High-k polymer nanocomposites with 1D filler for dielectric and energy storage applications

Accepted Manuscript High-k Polymer Nanocomposites with 1D Filler for Dielectric and Energy Storage Applications Xingyi Huang, Bin Sun, Yingke Zhu, Shengtao Li, Pingkai Jiang PII: DOI: Reference:

S0079-6425(18)30103-8 https://doi.org/10.1016/j.pmatsci.2018.10.003 JPMS 537

To appear in:

Progress in Materials Science

Received Date: Revised Date: Accepted Date:

20 February 2017 29 September 2018 21 October 2018

Please cite this article as: Huang, X., Sun, B., Zhu, Y., Li, S., Jiang, P., High-k Polymer Nanocomposites with 1D Filler for Dielectric and Energy Storage Applications, Progress in Materials Science (2018), doi: https://doi.org/ 10.1016/j.pmatsci.2018.10.003

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High-k Polymer Nanocomposites with 1D Filler for Dielectric and Energy Storage Applications Xingyi Huanga*, Bin Suna*, Yingke Zhua, Shengtao Lib and Pingkai Jianga* a

Department of Polymer Science and Engineering, Shanghai Key Laboratory of Electrical Insulation

and Thermal Ageing, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China; b

State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University,

Xi’an, China *Corresponding to X.H. (E-mail: [email protected]) or B.S. (E-mail: [email protected]), P.J. (E-mail: [email protected]) Abstract: High-k polymer nanocomposites have received increased research interest by virtue of integrating high dielectric constant nanofiller with high breakdown strength, flexibility, and ease of processing of a matrix. With outstanding anisotropy, high-aspect-ratio nanofillers have proved to be much more efficient enhancers of the dielectric properties of nanocomposites when compared with traditional zero-dimensional (0D) fillers, leading to many dielectric and energy storage applications. This review summarizes the latest research on one-dimensional (1D) and quasi-1D fillers based high-k polymer nanocomposites with the focus on the superiority of 1D or quasi-1D high-k fillers in enhancing the dielectric properties and energy storage capability of polymer nanocomposites. Dielectric anisotropy, which plays a critical role in determining the dielectric properties and energy storage capability of polymer nanocomposites, was highlighted and the experimental methodologies for achieving anisotropic dielectric polymer nanocomposites were reviewed. The fundamental electrical parameters, such as dielectric constant, dielectric nonlinearity, dielectric loss and electrical conduction, and breakdown strength of dielectric polymer composites, are also discussed. Given the recent progress, guidelines for the future development of high-k polymer nanocomposites with dielectric and energy storage applications were proposed. Keywords: High-k, Flexibility; Nanocomposites; Dielectrics; 1D Filler; Energy Storage;

1

Contents 1. Introduction∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙3 2. Basic Electrical Parameters of Dielectric Polymer Composites∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙6 2.1 Dielectric Constant∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙6 2.2 Dielectric Loss and Electrical Conduction ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙15 2.3 Dielectric Nonlinearity ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙18 2.4 Breakdown Strength∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙24 2.4.1 Routes to High-k Composites with High-Breakdown-Strength ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙28 2.4.2 Effect of filler alignment on breakdown strength of high-k polymer composites∙∙∙∙∙∙∙∙∙∙∙∙∙∙31 3. High-k Polymer Nanocomposites with 1D or Quasi-1D Filler∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙35 3.1 Superiority of High-Aspect-Ratio Filler∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙35 3.2 Role of Surface Functionalization of 1D Nanofiller∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙37 3.3 Role of Intrinsic Property of 1D Nanofiller∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙44 3.4 Effect of Microstructure of 1D Filler ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙46 3.5 Synergistic Effect of 1D Filler and Other Filler∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙51 4. Preparation Strategies for High-k Nanocomposites with Aligned 1D or Quasi-1D Filler∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙54 4.1 Dielectrophoresis∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙54 4.2 Uniaxial Strain Assembly∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙58 4.3 Template-Assisted Realization∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙60 4.4 High-k Nanorod Arrays ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙61 4.5 Electrospinning∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙62 4.6 Freeze Casting∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙65 4.7 Other Methods∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙66 5. Summary and Outlook∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙68 Acknowledgements∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙70 References∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙70

2

1. Introduction High dielectric constant (high-k) materials have attracted significant attention in recent years for their potential applications in the modern electronics and electrical industry, such as in electrostatic capacitors, [1-5] electrical stress control products [6, 7], high-power-density devices [8], dielectric elastomer actuators [2, 9-12], transistors [13], and so on. For example, the dielectric elastomer actuators (DEAs) shown in Figure 1 are usually designed by sandwiching a flexible dielectric (e.g., insulating elastomer) between two stretchable electrodes. A DEAs function is based on inducing an electric field deformation. The application of high-k elastomers can enhance the deformation capability of DEAs without increasing the applied electric field [11, 12]. Electrostatic capacitors are another typical example. The maximum energy density (Umax) of electrostatic capacitors is determined by the dielectric constant (k) of the dielectric material and the maximum electric field (EBD) that the dielectric can withstand [14, 15]: (1) As is evident from Equation 1, a high-k dielectric tends to store more electrical energy. Besides a high dielectric constant, an ideal high-k material should have as high as possible breakdown strength, and low dielectric loss and high electrical resistivity, which are critically important to real applications. With excellent properties such as high breakdown strength and ease of processing, organic polymers are often preferred over inorganic materials for use as dielectric materials [16]. In addition, the unique self-healing breakdown of dielectric polymer films ensures that the failure spots are spontaneously isolated from the rest of the metal film electrode, thus avoiding a catastrophic failure of the entire film capacitor [15, 17, 18], as shown in Figure 1c. However, most polymers have a low dielectric constant (where, k < 10 for most of polymers in comparison with inorganic dielectrics). 3

Recently, some polymers having relatively high dielectric constant have been synthesized, while either the other dielectric properties (e.g., high dielectric loss, high electrical conductivity, low breakdown strength) or the mechanical and processing properties can fulfill the requirement for dielectric and energy storage applications[2, 19-21]. In contrast, dielectric ceramics have large dielectric constants ranging from several hundreds to tens of thousands. Coupled with high stiffness and excellent thermal stability, ceramics exhibit small breakdown strength, difficult operability, high density, and poor flexibility characteristics that significantly limit their practical applications. It is not easy to find an individual material that combines all the desirable properties required for practical applications. However, significant efforts have been made throughout the last decade to achieve multifunctional highk materials. One effective approach is to combine the high dielectric constant of an inorganic filler with the high dielectric strength of polymers [22-25]. That is, introducing a high-k inorganic nanofiller into a polymer matrix to form dielectric polymer nanocomposites. Dielectric anisotropy plays an important role in determining the dielectric and energy storage performance of composite materials, which is dependent on the size, shape, and spatial arrangement of the inorganic filler [14]. It has been shown that well-designed anisotropic composites can provide a densely packed morphology that is capable of retarding the breakdown and carrier mobility, resulting in substantially improved properties for the polymer composites. Compared with the spherical nanofiller (hereafter, called nanoparticles or NPs); one-dimensional (1D) nanowires (NWs), nanofibers (NFs); and quasi-1D aligned NP assemblies; the high-k fillers have shown greater potential for constructing highperformance composites in dielectric and energy storage applications based on their high aspect ratio and/or anisotropic properties. For example, it has been revealed that, compared with composites filled with BaTiO3 NPs, the composites with BaTiO3 NWs reveal a 300 % enhancement of electromechanical 4

coupling [26], and therefore, there is an urgency to develop high-k polymer nanocomposites with 1D or quasi-1D filler. This review is aimed at providing a comprehensive overview of the recent progress in high-k polymer nanocomposites with 1D or quasi-1D fillers for dielectric and electrical energy storage applications.

Figure 1. Schematic illustration showing the effect of the dielectric constant on the deformation of dielectric elastomer actuators (a, b). Self-healing breakdown of metallized dielectric polymer film (c) [17].

Dielectric constant, dielectric nonlinearity, electrical conductivity and dielectric loss, and breakdown strength are the most important factors for determining and evaluating the dielectric properties and energy storage capability of polymer composites, and therefore, they are discussed in Section 2. Section 3 summarizes the recent progress in achieving enhanced dielectric properties and 5

energy storage capability of 1D high-k polymer nanocomposites. Dielectric anisotropy plays a critical role in determining the dielectric properties and energy storage capability of polymer composites, and therefore, Section 4 discusses the effect of filler alignment on the dielectric and energy storage capability of polymer composites in detail, with emphasis on the experimental methodology for achieving anisotropic dielectric polymer nanocomposites.

2. Basic Electrical Parameters of Dielectric Polymer Composites 2.1. Dielectric Constant Dielectric constant represents the static relative permittivity. In a physics text book, the dielectric constant usually refers to the ratio of the relative permittivity of a matter to the relative permittivity of the vacuum. In practice, the dielectric constant represents the electrical energy storage capability of a dielectric in comparison with the vacuum under an electric field, where a part of electrical energy will be used to polarize the dielectric. Taking electrostatic energy storage capacitors shown in Figure 2 as examples, where films are used as dielectrics. Compared with the vacuum dielectric capacitor in Figure 2a, where the stored charges can be defined as q when the voltage V is applied, the dielectric film capacitor shown in Figure 2b can storage the charge up to q + qm when the same voltage is applied. Here the increased charges qm originate from the energy for polarizing the dielectric film. If the dielectric constant of the dielectric film is increased by introduction of high-k inclusions (Figure 2c), the stored charges would be further increased by qp, which represents the polarization effects related with the introduced particles, resulting in the total charge of q + qm +qp on the capacitor plates. In this case, the increased electrical energy originate from the additional energy to polarize the particles and the interfacial region between the particles and the film matrix, and the dipole–dipole interaction energy among the introduced particles. 6

Figure 2. Scheme illustrating the electrical energy storage in electrostatic capacitors under an applied voltage V. (a) An vacuum capacitor with stored charge up to q. (b) A dielectric film capacitor with stored charge up to q + qm. (c) A high-k particles filled dielectric film capacitor with storaged charge up to q + qm + qp. (Reprinted with permission from [27])

Two approaches have been widely utilized to fabricate high-k polymer composites. One is utilizing the percolation theory [28], where composites were prepared by adding a conductive filler into an insulating polymer matrix and the composites’ dielectric constant ( ) obeys the following power law equation [29] (2) where

and s are the percolation threshold and critical exponent, respectively, and p represents the

volume fraction of conductive filler. Equation 2 indicates that the dielectric constant of a percolative composite can be significantly enhanced when the volume fraction of the conductive filler approaches the percolation threshold. Unfortunately, the breakdown strength of this type of composite usually substantially decreases even the filler fraction is far below the percolation threshold owing to the large electrical mismatch between the filler and the matrix [30]. Beale and Duxbury analyzed a model of the breakdown strength for dielectrics filled with conductive particles and concluded that the average initial breakdown strength follows [31] (3) 7

where L is the dimension of the conductive particle filled dielectrics. Equation 3 indicates that the breakdown strength of the conductive particle filled dielectrics approaches zero when p is close to

.

In addition, the conductive filler composites usually exhibit strong frequency dependent dielectric properties because of the existence of strong interfacial polarization and large leakage currents. High dielectric loss is another disadvantage of the conductive filler composites. Coating an insulating layer on conductive filler surface can suppress the dielectric loss with a low electric field [32-46], while in a high electric field, the suppression of the dielectric loss is marginal as a result of the electric tunneling effect [30, 47-53]. These disadvantages limit the usefulness of percolative composites for use in high-k dielectric and energy storage applications [54, 55]. Another approach is to introduce high-k inorganic filler into an insulating polymer [56-60]. The dielectric constant ( ) of this type of composite materials can be predicted by theoretical equations or empirical formula. Table 1 lists some of the representative theoretical equations, where are the volume fractions of the matrix and the filler, respectively, and constants of the inorganic filler and the matrix, respectively.

8

and

and

are the dielectric

Table 1. Theoretical equations to predict the dielectric constant of inorganic particles filled polymer composites Equations Lichtenecker

Formula or

Remarks

Ref.

This equation is commonly used to determine the dielectric constant of dielectric

[61-63]

mixtures where the spherical particles were randomly dispersed in the matrix. The equation itself has long been considered as a semi-empirical formula without firm theoretical justification. However, a recent investigation shows that this equation can be derived from the classic Maxwell’s equations by assuming that each component of the composite has randomly distributed shapes and orientations. Rayleigh

The composites were considered as a medium where the spherical particles were

[64]

randomly dispersed in the matrix in a rectangular order.

