Inlaid electrodes

Of the many complex transport geometries, some of the most important are those encountered with inlaid electrodes (Fig. 14) [25— 30], in which the electrode is planar and embedded in an insulator whose surface is a continuation of the electrode plane. If such an electrode is large, it may be appropriate to treat it as a case of planar transport, with a correction for the edge effect [31, 32], For a small inlaid electrode, however, or for experiments of long duration, such an approximation is no longer valid. 

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,... 

The inlaid disk and inlaid ring electrode can be combined to make an inlaid electrode in which the disk forms the interior which is surrounded by the ring. This is called a ring-disk electrode and when the entire assembly is rotated about its vertical axis it is referred to as a rotating ring-disk electrode (RRDE). Figure 4 illustrates a rotating disk electrode (RDE). 

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.,... 

Galceran, J., Taylor, S. L. and Bartlett, P. N. (1999). Application of Danckwerts expression to first-order EC reactions. Transient currents at inlaid and recessed microdisc electrodes, J. Electroanal. Chem., 466, 15-25. 

At an inlaid microdisk electrode, the dependence of the dimensionless net peak current on the sphericity parameter is given by the following equation [31] ... 

Figure 2.21 shows the dependence of dimensionless net peak currents of ferrocene and ferricyanide on the sphericity parameter (note that A0p = AT], andy = p)-The SWV experiments were performed at three different gold inlaid disk electrodes (ro = 30, 12.5 and 5 pm) and the freqnencies were changed over the range from 20 to 2000 Hz [26]. For ferrocene the relationship between AT], and p is linear A Fp = 0.88 + 0.74p. This indicates that the electrode reaction of ferrocene is elec-trochemically reversible regardless of the frequency and the electrode radius over the range examined. For ferricyanide the dependence of AT], on p appears in sequences. Each seqnence corresponds to a particular value of the parameter The results obtained with the same freqnency, but at different microelectrodes, are cormected with thin, broken lines. The difference in the responses of these... 

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. 

Several approaches to solving this expression for various boundary conditions have been reported [25,26]. The solutions are qualitatively similar to the results at a hemisphere at very short times (i.e., when (Dt),y4 rD), the Cottrell equation is followed, but at long times the current becomes steady-state. Simple analytical expressions analogous to the Cottrell equation for macroplanar electrodes or Equation 12.9 for spherical electrodes do not exist for disk electrodes. For the particular case of a disk electrode inlaid in an infinitely large, coplanar insulator, the chronoamperometric limiting current has been found to follow [27] ... 

An other interesting strategy is the modification of the surface of the electrodes with multiwalled carbon nanotubes (MWNTs) or single-walled carbon nanotubes (SWNTs) [13,32]. The MWNTs are grown on the electrodes covered with a nickel catalyst film by plasma-enhanced chemical vapour deposition and encapsulated in Si02 dielectrics with only the end exposed at the surface to form an inlaid nanoelectrode array [13]. In the other case, commercial SWNTs are deposited on SPE surface by evaporation [32], The carbon nanotubes are functionalised with ssDNA probes by covalent attachment. This kind of modification shows a very efficient hybridisation and, moreover, the carbon nanotubes improve the analytical signal. 

The quantitative SECM theory has been developed for various heterogeneous and homogeneous processes and for different tip and substrate geometries [56-59]. Here, we survey the theory pertinent to an inlaid disk electrode (Fig. 5) approaching a flat substrate, which can be considered infinitely large as compared to the tip size. The case of finite substrate size was treated by Bard et al. [60]. The theory for nondisk tips (e.g., shaped as a cone or a spherical cap) is discussed in Refs. [12-14] and [58], and in Section IV.B.2. 

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. 

Another type of nondisk-shaped SECM tips are UMEs shaped as spherical caps. They can be obtained, for example, by reducing mercuric ions on an inlaid Pt disk electrode or simply by dipping a Pt UME into mercury [15]. An approximate procedure developed for conical geometry was also used to model spherical cap tips [12]. Selzer and Mandler performed accurate simulations of hemispherical tips using the alternative direction implicit final difference method to obtain steady-state approach curves and current transients [14]. As with conical electrodes, the feedback magnitude deceases with increasing height of the spherical cap, and it is much lower for a hemispherical tip than for the one shaped as a disk. 

Carbon microelectrodes decorated with enzyme were prepared with two different methods (Horrocks et al. 1993). Type A electrode (Fig. 3.15a) was prepared by heat sealing carbon fibers, with diameter of 11 or 8 p,m, in 2-mm outer diameter (OD) Pyrex capillaries. The resulting tip geometry was an inlaid microdisk electrode. The carbon microdisk was then coated with the electrically wired enzyme by soaking the... 

Electrode geometry — Figure 2. Array geometries, a Random array of inlaid disk electrodes b ordered array of inlaid disk electrodes c double band array d interdigitated array... 

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... 

Rotating ring disk electrode (RRDE) — This electrode consists of a thin metallic ring inlaid around the metallic disk that is situated in the center of the base of the insulating cylinder. Because of the radial component of the solution movement, which is caused by the rotating of the cylinder, the products of the electrode reaction formed on the disk electrode are carried over the... 

A point electrode resembles a spot. It adopts a spherical-shaped concentration profile and potential distribution in the solution. As a result, such electrodes easily achieve a steady state and yield a steady-state current. This current is expected to be proportional to the characteristic length (radius) of the electrode. A typical point electrode is a disk electrode inlaid on an insulating plane. On the other hand, an ultrathin ring electrode shares characteristics of the point electrode and the line electrode. It appears as a point from a position distal from the electrode, but it resembles a curved line upon closer inspection. It exhibits a steady-state current because of the feature of the point electrode. Next, a plane electrode of interest is a microarray electrode, which is composed of point electrodes and line electrodes on a planar insulator. It is versatile in functionality by designing the geometrical arrangement. A mode of mass transport depends on whether elementary electrodes are a point or a line electrode. 

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] ... 

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