Totally irreversible systems

This system represented a somewhat less formidable problem than quasi-reversible charge transfer [15]. The surface flux equation is given by 

The rate constant in the reverse direction is considered to be insignificant for these systems. The numerical solution of the appropriate integral equation led to 

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Irreversible and Quasi-Reversible Systems For irreversible processes (those with sluggish electron exchange), the individual peaks are reduced in size and widely separated (Figure 2-5, curve A). Totally irreversible systems are characterized by a shift of the peak potential with the scan rate ... 

For irreversible systems the peak potential of a reduction process is shifted toward more negative potentials by about 0.030 V for a decade increase in the scan rate [Eq. (3.43)]. By analogy, a peak of an anodic process is shifted toward more positive potentials. The most characteristic feature of a cyclic voltammogram of a totally irreversible system is the absence of a reverse peak. However, it does not necessarily imply an irreversible electron transfer but could be due to a fast following chemical reaction. 

An electrochemical process such as A + ne P is said to be reversible if the Nernst equation is obeyed under the conditions of the experiment. In a totally irreversible system, either the forward or the reverse reaction is so slow as to be completely negligible. In a partially reversible system, the reaction in one direction is much slower than the other, but not totally insignificant. A process that appears reversible on a slow time scale may show signs of irreversibility when the time scale of the experiment is increased. 

As a prelude to a treatment of steady-state voltammetry in quasireversible and totally irreversible systems, it is useful to develop a very general description of current flow in a step experiment at a spherical electrode. In Section 5.4.2(a) the basic diffusion problem was outlined, and the following relationships arose without invoking a particular kinetic condition. 

When the wave is not reversible, the half-wave potential is not a good estimate of the formal potential and cannot be used directly to determine thermodynamic quantities in the manner discussed in Section 5.4.4. In the case of a totally irreversible system, the wave shape and position can furnish only kinetic information, but quasireversible waves can... 

If the electrode process is more complex than the one-step, one-electron model (e.g., n> with a rate-determining heterogeneous electron transfer), then the wave shape can become extremely difficult to analyze. An exception is the case where the initial step is the rate-determining electron transfer [Section 3.5.4(b)], in which case all that has been discussed for totally irreversible systems also applies, but with the current multiplied consistently by n. 

Tomes criterion and half-wave potential. As one can see from Table 5.5.1, 3/4 — 1/4 for a totally irreversible system provides a directly. That figure can then be used in conjunction with (5.5.30) [for early transients] or 5.5.49 [for steady-state voltammetry] to obtain l. Butler-Volmer kinetics are implicit and E must be known. 

Curve fitting. This method applies to voltammetry based on either transient or steady-state currents and proceeds essentially exactly as described for totally irreversible systems, except that the fitting function must be developed from (5.5.24) or (5.5.44). 

Equation 5.5.28 for early transients in a totally irreversible system having only species O present in the bulk. 

Koutecky treated the totally irreversible system at the DME and expressed the result as (29, 30)... 

Since a is usually between 0.3 and 0.7, both the wave slope and the Tomes criterion for a totally irreversible system are normally significantly larger than for a reversible system. These figures of merit are not without ambiguity, however. Consider the predicted wave slope of 63.8 mV for a = 0.85. Within the precision of normal measurements, one could diagnose the system as either reversible or irreversible. It is always a good idea to examine reversibility by a method, such as cyclic voltammetry, that allows a view of the electrode reaction in both directions. 

Table 6.2 - Diagnostic tests for totally irreversible systems at 25°C...

Although the cyclic voltammograms appear to be irreversible, they should not be. In the case of a totally irreversible system, we cannot expect to determine the reduction potential. To understand this apparent anomaly more fully, a study of the reversibility of the system was performed. The electrochemical current corresponds to the difference between the rate of the forward electron transfer kf[Bi2a] and its rate kb[Bi2a] for the reverse process. The reversibility factor f, for the methylcobalamin system is described as follows ... 

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