A Mathematical Model of Oxide/Carbon Composite Electrode for Supercapacitors

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. RuO₂/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 RuO₂ 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 RuO₂ decreases. Finally, the present model successfully provides a methodology to optimize cell configurations and operating conditions.