Electrode Processes Under Slow Diffusion Conditions

4 Electrode Processes Under Slow Diffusion Conditions 

Any electrode process has several stages and the electrochemical step is just one of them. For a consecutive series of transformations with a slow mass transfer step, the overall rate depends solely on the latter. Therefore, kinetic description of such process is determined by mass transfer of the starting material from bulk solution to the electrode surface and/or departure of the products from the reaction zone. Such processes are investigated by dijfusion kinetics and called dijfusion processes. Diffusion kinetics has three main equations. The first one represents a relationship between the process rate and distribution of the reactant concentration near the 

The second equation correlates the electrode potential to the surface concentrations of reactants, andC g  

We want to note that these concentrations are not the equilibrium ones, in contrast to the Nemst equation. Similarly, the potential ip is not the equilibrium potential 

These two equations allow to define a relationship between the process rate i and the electrode potential p. However, one needs to know the concentration distribution in the electrode vicinity. This can be found from the Pick s second law. For linear diffusion  

---

We can see that the process monotonously slows down during electrolysis and its rate asymptotically approaches zero. Therefore, the constant rate mode carmot be reached on planar electrode under given conditions. The obtained equation may be called the chronoamperogram equation of a diffusion process. Compare it to the relationship that describes the maximal rate of an electrode process under stationary linear diffusion ... 

A completely opposite situation is reached when Xe is large, but the excess factor is small, so that the substrate is consumed to a large extent. Its concentration at the electrode surface is then much smaller that in the bulk, implying that diffusion of the substrate toward the electrode surface may become the slow step of the catalytic process. Under these conditions (left-hand part of the zone diagram in Figure 2.17), the cyclic voltammetric responses are governed by the parameter... 

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. 

The process of oxide-layer growth on platinum has been thoroughly investigated for smooth platinum surfaces in aqueous electrolytes and in the gas phase (Angerstein-Kozlowska et al. 1973 Conway et al. 1990 Conway and Jerkiewicz 1992 Harrington 1997). While Conway et al. (1990) proposed rapid diffusion of oxide species followed by a slow oxide turnover process, Harrington (1997) opted for slow formation of the oxide species foUowed by rapid diffusion of oxide species across the surface. The kinetics of surface oxide formation on fuel-cell-type platinum catalysts has also been studied. Paik et al. (2004) observed that surface oxide formation on a platinum electrode occurs rapidly under realistic operating conditions of... 

In this section, a non-reversible electrode reaction will be addressed. An exact definition of a slow charge transfer process is not possible because the charge transfer reaction can be reversible, quasi-reversible, or irreversible depending on the duration of the experiment and the mass transport rate. So, an electrode reaction can be slow or non-reversible when the mass transport rate has a value such that the measured current is lower than that corresponding to a reversible process because the rate of depletion of the surface species at the electrode surface is less than the diffusion rate at which it reaches the surface. Under these conditions, the potential values that reduce the O species and oxidize the R species become more negative and more positive, respectively, than those predicted by Nemst equation. 

It can be seen that cyclic voltammograms at low scan rate have peak-to-peak separations close to the value theoretically expected for a reversible process of A p = 2.218 X 7 r/ = 57 mV at 298 K [47] and the peak current increases with the square root of the scan rate. Under these conditions, the process is diffusion controlled and termed electrochemically reversible or Nernstian within the timescale applicable to the experiment under consideration. Hence, as with all reversible systems operating under thermodynamic rather than kinetic control, no information concerning the rate of electron transfer at the electrode surface or the mechanism of the process can be obtained from data obtained at slow scan rate. The increase of A p at faster scan rate may be indicative of the introduction of kinetic control on the shorter timescale now being applied (hence the rate constant could be calculated) or it may arise because of a small amount of uncompensated resistance. Considerable care is required to distinguish between these two possible origins of enhancement of A p. For example, repetition of the experiments in Table II.l.l at... 

---