Faradaic impedance, calculated

The first estimations of for photoinduced processes were reported by Dvorak et al. for the photoreaction in Eq. (40) [157,158]. In this work, the authors proposed that the impedance under illumination could be estimated from the ratio between the AC photopotential under chopped illumination and the AC photocurrent responses. Subsequently, the faradaic impedance was calculated following a treatment similar to that described in Eqs. (22) to (26), i.e., subtracting the impedance under illumination and in the dark. From this analysis, a pseudo-first-order photoinduced ET rate constant of the order of 10 to 10 ms was estimated, corresponding to a rather unrealistic ket > 10 M cms . Considering the nonactivated limit for adiabatic outer sphere heterogeneous ET at liquid-liquid interfaces given by Eq. (17) [5], the maximum bimolecular rate constant is approximately 1000 smaller than the values reported by these authors. 

The faradaic impedance, Zf, and the total impedance how to calculate Zf from experimental measurements... 

Calculation of the Faradaic Impedance at the Equilibrium Electrode Potential... 

The total impedance of this ladder structure includes the Faradaic impedance, the double-layer capacitance, and the electrolyte resistance, which can be calculated as... 

B. In order to calculate the reaction faradaic impedance equations describing the current, j(ti, 0) [Eq. (127)] and the rate of formation of absorbed species (i], 0) [Eq. (129)] should be linearized, giving ... 

Treatments of cyclic ac voltammetry follow the familiar pattern. The ac and dc time scales are independently variable, but are assumed to differ markedly. Then a treatment of the dc aspect yields mean surface concentrations, which are used to calculate faradaic impedances that define the ac response by amplitude and phase angle. The electrode is assumed to be stationary and the solution is regarded as quiescent for the duration of the dc cycle. 

In a separate experiment under exactly the same conditions, but in the absence of the electroactive species, the cell resistance Rq is found to be 10 D, and the double-layer capacity of the electrode C is found to be 20.0 /xF. (a) From these data calculate at each frequency R and C and the phase angle cf) between the components of the faradaic impedance, (b) Calculate iq and for the reaction, and estimate D (assuming Dq = Dr). 

Recently, Michel et al. [169] carried out a numerical computation of the faradaic impedance of inlaid microdisk electrodes using a finite-element method and discussed the limitations of the Fleischmann and Pons [168] approach. Calculation of the functions 4 and 5 is shown in Exercise 4.8. 

The method presented above can be applied to any mechanism. In a later chapter it will be used for the calculation of impedances of other mechanisms. In general, in the faradaic impedance, inverse of resistances are proportional to rate constants and capacitances depend on the surface coverages (which contain the ratios of the rate constants that is depend on the equilibrium constants), although some lengthy rearrangements might be required to prove this. 

Additional linear simultaneous equations may be generated from Eqs (32), (34), and (35), and the set may be solved for 80J8E, 862 8E, 863 8E, and 8O4/8E. These values are then substituted into Eq. (46) to calculate the faradaic impedance, which in turn yields the interfacial impedance as... 

The adsorption parameters can be calculated from the extrapolated values of the faradaic impedance components at cu- O and w The relationship between the adsorption parameters and the impedance components in the series Rg and Cg circuit were given in [39] ... 

The impedance of a charge-transfer reaction at a porous electrode consisting of cylindrical pores is given in the previous section by Eq. (19.1) [23-26]. To simplify the calculations, the Faradaic impedance per unit real surface area was assumed to be potential-independent over a range of values that would exist along the entire pore, e. g., < 0.25 V, and thus consists only of a parallel combination of the charge transfer resistance and a double-layer capacitance, without a Warburg impedance. 

Typical values of o and a, as well as the faradaic resistance Rf, series resistance Rs (and the film resistivity p calculated thereby, assuming that the electrolyte resistance can be neglected) are presented in Table 3 for polycrystalline and single-crystal diamond electrodes and a DLC electrode [69-77]. By comparing the impedance... 

If diffusion limitation is considered, the overpotential decays more slowly, as shown in Fig. 7K. This should be evident, since the Warburg impedance -W- is added in series with the faradaic resistance / p. In this case the plot of logq versus t is not linear and a much more complex mathematical treatment, taking into account the diffusion equations, must be applied to calculate the kinetic parameters. 

The representation of an Ohmic impedance as a complex number represents a departure from standard practice. As will be shown in subsequent sections, the local impedance has inductive features that are not seen in the local interfacial impedance. As the calculations assumed an ideally polarized blocking electrode, the result is not influenced by Faradaic reactions and can be attributed only to the Ohmic contribution of the electrolyte. 

Use a Lissajous plot to calculate the phase angle and magnitude of the impedance for the system described in Example 7.1 at frequencies of 1 Hz and 10 kHz. This approach requires calculating dte potential perturbation, the charging current, and the Faradaic current as functions of time. 

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