Minimum grid digital simulation of chronoamperometry at a disk electrode

Abstract

a b s t r a c tWe seek to find the best ways to achieve a minimum grid with a given target accuracy in the computed current in the simulation of a diffusion limited chronoamperometric experiment at an ultramicrodisk electrode. We present some results for direct discretisation on the cylindrical geometry in (R, Z) space and in transformed coordinates (Â, ), comparing four commonly used transformations. In all cases, the use of multi-point spatial derivative approximations are explored to find an optimum. Orthogonal collocation is studied in the two dimensions, and found less efficient than an evenly divided grid and smaller multi-point approximations. The eigenvalue-eigenvector method is studied and found to be relatively inefficient but was useful in providing some information on error waves seen with three of the four transformations used. These error waves are not due to an error propagation, a fact that became clear from the eigenvalue-eigenvector method, which reproduced the waves.

Planar diffusion to macro disc electrodes—what electrode size is required for the Cottrell and Randles-Sevcik equations to apply quantitatively?

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“…At long times, however, diffusion at the electrode surface is no longer strictly planar, as the spherical growth of the diffusion layer permits radial diffusion to the electrode edge. [19][20][21][22] Thus, the Anson equation can be modied with a correction factor to account for radial diffusion Fig. 1 (equation c).…”

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“…Despite the approximate nature of N AB , it is still perceived as the “gold standard” of the theoretical maximum collection efficiency as of today. ,− N AB suggests that collection efficiency is only a function of the relative geometry of ring and disk and unaffected by the absolute size of electrodes and rotational speed. Nevertheless, in light of the results and modeling for the RDE discussed above, N AB may likely not hold true in some experimental scenarios.…”