Roles of Al2O3@ZrO2 Particles in Modulating Crystalline Morphology and Electrical Properties of P(VDF-HFP) Nanocomposites

Polymer materials with excellent physicochemical and electrical properties are desirable for energy storage applications in advanced electronics and power systems. Here, Al2O3@ZrO2 nanoparticles (A@Z) with a core-shell structure are synthesized and introduced to a P(VDF-HFP) matrix to fabricate P(VDF-HFP)/A@Z nanocomposite films. Experimental and simulation results confirm that A@Z nanoparticles increase the crystallinity and crystallization temperature owing to the effect of the refined crystal size. The incorporation of A@Z nanoparticles leads to conformational changes of molecular chains of P(VDF-HFP), which influences the dielectric relaxation and trap parameters of the nanocomposites. The calculated total trapped charges increase from 13.63 μC of the neat P(VDF-HFP) to 47.55 μC of P(VDF-HFP)/5 vol%-A@Z nanocomposite, indicating a substantial improvement in trap density. The modulated crystalline characteristic and interfaces between nanoparticles and polymer matrix are effective in inhibiting charge motion and impeding the electric conduction channels, which contributes to an improved electrical property and energy density of the nanocomposites. Specifically, a ~200% and ~31% enhancement in discharged energy density and breakdown strength are achieved in the P(VDF-HFP)/5 vol%-A@Z nanocomposite.


Introduction
Sustainable development based on clean energy has attracted extensive attention worldwide, which concerns storing energy in environmentally friendly ways and increasing the efficiency of electrical energy conversion [1]. Numerous devices, including electrochemical batteries, supercapacitors and dielectric capacitors, have been developed for electrical energy storage technologies [2,3]. The dielectric film capacitors serve as the key unit in electric vehicles, high-voltage direct current (HVDC) transmission systems and pulse power systems owing to their fast charging-discharging rates, superior power density, long cycle life and great reliability [1,4]. Among the various dielectric capacitor materials, such as ceramics, mica and synthetic polymers, polymer-based dielectrics feature high breakdown strength, light weight, flexibility and facile preparation.
Currently, the energy density of benchmark commercial biaxially oriented polypropylene (BOPP) polymer film capacitors is only~2 J cm −3 , which is far behind the demand of modern power electronic systems [5]. The hexafluoropropylene (HFP) monomers employed to copolymerize with vinylidene fluoride (VDF) break apart the large crystals and decouple the ferroelectric domains, which promotes polarization and reduces the remnant polarization [6,7]. The resultant copolymers P(VDF-HFP) ferroelectric polymers are considered one of the most promising polymer dielectrics for high-energy-density film capacitors owing to the P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites with different filler volume fractions are presented in Figure 1b-i. The thickness of the nanocomposite films is well controlled to be ~10 μm. Owing to the polar surface of metallic oxides [12,22,23], the ZrO2 and A@Z nanoparticles are well dispersed in the polymer matrix, showing no apparent filler aggregation on a large scale.

Thermal Characterization of the Nanocomposites
Differential scanning calorimetry (DSC) curves of the neat P(VDF-HFP), P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites are shown in Figure 2. A melting peak can be detected in the heating scan of all nanocomposites. The crystallinity (Xc) of nanocomposites can be calculated via the following expression: where ΔHm is the enthalpy of fusion derived from melting peaks, Φ is the mass ratio of the nanoparticle, ΔH0 is the heat of fusion for 100% crystalline P(VDF-HFP), which is reported to be 104.7 J/g [24]. As summarized in Table 1, the P(VDF-HFP)/5 vol%-A@Z nanocomposites present the largest Xc of 23.2%, compared with the values of 15.0% and 22.5% for the neat P(VDF-HFP) and P(VDF-HFP)/5 vol%-Zr nanocomposites, respectively. These results can be understood based on the intensified interaction among different molecules and increased heterogeneous nucleation points caused by the A@Z nanoparticles [9,24].

Thermal Characterization of the Nanocomposites
Differential scanning calorimetry (DSC) curves of the neat P(VDF-HFP), P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites are shown in Figure 2. A melting peak can be detected in the heating scan of all nanocomposites. The crystallinity (X c ) of nanocomposites can be calculated via the following expression: where ∆H m is the enthalpy of fusion derived from melting peaks, φ is the mass ratio of the nanoparticle, ∆H 0 is the heat of fusion for 100% crystalline P(VDF-HFP), which is reported to be 104.7 J/g [24]. As summarized in Table 1, the P(VDF-HFP)/5 vol%-A@Z nanocomposites present the largest X c of 23.2%, compared with the values of 15.0% and 22.5% for the neat P(VDF-HFP) and P(VDF-HFP)/5 vol%-Zr nanocomposites, respectively. These results can be understood based on the intensified interaction among different molecules and increased heterogeneous nucleation points caused by the A@Z nanoparticles [9,24]. the P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites with different filler volume fractions are presented in Figure 1b-i. The thickness of the nanocomposite films is well controlled to be ~10 μm. Owing to the polar surface of metallic oxides [12,22,23], the ZrO2 and A@Z nanoparticles are well dispersed in the polymer matrix, showing no apparent filler aggregation on a large scale.

