Surface relaxation impedance

On the basis of this model and the equivalent circuit shown in Figure 4.5.67, the changes and differences, depending on the used anode in the fuel cell (Pt/C or PtRu/C) in the impedance spectra during the experiment, are dominated by the changes of the charge transfer resistance of the anode (Raj), the surface relaxation impedance (Rg, tg) and the finite diffusion impedance (Z ). 

Impedance Spectra with Inductive Behavior at Low Frequencies Relaxation Impedance. Based on the concept of impedance elements, Gdhr [1986] described the Faradaic impedances as connections of impedance elanents each of which is associated with a single process. One of such an impedance element is the relaxation impedance, desalbing the surface relaxation of the interface and explaining the development of the pseudoinductive behavior in the low frequency range (frequency < 3 Hz) in the impedance spectra of the fuel cell. This behavior was first found by Muller et al. [1999] during poisoning the anode of a PEFC with... 

The actual nature of the surface species participating in the impedance response and the use of an adhoc surface relaxation time constanf [68]... 

Nyquist diagrams of the electrochemical impedances corresponding to a two-consecutive step anodic dissolution. Points stand for the result of Monte Carlo simulations without surface relaxation (open circles) and with surface relaxation (solid circles) for a. Number of cycles is n = 20 and V = O.lmV. Frequency values range from CO = 0.005 to co = 10 s. Continuous solid line corresponds to inductive loop behavior of Zp (ffl) predicted by Equation 3.15. Dashed line stands for an analytical approach of the rough case. (From Cdrdoba-Torres, P., Keddam, M., and Nogueira, R.P., Electrochim. Acta, 54, 518,2008. With permission.)... 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

The appearance of capacitive or inductive impedance depends essentially on the value of the rate constants. Low frequency loops, in a general case, are all very sensitive to the pH of the electrolyte. The different time constants are attributed to the relaxation of surface coverage by a corresponding number of reaction Intermediates. 

In the EHD impedance method, modulation of the flow velocity causes a modulation of the velocity gradient at the interface which, in turn, causes a modulation in the concentration boundary layer thickness. As demonstrated previously in Section 10.3.3 and Fig. 10.3 the experiment shows a relaxation time determined solely by the time for diffusion across the concentration boundary layer. Although there is a characteristic penetration depth, 8hm, of the velocity oscillation above the surface, and at sufficiently high modulation frequencies this is smaller than the concentration boundary layer thickness, any information associated with the variation of hm with w is generally lost, unless the solution is very viscous. The reason is simply that, at sufficiently high modulation frequencies, the amplitude of the transfer function between flow modulation and current density is small. So, in contrast to the AC impedance experiment, the depth into the solution probed by the EHD experiment is not a function... 

On a RDE, in the absence of a surface layer, the EHD impedance is a function of a single dimensionless frequency, pSc1/3. This means that if the viscosity of the medium directly above the surface of the electrode and the diffusion coefficient of the species of interest are independent of position away from the electrode, then the EHD impedance measured at different rotation frequencies reduces to a common curve when plotted as a function of p. In other words, there is a characteristic dimensionless diffusional relaxation time for the system, pD, strictly (pSc1/3)D, which is independent of the disc rotation frequency. However, if v or D vary with position (for example, as a consequence of the formation of a viscous boundary layer or the presence of a surface film), then, except under particular circumstances described below, reduction of the measured parameters to a common curve is not possible. Under these conditions pD is dependent upon the disc rotation frequency. The variation of the EHD impedance with as a function of p is therefore the diagnostic for... 

Two impedance arcs, which correspond to two relaxation times (i.e., charge transfer plus mass transfer) often occur when the cell is operated at high current densities or overpotentials. The medium-frequency feature (kinetic arc) reflects the combination of an effective charge-transfer resistance associated with the ORR and a double-layer capacitance within the catalyst layer, and the low-fiequency arc (mass transfer arc), which mainly reflects the mass-transport limitations in the gas phase within the backing and the catalyst layer. Due to its appearance at low frequencies, it is often attributed to a hindrance by finite diffusion. However, other effects, such as constant dispersion due to inhomogeneities in the electrode surface and the adsorption, can also contribute to this second arc, complicating the analysis. Normally, the lower-frequency loop can be eliminated if the fuel cell cathode is operated on pure oxygen, as stated above [18],... 

The experimental situation is inconclusive and sometimes even the same experimental techniques used by different groups give contrary results. Especially for the compounds k-(ET)2Cu(NCS)2 and K-(ET)2Cu[N(CN)2]Br many different techniques have been employed to measure A(T). Evidence for non BCS-like behavior has been obtained by complex ac susceptibility [220], radio-frequency penetration depth [221], muon spin relaxation (//SR) [222], and microwave surface impedance measurements [223]. In contrast, results consistent with conventional BCS theory, sometimes revealing a tendency towards strong coupling, are reported for measurements of the //SR [224], microwave surface impedance [225, 226], and dc magnetization [227]. 

The most satisfactory experimental methods are (a) analysis of potential relaxation after current interruption from a prior steady-state potentials and (b) ac impedance spectroscopy at steady-state potentials. These methods have been referred to in Section VI. They both have the advantages that no H2 reoxidation occurs and no surface oxidation of the electrode takes place, as can arise in the current pulse method (121). The principal applications of the potential-relaxation method to determination of OPD H have been in the work of Bai and Conway (75) on H adsorption in the HER at Ni, Ni-Mo composites, and Pt (136), and by Conway and Brousseau (162) at bulk, single-phase Ni-Mo alloys (Mo 0 to 19 at%). 

The models that consider this approach are largely based on the assumption of effectively homogeneous local relaxation processes related to transport in each of the phases and electrical charge exchange between them. Thus, the complex problem of an uneven distribution of electrical current and potential inside the electrode can be described analytically, and impedances can be calculated. Furthermore the models may be conveniently pictured as a double-channel transmission line (Fig. 3.5). In several papers, the theory of the impedance of porous electrodes has been extended to cover those cases in which a complex frequency response arises in the transport processes [100] or at the inner surface [194,203]. 

---