Maxwell–

This equation is useful when there is a low fraction of spherical particles randomly

Garnett

dispersed in a matrix. Also named the Maxwell-Wagner equation.

Bruggeman

The equation was derived by assuming a low fraction of spherical particles were

[65, 66]

[67]

randomly embedded into the matrix. Jayasundere–

The equation was derived by considering the interaction among the spherical

Smith

particles in 0-3 composites and requiring

Yamada

The effect of particle shape on the dielectric constant of composites was considered

.

here, where η is a parameter associated with the shape and orientation of ellipsoidal particles in a 0-3 composite.

9

[68]

[69]

Xue

The composites were treated as a medium where the core-shell spherical particles were randomly dispersed in the matrix. Here, r is radius of the spherical particles, R is the outer radius of equivalent composite spheres.

is the dielectric constant of

interphase. and

This importance of this equation is that it demonstrated that the dielectric constant of composites is not only related to the dielectric constants of the particle and the matrix but also closely associated with dielectric constant of the interfacial region.

10

[70]

Depending on the volume fraction, shape, and orientation of the particles in the filler, the dielectric constant ratio between the filler and the matrix and the filler/matrix interaction, the dielectric constant of composites can be predicted by one or more of the equations in Table 1 [63, 71-74]. A comparison of the theoretically predicted values with the experimentally obtained values for the dielectric constant of epoxy composites with the spherical BaTiO3 particles indicates that the Lichtenecker equation and the Jayasundere–Smith equation best fits the experimental data [75]. Figure 3 shows typical experimental results of a fraction dependent dielectric constant for high-k inorganic particle polymer composites. The dielectric constant of each composite increases with BaTiO3 loading up to a critical fraction, where it starts to decrease. Here, the critical fractions are related to the close packing density of the particles. Reducing the particle size to nanoscale results in particle agglomeration due to the significantly enhanced particle–particle interactions, and this causes the critical fraction to decrease with decreasing particle size. Beginning with the critical concentration, a further increase of particle loading results in porosity, and consequently, a decrease in the dielectric constant after the critical fraction [75]. Below the critical fraction, the composites with particles with different sizes exhibit different dielectric constants for specific concentrations [75-82]. This is because the dielectric constant of the BaTiO3 particles is dependent on their size [8385]. The finite element analysis investigation shown in Figure 4 suggests that particles with a higher dielectric constant are preferred for high-k composite materials.

11

Figure 3. Observed dielectric constants of epoxy resin composites with BaTiO 3 of different sizes. (Reprinted with permission from [75].)

In physics, the dielectric enhancement for high-k particle filled polymer composites primarily originates from the electric field enhancement in the polymer matrix and the electrostatic (dipoledipole) interactions between the high-k particles[86]. At a low concentration of high-k ceramic particles, the particle interactions are weak, and there is only a little electric field enhancement in the polymer matrix (Figure 4). Therefore, a low concentration of high-k particles results in little enhancement of the dielectric constant for the polymer composites, as shown in Figure 4d. When the ceramic particle concentration approaches a critical value (about 0.5 for spherical particles), the electric field enhancement increases rapidly in the matrix, allowing the high dielectric constant of the ceramic particles to be rapidly transferred into the composites.

12

Figure 4. Simulated local electric field (EL) distributions in three-dimensional randomly dispersed composites with (a) 10, (b) 20, and (c) 30 vol % of NPs (black). The applied field (E0) is along the z axis. The relative dielectric constants of the matrix and NPs are set as 2.25 and 120, respectively. (Reprinted with permission from [87]). (b) Comparison of the calculated normalized dielectric constant (ratio of the dielectric constant of composites to the dielectric constant of the matrix) versus the particle volume fraction with dielectric contrasts between the particle and the matrix. The calculated average electric field for the matrix (c) and the particles (d) versus the particle volume fraction and dielectric contrasts between the particle and the matrix. The average electric field in the composites is set at 1 V/m. (Reprinted with permission from[86]) 13

Aligning high-k particles into chains along one direction, with the 1-3 perpendicular (x–yaligned) and the 1-3 parallel (z-aligned) fillers, as shown in Figure 5, results in a higher dielectric constant of composites than that of a randomly dispersed filler [76], or that of a conductive filler [8795]. Randall et al. documented the effect of particle alignment on the dielectric constant of polymer composites [96]. As shown in Figure 5, the aligned polyurethane/Ba0.55Sr0.45TiO3 (BST) composites result in approximately twice the enhancement of the dielectric constant when compared with the unaligned composites. Further research by Randall et al. showed that both the 1-3 perpendicular (x– y-aligned) and the 1-3 parallel (z-aligned) composites had higher dielectric constants than the 0-3 composites (Figure 5e) [96]. NWs can be considered as aligned particle chains, yielding improved dielectric properties in the composites with high-aspect-ratio high-k particles [97, 98]. This is consistent with the predictions by the Yamada equation shown in Table 1, where the high-aspectratio particles have higher η values, resulting in a higher dielectric constant for the composites. The superiority of using high-aspect-ratio high-k particles in enhancing the dielectric constant of composite materials will be summarized in Section 3.1. Unlike the percolative composites, where an increase in the dielectric constant results in a substantial decrease of the breakdown strength [30, 31, 47, 99-102], high-k inorganic particle based polymer composites can exhibit both enhanced dielectric constant and increased breakdown strength, as will be seen later in Section 2.4. This is why high-k inorganic particle based polymer composites are more favorable for dielectric and energy storage applications.

14

Figure 5. Schematic diagrams of (a) 0-3, (b) 1-3 perpendicular (x–y-aligned), and (c) 1-3 parallel (zaligned) composites. Effect of filler assembly/dispersion on the dielectric constant of (d) polyurethane composites with 22 vol % BST (Reprinted with permission from [103]) and (e) epoxy resin/BaTiO3 composites (Reprinted with permission from [96]). 2.2. Dielectric Loss and electrical conductivity When an alternating voltage is applied to a dielectric, some power will be dissipated in the dielectric. The dielectric loss is defined as the amount of the power loss in the dielectric. For a single dielectric, the dielectric loss mainly originates from relaxation behavior and electrical conduction. For either a

15

dielectric mixture or a composite, the interfacial polarization caused by the charge accumulation at the interface is due to the dielectric constant/conductivity mismatch, and is an additional and important source of dielectric loss [104, 105]. The dielectric loss is undesirable for both energy storage and dielectric applications. The following several aspects should be considered in preparation of low loss polymer composites: (1) combining a low loss polymer matrix with low loss ceramics particles; (2) reducing the introduction of impurities as much as possible, especially ions that can transport through the dielectric; and (3), increasing the interfacial compatibility as the incompatible interface will induce microvoids where the charge carriers have enhanced mobility under applied electric field. The electrical conductivity is dependent on the hopping ability carriers between localized states or traps, and the escape from a localized state can only take place when a carrier obtains enough energy to overcome the potential barrier of a trap. Therefore, the electrical conduction in a dielectric is highly rely on the applied field and temperature. The ionic hopping is the main mechanism for electrical conduction of dielectrics at low electric field, while the injected electrons become important for the electrical conduction at high electric field. The addition of inorganic NPs such as Al2O3 and MgO can introduce deep traps, resulting in decreased concentration of mobile carriers and remarkable reduction of electrical conduction [106]. Figure 6 shows that at 125 ℃, the conduction current of poly(tetrafluoroethylene-hexafluoropropylene-vinylidene fluoride) [P(TFE-HFP-VDF)] can be reduced by more than two orders of magnitude after the introduction of 0.5-1.0 wt% Al2O3 NPs (30-50 nm). Figure 6 also shows that there is an optimum NP content (< 2 wt%), and further increase of NPs causes an increase in the electrical conductivity. This has been attributed to the increased shallow traps, which start to form conducting paths, resulting in high electrical conductivity. 16

Figure 6. (a) Conduction current of neat P(TFE-HFP-VDF) (written as THV in the figure) and the nanocomposites at 125 ℃ and (b) electrical conductivity versus alumina concentration at 60 MV/m. Dashed lines are only for eyes. (Reprinted with permission from [106]) It should be noted that the filler spatial arrangement and alignment show significant influence on the dielectric loss of polymer composites. Randall et al. performed a comparative investigation on the dielectric loss of 1-3 parallel (z-aligned), 1-3 perpendicular (x–y-aligned) and 0-3 PDMS/BaTiO3 composites by measuring the field-dependent dielectric displacement behavior D-E, (here, D = ε0E + P, where P is the electric polarization) and the loops of the composites [96]. A linear dielectric with super-low dielectric loss usually shows a linear behavior of electric displacement versus the electric field (Figure 7a). However, a high-loss material exhibits a widened D–E loop, which deviates from the linear relationship of the electric displacement versus electric field for linear dielectrics and should result from the electrical conduction and dielectric loss. As shown in Figure 7 Randall’s research provides the typical loss feature of high-k polymer composites: (i) the dielectric loss of the composites increases with the electric field; (ii) 1-3 parallel (z-aligned) composites have the highest dielectric loss among the three types of composites and the top part of bipolar loops show upright; and (iii) 1-3 perpendicular (x–y- aligned) composites have the lowest dielectric loss among the three

17

types of composites. The higher dielectric losses in z-aligned composites can be expected by reducing the distance between neighboring particles along the z-aligned (applied electric field) direction, which results in a large local electric field enhancement and a high electrical conduction loss[87]. Similarly, the decreased dielectric losses in x–y-aligned composites should be attributed to the large distance between neighboring particle chains [96].

Figure 7. D–E loops of polydimethyl siloxane (PDMS) and its composites with 25 vol% BaTiO 3 NPs versus electric field, (a) pure PDMS, (b) 0-3 composites, (c) 1-3 (z-aligned) composites, and (d)1-3 (x–y-aligned) composites. (Reprinted with permission from [96].) 2.3. Dielectric Nonlinearity The electrical energy (U) stored in a dielectric material is determined by the applied electric field and the electric displacement (D) of the dielectrics [15]: (4) where ε0 = 8.85 × 10−12 F m-1 is the vacuum dielectric constant, and k(E) is the dielectric constant of the dielectric, which is dependent on the electric field. In linear dielectrics with electric field 18

independent of the dielectric constant, the energy density (Ue) can be described as follows and the maximum energy density (Umax) is simplified to Equation 1. Figure 8 shows the electric field dependent electric displacement of dielectric materials with increasing dielectric nonlinearity. In linear dielectrics, there is almost no energy loss and the energy storage is dominated by the field being applied to the dielectrics, which is limited by the breakdown strength (EBD) of the dielectrics. However, as the dielectric nonlinearity increases, the energy loss (represented as the area enclosed within the electric field dependent electric displacement) increases as a result. The existence of nonlinearity suggests that integrating the charge curve against the polarization axis is the most reliable way to calculate the real energy storage density for a dielectric material.

Figure 8. Schematic showing the electric field dependent electric displacement (D) of dielectric materials with increasing nonlinearity. The green area is proportional to the discharged energy.

19

Some high-k ceramics, such as BaTiO3, are ferroelectrics, and exhibit nonlinear dielectric behavior, demonstrating an electric field dependent dielectric constant [107]. As shown in Figure 8, the dielectric constant of normal ferroelectrics decreases with the electrical field. The so called ‘polar nano-region’ concept has been used to understand this phenomenon. The polar nano-regions were defined as nanoscale regions showing parallel oriented spontaneous polarization, which are susceptive to the electric filed disturbance and inclined to redirect along the applied electric field vector even the electric field is low. In this case, the dielectric nonlinearity can be understood that the polar nano-regions lose their susceptibility by merging into large sized domains under a high enough electric field[108]. Despite the decrease of dielectric constant with electric field, the ferroelectrics such as BaTiO3 have improved energy storage capability when compared with the linear dielectrics such as BOPP at moderate fields because of their much higher polarization. However, the polarization saturates rapidly at high electric field after that the energy density do not increase with the electric fields. Anti-ferroelectric materials consist of ordered dipole arrays in which the adjacent dipoles are oriented in antiparallel directions (Figure 8). An anti-ferroelectric material can have a very large polarization at high electric field and thus it shows very high dielectric constant at high field. When the electric field is high enough, the dipoles all start pointing in the same direction and the antiferroelectric to ferroelectric transition takes place, resulting in peaks of dielectric constant at the switching field. This character is useful because the field-induced phase transition enables much larger storage capability of recoverable electrical energy than either the linear dielectric or the ferroelectric.

