Finite conical electrode

Fig. 3.13 Popular ultra-micro electrode (UME) geometries, a radius of disk or finite conical electrode, r0 radius of hemispherical electrode, b inner radius of ring electrode, and c outer radius of ring electrode (after Zoski 2002)...

Zoski CG, Liu B, Bard AJ (2004) Scanning electro-chanical microscopy theory and characterization of electrodes of finite conical geometry. Anal Chem 76(13) 3646-3654. doi 10.1021/ac049938... 

FIGURE 5.10 Steady-state current-distance curves for a conical tip over conductive (A) and insulating (B) substrates corresponding to the values of the parameter f/=/i/a shown in the figure. L is the distance between the substrate and the point of tip closest to it normalized by the base radius. The upper curve in (A) and the lower curve in (B) were computed for a disk-shaped tip. (Adapted from Zoski, C.G., Liu, B., and Bard, A.J., Scanning electrochemical microscopy Theory and characterization of electrodes of finite conical geometry. Anal. Chem., 76, 3646-3654, 2004. Copyright 2004 American Chemical Society.)... 

If a small (submicrometer) tip is to be used in quantitative measurements, it is important to show that the metal surface is not recessed into the insulator since the mass transport coefficient will be altered. This is possible via a study of the approach curve a recessed tip does not produce as large a positive feedback [26]. Recessed tips have also been produced intentionally for single molecule experiments [79, 80]. Fan and coworkers [80] simulated a special case of the recessed electrode with the radius of the circular hole in the insulator equal to the disk radius. An analytical approximation for recessed tips with the hole in the insulator sheath different from the disk radius is also available [25]. The feedback effect is also reduced for tips, which are conical or spherical caps, but the shape of the approach curve provides some information on the tip geometry, for example, the solid angle [26]. Accurate numerical simulations of such tips by the finite difference method are more costly than for microdisks, but have been... 

In employing the finite-element method to solve the PDFs, the irregular-shaped conical nanopore is divided into many small components in order to obtain an approximate simultaneous solution to the differential equations. This approach is validated by solving simple electrochemical problems (e.g., EDL structure near a flat metal electrode ) and comparing the simulation results with analytical solutions. 

Nann and Heinze [39] developed and used an adaptive finite element (AFE) algorithm to carry out simulations of steady-state, chronoamperometric, and voltammetric SECM responses for various nondisk tip geometries, for example, hemispherical, conical, and capillary electrodes. 

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