Limited currents

In contrast to a direct injection of dc or ac currents in the sample to be tested, the induction of eddy currents by an external excitation coil generates a locally limited current distribution. Since no electrical connection to the sample is required, eddy current NDE is easier to use from a practical point of view, however, the choice of the optimum measurement parameters, like e.g. the excitation frequency, is more critical. Furthermore, the calculation of the current flow in the sample from the measured field distribution tends to be more difficult than in case of a direct current injection. A homogenous field distribution produced by e.g. direct current injection or a sheet inducer [1] allows one to estimate more easily the defect geometry. However, for the detection of technically relevant cracks, these methods do not seem to be easily applicable and sensitive enough, especially in the case of deep lying and small cracks. 

The expression for the mass-transport-limiting current density may be employed together with the Nemst equation to deduce the complete current-potential response in a solution containing only oxidized or reduced species... 

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

The effects of ultrasound-enlianced mass transport have been investigated by several authors [73, 74, 75 and 76]. Empirically, it was found that, in the presence of ultrasound, the limiting current for a simple reversible electrode reaction exhibits quasi-steady-state characteristics with intensities considerably higher in magnitude compared to the peak current of the response obtained under silent conditions. The current density can be... 

In an alternative design, the actual tip of the ultrasonic hom may be used as the working electrode after insertion of an isolated metal disc [77, 78 and 79]. With this electrode, known as the sonotrode, very high limiting currents are obtained at comparatively low ultrasound intensities, and diflflision layers of less than 1 pm have been reported. Furdiemiore, the magniPide of the limiting currents has been found to be proportional to D, enabling a parallel to be drawn with hydrodynamic electrodes. 

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

Thus, the limiting current, is a linear function of the concentration of O in bulk solution, and a quantitative analysis is possible using any of the standardization methods discussed in Chapter 5. Equations similar to equation 11.35 can be developed for other forms of voltammetry, in which peak currents are related to the analyte s concentration in bulk solution. 

Determination of limiting current and halfwave potential in linear scan hydrodynamic voltammetry. 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

The limiting current was 5.15 )J,A. Show that the reduction reaction is reversible, and determine values for n and 1/2. 

A sample was prepared for analysis by diluting a 0.246-g sample to volume in a 100-mb volumetric flask. The limiting current for the sample was found to be 444 pA. Report the purity of this sample of K3be(CN)6. 

The limiting current was 5.67 tA. Verify that the reduction reaction is reversible, and determine values for n and 1/2. The half-wave potentials for the normal pulse polarograms of Pb + in the presence of several different concentrations of OH are shown in the following table. 

Limit dextrins Limiting amino acid Limiting current... 

The limiting current density /) for the transport of species i to the reacting site is given from Fick s law by ... 

Fig. 3. Conditions of limiting current, (a) Current density on the electrode surface as a function of surface potential, showing points A, B, and C. The dashed line is for a second Faradaic reaction, (b) The concentration profiles corresponding to points A, B, and C.

Under conditions of limiting current, the system can be analyzed using the traditional convective-diffusion equations. For example, the correlation for flow between two flat plates is... 

Mass Transport. Probably the most iavestigated physical phenomenon ia an electrode process is mass transfer ia the form of a limiting current. A limiting current density is that which is controlled by reactant supply to the electrode surface and not the appHed electrode potential (42). For a simple analysis usiag the limiting current characteristics of various correlations for flow conditions ia a parallel plate cell, see Reference 43. 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

Tertiay Current Distribution. The current distribution is again impacted when the overpotential influence is that of concentration. As the limiting current density takes effect, this impact occurs. The result is that the higher current density is distorted toward the entrance of the cell. Because of the nonuniform electrolyte resistance, secondary and tertiary current distribution are further compHcated when there is gas evolution along the cell track. Examples of iavestigations ia this area are available (50—52). 

In oxygen-free seawater, the J(U) curves, together with the Tafel straight lines for hydrogen evolution, correspond to Eq. (2-19) (see Fig. 2-2lb). A limiting current density occurs with COj flushing for which the reaction ... 

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