Understanding the Capacitive Charge in Bulk Porous Electrodes by Mathematical Modeling

Supercapacitors exhibit immense potential in electric vehicles and national grids due to their high power density. The power and energy density of supercapacitors largely depend on the design of electrodes and the composition of electrolytes, which dominate the capacitive charging process. However, the availability of only a few mathematical models for capacitive charging in bulk porous electrodes has limited the rational design of a supercapacitor in practice. Herein, a mathematical model is proposed to predict the charging process in a porous electrode and is then experimentally validated. In this model, the dependence of capacitive behavior on the conductivity of both the electrode and electrolyte, as well as the porosity and thickness of electrode, are systematically discussed. Moreover, different charging modes, e.g., potentiostatic charging, potentiodynamic charging, and galvanostatic charging, are studied. The results of this model indicate that the conductivity of the electrolyte (even though it is an aqueous electrolyte) is the bottleneck that limits the charging rate of a supercapacitor, in particular, in thick electrode films. This mathematical model could be a powerful tool for optimizing the design of both electrodes and electrolytes for high-performance supercapacitors.