Modelling and Optimization of Electrodes Utilization in Symmetric Electrochemical Capacitors for High Energy and Power
Authors: Ike Innocent Sunday , Iyuke Sunny E , Sigalas Iakovos Jack 
Published: February 2020

Low energy density of existing electrochemical capacitors (ECs) limits their general application [1–4]. Best EC performance in terms of gravimetric energy and power densities are achieved when electrodes of low density are used and only electrodes mass were taken as mass of the device because large, non-tortuous pores and low solution resistances make conduction of electrolyte ions faster [5–8], but energy and power values based on mass of electrodes and electrolyte are more practical/realistic [9–11]. Values of high density electrodes have been recently presented by various researchers [12–16], but effects of electrodes density on energy and power densities was studied by Merrill at al[17] and presented that lowering cell’s mass with smaller electrolyte fraction using high electrode density is as effective as using electrolytes with wider working potential range [17]. Also, specific capacitance and specific energy of device with given electrodes thickness, and electrodes and electrolyte effective conductivities decreases along with increase in current density, while specific power increases [18].
In order to achieve higher energy densities per device mass with high electrode densities while retaining greater power, expressions and guidelines for determination of electrode effective thickness, optimum charging current density and electrode utilization in device with certain electrodes and electrolyte effective conductivity were developed, and used systematically to study performance of capacitors. Effective thickness of electrode increases along with increase in effective conductivity of electrolyte and decreases with increase charging current density. Every current density applied to device of specific electrode and electrolyte effective conductivity has corresponding electrodes effective thickness, and when charged at current density higher than its maximum, materials (electrodes) utilization was less than 100%. Also, when device with electrodes thickness higher than the effective thickness was charged at its maximum current density, materials (electrodes) utilization reduced below 100%. Materials utilization decreases along with increase in current density and electrode thickness, but increases as effective conductivity of electrode and electrolyte are increase. Therefore, optimum/effective thickness of electrode and optimum current density must be employed in charging device of given electrode and electrolyte effective conductivity for maximum materials utilization and performance (with minimum or no potential drop). Optimum current density beyond which energy density decays increases along with increase in electrode and electrolyte effective conductivity and decrease in electrode thickness. Use of optimum current density and effective electrode thickness to maximize energy and power densities is inevitable, because increase in current density results in increase in power density and decrease in energy density.

Key words:Electrode thickness; Current density; Effective conductivity; Modelling and simulation; Electrode utilization; and Potential drop.

References

1. G. Wang, L. Zhang, and J. Zhang, Chem. Soc. Rev. 41, 797 (2012).
2. C. Liu, Z. Yu, D. Neff, A. Zhamu, and B. Z. Jang, Nano Lett. 10, 4863 (2010).
3. M. Epifani, T. Chávez-Capilla, T. Andreu, J. Arbiol, J. Palma, J. R. Morante, and R. Díaz, Energy Environ. Sci. 5, 7555 (2012).
4. K. Fic, G. Lota, M. Meller, and E. Frackowiak, Energy Environ. Sci. 5, 5842 (2012).
5. C. Du, J. Yeh, and N. Pan, Nanotechnology 16, 350 (2005).
6. C. Niu, E. K. Sichel, R. Hoch, D. Moy, and H. Tennent, Appl. Phys. Lett. 70, 1480 (1997).
7. C. Emmenegger, P. Mauron, P. Sudan, P. Wenger, V. Hermann, R. Gallay, and A. Züttel, J. Power Sources 124, 321 (2003).
8. L. Basiricò and G. Lanzara, Nanotechnology 23, 305401 (2012).
9. A. Lewandowski and M. Galinski, J. Power Sources 173, 822 (2007).
10. L. L. Zhang and X. S. Zhao, Chem. Soc. Rev. 38, 2520 (2009).
11. R. Kötz and M. Carlen, Electrochimica Acta 45, 2483 (2000).
12. Y. J. Kim, C.-M. Yang, K. C. Park, K. Kaneko, Y. A. Kim, M. Noguchi, T. Fujino, S. Oyama, and M. Endo, ChemSusChem 5, 535 (2012).
13. T. Kim, G. Jung, S. Yoo, K. S. Suh, and R. S. Ruoff, ACS Nano 7, 6899 (2013).
14. J. Hu, Z. Kang, F. Li, and X. Huang, Carbon 67, 221 (2014).
15. Y. Tao, X. Xie, W. Lv, D.-M. Tang, D. Kong, Z. Huang, H. Nishihara, T. Ishii, B. Li, D. Golberg, F. Kang, T. Kyotani, and Q.-H. Yang, Sci. Rep. 3, (2013).
16. X. Yang, C. Cheng, Y. Wang, L. Qiu, and D. Li, Science 341, 534 (2013).
17. M. D. Merrill, E. Montalvo, P. G. Campbell, Y. M. Wang, M. Stadermann, T. F. Baumann, J. Biener, and M. A. Worsley, RSC Adv. 4, 42942 (2014).
18. I. S. Ike, I. Sigalas, and S. E. Iyuke, Phys. Chem. Chem. Phys. 18, 28626 (2016).