Thermal Characterization of the Nanocomposites
Differential scanning calorimetry (DSC) curves of the neat P(VDF-HFP), P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites are shown in Figure 2. A melting peak can be detected in the heating scan of all nanocomposites. The crystallinity (Xc) of nanocomposites can be calculated via the following expression: where ΔHm is the enthalpy of fusion derived from melting peaks, Φ is the mass ratio of the nanoparticle, ΔH0 is the heat of fusion for 100% crystalline P(VDF-HFP), which is reported to be 104.7 J/g [24]. As summarized in Table 1, the P(VDF-HFP)/5 vol%-A@Z nanocomposites present the largest Xc of 23.2%, compared with the values of 15.0% and 22.5% for the neat P(VDF-HFP) and P(VDF-HFP)/5 vol%-Zr nanocomposites, respectively. These results can be understood based on the intensified interaction among different molecules and increased heterogeneous nucleation points caused by the A@Z nanoparticles [9,24].  According to the cooling scan of DSC measurements, the crystallization temperature (T c ) of the composites is increased with addition of the nanoparticles. As shown in Table 1, the T c are 121.7 • C, 124.0 • C, and 124.3 • C for the neat P(VDF-HFP), P(VDF-HFP)/5 vol%-Zr, and P(VDF-HFP)/5 vol%-A@Z nanocomposites, respectively. It is believed that the nanoparticles act as nucleating agents and physical barriers to block the motion of polymer chains, making the nanocomposites crystallize at higher temperatures [15]. Table 1. DSC results of the P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites.

Mechanical Properties of the Nanocomposites
The stress-strain behavior and Young's modulus results are illustrated in Figure 3a,b. As shown in Figure 3b, taking the P(VDF-HFP)/5 vol%-A@Z as an example, the stressstrain curve has four distinct regimes [25]: elastic regime, yield regime, softening regime and hardening regime. In the elastic regime, the stress increases nearly linearly with increasing applied strain. Upon reaching the yield point, the stress shows a slight decrease, suggesting that the material enters the softening region. Further deformation of the P(VDF-HFP)/nanoparticle nanocomposites causes an increase in strain hardening. According to the cooling scan of DSC measurements, the crystallization temperature (Tc) of the composites is increased with addition of the nanoparticles. As shown in Table  1, the Tc are 121.7 °C, 124.0 °C, and 124.3 °C for the neat P(VDF-HFP), P(VDF-HFP)/5 vol%-Zr, and P(VDF-HFP)/5 vol%-A@Z nanocomposites, respectively. It is believed that the nanoparticles act as nucleating agents and physical barriers to block the motion of polymer chains, making the nanocomposites crystallize at higher temperatures [15].

Mechanical Properties of the Nanocomposites
The stress-strain behavior and Young's modulus results are illustrated in Figure 3a,b. As shown in Figure 3b, taking the P(VDF-HFP)/5 vol%-A@Z as an example, the stressstrain curve has four distinct regimes [25]: elastic regime, yield regime, softening regime and hardening regime. In the elastic regime, the stress increases nearly linearly with increasing applied strain. Upon reaching the yield point, the stress shows a slight decrease, suggesting that the material enters the softening region. Further deformation of the P(VDF-HFP)/nanoparticle nanocomposites causes an increase in strain hardening. The relationship between the Young's modulus and breakdown strength for the P(VDF-HFP)/nanoparticle nanocomposites can be described via Equation (2) [26,27] where Y is the Young's modulus, Eb is the breakdown field. The Young's modulus of nanocomposites determines the electromechanical failure caused by the coulombic force The relationship between the Young's modulus and breakdown strength for the P(VDF-HFP)/nanoparticle nanocomposites can be described via Equation (2) [26,27], where Y is the Young's modulus, E b is the breakdown field. The Young's modulus of nanocomposites determines the electromechanical failure caused by the coulombic force under an applied field. As shown in the inset of Figure 3a, the maximum Young's modulus of the P(VDF-HFP)/A@Z nanocomposites is 6.72 GPa at the filler content of 5 vol%, which is 86.7% and 38.0% higher than that of the neat P(VDF-HFP) (3.60 GPa) and P(VDF-HFP)/5 vol%-Zr (4.87 GPa), respectively. It is thus reasoned that interfaces created by A@Z nanoparticles may improve the electromechanical behavior of the nanocomposites under a high electrical field [26]. However, the Young's modulus and mechanical flexibility of nanocomposites were reduced when more nanoparticles were introduced, which may result in filler aggregation and induce the micro-crack sites at the interfaces between the fillers and polymer matrix [27].

