Arrays of Microdisc Electrodes

The radius, ra, of the circular base may therefore be calculated by equating the areas of the two shapes  

Previous studies have demonstrated that the results of simulations using the diffusion domain approximation show very good agreement with experiments [19]. 

As with the isolated microdisc simulations in Chapter 9, we here consider the simulation of the cyclic voltammetry of a simple fully reversible one-electron reduction. For an array, since each unit cell is identical, the concentrations of the electroactive species will necessarily be the same on either side of the cell boundary and there can be no flux of electroactive material across the boundary. After using the diffusion domain approximation, this boundary is at a distance r = Vd, therefore 

The cell radius is normalised against the disc radius  

The normalised radius, Rd, may therefore be calculated from a specified value of surface coverage by 

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Fig. 10.2. Hexagonal array of microdisc electrodes with centre-to-centre separation, d.

Fig. 10.4. The four limiting cases of diffusional behaviour to an array of microdisc electrodes.

We now turn our attention to randomly distributed arrays of microdisc electrodes as illustrated in Figure 10.5 though they are not as commonly encountered as regularly distributed microdisc arrays, techniques do exist for their fabrication [22] and so here we consider the simulation of such arrays. Though the specific example of a randomly distributed microdisc array is of limited utility, the techniques for generating a random distribution of particles are applicable to a range of electrochemical problems. 

T. J. Davies, S. Ward-Jones, C. E. Banks, J. del Campo, R. Mas, F. X. Mnnoz, and R. G. Compton. The cyclic and linear sweep voltammetry of regnlar arrays of microdisc electrodes Fitting of experimental data, J. Elec-troanal. Chem. 585, 51-62 (2005). 

Davies TJ, Ward-Jones S, Banks CE, del Campo J, Mas R, Munoz FX, Compton RG (2(X)5) The cyclic and linear sweep voltammetry of regular arrays of microdisc electrodes fitting of experimental data. J Electroanal Chem 585 51-62... 

Davies TJ, Compton RG (2005) The cyclic tmd linetir sweep voltammetry of regular and random arrays of microdisc electrodes theory. J Electroanal Chem 585 63-82... 

Ordeig, O., Banks, C.E., Davies, T.J. et al. (2006) The linear sweep voltammetry of random arrays of microdisc electrodes fitting of experimental data. Electroanal. Chem., 592, 126. 

The unit cell and coordinates are illustrated in Figure 10.14(b). As with the array of microdiscs model, the unit cell is cylindrically symmetrical about an axis that passes through the centre of the pore, perpendicular to the electrode surface. The problem may thus be reduced from a three-dimensional one to a two-dimensional one. As with the microdisc electrode, this is a two-dimensional cylindrical polar coordinate system, and Pick s second law in this space is given by Eq. (9.6). The simulation space for the unit cell with its attendant boundary conditions is shown in Figure 10.15. 

The limits of independently addressable microbiosensors in an array have been explored on the basis of microdisc electrode arrays fabricated by thin-film technology. Cross-talk between the discrete enzyme-containing sensor elements was observed and the proximity limit was found to be about 100 (xm [261]. 

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... 

In Chapter 9, we studied the problem of a single electroactive microdisc on an infinite supporting surface. Here we consider the situation where an array of such microdiscs are embedded in a surface in a regular distribution as illustrated in Figure 10.1. It is assumed that electroactivity only occurs at the microdisc electrodes, not on the supporting surface. 

FIGURE 12.14 Schematic of various microfabricated electrode array devices manufectured by ABTECH Scientific, Inc. (A) Interdigitated microsensor electrodes (IMEs), (B) independently addressable microband electrodes (lAMEs), (C) independently addressable interdigitated microsensor electrodes (lAlMEs), (D) microdisc electrode array (MDEA), and (E) electrochemical cell-on-a-chip MDEA (ECC MDEA 5037). 

In other electrode configurations, the electrodes, either a microdisc or an array of electrodes, can be recessed, that is, the electrode is not planar to the insulating material and consequently the diffusional profiles will quantitatively change [10] recessed electrodes are typically produced unintentionally when photolithography is used. In the case of an array of recessed microdiscs. 

An array of microwells filled with the bacteria gel was prepared. The PAP was detected in the wells. The release of PAP into the extracellular liquid indicated the P-Gal activity that is the solubility of the MBP. The authors used a Pt microdisc electrode (radius, 10 mm) as the probe set to 0.30 V vs. Ag/AgCl to record the oxidation current of PAP produced in pGal catalyzed hydrolysis of PAPG. 

Fig. 3 Schematic illustration of a microfabricated multi-element array A comprising 32 interdigitated microsensor electrodes, and B comprising 64 independently addressable microdisc voltametric electrodes. Each device shows the large area counter electrode (middle) and the reference electrode as a band around the counter electrode...

Tsunozaki, K., Einaga, Y., Rao, T.N. and Fujishima, A. (2002) Fabrication and electrochemical characterization of boron-doped diamond microdisc array electrodes. Chem. Lett., 5, 502. 

Not only metallic MEA were prepared by electrode assembly methods. Martin et al. reported a procedure for preparing a carbon microdiscs array by filling the pores of a microporous membrane (3, 8, and 13 pm pores diameter) with carbon paste.Jin and coworkers proposed another procedure to produce carbon MEA. A small amount of mercury was first inserted into a glass capillary (Fig. 20.4a). Then about 90 carbon fibers were carefully inserted into the other end of the glass capillary (Fig. 20.4b). The carbon fiber array was sealed to the tip of... 

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