Ultramicrodisk electrode

Ferrigno et al. [239] describe the use of FEM for steady state simulations of recessed, flush and protruding ultramicrodisk electrodes, giving a good description of FEM. The method was made adaptive by Nann (and Heinze) [407,408], and Harriman et al. later published an extensive series of papers on adaptive FEM [287,288,289,290,291]. 

Blitz D, 0sterby O, Strutwolf J (2008) Comparison of flux approximations in electrochemical digital simulation. Part 2 complications due to homogeneous chemical reactions, chaige estimation and application to the ultramicrodisk electrode. J Electroanal Chem 622 51-58... 

Strutwolf J, Britz D (2004) Higher-order discretisations in electrochemical digital simulation. Part 5. Application to stationary ultramicrodisk electrode simulation. J Electroanal Chem 566 15-23... 

Che G, Dong S (1992) Application of ultramicroelectrodes in studies of homogeneous catalytic reactions- Part 111. The condition for quasi-first and second order homogeneous catalytic reactions at ultramicrodisk electrodes in the steady state. Electrochim Acta 37 2701-2705... 

The above applies largely to one-dimensional problems, but two-dimensional simulations are more and more the norm. All the methods described can be applied to these, but there are some sensible choices. For the ultramicrodisk electrode case, the present authors have recently done a detailed study and concluded [79] that one of the more useful transformations such as the Verbrugge/Baker [80] (see Chap. 12 for this and others) is best, combined with multipoint approximations (optimally using five or seven points), and either BI with extrapolation or BDF with the BI start. 

For 2D simulations testing new algorithms, and where there are no proper analytical solutions it is convenient to have reliable reference flux values to compare with. We have provided some of these UMDE REF FLUX for the ultramicrodisk electrode, BAND REF FLUX for the band, and CYL REF FLUX for the cylinder electrode. 

Pyo, M., Bard, A. J. Scanning electrochemical microscopy. 35. Determination of diffusion coefficients and concentrations of Ru(NH3)6 and methylene blue in polyacrylamide films by chronoamperometry at ultramicrodisk electrodes. Electmchim. Acta 1997, 42, 3077. 

Cheng IF, Martin CR (1988) Ultramicrodisk electrode ensembles prepared by incorporating carbon paste into a microporous host membrane. Anal Chem 60 2163-2165... 

Three-dimensional simulations of single electrodes have been done by explicit FD [96, 276], ADI [277] and FEM (COMSOL Multiphysics ) [278]. A three dimensional dual ultramicrodisk system was simulated by FuUan and Fisher using the boundary element method (BEM) [279]. BEM[87, 176, 177, 280] and FEM (using COMSOL Multiphysics ) [281] were employed to simulate complex three dimensional tip-substrate geometries in SECM. Arrays with a small number of electrodes were simulated using ADI [282] and commercial FEM packages Fluxexpert [283, 284] and COMSOL Multiphysics [285, 286]. 

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