Chapter 1: 2D High-κ Dielectric Ceramic Nanoplatelets for Polymer Nanocomposite Capacitors

Polymer-based capacitor materials continue to attract interest in applications such as laser guns, railguns, radar systems, artificial skins, muscles, and flexible electronics due to their advantages of super-high power density.^1–3  Commercial dielectrics for capacitors are mainly based on biaxial tensile polypropylene (BOPP), and the energy density of BOPP is ∼2 J cm⁻³ under a high breakdown strength of ∼600 kV mm⁻¹. In this case, commercial devices based on BOPP have to be large and heavy.^4–6  Therefore, routes to enhance the energy density of capacitors is essential. The permittivity and breakdown strength are two key factors to determine the energy density of dielectrics. Ceramic/polymer composites are considered as good candidates for capacitors due to the advantages of combination of high permittivity from the ceramic phase and high breakdown strength of the polymer matrix.^6,7  High-permittivity ceramics, such as Pb_{1 − x}Zr_xTiO₃ (PZT), BaTiO₃ (BT), TiO₂, and Ba_{1 − x}Sr_xTiO₃ (BST), are often used to increase the permittivity of the polymer composites. The filler material, interface modification and interface polarisation within these composites, filler morphology, distribution, and loading are key factors in determining the properties of the ceramic/polymer composites.

In this chapter, we will provide an overview of the effects of filler morphology on the dielectric and energy storage properties of ceramic/polymer composites. The synthesis methods of two-dimensional (2D) nanoplatelets, the classification of the polymer-based composites, and the role of the intrinsic properties of different anisotropic morphologic nanofillers in the composites will be discussed. The design strategy of 2D nanocomposites for dielectric and high energy storage properties and the interfacial models and electric simulations for the composites with 2D fillers will be discussed in detail.

Hydrothermal and solvothermal methods are often used for synthesis of nanomaterials, which are generally defined as crystal synthesis or crystal growth, by chemical reactions of substances in a sealed heated solution under high-temperature and high-pressure conditions. For ceramic nanoparticle synthesis, hydrothermal/solvothermal methods reduce the time and energy consumption for processing, since high-temperature calcination, mixing, and milling steps are minimised. In addition, during crystallisation processes, crystallised ceramic powders are directly precipitated from solution. The rate and uniformity of nucleation, growth, and ageing can be highly regulated by adjusting the processing parameters, such as reaction temperature, duration, stirring rate, and types and concentrations of reactants, surfactants, and mineralisers, which results in excellent control of morphology and size, and reduced degree of agglomeration. The synthesis of 2D ceramic nanoplatelets by hydrothermal or solvothermal methods has attracted much attention recently due to the ability for precision control of the morphologies of a number of ceramic particles, such as TiO₂,⁸  ZnO,⁹  Fe₂O₃,¹⁰  Al₂O₃,¹¹  MoS₂,¹²  Bi₂Te₃,¹³  Bi₄Ti₃O₁₂ (BIT),¹⁴  and BiFeO₃.¹⁵ 

Xie et al. successfully synthesised ultrathin defect-free MoS₂ nanosheets using a hydrothermal method,¹²  and He et al. utilised MoS₂ nanosheets synthesised by similar procedures to fabricate polymer nanocomposites with high dielectric performance.¹⁶  In the hydrothermal method, Xie et al. designed a reaction with a high concentration of precursors. Hexa-ammonium heptamolybdate tetrahydrate ((NH₄)₆Mo₇O₂₄ · 4H₂O) and thiourea (Mo : S ratio = 1 : 2) were dissolved in deionised water under vigorous stirring to form a homogeneous solution. Then, the solution was heated and defect-free MoS₂ nanosheets were obtained by a quantitative reaction and oriented crystal growth. The thiourea was employed as the reductant to reduce Mo⁶⁺ to Mo⁴⁺ and was also effective to stabilise the ultrathin nanosheet morphology. In the work of He et al., the lateral size of the MoS₂ nanosheets was in the range of ∼100–200 nm, as shown in Figure 1.1(a). Figure 1.1(b) further illustrates the ultrathin nanosheet morphology of the MoS₂. Corresponding high-resolution transmission electron microscopy (HRTEM) images from the side and the top view are presented in Figure 1.1(c) and (d), respectively. The interplanar spacing was measured as 2.7 nm, which is consistent with the d spacing of (100) planes of hexagonal MoS₂. Furthermore, the thickness of the typical layer is approximately 6 ∼ 8 nm, with an interlayer spacing of 0.62 nm.

Ultrathin anatase TiO₂ nanosheets with dominant {001} facets are fabricated by a one-step solvothermal reaction.¹⁷  Tetrabutyl titanate (Ti(OBu)₄), hydrofluoric acid (HF), and absolute ethanol (C₂H₆O) were used as raw materials. Ethanol was employed as both a reaction solvent and alkoxy group source to tailor the growth of anatase TiO₂. Fluoride (F⁻) was employed as a capping agent to stabilise {001} facets and enhance their exposure. The introduction of ethanol solvent effectively improved the content of surface-chemisorbed F⁻ on TiO₂. By this approach, anatase TiO₂ nanosheets were synthesised successfully, and exhibited a rectangular shape with a size of ∼200 nm, a thickness of ∼2.5 nm, and a side length of ∼200 nm. Moreover, the nanosheets were dominated by {001} facets.

Molten salt synthesis is an effective method for preparation of high purity and nanoscale inorganic oxides with controllable compositions and morphologies. Inorganic molten salt serves as the reaction medium and the reactant oxides exhibit short diffusion distances and large mobility in the molten salts, which are beneficial for enhancing the reaction rate and reducing the reaction temperature. Moreover, the morphology of the final products can be controlled by adjusting the processing parameters, including the types and quantities of the used molten salts, heating temperatures and duration, and heating/cooling temperatures. In recent years, the molten salt synthesis method has been successfully used to prepare a variety of 2D ceramic nanoparticles, such as BIT,¹⁸  Na_0.5Bi_4.5Ti₄O₁₅ (NBIT),¹⁹  Na_0.5Bi_0.5TiO₃ (NBT),¹⁹  BT,²⁰  SrTiO₃ (ST),²¹  BST²²  and NaNbO₃ (NN)²³  platelets, that are applicable for the fabrication of ceramic/polymer composites.

As an example, by a two-step molten salt synthesis method, Jiang et al. synthesised 2D single-crystalline NBT-BT platelets with a perovskite structure, using the layer-structured NBIT plates as precursors,²⁴  which were used in sandwich-structured polymer nanocomposites.²⁵  Figure 1.2(a) and (b) shows the prepared NBIT and NBT-BT platelets, demonstrating a high aspect ratio with an average size of 10 μm and thickness of 600 nm. First, NBIT platelets were synthesised in the first-step of the molten salt method. The reactant oxides Bi₂O₃, TiO₂, and Na₂CO₃ were fully dissolved within the molten salt NaCl, and the NBIT platelets were formed through a complete reaction between reactant oxides after heating at 1050 °C for 4 h. In the second -step of the molten salt method, the NBT-BT platelets were formed by topochemical transformation from NBIT precursors, as shown in Figure 1.2(c). In this process, NaCl molten salts were used as a reaction medium, and Na₂CO₃, BaCO₃, and TiO₂ were used as the reactant powders; the reaction was completed after heating at 950 °C for 4 h. It is known that NBIT exhibits an Aurivillius layer-type structure consisting of perovskite-like blocks interleaved with layers of (Bi₂O₂)_n^{2n +}, represented by a formula (Bi₂O₂)_n^{2n +}(Na_0.5Bi_2.5Ti₄O₁₅)_n^{2n −}, where Bi³⁺ and Na⁺ ions correspond to the perovskite A-site with 12-fold coordination, and Ti⁴⁺ is the perovskite B-site cation in six-fold coordination. During the topochemical transformation from NBIT to NBT-BT, the bismuthate layers were effectively replaced by perovskite layers, and Bi³⁺ ions throughout the structure were partially replaced by Na⁺ and Ba²⁺ ions without extensive rearrangement of the structural framework. Therefore, the plate morphology was maintained after the second-step molten salt synthesis.

Similarly, NN platelets can also be prepared by a two-step molten salt synthesis method.²⁶  First, Bi₂O₃ and Nb₂O₅ were heated in a NaCl flux at 1000 °C for 2 h. The Bi_2.5Na_3.5Nb₅O₁₈ platelets were obtained and used as precursors for the second-step molten salt process. Then, the Bi_2.5Na_3.5Nb₅O₁₈ platelets were mixed with NaCl and reacted at 1000 °C for 2 h to obtain NN platelets. As shown in Figure 1.3(a) and (b), the Bi_2.5Na_3.5Nb₅O₁₈ and NN platelets both exhibited large aspect ratios. The perovskite-structured NN platelets with dimensions of ∼2–5 μm and thicknesses of ∼100–500 nm were prepared by topochemical conversion of layer-structured Bi_2.5Na_3.5Nb₅O₁₈ platelets as templates, as shown Figure 1.3(c) and (d).