20

Dielectrics based electrostatic capacitors are a key component of pulsed power circuits because of their high power density (i.e., delivering a large amount of energy in a very short period), resulting in many applications, including: (1) medical devices such as defibrillators; (2) weapons platforms such as lasers, radio frequency, microwave and X-ray, detonators, electromagnetic armor and launchers; (3) DC/DC converters of hybrid electric vehicle, etc. Figure 9 shows an electromagnetic aircraft launch system for aircraft carrier, where the energy storage need a very high power density; In all these systems, the electrical energy is stored in capacitor banks, which now have large size because of the low energy density. The main strategy to improving these systems is to increase the energy density of the capacitors.

Figure 9. Schematic illustration showing an electromagnetic launch system for aircraft carrier. Composites with a ferroelectric filler also exhibit dielectric nonlinearity, especially in a strong electric field [109-112]. Unlike the ferroelectric ceramics, the dielectric constant of the dielectric polymer composites with high-k filler increases with the electric field, which results in many useful applications, such as suppressing partial discharge in power electronic modules[110] and releasing the electric stress in high voltage bushings [113] and cable terminations [112, 114]. Gefle et al. investigated the nonlinear dielectric behavior of lead zirconate titanate (PZT) particles in 21

polyvinylchloride (PVC) composites, with an average particle size of 1 μm, and volume fractions of 30 to 45%. Their results indicate that the dielectric enhancement is marginal for weak electric fields, E < 0.2 Eb (where E is the applied electric field and Eb is the average breakdown strength of the corresponding composite samples), while the nonlinear increase of the dielectric constant is more significant in a stronger electric field (E > 0.2 Eb) [115]. It was shown by Robertson et al that, as shown in Figure 10, the acrylic resin/BaTiO3 composites obviously exhibit dielectric nonlinearity [111, 116]. In addition, the composites filled with small sized BaTiO3 have increased nonlinearity as they exhibit higher percentage change of dielectric constant with electric field. However, large sized BaTiO3 particles can generate much higher dielectric constant in the composites[111]. Polymer composite tubes with field dependent high dielectric constant have been used for electric stress control in medium cable terminations[114]. As shown in Figure 10, the electrical field distribution is changed in the interface between the insulation and high-k (k2) materials. The ratio of the electrical stress in the environment (k3) to the electrical stress in the insulation can be adjusted by the third high-k layer (k2) between them. The high electrical stress can be released in this way. The nonlinear dielectric behavior of the ferroelectric ceramic/polymer composites may exhibit enhanced applications for electric stress control in power cable terminations [7, 112, 115, 116]. Recent investigation suggest that the non-linear dielectric constant and non-linear electrical conductivity should be simultaneously used to adjust and control the electric filed distribution in power equipment [117, 118]

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Figure 10. (a) Electric field and particle concentration dependence of dielectric constant of acrylic resin composites with 4 μm BaTiO3. (Reprinted with permission from [116].) (b) Schematic illustration showing the electrical stress control in cable terminations by high-k materials.

The dielectric nonlinearity of a single phase material may originate from the ferroelectricity, antiferroelectricity, electrical conduction and dielectric loss, while the origin of the dielectric nonlinearity in polymer composites is more complex. It was shown that the field-dependent dielectric constant of the silicon/ZnO composites originates from the relaxation of conduction current and the 23

capacitive component of the nonlinear loss[117]. Zhu and Tang investigated the dielectric nonlinearity of polypropylene (PP) nanocomposites with POSS (polyhedral oligomeric silsesquioxanes) functionalized BaTiO3 and concluded that the dielectric nonlinearity originates from the substantial internal AC space charges conduction in the BaTiO3 NPs, which causes high dielectric losses[87]. Such a conclusion was derived according to the following facts. One is the bipolar D-E loops at a temperature (e.g., 130 °C) higher than the Curie temperature (121 °C) for 2 μm BaTiO3 particles still show the dielectric nonlinearity (Figure 11), indicating that the weak ferroelectricity of the BaTiO3@POSS NPs is unlike to cause significant nonlinearity in the bipolar D-E loops of the PP/BaTiO3@POSS nanocomposites. The second is that the top part of the bipolar D-E loops do not show upshift and the electrical conduction is extremely low. The dielectric loss of the PP/BaTiO3 was further decreased by depositing a layer (5 nm) of amorphous TiO2 on BaTiO3 NP surface (Figure 11d). The deposited is amorphous TiO2 nanolayer have higher electrical resistivity, which reduced the boundary layer conduction of BaTiO3, resulting in significantly suppressed dielectric loss and dielectric nonlinearity.

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Figure 11. (a) Bipolar electric field dependent electric displacement loops at 10 Hz. (a) PP at room temperature, (b) PP/BaTiO3@POSS at 130°C, (c) PP/BaTiO3@POSS at room temperature, (d) PP/BaTiO3@TiO2@POSS at room temperature. BT is the abbreviation of BaTiO3. (Reprinted with permission from [87])

2.4. Breakdown Strength The measured breakdown strength of a dielectric is dependent on the sample thickness, voltage frequency and control, electrode geometry and contact, ambient medium, temperature and humidity [30, 119-121]. Provided that these conditions are controlled, the short time breakdown of a solid dielectric is usually attributed to three mechanisms: intrinsic electric breakdown, thermal breakdown and electromechanical breakdown[122]. Intrinsic electric breakdown is caused by electron avalanche and it takes place at very low temperature. The electrons can originate from the electrode injection,

25

emission from impurities and collision ionization. Thermal breakdown takes place when the heat produced by dielectric loss and joule heating is much higher than the dissipated via conduction/convection. The thermal and current continuity equation can describe the thermal instability between heat production and dissipation (5) where Cv and T are the specific heat per unit volume and temperature, respectively.

and

are the

thermal and electrical conductivity, respectively. Equation 5 indicates the breakdown strength decrease exponentially as the temperature increases. Electromechanical breakdown originates from the deformation of flexible organic materials or fracture of inorganic materials caused by electrostatic compressive forces, which were induced by the attraction between the negative and positive charges isolated by the dielectric. Electromechanical breakdown can be evaluated by (6) (7) where Y is the Young's modulus, and do and d are the original and reduced thicknesses of the specimen, respectively. Under work conditions, the long time breakdown or failure of a solid dielectric is highly associated with partial discharge, which includes internal (e.g., in voids and pores), surface (e.g., at particle/matrix interfaces), and corona (e.g., at sharp points) discharges[121]. In each case, the electric stress is much higher than the average one in the dielectric, causing erosion, tracking, treeing, pitting, space charge buildup and migration, dielectric losses, electrochemical changes, and breakdown[123, 124].

26

In a heterogeneous material such as polymer composite, the breakdown strength is associated with many factors, including the electrical (e.g., conductivity, dielectric constant) contrast, filler size and shape (e.g., particles, fibers, flakes), microstructure (e.g., filler dispersion and distribution), defects (e.g., voids, pores), filler/matrix interface, thermal conductivity and mechanical property (e.g., Young's modulus) [98, 125-127]. In addition, large particle agglomerates can be considered as defects that enhance the electric field within their immediate locality, when compared with single particles. Shen and Wang developed a continuum phase-field model to investigate the electrostatic breakdown propagation in PVDF/BaTiO3 nanocomposites[128]. As shown in Figure 12, the breakdown phase starts to grow from the nucleation within the nanocomposites when the electric field is high than the threshold (i.e., 165 kV mm1 here). The breakdown phase tends to grow at first in the vulnerable NPs/polymer interfaces and then pass through the NPs near the breakdown path. In the NFs based composites, straighter breakdown path can be observed as displayed in Figure 12c, d. In addition, it was found that the breakdown phase cannot penetrate through a NF until the electric field shoulder is higher than a threshold. As a result, NFs based composites exhibit a higher breakdown field in comparison with the NP composites. Figure 12e quantitatively demonstrated the breakdown phase growth behaviors of the aforementioned nanocomposites. One can see that the breakdown phase fraction does not increase until the electric field is higher than 140 kV mm-1 (point A in Figure 12e). When the electric field is higher than 140 kV mm-1, the breakdown phase fraction starts to increase and the NP composite exhibits a higher increase rate. The NP composite is totally breakdown when the electric field approaches 200 kV mm-1 (point C in Figure 12e), where the breakdown phase become saturated. In contrast, breakdown cannot take place until the electric field 27

approaches 225 kV mm-1 in the NF composite (point B in Figure 12e). The difference in breakdown strength is caused by the electric field distribution, which is shown in the insets of Figure 12e. In the NP based composites, the field concentrates at the two NP poles along the field direction. In the NFs based composite, the electric field concentration take places at the NF vertices. In this case, the breakdown phase is easier to get round the NPs and thus the NP composite shows lower breakdown strength in comparison with the NF composite. Using an electro-thermal phase-field model, Shen et al also simulated the effect of temperature on breakdown phase evolution in polymer nanocomposites[129]. It was found that as the temperature increases, the Joule heating energy density exhibit an exponential increase, which accelerates the evolution of breakdown strength. The negative effects of heating on breakdown of polymer nanocomposites can be suppressed by both increasing the thermal conductivity and reducing the electrical conductivity, whereas it was found that the reduction of electrical conductivity is more effective [129].

Figure 12. The breakdown simulation results of nanocomposites filled with 10 vol% (a, b) NPs and (c, d) NFs with height/radius ratio of 20, and (e) the evolution of breakdown phase volume fraction under Exapp (the horizontal direction electric fields). Insets in (e) indicate the distribution of electric field of corresponding composites. (Reprinted with permission from [128]) 28

2.4.1. Routes to High-k Composites with High-Breakdown-Strength Simultaneous enhancement of dielectric constant and breakdown strength in dielectric materials are highly desirable for dielectric and energy storage applications. However, in many cases, the increase in the dielectric constant results in the decrease of the breakdown strength due to the large dielectric constant mismatch between the filler and the matrix [130, 131]. In order to improve dielectric properties and enhance the energy storage capability, several strategies have been developed to increase the dielectric constant while retaining the high breakdown strength of the composites: engineering the interface between the inorganic filler and polymer matrix [7, 132-146], controlling the filler orientation, spatial arrangement, and alignment [96, 147-153], introducing the third phase [154-157], and enhancing the thermal conductivity of polymer composites[1, 129, 156]. Core-shell structured particles have their unique merits in optimizing the dielectric properties of the polymer composites [7, 32, 37, 76, 134-141, 157-165]. A typical example is the utilization of core-shell particles composed of a high-k core and shells with an intermediate dielectric constant, where the dielectric constant gradually decreases from the core to the matrix [136, 137]. The outer shells of the filler are used as the dielectric buffer between the high-k particle core and the low-k matrix, which can reduce the electric field distortion, resulting in a high breakdown strength of the polymer composites. Wang and Tan performed a computational study on the local electric field distribution of core-shell particle filled composites, and the results are shown in Figure 13[76]. When the particle dielectric constant is much higher than that of matrix, the Ey component is significantly enhanced along the applied electric field E ex, suggesting the existence of a severe electric field distortion near the two polarized particle poles. However, a small electric field enhancement is observed inside the core-shell particles. It is the depolarization field generated by the 29

electric charges accumulated in the filler/matrix interface that partially cancels the applied electric field Eex inside the filler. Experimentally, Yao et al. performed a comparative study on the dielectric constant and breakdown strength of poly(vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) composites with BaTiO3 and TiO2 encapsulated BaTiO3 (BaTiO3 @TiO2) NPs [134], finding that compared with using BaTiO3 as filler, using the core-shell structured BaTiO3 @TiO2 not only resulted in an unexpected higher dielectric constant (up to 3 times greater) in the composites, but also achieved an improved breakdown strength of the composites, as shown in Figure 14. Some dielectric filler can enhance the breakdown strength of polymers and polymer composites by acting as barriers or scattering sites for high-energy charge carriers or enhancing the mechanical property of the composites [1, 154, 156]. It has been found that 2D boron nitride nanosheets (BNNSs) can significantly enhance the breakdown strength of many polymers [e.g., polyethylene (PE), poly(phenylene sulfide) (PPS), poly(vinylidene fluoride-chlorotrifluoroethylene) (PVDFCTFE)] and polymer/BaTiO3 composites, even at high temperatures [1, 154, 156, 166]. A breakdown strength catalog of P(VDF-CTFE) ternary nanocomposites with systematically varied loading levels of BNNS and BaTiO3 filler, was given by Wang and Li [154]. It was determined that low loading levels of BaTiO3, with a proper concentration of BNNSs, significantly enhances the breakdown strength of the P(VDF-CTFE)/BNNs/BaTiO3 nanocomposites. As an example, the addition of 12 wt% BNNs can result in a high breakdown strength of about 550 MV/m from less than 400 MV/m for the P(VDF-CTFE) nanocomposite with 15 wt% BaTiO3 NPs (Figure 14c).

