Microelectrode geometry

The planar, cylindrical, and spherical forms of Fick s second law, and combinations of those forms, are sufficient to describe diffusion to most microelectrode geometries in use today. Just as was illustrated in Chapter 2, the appropriate form of Fick s second law is solved, subject to the boundary conditions that describe a given experiment, to provide the concentration profile information. The sought-after current-time or current-voltage relationship is then obtained by evaluating the flux at the electrode surface. 

In Fig. 2.10, the boundary between the enzyme-containing layer and the transducer has been considered as having either a zero or a finite flux of chemical species. In this respect, amperometric enzyme sensors, which have a finite flux boundary, stand apart from other types of chemical enzymatic sensors. Although the enzyme kinetics are described by the same Michaelis-Menten scheme and by the same set of partial differential equations, the boundary and the initial conditions are different if one or more of the participating species can cross the enzyme layer/transducer boundary. Otherwise, the general diffusion-reaction equations apply to every species in the same manner as discussed in Section 2.3.1. Many amperometric enzyme sensors in the past have been built by adding an enzyme layer to a macroelectrode. However, the microelectrode geometry is preferable because such biosensors reach steady-state operation. 

This sensor uses cylindrical microelectrode geometry (Fig. 7.14) for which the diffusion-reaction reaction is written in spherical coordinates, similar to (2.24). 

Scheme 2.4 Most common electrode and microelectrode geometries and their diffusion fields...

The current for a reversible EE mechanism can achieve a stationary feature when microelectrodes are used since in these conditions the function fG(t, qa) that appears in Eq. (3.150) transforms into fG,micro given in Table 2.3 of Sect. 2.6. For microelectrode geometries for which fo.micro is constant, the current-potential responses have a stationary character, which for microdiscs and microspheres can be written as [16] ... 

The analysis of the EC and CE mechanisms under steady-state conditions at other microelectrode geometries is much more complex. In the case of microdiscs,... 

In this chapter, although the various microelectrode geometries are described and literature is provided both to theory and simulation work, the emphasis is laid on the UMDE. The principles of simulation at this electrode are then applicable to the others. 

At macroelectrodes, semi-infinite linear or one-dimensional diffusion is appropriate. For microelectrode geometries, the nature of diffusion is more complex, as significant diffusion occurs in more than one dimension (Section 5). 

Fig.1 The most common microelectrode geometries and their associated diffusion fields.

The BEM has been applied in scanning electrochemical microscopy applications by Fisher and Denuault [169] to examine the influence of probe and substrate surface topography. In addition, time-dependent phenomena have been assessed in oil droplets [170, 171] and a range of microelectrode geometries using the dual reciprocity method (DRM) [172] closely related to the BEM [173]. 

Effect of nonideal microelectrode geometry on resistance and capacitance ... 

Expression for the limiting current at various microelectrode geometries... 

Last, Fig. 2.18 shows the different microelectrode geometries that can be readily encountered in electrochemistry. For an elegant overview of microelectrodes and their benefits and applications, readers are directed to Ref [7]. 

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