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

Abstract

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.

Mapping the ionic fingerprints of molecular monolayers

“…In the specific case of ionic (distinguishable particles) contributions to electric field screening, the classical approximation can be applied, such that d r /d = 2 0 / and, therefore, 2 = [( ) 2 2 0 / ]/ r 0 . The Debye-Hückel model is thus confirmed to be a particular example of Tomas-Fermi predicting screening 41 and Eqn. (2) a particular application of Eqn.…”

“…The electrochemical capacitance ( ̅ ) encompasses 40,41 not only geometrical electrostatic capacitance ( ) but also non-faradaic phenomena generally including, for instance, those arising from the double layer formed on exposure of electrode interfaces to a (redox) inert electrolytic solution. The simplest representation of such interfaces considers a term as the inverse Debye length ( = 1/ ) such as…”

“…wherein is the valence number of the ions, is the elementary charge, is the relative permittivity of the dielectric environment, 0 is the dielectric permittivity of the vacuum ( 8.85 x 10 -12 F m -1 ), is the relative permittivity, is the Boltzmann constant and is the absolute temperature and finally 0 the ionic concentration in the interface (the "static" concentration of ions physically adsorbed at the surface of electrode). The associated interfacial ionic capacitance ( ) per unit area is 29 = 0 .…”

“…The simplest way to demonstrate this is to appeal to the Thomas-Fermi model, 29 a straightforward approximation of Lindhard's formulation of the electric field screening. 44 In this model the wave vector, , previously associated to the inverse of Debye length, is given by 2 = [( ) 2 d r /d ]/ r 0 , wherein it can be recognized that…”

“…[7][8][9] Many SAM-based applications are electrochemical in nature and are accordingly sensitive to structural, dynamic and electronic changes within the films, 8,[10][11][12][13][14][15][16][17][18][19][20] as well as to the effects of ionic ingress. [21][22][23][24][25] We [26][27][28][29] and others [21][22][23][24][25][30][31][32][33][34][35] have investigated the electrochemical and dielectric properties of these interfaces by employing electrochemical impedance spectroscopy (EIS) and capacitance spectroscopy (CS), the latter an impedance-derived immittance approach 10 which resolves the timedependent responses both within the organized organic components and solution phase electrolyte. 17,36 Standard EIS methods have been shown to have value in characterizing the electronic, 1, 37, 38 ionic 23, 25, 31 steric blocking effects of these insulating layers using a redox probe in solution, where both the current (in classical cyclic voltammetry) and charge transfer resistance ( , in impedimetric analysis) are responsive (usually, a concomitant decrease in current and an increase in are observed from bare electrode to SAM modified electrode.…”