Global and Local Impedances

Following Hueing et al., ° a notation is presented in Section 7.5.2 that addresses the concepts of a global impedance, which involved quantities averaged over the electrode surface a local interfacial imgedance, which involved both a local current density and the local potential drop V — Oo(r) across the diffuse double layer a local impedance, which involved a local current density and the potential of the electrode V referenced to a distant electrode and a local Ohmic impedance, which involved a local current density and potential drop Oo(r) from the outer region of the diffuse double layer to the distant electrode. The corresponding list of symbols is provided in Table 7.2. 

The local impedance z can be represented by the sum of local interfacial impedance Zo and local Ohmic impedance z as 

Huang et al. ° ° demonstrated for blocking disk electrodes that, while the local interfacial impedance represents the behavior of the system unaffected by the current and potential distributions along the surface of the electrode, the local impedance shows significant time-constant dispersion. The local and global Ohmic impedances were shown to contain the influence of the current and potential distributions. 

The characteristic frequency K// = 1 is associated with the RfCo-time constant for the Faradaic reaction. 

The frequency K = 1 at which the current and potential distributions begin to influence the impedance response can be expressed as 

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Figure 7.10 The location of current and potential terms that make up definitions of global and local impedance.

V. M.-W. Huang, V. Vivier, I. Frateur, M. E. Orazem, and B. Tribollet, "The Global and Local Impedance Response of a Blocking Disk Electrode with Local CPE Behavior," Journal of The Electrochemical Society, 154 (2007) C89-C98. 

V. Mie-Wen Huang, V. Vivier, M. E. Orazem, N. Pebere, B. Tribollet, The global and local impedance response of a blocking disk electrode with local constant-phase-element behavior, J. Electrochem. Soc., 2007,154,2, pp. C89-C98. 

A 3-D distribution of blocking components in terms of resistors and constant-phase elements is presented in Figure 13.1(b). Such a system will peld a local impedance with a CPE behavior, even in the absence of a 2-D distribution of surface properties. If the 3-D system shown schematically in Figure 13.1(b) is influenced by a 2-D distribution, the local impedance should reveal a variation along the surface of the electrode. Thus, local impedance measurements can be used to distinguish whether the observed global CPE behavior arises from a 2-D distribution, from a 3-D distribution, or from a combined 2-D and 3-D distribution. 

While the calculations presented here were performed in terms of solution of Laplace s equation for a disk geometry, the nature of the electrode-electrolyte interface can be imderstood in the context of the schematic representation given in Figure 13.5. Under linear kinetics, both Co and Rt can be considered to be independent of radial position, whereas, for Tafel kinetics, 1/Rf varies with radial position in accordance with the current distribution presented in Figure 5.10. The calculated results for global impedance, local impedance, local interfacial impedance, and both local and global Ohmic impedances are presented in this section. 

Newman found that at disk electrodes current distribution is nonuniform in the radial direction (known as the primary [355] and secondary [356] current distributions), which leads to impedance dispersion [357]. Recently, Huang et al. [310,358, 359] continued these studies in more detail using a local impedance approach. Global admittance corresponds to the integration of the local admittances over the total disk area. Impedance can also be defined (and experimentally measured) locally as a function of the position on the electrode surface. In the case of the disk geometry, it changes radially from the disk center, r = 0, to the disk radius, r = ro- The authors distinguished two types of distribution of time constants ... 

It is important to distinguish between LEIS/LEIM (a five-electrode technique with the AC perturbation applied to the substrate) and AC-SECM (a three-electrode technique with the AC perturbation applied to the probe). Additionally, it should also be noted that LEIS/LEIM as usually implemented does not provide the true local impedance since it is computed from the local current using the global potential, not the local potential. To obtain true local impedance, the local potential must also be measured (or controlled), and some efforts in this direction have been made [52]. 

The geometry-induced current and potential distributions cause a frequency or time-constant dispersion that distorts the impedance response of a disk elec-trode. Huang et ai, 7,i02.,205 j ye shown that current and potential distributions induce a high-frequency pseudo-CPE behavior in the global impedance response of a disk electrode with a local ideally capacitive behavior, a blocking disk electrode exhibiting a local CPE behavior, and a disk electrode exhibiting Faradaic behavior. 

The US Food and Drug Administration (FDA) definition states (1997) (a) Identification. A rheoencephalograph is a device used to estimate a patient s cerebral circulation (blood flow in the brain) by electrical impedance methods with direct electrical connections to the scalp or neck area. In other words, the FDA definition includes the word flow. On the basis of previous data, REG is actually a reflection of volume rather than flow (Nyboer, 1960). REG and cerebral blood flow (CBF) correlation have been described earher (Hadjiev, 1968 Jacquy et al., 1974 Moskalenko, 1980 Jenkner, 1986). However, the correlation of global, local CBF, and carotid flow was not investigated. 

This means that the deviations from the ideal capacitive behavior observed for global impedance at high frequencies originate from the behavior of the local ohmic solution impedance (Fig. 8.16) caused by a nonlinear current and potential distribution at disk electrodes [360]. Similar effects were observed in the presence of faradaic reactions [310, 361, 362]. Theory discussed above was experimentally verified for corroding materials [359, 360, 363] or film thickness [311, 364, 365]. It is important to note that the Bmg et al. formula, Eqs. (8.15) and (8.16), seems to work much better than that of Hsu and Florian, Eq. (8.15) [310]. Moreover, the recessed disk electrodes for which the current distribution is uniform do not show such impedance dispersion and behave ideally [366]. 

The graph shows that the measured impedance as well as its derivative is 10 times lower than in humans (peak-to-peak 0.03 12). Nevertheless, all important characteristic points can be extracted. In fig. 4 one can see the successful extraction of the standard B- and X-point, resulting in an LVET of 335 ms which is in a normal range. Although there are other possibilities to extract characteristic points, only one approach has been used for this work. The B-point was assessed using the local minimum before the C-point and the X-point using the global minimum after the C-point in a certain time interval [5,6]. 

Galicia, G., N. Pebere, B. Tribollet, and V. Vivier, Local and global electrochemical impedances apphed to the corrosion behaviour of an AZ91 magnesium alloy. Corrosion Science, 51, 2009, 1789. 

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