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Figure 13. Local electric field distribution around a particle (a) without and (b) with core-shell structures in a matrix. Eex is the electric field applied on the composites, and the arrow indicates its direction. Ex and Ey represent the total electric field distribution of x-axis and y-axis components, respectively. The color scale indicates the enhancement magnitude of the respective electric field components. (Reprinted with permission from [76].) Conventional metal particles have an extremely large electrical mismatch with most polymers, significantly decreasing the breakdown strength of the composites [30, 47-49, 167]. In contrast, some metal particles start to exhibit unique nanoeffects, such as the quantum confinement effect and the Coulomb-blockade effect, when their diameter is reduced to a critical size (≈ 10−9 m) at 20 °C [155]. The nanoeffects of ultra-small metal NPs have been used to enhance the breakdown strength of highk polymer nanocomposites, and when compared with the conventional ferroelectric polymer/BaTiO 3 nanocomposites, the ultra-small nano-Ag or nano-Pd decorated BaTiO3 NP based composites can exhibit a significantly enhanced breakdown strength (Figure 14d), resulting in higher energy density and higher energy storage efficiency [155, 157, 168].

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Figure 14. Dielectric constant (a) and breakdown strength (b) of PVDF-HFP/BaTiO3 composites and PVDF-HFP/TiO2@BaTiO3 composites with filler loading (Reprinted with permission from [134]). (c) Breakdown strength of PVDF-CTFE/BNNS/BaTiO3 composites with BNNS loading (Reprinted with permission from [154]). (d) Breakdown strength of PVDF/BaTiO3 composites and PVDFHFP/Ag@BaTiO3 composites with filler loading (Reprinted with permission from [155]). 2.4.2. Effect of filler alignment on breakdown strength of high-k polymer composites When the filler were aligned in the composites, the breakdown strength is dependent on the aligning direction of the filler, exhibiting increased or decreased values in comparison with 0-3 composites. This is due to the local electric field distribution in composites having a strong dependence on the filler arrangement. Wang and Tan performed a computational study on the effect of particle arrangement on local electric field distribution in composites, and the results are shown in Figure 15 [76]. When the particles were aligned into chains along the applied electric field Eex, the local electric field in the matrix is the significantly enhanced between the gaps of particles. However, when the aligned particle chains were perpendicular to the applied electric field Eex, the dielectric 32

constant is much higher than that of matrix, and the local electric field in the matrix is weaker when compared with randomly dispersed composites. Since the breakdown strength of the composites is critically determined by the local electric field enhancement, the composites with anisotropic particle arrangement have a strong anisotropy in breakdown strength. Experimentally, Randall et al. performed a comparative investigation on the breakdown strength of 1-3 parallel (z-aligned), 1-3 perpendicular (x-y-aligned) and 0-3 PDMS/BaTiO3 composites [96]. As shown in Figure 15c, the xy-aligned composites show the highest values of the breakdown strength, while the breakdown strength of the z-aligned composites is among the lowest of the three types of composites. In the zaligned composites, the aligned particle chains are parallel with the direction of the applied electric field. In this case, there exists a significantly enhanced electric field between the neighboring particles because of the small inter-particle distance along the direction of the applied electric field that can initiate breakdown channels travelling along particle chains when the applied electric field is relatively low. In the x–y-aligned composites, the aligned particle chains are perpendicular with the applied electric field, acting as barriers or scattering sites for high energy charged carriers, resulting in enhanced breakdown strength when compared with the other types of composites [96]. Considering that the x–y-aligned composites exhibit a higher dielectric constant in comparison with the 0-3 composites, this investigation suggests new methods to achieve high-k composites for dielectric and energy storage applications.

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Figure 15. Local electric field distribution in composites with different filler arrangements (a, b). Eex is the electric field applied on the composites and the arrow indicates its direction. E x and Ey represents the total electric field distribution of x-axis and y-axis components, respectively. The color scale indicates the enhancement magnitude of the respective electric field components; Weibull plots of dc breakdown strength of PDMS/BaTiO3 composites (c). (Reprinted with permission from [96].) Xie et al conducted a physical-assisted casting method and fabricated aligned BaTiO3 NWs in P(VDF-CTFE) matrix (Z-aligned and X-Y aligned)[169]. After introducing BaTiO3 NWs into P(VDF-CTFE), the dielectric constant was enhanced. Interestingly, when the BaTiO3 NWs align parallel to the electric field, its enhancement on dielectric constant is more obvious. As for 34

breakdown strength, the tendency is just the opposite. Nanocomposite with BaTiO3 NWs parallel to the electric field exhibits a lower breakdown strength than nanocomposite with BaTiO3 NWs perpendicular to the electric field. This might be contributed to the Z-aligned BaTiO3 NWs increased the path connection in the electrical tree processing [169]. Using high-throughput phase-field design, Shen et al demonstrated the effect of nanofiller alignment on the breakdown strength of polymer nanocomposites[128]. As shown in Figure 16, the polymer nanocomposites with different microstructure show different breakdown phase growth behavior. Breakdown is the easiest to take place in the vertical NFs nanocomposite, whereas breakdown is the hardest to take place in the parallel NS nanocomposite. This is because that the vertical NFs make the electric field more condensed in the nanocomposites, while the parallel NSs in the nanocomposites can make the electric field more dispersed. Figure 16c shows the extracted values of breakdown strengths from Figure 16b and they show the order of vertical NF (151 kV mm1

) < vertical NS (195 kV mm-1) < random NP (216 kV mm-1) < parallel NF (223 kV mm-1) < pure

polymer (230 kV mm-1) < parallel NS (310 kV mm-1). One can see that at a nanofiller fraction of 10 vol%, all the nanocomposites except the sample with parallel NSs have a lower breakdown strength in comparison with the pure polymer. This result indicates that volume fraction of nanofiller should be not higher than 10% when designing polymer nanocomposites for dielectric and energy storage applications where high breakdown strengths are highly desirable.

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Figure 16. Simulations of the effects of microstructure on breakdown of nanocomposites with a nanofiller of 10 vol%. (a) The morphology of breakdown phase in the polymer nanocomposites with different microstructures; (b) Evolution of the breakdown phase fraction with the electric field; (c) Extracted values of breakdown strength for different nanocomposites. The NF has a height/radius ratio of 20 and the NS length scale is 1 : 6 : 6. (Reprinted with permission from [128] ).

3. High-k Polymer Nanocomposites with 1D or Quasi-1D Filler 3.1. Superiority of High-Aspect-Ratio Filler Compared with spherical particles and low-aspect-ratio filler (e.g., nanorods), high-aspect-ratio 1D filler such as NWs and NFs have been shown to enhance the dielectric properties of nanocomposites more efficiently [97, 98, 170-173]. Considering the dielectric enhancement, the advantages that make a highaspect-ratio 1D filler attractive in preparing high-k polymer composites are: (i) a high-aspect-ratio filler reaches the contact percolation easier than a low-aspect-ratio filler that allowed connectivity or continuous passage in the composites, resulting in a higher dielectric constant and/or a higher thermal conductivity[174-176]; (ii) compared with a low-aspect-ratio filler, the lower surface area of the highaspect-ratio filler helps to reduce surface energy, preventing filler agglomeration in the systems; and (iii) 36

the large dipole moment of the high-aspect-ratio filler results in a higher dielectric enhancement of composites at lower loading [177]. For example, BaTiO3 NWs can enhance the dielectric constant of composites more efficiently in comparison with BaTiO3 NPs [173]. The dielectric constant of composites with BaTiO3 NWs can reach up to 69.5 at 17.5 vol% loading, while only ≈ 52 for a composite with 30 vol% NPs (Figure 17a). Tang et al. also demonstrated that the composites with Ba0.2Sr0.8TiO3 (BST) NWs have higher dielectric constants in comparison with those with Ba0.2Sr0.8TiO3 nanorods, as shown in Figure 17b [172]. This enhancement was attributed to a higher aspect ratio of the NWs yielding a higher electromechanical coupling in the nanocomposites. Furthermore, it is observed that the dielectric constant of composites increased as the aspect ratio of the nanofiller increased (Figure 17c). The BaTiO3 NWs composites revealed about 1.4 times the enhancement of the dielectric constant as the aspect ratio of NWs increased from 9.5 to 45.8. More importantly, the dielectric loss tangent is kept at a low level and is almost independent of the aspect ratio and volume fraction of the BaTiO3 NWs, as shown in Figure 17d [177]. Apart from the dielectric constant, an increased breakdown strength of the composites using highaspect-ratio 1D high-k filler can also be achieved. Shen and Nan have found that the composites filled with BaTiO3 NFs exhibited a higher breakdown strength than a pure polymer or the composites with NPs [132]. Compared with BaTiO3 NPs, the BaTiO3 NFs with large aspect ratios tend to orient in the inplane directions of the composite films during the preparation. When subjected to an electric field applied in the out-of-plane direction of the composite films, the NFs oriented in the in-plane directions gave rise to anisotropy in the susceptibility of the composite films, leading to a lower electric field in the polymer matrix. The apparent breakdown strength is thus enhanced with a more homogeneous distribution of the local electric field. 37

Figure 17. Comparison of dielectric constant (1kHz) of BaTiO3 nanocomposites as a function of NW or NP concentration (a) (Reprinted with permission from [173]). Comparison of dielectric constant (1 kHz) for nanocomposites with BST NWs or nanorods (b) (Reprinted with permission from [172]). Dielectric constant (c) and loss tangent (d) of the nanocomposites at 1 kHz as a function of the aspect ratio and the volume fraction of BaTiO3 NWs (Reprinted with permission from [177]). 3.2. Role of Surface Functionalization of a 1D Nanofiller As previously stated, simultaneous enhancement of the dielectric constant and the breakdown strength has been achieved in polymer composites with high-aspect-ratio 1D high-k filler, making the corresponding composites highly desirable for dielectric and energy storage applications. However, this is only possible when the filler/polymer interface is correctly designed. A compatible filler/matrix interface is of vital importance for achieving enhanced properties of for the composites, which may remove the impurities such as water molecules and ions, and thus

38

eliminating the defects such as large sized filler aggregates and voids/pores, or thereby significantly reducing impurities and defects. Defects such as large sized filler aggregates and voids/pores can cause highly inhomogeneous electric fields in the composites, leading to a drastically reduced effective breakdown strength for the composites. The surface functionalization of the filler is an effective way to improve compatibility with the polymer matrix [178]. Until recently, a variety of surface functionalization approaches to 1D nanofillers (BaTiO3, SrTiO3, BaxSr1-xTiO3, and TiO2) have been utilized to enhance the dielectric properties and energy storage density of polymer composites. Table 2 summarizes the recent research works related to high-k polymer nanocomposites with a high-aspectratio 1D nanofiller. Typical examples are documented by Huang and Wang[142]. By grafting poly(pentafluorophenyl acrylate) (PPFPA) on Ba0.7Sr0.3TiO3 NWs via in situ reversible addition-fragmentation chain transfer (RAFT) polymerization, Huang and Wang first observed enhanced energy storage efficiency and breakdown strength in the PVDF-HFP nanocomposites. They also observed that the composites with fluoro-polydopamine functionalized BaTiO3 or TiO2 NWs exhibit significantly enhanced breakdown strength and discharge energy density in comparison with the bare NW composites, particularly with high NW loading [179, 180]. Figure 18 shows that the functionalization of BaTiO3 NWs by fluoro-polydopamine increases the breakdown strength of the nanocomposites, resulting in enhanced discharged energy density. The nanocomposite film with 5 vol% functionalized BaTiO3 NWs has a discharged energy density of 12.87 J cm-3 at 480 MV m-1[179]. Zhai and Liu found the composites with the hydroxylated filler exhibit a higher dielectric constant, lower dielectric loss tangent and a higher breakdown strength as compared to the PVDF composites prepared using Ba0.6Sr0.4TiO3 NFs [181]. The enhanced properties of the composites with functionalized NWs should be mainly attributed to the improved filler dispersion and the enhanced filler/polymer 39

compatibility via strong interactions between the fluoropolymer matrix and the functional groups of the filler surface, which reduces the contact percolation pathways of the charge transfer and prevents the NWs from agglomerating. It should be noted that the orientation of the 1D filler facilitated by the surface functionalization in the in-plane directions of the composite films, might also be responsible for the improved properties. When the electric field was applied in the out-of-plane direction of the composite films, the susceptibility of the nanocomposites could be reduced by the high-aspect-ratio 1D filler perpendicular to the external electric field, leading to a lower electric field in the polymer matrix [181].

