Microelectrodes shapes

Figure 4.13 (a) Microelectrode-shaped voltammograms obtained on the graphenedecorated SAM Au electrode, (b) Schematic of the microelectrode fabrication. (Reprinted from Ref. [110].)... 

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

Size and Shape Selective Synthesis of Metal Nanoparticles by Seed-Mediated Method and the Catalytic Activity of Growing Microelectrodes (GME) and Fully Grown Microelectrodes (FGME)... 

Thus the time during which the transport process attains the steady state depends strongly on the radius of the sphere r0. The steady state is connected with the dimensions of the surface to which diffusion transport takes place and does, in fact, not depend much on its shape. Diffusion to a semispherical surface located on an impermeable planar surface occurs in the same way as to a spherical surface in infinite space. The properties of diffusion to a disk-shaped surface located in an impermeable plane are not very different. The material flux is inversely proportional to the radius of the surface and the time during which stationary concentration distribution is attained decreases with the square of the disk radius. This is especially important for application of microelectrodes (see page 292). 

Under these conditions, as sketched on the left-hand side of Figure 4.16, the linear diffusion layer has become very thin, on the same order as the constrained diffusion layer. The response amounts therefore to the steady-state response of an assembly of nas independent disk microelectrodes. The shape of the S-wave and the location of the half-wave potential is a function of the last term in the denominator on the right-hand side of equation (4.18). The parameter that governs the kinetic competition between electron transfer and constrained diffusion is therefore... 

It essentially makes use of two identical, stationary microelectrodes immersed in a well stirred solution of the sample. A small potential ranging between these electrodes and the resulting current is measured subsequently as a function of the volume of reagent added. The end-point is distinctly characterized by a sudden current rise from zero or a decrease in the current to zero or a minimum at zero in a V-shaped curve. 

For the sake of completeness, glass microelectrodes [48, 59, 184] will first be mentioned. Two types of these electrodes are used, spear-shaped microelectrodes [59] and recessed-tip microelectrodes [165] (see fig. 4.5). In the former case, the microelectrode is drawn from a capillary of an ion-exchanger glass and is insulated on the outside, except for the tip, by inserting the microelectrode into a micropipette made of an inactive glass. In the latter case, the outer micropipette extends over the microelectrode tip. The two capillaries are sealed together and the ISM is in contact with the liquid between the two capillaries. 

The use of microelectrodes can be avoided in measurements on samples with micro litre volumes if the measurement is performed in a thin layer of the sample solution between a flat ISE and a plate-shaped reference electrode which are placed close together [153]. 

Arrays. One can compensate for the tiny currents produced by microelectrodes by working with many of them placed together within a board of an insulating material (connected at the back so that all the currents add) (see Fig. 7.34). Then, if r is the radius of each electrode (assumed to be disklike in shape) and ti the number per unit area, rrtrp is the total active area. If L is the distance between the spots," (VnL)2 is the total area. Hence,... 

Figure 11.6 Fabrication procedure of an IDA microelectrode. An oxidized silicon wafer (A) is coated with platinum (B). Carbon film is pyrolyzed on it (C). The substrate is coated with photoresist, which is exposed and developed (D) unnecessary portions are then removed by reactive ion etching (E). After removing the photoresist, an Si3N4 layer is deposited on the substrate (G). The substrate is coated with photoresist, which is exposed and developed (H) then the desired shape of the carbon electrode is exposed by reactive-ion etching (I). [Adapted from Ref. 36.]...

As described in the introduction, submicrometer disk electrodes are extremely useful to probe local chemical events at the surface of a variety of substrates. However, when an electrode is placed close to a surface, the diffusion layer may extend from the microelectrode to the surface. Under these conditions, the equations developed for semi-infinite linear diffusion are no longer appropriate because the boundary conditions are no longer correct [97]. If the substrate is an insulator, the measured current will be lower than under conditions of semi-infinite linear diffusion, because the microelectrode and substrate both block free diffusion to the electrode. This phenomena is referred to as shielding. On the other hand, if the substrate is a conductor, the current will be enhanced if the couple examined is chemically stable. For example, a species that is reduced at the microelectrode can be oxidized at the conductor and then return to the microelectrode, a process referred to as feedback. This will occur even if the conductor is not electrically connected to a potentiostat, because the potential of the conductor will be the same as that of the solution. Both shielding and feedback are sensitive to the diameter of the insulating material surrounding the microelectrode surface, because this will affect the size and shape of the diffusion layer. When these concepts are taken into account, the use of scanning electrochemical microscopy can provide quantitative results. For example, with the use of a 30-nm conical electrode, diffusion coefficients have been measured inside a polymer film that is itself only 200 nm thick [98]. 

