Kinetically controlled current

Figure 4. Effects of dihydro-brevetoxin B (H2BVTX-B) on Na currents in crayfish axon under voltage-clamp. (A) A family of Na currents in control solution each trace shows the current kinetics responding to a step depolarization (ranging from -90 to -I-100 mV in 10 mV increments). Incomplete inactivation at large depolarizations is normal in this preparation. (B) Na currents after internal perfusion with H2BVTX-B (1.2 a M). inactivation is slower and less complete than in the control, and the current amplitudes are reduced. (C) A plot of current amplitudes at their peak value (Ip o, o) and at steady-state (I A, A for long depolarizations) shows that toxin-mOdified channels (filled symbols) activate at more negative membrane potentials and correspond to a reduced peak Na conductance of the axon (Reproduced with permission from Ref. 31. Copyright 1984 American Society for Pharmacology and Experimental Therapeutics).

When concentration changes affect the operation of an electrode while activation polarization is not present (Section 6.3), the electrode is said to operate in the diffusion mode (nnder diffusion control), and the cnrrent is called a diffusion current i. When activation polarization is operative while marked concentration changes are absent (Section 6.2), the electrode is said to operate in the kinetic mode (under kinetic control), and the current is called a reaction or kinetic current i,. When both types of polarization are operative (Section 6.4), the electrode is said to operate in the mixed mode (nnder mixed control). 

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... 

Curve 1 in Fig. 6.9 shows the influence of constant k, (or of parameters or which are proportional to it) on the current density at constant potential for a reaction with an intermediate value of k°. Under diffusion control (low values of/) the current density increases in proportion to/ . Later, its growth slows down, and at a certain disk speed kinetic control is attained where the current density no longer depends on disk speed. The figure also shows curves for the kinetic current density 4 and the diffusion current density /. 

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... 

Before the measurement of HOR activity, a pretreatment of the alloy electrode was carried out by potential sweeps (10 V s ) of 10 cycles between 0.05 and 1.20 V in N2-purged 0.1 M HCIO4. The cyclic voltammograms (CVs) at all the alloys resembled that of pure Pt. As described below, these alloy electrodes were electrochemically stabilized by the pretreatment. Hydrodynamic voltammograms for the HOR were then recorded in the potential range from 0 to 0.20 V with a sweep rate of 10 mV s in 0.1 M HCIO4 saturated with pure H2 or 100 ppm CO/H2 at room temperature. The kinetically controlled current 4 for the HOR at 0.02 V was determined from Levich-Koutecky plots [Bard and Faulkner, 1994]. 

The kinetically controlled current 7k at 0.02 V was determined from a well-defined equation [Levich, 1962 Gerischer et al., 1965], i.e., plotting the inverse of the current... 

The normalized steady-state current vs. tip-interface distance characteristics (Fig. 18) can be explained by a similar rationale. For large K, the steady-state current is controlled by diffusion of the solute in the two phases, and for the specific and y values considered is thus independent of the separation between the tip and the interface. For K = 0, the current-time relationship is identical to that predicted for the approach to an inert substrate. Within these two limits, the steady-state current increases as K increases, and is therefore diagnostic of the interfacial kinetics. 

As discussed earlier, it is generally observed that reductant oxidation occurs under kinetic control at least over the potential range of interest to electroless deposition. This indicates that the kinetics, or more specifically, the equivalent partial current densities for this reaction, should be the same for any catalytically active feature. On the other hand, it is well established that the O2 electroreduction reaction may proceed under conditions of diffusion control at a few hundred millivolts potential cathodic of the EIX value for this reaction even for relatively smooth electrocatalysts. This is particularly true for the classic Pd initiation catalyst used for electroless deposition, and is probably also likely for freshly-electrolessly-deposited catalysts such as Ni-P, Co-P and Cu. Thus, when O2 reduction becomes diffusion controlled at a large feature, i.e., one whose dimensions exceed the O2 diffusion layer thickness, the transport of O2 occurs under planar diffusion conditions (except for feature edges). 