Figure 18. Scheme illustrating the fabrication process of fluoro-polydopamine functionalized NWs (f-DOPA@BaTiO3) (a). A photograph of a mussel was inset. TEM images of a f-DOPA@BaTiO3 NW (b, c). Breakdown strength of PVDF-HFP nanocomposites with f-DOPA@BaTiO3 NWs and unfunctionalized NWs (d). Electric field dependent discharged energy densities of PVDF-HFP nanocomposites with f-DOPA@BaTiO3 NWs and 15 vol % unfunctionalized NWs (e) (Reprinted with permission from [179]). 40

It has been shown that the dielectric property and energy storage capability of particulate composites can be optimized by tailoring the electrical properties (e.g., dielectric constant) of the interfacial regions between the filler and the polymer matrix [134-137], suggesting that the compatibility and electrical properties of the modifiers are also important factors to be considered in filler functionalization [182, 183]. Few efforts have been focused on the effect of organic modifiers on the dielectric property and energy storage of polymer composites with 1D filler.

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Table 2. Summary of polymer nanocomposites with functionalized 1D nanofiller for dielectric and energy storage applications Matrix

PVDF

Filler

Modifier for filler

Contents (vol %)

BaTiO3 NFs

Polydopamine

2–11

Ba0.6Sr0.4TiO3 NFs

Polydopamine

2.1–11.2

BaTiO3 NWs

Ethylenediamine

5–30

BaTiO3 NFs

Perfluoroalkylsilane

5–20

Ba0.2Sr0.8TiO3 NWs

Ethylenediamine

2.5–7.5

Ba0.6Sr0.4TiO3 NFs

H2O2

2.5–10

Ba0.6Sr0.4TiO3 Nanotubes

H2O2

2.5–10

SrTiO3 NFs

Polyvinyl pyrrolidone

2.5–7.5

TiO2 NWs

3-Aminopropyltriethoxysilane

2.5–7.5

Dielectric Property and Energy Storage Capability of the Composites The dielectric constant of the composite with 11 vol % NFs is 30 at 1 kHz, and a breakdown strength of 240 kV/mm was achieved in the composites with 4.4 vol% NFs. The composite with 11.2 vol % modified NFs has a dielectric constant of 22.4 at 1 kHz and the composite with 2.1 vol % modified NFs has a high breakdown strength of 405 kV/mm. The maximum energy density of the composites was 5.24 J/cm3 at 4.4 vol % NFs, nearly two times of pure PVDF. The composite with surface modified 30 vol % NWs had a high dielectric constant of 44.3 (3.5 times larger than the neat polymer) and the low loss tangent was of 0.04 at 1 kHz. The dielectric constant of the composite with 20 vol % modified NFs was of 22 at 1 kHz, almost 30 % higher than that of the composite with unmodified NFs and about twice of that of PVDF. The surface modification also results in decrease of dielectric loss of the composites. The composite with 7.5 vol % NWs has a dielectric constant of 17.5 at 1 kHz, exhibiting the maximum energy density of 14.86 J/cm3 under an electric field of 450 kV/mm, 42.9 % higher than that of PVDF, and 1138% greater than that of commercial BOPP (energy density of 1.2 J/cm3 at 640 kV/mm). Owing to the surface modification of NFs, the composite with 2.5 vol % NFs has enhanced breakdown strength of 398 kV/mm, which is 60% higher than the resulting composite with unmodified NFs. The maximum energy density of the composite with 2.5 vol% NFs was 6.4 J/cm3 at 400 kV/mm, more than doubled that of PVDF. The composite with 10 vol% nanotubes has a dielectric constant of 48.2 at 1 kHz, about 37% higher than that of the composite with untreated nanotubes, and 6.1 times higher than that of PVDF. The breakdown strength of the composite with 2.5 vol% NFs is 380 kV/mm, while the resulting composite with unmodified NFs has breakdown strength of about 290 kV/mm. The maximum energy density of the composite with 2.5 vol% NFs is 6.8 J/cm3 at 380 kV/mm, which is more than twice of PVDF (2.8 J/cm3 at 400 kV/mm). The maximum energy density of the composite with 7.5 vol% NWs is 12.4 J/cm3 at 450 kV/mm, nine times larger than that of commercial BOPP capacitors (1.2 J/cc at 640 MV/m).

42

Ref. [132]

[184]

[177]

[181]

[172]

[181]

[185]

[186]

[187]

PVDFHFP

P(VDFTrFECFE) P(VDFTrFE)

Epoxy

TiO2 NWs

Fluoropolydopamine

2.5–15

BaTiO3 NWs

Fluoropolydopamine

2.5–15

BaTiO3 NWs

Liquid crystalline polymer

2.5-7.5

Na2Ti3O7 NFs

Liquid crystalline polymer

2.5–10

BaTiO3 NWs

Ethylenediamine

5–17.5

BaTiO3 NFs

Polydopamine

3–10.8

BaSrTiO3 NFs

Polydopamine

4.1–27.7

BaTiO3 NFs

Polydopamine

1.8–6.7

The nanocomposite with 2.5 vol% functionalized NWs has a discharged energy density of 11.48 J/cm3 at 530 MV m−1, which is 2 times higher than that of BOPP (3.56 J cm −3 at 600 MV/m). A high energy density of 9.12 J/cm3 was achieved for nanocomposites with 15 vol % functionalized NWs at relatively low electric field of 360 MV/m, nearly 2 times of pure PVDF-HFP (4.76 J/cm3 at 360 MV/m). The functionalization of NWs results in enhanced breakdown strength and suppressed dielectric loss of the nanocomposites in comparison with unfunctionalized NWs. 5 vol% functionalized NWs filled nanocomposite has a discharged energy density of 12.87 J/cm at relatively low electric field of 480 MV/m, which is 2.5 times higher than that of BOPP. At 1 kHz, the dielectric constant increase to 22.5 from nanocomposite with 7.5 vol% functionalized NWs from 6.9 of polymer but maintaining the low dielectric loss (< 0.05). When the coated polymer thickness is about 33 nm, the nanocomposites exhibit a discharged energy density of 7.5 J/cm3 and an energy efficiency of 55.1% at 300 MV/m. The dielectric constant and dielectric loss of the nanocomposites is related with the thickness of the liquid-crystalline polymer (poly(2,5-bis[(4-methoxyphenyl)oxycarbonyl]styrene) which was used to functionalized the NFs. It reveals that the increase of liquid-crystalline polymer thickness results in the increase of dielectric loss and the stronger frequency dependence of the dielectric constant. With a dielectric constant of 69.5 at 1 kHz, the maximum energy density of the composite with 17.5 vol% NWs is 10.48 J/cm3 and 300 kV/mm, more than 45.3% increase when compared with pure P(VDF-TrFE-CFE) polymer (7.21 J/cm3), and more than 7 times larger than that of BOPP capacitors. Dielectric constant of 30 at 1 kHz was achieved in the composite with 10.8 vol% NFs. The composite with 27.7 vol% NFs has a dielectric constant of 34 at 1 kHz. At 4.1 vol%, the composite has a breakdown strength of 227.5 kV/mm, exhibiting the maximum energy density of 4.72 J/cm3 at 155 kV/mm, which is 4 times higher than that of PVDF-TrFE (1.13 J/cm3 at 130 kV/mm) The dielectric constant of the composite with 6.7 vol % modified NFs is 18 at 1 kHz, while that with the unmodified was about 15. The breakdown strength was of 202.7 kV/mm at 1.8 vol%, almost doubled that of the composite with unmodified NFs and ~4 times higher than that of epoxy.

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[188]

[179]

[189]

[190]

[173]

[191]

[192]

[132]

3.3 Role of the Intrinsic Property of the 1D Nanofiller The breakdown strength is an important parameter in determining the dielectric property and energy storage capability of a dielectric. However, for practical applications, electric equipment and electronic devices usually work under an electric field far below the breakdown strength. The intrinsic properties of the filler are important to consider in determining the dielectric properties and energy storage capability of the composites, as shown in Table 2. One can see that the composites with different 1D nanofiller demonstrate different dielectric properties, even with the same polymer matrix and the same filler modifier. Huang and Wang investigated the influence of the intrinsic properties of high-k inorganic NWs on dielectric properties and energy storage capabilities of polymer nanocomposites [133], where P(VDF-HFP)-based nanocomposites containing four types of dopamine functionalized NWs have been prepared: nonferroelectric Na2Ti3O7 and TiO2, ferroelectric BaTiO3, and paraelectric SrTiO3. The results reveal that the inherent property of NWs have an unambiguous effect on the performance (dielectric constant, breakdown strength, energy storage capability, and energy storage efficiency) of the nanocomposites. The dielectric properties and energy storage capability of polymer nanocomposites are mainly dependent on the dielectric constant and/or electrical conductivity of the inorganic filler. As shown in Figure 19, the dielectric constant and energy storage capability of the composites were directly related to the dielectric constant of the inorganic filler. Among the four types of NWs, BaTiO3 result in the highest dielectric enhancement while Na2Ti3O7 give the lowest dielectric enhancement in the composites, which is consistent with the prediction from the effective medium theory [193]. Under a DC electric field, the breakdown strength of the composites are mainly associated with the electrical conductivity mismatch between the filler and matrix, and thus the composites with the high-electrical-conductivity Na2Ti3O7 NWs showed the lowest breakdown strength. The high electrical conductivity of the Na2Ti3O7 NWs and corresponding nanocomposites have a

44

high dielectric loss, resulting in the low energy storage efficiency for the Na2Ti3O7 nanocomposites.

Figure 19. (a) Filler loading dependent dielectric constant of PVDF-HFP/NWs nanocomposites at 1 kHz. (b) Weibull characteristic breakdown strength of PVDF-HFP/NWs nanocomposites. (c) Discharged energy density and charge-discharge efficiency (d) of PVDF-HFP/NWs nanocomposites. (Reprinted with permission from [133].) (Note: dopa@ means that the NWs were functionalized by dopamine). Chi et al prepared different NFs (TiO2, BaTiO3, CaCu3Ti4O12 and 0.5Ba(Zr0.2Ti0.8)O3– 0.5(Ba0.7Ca0.3)TiO3) via an electrospinning technique and compared the dielectric and energy storage properties of their PVDF composites[194]. As shown in Figure 20, CCTO/PVDF possesses the highest dielectric constant along with the highest dielectric loss and conductivity among all composites. However, CCTO/PVDF exhibits the lowest breakdown strength and hence the lowest energy density because of their high electrical conductivity. Among these composites, BZT-BCT/PVDF shows the highest energy density because of the high dielectric constant and moderate electric conductivity of BZT-BCT. 45

