Regular Arrays of UMDEs

UMEs are usually arranged in a regular pattern to form an array. Multitudes of parallel UMBEs are present in an IDA electrode. Disks or square shaped UMEs can be arranged in a square or hexagonal lattice. Randomly distributed UMDEs—if they are not too closely packed—can be modelled by estimating the nearest-neighbour distribution [342] and statistical considerations, as has been done by Scharifker [343] and later by Compton et al. [344-348] and others [77, 349]. The next section looks into the simulation approach for regular arrays of UMDEs. 

As mentioned before, a motivation for operating a UMDE array in parallel mode is to multiply the electrochemical response of a single UMDE in the array, for example to decrease the detection limit of an analyte. However, the behaviour of the array response depends on the design of the array and four parameters are crucial for this (1) the size of the UMDEs, given by their radius a (2) the centre-to-centre distance I between the nearest neighbour electrodes (3) the total number Ng of UMEs in the array (4) the duration of the experiment or observation time. For the regular array we assume that both I and a have the same values for all electrodes. Points (2) and (3) also determine the overall size of the array. In practice this size is often restricted by experimental conditions, e.g. the dimension of the electrochemical cell. 

For ahexagonal configuration, illustrated in Fig. 12.14b, the equivalence of the areas of the hexagon and the circle concentric with the UMDF results in 

Using these approximations the simulation task becomes essentially the same as already described for the simulation of a UMDF undisturbed by other electrodes. The pde to solve is given by (12.2). Normalisation is done as already described for a single UMDF, resulting in Fq. (12.17) for potential step or (12.27) for LSV conditions. The difference is that the UMDF is now in effect embedded in a walled area of base radius d, i.e. the radius of the diffusion domain, so that r ax = d and the boundary condition changes from 

Equation (12.19) is applied to calculate the current at a single electrode. To calculate the current of the array, (12.19) is multiplied by Ne, the number of electrodes of the array. 

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Fig. 12.13 Top view of sections of regular arrays of UMDEs arranged in (a) a square and (b) hexagonal lattice...

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