A Mathematical Model of Oxide/Carbon Composite Electrode for Supercapacitors

TLDR: In this article, a pseudo-two-dimensional model for the general application of supercapacitors consisting of an oxide/carbon composite electrode was developed for the purpose of optimizing cell configurations and operating conditions.

Abstract: A pseudo two-dimensional model is developed for the general application of supercapacitors consisting of an oxide/carbon composite electrode. The model takes into account the diffusion of protons in the oxide particle by employing the method of superposition. RuO 2 /carbon system is modeled as a specific example. From the simulation data, it is found that the oxide particle size and proton diffusion coefficient have an enormous effect on the performance at high discharge rate due to the limitation of proton transport into RuO 2 particles. With increasing carbon ratio, the porosity of electrode increases, which causes the potential drop in solution phase to decrease. However, excess of carbon lowers the total capacitance because the pseudocapacitance from RuO 2 decreases. Finally, the present model successfully provides a methodology to optimize cell configurations and operating conditions.

Figures

Figure 8. Electrochemical performance of the RuO2/carbon composite electrode ~60 wt % RuO2) at different constant current discharge values.

Figure 6. Local utilization of RuO2 at the positive electrode-separator interface as a function of particle size at different discharge rates.

Figure 7. Dimensionless parameter,Sc ~diffusion in the solid/discharge time!, as a function of particle size of RuO2 . RuO2 : 40 wt %, porosity: 0.214,Ct : 0.015 mol/cm 3.

Figure 9. Electrolyte concentration distribution of the cell at the end of discharge with different current densities. RuO2 : 60 wt %, porosity: 0.181, particle size: 50 nm.

Figure 11. Potential distribution in the electrolyte at the end of discharge for different electrode porosities.

Figure 12. Discharged charge density as a function of RuO2 content and particle size of RuO2 at the constant discharge rate of 1.5 A/cm

Frequently asked questions

Q1. What have the authors contributed in "A mathematical model of oxide/carbon composite electrode for supercapacitors" ?

Except as provided under U. S. copyright law, this work may not be reproduced, resold, distributed, or modified without the express permission of The Electrochemical Society ( ECS ). The archival version of this work was published in the Journal of the Electrochemical Society. 

Q2. What causes the depletion of electrolyte in the positive electrode?

Increasing cell current density causes significant depletion of electrolyte in the positive electrode due to consumption in the faradaic reaction. 

Q3. What is the main factor for limiting the capacitor performance at high discharge rates?

The significant depletion of electrolyte that develops in the porous electrode phase is another dominant factor for limiting the capacitor performance at high discharge rates. 

Q4. What is the effect of increasing the porosity of the electrode?

Increasing the porosity has the simple effect of making the electrolyte more accessible to all the pores within the electrode thereby leading to a decrease in the concentration polarization in the cell. 

Q5. How can the authors improve the transport of the electrolyte?

To improve the transportation of the electrolyte, it is necessary to increase the porosity of electrode, which can be accomplished by increasing the carbon content in the electrode. 

Q6. What is the primary objective of the present model?

The primary objective of the present model is to study the effect of proton diffusion in the particle on the capacitor performance. 

Q7. What is the effect of particle size on the discharge energy density?

With increasing particle size, the discharge energy density falls tremendously and a sharp drop in potential at the start of discharge, which is associated with faradaic kinetic resistance, is observed. 

Q8. What is the role of particle size in the performance of the ruO2 cell?

The particle size of oxide is still a critical factor in determining the performance especially at high discharge rates because diffusion in the oxide is the limiting step. 

Q9. How is the diffusion coefficient of proton in the oxide?

According to previous studies, it is known that the diffusion coefficient of proton in the oxide is strongly dependent on factors such as oxide annealing temperature, hydration number, and the degree of crystallinity. 

Q10. How can The authoruse this model to optimize the composition of the electrode?

Figure 12 demonstrates how this model can be used to optimize the composition of the electrode at discharge rate of 1.5 A/cm2 when different particle sizes of RuO2 and carbon are physically mixed. 

Q11. How much energy density can be achieved with RuO2?

When the ratio of RuO2 is 40 wt %, nanosize of particles and high porosity are achieved, generating the highest energy density at 5 kW/kg of power load. 

Q12. What is the cost of a supercapacitor?

This data suggests that decreasing the particle size and increasing the porosity of the electrode can reduce the cost of the supercapacitor. 

Q13. What is the reason for the low porosity of the electrode?

This simulation result shows that RuO2 alone cannot be used as capacitor electrodes due to its poor rate capability resulting from the low porosity and the large particle size.