Equation for the limiting current

A generalized equation for the limiting-current response of different detectors, based on the dimensionless Reynolds (Re) and Schmidt (Sc) numbers has been derived by Hanekamp and co-workers (62) ... 

Derive the Levich equation for the limiting current at the rotating disk electrode [based on combining equations (4-4) and (1-12)]. 

Assuming that the orifice is disk-shaped, one can calculate the steady-state diffusion-limiting current to a pipette from Eq. (1). However, current values about three times higher than expected from Eq. (1) were measured for interfacial IT [18] and ET [5]. The following empirical equation for the limiting current at a pipette electrode was proposed [18bj ... 

Drop growth causes an increase in the concentration gradient which results in a multiplicative factor of V(7/3). The final equation for the limiting current (Ilkovic equation), with c , measured in mol cm-3 and D in cm2s-1, is... 

The wall-jet electrode is highly non-uniformly accessible as shown by the streamlines and by the equation for the limiting current, /L... 

The RRDE is constructed in such a way that both electrodes are in the same plane, and in close proximity to each other. The dimensions of the electrode are defined by three radii the radius of the disc (r ), the inner radius of the ring (r ) and its outer radius (r ), as shown in Fig. 12D(b). Since both electrodes are in the same flow regime (evidently the convective flow of the liquid cannot distinguish between the disc electrode, the insulator, and the ring electrode), the equations for the limiting current at both the disc and the ring electrode can be solved simultaneously. 

Since flow is laminar, it is possible to calculate rigorously the rate of mass transport. The corresponding equation for the limiting current density, developed by Levich, is... 

The behavior of systems at the RDE undergoing the general ECE/DISP scheme (Section 12.3.8) can be analyzed by means of the zone diagrams employed for voltammetry with the appropriate expressions for A and A j. Most RDE treatments, however, have been concerned with the Ei-CiEj. sequence, which has been treated at several different levels of approximation. Karp (87) proposed the following equation for the limiting current ... 

The new equation for the limiting current in this case can then be introduced (see section 4.3.3.1, with a thickness equal to L/2 and a diffusion coefficient equal to B+) ... 

Silanized pipets give more reliable information about the interface since there is no leakage of aqueous solution from the tip, and the equation for the limiting current is ... 

Since both electrodes are part of the same flow regime (evidently the convective flow of the liquid cannot distinguish between the disc electrode, the insulator and the ring), the equations for the limiting current at both the disc and the ring electrodes can be solved simultaneously. 

A more rigorous treatment takes into account the hydrodynamic characteristics of the flowing solution. Expressions for the limiting currents (under steady-state conditions) have been derived for various electrodes geometries by solving the three-dimensional convective diffusion equation ... 

Equations of this type are most often used by experimentalists to fit their data to theory,52"54 as indications of an exponential 7(E) dependence are numerous. Vervey55 has used a similar approach to consider the volume-limited processes of ionic migration and obtained the same equation. In order to explain deviations of experimental behavior from that predicted by Eq. (40), Vermilyea56 has also taken into consideration the effect of electrostriction modifying the activation distance for migrating ions and obtained the following equation for the ionic current flow ... 

The rate of the partial reaction of the oxygen reduction is given by the equation for the limiting oxygen diffusion current (bulk oxygen concentration Cq, diffusion layer... 

In the particular case of where the interfacial concentration of the consumed species is zero, or more precisely is negligible compared to the bulk concentration, the following equation emerges for the limiting current ... 

Introducing this expression into equation (4.142) and setting for the transport number of the anion, r = 1 - we obtain another expression for the limiting current density... 

All equations given in this table are valid at sufficient negative/posi-tive potentials of the working electrode the current is thus limited by the bulk concentration of the electroactive species, c (mol m ), and its transport to the electrode surface only. The generalized volume flow, (m s ) results in expressions for the limiting current, I, (in Amps) if all quantities are inserted in SI units. 

For the analytical application, the equation expressing the limiting current density, j, is the most important... 

For potentials where the surface concentration of the electroactive species is zero, the equation relating the limiting current density (for an oxidation) and the rotation rate is found by combining Equations (4.12)-(4.15) ... 

The mercury dropping electrode was first introduced to electrolysis by J. Heyrovsky.< > The most important milestones in the theoretical development of polarography were the exact deduction of the equation for the limiting diffusion current by D. Ilkovi(5,< > of the equation for the shape of polarographic wave by J. Heyrov-sky and D. Ilkovic, the introduction of the conception of halfwave potentials by the same authors, the recognition of catalytic< > and adsorption currents by R. Brdicka and the development of the theory of kinetic currents by K. Wiesner, R. Brdicka, J. 

From the concentration profile is derived an expression for the limiting current, known as the Levich equation ... 

In the laboratory one frequently uses rotating-disk electrodes for the study of mass transport effects. According to the Levich equation [9], the limiting current density for a cathodic reaction at a rotating-disk electrode under laminar flow conditions varies linearly with the square root of the rotation rate. 

From Equation 6.131a for the limiting current density with mass transfer limited by diffusion resistance, the reactant concentration in the bulk gas flow in the channels is written as... 

The equivalent expression for the limiting current derived from equation 3.87 is... 

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