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158                Polymer-based Nanocomposites for Energy and Environmental Applications

         % (at 1 kHz). Different amounts of GNs (1–4 phr, where phr refers to pounds of GNs
         added in 100 lb of PVDF) were added to a fixed weight ratio of 80/20 of BaTiO 3 /
         PVDF. The percolation threshold for the GNs was observed to be 2.5 phr. The intro-
         duction of GNs enhanced the dielectric constant up to 492.0 (at 1 kHz) at BaTiO 3 /GN/
         PVDF¼20/3/80 with a loss tangent of 49.1, which was not suitable to use for high-
         energy-density applications. Wang et al. explored BaTiO 3 and PANI-functionalized
         GNs as fillers in the PVDF matrix [236]. For two-phase RGO/PVDF nanocomposites,
         the permittivity and the loss tangent were 300, almost 30 times that of the pure PVDF
         and  4, respectively, at the percolation threshold of 1.49 vol%. Also, the dielectric
         constant was improved with BaTiO 3 content for a given RGO fraction. Like, the
         dielectric constant was enhanced from  27 to  54 as the BaTiO 3 loading was
         increased from 10 to 30 vol% for 0.63 vol% of RGO. Same way, at RGO loading
         of 1.25 vol%, the dielectric constant was enhanced to 170 for 30 vol% BaTiO 3 loading
         in comparison with  60 at 10 vol% loading. The loss tangent of three-phase
         nanocomposite was found to be less than that of the two-phase nanocomposites,
         namely, the loss tangent of RGO/PVDF was  0.7 (at 1 kHz) at an RGO loading of
         1.40 vol%, while that of RGO/BaTiO 3 /PVDF was  0.25 (at 1 kHz) at RGO and
         BaTiO 3 loadings of 1.25 and 30 vol%, respectively. Therefore, the dielectric proper-
         ties could be tuned by changing the ratio of BaTiO 3 or RGO.
            Hence, to acquire the optimized dielectric properties, a thorough knowledge
         regarding the fillers, the matrix, and the preparation techniques is highly desired. From
         this discussion, it could be realized that the dielectric properties of the three-phase
         nanocomposites containing nanoparticles and nanofibers were improved as compared
         with those of nanoparticles and nanofibers used individually. Therefore, a lot of effort
         is imperative in the future to design three-phase dielectric nanocomposites and opti-
         mize various dielectric parameters.

         5.3.3  Titania-based polymer nanocomposites

         Titanium dioxide (TiO 2 and TO) can be found in three crystalline forms at atmo-
         spheric pressure, namely, anatase, rutile, and brookite. The rutile contains chains of
         trans-edge-sharing TiO 6 octahedra, connected by sharing corners. Contrarily, the ana-
         tase phase is a framework of distorted TiO 6 octahedra that share four edges. This struc-
         tural difference is believed to be responsible for a higher dielectric permittivity in
         rutile than in anatase phase. As mentioned earlier, it is believed that the introduction
         of high-dielectric-permittivity fillers into relatively low dielectric permittivity poly-
         mers may not be ideal to obtain an appreciable increase in the energy density of
         the composite. This is based on the belief that if the filler has a much higher permit-
         tivity than the polymer matrix and most of the increase in the effective dielectric per-
         mittivity comes through an increase in the average field in the polymer matrix, then
         very little of the energy will be accumulated in the high-permittivity filler phase [237].
         Also, a huge difference in permittivity of the polymer and filler phases generates an
         inhomogeneous electric field that substantially lowers the effective breakdown
         strength of the nanocomposite. Thus, the titania got much attention as its average
         dielectric permittivity of  47 is much closer to the permittivities of many polymer
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