Levich plot

The experiments showed that the properties of the Pt monolayer were modified differently by the different supporting metal (Fig. 9.13). PtML/Pd(lll) and PIml/ Ru(OOOl) are the most and least active of these surfaces, respectively. When the ORR kinetic currents obtained from Koutecky-Levich plots are plotted against the... 

One also needs to be careful when using the slope of the Koutecky-Levich plot to determine av of the catalytic film. Examples of metaUoporphyrin-catalyzed ORR have been reported where, above a certain value of the electrode rotational frequency, the catalytic currents became independent of Koutecky-Levich model, either because the rate of charge or substrate transfer within the film became rate-limiting or the catalyst became partially samrated with O2 [Boulatov et al., 2002 Song et al., 1998 CoUman et al., 1980]. In other cases, the versus graphs may remain mostly linear within the experimental... 

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. 

Figure 14.3 Koutecky-Levich plot for four different overpotentials.

The current-potential characteristics of a redox reaction can thus be measured in the following way An overpotential rj is applied, and the current is measured for various rotation rates in. From a Koutecky-Levich plot the corresponding kinetic current jk(rj) is extrapolated. This procedure is repeated for a series of overpotentials, and the dependence of jk on rj is determined. 

The tungsten carbonyl, Wx(CO) was synthesized and studied as a catalyst for ORR reactions.198-200 Through these studies, it was found that the tungsten carbonyl was active for ORR. The Koutecky-Levich plots showed that the electrons transferred approached four during ORR.199 It was also found that the tungsten carbonyl was active for the electrolysis of water.199... 

The rate constant, k, may then be derived from variation of the plateau current with the rotation rate by means of the popular Koutecky-Levich plots, where the inverse of the plateau current is plotted against the inverse of the square root of the rotation rate (Figure 4.12). The intercept allows the determination of the kinetic constant kr°, and of the rate constant k, if the amount of catalyst on the electrode surface is known. 

FIGURE 4.12. Koutecky-Levich plot of the variation of the RDEV plateau current with the rotation rate. 

In zone R, all three phenomena that take place in the film are fast compared to the diffusion of the substrate from the bulk of the solution to the film-solution interface. The concentrations of both Q and A are constant through the film. The RDEV response is similar to that of a monolayer coating (Section 4.3.2), except that more catalytic material is present on the surface of the electrode (it is multiplied by the number of layers in the multilayered coating). A linear Koutecky-Levich plot is obtained from the intercept, from which the kinetics of the catalytic reaction can be characterized. 

It is interesting to note that there is no complete symmetry between the role of substrate diffusion and electron transport in their combination with the catalytic reaction, as can be seen in the structures compared in the equations and also in the fact that linear Koutecky-Levich plots are not obtained in all cases, as noted in Table 4.1. 

Fig. 14.23 Koutecky-Levich plots for the ORR of unpyrolyzed and pyrolyzed Ppy-C-Co catalysts at 0.3 V (zs. RHE) in 0.5 M H2S04 under saturated 02 and 0.122 mgcrn-2 Ppy-C-Co loading. The current densities were normalized to the geometric area (Reprinted from [224] with permission from Elsevier).

The nanostructured Au and AuPt catalysts were found to exhibit electrocatalytic activity for ORR reaction. The cyclic voltammetric (CV) curves at Au/C catalyst reveal an oxidation-reduction wave of gold oxide at +200 mV in the alkaline (0.5 M KOH) electrolyte but little redox current in the acidic (0.5 M H2SO4) electrolyte. Under saturated with O2, the appearance of the cathodic wave is observed at -190 mV in the alkaline electrolyte and at +50 mV in the acidic electrolyte. This finding indicates that the Au catalyst is active toward O2 reduction in both electrolytes. From the Levich plots of the limiting current vs. rotating speed data, one can derive the electron transfer number (w). We obtained n = 3.1 for ORR in 0.5 M KOH electrolyte, and 2.9 for ORR in 0.5 M H2SO4 electrolyte. The intermittent n-value between 2 and 4 indicates that the electrocatalytic ORR at the Au/Ccatalyst likely involved mixed 2e and 4e reduction processes. 