Layered materials represent a diverse and largely untapped source of 2D systems with exotic electronic properties and high specific surface areas, such as transition metal oxides, transition metal dichalcogenides, transition metal carbides and nitrides, and other 2D compounds; for example, BN, Bi₂Te₃, and Bi₂Se₃. In the past decades, researchers have been exploring simple methods to exfoliate layered materials to obtain mono- or few-layer nanosheets, which have significant potential in sensing, catalysis, electronic, and energy storage applications.

In 2009, Zhi et al.²⁷  reported the chemical exfoliation method to prepare BN nanosheets in large quantities from the hexagonal BN (h-BN) particles. h-BN is used as an ultraviolet-light emitter, or as an electrically insulating but thermally conductive filler in composites. It is believed that h-BN nanosheets would be valuable to exploit many unique properties of a graphitic-like (002) plane, such as superb high thermal conductivity and mechanical strength. h-BN has a layered structure, where a sequence of atomic planes stack via van der Waals interactions to form a three-dimensional (3D) crystal. h-BN is stacked with the boron atom on the top of the nitrogen atom and vice versa. For the preparation of BN nanosheets, a strong polar solvent, N,N-dimethylformamide (DMF), was used to facilitate exfoliation due to the strong interactions between the polar DMF molecules and a BN surface. In experimental processes, h-BN powders were dispersed in DMF, and subjected to ultrasonication. Vigorous sonication was able to exfoliate BN nanosheets from the h-BN particles. Then, the solution was centrifuged in order to remove residual large-size h-BN particles. Due to a layered structure, most of the h-BN particles are thinner along one direction, with a thickness of micrometres. After exfoliation, the BN nanosheets were successfully prepared. The BN nanosheets exhibited micrometre dimensions, smaller than that of pristine particles, and a typical six-fold natural symmetry. Intriguingly, the thickness of the BN nanosheets was dependent on the centrifugation speed. At 5000 rpm, most of the BN nanosheets have less than 20 layers, with a thickness less than 7 nm. Wu et al.²⁸  successfully utilised a similar exfoliation method to prepare the BN nanosheet and fabricate polymer-based nanocomposites with large energy density. Figure 1.4(a) shows a schematic for the preparation of BN nanosheets. The morphology of BN nanosheets observed by scanning electron microscopy (SEM) exhibited the lateral size of ∼500 nm to 1 μm, as shown in Figure 1.4(b). The TEM images in Figure 1.4(c) and (d) suggest that the thickness was approximately 2–10 nm. Figure 1.4(e) shows the statistical analysis on the thickness of the boron nitride nanosheets (BNNSs) over 106 pieces, indicating the successful exfoliation of h-BN through ultrasonication.

Coleman et al.²⁹  developed liquid exfoliation of layered transition metal dichalcogenides for producing 2D nanosheets. The transition metal dichalcogenides consist of hexagonal layers of metal atoms (M) sandwiched between two layers of chalcogen atoms (X), with stoichiometry MX₂. Although the bonding within these trilayer sheets is covalent, adjacent sheets stack via van der Waals interactions to form a 3D crystal. The authors have demonstrated the exfoliation of bulk MX₂ crystal in common solvents to give mono- and few-layer nanosheets, including MoS₂, MoSe₂, WS₂, MoTe₂, TaSe₂, NbSe₂, and NiTe₂. In the experimental procedures, commercial MoS₂ and WS₂ powders were sonicated in a number of solvents with varying surface tensions. The resultant dispersions were centrifuged and the supernatant was decanted. The mass remaining in the supernatant was estimated by measuring the UV–visible–infrared (IR) absorption spectrum. It indicated that the amount of material retained (characterised by A/l = αC, where A/l is the absorbance per length, α is the extinction coefficient, and C is the concentration) was maximised for solvents with a surface tension, γ, close to ∼40 mJ m⁻². The analysis results showed that successful solvents were those with dispersive, polar, and H-bonding components of the cohesive energy density within certain well-defined ranges. In other words, the successful solvents are those that minimise the energy of exfoliation. Some solvents, such as N-methyl-pyrrolidone (NMP) and isopropanol (IPA), were indicated as promising for liquid exfoliation. The prepared MoSe₂ and WS₂ nanosheets show a lateral size of ∼50–1000 nm and hexagonal symmetry. This exfoliation method is insensitive to air and water and can potentially be scaled up to produce large quantities of exfoliated material.

Layered ternary metal carbides and nitrides, referred to as the MAX phases (M_{n + 1}AX_n, n = 1, 2 or 3), were also utilised to prepare nanosheets, where M is a traditional metal, A is a group IIIA or IVA element, and X is carbon or nitrogen atoms. MAX phases show unique combination of metallic and ceramic properties, such as excellent resistance to oxidation, heat, and corrosion, high electrical conductivity, high strength and elastic modulus, attributed to their inherent lamellar structure with alternately arranged MX and A layers. Usually, the 2D nanosheets show enhanced properties with respect to their corresponding bulk counterpart. However, the MAX phases possess relatively strong bonds between the MX and A layers, and are hard to exfoliate into ultrathin nanosheets using simple exfoliation processes. Naguib et al.³⁰  first reported exfoliation of the MAX phases: Ti₂AlC, Ta₄AlC₃, (Ti_0.5, Nb_0.5)₂AlC, (V_0.5, Cr_0.5)₃AlC₂, and Ti₃AlCN. A schematic of the exfoliation process is shown in Figure 1.5(a). In a typical process, the powders were simply immersed in hydrofluoric acid (HF) of varying concentrations at room temperature for times varying between 10 and 72 h. This procedure led to selective etching of the aluminium (Al) layers and their replacement by hydroxyl, OH, and fluorine (F) surface groups. By sonication, the ‘A’ group layer was removed from the MAX phases and 2D nanosheets were obtained, which were labelled as MXenes by the authors to denote the loss of the A element and emphasise their structural similarities with graphene. As a representative example, Figure 1.5(b) shows the SEM image of Ti₃AlCN after HF treatment, indicating the obvious exfoliation. Figure 1.5(c) shows the TEM image of 2D Ti₃CN_x layers exfoliated from Ti₃AlCN, which are transparent to the electron beam.

Zhang et al.³¹  also successfully prepared ultrathin nanosheets of MAX phases with enhanced thermal and mechanical properties in polymeric compositions: Ti₃Si_0.75Al_0.25C₂. In this study, the authors developed a green, facile, and effective exfoliation method for the preparation of ultrathin nanosheets of MAX phases. Although MAX phases are chemically stable, the A layers are more reactive than the MX layers. By substituting a portion of the A atoms, the A layers were activated and a substitutional solid solution was obtained. The as-doped MAX phases could be exfoliated by breaking. Using Ti₃SiC₂ MAX phase as an example, the doped phase of Ti₃Si_0.75Al_0.25C₂ (TSAC) was fabricated by a modified high-temperature self-propagation synthesis. The TSAC nanosheets were obtained by liquid exfoliation of TSAC powder in different solvents under ultrasound. In comparison, pure Ti₃SiC₂ powder cannot be exfoliated into nanosheets in these same solvents. Moreover, various solvents have been indicated to be effective for preparation of MAX phase nanosheets, such as ethanol, formamide, DMF, and NMP, indicating the wide applicability of the substitutional solid solution-based exfoliation method. The as-exfoliated TSAC nanosheets showed a size of ∼100–200 nm and were indicated to be exfoliated along the z-axis and to possess single-crystalline nature.

There are also many transition metal oxides that can be produced in 2D states by chemical exfoliation methods, such as RuO₂,³²  MnO₂,³³  and MoO₃.³⁴  For instance, Coellho et al.³³  prepared MnO₂ nanosheets by a single-step liquid-phase exfoliation method that produces a mix of flat and flower-like nanosheets. In the experimental process, manganese oxide flower-like nanostructures (MOFN) were first synthesised. Manganese nitrate tetrahydrate (Mn(NO₃)₂·4H₂O) was dissolved in deionised water with the addition of poly(ethylene glycol)-block-poly(propylene glycol)-block-poly(ethylene glycol) (PEG-PPG-PEG). The solution was heated up and maintained at a given temperature and was kept under vigorous stirring while KMnO₄ solution was added drop by drop. The brownish precipitate obtained was washed, vacuum filtrated, and dried. Then, the as-prepared MOFN was used to fabricate manganese oxide nanosheets (MON) by liquid-phase exfoliation. The MOFN was mixed with isopropyl alcohol and processed in an ultrasonic bath, followed by centrifugation and collection of the supernatant. The obtained dispersions consisted of MON and the quality can be assessed by UV–visible spectroscopy. Figure 1.6(a) and (b) present TEM images of the MOFN, showing a characteristic flower-like morphology. Figure 1.6(c) and (d) display the TEM and HRTEM images of the MON, showing typical dimensions of ∼20–40 nm and favourable crystallinity.