Leakage Current Density of the Nanocomposites
In general, leakage current is mainly caused by the movement of charge carriers such as ionic impurities or electrons injected from electrodes [21]. It has been demonstrated that the leakage current density plays a dominant role in determining the electrical conduction and energy loss of dielectrics. It is evident in Figure 4a that the leakage current density of the P(VDF-HFP)/Zr nanocomposites is minimized at a filler content of 5 vol%. For instance, the leakage current density measured at 50 MV/m decreases from 1.62 × 10 −7 A/cm 2 of the neat P(VDF-HFP) to 2.60 × 10 −8 A/cm 2 of P(VDF-HFP)/5 vol%-Zr (Figure 4b). The reduction in leakage current is mainly associated with the organic/inorganic interfaces, which may serve as trapping centers to hinder carrier transportation [9,28]. Taking advantage of the excellent insulation property of the Al 2 O 3 layer, the P(VDF-HFP)/5 vol%-A@Z nanocomposite displays the minimum leakage current density of 1.54 × 10 −8 A/cm 2 at 50 MV/m, as shown in Figure 4c,d, which is 90.5% and 40.8% lower than neat P(VDF-HFP) and P(VDF-HFP)/5 vol%-Zr, respectively.

Dielectric Breakdown Strength of the Nanocomposites
The dielectric breakdown strength of nanocomposites is analyzed based on a twoparameter Weibull statistic model [9]:

Dielectric Breakdown Strength of the Nanocomposites
The dielectric breakdown strength of nanocomposites is analyzed based on a twoparameter Weibull statistic model [9]: where P is the cumulative probability of dielectric failure, E is the measured discrete breakdown strength, E b is the Weibull characteristic breakdown strength and β is the shape parameter which reflects the dispersion degree of the data. As depicted in Figure 5a Figure 5c, an obvious electric field distortion occurs around the nanoparticles due to the large difference in dielectric permittivity and conductivity between ZrO 2 and P(VDF-HFP) matrix [29,30]. Thus, the adjacent nanoparticles may form conducting channels and generate a potential partial breakdown in the nanocomposite [31], as illustrated in Figure 5f. Remarkably, the local electric field near the A@Z nanoparticles in P(VDF-HFP)/A@Z nanocomposite ( Figure 5d) is lower and less distorted compared with the P(VDF-HFP)/Zr nanocomposite. In Figure 5e, the results show that the maximum local electric field of P(VDF-HFP)/A@Z nanocomposites is 427.2 MV/m, which is about 9.2% lower than that in P(VDF-HFP)/Zr nanocomposites (i.e., 470.6 MV/m), suggesting that the Al 2 O 3 shell layer successfully impedes the propagation of conducting channels and modulates the local inhomogeneous electrical field. As a result, the P(VDF-HFP)/A@Z nanocomposites show a larger breakdown field at the same filling content.

Energy Storage Properties of the Nanocomposites
The charge-discharge efficiency (η) is an important metric of polymer materials, as the heat generated by unreleased energy is detrimental to the performance and reliability of capacitors. The energy loss of P(VDF-HFP), including those from electrical conduction and polarization hysteresis caused by irreversible dipoles, can be manifested directly by the remnant displacement (D r ), i.e., the electric displacement at zero electric field [26,28]. As shown in the insets of Figure 6a, the D r at 300 MV/m decreases from 0.92 C/cm 2 of the neat P(VDF-HFP) to 0.86 C/cm 2 of P(VDF-HFP)/Zr nanocomposite with 5 vol% of ZrO 2 and further decreases to 0.64 C/cm 2 of P(VDF-HFP)/5 vol%-A@Z nanocomposite. The incorporation of nanoparticles suppresses the polymer recrystallization and brings about a decline in the crystallite size of nanocomposites [9,26]. The polymer crystals with smaller sizes facilitate the dipole orientation and inhibit the hysteresis loss [9,13,26]. Consequently, the incorporation of A@Z nanoparticles can significantly mitigate the reduction of η with applied field, e.g., the η of P(VDF-HFP)/5 vol%-A@Z nanocomposite is 71.4% at 300 MV/m compared to 51.4% of the neat P(VDF-HFP) and 64.2% of the P(VDF-HFP)/5 vol%-Zr nanocomposite.
The discharged energy density (U d ) of the neat P(VDF-HFP), P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites are calculated from the D-E loops (Figure 6b-d) and summarized in Figure 7a,b. As plotted in Figure 7b, the maximum U d of the P(VDF-HFP)/A@Z nanocomposites can reach up to 11.8 J/cm 3 at the filler content of 5 vol%, which is 202.6% and 49.4% higher than neat P(VDF-HFP) (3.9 J/cm 3 ) and P(VDF-HFP)/5 vol%-Zr nanocomposite (7.9 J/cm 3 ), respectively. This could contribute to the synergetic increase in E b and η as well as the decrease in leakage current density [8].   Figure 7b, the maximum Ud of the P(VDF-HFP)/A@Z nanocomposites can reach up to 11.8 J/cm 3 at the filler content of 5 vol%, which is 202.6% and 49.4% higher than neat P(VDF-HFP) (3.9 J/cm 3 ) and P(VDF-HFP)/5 vol%-Zr nanocomposite (7.9 J/cm 3 ), respectively. This could contribute to the synergetic increase in Eb and η as well as the decrease in leakage current density [8].