Our last example does not involve the rate of a chemical reaction, but instead, the effect of temperature on diffusion rates [25]. One of the motivations for using microelectrodes as in the previous example is to allow fast experiments without appreciable iR drop. When used in the opposite extreme of very small scan rates, microdisk electrodes produce steady-state voltammograms that have the same sigmoidal shape as dc polarograms and RDE voltammograms (cf. Chap. 12). 

Figures 8.7a and b show cyclic voltammograms obtained on the skin with a platinum microelectrode and with a gold microelectrode, respectively. The shape of the current-potential curves was different.

For more than 300 platinum microelectrodes produced, the average metallic wire radius is 30 + 3 pm (i.e. an accuracy of 10%). This value is coherent with the wire radius commercially indicated and shows the good repeatability of microelectrodes fabrication. In addition, more than 100 reproducible cyclic voltammograms can be recorded successively in the ferricyanide solution without modification of the curve shape. 

Special attention should be paid to spherical geometry, since the mathematical treatment of spherical microelectrodes is the simplest and exemplifies very well the attainment of the steady state observed at microelectrodes of more complex shapes. Indeed, spherical or hemispherical microelectrodes, although difficult to manufacture, are the paragon of mathematical model for diffusion at microelectrodes, to the point that the behavior of other geometries is always compared against them. 

Note that Eq. (5.99) does not contain parameters related to the microelectrode itself. Therefore, this equation applies to any steady-state microelectrode cell, regardless of the shape and size of the electrode, and with the sole provision that the cell has a geometry that permits a diffusive steady state and that the auxiliary electrode is large enough to remain depolarized. 

The forward and reverse currents i/rf and i//( of the square wave voltammograms corresponding to Fig. 7.5c are shown in Fig. 7.6a for microelectrodes of the four electrode geometries considered. From these curves, it can be seen that both currents present a sigmoidal shape and they are separated by 2Esw in the case of spheres and discs. This behavior clearly shows that the steady state has been attained. On the other hand, in the case of cylinders and bands, y/f and i/// show a transient behavior under these conditions. From Fig. 7.6b, c, it can be verified that a decrease in the radius, ((w/2) = rc = 0.1 pm) and that of both radius and frequency (Fig. 7.6c, (w/2) = rc = 0.1 pm and/= 10 Hz) do not lead to a stationary SWV response at cylinder and band microelectrodes. 

The actual retina contact structure incorporates 12 or 24 independent electrodes, respectively. The electrodes were arranged concentrically to minimize the electrical stray field during stimulation. We established the microfabrication process for double metallization layers needed to obtain concentric microelectrodes. In a temper step, the electrodes were formed into a convex shape according to the curvature of the eye. The generation of convex shapes was possible since the stimulator was designed in concentric rings interconnected by s-shaped bridges (Fig. 26). 

Compared to conventional (macroscopic) electrodes discussed hitherto, microelectrodes are known to possess several unique properties, including reduced IR drop, high mass transport rates and the ability to achieve steady-state conditions. Diamond microelectrodes were first described recently diamond was deposited on a tip of electrochemically etched tungsten wire. The wire is further sealed into glass capillary. The microelectrode has a radius of few pm [150]. Because of a nearly spherical diffusion mode, voltammograms for the microelectrodes in Ru(NHy)63 and Fe(CN)64- solutions are S-shaped, with a limiting current plateau (Fig. 33a), unlike those for macroscopic plane-plate electrodes that exhibit linear diffusion (see e.g. Fig. 18). The electrode function is linear over the micro- and submicromolar concentration ranges (Fig. 33b) [151]. 

Fig. 3.15 Schematic shape of two different types of carbon microelectrodes decorated with enzyme (after Horrocks et al. 1993)...

The choice of an appropriate electrochemical sensor is governed by several requirements (1) the nature of the substrate to be determined (ions or redox species) (2) the shape of the final sensor (microelectrodes) (3) the selectivity, sensitivity, and speed of the measurements and (4) the reliability and stability of the probe. The most frequently used sensors operate under potentiometric or amperometric modes. Amperometric enzyme electrodes, which consume a specific product of the enzymatic reaction, display an expanded linear response... 

Figures 1IC-E show SEM images of test patterns of silver that were fabricated using pCP with hexadecanethiol, followed by selective chemical etching [102], The SAMs protect the underlying substrates from dissolving by blocking the dilSisional access of etchants. The ability to generate arrays of microstructures of coinage metals with controlled shapes and dimensions is directly useful in fabricating sensors and arrays of microelectrodes.

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