In the study of polymer-based dielectric nanocomposites, the most investigated nanofillers are ferroelectric ceramics with the perovskite structure, such as BaTiO₃ (BT), (Ba_{1 − x}Sr_x)TiO₃ (BST), and Pb(Zr_{1 − x}Ti_x)O₃ (PZT). The relative permittivity of this kind of filler ranges from hundreds to thousands, which is much higher than that of the polymer matrix. Hence, it is a common strategy to incorporate nanofillers into the polymer matrix to raise the permittivity of the nanocomposite dielectrics. The nanofillers can be considered at a range of dimensions, namely, zero-dimensional (0D) nanofillers, which include spherical nanoparticles, nanocubes, and nanoparticles with irregular morphologies; one-dimensional (1D) nanofillers, which include nanowires, nanofibres, nanotubes, and nanoribbons; and two-dimensional (2D) nanofillers, which include nanoplates, nanosheets, and nanoclays.³⁵ 

For composites filled with spherical nanoparticles, current research mainly focuses on the improvement of compatibility, interface bonding, and dispersion between nanoparticles and polymers through surface modification and coating of nanoparticles. Dang et al.³⁶  prepared a novel calcium copper titanite (CaCu₃Ti₄O₁₂; CCTO)/polyimide (PI) composite film. At a volume fraction of 40 vol% CCTO particles, the relative permittivity of the composite was 49 at 100 Hz, which was 14 times that of pure PI. The addition of nanoparticles to the polymer matrix could increase the permittivity of the system to some extent, but optimum dielectric properties are usually obtained with a high volume fraction of nanoparticles. Theoretical calculations show that when the loading of 0D nanoparticles reaches more than 39.7 vol%, holes and agglomerations are inevitably introduced into the composites, which act to deteriorate the dielectric properties and breakdown strength, as well as the mechanical properties of the composites.

Consequently, numerous studies are aimed at interfacial effects using the surface modification method to improve the dispersion and compatibility between the nanoparticles and the polymer matrix. Yu et al.³⁷  treated the surface of BT nanoparticles with polyvinylpyrrolidone (PVP), then compounded them with PVDF to prepare the composite film. At a filler volume fraction of 10 vol% BT, the breakdown strength of the film increased by 38% compared with the composite without PVP modification. Almadhoun et al.³⁸  introduced hydroxyl groups into the surface of BT to form h-BT bonds by means of the hydrogen peroxide water treatment. Hydrogen bonds were formed between the hydroxyl groups and fluorine of the P(VDF-TrFE) matrix, which enhanced the interface combination intensity. The h-BT/P(VDF-TrFE) composite achieved a lower leakage current, higher breakdown strength, and also showed better frequency and temperature stability.

Furthermore, the macromolecule coating of active functional groups can be directly grown on the surface of the filler by a chemical synthesis method, which can improve the effective dispersion of the filler and promote its bonding with the polymer matrix. Yang et al.³⁹  mixed BT nanoparticles with fluoroalkyl acrylate and coated BT particles with a layer of trifluoroethyl acrylate (PTFEA) approximately 5 nm thick by reversible addition-fragmentation chain-transfer polymerisation. Since both PTFEA- and PVDF-based polymer matrices contain fluorine, the dispersion of particles was obviously improved. In addition, the existence of an organic insulating layer limits the accumulation and migration of space charge, thus significantly reducing the dielectric loss of composites and increasing the energy storage density by 50%. Xie et al.⁴⁰  prepared BT/ poly(methyl methacrylate) (PMMA) composites by atom transfer radical in situ polymerisation (ATRP) on the surface of BT coated with PMMA of different thickness. The effects of different shell thickness on the dielectric properties of the composites were studied. The PMMA layer prepared by ATRP reaction has good binding with the BT nanoparticle filler and effectively prevents carrier migration and reduces dielectric loss. Subsequently, a branched aromatic polyamide (HBP) with a medium permittivity was placed between the PMMA and BT as a transition layer to form a core@double-shell structure. The existence of the HBP layer enhances the interfacial polarisation, restricts the dipole movement in PMMA side groups, and reduces the friction between molecules. The energy density of the dielectric nanocomposite showed a significant increase as a result of the further improved permittivity and weakened dielectric loss.

Compared with 0D nanofillers, 1D nanowires show the following advantages. First, the lower surface energy of nanowires caused by the larger aspect ratio and smaller specific surface area, which contributes to improving the dispersion of fillers in the polymer matrix. Second, because the nanowires have a large dipole moment, the dielectric property of the composites can be significantly increased even at low filler loading levels. At present, nanowire materials are mainly chosen as the fillers in dielectric composites, which include TiO₂, BT, BST, and PZT nanowires.

Many theoretical calculations and experiments have found that 1D fillers can improve the dielectric properties of composites more effectively than spherical or quasi-spherical fillers. Guo et al.⁴¹  have compounded spherical BT, spherical TiO₂, and rod TiO₂ as fillers with the PP polymer matrix, respectively. At the same filler loading of 3 vol%, the relative permittivity of a rod TiO₂ composite was 4.1, which is higher than that of spherical TiO₂ composite and rod TiO₂ composite. The results showed that the enhancement effect of the rod-like TiO₂ was better than that of BT spherical particles with higher permittivity.

The length to diameter ratio of 1D fillers has an influence on the dielectric properties of the composites. Tang et al.⁴²  obtained BT nanowires with different length to diameter ratio by altering the reaction temperature of the hydrothermal method, then studied the effect of length to diameter ratio on the permittivity of BT/PVDF nanocomposites. At a BT nanowire volume fraction of 30 vol%, the relative permittivity of the composite with a filler length diameter ratio of 45.8 was found to be 44.3, which was 35.7% and 352% higher than that of the composite with the aspect ratio of 9.3 and the pure PVDF, respectively. Liu et al.⁴³  adopted high aspect ratio SrTiO₃ nanowires surface-modified by PVP to prepare SrTiO₃/PVDF composites. At a low filler loading of 2.5 vol%, the permittivity of the nanocomposite improved significantly without apparent decrease in breakdown strength. The reason for the enhanced permittivity is that the large aspect ratio makes it easier to reach the percolation threshold, increases the dipole motion, and reduces the interface area, thus inhibiting the agglomeration of nanofibres. As a result, the energy storage density of the SrTiO₃/PVDF nanocomposite is more than twice that of PVDF.

Owing to the existence of nanowire anisotropy, the orientation of the nanowires has a significant influence on the dielectric properties of composites. The construction of 1D filler alignment in nanocomposites is also an effective way to improve the dielectric and energy storage properties of dielectric capacitors. Sodano et al.⁴⁴  have aligned PZT nanowires (NWs) in the PVDF matrix and formed an array distribution of nanocomposites by a uniaxial strain assembly method. It was found that the relative permittivity in the nanocomposites aligned in the 3-direction (the orientation of PZT NWs parallel to the direction of the electric field) is much larger than that of the PVDF composites with random PZT at the same loading, e.g., ≈34 for the aligned nanocomposite versus ≈25 for the random nanocomposite at 30 vol% PZT. It was also shown that the 3-direction-aligned PZT NW nanocomposites have a larger electric displacement than the random and 1-direction-aligned (the orientation of PZT NWs perpendicular to the direction of electric field) PZT NW nanocomposites, as a result of the higher dielectric permittivity of the samples. Moreover, the composite with 40 vol% aligned PZT in PVDF can achieve a maximal calculated energy density of ≈1.28 J cm⁻³ at a low electric field of 15 MV m⁻¹. A similar investigation was conducted with aligned BT nanowires by Xie et al.⁴⁵  As shown in Figure 1.7, they fabricated the X–Y-aligned nanocomposite (nanowires aligned perpendicular to the applied electric field) with the help of shear stresses, and the Z-aligned nanocomposite (nanowires aligned in the direction of the applied electric field) under the guidance of the inner wall of a Teflon tube. The result showed that, compared with the pristine P(VDF-CTFE) matrix, the polarisation and breakdown strength of the X–Y-aligned nanocomposite were enhanced simultaneously, resulting in an improved energy storage performance. Furthermore, a superior performance was achieved through the Z-aligned nanocomposite, where the energy density and efficiency were improved to 10.8 J cm⁻³ and 61.4%, respectively, at a lower electric field of 2400 kV cm⁻¹.

