general, the stored electrical energy density (Us) in the dielectric materials can be expressed as
where E is the applied electric field and D is the electric displacement [15]. To measure the stored energy density, discharged energy density (Ud), and charge/discharge efficiency (η) of the dielectrics, the electric displacement (D) is measured as a function of applied electric field (E) during the charging and discharging processes, which is also called as the D‐E loop. The schematic of typical D‐E loop of the dielectric material is shown in Figure 1.1. The stored energy density can be calculated by integrating the area bounded by the charging curve, the D‐axis, and the horizontal line y = Dmax. Similarly, the discharged energy density can be calculated by integrating the area bounded by the discharging curve, theD‐axis, and the horizontal line y = Dmax. The energy loss (Ul) during the charge/discharge circle can be represented by the area bounded by the charging and discharging curves. Apparently, the stored energy density equals to the discharged energy density plus the energy loss, that is, Us = Ud + Ul. The charge/discharge efficiency is defined as η = Ud/Us× 100%. For linear dielectrics, the electric displacement increases linearly with the applied electric field, i.e. D = ε0εrE, where ε0 is the vacuum dielectric constant (8.85 × 10−12 F/m) and εr is the relative dielectric constant of the dielectric material [16–18]. As a result, the stored energy density of linear dielectrics can be simplified as
It is suggested from Eqs. (1.1) and (1.2) that the energy density of dielectric materials can be improved by increasing at least one of the two parameters, i.e. the dielectric constant (εr) and the electrical breakdown strength (Eb). This is because the dielectric constant determines the electric displacement, while the electrical breakdown strength determines the maximum electric field that can be applied on the dielectric material. For polymer dielectric materials, the dielectric constant is relatively lower than their ceramic counterparts [19–21], so inorganic nanofillers with high dielectric constant are introduced to improve the dielectric constant of polymer dielectrics. In terms of improving the breakdown strength, highly insulated nanofillers are incorporated into the polymer dielectrics.
Figure 1.1 Schematic of typical D‐E loop of dielectric materials.
For capacitive energy storage in dielectric materials, the stored energy density cannot be fully discharged at the removal of the applied electric field because of various energy losses, such as polarization loss, conduction loss, and hysteresis loss [22]. In most cases, the energy loss would be converted into waste heat, which accelerates the dielectric aging and even causes thermal runaway of the dielectric materials [23, 24]. Therefore, the charge/discharge efficiency is another key parameter for dielectric materials. Since the energy loss is converted into waste heat, which is harmful to the operation of dielectric materials, it is more meaningful to concurrently improve the energy density and the charge/discharge efficiency of the dielectric materials, rather than simply increasing the energy density. In order to increase the charge/discharge efficiency, the energy loss, especially conduction loss under high electric field, should be suppressed. To achieve the inhibition of conduction loss, some highly insulated nanofillers have been introduced into the polymer dielectrics.
Simultaneous enhancement of dielectric constant and breakdown strength is highly desired in the development of high performance polymer composites for electrical energy storage. However, in most cases, the increase in dielectric constant would result in the decrease of breakdown strength, which restricts the improvement of the energy density. So achieving high dielectric constant while maintaining high breakdown strength is still a great challenge. Because of the large mismatch of the electrical parameters between the inorganic nanofillers and polymer matrix, the electric field at the nanofiller/polymer interface is greatly enhanced, which results in the reduced breakdown strength. Moreover, the dispersion of inorganic nanofillers into polymer matrix is always a challenge in the development of polymer composites because of the high surface energy of nanofillers and the different surface physical and chemical properties between the nanofillers and polymer matrix. As a result, nanofiller aggregation is observed in polymer composites. The aggregation of nanofillers would introduce numerous defects in the polymer matrix, which would decrease the electrical breakdown strength and increase the conduction loss. To address these issues, various strategies have been proposed to develop high performance polymer composites for electrical energy storage, including controlling the nanofiller dimension and morphology, controlling the nanofiller distribution and orientation, modifying the nanofiller/polymer interface, introducing multiple nanofillers, and constructing multilayered composites.
1.3 Effect of Nanofiller Dimension
To increase the capacitive energy storage performance of the polymer composites, various inorganic nanofillers have been used to utilize the interfacial polarization and the high dielectric constant of the nanofillers, as well as the inhibition of conduction loss and electrical breakdown. Nanofillers with high dielectric constant, such as titanium oxide (TiO2), barium titanate (BaTiO3, BT), strontium titanate (SrTiO3), barium strontium titanate (BaxSr1 − xTiO3, BST), lead zirconate titanate (PbZrxTi1 − xO3, PZT), and calcium copper titanate (CaCu3Ti4O12, CCTO), have been used to improve the dielectric constant and energy density of the polymer composites [25–30]. Moreover, nanofillers with moderate dielectric constant but highly insulating performance, such as magnesium oxide (MgO), aluminum oxide (Al2O3), and silicon oxide (SiO2), have been used to enhance the breakdown strength and suppress the conduction loss [31–33].
The dimension of the nanofillers can significantly influence the performance of the polymer composites. There are mainly three categories of the nanofillers: 0D fillers, 1D fillers, and 2D fillers. 0D fillers have nanoscale dimensions in all three directions, such as spherical nanoparticles. 1D fillers have nanoscale dimensions in two directions, suchas nanowires and nanofibers. 2D fillers have nanoscale dimension in only one direction, such as nanoplates and nanosheets.
Compared with 0D nanofillers, 1D nanofillers are more efficient to increase the dielectric constant of polymer composites at relatively low nanoparticle content because of the lower percolation threshold of the high‐aspect‐ratio 1D nanofillers compared with 0D nanofillers [34]. For example, Tang et al. showed that the use of high‐aspect‐ratio BT nanowires can enhance the dielectric constant of poly(vinylidene fluoride‐trifluoroethylene‐chlorofluoroethylene) [P(VDF‐TrFE‐CFE)] terpolymer more efficiently than the BT nanoparticles [35]. The dielectric constant of P(VDF‐TrFE‐CFE)/BT nanowire composite can reach up to 69.5 at 17.5 vol% of BT nanowires, while the dielectric constant of P(VDF‐TrFE‐CFE)/BT nanoparticle composite is only around 52 at 30 vol% of BT nanoparticles. As the result of enhanced dielectric constant, the P(VDF‐TrFE‐CFE)/BT nanowire composites exhibit a high discharged energy density of