Figure 20. Comparison of (a) dielectric constant and (b) discharged energy densities and chargedischarge efficiencies of PVDF and nanocomposites with BT NPs, BT NFs, TiO2 NFs, CCTO NFs or BZT-BCT NFs under different electric field. CCTO and BZT-BCT are the abbreviations of CaCu3Ti4O12 and 0.5Ba(Zr0.2Ti0.8)O3–0.5(Ba0.7Ca0.3)TiO3, respectively. (Reprinted with permission from[194]). 3.4 Effect of Microstructure of the 1D Filler Theoretically, one can enhance the dielectric constant of composites by increasing the high-k filler loading or by utilizing an interfacial polarization between the filler and the polymer matrix [105]. However, increasing the filler loading usually introduce undesirable defects, such as voids and other structural imperfections, resulting in decreased breakdown strength and increased dielectric loss/leakage currents. Apart from engineering the filler surface using modifiers, two approaches have been used to achieve higher dielectric constants while retaining the high breakdown strengths and low dielectric loss of the composites. One is to use the core-shell structured 1D filler [195, 196], and the other is utilizing the hierarchical quasi-1D filler [197-199]. Both strategies utilize the merits of high aspect ratios of the filler and the additional interfacial polarization resulting from the 46

inner structure of the filler, allowing the composites to achieve a high dielectric constant at low filler loading. Therefore, significantly enhanced energy storage capability was achieved in the corresponding nanocomposites. The work of Hu et al. demonstrated the advantage of using the core-shell 1D filler [161]. They fabricated core-shell BaTiO3@TiO2 NFs by coaxial electrospinning, which consist of an inner BaTiO3 NF and an outer TiO2 nanotube. The dielectric constant and electric displacement of the core-shell NF composites were highly enhanced when compared with the nanocomposites with BaTiO3 NFs. In addition, the breakdown strength was well maintained because of the buffer layer effect of TiO2 nanotubes. The core-shell NF composites can withstand an electric field of 360 kV mm−1 and exhibit a large energy density of 10.94 J cm−3 accordingly. However, the composites with BaTiO3 NFs cannot withstand an electric field higher than 330 kV mm−1，and the maximum energy density is only 7.13 J cm−3. The enhanced breakdown strength of BaTiO3 @TiO2 NFs composites can be explained by the computational study [76], which demonstrated that the core-shell filler structure can effectively mitigate the severe electric field distortion caused by the large dielectric constant mismatch between the filler and the matrix. The study of Huang and Wang revealed that the dielectric property of the P(VDFHFP)/BaTiO3 @TiO2 nanocomposites may be optimized by adjusting the TiO2 buffer layer thickness. The nanocomposites with NWs of 50 nm buffer layer thickness show higher breakdown strength and lower leakage current density in comparison with the nanocomposites with NWs of 130 nm buffer layer thickness[200]. Core–double-shell structured BaTiO3@TiO2 @Al2O3 (Figure 21) NFs were prepared by Pan and Zhai via coaxial electrospinning. Compared with the BaTiO3 and BaTiO3 @TiO2 based composites, as shown in Figure 21, the BaTiO3 @TiO2@Al2O3 nanocomposites shows much enhanced breakdown strength, and suppressed leakage current densities, which result in much higher energy density and energy efficiency. At a BaTiO3@TiO2@Al2 O3 loading of 3.6 vol%, the nanocomposite shows an energy density of 14.8 J/cm3 at 450 MV/m, which is around 12 times higher than 47

that of BOPP (1.2 J/cm3 at 640 MV/m) [196].

Figure 21. (a) TEM image and schematic illustration of core–double-shell BT@TO@AO NF; (b) Dielectric constant and dielectric loss tangent at 1 kHz and leakage current density at 100 MV/m of the BT@TO@AO nanocomposites; (b) Energy density and efficiency of the BT@TO@AO nanocomposites. BT@TO@AO is the abbreviation of BaTiO3 @TiO2 @Al2O3. (Reprinted with permission from [196]).

Recently, Huang and Kang reported the application of core-shell structured BaTiO3@TiO2 NWs composed of inner moderate-k TiO2 core and outer high-k BaTiO3 shell[201], which exhibit an advantage on enhancing the energy storage capabilities of P(VDF-HFP) over TiO2 NWs or BaTiO3 NWs. As shown in Figure 22, the composite with 5 wt% BaTiO3@TiO2 exhibits a high discharged energy density of 9.95 J cm-3 at 500 MV/m, which is higher in comparison with the composites containing TiO2 or BaTiO3 NWs. Meanwhile, the chargedischarge efficiencies of composites with BaTiO3@TiO2 are clearly higher than those of the composites with TiO2 or BaTiO3 NWs. This work indicates that both dielectric constant and electrical conductivity of inner and outer layers should be simultaneously considered when designing core-shell filler for dielectric polymer nanocomposites.

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Figure 22. Electric field dependent of discharged energy densities (a) and energy efficiency (b) of nanocomposites containing TiO2, BaTiO3 or BaTiO3@TiO2 NWs. (Reprinted with permission from[201]).

For the NWs possessing high electrical conductivity such as CaCu3Ti4O12, Bi2S3 and Bi2Te3[202-204], surface coating of an insulating layer is an effective way to lessen its intrinsic disadvantages. Taking the SiO2 encapsulated Bi2S3 nanorods (Bi2S3@SiO2) as an example, the core-shell structure of Bi2S3@SiO2 dramatically suppressed the dielectric loss tangent and reduced the electrical conductivity of the PVDF composites, but maintained the high dielectric constant of the composites. In addition, the dielectric property of the composites can be tailored by adjusting the SiO2 shell thickness and higher energy storage capacity and efficiency were achieved in the composites with thinner shell thickness [203]. The work of Shen and Nan present the merits of hierarchical 1D filler in enhancing the energy storage capability of polymer composites, which were prepared by embedding BaTiO3 NPs into 49

high-aspect-ratio TiO2 NFs via electrospinning (Figure 23) [197, 198]. In this case, hierarchical interfaces were introduced into the composites, including the interfacial region between BaTiO3 NPs and TiO2 NF matrix and the interface between NF and polymer. Compared with composites with TiO2 NFs, the additional BaTiO3/TiO2 interface in the NFs induce substantially enhanced interfacial polarization, and thus, the composites with hierarchical 1D NFs have enhanced dielectric constant and electric displacement. This, in combination with the enhanced breakdown strength, gives the hierarchical NFs based composites a giant energy density of about 20 J cm−3 at about 646 kV mm−1, which is about 1675 % higher than that of biaxialoriented polypropylene (BOPP) (about 1.2 J cm−3 at about 640 kV mm−1). Moreover, a high discharge efficiency of about 75 % is also achieved[197].

Figure 23. (a) Scheme showing the nanocomposites with hierarchical structured BaTiO3@TiO2 NFs. (b) TEM image of BaTiO3@TiO2 NFs (Inset: elements mapping image of BaTiO3@TiO2 NFs). (c) Electric displacement and breakdown strength of different nanocomposites. (d) Variations of discharge energy density with electric field for the PVDF/BaTiO3@TiO2 NF nanocomposites (Reprinted with permission from [197, 198]).

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3.5. Synergistic Effect of 1D Filler and Other Filler The introduction of the hierarchical 1D nanofiller can bring additional interfacial polarization, resulting in an enhanced energy density of polymer nanocomposites. However, there are still challenges in the large-scale fabrication of uniformly structured hierarchical 1D nanofillers. Therefore, it is helpful to utilize the synergistic effects of 1D filler and 0D NPs in other ways [192, 205]. Shen and Nan successfully utilized the synergistic effects of 1D and 0D fillers by constructing sandwich structured polymer composites, where the TiO2 NPs (for achieving high electric displacement) were dispersed into the top and bottom layers, while Bi2O3-doped Ba0.3Sr0.7TiO3 NFs (for achieving high breakdown strength) were introduced into the middle layer [192]. The middle layer played a significant role in enhancing the breakdown strength of the laminated nanocomposite dielectrics because of the “barrier effects” at the layer boundary. A high breakdown strength of 385 kV/mm was achieved in the sandwich structured polymer nanocomposites, while the breakdown strength of top or bottom layers (i.e., composites with TiO2 NPs) was only around 110 kV/mm. Such a sandwich structured polymer nanocomposite provides a largely enhanced discharged energy density of ~8 J cm−3 at 300 kV/mm. In another work of Shen and Nan, BaTiO3 NFs were used in the middle layer whereas BaTiO3 NPs were introduced into the outer layers to induce higher electrical polarization [205]. A simultaneously enhanced electric displacement and breakdown strength was demonstrated in the sandwich structured polymer/BaTiO3 nanocomposite. In particular, in the case of the outer layers with 10 vol% of BaTiO3 NPs, the maximum electric displacement of the sandwich structured polymer/BaTiO3 nanocomposites was increased to 6.0 μC/cm2 (with 2 vol% BaTiO3 NF in the middle layer) from ∼5.2 μC/cm2 (without a middle layer with BaTiO3 NFs), showing an enhancement of ∼16%. Concomitantly, the breakdown strength was also enhanced by 67%, i.e., from ∼228 kV/mm for 0 vol% to ∼382 kV/mm for 2 vol% of BaTiO3 NFs. In most cases, electric field is usually applied in the through thickness direction of film samples, which induces electromechanical stress and initiates the electrical treeing along the 51

through thickness direction. Therefore, modulating the composite nanostructure in the through thickness direction can allow us to tailor the electromechanical stress distribution throughout the composites, to control the electrical treeing evaluation and to eventually achieved polymer nanocomposites with much enhanced breakdown strength and electrical energy storage capability. More recently, Shen and Zhang proposed and demonstrated an approach to prepared artificial dielectric polymer nanocomposites by regulating the orientation and 3D distribution of 0D and 1D NPs in the nanocomposites[153]. As shown in Figure 24, compared with the neat polymer (644.1 kV/mm) the nanocomposites filled with sphere-SLS (653.6 kV/mm), fiber-parallel (662.2 kV/mm) and fiber-orthotropic (691.9 kV/mm) configurations exhibit enhanced breakdown strength, while the other three nanocomposites show lower breakdown strength and the spheres-random nanocomposites have the lowest breakdown strength of 585.5 kV/mm. The breakdown strength can be understood by the local electric field distribution. As shown in Figure 24, the electric field is weak in the outer layer of the sphere-SLS composites (Figure 24C) while the electric field is intensified in the outer layers of the sphere-LSL composites (Figure 24C) because of the presence of 0D BaTiO3. In the case of composites with randomly distributed 0D and 1D NPs, the local electric field distribution is substantially inhomogeneous within the whole composites. While for the composites with aligned NFs, the local electric field concentration is released by the wellaligned NFs. The dielectric constant and dielectric loss are almost independent on the configurations of the nanocomposites. Accordingly, the enhancement of energy storage is mainly dependent on the breakdown strength. The highest energy density of 25.5 J cm3 (at 690 kV mm1) with an energy efficiency of 76.3% is achieved in the nanocomposite with orthotropic oriented BaTiO3 NFs. Compared with the pure polymer, the energy density shows an enhancement of 45.8%, while only 3.9% enhancement is observed in the nanocomposites with randomly oriented NF. This approach provides insights in designing and modulating high performance dielectric nanocomposite films fabricated by roll-to-roll technique. 52

Moreover, Liu et al. fabricated a trilayered nanocomposite with PVDF/BNNS (Boron nitride NSs) in the outer layer and PVDF/BST in the middle layer[206]. BNNS and BST act as leakage current blocker and dielectric constant enhancer, respectively. Meanwhile, the breakdown strength of nanocomposite was also improved because of high breakdown strength of BNNS, which leads to a high discharged energy density of 20.5 J cm-3 at 588 MV/m.[206].

Figure 24. (a) Schematic illustration showing configurations of P(VDF-HFP)/BaTiO3 nanocomposites: (1) sphere-SLS, (2) sphere-LSL, (3) sphere-random, (4) fiber-parallel, (5) fiber-orthotropic, and (6) fiber-random. (All nanocomposites have a NP volume fraction of 5%). (b) Weibull statistics characteristic breakdown strength and (c) the simulated electric field distribution in P(VDF-HFP)/BaTiO3 nanocomposites of different configurations. (d) Frequency dependent dielectric constant (solid) and dielectric loss tangent (open) of P(VDFHFP) nanocomposites with 0D BaTiO3 NPs (left) and 1D BaTiO3 NPs (right). (e) The energy density enhancement of nanocomposites with different configurations in comparison with polymer matrix, discharged energy density (green) and energy efficiency (gray) of nanocomposites with different configurations. (Reprinted with permission from [153]).

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4. Preparation Strategies for High-k Nanocomposites with Aligned 1D or Quasi-1D Aligned Filler Taking the aforementioned review into account, one can conclude that, compared with their random counterparts, polymer nanocomposites with 1D nanofiller demonstrate much more fascinating performance such as higher dielectric constant and higher energy storage capability. The enhanced dielectric properties and energy storage capability should mainly, or at least partly, benefit from the tailored architecture (such as orientation and alignment) of 1D nanofiller in the composites. Therefore, it is important to develop techniques that can control of 1D nanofiller configuration in a polymer matrix. Below, we briefly introduce the state-ofthe-art fabrication techniques of high-k polymer nanocomposites with aligned 1D nanofiller or quisa-1D filler (e.g., aligned NP chains), including dielectrophoresis, uniaxial strain assembly, electrospinning, freeze casting, and some other methods. The improved properties and potential applications of high-k nanocomposites in dielectric and electrical energy storage have been discussed.