In recent years, 2D fillers with high aspect ratio in-plane, such as BNNSs,^28,46,47  MoS₂ nanosheets,^16,48  ZrO₂ nanosheets,⁴⁹  montmorillonite nanosheets (MMTs),^50,51  and graphene nanosheets (GNs),^52–55  have been extensively explored in ferroelectric polymer nanocomposites, to tailor the dielectric and energy storage properties. For example, conductive graphene has been introduced into a polymer enabling improvement of the dielectric permittivity due to the microcapacitor effect; while incorporation of insulating BNNSs or MMT nanoplatelets can enhance the breakdown strength, owing to their barrier effect. According to the characteristics of fillers and their action mechanisms in the composite, three types of insulation filler polymer systems and conductive filler polymer systems are classified and are summarised in the following sections.

Theoretically, 2D insulation fillers, such as nanosheets and nanoribbons, can be regarded as a large number of barriers perpendicular to the direction of electric field that prevent the expansion of conductive channels and enhance carrier scattering. This plate-like structure is also conducive to heat dissipation and restraining the formation of thermal breakdown and electromechanical breakdown paths along the electric field direction, thus effectively enhancing the breakdown field strength of the composites. Among the 2D insulating fillers, BNNSs, MMTs, ZrO₂ nanosheets, BT nanosheets,⁵⁶  and NaNbO₃ platelets⁵⁷  have attracted the greatest interest from scientists and have been employed in nanoelectronics.

The material h-BN, referred to as ‘white graphene’ and the most stable crystalline form of boron nitride, is a layered van der Waals crystal, which is similar to graphite. It shows high mechanical strength and thermal conductivity resulting from a graphitic-like structure of strong B–N covalent sp² bonds in the (002) plane. In addition, insulating hexagonal boron nitride has a wide band gap (6 eV), relatively low relative permittivity (3–4), and high breakdown strength (800 kV mm⁻¹). This unique structure and physical performance of hexagonal boron nitride promote its applications as a dielectric layer in nanocomposites.^58–60 

Li et al.⁵⁹  obtained ultrathin BNNSs by a sonication–centrifugation method, and then prepared P(VDF-TrFE-CFE)/BNNS nanocomposite films via a simple solution-casting method, as shown in Figure 1.8. Due to the polar surface induced by B–N bonds, a proper fraction of bare BNNSs without any chemical modification can be uniformly dispersed in a matrix of polar polymer. Generally, inorganic fillers often have many defects in the polymer matrix due to their poor compatibility, which hinders improvement of the composite properties. Researchers usually use ligands with long hydrocarbon chains to activate the surface of the filler to improve the compatibility of the two phases for good dispersion and distribution. However, low permittivity of the modified surface results in a large contrast for the high-permittivity ferroelectric polymer and inorganic dopant phases, which becomes a vulnerable local region to localised electric fields in the nanocomposite, and, accordingly, degrades the overall dielectric strength. For BNNSs, the high aspect ratio and specific surface area not only simplifies the preparation process of the polymer nanocomposites, but also eliminates the steps of chemical modification. Thus, a dense network-like microstructure was formed in the polymer matrix via a simple solution- casting technique, which is conducive to increasing the breakdown field strength of the composites.

The results show that the breakdown strength of nanocomposites filled with 12 wt% of BNNSs reaches 610 MV m⁻¹, which is 70% higher than that of pure polymers, and the shape parameter β, standing for less scattering of E_b, also increases from 8.44 to 15.8, which means that the dielectric stability of the composites is significantly enhanced. It is reasoned that BNNSs within the polymer matrix create a robust scaffold to hamper the onset of electromechanical failure, and act as an efficient barrier against leakage current and space charge conduction. In addition, a discharge energy density of 20.3 J cm⁻³ was achieved at 650 MV m⁻¹, while the charge–discharge efficiency remains above 80% at 600 MV m⁻¹, which resulted from the suppressed conduction loss and high field resistivity of the presence of BNNSs under the electric field. It should be emphasised that with the introduction of BNNSs into the terpolymer matrix, the thermal conductivity is increased six-fold, from ∼0.2 W m⁻¹ K⁻¹ for the terpolymer, to over 1.2 W m⁻¹ K⁻¹ for the nanocomposite filled with 14 wt% of BNNSs, which benefits the breakdown stability and lifetime of polymer capacitors.

In addition, the most common 2D insulation fillers for nanocomposites are MMT nanosheets, which are layered silicate sheets and are an environmentally friendly and naturally occurring smectite clay. This material becomes a good choice for designing polymer nanocomposites due to its low cost and rich intercalation chemistry, allowing improved compatibility with the polymer matrix, to enable higher polarisation and improved dielectric performance and breakdown strength.

Ghosh et al.⁶¹  reported a flexible polymer nanocomposite (PCN) by incorporation of unmodified MMT nanoclay into the PVDF polymer matrix. The results showed that the uniform intercalation of PVDF chains into the layered silicates of unmodified MMT nanoclay induces a α–γ phase conversion in the PCN films, which was a consequence of interfacial interaction between the negatively charged surface of the MMT nanoplatelets and the electropositive CH₂ dipoles of PVDF, as shown in Figure 1.9. The obtained PVDF/MMT clay nanocomposite films stabilise the phase and increase the path tortuosity via strong intercalation of the PVDF matrix into inorganic layered silicates, without sacrificing the quality of the surface morphology. The PCN films exhibit superior dielectric properties (up to ɛ_r ∼ 28 and tan δ ∼ 0.032 at 1 kHz) compared with that of pure PVDF because the MMT clay acts as an efficient insulating barrier against the leakage current and space charge conduction. Moreover, the MMT nanoplatelets, arranged in a layer-by-layer structure within the PVDF matrix, formed tortuous paths between the electrodes that block the path of the applied electric field. As a result, a large increase in E_b of 873 kV mm⁻¹ and U_e of 24.9 J cm⁻³ is achieved. Consequently, the PCN films possess more than 60% charge–discharge efficiency even at higher electric field. This environmentally friendly MMT would not only simplify the fabrication of the PVDF/clay nanocomposites by eliminating the chemical modification step, but also enhance the breakdown strength and energy density of ferroelectric polymers as high energy density capacitors for green energy technologies.

MoS₂ nanosheets, as an emerging class of transition metal dichalcogenides with an excellent on/off ratio of 10⁸ and high carrier mobility of 200 cm² V⁻¹ s⁻¹ at room temperature, have attracted considerable interest in recent years due to their outstanding thermal and mechanical properties, as well as attractive photocatalytic and electrical properties.¹⁶  These characteristics enable them to be applied to transistors in lubricants, photoactive materials, and thin films. In particular, MoS₂ is also a semiconductor with an appreciable band gap of 1.8 eV, high specific surface area, and good chemical stability, and it has triggered increasing interest as a promising dielectric material for adjusting permittivity and electric field.

Cheng et al.⁶²  investigated the effects of MoS₂ nanosheets on the dielectric properties and breakdown strength of polymer composites. First, by using the liquid-phase exfoliation method, MoS₂ nanosheets were produced from their bulk powder in triethanolamine (TEOA) solution and then incorporated into poly(amic acid) (PAA) solution to thermally imidise and yield MoS₂/PI nanocomposite films. With increasing MoS₂ content, the relative permittivity of the nanocomposite films showed obvious improvement, which can be attributed to the relatively larger relative permittivity of the MoS₂, as well as the interfacial polarisation. Meanwhile, the dielectric loss of the composite maintained low values below 0.02 in the frequency range of 100 Hz to 1 MHz. For breakdown strength performance, a small quantity of MoS₂ nanosheets is beneficial to achieve an elevated breakdown strength, because of its efficient conduction barrier effect, which limits the charge migration and hinders the growing electric tree. However, when the MoS₂ content increases further to 1.5 vol%, concentration of the local electric field caused by aggregate defects in the composites leads to deterioration of the breakdown strength. Therefore, the MoS₂/PI nanocomposite film with 1 vol% MoS₂ reached a high energy density of 3.35 J cm⁻³ at 395 MV m⁻¹ and maintained the energy efficiency at over 80%. In addition, self-passivated aluminium flakes (AFs) were introduced to MoS₂/PVDF ternary composites to obtain MoS₂/AFs/PVDF by He et al.¹⁶  Figure 1.10(a) shows that this type of composite is comprised of a network of nanocapacitors. The dielectric spectra as temperature and frequency of pristine PVDF, MoS₂/PVDF, and MoS₂/AFs/PVDF composites are shown in Figure 1.10(b–d), respectively. The permittivity of pure PVDF matrix exhibits a slow increase with increasing temperature at low frequency. For the MoS₂/PVDF composite, the shape of the curves in the composites with MoS₂ nanosheets is similar to those of PVDF, but the permittivity exhibits a sharp enhancement and strong frequency dependence over the whole frequency range. However, the permittivity of the MoS₂/AFs/PVDF composite is obviously reduced with the addition of AFs, and the variation in the trend of permittivity of the three-phase composite is similar to that of the MoS₂/PVDF composite. It is speculated that the introduction of AFs successfully weakens the effect of the MoS₂-PVDF polarisation.

