Faradaic pseudocapacitance

A persistent question regarding carbon capacitance is related to the relative contributions of Faradaic ( pseudocapacitance ) and non-Faradaic (i.e., double-layer) processes [85,87,95,187], A practical issue that may help resolve the uncertainties regarding DL- and pseudo-capacitance is the relationship between the PZC (or the point of zero potential) [150] and the point of zero charge (or isoelectric point) of carbons [4], The former corresponds to the electrode potential at which the surface charge density is zero. The latter is the pH value for which the zeta potential (or electrophoretic mobility) and the net surface charge is zero. At a more fundamental level (see Figure 5.6), the discussion here focuses on the coupling of an externally imposed double layer (an electrically polarized interface) and a double layer formed spontaneously by preferential adsorp-tion/desorption of ions (an electrically relaxed interface). This issue has been discussed extensively (and authoritatively ) by Lyklema and coworkers [188-191] for amphifunctionally electrified... 

The electrochemical response of CNTs is dominated by double-layer charging with only a small contribution of faradaic pseudocapacitance due to surface oxides (Frackowiak and Beguin, 2000 Kavan et al., 2001), so that faradaic processes are essentially absent. In contact with aqueous electrolytes, however, weak peaks may eventually appear. These peaks are presumably due to faradaic pseudocapacitance associated with oxygen-containing surface functionalities on CNTs and/or... 

Porous carbons and nanotubes have attracted considerable attention in relation to such practical issues as hydrogen storage, lithium batteries, and supercapacitors. In general, the electrochemical behavior of porous carbons and CNTs solely consists of double-layer charging processes with small or zero contribution of faradaic pseudocapacitance of surface oxide functionalities. This is in sharp contrast with the rich electrochemistry of fullerenes. 

Electrochemical capacitors based on carbon materials can be divided into doublelayer capacitors, where only a pure electrostatic interaction between ions and charged electrode surfaces occur, and supercapacitors, based on the occurrence of faradaic pseudocapacitance reactions (see Chapter 10). It is generally assumed that the charge is mainly stored, in porous carbons, in the double layer at the electrode/electrolyte... 

While treatment of the impedance spectrum of a unit capacitor is simple, if not trivial, when the problem of response of double-layer capacitance at the interface of an high-spedfic-area matrix, for example of carbon powder, felt or aerogel, is to be evaluated, the problan becomes very complex owing to the distributed series-parallel RC configurations throughout the electrode matrix, not to mention some usual contribution of 5 10% from Faradaic pseudocapacitance due to reactive functionalities at the extended carbon surface. 

In a paper by Kemer and Pajkossy [2002], anion adsorption rates have been measured by impedance spectroscopy at Au (111), for SO4, Cr, Br and T. Cr ion adsorption is very fast, so the equivalent circuit for the process not only has to include a Faradaic pseudocapacitance and its corresponding reaction resistance, but also a Warburg element for the anion diffusion. The interfacial capacitance is then plotted in the Nyquist plane as real vs. imaginary capacitance components, C and... 

PSEUDOCAP I CT2 herc R as "leakage resistance of pseudocapacitor" may not be present. Such a system in principle illustrates pseudocapacitance originating from specific adsorption, similar to what was discussed above for "kinetic" representation of composition with the adsorption and the double-layer capacitors in parallel. In multicomponent systems several combinations of R elements may be present. For such complex cases it is fundamentally impossible to accurately distinguish between and parallel Faradaic pseudocapacitance [17], apart from cases where sepa-... 

The control experiment in pure supporting electrolyte (dotted lines in Fig. 13.2) shows a sharp faradaic current spike, which is mainly due to pseudocapacitive contributions (adsorption of (bi)sulfate and rearrangement of the double layer) plus oxidation of adsorbed Hupd (dotted lines in Fig. 13.2a), but no measurable increase in the CO2 partial pressure (m/z = 44 current) above the background level (dotted lines in Fig. 13.2b). Therefore, a measurable adsorption of trace impurities from the base electrolyte can be ruled out on the time scale of our experiments. Moreover, this experiment also demonstrates the advantage of mass spectrometric transient measurements compared with faradaic current measurements, since the initial reaction signal is not obscured by pseudocapacitive effects and the related faradaic current spike. 

The calibrated m/z = 44 and m/z = 60 ion currents were converted into the respective partial reaction faradaic currents as described above, and are plotted in Fig. 13.3c as dashed (m/z = 44) and dash-dotted (m/z = 60) lines, using electron numbers of 6 electrons per CO2 molecule and 4 electrons per formic acid molecule formation. The calculated partial current for complete methanol oxidation to CO2 contributes only about one-half of the measured faradaic current. The partial current of methanol oxidation to formic acid is in the range of a few percent of the total methanol oxidation current. The remaining difference, after subtracting the PtO formation/reduction currents and pseudocapacitive contributions as described above, is plotted in Fig. 13.3c (top panel) as a dotted line. As mentioned above (see the beginning of Section 13.3.2), we attribute this current difference to the partial current of methanol oxidation to formaldehyde. This way, we were able to extract the partial currents of all three major products during methanol oxidation reaction, which are otherwise not accessible. 

In supercapacitors, apart from the electrostatic attraction of ions in the electrode/electrolyte interface, which is strongly affected by the electrochemically available surface area, pseudocapacitance effects connected with faradaic reactions take place. Pseudocapacitance may be realized through carbon modification by conducting polymers [4-7], transition metal oxides [8-10] and special doping via the presence of heteroatoms, e.g. oxygen and/or nitrogen [11, 12]. 

Although in charge storage pseudocapacitance due to a Faradaic process is considered beneficial, it has been argued [234] that in electrosorption Faradaic processes... complicate the electrosorption... 

We will see below that R [ is primarily determined by the heterogeneous charge-transfer kinetics, and we have already observed above that the terms crlo) and Hcro) come from mass-transfer effects. Recognition of this situation has led to a division of the faradaic impedance into the charge-transfer resistance, R i, and the Warburg impedance, Z, as shown in Figure 10.1.14. Equations 10.2.25 and 10.2.26 demonstrate that this latter impedance can be regarded as a frequency-dependent resistance, = alo), in series with the pseudocapacitance, = Cg = Thus the total faradaic impedance,... 

FIGURE 25-7 Circuit model of an eteclrochemical cell. is the cell resistance, C j is the double-layer capacitance, and 7, is the faradaic impedance, which may be represented by either of the equivalent circuits shown. is the cel) resistance, C is the so-called pseudocapacitance, and is the Warburg impedance. (Adapted from A. J. Bard and L. R. Faulkner. ElectrochemicSl Methods, 2nd ed, p. 376, New York Wiley, 2001. Reprinted by permission of John Wiley Sons, Inc.)... 

The enhancement of specific capacitance for carbon materials is generally realized by the usage of pseudocapacitance effects, which depend on the surface functionality of carbon and on the presence of electro-active species (termed supercapacitors) [162-164]. Several modifications (i.e., oxidation of carbon for increasing the surface functionality, formation of carbon/conducting polymers composites or insertion of electroactive particles of transition metals) can be carried out to increase the pseudocapacitance that arises fi om faradaic reactions. However, the enhancement of the capacitance connected with faradaic reactions of surface groups often contributes to an increase in the self-discharge of the capacitor due to the instability of the functionalities [165]. 

The enhancement of the double layer capacitance of carbon electrodes may be connected with the pseudocapacitance effects that appear at the carbon surfece. This is attributed to faradaic reactions involving electron transfer reactions of functional groups at the carbon surface. 

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