The optimal energy density of electrochemical capacitors using two different electrodes

Formulas describing the energy density of electrochemical capacitors, which consist of two different capacitive electrodes, were derived. From these formulas, optimal mass ratio of two electrodes and the maximum energy density of the capacitor can be obtained based on the oxidation and reduction current densities of positive and negative electrodes, respectively, from cyclic voltammetric (CV) measurements. For some practical systems, including activated carbon in aqueous and nonaqueous electrolytes, anhydrous and hydrous ruthenium oxides in aqueous electrolyte, it was calculated numerically that the maximum energy density at the optimal mass ratio was only a fractional percentage higher than those with two identical electrodes. A relationship of the maximum energy density to the ratio of two electrodes' masses and the ratio of oxidation and reduction currents was developed. It was determined that the energy density is insensitive to the mass ratio of two electrodes. For example, when the current density ratios of two electrodes are 2 and 4, the maximum energy densities at optimal mass ratio are only 3 and 11% greater than those with identical electrodes, respectively. However, it was determined that the energy density estimation based on CV curves is sensitive to the potential range of CV measurements. The actual energy density of a capacitor made with activated carbon and aqueous electrolyte is only 42% of the energy density estimated based on the CV curve in whole-range potential. The effects of electrolyte mass and operational voltage to the optimal mass ratio and the maximum energy density are also discussed.