Graphene is the most attractive 2D conductive filler in the study of percolation-type composites. Because of its excellent mechanical, electrical, and thermal conductivity, as well as large specific surface area (2630 m² g⁻¹), graphene is considered as an ideal filler for preparing high dielectric composites.^63,64  For example, graphene/polymer composites with a small volume fraction have excellent dielectric properties.

Due to its large specific surface area, numerous local microcapacitors can be constructed in the composite system to markedly improve the permittivity, while the percolation threshold can be reduced to 0.31 vol%, or even lower. For example, Tan et al.⁶⁵  prepared reduced graphene oxide (rGO) and dispersed it into a PVDF matrix to yield a rGO/PVDF dielectric composite. The experimentally measured percolation threshold of the composite was only 0.18 vol%. At the volume fraction of 0.177%, the relative permittivity and loss were 180 and 0.98 at 1 kHz, respectively. Conductive fillers such as graphene can effectively improve the permittivity and energy storage density of composites. However, during the preparation process it is necessary to control the number of fillers accurately. If too much filler is added, conductive paths are easily formed in the composites, resulting in larger leakage current and dielectric loss, thus reducing the breakdown strength of the composites. The reason for agglomeration of the filler is a strong van der Waals force between the graphene layers, and uniformly dispersing the conductive filler in the polymer matrix is a key requirement to improving the composite material. Therefore, the dispersibility can be improved by surface modification of graphene to increase the permittivity and reduce the dielectric loss.

Generally, chemical modification is used to improve the compatibility of the graphene sheet with the polymer matrix, such as introducing –OH, –COOH, or O groups onto the surface of graphene. For example, Yang et al.⁶⁶  synthesised dopamine-coated rGO (PDA-rGO) and fluorinated functional group rGO (PF-PDA-rGO) to prepare dielectric composites. Compared with PDA-rGO obtained by traditional methods, the filler PF-PDA-rGO could be better dispersed in a ferroelectric polymer P(VDF-HFP) and has strong interfacial adhesion with the matrix, resulting in composites with a low percolation threshold and excellent flexibility. At a filler volume fraction of 10 vol%, the relative permittivity and loss of P(VDF-HFP)/PF-PDA-rGO composite are 107.9 and 0.07 at 1 kHz, respectively. Wen et al.⁶⁷  incorporated functionalised graphene in the double-bonded P(VDF-TrFE) copolymer. The covalent bonding effect between graphene and the matrix means that the filler is well dispersed and has a strong interfacial effect in the interface area. Thus, the relative permittivity of the composites reached 74 at 100 Hz, which is seven times higher than that of pure polymers. Tong et al.⁶⁸  produced a rGO/P(VDF-HFP) composite by the spin-coating method. Due to the good dispersibility and orientation distribution of graphene in the polymer matrix, at a rGO loading of only 0.7 vol% the relative permittivity of rGO/P(VDF-HFP) reached 54 and the dielectric loss was only 0.27. In addition, a three-phase co-filling system was employed to improve the properties of the composites. For example, Shen et al.⁶⁹  filled the PVDF with conductive rGO and ceramic BT to effectively improve the permittivity and breakdown strength of the composite. This co-filling system could overcome the shortage of leakage current caused by the conductivity of graphene itself, and at the same time reduce the amount of BT added in the matrix. Therefore, the combination of conductive material and ceramics as fillers and utilising the synergistic effect of the two phases is expected to produce high-performance dielectric materials.

Generally, poor dispersibility and aggregation of nanofillers in the polymer matrix tend to induce high dielectric loss and conductivity, resulting in a weakened breakdown strength and polarisation effect. Therefore, the interfacial compatibility between the polymer matrix and the nanofillers is crucial for high-performance composites. Interface design is achieved by introducing a series of interfacial layers to create a core–shell structure, including the use of inorganic, organic, and conductive outer shell layers on the nanofillers, for surface functionalisation.

Inorganic modifiers are often employed to enhance compatibility and dispersion of the filler in the polymer matrix. Commonly, several valve metal oxides, such as aluminium oxide (Al₂O₃), silica (SiO₂), and TiO₂, have been chosen as the shell layer coating on the nanofiller core–shell structured formation due to their high insulation and intermediate relative permittivity. For example, Chen et al.⁷⁰  have reported a novel nanocomposite film by incorporating the Bi₂Te₃@Al₂O₃ core–shell structure filler into a PVDF matrix, as shown in Figure 1.11. The schematic shows the accumulation of interfacial charges at the interfaces of Bi₂Te₃–Al₂O₃ and Al₂O₃–PVDF. As displayed, interfacial charges produced a Gouy–Chapman–Stern layer at the surface of the Bi₂Te₃, which is highly conductive and can be easily moved through by charges. The overlapped layers led to a large electrical leakage current and low breakdown field. It was the presence of the Al₂O₃ layer that formed the strong bonding with the polymer matrix, thus preventing the formation of a current channel of composites. As a result, the composite film loaded with 10 vol% 2D Bi₂Te₃@Al₂O₃ nanoplates exhibited a high relative permittivity of 140 and a relatively low dielectric loss of 0.05 at 1 kHz. Similarly, SiO₂ was subsequently employed as a filler shell to prepare composites, by Chen et al.⁷¹  It was found that due to the highly insulating SiO₂ shell effectively reducing the concentration and mobility of the charge carriers, the alternating current conductivity of Bi₂Te₃@SiO₂/P(VDF-HFP) composite films is two orders of magnitude lower than that of Bi₂Te₃/P(VDF-HFP) composites.

Other novel nanocomposites are films comprising 2D core–shell NaNbO₃@Al₂O₃ platelets (2D NN@AO Ps) and poly(vinylidene fluoride-hexafluoropropylene) (P(VDF-HFP)), which were prepared by Pan et al.⁷²  The heterogeneous structure of the 2D NN@AO Ps was characterised by TEM, X-ray diffraction (XRD) patterns, and elemental mapping analyses, as shown in Figure 1.12, which suggest that a homogeneous and tight AO coating layer is obtained. The 2D NN@AO Ps/P(VDF-HFP) nanocomposite films have larger relative permittivity, ε_r, and lower tan δ compared to those of the 2D NN P/P(VDF-HFP) nanocomposite films. This could be explained by the following: (1) the highly insulating AO layer efficiently reduces the Maxwell–Wagner–Sillars (MWS) interfacial polarisation and space charge polarisation in the NN@AO P/P(VDF-HFP) nanocomposite films, thus improving the ε_r value; (2) the lower dielectric loss could be attributed to the reduction in the amorphous structural defects at the AO interface, resulting in enhanced microstructural uniformity of the nanocomposite film; and (3) the insulating AO layer can also effectively obstruct the current channels generated by the interfacial charge carriers. Finally, the NN@AO P/P(VDF-HFP) nanocomposite films yield the maximal energy density of 14.59 J cm⁻³ for an electric field of 440 kV mm⁻¹, as well as, simultaneously, an outstanding discharge efficiency of 70.1%.

Organic modifiers can be physically adsorbed onto the filler surface through electrostatic interactions, or by hydrogen bonding. A variety of modifiers have been used, which include dopamine, cetrimonium bromide, polyethyleneimine, poly(vinyl pyrrolidone), ethylene diamine, polyvinyl alcohol, paraffin, and so on. These organic compounds have been utilised to modify the surface of inorganic fillers and are of interest due to their simple treatment process, for example, by solution mixing. To reduce agglomeration and improve the poor dispersibility of filler in the polymer matrix, Wang et al.⁵¹  choose cetrimonium bromide (CTAB) as the surfactant to modify the nanolaminate-shaped MMT clay. The long alkyl chain of CTAB could not only be intercalated into the interlayers of MMT to improve the dispersity of the nanolaminates, but also provide positive surface charge, which can tune the polarisation of negatively charged MMT nanolaminates. Thus, compared to the pristine PVDF film, the energy density was increased from 5.34 J cm⁻³ to 5.91 J cm⁻³ at 1 wt% MMT content and the maximum energy density could reach 10.2 J cm⁻³. In addition, Wang et al.⁷³  treated MoS₂ nanosheets by the mussel-inspired co-modification of poly(dopamine) (PDA) and polyethyleneimine (PEI). Due to the formation of covalent bonds between PDA and PEI, a stable and uniform coating layer with rich polar groups (–NH₂ and –OH groups) was obtained. In addition, improvement of the interfacial compatibility between MoS₂ nanosheets and the poly(arylene ether nitrile) (PEN) matrix can be achieved by strong interfacial interactions, as shown in Figure 1.13. As a consequence, the MoS₂/PEN composites show excellent mechanical strength and thermal stability, high permittivity, low dielectric loss, and good frequency stability, and can be potentially used as high-performance dielectric materials.