Fig. 18b.6. (a) Shape of the voltage pulses for diffusion control, mixed diffusion-kinetic control, and kinetic control, (b) concentration gradient of O showing expansion of the diffusion layer with time for complete diffusion controlled reaction, and (c) current transients show diffusion controlled, mixed kinetics and diffusion control, and complete kinetics controlled reactions corresponding to voltage pulses shown in (a). Note that the equations are derived only for the diffusion controlled case. 

The electrochemical response, here the plateau current, first increases with the substrate concentration before reaching a limit as the kinetic control passes from reaction (1) to reaction (2). The variation with substrate concentration is never linear over the entire concentration range. 

As in the homogeneous case, expression of the plateau current in equation (5.20) gives a simple representation of the competition between substrate and cosubstrate in the kinetic control of the enzymatic reaction. Equation (5.19) suggests the construction of primary and secondary plots allowing the derivation of the kinetic constants, as will be shown in the next section. 

This is no longer true when substrate diffusion interferes in the kinetic control as discussed next. From equations (5.15) to (5.18), one obtains a relationship between the concentration of substrate at the electrode surface and the catalytic current ... 

The outcome of the competition is represented in Fig. 5 in terms of the location of the half-wave potential of the RX reduction wave (i.e. the current-potential curve), relative to the standard potential of the RX/ RX- couple, E° (Andrieux et al., 1978). As concerns the competition, three main regions of interest appear in the diagram. On the left-hand side, the follow-up reaction is so slow (as compared to diffusion) that the overall process is kinetically controlled by the parameter A, i.e. by electron transfer and diffusion. Then, going upward, the kinetic control passes from electron transfer to diffusion. In the upper section d in the lower section... 

Figure 7.13 Tafel plot constructed with the data from worked example 7.4. These data refer to a solution containing [Fe"(CN)6] ] = [Fe" (CN)6]2 ] = 20 mmol dm and [KCl] = 0.1 mol dm" . Only those data (both anodic and cathodic) corresponding to kinetic control are included. The logarithmic current where the two lines intercept is log I /(). ...

With both approaches, it is key to establish the current regions where samples are under kinetic control to allow the correct comparison. Many reported comparisons of catalysfs in MEA sfrucfures point to differences in performance, which are attributed to intrinsic catalyst differences when it is clear that differences are due to mass fransport effects because of catalyst layer structure. To help overcome these difficulties, it is recommended that, for catalyst evaluation, pure reactants be used (e.g., O2 instead of air) and at relatively high stoichiometries. Use of current-voltage curves should be corrected for elecfrolyte or membrane resistances and Tafel analysis used to identify fhe kinefically confrolled current regions. 

The kinetic control of vesicle transport, from vesicle budding in the Golgi (and other origins) to fusion of the vesicle with the target membrane, is currently a vigorous area of research. The formation of COP-coated vesicles... 

In principle, there are two possible ways to measure this effect. First, there is the end-point measurement (steady-state mode), where the difference is calculated between the initial current of the endogenous respiration and the resulting current of the altered respiration, which is influenced by the tested substances. Second, by kinetic measurement the decrease or the acceleration, respectively, of the respiration with time is calculated from the first derivative of the currenttime curve. The first procedure has been most frequently used in microbial sensors. These biosensors with a relatively high concentration of biomass have a longer response time than that of enzyme sensors. Response times of comparable magnitude to those of enzyme sensors are reached only with kinetically controlled sensors. 

This process can be described in terms of a heterogeneous reaction in which ferri-cyanide (or hexacyanoferrate(III)) ions, [Fe(CN)g], are formed. At the beginning of the voltammetric peak, the current is controlled by the kinetic of the electron transfer across the electrode/electrolyte barrier so that the current increases somewhat exponentially with the applied potential. The value of the current is controlled 150-200 mV after the voltammetric peak by the diffusion rate of ferrocyanide ions from the solution bulk toward the electrode surface. 

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