The Effect of Self-Discharge on the Performance of Symmetric Electric Double Layer Capacitors: Insights from Mathematical Modeling and Simulation

Varieties of symmetric electrochemical capacitors ECs models have been presented in the literature [1-12], but none was derived and solved subject to a particular mechanisms or amalgamation of distinct mechanisms of self-discharge. All the existing models were built on the assumption that the electrodes or the capacitor does not have self-discharge, in order to either simplify the models or to facilitate a solution of the models.

Motivated by this knowledge gap, we have developed a generalized mathematical model of symmetric electric double layer capacitors (EDLCs) that incorporates the self-discharge effect during charging and discharging of the electrochemical device.     This model is generic and applies to any symmetric EDLC using specific self-discharge mechanism or a combination of different self-discharge mechanisms applicable in EDLCs. Analysis and simulations were carried out on the model with self-discharge effects and the model without self-discharge. It was found from the analysis that the model with self-discharge took longer time to charge the capacitor to the designed voltage than the model without self-discharge. Also, the model with self-discharge discharges the stored energy faster than the model without self-discharges. The self-discharge current I_selfdis and energy loss due to self-discharge E_selfdis during charge and discharge processes of the capacitor with electrode’s effective conductivity α₁=0.05 S/cm are 0.786 A and 9.73 Wh, respectively. A fully charged capacitor with self-discharge and electrodes effective conductivity α₁=0.05 S/cm on storage takes 7.2 days for the capacitors to be fully discharged by self-discharge process. The energy efficiency of the first and second charge–discharge cycle and  for the capacitor with self-discharge and with electrodes effective conductivity α₁=0.05 S/cm are 64.62 % and 64.63 % while those for same capacitor without self-discharge are 84.241 % and 84.244 %, respectively.

In summary, we prove from our models that the charging, discharging and storage time of the symmetric ECs significantly depend on self-discharge. In this presentation, we will show that the effect of self-discharge is so enormous to be ignored as exemplified in the presentations, where the potential profile φ_ne/pe for the electrodes with and without self-discharge effect as a function of position after charging and discharging by constant current with different parameters of α₁ and α₂. 

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