Disk ultramicroelectrodes methods

Differential-pulse polarography was reported to evaluate the content of THBQ in edible oils (Tonmanee and Archer, 1982 Cortes et al., 1993). Differential-pulse voltammetry using a carbon paste electrode modified with nickel phthalocyanine was applied to determine BHA in potato flakes (Ruiz et al., 1995). Square-wave voltam-metric methods employing carbon-disk ultramicroelectrodes (UME) (Ceballos and Fernandez, 2000), glassy carbon electrodes (Raymundo et al., 2007), platinum electrodes... 

Electrode processes are often studied under steady-state conditions, for example at a rotating disk electrode or at a ultramicroelectrode. Polarog-raphy with dropping electrode where average currents during the droptime are often measured shows similar features as steady-state methods. The distribution of the concentrations of the oxidized and reduced forms at the surface of the electrode under steady-state conditions is shown in Fig. 5.12. For the current density we have (cf. Eq. (2.7.13))... 

In the case of the ultramicroelectrodes such as the disk electrode, it is necessary to integrate over the surface, and sometimes there will be unequally spaced points along the surface, as for example, in direct discretisation on an unequal grid in the example program UME DIRECT. As mentioned in Chap. 12, it is found that due to the errors in the computed concentration values, the local fluxes are so inaccurate that any integration method better than the simple trapezium method is not justified. The routine U TRAP is thus recommended here. It integrates local current densities, precalculated by using the above routine U DERIV. 

These methods constitute the frame on which any particular method can be elaborated. Yet in practice, the experimental difficulty is that with standard apparatus, 5 /D cannot be varied over an extremely wide range. For example, with the rotating disk electrode (RDE), which is the most convenient steady-state method (with the exception of ultramicroelectrodes [109]), 8 depends on the rotation frequency w of the electrode (see Chapter 2). Yet to maintain correct hydrodynamic conditions w cannot be varied, with... 

As was written in the foregoing, the major problems in electrochemical digital simulation in one dimension have now been solved. The new frontier is in two-and more-dimensional systems. During the last 20 years or so, ultramicroelectrodes have more or less replaced the mercury drop, and these form a two-dimensional diffusion space, whether they be single disks, or disk arrays, or (arrays of) strips or generator-collector strips, and so forth. Here, the problems include the fact of the large numbers of nodes required for reasonably accurate computations, and thus, long computation times and extreme computer memory needs, at the least as well as the fact that discretization usually produces (widely) banded systems of equations, so that sophisticated methods of solution need to be used in order to have sufficient memory and realistic computation times. There is also a lack of theoretical work on the numerical methods used. It is by no means certain that the familiar stability criteria will apply with these systems, which often have... 

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