Microelectrode microdisc

Of course, in order to vary the mass transport of the reactant to the electrode surface, the radius of the electrode must be varied, and this unplies the need for microelectrodes of different sizes. Spherical electrodes are difficult to constnict, and therefore other geometries are ohen employed. Microdiscs are conunonly used in the laboratory, as diey are easily constnicted by sealing very fine wires into glass epoxy resins, cutting... 

The geometry of the microelectrodes is critically important not only from the point of view of the mathematical treatment, but also their performance. Thus, the diffusion equations for spherical microelectrodes can be solved exactly because the radial coordinates for this electrode can be reduced to the point at r = 0. On the other hand, a microelectrode with any other geometry does not have a closed mathematical solution. It would be advantageous if a microdisc electrode, which is easier to fabricate, would behave identically to a microsphere electrode. This is not so, because the center of the disc is less accessible to the diffusing electroactive species than its periphery. As a result, the current density at this electrode is nonuniform. 

In this section, microdisc electrodes will be discussed since the disc is the most important geometry for microelectrodes (see Sect. 2.7). Note that discs are not uniformly accessible electrodes so the mass flux is not the same at different points of the electrode surface. For non-reversible processes, the applied potential controls the rate constant but not the surface concentrations, since these are defined by the local balance of electron transfer rates and mass transport rates at each point of the surface. This local balance is characteristic of a particular electrode geometry and will evolve along the voltammetric response. For this reason, it is difficult (if not impossible) to find analytical rigorous expressions for the current analogous to that presented above for spherical electrodes. To deal with this complex situation, different numerical or semi-analytical approaches have been followed [19-25]. The expression most employed for analyzing stationary responses at disc microelectrodes was derived by Oldham [20], and takes the following form when equal diffusion coefficients are assumed ... 

In view of the expressions of the stationary current-potential responses of microspherical and microdisc electrodes (Eqs. (3.74) and (3.95), respectively), it is clear that an equivalence relationship between disc and hemispherical microelectrodes, like that shown for fast charge transfer processes (see Eq. (2.170) of Sect. 2.7), cannot be established in this case. 

The current for a reversible EE mechanism can achieve a stationary feature when microelectrodes are used since in these conditions the function fG(t, qa) that appears in Eq. (3.150) transforms into fG,micro given in Table 2.3 of Sect. 2.6. For microelectrode geometries for which fo.micro is constant, the current-potential responses have a stationary character, which for microdiscs and microspheres can be written as [16] ... 

The analysis of the EC and CE mechanisms under steady-state conditions at other microelectrode geometries is much more complex. In the case of microdiscs,... 

The evolution of the peak current (/ dlsc,peak) with frequency (/) is plotted in Fig. 7.37 for the first-order catalytic mechanism with different homogeneous rate constants at microdisc electrodes. For a simple reversible charge transfer process, it is well known that the peak current in SWV scales linearly with the square root of the frequency at a planar electrode [6, 17]. For disc microelectrodes, analogous linear relationships between the peak current and the square root of frequency are found for a reversible electrode reaction (see Fig. 7.37 for the smallest kx value). 

Anion detection at microelectrodes has not been studied widely. Amongst the first was the work of de Beer et al. [ 111 ] who manufactured a nitrite sensor with a tip just a few microns in diameter, which could detect nitrite ions down to 1 pM. This proved to be suitable for profiling the concentrations of nitrite anion within biofilms less than 1-mm thick inside water treatment plants. Other workers have found that use of an interdigitated microelectrode array [ 112] allows measurement of iodide via monitoring of its redox peak down to sub-micromole levels, making it a suitable technique for analysing mineral water. Carbon nanotubes coated onto Pt microdiscs have been utilised to make a nitrite sensor [113,114] with detection levels of 0.1 pM. Sulphide has also been detected at nickel microdiscs (50 pm diameter) [115]. 

