Kinetic currents, voltammetry

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... 

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.)...

Chapter 9) or potential pulses (Chapter 10) alternating current voltammetry (Chapter 11) and so on. Additionally, kinetic and mechanistic information can sometimes be obtained from the same set of experiments. 

This equation corresponds to the Lineweaver-Burk kinetic equation (Lyons et al., 1992, 1994) and can be transformed into an equation giving the dependence of kinetic currents, 4, on the concentration of substrate in the solution bulk. Values of /), at different concentrations of substrate can be determined from the limiting, steady-state currents, tht.i, obtained, for instance, as plateau currents in rotating disk voltammetry, using Equation (3.6). For the case of thin films with a surface concentration of catalytic centers (rnol/crn ) over an electrode of area A, one can write ... 

In this section, we will treat the one-step, one-electron reaction O + R using the general (quasireversible) i-E characteristic. In contrast with the reversible cases just examined, the interfacial electron-transfer kinetics in the systems considered here are not so fast as to be transparent. Thus kinetic parameters such as kf, and a influence the responses to potential steps and, as a consequence, can often be evaluated from those responses. The focus in this section is on ways to determine such kinetic information from step experiments, including sampled-current voltammetry. As in the treatment of reversible cases, the discussion will be developed first for early transients, then it will be redeveloped for the steady-state. 

Figure 5.5.2 General kinetic function for chronoamperometry and sampled-current voltammetry.

The mean surface concentrations enforced by depend on many factors (a) the way in which is varied (b) whether or not there is periodic renewal of the diffusion layer (c) the applicable current-potential characteristic and (d) homogeneous or heterogeneous chemical complications associated with the overall electrode reaction. For example, one could vary sequential potentiostatic manner with periodic renewal of the diffusion layer, as in sampled-current voltammetry. This is the technique that is actually used in ac polarography, which features a DME and effectively constant during the lifetime of each drop. Alternatively one could use a stationary electrode and a fairly fast sweep without renewal of the diffusion layer. Both techniques have been developed and are considered below. The effects of different kinds of charge-transfer kinetics will also be examined here, but the effects of homogeneous complications are deferred to Chapter... 

Despite the dependence of ip on charge-transfer kinetics (eqns [5] and [6]), the sensitivity of LSV is almost independent of the reversibility degree (only a decrease of 25% is found on passing from a Nernstian to a totally irreversible process with a = 0.5). This fact makes LSV the most sensitive voltammetric technique for analytes involved in irreversible processes because pulsed voltammetric methods or alternating current voltammetry provide for these processes very low signals. 

Kinetic Currents. In kinetic currents, the limiting current is determined by the rate of a chemical reaction in the vicinity of the electrode, provided this precedes the cell reaction. Electrochem-ically inactive compounds are converted into reducible or oxidizable forms (time-dependent protonation and deprotonation processes, formation and decomposition of complexes, etc.). Conversely, during a chemical reaction after the cell reaction, the product of the electrode reaction is converted to an electrochemically inactive form without influence on the current. However, owing to the changed equilibria between the concentrations of the oxidized and reduced forms at the electrode surface, the half-wave and peak potentials are shifted (Section 25.2.1). In evaluating kinetic effects, cyclic voltammetry can be helpful (Section 25.2.4). 

A large number of potential-relaxation and current-relaxation techniques have been developed in 1950s-1980s for fast kinetic measurements (8). The later advances in UMEs resulted in a less frequent use of relaxation techniques in kinetic experiments. Because of the space limitations, only one large-perturbation method (sampled-current voltammetry) and one small-perturbation technique (alternating current voltammetry) will be considered. 

The most general way to determine kinetic parameters from sampled-current voltammetry is to fit an experimental i/i vs. E dependence to the theory [equation (15.6)] using IF, a, and E° as adjustable parameters. This can be done using a number of commercially available programs, e.g., TableCurve 2D. 

Typical measurement is performed using RDE or RRDE voltammetry. In the first case one can control diffusion limitation, enabling more reliable extraction of kinetic currents. In the case of RRDE voltammetry selectivity is also assessed. Alternatively, one can estimate selectivity of O2 reduction to H2O (OH ) using K-L analysis (see Section 2.2) In order to obtain proper ORR j-E curves several steps are necessary (clearmess of electrochemical cell and the electrolyte is assumed, which in some case requires the use of specifically prepared cell) ... 

As the field of electrochemical kinetics may be relatively unfamiliar to some readers, it is important to realize that the rate of an electrochemical process is the current. In transient techniques such as cyclic and pulse voltammetry, the current typically consists of a nonfaradaic component derived from capacitive charging of the ionic medium near the electrode and a faradaic component that corresponds to electron transfer between the electrode and the reactant. In a steady-state technique such as rotating-disk voltammetry the current is purely faradaic. The faradaic current is often limited by the rate of diffusion of the reactant to the electrode, but it is also possible that electron transfer between the electrode and the molecules at the surface is the slow step. In this latter case one can define the rate constant as ... 

De Jong, H. G. and van Leeuwen, H. P. (1987). Voltammetry of metal-complex systems with different diffusion-coefficients of the species involved. 2. Behaviour of the limiting current and its dependence on association/dissociation kinetics and lability, J. Electroanal. Chem., 234, 17-29. 

How electron transfer kinetics may be investigated by means of an electrochemical method such as cyclic voltammetry is the question we address now, starting with the case where the reactants are immobilized on the electrode surface, as in the beginning of Section 1.2. The key equations are those that relate the surface concentrations rA and rB to the current. The first of these expresses the Faradaic consumption of A and production of B as the current flows ... 

FIGURE 1.17. Cyclic voltammetry of slow electron transfer involving immobilized reactants and obeying a Butler Volmer law. Normalized current-potential curves as a function of the kinetic parameter (the number on each curve is the value of log A ) for a. — 0.5. Insert irreversible dimensionless response (applies whatever the value of a). 

FIGURE 2.8. CE reaction scheme in cyclic voltammetry. Kinetic zone diagram showing the competition between diffusion and preceding reaction as a function of the equilibrium constant, K, and the dimensionless kinetic parameter, X [equation (2.1)]. The boundaries between the zones are based on an uncertainty of 5% at 25°C on peak of plateau currents. 

As with the other reaction schemes involving the coupling of electron transfer with a follow-up homogeneous reaction, the kinetics of electron transfer may interfere in the rate control of the overall process, similar to what was described earlier for the EC mechanism. Under these conditions a convenient way of obtaining the rate constant for the follow-up reaction with no interference from the electron transfer kinetics is to use double potential chronoamperometry in place of cyclic voltammetry. The variations of normalized anodic-to-cathodic current ratio with the dimensionless rate parameter are summarized in Figure 2.15 for all four electrodimerization mechanisms. 

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