Dielectric Loss of the Nanocomposites
The dielectric loss (ε″) versus frequency (ε″ − f) of the neat P(VDF-HFP), P(VDF-HFP)/5 vol%-Zr and P(VDF-HFP)/5 vol%-A@Z nanocomposites at various temperatures are shown in Figure 8. It is evident that ε″ increases with increasing temperatures due to

Dielectric Loss of the Nanocomposites
The dielectric loss (ε") versus frequency (ε" − f ) of the neat P(VDF-HFP), P(VDF-HFP)/5 vol%-Zr and P(VDF-HFP)/5 vol%-A@Z nanocomposites at various temperatures are shown in Figure 8. It is evident that ε" increases with increasing temperatures due to the accelerated segmental motions at high temperatures [32,33]. In the low-frequency interval, ε" of all nanocomposites decreases linearly with the increasing frequency, which is a typical DC conduction process [32,34]. DC conduction is a result of localized charges jumping to neighboring sites and forming continuous connected networks, allowing the conduction current throughout the entire physical dimensions of the samples [33,35].
In Figure 8a-c, relaxation 1 over the high-frequency range is associated with the reorientation of the dipoles in the nanocomposites [33]. Interestingly, as illustrated in Figure 8b and c, a new relaxation process, i.e., relaxation 2 is introduced in both the P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites, while it is absent in the neat P(VDF-HFP) (Figure 8a). As shown in the insets of Figure 8, the ε − f at 25 • C is fitted by Havriliak-Negami (H-N) equation to reveal this new character [36]: where ε s and ε ∞ are the unrelaxed and relaxed values of the relaxation for dielectric permittivity, respectively, ∆ε = ε s − ε ∞ is the dielectric strength of the relaxation, α and β (0 < α, β < 1) are the shape parameters which describe the symmetric and asymmetric broadening of the relaxation peak, respectively, and f /f 0 takes the place of the product of relaxation time τ and angular frequency ω. Since the ε" − f of the nanocomposites contains the DC conduction term as well as multiple relaxations, Equation (4) can be modified as: where k 0 is the component coefficient of DC conduction, k is the order of relaxation processes. The strong nanoparticles/matrix interfacial barrier effect gives rise to relaxation 2 and decreases the hopping distance of charge carriers. Thus, the charge carriers possess reciprocating movement and can barely induce percolation paths in the nanocomposites [32,33]. The fitted parameters for the samples are listed in Table 2. It can be seen that the P(VDF-HFP)/5 vol%-A@Z nanocomposite has longer relaxation times compared to the neat P(VDF-HFP) and P(VDF-HFP)/5 vol%-Zr nanocomposite, indicating that the incorporation of A@Z nanoparticles modulates the hopping mechanism and restrains the motion of the charge carriers. In order to figure out the dynamic relaxation processes, the temperature dependences of the relaxations are presented in Figure 9. The peak 1 observed at the low-temperature range corresponds to the dipolar relaxation in the amorphous phase [20,21]. The relaxation 2 around 25 • C can be attributed to the nanoparticles/matrix interfaces, which is absent in neat P(VDF-HFP) of Figure 9a [16]. It is worth noting that the relaxation 3 covered by the DC conduction processes at low frequency in Figure 8 can be observed in the dielectric spectrum, varying with temperature, as shown in Figure 9.
where k0 is the component coefficient of DC conduction, k is the order of relaxation processes. The strong nanoparticles/matrix interfacial barrier effect gives rise to relaxation 2 and decreases the hopping distance of charge carriers. Thus, the charge carriers possess reciprocating movement and can barely induce percolation paths in the nanocomposites [32,33]. The fitted parameters for the samples are listed in Table 2. It can be seen that the P(VDF-HFP)/5 vol%-A@Z nanocomposite has longer relaxation times compared to the neat P(VDF-HFP) and P(VDF-HFP)/5 vol%-Zr nanocomposite, indicating that the incorporation of A@Z nanoparticles modulates the hopping mechanism and restrains the motion of the charge carriers.   In order to figure out the dynamic relaxation processes, the temperature dependences of the relaxations are presented in Figure 9. The peak 1 observed at the low-temperature range corresponds to the dipolar relaxation in the amorphous phase [20,21]. The relaxation 2 around 25 °C can be attributed to the nanoparticles/matrix interfaces, which is absent in neat P(VDF-HFP) of Figure 9a [16]. It is worth noting that the relaxation 3 covered by the DC conduction processes at low frequency in Figure 8 can be observed in the dielectric spectrum, varying with temperature, as shown in Figure 9.