Consideration of Fig. 32 implies that chemical information may be extracted from microelectrode experiments either via steady-state measurements or via transient, often cyclic voltammetric, approaches. In the former approach, measurements are made of the mass transport limited current as a function of the electrode size - most usually the electrode radius for the case of a microdisc electrode. This may be illustrated by reference to a general ECE mechanism depicted by (23a)-(23c) where k is the rate constant for the C step. 

A mercury-supported tBLM was formed at the tip of a microelectrode for measuring single-channel activity [90]. To this end, use was made of a platinum wire embedded in a thin glass capillary and terminated with a platinum microdisc. 

Earlier in this discussion, the low iRu drop associated with microelectrodes was mentioned. In fact, it can be shown [25] that the total resistance between a microdisc electrode and a large secondary electrode located a long way from it is given by... 

Figure 11.3 exhibits few examples of microelectrodes such as (a) microdisc electrode with diameter of 10 pm within a glass tube of 20 pm for amperometric measurements [5], (b) STM-Tip, which can measure with resolution in atomic dimension, (c) pH-sensitive microelectrode used in biological research, (d) microelectrode array for research [14], and (f) electrode array for glucose... 

Highly oriented carbon fibers ( graphite fibers ) are a very convenient starting material for preparation of microelectrodes, namely because of their mechanical stability, high electronic conductivity and good biological compatibility. Preparation of encapsulated microdisc electrodes with diameter up to 1 /xm will be discussed. 

Unfortunately the use of planar and (hemi)spherical electrodes is not always appropriate or possible in electrochemical studies. Electrodes with large areas lead to problems derived from large ohmic drop and capacitive effects, and the fabrication of (hemi)spherical microelectrodes is difficult. Consequently microdisc electrodes are ubiquitous in electrochemical experiments since they allow for the reduction of the above undesirable effects and are easy to manufacture and clean. This is also true in the case of band electrodes and electrodes with heterogeneous surfaces due to the non-... 

A microdisc electrode is a micron-scale flat conducting disc of radius r. that is embedded in an insulating surface, with the disc surface flush with that of the insulator. It is assumed that electron transfer takes place only on the surface of the disc and that the supporting smlace is completely electroinactive under the conditions of the experiment. These electrodes are widely employed in electrochemical measurements since they offer the advantages of microelectrodes (reduced ohmic drop and capacitive effects, miniaturisation of electrochemical devices) and are easy to fabricate and clean for surface regeneration. In Chapter 2, we considered a disc-shaped electrode of size on the order of 1 mm. In that case we could approximate the system as one-dimensional because the electrode was large in comparison to the thickness of the diffusion layer, such that the current was essentially uniform across the entire electrode surface. Due to the small size of the microdisc, this approximation is no longer valid so we must work in terms of a three-dimensional coordinate system. While the microdisc can... 

As discussed for the case of (hemi)spherical microelectrodes in Chapter 4, the response in cyclic voltammetry at microdiscs varies from a transient, peaked shape to a steady-state, sigmoidal one as the electrode radius and/or the scan rate are decreased, that is, as the dimensionless scan rate, a = Y r lv/TZTD, is decreased. The following empirical expression describes the value of the peak current of the forward peak for electrochemically reversible processes [11] ... 

A number of methods exist for fabricating microelectrode arrays [6] and a variety of array geometries are encountered with the most common being arrays of microdiscs and arrays of microbands. Microdiscs are most frequently arranged as a regularly distributed (i.e., a square or... 

If we approximate each of the inert blocking particles as being discshaped and of the same size, the modelling of a PBE is only very slightly different from modelling a random array of microelectrodes. In the latter case we considered an array of electroactive discs on an inert surface whereas for a PBE we consider an array of inert discs on an electroactive surface. The simple solution then is to use exactly the same simulation model as for the random array of microdiscs except that the surface boundary conditions... 

Early two-dimensional simulations focused on the evaluation of the current distribution at microdisc electrodes [107, 108] and simulations of a variety of electrode geometries [109-111] including the influence of recessed microelectrode configurations [112]. Work has been also extended to cases involving coupled homogeneous kinetics, adsorption [113], and time-dependent redox polymer electrochemistry [114]. 

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