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The electronic density of states and its contribution to the capacitance of graphene compounds (oxidized and reduced) were investigated using an electrochemical impedance-derived capacitance spectroscopic approach. It is clearly demonstrated that graphene oxide, which is known to exhibit semiconductor electronic characteristics, has little influence on the magnitude of the measured capacitance. Moreover, when graphene oxide is electrochemically reduced to graphene, the capacitance increases dramatically by about three orders of magnitude (from microfaradays to millifaradays). This increased capacitive effect has been interpreted as being directly associated with the electrochemical non-faradaic (super- or ultracapacitive) characteristics of the interface (i.e. associated with its electroactive area, for instance). The results obtained and interpretation made in this work demonstrate that the magnitude of the measured capacitance is a consequence of an electrochemical capacitive phenomenon (mesoscopic in essence; thus, the associated capacitance is equivalently termed mesoscopic capacitance) that energetically contains, in series, both electrostatic (geometrical) and quantum effects, thus being essentially different from those exclusively related to the amount of existing interfacial sites for ions (i.e. beyond those associated with pure double-layer capacitive effects). Conceptually, it is proposed that the mesoscopic capacitance of reduced graphene can be explained mainly through quantum chemical effects, ultimately following first-principles quantum mechanics supported on density functional theory, wherein the density of states is central.

Mesoscopic behaviour of multi-layered graphene: the meaning of supercapacitance revisited