Pseudocapacitance parameters

Summarizing the above, it may be stated that activated carbons and pseudocapacitive materials in EC electrode structure are responsible for the energy storage parameters (specific energy), while non-active highly conductive carbon additives are responsible for the electrode internal resistance (EC specific power). 

There is an apparent discrepancy between the treatment of electrode kinetics under Temkin conditions, at intermediate values of the coverage, and the results shown in Fig. 141(b) for the adsorption pseudocapacitance in the same region. For the purpose of calculating the kinetic parameters, we have assumed that 0 is a linear function of potential. This is a valid assumption, as we can see in Fig. 21. Yet such a linear dependence of 6 on should give rise to a constant value... 

Since, by definition, 0 < 0 < 1, Eq. 591 has physically meaningful solutions only for / < - 4. A plot of the Frumkin isotherm for negative values of the parameter / is shown in Fig. 171. For / = - 12, the solution of Eq. 591 yields 0 = 0.11 and 0.89. Between these values, the coverage appears to increase with decreasing potential, which would imply a negative value of the adsorption pseudocapacitance. This does not represent physical reality, of course. If we trace the potential in the positive direction, 0 will Jump from 0.11 to 0.999. When the... 

Te and Cu monolayers on gold, as well as Ag and Bi monolayers on platinum were obtained by cathodic underpotential deposition and investigated in situ by the potentiodynamic electrochemical impedance spectroseopy (PDEIS). PDEIS gives the graphical representation of the real and imaginary interfacial impedance dependencies on ac frequency and electrode potential in real-time in the potential scan. The built-in analyzer of the virtual spectrometer decomposes the total electrochemical response into the responses of the constituents of the equivalent electric circuits (EEC). Dependencies of EEC parameters on potential, especially the variation of capacitance and pseudocapacitance of the double layer, appeared to be very sensitive indicators of the interfacial dynamics. 

Conducting polymers have been studied using the whole arsenal of methods available to chemists and physieists. Eleetrochemical teelmiques, mostly transient methods such as cychc voltarmnetiy (CV), chronoamperometry (CA) and chronocoulom-etry (CC), are the primary tools used to follow the formation and deposition of polymers, as well as the kineties of their charge transport processes. Electrochemical impedance speetroseopy (EIS) has become the most powerful technique used to obtain kinetic parameters sueh as the rate of charge transfer, diffusion coefficients (and their dependenee on potential), the double layer capacity, the pseudocapacitance of the polymer film, and the resistance of the film... 

This kinetic parameter is inversely proportional to the rate constant of the electrode process of adsorption. On the other hand, the adsorption pseudocapacitance reduces to... 

To obtain the total impedance, the faradaic impedance, Eq. (5.19), must be inserted into the total impedance (Fig. 4.1b). The complex plane and Bode plots of the total impedance are as in Fig. 2.35. The circuit parameters R i and Cp depend on the potential, as illustrated in Fig. 5.1. The charge transfer resistance displays a minimum at Ep and its logarithm is linear with the potential further from the minimum, while the pseudocapacitance displays a maximum. These values at the potential Ep are... 

It is evident that an increase in the repulsion between H atoms causes a flattening of both curves and a decrease in the maximum of the pseudocapacitance. It can be added that the Frumkin isotherm was fotmd to describe HUPD at Pt(lOO) in HCIO4, Pt(llO) in H2SO4, and Pt(lll) in both acids [241]. The value of the parameter g at Pt(lll) was approximately 12. Unfortunately, the isotherms at other surfaces or metals are much more complicated. The HUPD kinetics was studied on different poly crystalline metals. It was found that the kinetics at Pt [242] was about three orders of magnitude faster than that at Ru [243], Pd [244, 245], or Rh [246] electrodes, while that at Ir was intermediate between those groups [247] (on the... 

Estimates of the diffusion parameters R and capacitance Cd obtained from data fitting can be used to calculate the chemical diffusion coefficient D (cm sec ), if the particle radius is known, as D = t l(3CdRd)- The diffusion pseudocapacitance Cd is related to the Emf-relation of the material so dEldc (volt cmVmole) can be obtained from Cd as dEldc = AFzia SIOCd)- All these specific parameters can be used as sample-independent characteristics of a particular intercalation material and allow one to predict the change of impedance spectra (and battery performance) with changing active layer particle size or thickness (Barsoukov et al. [2000]). 

CPE with a depressed semicircle has been used to describe both the doublelayer capacitance and the low-frequency pseudocapacitance (Section 5-3). The "double layer capacitor" in electrochemical experiments often shows a CPE-like distributed behavior instead of that of a pure capacitor. Several theories have been proposed to accoimt for the nonideal behavior of the double layer, but none has been universally accepted. As a first approximation, one can treat a as an empirical constant and not worry about its physical basis. For double-layer analysis, the parameter Q, expressed in [s ohm cm ], is... 

The dependence of Cadsorption pseudocapacitance on potential is shown in Figure 11.5b. This... 

Bearing in mind that the maximum value of the pseudocapacitance always occurs at 0 = 0.50, irrespective of the value of the parameter/(cf Figure 11.5). This yields... 

In another study of DMFC anodes, shovm in Figure 16.10, the complex-plane impedance plots were studied as a function of the current density applied. The diameters of the semicircles were found to decrease with increasing current density, as expected, but the new feature observed is an inductive branch of the curves. This can be modeled, of course, by adding an inductive element to the equivalent circuit representation, in series with the Faradaic resistance, but the physical origin of this added circuit element is still open for debate. There is a tendency to associate it with sluggish adsorption of CO, formed as an intermediate in the oxidation of methanol. However, unlike the adsorption pseudocapacitance, which is well understood (cf Section 11.2), there is no theory for the dependence of the pseudoinductance on potential, coverage or any other measured parameter. 

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