocomposite system can be explained through an improved Maxwell-Wagner capacitor model. Initially, the introduction of ultrafine BaTiO 3 ceramic shell layers augments the interface polarization effect between Fe 3 O 4 @BaTiO 3 composite particles and the PEI matrix, resulting in a heightened dielectric constant of the nanocomposite. Simultaneously, due to the inherent high dielectric constant and ultra-small size of barium titanate, considerable interfacial polarization occurs between the barium titanate grains, thereby sustaining the elevated dielectric constant of the nanocomposite. Furthermore, the reduction in dielectric loss and conductivity in the Fe 3 O 4 @BaTiO 3 /PEI composite can be attributed to two factors. Firstly, the deposition of a continuous and dense layer of BaTiO 3 ceramic on the conductive Fe 3 O 4 surface prevents the formation of conductive pathways within the PEI matrix. Secondly, and more importantly, the numerous grain boundaries in the nano-sized BaTiO 3 serve as traps for capturing internal free charges, making the transfer of space charges difficult. This leads to reduced energy loss, thereby suppressing dielectric loss and conductivity. The mitigation of dielectric loss is also observed in the Fe 3 O 4 @SiO 2 /PEI nanocomposite, where the dielectric constant of the 9 wt% Fe 3 O 4 @SiO 2 /PEI nanocomposite reaches 5.7 at 1 kHz, and the dielectric loss is reduced to 0.015 compared to the Fe 3 O 4 /PEI nanocomposite. This is attributed to the favorable compatibility between the SiO 2 shell and the polymer matrix, which is crucial for achieving high-performance dielectric composites. Additionally, silica exhibits excellent insulating material that effectively inhibits charge migration and enhances the dielectric performance of the material. 9 wt% Fe3O4@SiO2/PEI nanocomposite reaches 5.7 at 1 kHz, and the dielectric loss is reduced to 0.015 compared to the Fe3O4/PEI nanocomposite. This is a ributed to the favorable compatibility between the SiO2 shell and the polymer matrix, which is crucial for achieving high-performance dielectric composites. Additionally, silica exhibits excellent insulating material that effectively inhibits charge migration and enhances the dielectric performance of the material. Figure 4d-f illustrate the spectra of the dielectric constant, dielectric loss, and AC conductivity of Fe3O4@BaTiO3@SiO2/PEI nanocomposite films with varying component contents in the frequency range of 10 0 -10 6 Hz. As the filler mass fraction increases from 0 wt% to 15 wt%, the dielectric constant of the Fe3O4@BaTiO3@SiO2/PEI nanocomposite rises from 3.17 to 19.90. However, this value is still lower than the dielectric constant of 65.54 observed in the Fe3O4/PEI nanocomposite under percolation effects, which is a ributed to the presence of numerous microcapacitor structures within the Fe3O4/PEI nanocomposite. Interestingly, when the filler content is below 6 wt%, the Fe3O4@BaTiO3@SiO2/PEI nanocomposite exhibits a higher dielectric constant than the Fe3O4/PEI nanocomposite. This phenomenon can be a ributed to the introduction of highly polarizable BaTiO3 Figure 4d-f illustrate the spectra of the dielectric constant, dielectric loss, and AC conductivity of Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite films with varying component contents in the frequency range of 10 0 -10 6 Hz. As the filler mass fraction increases from 0 wt% to 15 wt%, the dielectric constant of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite rises from 3.17 to 19.90. However, this value is still lower than the dielectric constant of 65.54 observed in the Fe 3 O 4 /PEI nanocomposite under percolation effects, which is attributed to the presence of numerous microcapacitor structures within the Fe 3 O 4 /PEI nanocomposite. Interestingly, when the filler content is below 6 wt%, the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite exhibits a higher dielectric constant than the Fe 3 O 4 /PEI nanocomposite. This phenomenon can be attributed to the introduction of highly polarizable BaTiO 3 nanoceramics in the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite at lower filling amounts, enhancing the orientational polarization of the composite. Furthermore, the double-shell structure introduces abundant interfaces, whether between the different shell layers or among the nano-sized barium titanate grains, effectively enhancing the interface polarization effect of the composite.