Zhi et al.⁷⁴  developed a facile and efficient approach to simultaneously functionalise and tune the reduction state of graphene oxide (GO) with c-aminopropyl triethoxysilane (APTES), then incorporated APTES-functionalised GO sheets (GO-APTES) into nitrile butadiene rubber (NBR) by latex co-coagulation, to form GO-APTES/NBR composites, as in Figure 1.14. In the system of composites, APTES acted as a coupling agent, while its amine groups interact with the functional groups on the GO sheets to remove many surface groups of the GO sheets to increase the conductive areas between the insulating barriers. The results showed that the high aspect ratio of GO-APTES sheets leads to an increase in the permittivity of the composite, while the intrinsic barriers of GO limit the leakage current and avoid a high dielectric loss. The GO-APTES/NBR composites exhibit a relatively high permittivity of 30.8 and small loss factor of 0.04 at 1 kHz, as well as a good insulating property.

Recently, many investigations have indicated that filler orientation and spatial distribution play an important role in determining and improving the energy storage capabilities of nanocomposites. Tomer et al.⁷⁵  prepared polyethylene/montmorillonite nanocomposites by an extrusion blow moulding and hot-pressing process method. The effect of the spatial arrangement of the high aspect ratio nanofillers on the dielectric and breakdown behaviour were investigated. The nanocomposite with randomly oriented fillers showed markedly higher losses (broader D–E loop) compared to the nanocomposite containing oriented fillers, which can be explained by the fact that oriented-filler composites are expected to provide more ordered trapping centres and more efficient scattering for the injected charge, thus obstructing its ability to traverse the sample to the opposite electrode. Nevertheless, nanocomposites with no filler orientation had more losses at high electric fields due to the lower obstruction effect. In addition, Weibull statistics methods were used to analyse the electric breakdown strength of the composite, and composites with oriented fillers showed constantly larger electric breakdown strength than both the unfilled polymer and composites with random fillers. First, the array distribution of the filler can impede the progress of electric trees, since it needs a more tortuous path for electric trees to penetrate throughout the samples, causing the occurrence of breakdown. Second, oriented fillers can be used as structured scattering centres for conducting electrons, resulting in weakening of kinetic energies. More importantly, considering both the displacement and high electric field behaviour, nanocomposites with aligned fillers showed a marked improvement in recoverable energy density and the energy efficiency of the polymer. Wang et al.⁷⁶  synthesised plate-like (Ba_0.6Sr_0.4)TiO₃ (P-BST) via a topochemical microcrystal conversion, and fabricated P-BST/PVDF textured composites using a tape-casting and hot-pressing method, as shown in Figure 1.15. It was found that the particles with larger size are more sensitive to the shear force generated during tape-casting and to be textured along the casting direction. The textured arrangement enhanced the uniform dispersion of these particles in the matrix, while reducing the structural defects. In addition, BST microcapacitors are also easily connected in series and in parallel to form the capacitance in textured composites. As a result, P-BST/PVDF textured composites exhibited a higher relative permittivity of 62.2 and lower dielectric loss of 0.042 compared with the composite with a disordered array of particles. The maximum energy density of the composite, of 6.36 J cm⁻³, was obtained at an electric field of 29 kV mm⁻¹.

Sandwich or multilayer structure design is an effective strategy to synchronously enhance permittivity and electric breakdown strength so as to achieve high energy density of the polymer nanocomposites.⁷⁷  As shown in Figure 1.16, Pan et al.⁵⁷  synthesised 2D NN platelets by a two-step melt-salt process, and then designed a trilayered architecture composite with high-permittivity NN/PVDF as the two outer layers and high breakdown strength pristine PVDF as the middle layer. The results showed that the breakdown strength of the trilayered architecture composite films could be improved significantly compared with the single-layer composite films. For example, the 5-0-5 trilayered architecture composite films have the highest breakdown strength of 400 MV m⁻¹, which is 14.3% higher than pristine PVDF (350 MV m⁻¹) and 25% higher than the corresponding single-layer composite film (300 MV m⁻¹). This can be explained by the following. First, the electric field redistribution caused by the incorporation of high-permittivity 2D NN platelets into the outer layers, and a weak electric field region is formed in the outer layers, so that the trilayered architecture composite films could tolerate a higher electric field than single-layer composite films at the same applied electric field. In addition, the strong interfacial barrier effect between the outer layer and middle layer also enhances breakdown strength in trilayered architecture composite films. Finally, due to the synergistically enhanced breakdown strength and electric displacement, the 5-0-5 composite film exhibited a higher discharge energy density of 13.5 J cm⁻³ and energy efficiency of 66.9% than the corresponding single-layer composite film.

As shown in Figure 1.17, 2D NBT-BT platelets coated with polyvinylpyrrolidone (PVP) were introduced as fillers for the preparation of NBT-BT@PVP/P(VDF-HFP) composites.⁷⁸  The multilayer films were designed with 1 vol% NBT-BT loadings as the central hard layers, and 30 vol% NBT-BT loadings as neighbouring soft layers. The five-layered (30-1-1-1-30) nanocomposites showed a maximum energy storage density of 14.95 J cm⁻³ at 258 kV mm⁻¹. The energy efficiency remained at 90% at 200 kV mm⁻¹. This excellent performance was attributed to the combination of the high relative permittivity and high dielectric strength of the multilayer structure. The former derives from the top and bottom soft layers (30 vol% NBT-BT loading), while the latter mainly comes from the central hard layers (1 vol% NBT-BT loading). The central hard layers act as electron traps that limit electron tunnelling through the film, resulting in improved breakdown strength.

Li et al.⁷⁹  developed a high-temperature dielectric polymer nanocomposite consisting of a sandwich structure, by sequentially casting three layers of c-BCB/(BNNSs), c-BCB/BT, and c-BCB/BNNSs, respectively, with a thickness ratio of 1 : 2 : 1 (c-BCB represents cross-linked divinyltetramethyldisiloxane-bis(benzocyclobutene)). Compared with a conventional single-layer configuration, this nanocomposite is capable of integrating the complementary properties of spatially organised multicomponents in a synergistic fashion to raise permittivity, and subsequently improve discharge energy densities, while retaining low loss and high charge–discharge efficiency at elevated temperatures. For example, an energy density of 1.1 J cm⁻³ with energy efficiency of 93% have been realised in a sandwich-structured polymer nanocomposite at 150 °C and 200 MV m⁻¹.

The dielectric properties of polymer-based nanocomposites with inorganic nanofillers are dependent not only on the intrinsic properties of polymers and nanofillers, but also on the properties of the interfacial regions. Moreover, the volume fraction of the interface becomes more significant with a decrease in the filler size. For example, the volume fraction of the interfacial region (f_interface) of a spherical nanocomposite filler can be calculated by eqn (1.1):

where t is the thickness of the interfacial region, d is the diameter of the nanoparticle, and f_particle is the volume fraction of the filler.⁸⁰  As presented in Figure 1.18(b), when f_particle is fixed at 5% and t is fixed at 5 nm, the interface volume fraction (f_interface) is less than 10% for nanoparticles with d = 10 nm, but the f_interface dramatically increases to over 50% for nanoparticles with d < 10 nm. In these regions, the chemical and physical properties are different to the nanofillers and polymer matrix, such as polymer chain mobility, chain confirmation, crystallinity, and coulombic potential. Therefore, the polymer-based nanocomposites contain three phases: continuous phase of basic polymer, dispersed phase of inorganic filler, and interfacial phase (see Figure 1.18(a)). To understand the effect of interfaces in polymer nanocomposites, several models and theories concerning the interfacial regions have been hypothesised.^81,82  In this section, the effects of interfaces on the dielectric properties are discussed.

A multilayered core model resulting from the ‘interaction zones’ was proposed by Tanaka and is displayed in Figure 1.19(a).⁸³  This model is constructed on the basis of both chemical and electrical analysis, but it is still a working hypothesis. As can be seen from Figure 1.19(a), the interfacial layer consists of three layers, including a bonded layer, a bound layer, and a loose layer. The first layer corresponds to the bonded layer. Usually, inorganic fillers are difficult to fully disperse in the organic polymer matrices due to surface tension between the two phases. In order to reduce the difference in surface tension, a silane coupling agent is widely used to modify the surface of the nanoparticles, resulting in a bonded layer being formed via hydrogen bonding between the polymer and silane coupling. The total thickness of the bonded layer is approximately 1 nm. The second layer is a bound layer in which a layer of polymer chains is strongly bound and/or interacts with the first layer and the surface of the inorganic particle. The thickness of this layer ranges from 2 to 9 nm, depending on the strength of the polymer–particle interaction. The third layer, denoted as a loose layer, is a region that loosely couples and interacts with the bound layer. Compared with the bonded layer and bound layer, the thickness of the loose layer can extend to several tens of nanometres. In this loose layer, the polymer produces different chain conformation, chain mobility, free volume, or crystallinity compared with the polymer matrix.