AC Conductivity of the Nanocomposites
In order to further study the conduction mechanism, the AC conductivity (σ AC ) of the P(VDF-HFP)/nanoparticle nanocomposites at various temperatures is given as a function of frequency in Figure 10. The plateau-like behavior observed at the low-frequency range of all the samples is defined as DC-like conductivity (σ DC ) [29,31]. The regime at higher frequency is characterized by a frequency-dependent conductivity, which manifests that the σ AC results from the MWS contributions and conforms to the dipolar relaxation modes [30]. The A@Z nanoparticles are effective in hindering electrical conduction, e.g., the σ AC of P(VDF-HFP)/5 vol%-A@Z nanocomposite is 2.26 × 10 −10 S/cm at 125 • C and 10 −1 Hz, which is lower than the P(VDF-HFP)/5 vol%-Zr nanocomposite (8.21 × 10 −10 S/cm) and the neat P(VDF-HFP) (2.95 × 10 −9 S/cm), respectively. It has been reported that the wide bandgap feature of the Al 2 O 3 shell may create higher energy barriers and limit the electrical conduction; therefore, the dielectric loss from DC-like conductivity and molecular relaxations is obviously lowered, as presented in Figure 8 [12,13,37].

TSDC Analysis of the Nanocomposites
The reduction in conductivity denotes a higher level of trap density arisen from the encapsulation of the Al2O3 shell, which can be further validated by the TSDC measurements [12,38]. As shown in Figure 11, multimodal Gaussian fitting is carried out to fit and split TSDC peaks of the nanocomposites for investigating various molecular relaxation mechanisms. The peak 1 observed at ~−45 °C is correlated with glass rubber transition and it can be attributed to the dipolar relaxation in the amorphous phase [20,21]. The TSDC peaks 2 at ~100 °C is originated from the interfacial relaxation due to charges accumulated in the amorphous/crystalline interfaces [20,39]. Obviously, the nanocomposite loaded with 5 vol% A@Z nanoparticles displays the most vigorous peak 2, confirming that the strong interfacial effect was caused by the addition of A@Z nanoparticles. Furthermore, it is inferred that the incorporated nanofillers can act as extensive carrier trap sites, as manifested by the occurrence of peak 3 at ~50 °C.

