Steady-state current microdisc

By far, the most common UME geometry is that of a microdisc inlaid in an insulating sheath but, unlike spherical electrodes, the surface of an iiflaid microdisc UME is not uniformly accessible as electrolysis at the edges of the microdisc diminishes diffusion to the disc centre. A rigorous mathematical treatment of the steady-state current at a microdisc is not possible but similar considerations to those described above apply. The faradaic current flowing at a microdisc UME during the electrolysis of a redox-active species contains contributions from a transient component... 

So, in the case of microdiscs under steady-state conditions, the following general expression for the current can be written ... 

Figure 7.36a-c shows the forward and reverse components of the square wave current. When the chemical kinetics is fast enough to achieve kinetic steady-state conditions (xsw > 1.5 and i + k2 > (D/rf), see [58,59]), the forward and reverse responses at discs are sigmoidal in shape and are separated by 2 sw. This behavior is independent of the electrode geometry and can also be found for spheres and even for planar electrodes. It is likewise observed for a reversible single charge transfer at microdiscs and microspheres, or for the catalytic mechanism when rci -C JDf(k + k2) (microgeometrical steady state) [59, 60]. 

The peak height of the SWV net current increases in all the cases with the square wave amplitude until it reaches a constant value (plateau) for sw > lOOmV. This value depends on the electrode shape and size and also on the catalytic rate constants. Under steady-state conditions, the plateau current at microspheres and microdiscs is given by... 

For the case of a microdisc electrode convergent diffusion leads to a steady-state limiting current given by (91). 

Consideration of Fig. 32 implies that chemical information may be extracted from microelectrode experiments either via steady-state measurements or via transient, often cyclic voltammetric, approaches. In the former approach, measurements are made of the mass transport limited current as a function of the electrode size - most usually the electrode radius for the case of a microdisc electrode. This may be illustrated by reference to a general ECE mechanism depicted by (23a)-(23c) where k is the rate constant for the C step. 

For many mechanisms, the steady-state Eia or N tt value is a function of just one or two dimensionless parameters. If simulations are used to generate the working curve (or surface) to a sufficiently high resolution, the experimental response may be interpolated for intermediate values without the need for further simulation. A free data analysis service has been set up (Alden and Compton, 1998) via the World-Wide-Web (htttp //physchem.ox.ac.uk 8000/wwwda/) based on this method. As new simulations are developed (e.g. for wall jet electrodes), the appropriate working surfaces are simulated and added to the system. It currently supports spherical, microdisc, rotating disc, channel and channel microband electrodes at which E, EC, EC2, ECE, EC2E, DISP 1, DISP 2 and EC processes may be analysed. 

As discussed for the case of (hemi)spherical microelectrodes in Chapter 4, the response in cyclic voltammetry at microdiscs varies from a transient, peaked shape to a steady-state, sigmoidal one as the electrode radius and/or the scan rate are decreased, that is, as the dimensionless scan rate, a = Y r lv/TZTD, is decreased. The following empirical expression describes the value of the peak current of the forward peak for electrochemically reversible processes [11] ... 

For the case of a microelectrode (a microdisc), a steady-state (limiting) current (4) is observed (see Figure 6.1) which is quantitatively described by... 

Steady-State Limiting Current at a Microdisc Problem... 

Use this equation to predict the steady-state limiting current at the microdisc electrode for an n-electron process. Comment on any possible limitations of the... 

The steady-state diffusion-controlled current at the microdisc electrode is given by... 

The electroreduction of an approximately 2mM solution of nitrobenzene in acetonitrile/0.1 M tetrabutylammonium perchlorate was studied using a platinum microdisc electrode of radius, r, 24 fim. A steady-state limiting current of —4.05 X 10 A was observed at long time, while at short times the following current (f)-time (t) data were collected. 

First, in the case of microdiscs, microrings, and microhemispheres, the current reaches a steady state value. The ohmic loss is much smaller than on larger electrodes and the steady-state ohmic loss is independent of the electrode geometry. This allows electrochemical experiments to be carried out in resistive media. 

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