In addition to the enhanced orientational polarization and interface polarization, the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite also contains microcapacitor structures within its internal composition. As shown in Figure 5, when we consider the conductive nanoscale Fe 3 O 4 as the plates of a capacitor and the medium between adjacent composite nanospheres as a multilayer dielectric of the capacitor, it reveals the presence of an effective microcapacitor structure within the nanocomposite. This contributes to the excellent dielectric performance of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite. The fabricated core-doubleshell-structured nanocomposite exhibits outstanding dielectric properties, with a dielectric constant of 10.6 at 1 kHz and a filler content of 9 wt%, which is 3.35 times higher than that of pristine PEI. Furthermore, the dielectric loss is significantly reduced to 0.017. among the nano-sized barium titanate grains, effectively enhancing the interface polarization effect of the composite.
In addition to the enhanced orientational polarization and interface polarization, the Fe3O4@BaTiO3@SiO2/PEI nanocomposite also contains microcapacitor structures within its internal composition. As shown in Figure 5, when we consider the conductive nanoscale Fe3O4 as the plates of a capacitor and the medium between adjacent composite nanospheres as a multilayer dielectric of the capacitor, it reveals the presence of an effective microcapacitor structure within the nanocomposite. This contributes to the excellent dielectric performance of the Fe3O4@BaTiO3@SiO2/PEI nanocomposite. The fabricated coredouble-shell-structured nanocomposite exhibits outstanding dielectric properties, with a dielectric constant of 10.6 at 1 kHz and a filler content of 9 wt%, which is 3.35 times higher than that of pristine PEI. Furthermore, the dielectric loss is significantly reduced to 0.017. Figure 5. Novel microcapacitive structure and interface polarization effect within the nanocomposite thin film of Fe3O4@BaTiO3@SiO2/PEI, incorporating a core-double-shell structure for the fillers.
As expressed using the equation = 1/2 , the breakdown strength of the dielectric is a crucial parameter that determines the working electric field and energy density. In this study, we employ the dual-parameter Weibull distribution function to analyze the dielectric breakdown behavior of both the pristine PEI and its nanocomposite films: Here, P(E) represents the cumulative probability of electrical failure, β denotes the shape parameter, and E and Eb, respectively, correspond to the experimental breakdown strength and characteristic breakdown strength when the cumulative failure probability is 63.2%. A higher β value signifies superior film quality and exceptional structural integrity. The breakdown strength of the Fe3O4@BaTiO3@SiO2/PEI nanocomposite film is significantly improved compared to Fe3O4/PEI. Specifically, at a filler content of 3 wt%, the Fe3O4@BaTiO3@SiO2/PEI demonstrates a remarkable breakdown strength of 406 MV m −1 , which is 1.43 times higher than that of Fe3O4/PEI nanocomposite ( Figure S6) with the same filler content (284 MV m −1 ). Similarly, both Fe3O4@BaTiO3/PEI and Fe3O4@SiO2/PEI exhibit superior breakdown strength compared to Fe3O4/PEI. This can be a ributed to the ability of the BaTiO3 shell to capture free charges and the insulating effect of the high bandgap As expressed using the equation U e = 1/2ε r ε 0 E b 2 , the breakdown strength of the dielectric is a crucial parameter that determines the working electric field and energy density. In this study, we employ the dual-parameter Weibull distribution function to analyze the dielectric breakdown behavior of both the pristine PEI and its nanocomposite films: Here, P(E) represents the cumulative probability of electrical failure, β denotes the shape parameter, and E and E b , respectively, correspond to the experimental breakdown strength and characteristic breakdown strength when the cumulative failure probability is 63.2%. A higher β value signifies superior film quality and exceptional structural integrity. The breakdown strength of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite film is significantly