4.1 Dielectrophoresis Positioning nanoconstructs precisely on a substrate by dielectrophoretic (DEP) effect was first introduced by Pohl et al. [207, 208]. In this case, the polarizable nanoconstructs (e.g., NPs and NWs) are first added into a certain solution, whose polarizability is different from the nanoconstructs. When a non-uniform electric field was applied, the neutral NPs or NWs become polarized and can be pushed towards the regions with an opposite charge [209-213]. Namely, the dipole-dipole interactions between nanoconstructs lead to the formation of chains or fibrils parallel to the applied electric field. Thus, the dielectrophoretic system must generate sufficient DEP forces to overcome the influential parameters such as hydrodynamic drag, gravity, electrothermal, and intra-particle and surface-particle adhesive forces to be able to guide the nanostructures effectively within the system. 54

Dielectrophoretic assembly has been applied to assemble aligned homogeneous NWs, such as Si [214-217] and InAs [214, 218], for the application of sensing, optics, and electronics. However, most of the aligned nanoconstructs are NPs in the fabrication of high-k polymer nanocomposites [96, 103, 219-224]. For example, using dielectrophoretic assembly, Randall et al. fabricated anisotropic polymer composites where BaTiO3 NPs were aligned into pearl chainlike structures inside a PDMS matrix [96], as shown in Figure 25. It is found that at the same loading of BaTiO3 NP, the field-structured composites demonstrated significantly higher dielectric constants in the z-axis of the structuring field than that of the x–y aligned one, and the dielectric constants of the x–y aligned composites were slightly higher than the corresponding randomly dispersed ones. In addition, the x–y-aligned composites have higher breakdown strength when compared with both z-aligned and randomly dispersed composites (See Section 2.3.3), finally making the energy density enhancement of the x–y aligned composites is far larger than that of the pure polymer, z-aligned, and randomly dispersed composites, as shown in Figure 25c [96]. The alignment of nanostructures under DEP forces is influenced by the electric field, frequency, and viscosity of the medium [222, 225]. For instance, under high frequency AC voltages, the effective polarization of the particles cannot match the applied changing field, leading to insufficient transient dielectrophoretic force for particle chaining in the matrix. In addition, the orientation, chain length, and depletion zone of the chained particles decreases with the increase of viscosity. Therefore, by controlling these parameters, DEP can be tailored to work with nanofiller based on various materials and allows for integration upon multi-types of substrates.

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Figure 25. (a) Scheme illustrating the setup for anisotropic composites. Note that Plate 2 shown in B is flipped 180° horizontally for a better understanding of the electrode assembly. (b) SEM image showing the aligned BaTiO3 NPs in cured PDMS. (c) Discharged energy density versus electric field for different systems. The x–y aligned composites show higher energy density than their counterparts (Reprinted with permission from [96]). In order to prepare composites with an aligned filler on a large scale, Guo and Cakmak developed a roll-to-roll continuous processing method [226, 227]. As shown in Figure 26, the preparation process can be accomplished in several steps: (a) casting a two-layer solution on a substrate, where the top layer is for contacting the electrode and the bottom layer is polymer solution with BaTiO3 NPs, and peeling off the top layer after the assembling process; (b) the casted layers were sent to the roll-to-roll electric field apparatus and an electric field was applied between the mesh (high voltage) and the substrate (bottom electrode) until the solvent was thoroughly removed from the pores of the mesh, making NP chains to be formed in the bottom layer by dipole–dipole interaction; and (c) peeling off the top layer. It should be noted 56

that the NP chains may tilt away from the electric filed direction because of the film bending caused by the different solvent removal speed. A high electric field is needed to achieve aligned NP chains along the electric filed direction. This is because enhancing the electric field can overcome the compression effect. Compared with the composites with randomly dispersed NPs, those with aligned NPs show significantly enhanced dielectric constant and the dielectric enhancement increases with the increase of roll-to-roll electric field strength. For instance, the dielectric constant shows 43% increase in the PS composites with 10% BaTiO 3 NPs under roll-to-roll electric field of 2000 V/mm.

Figure 26. (a) Scheme illustrating the roll-to-roll processing for composites with aligned NPs. (b) Roll-to-roll electric field apparatus for composite solution casting. (c) SEM image showing the fractured surface morphology of PS composites with aligned BaTiO3 NPs. (d) Frequency dependence of dielectric constant and dielectric loss tangent of PS and PS/BaTiO 3 composites. (Reprinted with permission from [226].) 57

4.2 Uniaxial Strain Assembly Although dielectrophoresis allows fabricating bulk nanocomposites with an aligned filler, it is only proper to fabricate composites with low volume fraction of aligned filler. In addition, the introduction of high volume fraction NWs would meet more trouble here in preparing defect free composites because of the lower packing density of randomly aligned wires than spherical particles. Uniaxial strain assembly has been regarded as an effective technique to align nanofiller in bulk nanocomposites even at high filler concentrations, in which the dielectrophoresis usually failed [92, 150, 151]. Tang et al. fabricated nanocomposites with lead zirconate titanate (PZT) NWs aligned in the PVDF matrix by uniaxial strain assembly [150], as shown in Figure 27. It is found that the dielectric constant of 1-3 parallel (z-aligned) PZT NW samples are much larger than that of random (0-3) and 1-3 perpendicular (x-y-aligned) PZT NW samples at the same filler volume fraction, as shown in Figure 27b, and the z-aligned PZT NWs nanocomposites have larger electric displacement than the random and x–y-aligned PZT NW nanocomposites because of the higher dielectric constant of the samples. Further, it demonstrated that the energy density of the nanocomposites is strongly dependent on the orientation of the PZT NWs. Figure 27c indicates that the energy density increases with the electric field and the PZT concentration. In particular, the energy density of the z-aligned aligned PZT NW composites shows higher energy density than that of the random PZT NWs composites at any NW concentration (e.g., the measured energy density with 40 vol% filler aligned in the field direction is 0.0431 J cm−3 at an electric field 15 kV mm−1, which is 36.0 % larger than that of the 40% random PZT NWs composite (0.0317 J cm−3)). However, the breakdown strength does not show a dependence on the orientation of the filler. The reason can be ascribed to the fact that, during uniaxial strain assembly, each NW is still surrounded by a layer of polymer, which keeps the breakdown strength high and equivalent to the randomly oriented samples.

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In addition, it is noted that the draw ratio and tensile strain can affect the orientation degree of the nanofiller, and the orientation degree of the nanofiller can affect the dielectric properties of the nanocomposites [92, 151]. By using Herman’s orientation factor (HOF) to identify the degree of orientation in the nanocomposites, Tang et al. found that the dielectric constant of the nanocomposites was improved efficiently by the alignment enhancement of the filler rather than by adding an extra filler that causes defects in the nanocomposites [151]. As an example, the dielectric constant of the nanocomposites with 20 vol% PZT NWs reached as high as 28.7 at a HOF of 0.481 (Here, most embedded PZT NWs are aligned in the PVDF matrix), while the composite with randomly oriented PZT NWs only has a dielectric constant of 19.4.

Figure 27. (a) Schematic illustration showing the alignment of PZT NW in PVDF. Nanocomposites with 10% randomly dispersed PZT NWs (b) and aligned PZT NWs in PVDF matrix under uniaxial stretching (c). (d) Comparison of measured dielectric constant (at 1 kHz) of nanocomposites under different orientation (Random, z-aligned, and x–y-aligned) as a function of PZT NW volume fraction. (e) The dependence of energy density on the PZT 59

volume fraction in the PVDF matrix under 15 kV mm−1: z-aligned PZT NW-PVDF and random PZT NW-PVDF nanocomposites. (Reprinted with permission from [150]). 4.3 Template-Assisted Realization Template assisted fabrication strategy offers a versatile route to produce composites with ordered structure [228-231]. Toward this aim, nanoporous anodic aluminum oxide (AAO) and block copolymers have been used as templates to produce a wide range of materials with controlled structure. High energy density dielectric capacitor has been prepared using nanoporous AAO membrane as the dielectric material. As shown in Figure 28, the AAO membrane has two sets of straight nanopores, which are interdigitated, isolated and open to opposite planar surfaces. Carbon nanotubes were deposited in both sets of pores inside the AAO membrane serving as electrode (Figure 28B). The equivalent capacitance of the prepared dielectric capacitor can be calculated by Ctotal ≈ C1 + C2 + C3, where C1 represent the capacitance isolated by two reverse neighboring small-diameter and large-diameter CNT electrodes. C2 and C3 represent the capacitance between the two CNT coated array tips and the reverse electrodes (current collectors), respectively. C1 plays a dominated role in the total capacitance because of the large surface areas of CNTs. when an electric field is across the dielectric, negative charges appear on the large-diameter CNT surface and positive charges on the small-diameter CNT surface (or vice versa). In this case, electrostatic energy is stored in the form of polarization. Benefit from the unique 3D nanoarchitectural electrodes, the energy density can reach about 2 Wh/kg through optimizing the fabrication process. The use of block copolymers also offers the opportunity for controlling the distribution of NPs in the matrix. Using PS-b-PMMA as polymer matrix, vertically oriented PS nanocylinders filled with PS-functionalized BaTiO3 NPs were achieved by exposing the PS-bPMMA/BaTiO3 nanocomposite films to the selective solvent (e.g., acetone) vapor for the PMMA block. It was found that both molecular weight of block polymer PS-b-PMMA and the NP size affect the spatial organization of NPs and the dielectric properties of the PS-bPMMA/BaTiO3 nanocomposites[57]. 60

Figure 28. Schematic illustrations of the structure (A), three parts (B), the fabrication process of AAO template (C), and energy storage mechanism of the template-assisted dielectric capacitor (Reprinted with permission from [229]).

4.4 High-k Nanorod Arrays As Filler High-throughput phase-field calculation reveals that composites with 1D nanofiller aligned in the Z direction possess a higher dielectric constant in comparison with the X-Y aligned 1D nanofiller composites[128]. In this case, the high-k nanorod array is the ideal structure of Zaligned 1D nanofiller in the composites. Recently, high-k nanorod array has been really utilized to prepare dielectric polymer nanocomposites [232-237]. Taking the TiO2 nanorod array as an example, the preparation process of the nanocomposites is shown in Figure 29. First, TiO2 nanorod array was achieved on a fluorine-doped tin oxide (FTO) substrate via a hydrothermal reaction. Afterwards, TiO2 can transformed to other high-k nanorod (e.g., BaTiO3, PZT@TiO2). Finally, nanocomposites can be prepared by spin-coating the polymer 61

solution onto the surface of high-k nanorod array [235]. The typical SEM image of TiO2 nanorod array can be seen in Figure 29b. Some polymer can be embedded into the nanorods and the additional polymer can form individual layer on the array surface. By optimizing the fabrication process, the TiO2 nanorod array/P(VDF–HFP)nanocomposites can exhibit a relatively high energy density of 17.1 J cm-3 at 509 MV/m (Figure 29c).

Figure 29. (a) Schematic diagram showing the preparation process of P(VDF–HFP) nanocomposite. SEM images of cross-section (b, d) and top surface (c) of TiO2 nanorod array/P(VDF–HFP) composites. (e) Comparison of energy density and efficiency at various electric fields for nanocomposites with various spin-coating times (Reprinted with permission from [233]).

