Significantly Enhanced Energy Storage Density by Modulating the Aspect Ratio of BaTiO3 Nanofibers

There is a growing need for high energy density capacitors in modern electric power supplies. The creation of nanocomposite systems based on one-dimensional nanofibers has shown great potential in achieving a high energy density since they can optimize the energy density by exploiting both the high permittivity of ceramic fillers and the high breakdown strength of the polymer matrix. In this paper, BaTiO3 nanofibers (NFs) with different aspect ratio were synthesized by a two-step hydrothermal method and the permittivity and energy storage of the P(VDF-HFP) nanocomposites were investigated. It is found that as the BaTiO3 NF aspect ratio and volume fraction increased the permittivity and maximum electric displacement of the nanocomposites increased, while the breakdown strength decreased. The nanocomposites with the highest aspect ratio BaTiO3 NFs exhibited the highest energy storage density at the same electric field. However, the nanocomposites with the lowest aspect ratio BaTiO3 NFs achieved the maximal energy storage density of 15.48 J/cm3 due to its higher breakdown strength. This contribution provides a potential route to prepare and tailor the properties of high energy density capacitor nanocomposites.

Scientific RepoRts | 7:45179 | DOI: 10.1038/srep45179 spherical ceramic fillers [26][27][28] . Andrews et al. developed a micromechanics approach and finite element models to study the effect of ceramic filler aspect ratio on the electro-elastic properties of nanocomposites 29 . The results showed the electromechanical coupling can increase up to 60 times compared to its initial values when the aspect ratio was increased from 1 to 10 at 30 vol % of ceramic filler. Tang et al. demonstrated that nanocomposites based on high aspect ratio PZT nanowires exhibited an increased energy density, which was 77.8% higher than lower aspect ratio PZT nanowires 30 .
In this study, we have prepared P(VDF-HFP) nanocomposites with a range of aspect ratio BaTiO 3 nanofibers (NFs) synthesized by a two-step hydrothermal method. There have been a variety of reported methods for synthesizing BaTiO 3 NFs, such as the two-step hydrothermal method, one-step hydrothermal method, topochemical solid-state reaction and anodic aluminum oxide template method 25,[31][32][33] . The two-step hydrothermal method has attracted attention due to its superiority in terms of the synthesis of single crystalline nanofibers, morphology control, homogeneity at the molecular level, low temperature processing and simple experimental approach. The effects of aspect ratio and volume fraction of the BaTiO 3 NFs on the dielectric constant (relative permittivity), breakdown strength and energy storage density of the nanocomposites were investigated systematically. On increasing the BaTiO 3 NF volume fraction or aspect ratio, the dielectric constant and maximum electric displacement of the nanocomposites increased monotonically while the breakdown strength decreased monotonically. Under the same electric field, the nanocomposites with higher volume fraction or higher aspect ratio BaTiO 3 NFs possessed higher discharged energy density. The maximal energy storage density reached 15.48 J/cm 3 in nanocomposites containing 7.5 vol% BaTiO 3 NFs synthesized at 210 °C for 2 h under the electric field of 300 kV/mm.

