## 4 High-\(k\) Dielectric Nanocomposites  
The dispersed conducting nanoparticles inside the insulating dielectric matrix phase can be explained by the percolation theory. The theory very well explains the variation of dielectric constant in the heterogeneous systems (see Figure 5). The dielectric constant values slowly increase and reach the maximum value at the percolation threshold (\(P_{\rm t}\)). Where the conducting phase was separated by the optimal distance from the insulating dielectric phase, at the \(P_{\rm t}\) point, the capacitive behavior of the nanocomposites can be noticed with excellent charge storage capability. The inhomogeneous distribution of the electric field inside the heterogeneous nanocomposites can dramatically increase the dielectric constant values [137]. [PERSON], et al. recently explored the high-\(k\) percolative nanocomposites based on multi-walled carbon nanotubes (MWCNT) and PVC [138]. The authors noticed a sharp change in the dielectric constant of the PVC nanocomposites, even with a small loading of MWCNT (4-wt%) to PVC. The heterogeneous MWCNT/PVC nanocomposite with 4% MWCNT concentration exhibited the dielectric constant of 13,066. Typically, homogenously dispersed ZnO nanoparticles in high-\(k\) resin (styrene-butadiene block copolymer, commercially known as K-Resin(r) KR20) were used for gate dielectric, with the aim of enhancing the dielectric permittivity [139]. [PERSON], et al. testified the dielectric performances of raspberry-shaped iron oxide (Fe\({}_{3}\)O\({}_{4}\)) nanoparticles incorporated in PDMS, magnetite-rich PDMS nanocomposites showing a dielectric constant of 9.0 for a maximum loading of 60 wt% [140]. The authors specified the enhanced piezoelectric properties after embedding the iron oxide nanoparticles in the dielectric silicone matrix [140]. The dielectric constant values of some selected high-\(k\) nanocomposites are listed in Table 3.  
Figure 5: Sketch representing the percolation theory model, where \(P_{\rm t}\) = percolation threshold. Barium titanate (BaTiO\({}_{3}\)), a well studied ferroelectric ceramic material exhibiting piezoelectric properties has broadly been used in energy storage and capacitor applications. From Table 3, we can determine that a high dielectric constant of 108.0 was achieved by loading nanowires of BaTiO\({}_{3}\) in P(VDF-TrFE-CFE). A loading of 50-wt% of surface modified BaTiO\({}_{3}\) by PVP to PVDF matrix can result in a \(>\) 80.0 dielectric constant. The strontium-doped BaTiO\({}_{3}\) shows comparably less dielectric constant (18.0) but with minimal (7.5-wt%) loading to PVDF. However, a very small volume fraction of Nickel to BaTiO\({}_{3}\) has drastically improved the dielectric constant of PVDF composites to a maximum of 800.0. We can also notice that with a minimum loading (3-wt%) of silicon dioxide to the DGE-BA polymer improved the dielectric constant to 11.4. Consequently, one should note the salient features of high-\(k\) nanoparticles, compositions of high-\(k\) dielectric polymeric matrix and other synthetic parameters, which open up a plethora of applications in organic electronics by tuning the dielectric properties. With the advent of flexible electronics and advanced organic electronic power systems, practical applications for fabricating flexible polymeric dielectric nanocomposites became a more serious goal. The inclusion of multi-dimensional nano-fillers into dielectric polymers makes them desirable to use exclusively in the energy-storage applications [150; 151; 152]. Besides ceramic-based composites, the recent studies on polymer-based nanocomposites provide more advantage options for tuning desirable dielectric properties, low-temperature processability, mechanical flexibility with economically low-cost benefits. The acquired high-\(k\) material candidates find their active use in embedded capacitor applications [153; 154].