Geometry of a Regular Array

Suppose that a microdisc array consists of a hexagonal array of microdiscs separated by insulating material, each disc having radius r = 1 /rm, and a line-of-centres separation between discs of 10 fjtm. 

If we apply a zero-flux boundary at r = rt)D h is approximately equivalent to simulating an infinite hexagonal array described as above, but the simulation involves a two-dimensional space rather than a three-dimensional space, and therefore is much faster. Extensive studies have shown this approximation to be accurate for the purpose of analysing many experiments. 

Therefore, Case 1 behaviour (the CottreU/Randles-Sevcflc regime) is only significant for this example at timescales less than a millisecond, as would be expected for a microdisc electrode. 

The transition from Case 2 to Case 3 occurs with diffusion layer overlap, which will occur after diffusion layers from each electrode have extended about 5.25 fjtm and therefore encoimtered each other and begun to shield each other s diffusion zones. Since the mean diffusion layer extent in any direction is Xdiff s/2Dt, to diffuse a characteristic distance of 5.25 fim requires  

Therefore, a true Case 2 behaviour (steady-state voltammetry to an isolated microdisc) is not likely to be observed, since diffusion layers will interact for this array after only tens of microseconds. 

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