Results and Discussion
In order to obtain BaTiO 3 nanofibers (BT NFs), an initial hydrothermal reaction was used to synthesize Na 2 Ti 3 O 7 nanofibers (NT NFs) due to its extensive research history and easily controlled nanofiber morphology 25 . Figure 1a shows the morphology of hydrothermally synthesized Na 2 Ti 3 O 7 nanofibers (NT NFs) which exhibited a high aspect ratio and favorable dispersibility. Figure 1b shows the XRD pattern of NT NFs indexed to monoclinic Na 2 Ti 3 O 7 (PDF card NO. . The corresponding TEM images were shown in Fig. 1c. The NT NFs possessed a smooth surface with a diameter of approximately 100 nm. The clear lattice fringes shown in Fig. 1c demonstrate that the NT NFs were single-crystalline. The parallel lattice spacings were approximately 0.19 nm and 0.28 nm, which correspond to the (020) and (003) planes, respectively, and reveal that the NT NFs grew in the [010] direction. Figure 1d shows the SEM image of H 2 Ti 3 O 7 nanofibers (HT NFs), which retained the morphology of the Na 2 Ti 3 O 7 nanofibers. The HT NFs were transformed to BaTiO 3 NFs by a second hydrothermal reaction. The H 2 Ti 3 O 7 phase is a layered titanate, which is a good precursor for soft chemical synthesis because of its open structure that enables ion exchange and topochemical transformation. Figure 2a,b shows schematic diagrams of the crystalline structures of H 2 Ti 3 O 7 and BaTiO 3 , respectively. During the second hydrothermal reaction, the Ba 2+ ions diffuse into the host lattice of H 2 Ti 3 O 7 by ion exchange with H + , which leads to a rearrangement of the octahedra sharing and structural transformation to perovskite BaTiO 3 . The Ba 2+ ions possess a higher positive charge compared with H + , thereby promoting the structural transformation. In addition, it is known that the edge sharing octahedra were driven into vertex sharing octahedra during the topochemical transformation 34 . Therefore, the HT NFs were successfully transformed into BaTiO 3 NFs. Figure 3a-c show the sizes and morphologies of BaTiO 3 NFs hydrothermally synthesized at 210 °C for 2-12 h, respectively. The corresponding XRD patterns are shown in Fig. 3d. The diffraction patterns indicate that tetragonal BaTiO 3 (PDF card NO. 75-0462) without any impurity phase can be obtained at 210 °C with a reaction time ranging from 2 h to 12 h and the crystallization of BaTiO 3 was improved at longer reaction times. When the reaction time was 2 h, the products were a mass of nanoparticles and few nanofibers, as shown in Fig. 3a. The amount of nanofibers increased significantly when reaction time increased to 6 h. Furthermore as the reaction time increased to 12 h, the nanofibers became dominant. Figure 3e shows a TEM image of BaTiO 3 NFs synthesized at 210 °C for 12 h. It can be observed that the surface of BaTiO 3 NFs was rough and a HRTEM image of a typical BaTiO 3 NF synthesized at 210 °C for 12 h is shown in Fig. 3f. The clear lattice fringes illustrated that the BT NF were single-crystalline. The parallel lattice spacing were about 0.406 nm and 0.286 nm corresponding to (001) and (101) planes of tetragonal BaTiO 3 respectively, which revealed that the NFs grew in the [001] direction. The corresponding selected area diffraction pattern (SADP) also exhibited the characteristics of a single crystal.
It was worth noting that with an increase of reaction time, the length of the BaTiO 3 NFs increased to a much greater extent compared to the diameter, leading to an increase in the fibre aspect ratio. The length and diameter of the BaTiO 3 NFs synthesized at 210 °C for 2 h, 6 h and 12 h were analyzed using SEM images by ImageJ software, as shown in Fig. 4. The aspect ratio of the BaTiO 3 NFs calculated from Fig. 4 were 3.5, 7.4 and 21.0 for the reaction time of 2 h, 6 h and 12 h, respectively and clearly shows that the aspect ratio of the BaTiO 3 NFs increased with an increase of reaction time.
