Levich-Koutecky equation

Although, in theory, the Koutecky-Levich equation can be applied to estimate n y and k at any part of the voltammogram (provided that the conditions stated above are satisfied), for practical reasons only limiting (plateau) currents can be acquired with adequate reproducibility to yield suitable Koutecky-Levich plots. 

It can be shown by rearranging the Levich equation and inserting via the Butler-Volmer equation that the Koutecky-Levich equation takes the following form ... 

Due to the formation of an intermediate complex, this type of reaction mechanism was described as being analogous to Michaelis-Menten kinetics [39]. A common error made when examining the behaviour of systems of this type is to use the Koutecky-Levich equation to analyse the rotation speed-dependence of the current. This is incorrect because the Koutecky-Levich analysis is only applicable to surface reactions obeying strictly first-order kinetics. Applying the Koutecky-Levich analysis to situations where the surface kinetics are non-linear, as in this case, leads to erroneous values for the rate constants. Below, we present the correct treatment for this problem based on an extension of a model originally developed by Albery et al. [42]... 

The elimination of transport effects is not so readily achieved. One relatively simple procedure is to measure currents (/m) as a function of electrode angular velocity (co) using a rotating disc electrode. Currents free of diffusive transport effects (/k) can then be obtained by application of the Koutecky-Levich equation,... 

Figure 9 Use of the Koutecky-Levich equation to correct for diffusive transport effects on the anodic dissolution of Cu in 1 mol dm-3 NaCl recorded on a rotating disk electrode.

The fit to the Koutecky-Levich equation, Fig. 9, demonstrates that the anodic dissolution of Cu occurs under mass-transport control, and extrapolation of these fits to co 1/2 = 0 yields kinetically controlled currents, 7k, free from transport effects and appropriately used in Tafel plots. 

Salimi, A., Banks, C.E., and Compton, R.G. (2003). Ultrasonic effects on the electroreduction of oxygen at a glassy carbon anthraquinone-modified electrode. The Koutecky-Levich equation applied to insonated electrocatalytic reactions. Phys. Chem. Chem. Phys., 5, 3988-93. 

The current will usually begin to level off at high rotation rate and the maximum value can be determined by plotting the reciprocal current against the reciprocal square root of the rotation rate, using the general Koutecky-Levich equation, eqn. 4-3A. 

Diffusion coefficient of the substrate (Dg) and diffusion coefficient of the electron-exchange (D ) were calculated from cyclic and disk current voltammograms by using the Koutecky-Levich equation and Fick s first law (14, 15) (Table II). Dg in the polymer domains was estimated as 10 - 10 cm /sec, much smaller than in solution (10 cm /sec). Dg is affected by charge density of the polymer domain, e.g., the diffusion of cations is suppressed in the positively charged domain composed of cationic polyelectrolyte, while anions moves faster. A larger Dg value was observed, of course, for the porous film and not for the film with high density. On the other hand, Dg in the polymer domain was also very small, i.e. 10" - 10" cm /sec. This may be explained as follows. An electron-transfer reaction always alters the... 

It is left as an exercise for the reader (Problem 9.10) to show that solving this equation for C oCy 0) and use of equations (9.3.23) and (9.3.38) lead to (9.3.39). For another rate-limiting process (e.g., diffusion of an electroreactant through a film coated on the electrode), the term k(E)Co(y — 0) would be replaced by the appropriate expression. This would yield an equation in the general form of the Koutecky-Levich equation, with the extrapolation to 0 allowing the determination of the kinetic parameter for that process [see, for example. Section 14.4.2]. 

The contribution of diffusion overpotential to the total overpotential can be achieved by an increase of convection near the electrode surface. In a very controlled manner this is possible with the rotating disc electrode. In the Koutecky—Levich equation the separation of diffusion contributions and charge transfer contributions to the overpotential was achieved. A general charge transfer reaction with exchange of n electrons was chosen. The Koutecky-Levich equation is... 

This Eqn (5.23) is called the Koutecky—Levich equation. The plot of vs based on the experiment data allows the estimation... 

RDE is a commonly used technique for investigating the ORR in terms of both the electron transfer process on electrode surface and diffusion—convection kinetics near the electrode. To make appropriate usage in the ORR study, fundamental understanding of both the electron transfer process on electrode surface and diffusion—convection kinetics near the electrode is necessary. In this chapter, two kinds of RDE are presented, one is the smooth electrode surface, and the other is the catalyst layer-coated electrode. Based on the electrochemical reaction 0 + ne R), the RDE theory, particularly those of the diffusion—convection kinetics, and its coupling with the electron-transfer process are presented. The famous Koutecky—Levich equation and its... 

Equation (39) reverts to the Levich equation for an irreversible reaction when the heterogeneous rate constant k is replaced hy kobsF- Inversion of Eq. (39) thus gives the corresponding Koutecky-Levich equation. 

Koutecky-Levich equation (A) nFAsjii = B Albery-Hillman equation (B) (nFAsliiy = nFAslii Bo> +... 

When the redox process is reversible, the shape of the wave should not depend on o). Hence, at any potential, the current should, like the limiting current, be proportional to If the shape of the curve depends on co, then the redox process is kinetically limited. In this case, one can measure the current at fixed potentials along the voltammogram and for each potential plot the inverse of the current vs. This is known as a Koutecky-Levich plot and follows the Koutecky-Levich equation ... 

The kinetic current and average number of electrons transferred per oxygen molecule (n) can be obtained through RDE experiments using the Koutecky-Levich equation (Eq. 1) ... 

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