Multiple-point electrodes

The problem with a plate electrode in some apphcations is the covering effect on the tissue. With a multiple-point electrode, humidity for instance can escape from the surface. Dependent on tip sharpness and electrode pressure the points may penetrate the superficial layers. 

If the mode of current supply to the electrode is replaced by a single point (Fig. 5.27a), the nonuniformity of current distribution is accentuated. It is advisable, therefore, to adopt at least a multiple-point connection along one electrode edge to approximate a uniform current feed. Because of problems associated with limitations in electrode conductivity, industrial reactors often operate with banks of bipolar electrodes (see Section 5.1.2). 

For current consoHdation, the basic circuits, used at each of the multiple power take-off points, are stacked into a Christmas tree topology to form a single power take-off terminal pair. Scale-up of these devices to commercial sizes is not expected to be a problem, as standard electrical components are available for all sizes considered. A different type of consoHdation scheme developed (117), uses dc to ac converters to connect the individual electrodes to the consoHdation point. The current from each electrode can be individually controUed by the converter, which can either absorb energy from or deHver energy to the path between the electrode and the consoHdation point. This scheme offers the potential capabiHty of controlling the current level of each electrode pair. 

However, if the pipeline has multiple drain points separated by distance V and the aim is that the pipeline electrode potential should just reach the protection potential at the mid-point (x = a/2), then is equal to (the overpotential required just to achieve the protection potential). At X = a/2 the current in the line is zero and (d nx/dx), 2 also zero. Thus ... 

Note that a number of complicating factors have been left out for clarity For instance, in the EMF equation, activities instead of concentrations should be used. Activities are related to concentrations by a multiplicative activity coefficient that itself is sensitive to the concentrations of all ions in the solution. The reference electrode necessary to close the circuit also generates a (diffusion) potential that is a complex function of activities and ion mobilities. Furthermore, the slope S of the electrode function is an experimentally determined parameter subject to error. The essential point, though, is that the DVM-clipped voltages appear in the exponent and that cheap equipment extracts a heavy price in terms of accuracy and precision (viz. quantization noise such an instrument typically displays the result in a 1 mV, 0.1 mV, 0.01 mV, or 0.001 mV format a two-decimal instrument clips a 345.678. .. mV result to 345.67 mV, that is it does not round up ... 78 to ... 8 ). 

If an electrode surface is considered to contain a multiple set of identically functioning single active centres/servers, where each ion can have a choice of several adjacent servers,28 the probability that exactly j number of severs is occupied at any given time may be computed by the Erlang formula (Eq. 15), provided that numerical values of X and //, or r = XI/a are known. From a practical point of view, two particular states are of interest s0, where the entire surface is free for an electrode reaction to proceed, and, vm, where the entire surface is covered by the reaction product m is the number of active centres, or clusters of active centres. A small value of r represents either a slow arrival of ions, or a fast electrode reaction, and vice versa. When r = 1, the arrival and surface rates are matched exactly. Table 6 shows the effect of r on (i) the probability of the entire electrode surface... 

Figure 5. An oxidation state diagram for Mo, Cr, Fe and Mn. For Mo and Cr, N = III for Fe and Mn, N = II. Potentials are given at standard states in acid solution relative to the hydrogen electrode. On such a diagram, die slope between any two points equals the redox potential. In conh ast to most other metals, multiple Mo oxidation states are accessible over a small range of potentials. Note also that Mo is oxidized to Mo(VI) at relatively low potential (similar to Fe(III). Figure modified after Frausto da Silva and Williams (2001).

To carry out amperometric or voltammetric experiments simultaneously at different electrodes in the same solution is not difficult. In principle, any number of working electrodes could be studied however, it is unlikely that more than two or three would ever be widely used in practice. The bulk of the solution can have only one controlled potential at a time (if there are significant iR drops, there will be severe control problems with multiple-electrode devices). It is necessary to use a single reference electrode to monitor the difference between this inner solution potential and the inner potential of W1 at the summing point of an operational amplifier current-to-voltage converter (this is the potential of the circuit common see OA-2 in Fig. 6.17). The potential difference between... 

To mimic the PG electrode surface for QCM measurements of layers adsorbed on the gold-quartz resonators, we first chemisorb a mixed monolayer of mercaptopropionic acid/mercaptopropanol. This layer is represented by the first point in Fig. 2, labeled MPA. The second layer is PDDA. Quartz crystal microbalance frequency decreasing in a roughly linear fashion and at regular intervals for the multiple adsorption steps demonstrates repeatable adsorption for the two DNA/en-zyme films. Relative precision of layer formation on multiple resonators within 15% can be achieved. Film thicknesses and component weights in Table 1 were obtained by analyzing the QCM data with Eqs. 1 and 2. 

Several problems will become apparent. The first one is that of the method used to arrive at (1.4) this will be dealt with later. There is, in fact, a multiplicity of methods and expressions used. The second problem is the concentration value at x = 0 there is no x i point, as would be needed for = 1. The value of Co is a boundary value, and must be determined by some other method. Another boundary value is the last x point we treat. How far out into the diffusion space should (need) we go Usually, we know good approximations for concentrations at some sufficiently large distance from the electrode (e.g., either bulk concentration, or zero for a species generated at the electrode), and we have pretty good criteria for the distance we need to go out to. Another boundary lies at the row for t = 0 this is the row of starting values. Again, these are supplied by information other than... 

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