Current pure kinetic

It follows from the figures and also from an analysis of Eq. (6.40) that in the particular case being discussed, electrode operation is almost purely diffusion controlled at all potentials when flij>5. By convention, reactions of this type are called reversible (reactions thermodynamically in equilibrium). When this ratio is decreased, a region of mixed control arises at low current densities. When the ratio falls below 0.05, we are in a region of almost purely kinetic control. In the case of reactions for which the ratio has values of less than 0.02, the kinetic region is not restricted to low values of polarization but extends partly to high values of polarization. By convention, such reactions are called irreversible. We must remember... 

Measurements must be made under kinetic control or at least under mixed control of electrode operation if we want to determine the kinetic parameters of electrochemical reactions. When the measurements are made under purely kinetic control (i.e., when the kinetic currents 4 are measured directly), the accuracy with which the kinetic parameters can be determined will depend only on the accuracy with which... 

Once a DISP mechanism has been recognized, the procedures for determining the rate constant of the follow-up reaction and the standard potential of the A/B couple from peak current and/or peak potential measurements are along the same lines as the procedures described above for the ECE mechanism. A distinction between the ECE and DISP mechanisms cannot be made when the pure kinetic conditions are achieved since the peak height, peak width, and variations of the peak potential with the scan rate and rate constant are the same, and so is its independence vis-a-vis the concentration of substrate. The only difference is then the absolute location of the peak, which cannot be checked, however, unless the standard potential of the A/B couple and the follow-up rate constant are known a priori. 

Calculation stability implies that At/Ay2 <0.5. The fulfillment of this condition may become a problem when fast reactions, or more precisely, large values of the kinetic parameter, are involved since most of the variation of C then occurs within a reaction layer much thinner than the diffusion layer. Making Ay sufficiently small for having enough points inside this layer thus implies diminishing At, and thus increasing the number of calculation lines, to an extent that may rapidly become prohibitive. This is, however, not much of a difficulty in a number of cases since the pure kinetic conditions are reached before the problem arises. This is, for example, the case with the calculation alluded to in Section 2.2.5, where application of double potential step chronoamperometry to various dimerizations mechanisms was depicted. In this case the current ratio becomes nil when the pure kinetic conditions are reached. 

Although the general case may readily be resolved as shown in Section 6.5.1, two limiting situations are of particular practical interest.9 One is when the system obeys pure kinetic conditions (Section 2.2.6), that is, when the diffusion of the cosubsrate and its involvement in a fast enzymatic reaction mutually compensate. Under these conditions, the current responses are governed by the kinetics of the enzymatic reaction. If at the same time, substrate consumption is moderate enough for its concentration to be considered as constant, the current responses are plateau-shaped and obey the following equation (see Section 6.5.1) ... 

FIGURE5.3. Ping-pong mechanism. Variation of the peak or plateau current with the kinetic parameter from no catalysis and the pure kinetic conditions leading to plateau-shaped responses for several values of the competition parameter s from top to hottom 0, 0.31, 0.725, 1.25, 2.5, 5, 10, 20, oo. Adapted from Figure 2 in reference 10, with permission from the American Chemical Society. 

The pure kinetic conditions, which are achieved for large values of A, implies that bo = t/ q/x/A —> 0 and thus, from equation (6.40), i//2 = (//,. It follows that the current is exactly the double of the irreversible EC current obtained under pure kinetic conditions along the entire current-potential curve. 

The current is then exactly twice that in the irreversible EC case under pure kinetic conditions after a shift of the potential scale by a factor of (-K.T/2F) In 2. 

The preceding chemical reaction causes the concentration of the electroactive A, to be lower than otherwise the effect of this will be largest when K is large, when a purely kinetic current dependent on the value of fe] will be observed. 

The first term in the right-hand side of Eq. (1.193) accounts for the pure kinetic resistance of the process (which has been called as activation term), whereas the second combines the influence of the potential and of the mass transport through the limiting current (see Eqs. 1.184 and 1.185). The overall behavior of the current-potential response can be seen in Fig. 1.22. 

For more negative potentials, the current (solid line) deviates from the activation control (given by the dashed line which corresponds to a pure kinetic behavior9) and begins to be influenced by the mass transport (second term in Eq. (1.193), which in practice means that c / c ), until for certain potentials at which the mass transport controls the overall current (erl —> 0 and kKa —> oo) and under these conditions... 