To improve the compatibility and dispersibility of BaTiO 3 NFs in the P(VDF-HFP) matrix, the BaTiO 3 NFs were surface functionalized by dopamine. As highlighted in the introduction, the breakdown strength of the nanocomposite is equally important as the dielectric constant with regard to the energy density and the breakdown strength tends to decrease with increasing volume fraction of ceramic filler. In order to improve the dielectric properties of nanocomposites and maintain a high breakdown strength, the nanocomposites were fabricated at a relatively low volume fraction of BaTiO 3 NFs in this study, varying from 2.5% to 7.5%. The upper-surface morphology of the BaTiO 3 NFs/P(VDF-HFP) nanocomposites are shown in Fig. 5. Figure 5a-c shows SEM images of the nanocomposites with 5.0 vol% of BaTiO 3 NFs synthesized at 210 °C for 2 h, 6 h and 12 h, respectively where it can be seen that the aspect ratio of the BaTiO 3 NFs in nanocomposites gradually increased. Figure 5d-f shows the SEM images of the nanocomposites with 2.5 vol%, 5.0 vol% and 7.5 vol% BaTiO 3 NFs synthesized at 210 °C for 12 h. The visibility of the BaTiO 3 NFs in nanocomposite became more pronounced with increasing BaTiO 3 NFs volume fraction. It can be observed that the BaTiO 3 NFs exhibited good compatibility and dispersibility in the P(VDF-HFP) matrix and the nanocomposites exhibited limited defects as the volume fraction of BaTiO 3 NFs approached 7.5%. This can be attributed to that the fact that the BaTiO 3 NFs were surface modified by dopamine and therefore formed a strong adhesive bonding force with the polymer matrix. Figure 6 shows the variation of the dielectric constant and loss of the nanocomposites with the BaTiO 3 NFs aspect ratio and volume fraction for a frequency range of 1 kHz to 10 MHz. The dielectric constant of the nancomposites increased with the increase of volume fraction of BaTiO 3 NFs since BaTiO 3 possess a higher dielectric constant compared with pure P(VDF-HFP) polymer. At the measurement frequency of 1 kHz, the dielectric constant of the nanocomposite with 7.5 vol% BaTiO 3 NFs synthesized at 210 °C for 12 h (aspect ratio 21.0) reached 23.4 while the dielectric constant of the samples with 7.5 vol% BaTiO 3 NFs synthesized at 210 °C for 6 h (aspect ratio 7.4) and 2 h (aspect ratio 3.5) was 17.8 and 14 respectively. This demonstrates that on increasing the aspect ratio of the BaTiO 3 NFs, the dielectric constant of the nancomposites was significantly improved. There are a number of previous reports and theoretical models that have demonstrated the increased dielectric constant as a result of using high aspect ratio ceramic fillers 14,[25][26] . For instance, the Maxwell-Garnet model can efficiently describe the effect of aspect ratio, as shown in equation 1 35,36 .   where N i is known as the depolarization factor of ellipsoids in the x, y, z direction. For BaTiO 3 NFs, where the radii a x > a y = a z . N i can be expressed as equation 2 The Maxwell-Garnet model indicates that the dielectric constant of the nanocomposites will increase on increasing the aspect ratio of BaTiO 3 NFs. However, there was no apparent variation about the dielectric loss on increasing the aspect ratio of BaTiO 3 NFs. For example, the dielectric loss of the nanocomposites with 7.5 vol% BaTiO 3 NFs synthesized at 210 °C for 2 h, 6 h and 12 h was 0.032, 0.037 and 0.046 at 1 kHz, respectively. The dielectric loss remained less than 0.06 (<100 kHz) for all samples which was attributed to the relatively low volume fraction of BaTiO 3 NFs and their good compatibility and dispersion in the polymer matrix. The dielectric properties of nanocomposites were efficiently improved by increasing the aspect ratio of the BaTiO 3 NFs, without the need for additional fillers. Figure 7a-c show typical electric displacement-electric field (D-E) loops of nanocomposites where the volume fraction of BaTiO 3 NFs ranged from 2.5% to 7.5% and the aspect ratio of the BaTiO 3 NFs were 3.5, 7.4 and 21.0 respectively. As can be seen from Fig. 6a, the maximum electric displacement (D max ) increased monotonically with an increase of the volume fraction of BaTiO 3 NFs. A similar trend can also be observed in Fig. 6b and c. Figure 6d summarizes the D max of nanocomposites with 7.5 vol% for various aspect ratios of BaTiO 3 NFs and the D max was enhanced with increasing the electric field. Figure 7d also clearly demonstrated that with increasing the aspect ratio of BaTiO 3 NFs, the D max of nanocomposites improved significantly. For instance, the D max of the nanocomposites with 7.5 vol% and higher aspect ratio (AR) BaTiO 3 NFs (AR = 21) reached 5.4 μ C/cm 2 while the value was only 3.9 μ C/cm 2 for lower aspect ratio BaTiO 3 NFs (AR = 3.5) under an electric field of 160 kV/mm. It has been demonstrated in Fig. 6 that the dielectric constant of nanocomposites increases on increasing the aspect ratio of the BT NFs. Since D = ε 0 ε r E, where ε 0 and ε r are free space and the relative of the permittivity of the nanocomposites respectively, then under the same electric field (E) an increase in D max can result from an increase of dielectric constant of the nanocomposites on increasing the volume fraction or aspect ratio of the BaTiO 3 NFs.