Although the multilayered core model is a working hypothesis that is not fully verified, there are many dielectric and electrical insulation phenomena that can be interpreted with it, such as permittivity, dielectric loss, conduction, space charge, thermally stimulated current, electroluminescence, photoluminescence, dielectric breakdown strength, electrical treeing, partial discharge resistance, tracking, glass transition temperature, and so on. For example, Tanaka explained the PD (partial discharge) resistance of polyamide-layered silicate nanocomposites according to the multicore model.⁸³  Tanaka considered that the third layer was the most susceptible to PD compared with the other two, resulting in PD degradation starting from the loose layer. As soon as the PD erodes the third layer, the second and the first would resist the extension of the PD, leading to that PD activity invading the weaker regions, such as the polymer region or the third layer of an adjacent nanoparticle. Hence, a zig-zag path was formed around the nanoparticles due to PD activity. In this way, the polymer nanocomposites exhibited an enhanced PD resistance. With regards to the permittivity of polymer nanocomposites, Tanaka considered that the first and second layers in the multicore model played the critical role of reduced permittivity.⁸⁴  The third layer played a positive role in increasing permittivity because it contained dipoles and ion carriers and larger free volume. Moreover, when the third layer trapped ions, the dielectric loss would become large at low frequency.

The addition of nanofillers in the polymer matrix produces numerous interfaces in nanometric dimensions. In order to understand these interfacial electrical and dielectric behaviours, Lewis proposed the diffuse electrical double layer model in the polymer nanocomposites, and the model is presented in Figure 1.19(b).^85,86  It can be seen that the surface of the nanofillers will be charged due to the difference in chemical potential or Fermi levels of the polymer matrix and the nanoparticles. In addition, the matrix develops counter charges near the surface of the nanoparticles, resulting in suppression of charge accumulation on the nanoparticles. For simplicity, in the Lewis model, the nanofillers possess a positively charged surface and the surface is considered to be planar; see Figure 1.19(b). For counter charges, there are two mechanisms to consider. One is that they refer to the induced polarisation of the polymer matrix, including the electronic polarisation and orientation of permanent dipoles, which usually occurs when a polymer contains polar components. Another is related to migration and redistribution of mobile charges on the polymer side due to coulombic attraction, leading to the formation of an electrical double layer consisting of a Stern layer and a Gouy–Chapman diffused layer (see Figure 1.19(b)). Due to the positively charged surface, a positive potential ψ_s is exhibited around the nanoparticles, which involves immobile charged impurities, trapped carriers, mobile electrons, and holes in the nanoparticle. Close to the positive layer, the negatively charged counter charges or dipoles are tightly absorbed to the particle surface to form the so-called Stern or Helmholtz double layer, which contains small molecules, special absorbed ions, and solvated ions, and cannot move freely. Outside this layer is the Helmholtz plane (OHP) with an electrical potential of ψ_o. The thickness of the Helmholtz double layer is approximately 1 nm.

The Gouy–Chapman diffused layer is formed outside and around the Stern layer by the distribution of negative and positive ions. The thickness of this layer is affected by the ion concentration in the polymer, as well as the potential difference between the polymer matrix and the nanoparticle surface. If the polymer matrix is highly conductive, a number of charge carriers concentrate at the polymer matrix region, leading to the diffuse layer shrinking into the OHP. However, if the polymer matrix is insulating, the diffuse layer may extend 10 nm or more. More importantly, this diffused layer potentially works as an ‘interaction zone’ to determine the dispersion of nanoparticles. The dielectric and electrical properties of the nanocomposite relate to the contained mobile charges, especially near the percolation threshold of the nanofillers (see Figure 19(b)). The distribution of charges in this layer is related to the electrical potential ψ(r) across the interface region. The value of ψ(r) is changed by the distance (r) from the particle surface and can be described with a combined Poisson–Boltzmann equation, and the ψ(r) function is shown as follows:⁸⁵ 

where ε is the permittivity of the medium, k is the Boltzmann constant, and z_i and n_i(∞) are the ion valency and concentration of ion species i in the bulk matrix, respectively. When the potential is small, the ψ(r) can be reduced further to the simple Debye–Hückel form and is shown below:

in which, κ is the Debye–Hückel parameter and has units of m⁻¹. The inverse of κ is called the Debye length and defines the extent of the exponential decay of the double layer. This equation indicates the potential variation in the diffused part of the double layer starting from the Stern layer.

The charge density (ρ_i) in the double layer is expressed as follows:³ 

At the nanoparticle surface (r = 0), the total charge density is

and is associated with the surface conductivity (σ) of the nanoparticles. The equation implies that ρ_i in the double layers can be increased be improving σ, which is useful to induce polarisation at opposite ends of the nanoparticles under an applied field E because the charges at the interfaces are efficiently transferred.

Based on Lewis’ model, Gupta et al. applied polydopamine (dopa)-functionalised TiO₂–BT–TiO₂ (TiO₂–BT–TiO₂@dopa) core@double-shell nanoparticles in PVDF for high energy density capacitor applications.⁸⁷  The composites showed a higher relative dielectric permittivity, breakdown strength, and energy density, which is accounted for by the polarisation at the interfaces inside the nanoparticles, as well as space charge accumulation at the nanoparticle interfaces. Due to the Fermi level difference between the n-type semiconductor TiO₂ and BT (>0.5 eV), the accumulation of positive and negative space charges is focused at the surface of TiO₂ and BT (see Figure 1.20). In addition, in order to maintain charge neutrality, the surface charge densities (σ′) in different layers of TiO₂–BT–TiO₂ nanoparticles follow the trend of σ′(TiO₂) core > σ′(BT) middle layer > σ′(TiO₂). The dopamine layer, in turn, responds by developing negative charges due to polar interaction with the positive TiO₂ layer. The interfacial charges present in the polymer matrix possessed a Gouy–Chapman–Stern layer at the interface of the TiO₂–BT–TiO₂ nanoparticles, resulting in an enhanced interfacial polarisation. Consequently, the PVDF-based nanocomposites displayed a high relative dielectric permittivity. In another case of core–shell BT@TiO₂ nanoparticle-filled P(VDF-HFP) composites, a large relative dielectric permittivity (>110) was obtained, which was more than three times higher than that of the P(VDF-HFP)/BT nanocomposites.⁸⁸  The improvement in the dielectric property was associated with the Maxwell–Wagner interfacial polarisation as a result of space charge accumulation and formation of Gouy–Chapman–Stern layers at the highly interactive interfaces among the multiple dielectric materials (see Figure 1.21). Pan et al. studied the dielectric behaviour of the Bi₂Te₃/PVDF and Bi₂Te₃@Al₂O₃/PVDF nanocomposites.⁸⁹  Compared with the Bi₂Te₃/PVDF nanocomposite, the Bi₂Te₃@Al₂O₃/PVDF composite film showed larger breakdown strength and lower dielectric loss. This is believed to be due to the reduced space charge polarisation by the highly insulating Al₂O₃ shell layer, and thus decreased thickness of Gouy–Chapman–Stern layer. In the Bi₂Te₃@Al₂O₃/PVDF composite systems, interfacial charges concentrated at the interfaces of Bi₂Te₃–Al₂O₃ and Al₂O₃–PVDF. These interfacial charges would form a Gouy–Chapman–Stern layer at the surface of Bi₂Te₃. When the highly conductive Gouy–Chapman–Stern layers of nanoparticles overlap, free charge movement may happen over a distance, leading to a large electrical leakage current and low breakdown field. The decrease in thickness of the Gouy–Chapman–Stern layer was favourable to prevent the formation of a current channel. Moreover, the strong bonding between the Al₂O₃ shells and the polymer matrix results in uniform dispersion of the core–shell nanoparticles, further restraining the formation of a current channel. Lei et al. reported the dielectric behaviour of a sandwich-structured PVDF-based composite, which has upper and lower layers filled with 0.5Ba(Zr_0.2Ti_0.8)O₃–0.5(Ba_0.7Ca_0.3)TiO₃ nanofibres and a middle layer filled with hybrid particles of hexagonal BNNSs coated by ferroferric oxide (Fe₃O₄@BNNSs).⁷⁷  The upper and lower layers can possess good ferroelectric hysteresis, and the middle layer contributes to high breakdown strength. In particular, the hybrid Fe₃O₄@BNNSs also enhanced the electric displacement and suppressed the remnant displacement of sandwiched nanocomposites. With the help of Lewis’ model, the authors considered that the increase in the dielectric properties of the PVDF-based composites originated from the interfacial polarisation, which may arise from the diffusion layer of the semiconductor–insulator structure at the interfaces between the insulating BNNSs and the semiconducting Fe₃O₄ (see Figure 1.22). Overall, some of the interfacial issues in the polymer-based nanocomposites can be explained by means of Lewis’ model.