4.5 Electrospinning Electrospinning is a simple and versatile technique for fabricating uniform micro/NFs in a continuous process and at long length scales. The electrospun fibers originating from polymer, metal, ceramic, and composites exhibit a series of outstanding properties, such as high lengthto-diameter ratio, flexible surface functionality, tunable surface morphologies, and superior mechanical performance, making them promising in various fields [238, 239]. 62

So far, multiple morphologies and structures (e.g., parallel and crossed fibrous arrays, wavy fibers, twisted fibrous yarns, patterned fiber webs, and 3D fibrous stacks) of synthetic or biological polymers, metals, metal oxides, ceramics, organic/organic, organic/inorganic, as well as inorganic/inorganic composite systems have been electrospun via modified electrospinning techniques, which paved the way for the wide applications of the resultant electrospun products [239]. So far, the strategies utilized for fabricating dielectric polymer nanocomposites with 1D aligned nanofiller can be categorized into two types. Type I, Nanoconstructs (e.g., NPs and nanotubes) were first dispersed into a precursor, and then electrospun with a polymer into 2D nonwoven fibrous mats [240-243]. Herein, the nanoconstructs are incorporated with the as-spun fibers owing to the high electrostatic and extensional forces, and they are arranged along the axial direction of the fibers because of the elongation of the fluid jet during electrospinning. Hou et al. fabricated polyimide/multi-walled carbon nanotubes (PI/MWCNTs) nanocomposites with good mechanical flexibility by electrospinning and subsequent hot-pressing [243]. The results showed that the homogeneously dispersed MWCNTs in the NFs were oriented along the NF axis. Apart from an excellent mechanical flexibility and thermal stability (the 5% weight loss temperature is higher than 535 °C), a high dielectric constant of 217 (at 1 kHz) was observed in the composite with 20 vol % MWCNTs, 57.5 times higher than that of the pure PI. The maximum energy storage density of 1.96 J cm−3 was achieved when the MWCNTs content was 12 vol %, which was almost five times of the maximum energy storage density of PI. Type II, the processing procedure is similar with those used in Type I, but difference is that the electrospun fibers herein are aligned, making the nanoconstructs incorporated in the fibers be well ordered along the axis of the fibrous groups [90, 244, 245]. Using this type of electrospinning method, Nan and Lin prepared polysulfone (PSF)/ MWCNT composites with high dielectric constant, low dielectric loss, and large energy density [245]. In their experiments, the electrospun NFs were first collected in the form of a sheet on a rotating 63

collector, and then, several plies of the sheets were stacked along the same fiber direction. These sheets with NFs lying down in the plane were finally molded by hot pressing near the softening temperature of PSF in the direction perpendicular to the fiber direction, resulting in the formation of the MWCNT array in the composite sheets (Figure 30). Herein, it is worth noting that the PSF coating on MWCNT not only acts as a barrier to prevent MWCNTs from direct connection, but also as a polymer matrix. In this case, the dielectric constant increased up to 58 as the content of MWNTs reached 25 vol%, while only a slight change in dielectric loss was observed (Figure 30d). As a result, a maximum energy density of 4.98 kJ L−1 was achieved at a MWNTs content of about 15 vol% (Figure 30e).

Figure 30. (a) Schematic for preparation of MWNT/PSF composites. The inset shows the cross-sectional SEM image of the composites perpendicular to the fiber direction, MWNTs are indicated by arrows. (b) TEM images for MWNT/PSF core/shell nanostructure. The SEM image in the inset shows the MWNT/PSF NFous sheet prepared by electrospinning. (c) Highresolution TEM image of a MWNT. (d) Dependence of the dielectric constant and loss of the composites on the MWNT loading, measured at room temperature and 1 MHz. The flexibility of the composite is demonstrated in the photograph in the inset. (e) Energy density and breakdown strength of the composites with different MWNT loading (Reprinted with permission from [245].) 64

Overall, electrospinning is a simple but effective technique to prepare high-k polymer nanocomposites with 1D assembled filler for dielectric and electrical energy storage applications. However, drawbacks still exist. As an example, the porous nature of the as-spun fibrous mats may unavoidably induce pores or voids into the nanocomposites, which results in a decrease in breakdown strength. Therefore, a subsequent heating treatment or a drying process is usually required.

4.6 Freeze Casting More recently, freeze casting has been used to prepare composites with aligned filler [246]. This method involves the controlled freezing of water suspensions containing inorganic filler, and thus, it is inexpensive [247]. In particular, inorganic filler suspensions can be frozen along the perpendicular line of the substrate, resulting in the formation lamella-like ice crystals. The organic filler were expelled as ice crystals grow. After removing the ice at low temperatures, a layered homogeneous inorganic filler scaffold can be obtained, which can then be filled with other polymer or polymer precursors so as to fabricate anisotropic composites, as shown in Figure 31. Kim et al. prepared epoxy composites with aligned BaTiO3 NPs by the freezecasting [248]. As shown in Figure 31, the BaTiO3 NPs are directionally aligned in the epoxy composites, resulting in enhanced dielectric constant in comparison with the composites with randomly dispersed NPs. In particular, the dielectric constant of the aligned composites is over two times higher than that of the randomly mixed composites, while the dielectric loss is almost the same, exhibiting strong potential for dielectric applications (Figure 31g). This method has the following merits: (i) the architecture of the composites can be tailored for different length scales by adjusting the suspension composition and the freezing kinetics; (ii) the inorganic filler lamellae thickness can be controlled by adjusting the freezing speed of the ice crystal front; (iii) the inorganic filler lamellae roughness can also be controlled at the submicrometre scale by using additives, which change the filler–water interfacial tension and 65

the suspension phase diagram; and (iv) the ice crystals can split and trap inorganic filler as they grow, resulting in the formation of inorganic bridges between ice crystals lamellae. All of these merits can be utilized for designing polymer composites with desirable dielectric and energy storage properties.

Figure 31. Schematic diagram of freeze casting method (a–d). SEM image of cross-section of BaTiO3/epoxy composite prepared by freeze casting method (e) (Reprinted with permission from [247]). Cross-sectional image of epoxy composite with homogeneously distributed BaTiO3 particles (f). The dielectric constant and dielectric loss of the BaTiO3/epoxy resin composite (g) (Reprinted with permission from [248]). 4.7. Other Methods Apart from aforementioned three approaches, many other methods have been utilized to prepare polymer nanocomposites with aligned fillers, including mechanical rolling, ball milling, and extrusion. It was reported by Qiu and Yang that a mechanical rolling process is capable of aligning TiO2@MWCNTs in the PVDF composites, resulting in significantly enhanced breakdown strength and suppressed dielectric loss tangent of the composites in comparison with the composites by solution casting [249]. The dielectric constant of the

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PVDF composites with aligned TiO2 @MWCNTs is much higher than that of the pure PVDF, although it is lower when compared with the composites by solution casting [87, 249]. Ball milling is traditionally used to reduce the particle size of ceramic materials and can also be used to disperse and align filler in thermoplastic polymers [250-252]. Zhang et al. fabricated PVDF composites with parallel aligned zinc flakes using ball milling, which exhibited anisotropic dielectric behaviors [95]. In the parallel direction, the dielectric constant of the composites was always higher in comparison with the perpendicular direction at any volume fraction of zinc flakes. However, the application of ball milling is constricted because of the relatively low rate of production, difficulties in decanting the products, and depending on the physical nature of the material [253, 254]. In contrast, extrusion techniques that have advantages such as continuous and scalable mechanochemical synthesis began to draw researchers' interests as a remarkably effective alternative to ball milling [253]. Extrusion is one of the basic processing methods for thermoplastic polymers, referring to a family of continuous processing techniques in which materials are forced through constrained spaces [255]. It is capable for fabricating polymer composites with oriented nanofiller along the extrusion direction, leading to desirable dielectric properties such as high dielectric constant, high breakdown strength, and/or low dielectric loss [256]. Randall et al. aligned nanoplatelets of organo montmorillonite (oMMT) into a polyethylene (PE) matrix using extrusion [149]. It is found that at high electric field, composites with aligned filler demonstrated a lower dielectric loss when compared with those containing randomly oriented ones. Moreover, both the breakdown strength and the recoverable energy density of the composites with aligned oMMT nanoplatelets were higher than that with unaligned filler. That is because that the nanofiller with good orientation can optimize the electric field distribution inside the nanocomposites and affect the electrical tree inception and propagation across a dielectric film.

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5. Summary and Outlook An ideal high-k material for dielectric and energy storage applications should not only have high dielectric constant but also low dielectric loss/leakage current, and more importantly, high breakdown strength. This review demonstrated that high-k 1D nanofillers (e.g., NWs and NFs) are better than the conventional high-k 0D NPs in terms of enhancing the dielectric properties and energy storage capability of the polymer nancomposites because of their high aspect ratio, unique hierarchical structures, and synergistic effect with other fillers. The high-aspect-ratio 1D high-k fillers have large dipole moment, exhibiting highly efficient enhancement of dielectric constant for the nanocomposites. More importantly, the high aspect ratio of 1D high-k filler allows us to achieve desirable dielectric anisotropy in the nanocomposites by tailoring their spatial arrangement in the polymer matrix. The hierarchical structures make the 1D high-k filler have additional interface within the filler, which allows us to enhance the dielectric constant of the composites without increasing the filler concentration. This is of vital importance to simultaneously enhance the dielectric constant and breakdown strength of polymer composites and retain the ease of processing of the nanocomposites. One can utilize the synergistic effect 1D and other filler by rational structure design of the nanocomposites, achieving a high dielectric enhancement from both filler and high breakdown from the 1D filler. High dielectric performance and energy storage capability, which cannot be achieved in composites with a single filler, might be realized in composites with 1D and other filler. This review also demonstrated that the polymer nanocomposites with aligned 1D or quasi-1D nanofiller can exhibit significantly enhanced dielectric properties and energy storage capability when compared with those having randomly dispersed filler. In addition, it is found that the dielectric property and energy storage capability of the nanocomposites can be 68

tailored by adjusting the alignment degree of 1D high-k filler. This opens a new way for fabricating high performance high-k polymer nanocomposites for dielectric and energy storage applications. High throughout calculation and machine learning are powerful materials design protocol, which can accelerate the design and discovery of polymer nanocomposites with desirable dielectric and energy storage properties. While currently high throughout calculation and machine learning techniques have not been widely used in the study of dielectric polymer nanocomposites. Future efforts should pay attention to the enhancement mechanism of dielectric and energy storage properties and revealing the novel microstructure of desirable nanocomposites. Despite remarkable achievements in fabricating high-k polymer nanocomposites by using 1D high-k filler, there are still some open challenges to the fabrication techniques. Methods such as dielectrophoresis, uniaxial strain assembly, template assisted fabrication, using high-k nanorod arrays as filler, electrospinning, freeze casting has been adopted in this field. However, each method has its drawback. For instance, dielectrophoresis cannot meet the requirement of large-scale production, while uniaxial strain assembly and electrospinning may unavoidably induce pores or voids into the nanocomposites, which results in a decrease in breakdown strength and energy density. In fact, the achievements on fabricating nanocomposites with 1D high-k filler is only at its primary stage and much more efforts should be made in the future. Apart from the design and synthesis of novel 1D high-k nanoarchitectures with less defects, focus should be put on developing simple and efficient access to the alignment of 1D or quasi-1D nanofiller in dielectric polymer matrix at large scale. More attention should be paid to 2D high-k filler, which can be considered as assembly of 1D filler. However, 2D highk fillers have not received significant interest, although they may have stronger potential to

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enhance the dielectric properties and energy storage capability of high-k polymer nanocomposites [257-259]. Finally, it is always a challenge to realize multifunctional composites. The successful integration of high dielectric constant, high breakdown strength, and low dielectric loss in dielectric polymer nanocomposites requires interdisciplinary and multidisciplinary theoretical and experimental research cooperation between physicist, chemists, materials scientists, and electrical engineers.

Acknowledgements X.H. and P. J. thank the continuous finical support from National Natural Science Foundation of China (nos. 51522703, 51477096, 51277117) and the Special Fund of the National Priority Basic Research of China (2014CB239503). X. H. thanks the continuous finical support from State Key Laboratory of Electrical Insulation and Power Equipment. B. S. thanks China Postdoctoral Science Foundation (No. 2016M601581).

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AUTHOR CV

Dr. Xingyi Huang is a professor and deputy director of Research Centre of Dielectrics and Electrical

Insulation of Shanghai Jiao Tong University. Huang’s research focuses on high-k polymers and nanocomposites for energy, thermal management and dielectric applications. He received his Ph.D. in Materials Science from Shanghai Jiao Tong University in 2008 and had a postdoctoral experience of Chemistry at the same university. He was a visiting scholar in Waseda University from 2011 to 2012, Japan. Huang was the Winner of NSFC Foundation for Excellent Young Scholars in 2015 and Winner of Young Chang Jiang Scholars Program in 2017. Huang is senior member of Institute of Electrical and Electronics Engineers (IEEE) and serves as Associate Editor of IEEE Transactions on Dielectrics and Electrical Insulation and as Associate Editor of High Voltage.

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