TSDC Analysis of the Nanocomposites
The reduction in conductivity denotes a higher level of trap density arisen from the encapsulation of the Al 2 O 3 shell, which can be further validated by the TSDC measurements [12,38]. As shown in Figure 11, multimodal Gaussian fitting is carried out to fit and split TSDC peaks of the nanocomposites for investigating various molecular relaxation mechanisms. The peak 1 observed at~−45 • C is correlated with glass rubber transition and it can be attributed to the dipolar relaxation in the amorphous phase [20,21]. The TSDC peaks 2 at~100 • C is originated from the interfacial relaxation due to charges accumulated in the amorphous/crystalline interfaces [20,39]. Obviously, the nanocomposite loaded with 5 vol% A@Z nanoparticles displays the most vigorous peak 2, confirming that the strong interfacial effect was caused by the addition of A@Z nanoparticles. Furthermore, it is inferred that the incorporated nanofillers can act as extensive carrier trap sites, as manifested by the occurrence of peak 3 at~50 • C. The trap site density of different TSDC peaks can be quantified based on the trapped charges, which are proportional to the intensity of TSDC curves [12,40]. As summarized in Table 3, the charges Q1, Q2 and Q3 corresponding to the TSDC peak 1, 2 and 3, respectively, were obtained, and we found that the total trapped charges QT (QT = Q1 + Q2 + Q3) increases from 13.63 μC of the neat P(VDF-HFP) to 29.20 nC of P(VDF-HFP)/5 vol%-Zr and 47.55 μC of P(VDF-HFP)/5 vol%-A@Z nanocomposites. It is believed that the presence of A@Z nanoparticles induces more trap sites at the interfaces of ZrO2/Al2O3 and Al2O3/P(VDF-HFP) in comparison to the uncoated ZrO2 nanoparticles, and thus the quantity of restricted charges is increased [13,19]. The schematic of the interfacial microstructures and crystalline morphology in the neat P(VDF-HFP), P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites are displayed in Figure 12a-c, respectively. From the morphological point of view, the interfaces between the amorphous and crystalline phase of P(VDF-HFP) or between the amorphous phase and the doped nanoparticles are of low density, leading to the formation of charge traps [41,42]. As depicted in Figure 12a, the trap sites at the crystalline/amorphous interfaces are attributed to the incorporation of nanoparticles that lead to conformational changes of polymer chain segments [43]. Haneef and Min reported that, under the steric The trap site density of different TSDC peaks can be quantified based on the trapped charges, which are proportional to the intensity of TSDC curves [12,40]. As summarized in Table 3, the charges Q 1 , Q 2 and Q 3 corresponding to the TSDC peak 1, 2 and 3, respectively, were obtained, and we found that the total trapped charges Q T (Q T = Q 1 + Q 2 + Q 3 ) increases from 13.63 µC of the neat P(VDF-HFP) to 29.20 nC of P(VDF-HFP)/5 vol%-Zr and 47.55 µC of P(VDF-HFP)/5 vol%-A@Z nanocomposites. It is believed that the presence of A@Z nanoparticles induces more trap sites at the interfaces of ZrO 2 /Al 2 O 3 and Al 2 O 3 /P(VDF-HFP) in comparison to the uncoated ZrO 2 nanoparticles, and thus the quantity of restricted charges is increased [13,19]. Table 3. The relevant parameters of TSDC fitting for the neat P(VDF-HFP), P(VDF-HFP)/5 vol%-Zr and P(VDF-HFP)/5 vol%-A@Z nanocomposites. The schematic of the interfacial microstructures and crystalline morphology in the neat P(VDF-HFP), P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites are displayed in Figure 12a-c, respectively. From the morphological point of view, the interfaces between the amorphous and crystalline phase of P(VDF-HFP) or between the amorphous phase and the doped nanoparticles are of low density, leading to the formation of charge traps [41,42]. As depicted in Figure 12a, the trap sites at the crystalline/amorphous interfaces are attributed to the incorporation of nanoparticles that lead to conformational changes of polymer chain segments [43]. Haneef and Min reported that, under the steric hindrance of nanoparticles, the spatial overlap between the adjacent molecular chains determines the intermolecular coupling and thereby introduces more traps at the crystalline/amorphous interfaces of P(VDF-HFP)/nanoparticle nanocomposites [35,44]. hindrance of nanoparticles, the spatial overlap between the adjacent molecular chains determines the intermolecular coupling and thereby introduces more traps at the crystalline/amorphous interfaces of P(VDF-HFP)/nanoparticle nanocomposites [35,44]. The interfaces between the nanoparticles and the amorphous phase of P(VDF-HFP) (interaction zone) can also generate traps, as depicted in Figure 12b,c. The width of the interaction zone is shorter than the mean free path of charges, restraining the movement of the carriers [41,42]. In comparison with pristine ZrO2, the A@Z nanoparticles provide a larger interaction zone, which is beneficial to the increase in the trap density in the P(VDF-HFP)/A@Z nanocomposite [45]. Therefore, more free charges could be trapped in the interfaces between the nanoparticles and the amorphous region.
Concurrently, the crystallization characteristics of the nanocomposites as well as the interaction between nucleation agents and molecular chains may modulate the physicochemical and electrical properties of the nanocomposites [45,46]. According to the DSC measurement ( Figure 2 and Table 1), the enhanced Tc of the P(VDF-HFP)/nanoparticle nanocomposites is the result of crystalline domain refinement effect [24]. It is known that the smaller size the crystalline domain is, the lower the free volume of the amorphous phase and the more crystalline/amorphous the interfaces are in the nanocomposites [24,26]. Since the mean free path of charge carriers in crystal region is much shorter than that in the amorphous region [47], the quantity of charges with restricted mobility in the P(VDF-HFP)/A@Z nanocomposite is increased, which may address the smaller leakage current density of the P(VDF-HFP)/A@Z nanocomposite than the neat P(VDF-HFP) and P(VDF-HFP)/Zr nanocomposites [9,24,48]. Low conduction current is beneficial to improved Eb, η and Ud of the P(VDF-HFP)/A@Z nanocomposite. These results provide direct insights into the decreased energy loss and increased energy density of nanocomposites. The interfaces between the nanoparticles and the amorphous phase of P(VDF-HFP) (interaction zone) can also generate traps, as depicted in Figure 12b,c. The width of the interaction zone is shorter than the mean free path of charges, restraining the movement of the carriers [41,42]. In comparison with pristine ZrO 2 , the A@Z nanoparticles provide a larger interaction zone, which is beneficial to the increase in the trap density in the P(VDF-HFP)/A@Z nanocomposite [45]. Therefore, more free charges could be trapped in the interfaces between the nanoparticles and the amorphous region.

