Current kinetic

The kinetic current, 4, of peroxydisulphate exalting the Cu(II) to Cu(I) wave is caused by a regenerative reaction consisting of the following steps... 

It should be mentioned that there is no decrease in the peroxydisulphate current in the presence of both iron(ril) and arsenic(III). Presumably, the iron(II)-peroxydisulphate reaction is too slow to compete with the reduction of peroxydisulphate at the DME at the given concentration. However, iron(III) reduces the kinetic current in the presence of copper(II) and arsenic(ril). This can be accounted for by the termination reactions... 

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). 

The kinetic and polarization equations described in Sections 6.1 and 6.2 have been derived under the assumption that the component concentrations do not change during the reaction. Therefore, the current density appearing in these equations is the kinetic current density 4. Similarly, the current density appearing in the equations of Section 6.3 is the diffusion current density When the two types of polarization are effective simultaneously, the real current density i (Fig. 6.6, curve 3) will be smaller than current densities and ij (Fig. 6.6, curves 1 and 2) for a given value of polarization. 

In those cases where i. (region A in Eig. 6.6), the real current density i essentially coincides with the kinetic current density i 4, and the electrode reaction is controlled kinetically. When 4 ik (region C), we practically have i 4, and the reaction is diffusion controiled. When 4 and 4 have comparable values, the electrode operates under mixed control (region B). The relative valnes of these current densities depend on the kinetic parameters and on the potential. 

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... 

For a reliable calculation of coefficient a from the potential dependence of kinetic cnrrents, experimental data are needed in which the kinetic currents are varied by at least an order of magnitnde. It follows that in at least one point the ratio 4/4 shonld not be higher than 3. In the case considered in Section 6.4, where 4,red = 4,ox this corresponds to valnes of 4/4 or k°/Kj which are not higher than 0.15. The highest valne of typically fonnd in aqneons solntions is about 2 X 10 cm/s. It follows that steady-state methods can yield reliable kinetic parameters only for reactions in which < 3 X 10 cm/s. At a component concentration of this corresponds... 

FIGURE 12.5 Calculation of the kinetic current from experimental data obtained with a rotating-disk electrode. 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

The current is recorded as a function of time. Since the potential also varies with time, the results are usually reported as the potential dependence of current, or plots of i vs. E (Fig.12.7), hence the name voltammetry. Curve 1 in Fig. 12.7 shows schematically the polarization curve recorded for an electrochemical reaction under steady-state conditions, and curve 2 shows the corresponding kinetic current 4 (the current in the absence of concentration changes). Unless the potential scan rate v is very low, there is no time for attainment of the steady state, and the reactant surface concentration will be higher than it would be in the steady state. For this reason the... 

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... 

Figure 9.14 Kinetic current density (squares) at 0.8 V for O2 reduction on the Pt monolayer deposited on various metal single-crystal surfaces in a 0.1 M HCIO4 solution, and calculated binding energies (circles) of atomic oxygen (BEq), as a function of calculated d-band center (relative to the Fermi level, ej — sp) of the respective surfaces. The data for Pt(lll) were obtained from [Markovic et al., 1999] and are included for comparison. Key 1, PIml/ Ru(OOOl) 2, PtML/Ir(lll) 3, PtML/Rh(lH) 4, PtML/Au(lll) 5, Pt(lll) 6, PIml/ Pd(lll). (Reproduced with permission from Zhang et al. [2005a].)...

Figure 9.16 ORR activity of two mixed-metal monolayer electrocatalysts supported on Pd(l 11), expressed as the kinetic current density at 0.85 V as a function of the M Pt ratio in the Pd-supported Pt-M monolayer. (Reproduced with permission from Zhang et al. [2005b].)...

Kinetic Data Catalyst Pt Dispersion (m /gpt) Half-Wave Potential at 1600rpm(V) Kinetic Current Density at 0.85 V (mA/cm ) Specific Kinetic Current Density at 0.85 V (A/m )... 