improved compared to Fe 3 O 4 /PEI. Specifically, at a filler content of 3 wt%, the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI demonstrates a remarkable breakdown strength of 406 MV m −1 , which is 1.43 times higher than that of Fe 3 O 4 /PEI nanocomposite ( Figure S6) with the same filler content (284 MV m −1 ). Similarly, both Fe 3 O 4 @BaTiO 3 /PEI and Fe 3 O 4 @SiO 2 /PEI exhibit superior breakdown strength compared to Fe 3 O 4 /PEI. This can be attributed to the ability of the BaTiO 3 shell to capture free charges and the insulating effect of the high bandgap SiO 2 shell in isolating charges. When designing the SiO 2 shell thickness in Fe 3 O 4 @BaTiO 3 @SiO 2 nanoparticles, we discovered that varying the thickness of the SiO 2 shell in Fe 3 O 4 @SiO 2 did not significantly impact the breakdown strength of Fe 3 O 4 @SiO 2 /PEI nanocomposite films. Considering the average polarization, the thickness of the SiO 2 shell in Fe 3 O 4 @BaTiO 3 @SiO 2 is also designed to be 5 nm ( Figure S7). Additionally, the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite exhibits a high β value (Figure 6c), indicating excellent film quality and uniformity. The 9 wt% Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite film demonstrates a defect-free surface, with fillers uniformly distributed within the PEI matrix and displaying good interfacial interactions with the polymer (refer to Figure S8). This diminishes the non-uniformity of the electric field distribution within the composite, thereby enhancing the breakdown strength.
TiO3@SiO2/PEI nanocomposite exhibits a high β value (Figure 6c), indicating excellent film quality and uniformity. The 9 wt% Fe3O4@BaTiO3@SiO2/PEI nanocomposite film demonstrates a defect-free surface, with fillers uniformly distributed within the PEI matrix and displaying good interfacial interactions with the polymer (refer to Figure S8). This diminishes the non-uniformity of the electric field distribution within the composite, thereby enhancing the breakdown strength. To be er understand the advantages of the core-double-shell nanostructure in nanocomposites, we employed COMSOL Multiphysics to computationally simulate the electric field distribution in Fe3O4@BaTiO3@SiO2/PEI nanocomposite films. The simulation results indicate that in the Fe3O4/PEI nanocomposite, the surrounding region of the conductive Fe3O4 nanoparticles experiences significantly high electric field intensities. Conversely, in the Fe3O4@BaTiO3@SiO2/PEI nanocomposite, the presence of the SiO2 insulating shell inhibits electric field distortions near Fe3O4. The yellow areas on both sides along the electric field direction turn blue after SiO2 modification, indicating a greater concentration of localized electric field release.
We next investigated the capacitive energy storage performance of the nanocomposites in terms of discharged energy density (Ue) and charge-discharge efficiency (η) by referring to the unipolar D-E loops. Although the Fe3O4/PEI nanocomposite material exhibits an enhanced electrical displacement compared to pristine PEI (Figure 7a) due to the increased dielectric constant, it also results in a decrease in charge-discharge efficiency (η) and breakdown strength (E). Consequently, the energy storage performance of the Fe3O4/PEI nanocomposite film is significantly diminished. However, the fabricated coredouble-shell-structured Fe3O4@BaTiO3@SiO2/PEI nanocomposite can effectively address To better understand the advantages of the core-double-shell nanostructure in nanocomposites, we employed COMSOL Multiphysics to computationally simulate the electric field distribution in Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite films. The simulation results indicate that in the Fe 3 O 4 /PEI nanocomposite, the surrounding region of the conductive Fe 3 O 4 nanoparticles experiences significantly high electric field intensities. Conversely, in the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite, the presence of the SiO 2 insulating shell inhibits electric field distortions near Fe 3 O 4 . The yellow areas on both sides along the electric field direction turn blue after SiO 2 modification, indicating a greater concentration of localized electric field release.
