# Carbon Allotropes/Epoxy Nanocomposites as Capacitive Energy Storage/Harvesting Systems
## 3 Results and Discussion
### Energy Storage and Harvesting
#### 3.3.2 DC Measurements  
The calculation of the of the stored and retrieved energy was performed by integrating the time-dependent current functions, under charging and discharging conditions, via Equation (3):  
\[\text{E}=\frac{1}{2}\frac{\text{Q}^{2}}{\text{C}}=\frac{1}{2}\frac{\left(\int \text{I}(\text{t})\text{dt}\right)^{2}}{\text{C}}, \tag{3}\]  
where E is the stored energy at the capacitor, Q the charge and C is the capacitance of each nanocomposite as evaluated via the BDS measurements at the lowest frequency [12]. A more detailed insight into the rationale and the methodology can be found in [8; 12]. Figure 7 depicts representative graphs of the stored and harvested energies for the nanocomposite systems with 3 phr filler content. The success of the energy storage/harvesting process is confirmed in the above diagrams for all examined systems. All charging curves are above the corresponding discharge curves. Systems quickly acquire high charging and discharge values (fast charge/discharge)--a characteristic feature of instantaneous power density capacitive systems. This ability to store and deliver a large amount of energy nearly instantaneously, sometimes called \"pulse power\", cannot be delivered by storage technologies such as batteries and has potential applications in numerous commercial and military devices that require increased power density as well as higher charge/discharge current capabilities. The stored and recovered energies increase significantly with increasing voltage since the applied field lowers the local potential barriers, thus facilitating the migration of the charges inside the nanocomposites. Figure 7: The stored and harvested (discharging procedure) energies as a function of time and voltages for the nanocomposites with 3 phr: (**a**) CB; (**b**) MWCNT; (**c**) GnP; (**d**) ND content. Figure 8 presents the comparative plots for the stored and retrieved energies for all examined systems at 100 V. Both energies increase with filler content due to the enhanced electrical properties of the carbonaceous nanoparticles compared to the polymer matrix as well as the interfacial effects due to the heterogeneity of the systems. It should be noted that, for the carbon black and MWCNT systems, above a critical concentration, reported as the percolation threshold in a previous study [16], the nanocomposites transition from the insulating to the conducting state. Therefore, no charge/discharge process could be established since the charge carriers do not accumulate inside the material but rather travel through it, either solely via a conducting path or in conjunction with hopping mechanisms [33]. However, the nanocomposite with 3 phr MWCNT concentration still exhibits the optimum performance. Another critical factor for the valuation of the nanocomposites' energy storage/harvesting performance is the calculation of the coefficient of energy efficiency (n\({}_{\text{eff}}\)), which is defined as the ratio of the recovered to stored energy with parameters the charging voltage and time [8; 12]. Figure 9 presents the results for the coefficient of energy efficiency at the same instant times of t = 5, 10 and 30 s in both charging and discharging procedures. The coefficient of energy efficiency diminishes over time for all systems, confirming once more the fast charge/discharge nature of the examined systems. n\({}_{\text{eff}}\) increases with filler content for the nanocomposites with carbon black and MWCNT filler content. The optimum energy efficiency was noted for the nanocomposite with 5 phr carbon black content with coefficient (n\({}_{\text{eff}}\)) values of 80 % at 100 V and 5 s. Unfortunately, once more, the nanocomposites  
Figure 8: Comparative plots for the harvested energy, at 100 V, versus time for the nanocomposites with (**a**) carbon Black; (**b**) MWCNT; (**c**) GnP; (**d**) ND. Insets depict the stored (charging procedure) energies as a function of time for the respective systems.