# Prospects for the Development of High Energy Density Dielectric Capacitors
## 4 Application of the Analysis to Capacitor Design  
The analysis in Section 3 has been applied to prepare an Excel model for the design of dielectric capacitors having specific characteristics. The Excel model permits the rapid calculation of cell characteristics for any inputs of interest. Models were prepared for both spherical and platelet carbon elements. The first step in the model preparation was to calculate the characteristics of a 1 m\({}^{2}\) section of the cell for which the characteristics of a  
The outputs of the Excel models indicate that the spiral wound dielectric cell can have an energy density close to that of lithium batteries if the carbon elements are 1-3 nm and the thickness of the dielectric cell winding is 3-4 \(\mu\) for a cell voltage of 1000 V. The power of the cell will be very high (MW/L) at very high efficiency (99%). The resistance of the cell will be due mainly to the thin aluminum layers (100 nm) distributing the electrical current to the dielectric winding. The detailed characteristics of two cell designs are shown in Table 2. The performance results shown in Tables 3 and 4 indicate the energy density is a strong function of the carbon element and cell winding dimensions. The dielectric constant ratio (\(\varepsilon_{2}/\varepsilon_{1}\)) is proportional to \(\delta/\text{r}_{\text{P}}\). The host polymer should have a high dielectric constant (\(\varepsilon_{1}\)) and breakdown strength (V/\(\upmu\)). Polvinylidene Fluoride (PVDF) seems like a good choice for the host polymer. According to a plastics spec sheet [9], \(\varepsilon_{1}=7.5\)-13.2 and the dielectric \begin{table}
\begin{tabular}{c c c} \hline
**Elements.** & **Spherical** & **Platelets** \\ \hline Total weight kg & 1.275 & 1.28 \\ \hline Wh/kg & 178 & 256 \\ \hline Breakdown V/\(\upmu\) & 250 & 333 \\ \hline Resistance mOhm & 4.2 & 3.3 \\ \hline Max. Power 99\% eff. kW & 1314 & 1672 \\ \hline kW/L 99\% eff. & 1030 & 1305 \\ \hline kW/kg 99\% eff. & 1635 & 2080 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline
**Vol. Frac.** & & & **Host Polymer** & **Host Polymer** \\ \(\mathbf{f_{v}=0.2}\) & & & \(\mathbf{\hat{c}_{r}=4}\) & \(\mathbf{\hat{c}_{r}=8}\) \\ \hline \multirow{4}{*}{Voltage} & Dielectric & & & \\  & Thick break & Element radius & & \\  & \(\upmu\) down & \(\ldots\) & \(\mathrm{nm}\) & Cell Wh/kg & Cell Wh/kg \\  & \(\mathrm{V/\upmu}\) & & & \\ \hline
1000 & 5 & 200 & 3 & 135 & 271 \\ \hline \multirow{4}{*}{Voltage} & & & 5 & 81 & 162 \\ \cline{2-5}  & & & 10 & 40 & 80 \\ \hline \multirow{4}{*}{Voltage} & 10 & 100 & 3 & 67 & 135 \\  & & & 5 & 41 & 82 \\ \hline \multirow{4}{*}{1000} & \multirow{4}{*}{5} & 10 & 20 & 40 \\  & & & & \\ \cline{1-1} \cline{3-5}  & & & 5 & 27 & 54 \\ \hline \multirow{4}{*}{500} & \multirow{4}{*}{5} & 10 & 13 & 27 \\ \cline{1-1} \cline{3-5}  & & & 10 & 13 & 27 \\ \cline{1-1} \cline{3-5}  & & & 5 & 20 & 40 \\ \hline \multirow{4}{*}{10} & \multirow{4}{*}{50} & \multirow{4}{*}{3} & 10 & 10 & 20 \\ \cline{1-1} \cline{3-5}  & & & 5 & 10 & 20 \\ \cline{1-1} \cline{3-5}  & & & 10 & 5 & 10 \\ \cline{1-1} \cline{3-5}  & & & 10 & 5 & 10 \\ \hline \multirow{4}{*}{15} & \multirow{4}{*}{33} & \multirow{4}{*}{3} & 11 & 22 \\ \cline{1-1} \cline{3-5}  & & & 5 & 7 & 14 \\ \cline{1-1} \cline{3-5}  & & & 10 & 3.5 & 7 \\ \hline \end{tabular}
\end{table} 
Table 3: Dielectric cell Wh/L using spherical carbon elements and host polymer. strength = 260-950 V/\(\mu\). Data for other polymers are given Table 5 taken from [48]. It is clear from Table 5 that selection of a host polymer will involve the trade-off of several performance characteristics (dielectric constant, conductivity, loss tangent, and breakdown strength). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Vol. Frac.