The Effect of Self-Discharge on the Performance of Symmetric Electric Double Layer Capacitors: Insights from Mathematical Modeling and Simulation
Authors: Ike Innocent Sunday 
Published: February 2020

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 Iselfdis and energy loss due to self-discharge Eselfdis 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 φne/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.

References

[1]. C. Lin, J. A. Ritter, B. N. Popov, and R. E. White, J. Electrochem. Soc., 146, 3168 (1999).
[2] V. Srinivasan and J. W. Weidner, J. Electrochem. Soc., 146, 1650 (1999).
[3] C. Lin, B. N. Popov, and H. J. Ploehn, J. Electrochem. Soc., 149, A167 (2002).
[4] S. A. Kazaryan, S. N. Razumov, S. V. Litvinenko, G. G. Kharisov, and V. I. Kogan, J. Electrochem. Soc., 153, A1655 (2006).
[5] J. A. Stasera, and J. W. Weidner,
J. Electrochem. Soc., 161(8) E3267-E3275 (2014).
[6] Verbrugge, M.W. and Liub P., J. Electrochem Soc., 152 (5) (2005) D79-D87.
[7] V. Srinivasan, J. W. Weidner, and R. E. White, J. Solid State Electrochem., 4, 367 (2000).
[8] K. Somasundaram, E. Birgersson, and A. S. Mujumdar, J. Electrochem. Soc., 158, A1220 (2011).
[9] G. Sikha, R. E. White, and B. N. Popov, J. Electrochem. Soc., 152, A1682 (2005).
[10] B. Pillay and J. Newman, J. Electrochem. Soc., 143, 1806 (1996).
[11] D. Fan and R. E. White, J. Electrochem. Soc., 138, 2952 (1991).
[12] H. Kim, B. N. Popov, and R. E. White, J. Electrochem. Soc., 150 (9) (2003) A1153-A1160.