Materials and Sample Preparation
Concurrently, the crystallization characteristics of the nanocomposites as well as the interaction between nucleation agents and molecular chains may modulate the physicochemical and electrical properties of the nanocomposites [45,46]. According to the DSC measurement ( Figure 2 and Table 1), the enhanced T c of the P(VDF-HFP)/nanoparticle nanocomposites is the result of crystalline domain refinement effect [24]. It is known that the smaller size the crystalline domain is, the lower the free volume of the amorphous phase and the more crystalline/amorphous the interfaces are in the nanocomposites [24,26]. Since the mean free path of charge carriers in crystal region is much shorter than that in the amorphous region [47], the quantity of charges with restricted mobility in the P(VDF-HFP)/A@Z nanocomposite is increased, which may address the smaller leakage current density of the P(VDF-HFP)/A@Z nanocomposite than the neat P(VDF-HFP) and P(VDF-HFP)/Zr nanocomposites [9,24,48]. Low conduction current is beneficial to improved E b , η and U d of the P(VDF-HFP)/A@Z nanocomposite. These results provide direct insights into the decreased energy loss and increased energy density of nanocomposites.
As presented in Figure 13, a nano-layer of Al 2 O 3 was coated on ZrO 2 nanoparticles via modified sol-gel method and the P(VDF-HFP) nanocomposites were fabricated via solution casting method. First, 0.1 mole of ammonium formate was dissolved into 500 mL deionized water under vigorous magnetic stirring. A certain amount of formic acid was added to adjust the mixture's pH to 4.6. Then, 1 g ZrO 2 powders and 1.10 g aluminum sulfate octadecahydrate (Al 2 (SO 4 ) 3 ·18H 2 O) were mixed with the resulting buffer solution. The above mixture was stirred at 70 • C for 5 h. Afterwards, the suspended particles were centrifuged and washed with deionized water at least 10 times. Finally, the solid sample was collected and heated at 600 • C for 10 h to obtain the core-shell structure A@Z nanoparticles (ZrO 2 core, Al 2 O 3 shell). The A@Z nanoparticles and P(VDF-HFP) powders were proportionally (0, 1, 3, 5 and 7 vol%) dispersed in DMF under ultrasonicating for 1.5 h. The suspension was cast on glass slides, followed by drying at 70 • C for 12 h in an air-circulating oven. After subsequently heating at 200 • C for 5 min, the samples were quenched in ice water. Finally, the samples were annealed at 105 • C for 24 h to remove solvent residue. The P(VDF-HFP) nanocomposites filled with raw ZrO 2 nanoparticles, abbreviated as P(VDF-HFP)/Zr, were prepared in the same manner. P(VDF-HFP) (Kynar Flex 2801) with 10% HFP was purchased from Arkema. ZrO2 (~40 nm) nanoparticles were purchased from US Research Nanomaterials, Inc. N, N-dimethylformamide (DMF), aluminum sulfate octadecahydrate, formic acid and ammonium formate were purchased from Sigma-Aldrich.
As presented in Figure 13, a nano-layer of Al2O3 was coated on ZrO2 nanoparticles via modified sol-gel method and the P(VDF-HFP) nanocomposites were fabricated via solution casting method. First, 0.1 mole of ammonium formate was dissolved into 500 mL deionized water under vigorous magnetic stirring. A certain amount of formic acid was added to adjust the mixture's pH to 4.6. Then, 1 g ZrO2 powders and 1.10 g aluminum sulfate octadecahydrate (Al2(SO4)3⋅18H2O) were mixed with the resulting buffer solution. The above mixture was stirred at 70 °C for 5 h. Afterwards, the suspended particles were centrifuged and washed with deionized water at least 10 times. Finally, the solid sample was collected and heated at 600 °C for 10 h to obtain the core-shell structure A@Z nanoparticles (ZrO2 core, Al2O3 shell). The A@Z nanoparticles and P(VDF-HFP) powders were proportionally (0, 1, 3, 5 and 7 vol%) dispersed in DMF under ultrasonicating for 1.5 h. The suspension was cast on glass slides, followed by drying at 70 °C for 12 h in an aircirculating oven. After subsequently heating at 200 °C for 5 min, the samples were quenched in ice water. Finally, the samples were annealed at 105 °C for 24 h to remove solvent residue. The P(VDF-HFP) nanocomposites filled with raw ZrO2 nanoparticles, abbreviated as P(VDF-HFP)/Zr, were prepared in the same manner.

