Active electrode radius

The general experimental setup is shown in Fig. 37.1. The probe is an amperometric disk-shaped UME that is embedded in an insulating sheath, typically made from glass. Most often the electrode is made from Pt but electrodes from Au and carbon fibers have been used as well. Typical probe diameters are 10 or 25 pm. Of course, smaller electrodes may be used and this area is currently extensively explored. As it will be evident later, it is convenient to characterize the probe by two important radii the radius rT of the active electrode area and... 

Fig. 51.2. An experimental approach curve for a 25 pm diameter Pt UME towards glass. The illustration shows the distance d0 — Offset — Zq between the active electrode surface and the sample in the moment of the mechanical touch by the insulating sheath. The z arrow illustrates the relation to the laboratory coordinate system in which the movement of the UME is measured, z — 0 corresponds to the start point of the approach curve, z0 is the coordinate of the active electrode area, when the insulating sheath touches the surface, zoffset is the coordinate of the surface. Note The tilt of the UME is greatly exaggerated in order to illustrate the principle, while the radius of the glass sheath is smaller in the sketch a real experiment RG = 10. The theoretical curve (solid line) was calculated according to Eq. (1) with the following coordinate transformations z = -rTL+z0ffset rT = 12.84 pm, zoffi5et = 201.52 pm, iT = iT>o0 = 5.554 nA.

Note that the product VbNA is the volume occupied by the gas bubbles if all nucleation sites are active at the same time. In order to take into account the wettability of the electrode surface, we write the volume of a single isolated bubble as Vb = crb dn, where ab= 1/iVis the surface occupied by this bubble and dn is its height written as the product of dn (the mean distance between two nucleation sites) and (the parameter describing the degree of flatness of the bubble). Note that, as shown in Fig. 3.16, is function of the wettability i and the electrode geometry. In particular, for small cylindrical electrodes, where the electrode radius is similar to the bubble radius, can typically reach values around 2. 

The amplitude of the discharges is also directly correlated to the size of the bubble. As shown by Han et al. [51], the amplitude of the discharge peaks follows the same inverse volcano dependence as the bubble diameter. The minimum is reached for an active electrode length equal to its radius. 

An array of microwells filled with the bacteria gel was prepared. The PAP was detected in the wells. The release of PAP into the extracellular liquid indicated the P-Gal activity that is the solubility of the MBP. The authors used a Pt microdisc electrode (radius, 10 mm) as the probe set to 0.30 V vs. Ag/AgCl to record the oxidation current of PAP produced in pGal catalyzed hydrolysis of PAPG. 

According to Eq. (23), the critical pore radius r greatly decreases with increasing electrode potential. It is seen that above a certain critical potential AE b the active barrier as well as the critical pore radius decreases steeply with anodic potential. This critical potential AE is the lowest potential of pore formation and below this potential the passive film is stable against electrocapillary breakdown because of an extremely high activation barrier and the large size of pore nucleus required. 

Figure 17. Energy for the nucleation of a surface film on metal electrode. M, metal OX, oxide film EL, electrolyte solution. Aj is the activation barrier for the formation of an oxide-film nucleus and rj is its critical radius. 7 a is the interfacial tension of the metal-electrolyte interface, a is the interfacial tension of the film-electrolyte interface. (From N. Sato, J. Electro-chem. Soc. 129, 255, 1982, Fig. 5. Reproduced by permission of The Electrochemical Society, Inc.)...

Capacitance of a single pore is proportional to its surface area. Therefore, for a cylindrical NP it is proportional to 2m l, where r is the NP radius, and / is its length. Inner resistance of NP is proportional to / as well. The NP parameters depend on how the activated carbon powder was obtained but they are normally not affected by treating the powder when fabricating the electrode. 

This is known as the Cottrell equation. It shows that the faradaic transient current, it, decays t 1/2. In contrast, the capacitance current decays exponentially and much faster. According to Eq. (18b.16) a plot of it vs. t 1/2 is a straight line, the slope of which can be used to calculate the D of the analyte if the area of the electrode is known. Eq. (18b. 16) is also used to measure the active area of an electrode by using species with known D. At a spherical electrode (such as HMDE) of radius, r, the Cottrell equation has an added spherical term... 

The selectivity of the fluoride electrode is usually superb - perhaps the best for any of the solid-state ISEs. The reason why hydroxide ought to be avoided in tandem with a fluoride ISE is because the OH and F ions have a very similar ionic radius, and so move through the doped LaF3 lattice with a similar velocity and activation energy, i.e. the OH and F" ions are virtually indistinguishable by this method. 

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,... 

A host of carriers, with a wide variety of ion selectivities, have been proposed for this task. Most of them have been used for the recognition of alkali and alkaline metal cations (e.g., clinically relevant electrolytes). A classical example is the cyclic depsipeptide valinomycin (Fig. 5.13), used as the basis for the widely used ISE for potassium ion (38). This doughnut-shaped molecule has an electron-rich pocket in the center into which potassium ions are selectively extracted. For example, the electrode exhibits a selectivity for K+ over Na+ of approximately 30,000. The basis for the selectivity seems to be the fit between the size of the potassium ion (radius 1.33 A) and the volume of the internal cavity of the macrocyclic molecule. The hydrophobic sidechains of valinomycin stretch into the lipophilic part of the membrane. In addition to its excellent selectivity, such an electrode is well behaved and has a wide working pH range. Strongly acidic media can be employed because the electrode is 18,000 times more responsive to K+ than to H+. A Nernstian response to potassium ion activities, with a slope of 59mV/pK+, is commonly observed... 

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