FIGURE 14.7. Levich plots of the limiting current from RDE curves for a Au8iPti9/C catalyst (24 wt.%) on GC electrode (0.2 cm ) in alkaline (closed circles 0.5 M KOH) and acidic (open circles 0.5 M H2SO4) electrolytes saturated with O2 (from Ref. 35). 

To learn that when the rate of electron transfer is slow, a useful approach is to construct Koutecky-Levich plots of (/(current) against l/Tafel plot from these mass-transport-limiting values of the current. 

In order to ascertain which rotation speeds correspond to laminar and which to turbulent flow, we construct a Levich plot of /um (as y ) against (as x ) (see Figure 7.5). Laminar flow is indicated by the linear part of the plot at... 

Construct a Levich plot using the data below in order to ascertain the maximum speed that the RDE can safely be rotated at before the onset of turbulent flow. 

In order to be sure of good quality analytical data, the analyst is recommended to construct a Levich plot such as that shown in Figure 7.5 before starting a series of analyses analysts will avoid those rotation speeds represented on the graph as turbulent flow. In the jargon of the subject, the analyst may say that a laminar regime is maintained. 

Do Levich plots deviate from linearity for reasons other than poor flow characteristics ... 

Yes. There are two other reasons why a Levich plot is non-linear at higher rotation speeds, as follows. ... 

Koutecky-Levich Plots and Measurement of the Rates of Electron Transfer... 

If 0) is not particularly fast, then there is no mass-transport control (we have not reached a horizontal plateau when we draw a Levich plot). At the same time, however, if rj is not extreme, then neither do we have kinetic control stated another way, I is no longer proportional to the bulk concentration of analyte. We have too many variables, so we re incapable of discerning whether mass or charge transport dictate the magnitude ofl. 

In order to resolve this conundrum, we draw a Koutecky-Levich plot of l/(current) (as y ) against lw (as x ). (Plots using these axes are also sometimes called inverse-Levich plots .)... 

What is the benefit of such a Koutecky-Levich plot ... 

The value of = 0 in a Koutecky-Levich plot implies that the rotation speed is infinite. We should appreciate that any current obtained at o) — 00 would automatically represent a mass-transport-limited quantity. So let us now look at what the non-limiting currents along the y-cpcis really mean when x is 0. 

Figure 7.14 Koutecky-Levich plots of l/(current) against as a function of...

By constructing a Koutecky-Levich plot and obtaining the value of the current from the intercept, we have simplified the problems from two unknowns to one the only limitation to the magnitude of the current on the y-axis (strictly speaking, it is the reciprocal of the value on the y-axis) is the rate of electron transfer. 

Occasionally, the analyst is required to determine the rate of electron transfer, ket, and can then use the Butler-Volmer equation (equation (7.16)) to determine 7o, from which ket is readily calculated by using equation (7.17). The preferred method of obtaining the exchange currents in such cases is under conditions of infinite rotation speed i.e. via a Koutecky-Levich plot. 

The Levich plot obtained should start to show a loss of linearity (because of turbulence) at frequencies above about 95 Hz. 

Figure 7. Levich plot of bare Cu electrode to obtain through ij values in 0.1 M HCIO in air, v = 5 mV/s, 25 C.

Figure 5.72 Typical Koutecky-Levich plots for the reduction of a 0.2 mM [Fe(H20)6]3+ solution in 0.1 M H2S04 at platinum electrodes modified with layers of different surface coverages of [Os(bpy)2(PVP)ioCl]+. From top to bottom, the surface coverages (in mol cm-2) are 1.7 x 10-1°, 1.8 x 10 9, 2.7 x 10-9, 5.0 x 10 9,1.1 x 10 8, and bare platinum. From R. J. Forster and J. G. Vos, /. Chem. Soc., Faraday Trans., 87,1863-1867 (1991). Reproduced by permission of The Royal Society of Chemistry...

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