We next investigated the capacitive energy storage performance of the nanocomposites in terms of discharged energy density (U e ) and charge-discharge efficiency (η) by referring to the unipolar D-E loops. Although the Fe 3 O 4 /PEI nanocomposite material exhibits an enhanced electrical displacement compared to pristine PEI (Figure 7a) due to the increased dielectric constant, it also results in a decrease in charge-discharge efficiency (η) and breakdown strength (E). Consequently, the energy storage performance of the Fe 3 O 4 /PEI nanocomposite film is significantly diminished. However, the fabricated core-double-shell-structured Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite can effectively address this issue, thus allowing for the achievement of high electrical displacement (D, 5.21 µ cm −2 ) while maintaining a superior charge-discharge efficiency (η, 72%). The enhancement in electrical displacement can be attributed to the synergistic influence of orientation polarization, interface polarization, and the collaborative effect of the internal microcapacitive structure, resulting in an amplified polarization intensity. The improvement in charge-discharge efficiency (η) originates from the restriction of free charges with the double-shell layers, along with the low energy loss of the composite film due to the excellent compatibility between the composite nanoparticles and the matrix, ensuring minimal energy dissipation. As shown in Figure 7b,c, the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite film exhibits a narrower DE loop and can withstand higher test voltages. The 9 wt% Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite achieves a high energy density of 5.82 J cm −3 , which is an increase of 477% compared to the pristine PEI polymer un-der the same electric field and 120% compared to the Fe 3 O 4 /PEI nanocomposite at the maximum tested electric field. Moreover, all of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposites exhibit a charge-discharge efficiency (η) greater than 70%. Compared to similar materials such as Fe 3 O 4 @C@PANI/PBO [23], BT-Fe 3 O 4 /PVDF [48], and C@BT@R-PANI/PEI [49], the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite demonstrates significant advantages in terms of dielectric loss, energy density, and operating temperature (as shown in Table S1). In addition, we also investigated the leakage current density of the four nanocomposite films (Figure 7f). At 50 MVm −1 , the introduction of Fe 3 O 4 nanoparticles (3 wt%) reduces the leakage current from 1.24 × 10 −8 A cm −2 for pristine PEI to 3.8 × 10 −7 A cm −2 for Fe 3 O 4 /PEI nanocomposite material. Similarly, the leakage current density of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite, with the same filler content, remains at 2.89 × 10 −8 A cm −2 . Both the core-shell and core-double-shell structures of the PEI composites exhibit a significant reduction in leakage current density, approximately an order of magnitude lower than that of the Fe 3 O 4 /PEI nanocomposite. This suggests that the BaTiO 3 and SiO 2 shell layers effectively block the conductive pathways formed by adjacent Fe 3 O 4 nanoparticles along the electric field direction.
charge-discharge efficiency (η) originates from the restriction of free charges with the double-shell layers, along with the low energy loss of the composite film due to the excellent compatibility between the composite nanoparticles and the matrix, ensuring minimal energy dissipation. As shown in Figure 7b,c, the Fe3O4@BaTiO3@SiO2/PEI nanocomposite film exhibits a narrower DE loop and can withstand higher test voltages. The 9 wt% Fe3O4@BaTiO3@SiO2/PEI nanocomposite achieves a high energy density of 5.82 J cm −3 , which is an increase of 477% compared to the pristine PEI polymer under the same electric field and 120% compared to the Fe3O4/PEI nanocomposite at the maximum tested electric field. Moreover, all of the Fe3O4@BaTiO3@SiO2/PEI nanocomposites exhibit a charge-discharge efficiency (η) greater than 70%. Compared to similar materials such as Fe3O4@C@PANI/PBO [23], BT-Fe3O4/PVDF [48], and C@BT@R-PANI/PEI [49], the Fe3O4@BaTiO3@SiO2/PEI nanocomposite demonstrates significant advantages in terms of dielectric loss, energy density, and operating temperature (as shown in Table S1). In addition, we also investigated the leakage current density of the four nanocomposite films (Figure 7f). At 50 MVm −1 , the introduction of Fe3O4 nanoparticles (3 wt%) reduces the leakage current from 1.24 × 10 −8 A cm −2 for pristine PEI to 3.8 × 10 −7 A cm −2 for Fe3O4/PEI nanocomposite material. Similarly, the leakage current density of the Fe3O4@BaTiO3@SiO2/PEI nanocomposite, with the same filler content, remains at 2.89 × 10 −8 A cm −2 . Both the coreshell and core-double-shell structures of the PEI composites exhibit a significant reduction in leakage current density, approximately an order of magnitude lower than that of the Fe3O4/PEI nanocomposite. This suggests that the