To understand the polarisation mechanism and breakdown behaviour of polymer-based nanocomposites, finite element simulation offers a simple and effective way to calculate the distribution of permittivity, polarisation, and electric field.^26,90,91  In the case of P(VDF-HFP)/TiO₂ nanocomposites containing different shapes of TiO₂ particles,⁸  it is found that 5 wt% 2D nanosheets produce a super-high discharged energy density of 13.0 J cm⁻³ at 570 MV m⁻¹. Finite element simulation was conducted to investigate the electric field distribution in nanocomposites, and the results are displayed in Figure 1.23. Compared with the 1D nanofiller, nanocomposites with 2D nanofiller exhibit a more uniform electric field, resulting in a higher discharged energy density due to the suppressed charge injection from electrode. To study the effects of 2D nanoplatelet content on the distribution of the local electric field and local polarisation in 2D BT/PVDF nanocomposites, finite element simulation using COMSOL Multiphysics was conducted, and the results are shown in Figure 1.24.⁹²  As displayed in Figure 1.24(a–c), the surface of platelets produced higher local electric field, suggesting that the nanoplatelets would amplify the local electric field strength. With increments in the nanofiller content, the local electric field became more concentrated on the surface of the nanoplatelets, resulting in a sharp decrease in the breakdown strength of the nanocomposites. Although a higher content of nanoplatelets leads to higher local electric field, the amplified local electric field tends to improve the induced polarisation. A higher polarisation achieved at a larger filler content at the same external electric field is presented in Figure 1.24(d–f). Utilising the finite element simulation, Fu et al. found that the distribution of electric field and energy density for PVDF composites containing 2D Ni(OH)₂ platelets was more uniform than for spheres and 3D flower-type Ni(OH)₂ (see Figure 1.25). As a result, the platelet 2D Ni(OH)₂/PVDF composite possessed the highest relative permittivity (16.3), breakdown strength (421 kV mm⁻¹), and energy density (17.3 J cm⁻³).⁹³  Through finite element simulation, Pan et al. confirmed that P(VDF-HFP)-based nanocomposite films with 2D NaNbO₃@Al₂O₃ platelets could endure a higher applied electric field than nanocomposite films with 2D NaNbO₃ platelets, as shown in Figure 1.26.⁷²  To better understand the electrical breakdown mechanism of nanocomposite films with 3 vol% 2D NN Ps and 2D NN@AO Ps, finite element simulations were performed. To determine a more exhaustive electric field distribution of nanocomposite films with 2D NN Ps and 2D NN@AO Ps, the cross-sectional images (Z–X, Z–Y, and Z–Z axes) are shown in Figure 1.26(c–h). Highly distorted regions in the electric field are observed between the adjacent nanofiller regions along the direction perpendicular to the electric field. The local electric field distortion of 2D NN Ps/P(VDF-HFP) nanocomposite films is greater than that of the NN@AO Ps/P(VDF-HFP) nanocomposite films. Therefore, the finite element simulation confirms that the breakdown field of such nanocomposite films could be improved by adding 2D NN@AO Ps. Furthermore, the highly insulating Al₂O₃ shell could alleviate the electric field concentration because the relative permittivity of Al₂O₃ (∼11) was similar to that of the polymer matrix (∼9.76), leading to the formation of a buffer layer between the high-ε_r NaNbO₃ platelets and the polymer matrix.

The electrostatic breakdown propagation of dielectric materials is complex; however, the use of a phase-field model is a good approach to understand the breakdown behaviour arising from electrostatic stimuli.⁹⁴  The model considers that the complete breakdown path of the composite is similar to the process of crack propagation, although it incorporates electric energy, gradient energy, and phase separation energy. The calculation process was described in detail by Shen's group as follows.⁹⁵  In the phase-field model, a continuous phase-field variable η(r, t) is introduced to record the electrothermal damage distribution in the nanocomposite, in which η(r, t) = 1 is the breakdown phase, η(r, t) = 0 is the non-breakdown phase, and the diffuse transitional region is the interface area. In the dielectric inhomogeneous system, the free energy, which is related to the phase separation, the interface, the temperature, and the electric field, can be expressed by

A modified Allen–Cahn equation was used to display the breakdown phase evolution,

where L₀ represents the kinetic coefficient referred to the interface mobility, H(f_elec − f_critical) represents the Heaviside unit step function (H(f_elec < f_critical) = 0 and H(f_elec > f_critical) = 1), and f_critical represents a position-dependent material constant referring to the maximal energy density of each component in the nanocomposite. In addition, the Heaviside function was introduced into the Allen–Cahn equation in order to assure the growth of breakdown phase only if the electric energy of a local point is greater than its maximal energy endurance. The spectral iterative perturbation method is used to gain the electric field distribution during the microstructure evolution process.

Through a continuum phase-field model, the microstructural effects on the effective relative permittivity, breakdown strength, and the energy density of polymer nanocomposites can be systematically studied, including the shape, orientation, and volume fraction of the nanofiller. In addition, in the case of a sandwich/multilayer-structured nanocomposite, phase-field simulation has also been used effectively to analyse the spatial distribution of the electric field in the nanocomposites. For example, Yang et al. studied the breakdown phase evolution of five types of 3D nanocomposites containing vertical nanofibres (S1), vertical nanosheets (S2), random nanoparticles (S3), parallel nanofibres (S4), and parallel nanosheets (S5).⁹⁶  Based on the results of simulation, the nanocomposite with vertical nanofibres (S1) is the easiest to break down, and the nanocomposite with parallel nanosheets (S5) is the hardest to break down. Moreover, according to the high-throughput calculation, Yang et al. designed the sandwich microstructure based on PVDF–BT nanocomposite in which the upper and lower layers were filled with parallel nanosheets and the middle layer was filled with vertical nanofibres. The results showed that the energy density of the nanocomposite was 2.44 times larger than that of pure PVDF polymer. Recently, Zeng and Nan et al. fabricated a series of single-layer and multilayer-structured P(VDF-HFP)-based nanocomposites with parallel BNNSs as the nanofiller.⁹⁷  The detailed structures of the nanocomposites and the simulated spatial distribution of the electric field are presented in Figure 1.27. The results of phase-field simulation implied that the 12L (12-layer) structured nanocomposites produced the most homogeneous spatial distribution of electric field compared with other structured nanocomposites, which benefits suppression of dielectric loss. The multilayer-structured nanocomposites containing a multi-interfacial region can effectively block the growth of electrical trees, and thus improve the breakdown strength and energy density. These results indicate that developing phase-field models and performing high-throughput calculations help the design of polymer nanocomposites with high storage properties and potential architectures.

More importantly, a comprehensive electrical–thermal–mechanical breakdown phase-field model was developed to study the breakdown process of polymer-based dielectrics by Yang et al.⁹⁸  Taking the P(VDF-HFP) as an example, the electrical, thermal, and mechanical effects on the breakdown strength were studied via parameterising the permittivity, electrical conductivity, and Young's modulus. The results showed that when incorporating electric, Joule heat, and strain energies, the phase-field model could predict breakdown strengths (E_b^{elec + Joule + strain}) of P(VDF-HFP) that were consistent with experimental measurements in the specified temperature range (295–363 K) (see Figure 1.28(a)). In addition, the breakdown strength of P(VDF-HFP)-based nanocomposites with 5 vol% nanofillers calculated from high-throughput phase-field simulations with different permittivity, electrical conductivity, and Young's modulus are shown in Figure 1.28(b). As shown, the breakdown strength is more related to the electrical conductivity than to the permittivity and Young's modulus.

Overall, the development of phase-field models and high-throughput calculations helps the design of polymer nanocomposites for high energy storage properties.

Polymer-based composites with 2D fillers, such as nanosheets and nanoplatelets are promising for high energy density capacitor applications. The synthesis methods of 2D nanosheets and nanoplatelets are introduced, including the hydrothermal/solvothermal method, molten salt method, and exfoliation method. The thickness of the synthesised 2D nanosheets and nanoplatelets ranges from nano- to micrometres. The 2D ceramic platelets tend to align in the perpendicular direction to the surface of the composite film with tape-casting treatment. Therefore, the polymer-based composites with 2D fillers can produce outstanding properties, such as high breakdown strength, low dielectric loss, and high energy density. Finite element simulation and phase-field simulation are useful methods to determine the polarisation and electric field distribution in the composites, and provide guidance for material design. The incorporation of 2D nanosheets and nanoplatelets into polymer matrices is an effective route to achieve high energy density capacitors.

The authors gratefully acknowledge support from National Natural Science Foundation of China (51672311), Hunan Natural Science Foundation (2019JJ40349), Science and Technology Project of Hunan Province, China (2016WK2022), and State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China.