# Development and Validation of a Capacitor-Current Circuit Model for Evaporation-Induced Electricity
## 4 Results and Discussion
### Model Fitting Results
Future work will aim to include comprehensive statistical analyses to further validate the findings. To evaluate the effect of individual parameters in the capacitor-current circuit model, a sensitivity analysis was conducted. The key output parameters--initial current peak \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Standard Error** & **Description** \\ \hline \(I_{\text{steady}}\) & 9.832 \(\mu\)A & \(\pm 0.003\)\(\mu\)A & Steady-state current \\ \hline \(I_{0}\) & 16.168 \(\mu\)A & \(\pm 0.044\)\(\mu\)A & Initial current peak amplitude \\ \hline \(\tau\) & 621.395 s & \(\pm 1.620\) s & Time constant \\ \hline Reduced Chi-Square & 0.293 & — & Goodness of fit measure \\ \hline \(R^{2}\) & 0.934 & — & Coefficient of determination \\ \hline Adjusted \(R^{2}\) & 0.934 & — & Adjusted coefficient of determination \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of fitted parameters for the simplified capacitor–current model along with goodness-of-fit measures. Figure 7: Short-circuit current vs. time (black) with fitting line (red) using the simplified capacitor–current model. (\(I_{0}\)), steady-state current (\(I_{\text{steady}}\)), and time constant (\(\tau\))--depend on the capacitance (\(C\)), internal resistance (\(R_{\text{int}}\)), and initial voltage (\(V_{0}\)) as expressed in the following relationships:  
1. \(I_{0}=\frac{V_{0}}{R_{\text{int}}}\)
2. \(I_{\text{steady}}=\frac{V_{0}}{R}\)
3. \(\tau=R_{\text{int}}C\)  
Our analysis reveals:  
For the capacitance (\(C\)), increasing \(C\) extends the time constant \(\tau\), leading to slower current decay and longer charge retention. Materials with higher dielectric constants or greater surface areas enhance device performance. For the internal resistance (\(R_{\text{int}}\)), a higher \(R_{\text{int}}\) increases \(\tau\), promoting better retention but reducing \(I_{0}\). Optimizing \(R_{\text{int}}\) involves balancing peak current with retention. For the initial voltage (\(V_{0}\)), a higher \(V_{0}\) proportionally increases \(I_{0}\) and \(I_{\text{steady}}\), emphasizing the importance of effective charge buildup. These findings are illustrated in Figure 8 which show the dependence of the time constant on capacitance for different values of \(R_{\text{int}}\) and the effect of \(R_{\text{int}}\) on current parameters. This analysis underscores the interplay between model parameters and their effect on device performance. Therefore, based on the above model fitting, we can obtain some physical insights about how to enhance device performance. To be specific, we should increase the current output and suppress the current leakage at the same time. As a result, we should increase the capacitance and decrease internal resistance by carefully modifying the material properties. The developed capacitor-current circuit model is based on the principles of ion transport and charge storage, which are broadly applicable to a range of materials with porous structures or aligned microchannels. This includes other wood-based materials, synthetic polymers, and ceramics with similar electrokinetic properties. However, the model has limitations when applied to materials with significantly different surface chemistries or conductivity levels. For instance, materials that undergo dynamic changes during operation, such as swelling or chemical reactions, may require additional factors to be incorporated into the model. Further studies are needed to validate and adapt the model for these cases. High capacitance allows the device to store great amounts of charge, enhancing the peak current and prolonging the time before significant current decay occurs. Hence, in practice, we suggest that the use of materials with a high dielectric constant and a high surface area to increase capacitance. At the same time, we also need to optimize the material  
Figure 8: Time constant vs. capacitance and steady-state current vs. internal resistance.