Equations (3.105)-(3.107) point out the existence of three different polarization causes. So, 7km is a kinetically controlled current which is independent of the diffusion coefficient and of the geometry of the diffusion field, i.e., it is a pure kinetic current. The other two currents have a diffusive character, and, therefore, depend on the geometry of the diffusion field. I((((s corresponds to the maximum current achieved for very negative potentials and I N is a current controlled by diffusion and by the applied potential which has no physical meaning since it exceeds the limiting diffusion current 7 ss when the applied potential is lower than the formal potential (E < Ef"). This behavior is indicated by Oldham in the case of spherical microelectrodes [15, 20, 25]. 

The measurement of peak potentials during LSV neglects much of the information present in the wave. For purely kinetic waves, the wave shape is dependent upon the mechanism of the process and can be used to distinguish between mechanisms. Although conclusions can be drawn by the direct comparison of the shape of the current-potential curve with theoretical data, such a comparison is subjective. Several procedures have been developed to analyse LSV wave shapes quantitatively for mechanism analysis. 

A more simple analysis of LSV waves can give essentially the same information as CPSV and NPSV. Analysis of theoretical current-potential data for Nemstian and purely kinetic waves revealed that a nearly linear region... 

Parker and Bethell, 1981a. Measurements at an Hg electrode at 23°C with MejNBF (sat.) as electrolyte. The numbers in parentheses refer to the standard deviations in 5 measurements. Peak potentials are relative to a bias setting of — 1.680 V vs Ag/Ag+ in acetonitrile. It should be noted that the reduction process does not fulfill the requirements for purely kinetic waves, linear current potential analysis indicates a slope at 100 mV s" of about 80 mV rather than 69 mV for a purely kinetic wave... 

In the pure kinetic region (KP), the i-E curve takes on an S-shape (rather than the usual peak-shape) and the current attains a steady-state value, /l, independent of v, given by... 

Parameters for the reaction can be determined from the variation of i with cu. Note that at small 0), the first term of the denominator predominates (8 /jl/K), and the observed current is the mass-transfer-controlled limiting current // (equation 9.3.22). At high CO (8 fJi/K), the pure kinetic current results ... 

Current Densities with Pure Kinetic Control (ij and Apparent First-Order Heterogeneous Rate Constants (kj Determined from Rotating Disk Electrode Data forOi-he O - at -0.32 / vs. SCE ... 

If the electrochemical reaction is totally controlled by pure kinetics, the cyclic voltammogram has no peak and the shape resembles a polarogram [12]. The kinetic current in this case is independent of the scan rates. The current observed in chronoamperometry also shows a constant value, independent of time. The kinetic current, i, observed from both techniques is exactly the same and expressed by the following equation assuming C l ... 

K is small (the equilibrium is shifted to the left) and X is large. The supply of the species A inside the time window is provided by the forward chemical reaction. This situation (characterized, for example, by 1 < 2 < 10 at K = lO " values) is called pure kinetic zone. The current-potential curves are perturbed by the coupled chemical reaction so that kinetic parameters can be evaluated (zone KZ) ... 

At high frequencies co (5 the pure kinetic current results in... 

Obviously, the limiting current I, in the pure kinetic zone is independent of the scan rate v, while the current function in this zone depends on v ... 

This situation arises when the rate of removal A by the forward electrode reaction is compensated by the rate of its generation by the chemical step. In the pure kinetic zone (Fig. 15) when A becomes large the LSV response looks similar to a polarographic wave of nernstian shape. The current-potential dependence resembles that of the reversible reduction wave... 

The ratio of the anodic to the cathodic limiting current (peak currents) in CV technique applied to this mechanism is always unity independent of X. In the pure kinetic zone, currents during the reverse scan tend to retrace the currents of the forward scan (see Fig. 16). In most experiments, it is assumed that the catalytic agent Z is present in excess, c c, so that its concentration remains unchanged during the electrolysis (pseudo-first order reaction). 

Fig, 15. Ratio of kinetic and diffusion-controlled peak currents vs. in LSV for ECgat mechanism. DZ diffusion-controlled zone, IZ intermediate zone, KZ pure kinetic zone. Adapted from ref. [81]. 

Many ce processes are rather simpler than the one discussed above the chemical step is irreversible and the equilibrium concentration of 0 is very low. For systems such as this it can be shown that, as for the slow electron transfer case, a plot of / vs should be a straight line at short times, and hence I,=q, which is the purely kinetic current (mass transfer rate is infinite at / = 0) can readily be obtained by extrapolation.kj can then be found from Equation (2.54)... 

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