The electric breakdown strength of the nanocomposites was analyzed by a two parameter Weibull cumulative probability function, as shown in equation 3,    Figure 9a presents the energy storage density of the nanocomposites with low aspect ratio BaTiO 3 NFs synthesized at 210 °C for 2 h as a function of electric field and volume fraction of BaTiO 3 NFs. This indicates that the energy storage density increased with an increase of electric field. Moreover, the nanocomposites with the higher volume fraction of BaTiO 3 NFs possessed the higher energy storage density under the same electric field. Figure 9b shows the energy storage density of the nanocomposites with 7.5 vol% BaTiO 3 NFs as a function of electric field and aspect ratio of the BaTiO 3 NFs. Similarly, the nanocomposites with the higher aspect ratio BaTiO 3 NFs exhibited a higher energy storage density under the same electric field. The higher energy storage density can be attributed to the significantly enhanced dielectric constant and D max of the nanocomposites on increasing the volume fraction and aspect ratio of the BaTiO 3 NFs. Figure 9b also indicates that the electric breakdown strength of the nanocomposites decreased with increasing aspect ratio of BaTiO 3 NFs. Under an electric field of 300 kV/mm, the maximal discharged energy density of 15.48 J/cm 3 was obtained in the nanocomposites with 7.5 vol% on low aspect ratio BaTiO 3 NFs synthesized at 210 °C for 2 h.
To provide a deeper understanding of the decrease in breakdown strength and increase in dielectric constant with an increase in BaTiO 3 NF volume fraction and aspect ratio, finite element modelling (Ansys APDL v15.0) was employed. A two dimensional electrostatic analysis of a single high permittivity BaTiO 3 NF (relative permittivity, ε r = 1500) embedded in a low permittivity P(VDF-HFP) matrix (ε r = 7) was used to investigate the effect of fiber aspect ratio and angle (with respect to applied field direction) on the maximum localized electric field. The inclusion of a high permittivity BaTiO 3 inclusion leads to the electric field concentrating in the low permittivity matrix, and such field concentrations are likely to be sites for initiating dielectric breakdown within these nanocomposites. This can be seen in Fig. 10a, which is a close up image of the field distribution around a BaTiO 3 fiber with an aspect ratio of 3.5 at 2.5 vol.%. The blue contours are low field regions and red contours indicate high field concentrations at the tips of the fiber. High aspect ratio fibers aligned almost perpendicular to the applied field direction (angle > 85°) produced slightly lower electric field concentrations compared to lower aspect ratios, however at angles below 85° the high aspect ratio fibers result in local electric fields that are significantly higher than the applied field, see Fig. 10b. The manufactured composites had a random orientation of fibers within the film (Fig. 5) and therefore a nominal fiber orientation of 45° to the applied field was used to demonstrate the effect of BaTiO 3 aspect ratio and volume fraction on the relative permittivity (dielectric constant) and field concentration, where an increase in local electric field leads to a reduced breakdown strength. The relative permittivity (Fig. 10c) and localized field concentrations (Fig. 10d) were found to increase with an increase in both fiber aspect ratio and volume fraction. These results agree well with the experimental observations that on increasing the aspect ratio and volume fraction of the BaTiO 3 NFs, the dielectric constant of the nanocomposites was improved (Fig. 6a-c) while the breakdown strength of the nanocomposites decreased (Fig. 8d).