BaTiO3 and SiO2 shell layers effectively block the conductive pathways formed by adjacent Fe3O4 nanoparticles along the electric field direction. In the realm of extreme application environments, the thermal stability of dielectric materials plays a significant role in assessing their long-term stability. To evaluate these properties, we conducted continuous testing of four different materials, measuring their In the realm of extreme application environments, the thermal stability of dielectric materials plays a significant role in assessing their long-term stability. To evaluate these properties, we conducted continuous testing of four different materials, measuring their dielectric constants and dielectric losses under a frequency of 1 kHz and temperatures ranging from 30 • C to 100 • C. The results, as depicted in Figure 8, reveal minimal variations in both the dielectric constant and dielectric loss of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite material across the entire temperature range. This notable temperature insensitivity demonstrates the exceptional thermal stability of the nanocomposite material, allowing it to maintain a stable dielectric performance even in high-temperature environments ( Figure S9). Such outstanding thermal stability can be attributed to both the inherent properties of the nanofillers themselves and the exceptional thermal stability of the PEI composite material. It is worth noting that the 9 wt% Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite material exhibits a dielectric constant of 11.0 and a dielectric loss of 0.023 at 100 • C. In conclusion, these findings affirm the reliable applicability of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite with its core-double-shell structure in high-temperature environments. This discovery provides crucial guidance and a solid foundation for the development of highly stable dielectric materials intended for extreme application conditions. vironments ( Figure S9). Such outstanding thermal stability can be a ributed to both the inherent properties of the nanofillers themselves and the exceptional thermal stability of the PEI composite material. It is worth noting that the 9 wt% Fe3O4@BaTiO3@SiO2/PEI nanocomposite material exhibits a dielectric constant of 11.0 and a dielectric loss of 0.023 at 100 °C. In conclusion, these findings affirm the reliable applicability of the Fe3O4@Ba-TiO3@SiO2/PEI nanocomposite with its core-double-shell structure in high-temperature environments. This discovery provides crucial guidance and a solid foundation for the development of highly stable dielectric materials intended for extreme application conditions.

Conclusions
This research work has centered around the successful development, characterization, and application of the novel core-double-shell-structured nanocomposite, Fe3O4@Ba-TiO3@SiO2/PEI. The unique design and fabrication of this nanocomposite aim to address the limitations of conventional materials in terms of dielectric performance, energy density, and operating temperature. We began by synthesizing core-double-shell-structured nanocomposites with Fe3O4 as the core, BaTiO3 and SiO2 as the shell layers, and PEI as the matrix, using hydrothermal and solvothermal methods. The composition and morphology of the nanocomposite were validated through various analytical techniques such as XRD, TEM, and FT-IR.
By evaluating the dielectric constant, dielectric loss, and AC conductivity in the frequency range of 10 0 -10 6 Hz with increasing filler mass fraction, we found that the Fe3O4@BaTiO3@SiO2/PEI nanocomposite demonstrates superior dielectric performance. Our results demonstrate a high dielectric constant of up to 10.6, with a dielectric loss of only 0.017 at a 9 wt% filler content, along with a significant improvement in breakdown strength compared to Fe3O4/PEI. These exceptional dielectric properties are primarily due to the polarization enhancement of the nanoceramic BaTiO3 and the microcapacitive structure of the multilayer dielectric capacitor. We noticed a significant improvement in the dielectric breakdown strength of the Fe3O4@BaTiO3@SiO2/PEI nanocomposite film, and the breakdown strength is 406 MV·m −1 at a 3 wt% filler content, which can be a ributed to the

Conclusions
This research work has centered around the successful development, characterization, and application of the novel core-double-shell-structured nanocomposite, Fe 3 O 4 @BaTiO 3 @SiO 2 / PEI. The unique design and fabrication of this nanocomposite aim to address the limitations of conventional materials in terms of dielectric performance, energy density, and operating temperature. We began by synthesizing core-double-shell-structured nanocomposites with Fe 3 O 4 as the core, BaTiO 3 and SiO 2 as the shell layers, and PEI as the matrix, using hydrothermal and solvothermal methods. The composition and morphology of the nanocomposite were validated through various analytical techniques such as XRD, TEM, and FT-IR.
