Quantum Effects on the Capacitance of Graphene-Based Electrodes

Quantum capacitance has been recently measured for electric double layers (EDL) at electrolyte/graphene interfaces. However, the importance of quantum capacitance in realistic carbon electrodes is not clear. Toward understanding that from a theoretical perspective, here we studied the quantum capacitance and total capacitance of graphene electrodes as a function of the number of graphene layers. The quantum capacitance was obtained from electronic density functional theory based on fixed band approximation with an implicit solvation model, while the EDL capacitances were from classical density functional theory. We found that quantum capacitance plays a dominant role in total capacitance of the single-layer graphene both in aqueous and ionic-liquid electrolytes but the contribution decreases as the number of graphene layers increases. The total integral capacitance roughly levels off and is dominated by the EDL capacitance beyond about four graphene layers. Because many porous carbons have nanopores with stacked graphene layers at the surface, this research provides a good estimate of the effect of quantum capacitance on their electrochemical performance.