High BaTiO 3 NF aspect ratios are also likely to reduce the average separation distance between high permittivity inclusions for the same volume fraction. A finite element model of two BaTiO 3 particles (aspect ratio of unity) within a P(VDF-HFP) matrix was used to demonstrate the effect of separation distance on electric field concentrations within the matrix. The 'worst-case' in terms of field concentration was occurred when two particles were aligned in the direction of the field, as in Fig. 10e. The ratio of the maximum local field to the applied field is shown in Fig. 10f as a function of the distance between the high permittivity particles, with the electric field concentration following an inverse separation law. These result indicate that a combination of electric field concentrations due to the presence of high permittivity fibers and fiber separation distance influence the permittivity and dielectric strength and the high aspect ratio fibers lead to a lower breakdown strength, as observed experimentally (Fig. 8d).

Conclusion
In this study, BaTiO 3 nanofibers (BT NF) with a variety of aspect ratios were synthesized by a two-step hydrothermal method. The effects of the aspect ratio and volume fraction of the BT NF on dielectric properties and energy storage densities of the P(VDF-HFP) based one-dimensional nanocomposites were investigated and modeled in detail. As the aspect ratio and volume fraction of the BaTiO 3 NFs was increased, the dielectric constant and D max of the nanocomposites were both increased monotonically while the breakdown strength decreased. The nanocomposites with highest aspect ratio and volume fraction of BT NFs exhibited the highest energy storage density under the same electric field. The maximal energy storage density reached 15.48 J/cm 3 in the nanocomposites with 7.5 vol% BT NFs synthesized at 210 °C for 2 h under the electric field of 300 kV/mm. This work provides a potential new route to prepare and tailor the properties of novel high energy density capacitor nanocomposites.

Methods
Synthesis of BaTiO 3 nanofibers. The BaTiO 3 nanofibers (BT NFs) were synthesized by a two-step hydrothermal method. Firstly, sodium titanate nanofibers (Na 2 Ti 3 O 7 NFs, NT NFs ) were synthesized. A 1.446 g mass of titanium oxide (TiO 2 , Anatase) was added to 70 ml NaOH solution (10 M) and the mixture was stirred for 2 h to form a homogeneous suspension. Hydrothermal reactions were carried out at 210 °C under an auto-generated pressure for 24 h in a 100 ml Teflon-lined autoclave. The products were washed by distilled water and then soaked in diluted 0.2 M hydrochloric acid (HCl, 37%) for 4 hours to obtain hydrogen titanate nanofibers (H 2 Ti 3 O 7 NFs). The BT NFs were synthesized by a second hydrothermal reaction where 0.150 g of H 2 Ti 3 O 7 NFs were dispersed in 70 ml Ba(OH) 2 •8H 2 O solution and the mixture was sonicated for 10 min. The hydrothermal reactions were carried out at 210 °C under an auto-generated pressure for 2-24 h in a 100 ml Teflon-lined autoclave to obtain BT NFs at a range of aspect ratios. The products were soaked in 0.2 M HCl solution briefly, then washed using distilled water several times and dried at 80 °C in an oven.
Fabrication of BT NFs/P(VDF-HFP) nanocomposite. The BT NFs were mixed with a solution of P(VDF-HFP) in N,N-dimethylformamide (DMF) by stirring and sonicating to form a homogeneous suspension. The suspension was then cast onto a clean glass and dried at 80 °C for 12 h under vacuum. The dried nanocomposite sheets were then compressed into films at 200 °C under a pressure of approximately 15 MPa. Gold electrodes were sputtered on both sides of the film using a mask with 2 mm diameter eyelets. Figure 10. (a) Contour plot of finite element analysis for BaTiO 3 fiber (2.5 vol.%) in P(VDF-HFP) matrix with aspect ratio 3.5 orientated at 30° to the applied field, where blue and red contours represent regions of high and low field, respectively; (b) effect of fiber angle and aspect ratio on maximum local field concentration (plotted as E local /E applied ); (c,d) show the effect of BaTiO 3 fiber aspect ratio and volume fraction at a 45° angle to applied field on dielectric constant and maximum local field concentration, respectively; (e) contour plot of two BaTiO 3 NFs aligned in field direction, showing field concentration between particles; (f) effect of separation distance on field concentration within P(VDF-HFP) matrix.