▎ 摘　　要

Capacitive double-layer expansion is a promising technology to harvest energy arising from the salinity difference between freshwater and seawater. Its optimal performance requires a careful selection of the operation potentials and electrode materials. While carbonaceous materials such as graphene and various forms of activated carbons are routinely used as the electrodes, there is little knowledge on how the quantum capacitance and the electric double-layer (EDL) capacitance, which are on the same order of magnitude, affect the capacitive performance. Toward understanding that from a theoretical perspective, here we study the capacitive energy extraction with graphene electrodes as a function of the number of graphene layers. The classical density functional theory is joined with the electronic density functional theory to obtain the EDL and the quantum capacitance, respectively. The theoretical results show that the quantum capacitance contribution plays a dominant role in extracting energy using the single -layer graphene, but its effect diminishes as the number of graphene layers increases. The overall extracted energy is dominated by the EDL contribution beyond about four graphene layers. Electrodes with more graphene layers are able to extract more energy at low charging potential. Because many porous carbons have nanopores with stacked graphene layers, our theoretical predictions are useful to identify optimal operation parameters for capacitive energy extraction with porous electrodes of different wall thickness.