# The Simulation of Dielectric Barrier Discharge for Breakdown Voltage in Starch Modification
## 3 Results and Discussion
### Effect of Starch Relative Permittivity  
In this section, we studied the impact of the relative permittivity of starch on the breakdown voltage. Table 3 shows the findings of simulations using parallel plate electrodes and mesh-plate electrodes, with gap distances between the electrodes of 0.2 and 1.0 cm at pressure 760 torr. The starch had a spherical shape, 150-micron diameter, and relative permittivity values of 3.1, 5.2, and 7.5, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Gap Distance (cm)**} & \multirow{2}{*}{_pd_**} & \multicolumn{6}{c}{**Breakdown Voltage (V)**} \\ \cline{3-8}  & & & \(\varepsilon_{r}\) = 3.1 & \multicolumn{2}{c}{\(\varepsilon_{r}\) = 5.2} & \multicolumn{2}{c}{\(\varepsilon_{r}\) = 7.5} \\ \cline{3-8}  & & **Plate** & **Mesh** & **Plate** & **Mesh** & **Plate** & **Mesh** \\ \hline
0.2 & 152 & 6006 & 5659 & 5854 & 5514 & 5746 & 5412 \\
0.3 & 228 & 7307 & 7185 & 7181 & 7062 & 7091 & 6974 \\
0.4 & 304 & 8865 & 8701 & 8758 & 8607 & 8600 & 8455 \\
0.5 & 380 & 10,570 & 10,369 & 10,435 & 10,237 & 10,225 & 10,050 \\
0.6 & 456 & 11,968 & 11,749 & 11,853 & 11,646 & 11,748 & 11,552 \\
0.7 & 532 & 13,464 & 13,221 & 13,363 & 13,134 & 13,289 & 13,050 \\
0.8 & 608 & 14,947 & 14,662 & 14,845 & 14,578 & 14,772 & 14,524 \\
0.9 & 684 & 16,399 & 16,086 & 16,294 & 16,012 & 16,230 & 15,958 \\
1.0 & 760.0 & 17,839 & 17,473 & 17,741 & 17,404 & 17,670 & 17,352 \\ \hline \hline \end{tabular}  
* Plate means the parallel plate electrode. Mesh means the mesh electrode with a mesh size of 1.5 cm\({}^{2}\).  
\end{table} 
Table 3: The breakdown voltage of different starch relative permittivity levels at pressure 760 torr. Figure 10: The Paschen curve of the four top electrodes. The mesh electrode can help to apply a lower voltage than typical electrodes for the same relative permittivity value because mesh electrodes have a stronger electric field than plate electrodes. The breakdown voltage of the mesh electrode is approximately 5-10% less than the breakdown voltage for the typical electrode at a small gap (\(pd\) = 152 torr cm), while at a large gap (\(pd\) = 760 torr cm), it is about 2-3%. The breakdown voltage increased with an increase in gap distance. Furthermore, simulation results show that the breakdown voltage decreases as the relative permittivity of starch increases for both electrode types. For instance, the polarization of the mesh electrode was 1.69 \(\times\) 10\({}^{-5}\) C/m\({}^{2}\), whereas the usual electrode is 1.56 \(\times\) 10\({}^{-5}\) C/m\({}^{2}\) at voltage 5000 V, gap 0.2 cm, and relative permittivity 3.1. The plate electrode's polarization varies depending on the relative permittivity, from 3.1 to 5.2 and 7.5, respectively, and was 1.56 \(\times\) 10\({}^{-5}\), 1.82 \(\times\) 10\({}^{-5}\), and 1.95 \(\times\) 10\({}^{-5}\) C/m\({}^{2}\). The polarization of the mesh electrode was 1.69 \(\times\) 10\({}^{-5}\), 2.14 \(\times\) 10\({}^{-5}\), and 2.30 \(\times\) 10\({}^{-5}\) C/m\({}^{2}\), and it varied with the relative permittivity from 3.1 to 5.2 and 7.5, respectively. The increase in polarization was consistent with the increase in the electric field [47]. When an external electric field is applied to a starch molecule, the charges bound in each molecule will respond to the applied field, which will result in the redistribution of charges, leading to a polarization of the starch [48]. The polarization that occurred from simulation in this work is a macroscopic quantity because it involves averaging the dipole moments over a volume containing many dipoles. We assumed that the polarization of the system response to the applied field is linear. Figures 11 and 12 illustrate the Paschen curve of each relative permittivity result using the information from Table 3.  
The simulation results and Figure 11 show that when the starch has a relative permittivity of 3.1, 5.2, and 7.5, the breakdown voltage of the mesh electrode in the case of a small gap (\(pd\) = 152 torr cm) is lower than that of the parallel plate electrodes, by about 5.6%.