Diffusion inlaid electrodes

Enhancement of the diffusion flux at the edge of an inlaid electrode. 

Edge effect — Enhanced diffusion to the edges of an inlaid electrode. See electrode geometry, and -> diffusion,... 

In a typical voltammetric experiment, a constant voltage or a slow potential sweep is applied across the ITIES formed in a micrometer-size orifice. If this voltage is sufficiently large to drive some IT (or ET) reaction, a steady-state current response can be observed (Fig. 1) [12]. The diffusion-limited current to a micro-ITIES surrounded by a thick insulating sheath is equivalent to that at an inlaid microdisk electrode, i.e.,... 

It must be emphasized again that the mid-peak potential is equal to E° for a simple, reversible redox reaction when neither any experimental artifact nor kinetic effect (ohmic drop effect, capacitive current, adsorption side reactions, etc.) occurs, and macroscopic inlaid disc electrodes are used, that is, the thickness of the diffusion layer is much higher than that of the diameter of the electrode. 

The analytical approximations presented above are best fits to numerical simulations of the diffusion problems for relatively simple and well-defined electrochemical systems, for example, an inlaid disk electrode approaching a flat, infinite, and uniformly reactive substrate surface. In most quantitative SECM experiments, the use of such approximations could be justified. However, no analytical approximations are available for more complicated processes and system geometries, and so one has to resort to computer simulations. 

Electrode geometry — Figure 3. Concentration profiles at an array of inlaid disks at different time in response to an electrochemical perturbation. a Semi-infinite planar diffusion at short times b hemispherical diffusion at intermediate times c semi-infinite linear diffusion due to overlap of concentration profiles at long times... 

As indicated in the right panel in this figure, rotation about the main axis of the cylinder forces the solution toward the flat end that contains the inlaid disk and ring electrodes. As the surface is closely approached, the solution spreads outward, forming a uniformly accessible diffusion layer along the surface of the disk. The RRDE has proven exceedingly useful in studies of 02 reduction, as solution phase... 

Several advantages of the inlaid disk-shaped tips (e.g., well-defined thin-layer geometry and high feedback at short tip/substrate distances) make them most useful for SECM measurements. However, the preparation of submicrometer-sized disk-shaped tips is difficult, and some applications may require nondisk microprobes [e.g., conical tips are useful for penetrating thin polymer films (18)]. Two aspects of the related theory are the calculation of the current-distance curves for a specific tip geometry and the evaluation of the UME shape. Approximate expressions were obtained for the steady-state current in a thin-layer cell formed by two electrodes, for example, one a plane and the second a cone or hemisphere (19). It was shown that the normalized steady-state, diffusion-limited current, as a function of the normalized separation for thin-layer electrochemical cells, is fairly sensitive to the geometry of the electrodes. However, the thin-layer theory does not describe accurately the steady-state current between a small disk tip and a planar substrate because the tip steady-state current iT,co was not included in the approximate model (19). 

It is known that the performance of an electrode with respect to temporal and spatial resolution and sensitivity scales inversely with the electrode radius. For an inlaid fiber electrode, the exposed end can be approximated as a disk-shaped electrode. As the electrode diameter is smaller than that of the diffusion layer thickness, electrochemical properties become fundamentally different from a conventional macroelectrode. In cyclic voltammetry (CV) measurements, the magnitude of the peak current of the redox signal is the sum of two terms linear diffusion as described in the Cottrell equation, and nonlinear radial diffusion [76] ... 

Most of the initial practical and theoretical work in cyclic voltammetry was based on the use of macroscopic-sized inlaid disc electrodes. For this type of electrode, planar diffusion dominates mass transport to the electrode surface (see Fig. II. 1.13a). However, reducing the radius of the disc electrode to produce a micro disc electrode leads to a situation in which the diffusion layer thickness is of the same dimension as the electrode diameter, and hence the diffusion layer becomes non-planar. This non-linear or radial effect is often referred to as the edge effect or edge diffusion . 

The current density on a stationary electrode immersed in a flowing solution is not uniform over the whole electrode surface. At an inlaid plate over which the solution flows, the diffusion layer thickness and the steady-state distance 8 increase downstream [57, 65, 66] ... 

Notes The inlaid disc of radius a and the hemispherical electrode of radius ro are considered deviations within 5% and 1% are computed according to Eq. (18). Diffusion coefficient D = 1 x 10" m s , diameter d calculated according to Fig. 5. 

If microelectrodes (hemispherical or inlaid-disc types) are used, the mass transport rate due to radial diffusion to the electrode is enhanced so that the current contribution of chemical steps is decreased relative to the diffusive transport. This statement can be easily verified on any EQrrE sequence at a macroelectrode of radius a 100 /zni the diffusion-controlled two-electron wave is observed when two one-electron electrode processes occurs at the same potential. At microelectrodes in steady-state regime the time scale is too short for the overall reaction and the number of electrons measured on the limiting current gradually declines to unity with decreasing electrode radius. On the other hand, the change in the current as a function of the electrode radius can be used to determine the rate constants of involved chemical steps. 

Figure 2.7 (a) Cyclic voltammograms simulated assuming two-dimensional semi-infinite diffusion to an inlaid disk electrode (—) (electrode A in Eigure 2.1) and one-dimensional diffusion to a planar electrode (--) (electrode B in Eigure 2.1) and the corresponding semiinte-... 

Using the standard inlaid disk electrode geometry that has been described, the equations in the planar and nonlinear diffusion limit are ... 

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... 

The complex time dependence of the diffusion process to an inlaid disk electrode is described by Eqs. (5.10) and (5.11), which are defined in terms of the dimensionless time parameter 0. It follows that under a specific set of experimental conditions, a unique ratio of Vd / will apply and this ratio can be defined as a single parameter, p. In order to obtain the convolved current, M(t), an initial estimate for p must be inputted into the convolution algorithm. If c is known and Ml can be obtained from the limiting convolved current plateau, then it is possible to iteratively refine p based on Eq. (5.7) for a known value of Tq ... 

A commonly enconntered experimental scenario arises when an inlaid disk electrode is nsed and the electron-transfer kinetics are quasireversible. The implication in this circnmstance is that the convolved current will no longer be directly proportional to the snrface concentration in the vicinity of the standard potential as described by Eq. (5.6), because the current is kinetically limited in this potential region. However, once the diffusion limited plateau is attained, then the convolved cnrrent is once again directly proportional to the surface concentration, and Eq. (5.7), which is the limiting form of Eq. (5.6), is applicable [46, 50],... 

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