Thin catalyst layers on a GC rotating disk electrode (RDE) or a rotating ring-disk electrode (RRDE) serve for studies of ORR kinetics. In order to separate the kinetic current from the measured current j, Schmidt and co-workers [Schmidt et al., 1998b] corrected the latter for the influence of oxygen diffusion in the aqueous electrolyte and in the polymer film using the foUowing equation ... 

Figure 15.7 Logarithm of the kinetic current for the ORR in oxygen-saturated liquid electrolytes versus inverse diameter for Pt particles supported on Vulcan XC-72 (1) 0.9 V vs. RHE at 60 °C [Gasteiger et al., 2005] (2) 0.85 V vs. RHE at room temperature [MaiUard et al., 2002] (3)0.85 V vs. SHE at room temperature [Guerin etal., 2004]. For curves 1 and 2, measurements were performed with the thin-layer RDE in 0.1 M HCIO4 for curve 3, they were performed with stationary voltammetry in 0.5 M H2SO4. (Curves have been replotted from MaiUard et al. [2002] Gasteiger et al. [2005], Copyright 2002 and 2005, with permission from Elsevier and from Guerin et al. [2004], Copyright 2004 American Chemical Society.)...

This is the Tafel equation (5.2.32) or (5.2.36) for the rate of an irreversible electrode reaction in the absence of transport processes. Clearly, transport to and from the electrode has no effect on the rate of the overall process and on the current density. Under these conditions, the current density is termed the kinetic current density as it is controlled by the kinetics of the electrode process alone. 

Cases (a) and (c) for relatively slow chemical reactions are particularly interesting when the electrode reaction is fast and unidirectional, so that the concentration of substance R at the surface of the electrode approaches zero. Then characteristic limiting kinetic currents are formed on the polarization curves. 

This relationship forms the basis for the method of determining the rate constants of fast chemical reactions from the kinetic current. 

According to R. Brdicka and K. Vesely the carbonyl form of formaldehyde is reduced and the limiting kinetic current is given by the rate of the chemical volume reaction of dehydration. An analogous situation occurs for the equilibria among complexes, metal ions and complexing agents if the rates of complex formation and decomposition are insufficient to preserve the equilibrium. A simple example is the deposition of cadmium at a mercury electrode from its complex with nitrilotriacetic COO"... 

Brdicka, R., V. Hanus, and J. Koutecky, General theoretical treatment of polarographic kinetic currents, in Progress in Polarography (Eds P. Zuman and I. M. Kolthoff), Vol. 1, p. 145, Interscience, New York, 1962. 

Koryta, J., Diffusion and kinetic currents at the streaming mercury electrode, Coll. 

Koryta, J., Electrochemical kinetics of metal complexes, AE, 6, 289 (1967). Koutecky, J., and J. Koryta, The general theory of polarographic kinetic currents, Electrochim. Acta, 3, 318 (1961). 

It is difficult to measure kinetic currents at high overpotentials, since then the reaction is fast and usually transport controlled (see Chapter 13). At small overpotentials only Butler-Volmer behavior is observed, and the deviations predicted by theory were doubted for some time. But they have now been observed beyond doubt, and we will review some relevant experimental results in Chapter 8. 

If transport were infinitely fast, the concentrations c x and c ed of nonadsorbing reacting species would be the same at the interface as in the bulk. The measured current density would solely be determined by the reaction, and would equal the kinetic current density. 

Since transport and electrochemical reactions are in series, the slower process determines the overall current. Hence we can obtain the rate constants of the reaction only, if the reversible current jrev is not much slower than the kinetic current. This limits the magnitude of the reaction rates that can be measured with any given method. 

Under these conditions a plot of j versus t1/2 gives a straight line, and the kinetic current can be obtained from the intercept. If the reaction is fast the straight portion can be too short for a reliable determination of jk in this case one should obtain estimates for y and A from this plot, and use them in fitting the whole curve to Eq. (13.3). 

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