Sample Characterization
TEM images of A@Z nanoparticles were obtained by ThermoFisher Scientific instrument (Waltham, MA, USA). SEM images of the P(VDF-HFP) nanocomposites were characterized using Quattro S instrument. A Q100 DSC instrument (TA Instruments) was used to conduct DSC measurements. All samples were heated from 30 °C to 250 °C at a rate of 10 °C/min under nitrogen atmosphere. After holding at the state (250 °C) for 5 min to eliminate the thermal history, the samples were cooled down to 30 °C at the same rate. Electric displacement-electric field loop (D-E loop) tests were conducted on a PK-CPE2020-AI-20 kV high-voltage test system (PolyK Technologies, Philipsburg, PA, USA). Dielectric breakdown strength was measured with a DC voltage ramp of 500 V/s using a Trek 610E as the voltage source. The electric field distribution of P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites were simulated by finite element model using COM-SOL. An electric field of 300 MV/m was vertically applied from top to bottom of the model Figure 13. The fabrication process of the A@Z core-shell nanoparticles and the P(VDF-HFP) nanocomposites.

Sample Characterization
TEM images of A@Z nanoparticles were obtained by ThermoFisher Scientific instrument (Waltham, MA, USA). SEM images of the P(VDF-HFP) nanocomposites were characterized using Quattro S instrument. A Q100 DSC instrument (TA Instruments) was used to conduct DSC measurements. All samples were heated from 30 • C to 250 • C at a rate of 10 • C/min under nitrogen atmosphere. After holding at the state (250 • C) for 5 min to eliminate the thermal history, the samples were cooled down to 30 • C at the same rate. Electric displacement-electric field loop (D-E loop) tests were conducted on a PK-CPE2020-AI-20 kV high-voltage test system (PolyK Technologies, Philipsburg, PA, USA). Dielectric breakdown strength was measured with a DC voltage ramp of 500 V/s using a Trek 610E as the voltage source. The electric field distribution of P(VDF-HFP)/Zr and P(VDF-HFP)/A@Z nanocomposites were simulated by finite element model using COMSOL. An electric field of 300 MV/m was vertically applied from top to bottom of the model while the bottom is set to be the ground. Dielectric spectra were obtained using Novocontrol CONCEPT 80, with temperature ranging from −50 • C to 125 • C and frequency from 10 −1 to 10 7 Hz. TSDC measurements were carried out in a Delta oven and the current was measured by a 6517B electrometer. Detailed measuring steps are as follows: (a) Placing the sample between electrodes and heating up to 180 • C. (b) Applying the electric field of 200 V for 20 min to generate dielectric polarization. (c) Cooling the sample to −100 • C rapidly under the applied field, where all the dipole/ionic motion is completely frozen. (d) Connecting the sample to a short circuit condition for 10 min. (e) Heating up to 125 • C at a linear rate and measuring the depolarization current as a function of temperature.

Conclusions
In conclusion, P(VDF-HFP) nanocomposites filled with ZrO 2 and Al 2 O 3 @ZrO 2 nanoparticles were developed. With the encapsulation of the wide-bandgap Al 2 O 3 shell, the crystallinity and crystallization temperature are improved owing to the refined crystal size, which leads to suppressed leakage current density and AC conductivity. The presence of A@Z nanoparticles intensifies the intermolecular coupling and increases the area of crystalline/amorphous interfaces of the nanocomposites. The change in the molecules' morphology and segmental motion in interfaces of the nanoparticles/amorphous phase modulate the charge hopping behavior, thus a new interfacial relaxation process is generated. The trapped charges during relaxation processes of P(VDF-HFP)/A@Z nanocomposite are increased, demonstrating that more trap sites are induced, which accounts for the stronger capability in inhibiting charges motion in the nanocomposites. Consequently, the P(VDF-HFP)/5 vol%-A@Z nanocomposite exhibits a substantial enhanced discharged energy density of 11.8 J/cm 3 . This study provides a new understanding for the improved dielectric and energy storage properties of the nanocomposites and also offers a promising strategy for the design and fabrication of the dielectrics for capacitors.