Current constriction

Workers have shown theoretically that this effect can be caused both at the microstructural level (due to tunneling of the current near the TPB) as well as on a macroscopic level when the electrode is not perfectly electronically conductive and the current collector makes only intermittent contact. ° Fleig and Maier further showed that current constriction can have a distortional effect on the frequency response (impedance), which is sensitive to the relative importance of the surface vs bulk path. In particular, they showed that unlike the bulk electrolyte resistance, the constriction resistance can appear at frequencies overlapping the interfacial impedance. Thus, the effect can be hard to separate experimentally from interfacial electrochemical-kinetic resistances, particularly when one considers that many of the same microstructural parameters influencing the electrochemical kinetics (TPB area, contact area) also influence the current constriction. 

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Figure 57. In the case of current constriction induced by a partially contacted metal electrode (shown by electrical potential lines in the inset, contact in the center, separation by an air gap otherwise) the impedance response ideally consists of two semicircles. At high frequencies the air gap (cf. distance between curved electrode and plane surface) becomes dielectrically permeable.286 Reprinted from J. Fleig and J. Maier, Electrochim. Acta, 41 (1996), 1003-1009. Copyright 1996 with permission from Elsevier.

The fact that in the case of the bicrystal in Figure 54 the effective thickness calculated from the low-frequency semicircle is very much greater than expected from the width of the boundary, while the activation energy is almost equal to that of the bulk, points towards a frequently overlooked complication, namely to current-constriction effects. Such constriction effects occur287 when the crystal grains are not ideally sintered together, if pores or second phases are included, and interrupt the lateral conductivity of boundaries, as is the case for inhomogeneous electrode contacts. 

R cc additional bulk resistance due to current constriction close to the three-phase boundary -Rongb resistance measured with a microelectrode on a grain boundary... 

In the dc case, the current has to flow to the electrochemically active sites close to the 3PB and a considerable current constriction results (Fig. 22b). Hence, the dc resistance consists of the resistance due to the electrochemical reaction and the bulk resistance, which includes the current constriction in the vicinity of the active ring. At higher frequencies, the inner part of the microelectrode becomes dielectrically permeable and the current flows to the entire microelectrode area (Fig. 22c). In other words, the current lines in the bulk, and thus the bulk resistance, are frequency-... 

Fig. 24. Ratio of the additional current constriction resistance to the conventional spreading resistance for different ring widths (7>nng) normalized to the diameter of the electrochemically inactive inner part (dme), indicating that for small active rings the additional resistance becomes rather important.

As in the case of the conductivity experiments, current-constriction effects can occur in the diffusion experiments, if lateral inhomogeneities are present. In this way resistivities occur that can be easily misinterpreted in terms of sluggish surface steps. A concise treatment of proper surface kinetics will be given now. 

Holm (1967) identifies the contact resistance between particles of clean metal to be the result of current constriction at the point of contact. This geometric constriction together with the volume and surface resistivities integrated over the remaining volume and surface of a particle constitute the total resistance measured between two contacts located at the poles of the particle. In addition, if a thin film exists between the particle contacts, the tunnel effect provides a current independent of the film resistivity. 

Figure 4.26 Body segment resistance distribution (no skin contribution, no current constriction). Values presented are as found with a four-electrode technique 500 Q is a one-finger contribution. Linear values according to Eq. 2.2 are not very dependent on current density levels.

Figure 6.3 Current constriction, (a) Monopolar system where the resistance is increased by the smaller electrode and current constricting geometry (b) bipolar system.

The bulk of the electrolyte obeys Ohm s law, Eq. (2.2). Accordingly, the bulk electrolyte is modeled as an ideal resistor Rsoiu in series with the electrode components. This is to indicate that bulk electrolytic conductance is considered frequency independent, but dependent on the geometry and possible current constrictional effects. If the bulk electrolyte is replaced by tissue, a more complicated equivalent circuit must replace Rsoi, and we are confronted with the basic problem of division between tissue and electrode contributions. 

Band electrodes are used as large-surface, low-impedance electrodes with the additional attractive feature of reducing the current constrictional effect found with smaller disk electrodes. This is important in two electrode apphcations such as impedance. 

If sample size varies, it is easier to use a guard ring (Figure 7.39(c)) around the measuring electrode and kept at the same voltage. The effect of stray fields or current constriction is then reduced. 

To analyze the situation with a tetrapolar electrode system in contact with, for example, a human body, we must leave our simplified models and turn to lead field theory (see Section 6.4). The total measured transfer impedance measured is the ratio of recorded voltage to injected current according to Eq. 6.39. The impedance is the sum of the impedance contributions from each small volume dv in the measured volume. In each small volume, the resistance contribution is the resistivity multiplied by the vector dot product of the space vectors (the local current density from a unit reciprocal current applied to the recording electrodes) and (the local current density from a unit current applied to the true current carrying electrodes). With disk-formed surface electrodes, the constrictional resistance increase from the proximal zone of the electrodes may reduce sensitivity considerably. A prerequisite for two-electrode methods is therefore large band electrodes with minimal current constriction. 

One of the first to introduce the method was Thomasset (1965), using a two-electrode method and 1 kHz signal frequency. With just two electrodes, it is important to use large-area band electrodes to reduce the contribution from the current constrictional zones near the electrodes. With a tetrapolar electrode system, it is easier to select the preferred... 

Experiment has shown that reactions in a nonporous pure metallic electrode are relatively difficult as the TPB sites are located exclusively in the contour of the electrode in contact with the electrolyte. Although gas molecules may adsorb over the entire surface of the electrode, most of them cannot react, providing or extracting oxygen ions from the electrolyte as the contacts gas/catalyst/electrolyte are only in the contour of the electrode. This low density of TPB sites causes a current constriction as a high fraction of the contact area between metal and YSZ is inactive (Sridhar et al. 1997 Aaberg et al. 2000). Subsequently, the response time of sensors with this structure is slow. 

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