By evaluating the dielectric constant, dielectric loss, and AC conductivity in the frequency range of 10 0 -10 6 Hz with increasing filler mass fraction, we found that the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite demonstrates superior dielectric performance. Our results demonstrate a high dielectric constant of up to 10.6, with a dielectric loss of only 0.017 at a 9 wt% filler content, along with a significant improvement in breakdown strength compared to Fe 3 O 4 /PEI. These exceptional dielectric properties are primarily due to the polarization enhancement of the nanoceramic BaTiO 3 and the microcapacitive structure of the multilayer dielectric capacitor. We noticed a significant improvement in the dielectric breakdown strength of the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite film, and the breakdown strength is 406 MV·m −1 at a 3 wt% filler content, which can be attributed to the BaTiO 3 shell's ability to capture free charges and the insulating effect of the SiO 2 shell. Through computational simulations using COMSOL Multiphysics, we found that the SiO 2 insulating shell in the Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite prevents electric field distortions near Fe 3 O 4 , resulting in a higher concentration of localized electric field release.
In addition, we also investigated the energy storage performance of nanocomposite materials in terms of discharge energy density (U e ) and charge-discharge efficiency (η). We found that the 9 wt% Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite achieved an impressive energy density of up to 5.82 J cm −3 , with a charge-discharge efficiency (η) exceeding 70%. This can be attributed to the synergistic effects of orientation polarization, interfacial polarization, and internal microcapacitor structures, as well as the confinement of free charges by the double-shell layer. Lastly, we evaluated the thermal stability of the nanocomposite. Our tests revealed minimal variations in both the dielectric constant and dielectric loss of the nanocomposite material across a temperature range from 30 • C to 100 • C, showcasing its outstanding thermal stability. Notably, even at a high temperature environment (100 • C), the 9 wt% Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite exhibited a dielectric constant of 11.0 and a dielectric loss of 0.023, affirming its reliable applicability under extreme application conditions.
In conclusion, this study provides critical guidance and a solid foundation for the development of highly stable dielectric materials for future applications in extreme conditions. Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/polym15143088/s1; Figure S1: TEM image of the ultrafine barium titanate at the edges of Fe 3 O 4 @BaTiO 3 nanoparticles; Figure S2: element detection report from the EDS analysis conducted on Fe 3 O 4 @BaTiO 3 @SiO 2 nanoparticles; Figure S3: (a) full XPS spectrum of Fe 3 O 4 @BaTiO 3 @SiO 2 , (b-f) XPS single spectra of Fe2p, Ba3d, Ti2p, Si2p, and O1s regions, respectively; Figure S4 Figure S7: Weibull distribution plots of Fe 3 O 4 @SiO 2 /PEI nanocomposite films with an SiO 2 shell thicknesses of 5 nm and 50 nm, respectively; Figure S8: (a,b) Surface SEM images (c,d) cross-section SEM and (e,f) optical photos (focusing on the circular region in the middle) of the pristine PEI film and the 9 wt% Fe 3 O 4 @BaTiO 3 @SiO 2 /PEI nanocomposite film, respectively. (The Chinese part represents the affiliation of the authors: East China University of Science and Technology.); Figure S9: thermogravimetric curves of PEI and its nanocomposite films; Table S1: performance parameters of dielectric composites have been reported in recent years in relation to this subject. Refs. [23,45,[48][49][50] are cited in the supplementary materials.