Irreversible and Quasi-Reversible Systems

2 Irreversible and Quasi-reversible Systems For irreversible processes (those with sluggish electron exchange), the individual peaks are reduced in size and widely separated (Fig. 2.5, curve A). Totally irreversible systems are characterized by a shift of the peak potential with the scan rate  

For quasi-reversible systems (with 10 1 k° 10 5cm/s) the current is controlled by both the charge transfer and mass transport. The shape of the cyclic voltammogram is a function of k°/ JnaD (where a = nFvIRT). As k°/JmD increases, the process approaches the reversible case. For small values of k°lVnal) (i.e., at very fast v), the system exhibits an irreversible behavior. Overall, the voltammograms of a quasi-reversible system are more drawn out and exhibit a larger separation in peak potentials compared to a reversible system (Fig. 2.5, curve B). 

FIGURE 2-5 Cyclic voltaimnograms for irreversible (curve A) and quasi-reversible (curve B) redox processes. 

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The scan rate is an important parameter for potential sweep methods such as CV or LSV The current is proportional to the square root of the scan rate in all electrochemical systems—irreversible, reversible, and quasi-reversible systems. Figure 4.4 shows the LSV for EMI—TFSl using a glassy carbon (GC) [49]. Note in this figure... 

Square-wave voltammetry of Osteryoung s type Application of SW techniques Linear sweep and cyclic voltammetry Principles of the linear sweep voltammetry Linear sweep voltammetry of reversible systems Irreversible and quasi-reversible processes Systems of two components and two-step charge transfers Distorting effects in LSV analysis... 

Recently, a method for the analysis of the DPP curves arising from slow electrode reaction has been presented [68, 69]. The influence of the first polarization time, of the pulse duration and potential step amplitude on the recorded current was clearly manifested. The solution may be applied to the static as well as to the dropping mercury electrodes. It was verified for the quasi-reversible system Cd(Hg)/Cd(II) in the presence of 2-(a-hydroxybenzyltriamine), a substance of biological interest. Also the irreversible system Cr(VI)/Cr(III) in NaOH medium (characterized by k° 10" m s" ) was followed according to this concept. 

Cyclic voltammograms of quasi-reversible systems show more or less pronounced backward peaks [114]. The separation of anodic and cathodic (backward and forward) peak potentials, dEp, increases with decreasing values of the dimensionless parameter defined in Eq. (88a). Typical results are given in Table 3. This method for estimating k requires to minimize the uncompensated resistance, R. Extrapolation of the data in Table 3 leads to the conclusion that a totally irreversible... 

The behaviour of systems where the electron transfer is either irreversible or quasi-reversible is fairly similar to the above, and is discussed fully by Wopschall Shain [18] who also consider the case where there is a coupled following chemical reaction. Other systems with coupled chemical reactions can be analysed in an analogous manner. 

The cathodic peak current is diffusion controlled, and the reduction potentials in the case of alkaline iodides are close to those already measured with the platinum interfaces. Also with TAAX salts, palladium shows a behavior similar to platinum. TMAX (X = halide) displays a quasi-reversible system. Contrarily, bulky TAA+ cations considerably enlarge the irreversibility of the charge-discharge process. Thns, while the potential difference AE between the cathodic and anodic peaks is abont 0.7 V when the cation is tetramethylammonium, it reaches almost 1.8 V when the cation is a tetra-n-octyl salt (Table 2.6). 

Cheh and co-workers [276—278] also investigated LSV at the RDE for first-order reversible, quasi-reversible, and irreversible systems. Whilst for the quasi-reversible case numerical solution cannot be approximated by any analytical expression, for the other cases this is possible. 

All potentials refer to SCE, except for Pd(5-H ) for which the potential refers to Fc" /Fc. The systems are reversible except in few cases indicated by qrev (quasi-reversible) or irr (irreversible). The potentials have been determined by cyclic voltammetry on both Pt and Hg electrodes, leading to identical values, unless otherwise noted. 

Redox potential (V) measured in CH3CN versus the saturated calomel electrode (SCE), determined by cyclic voltammetry at the platinum electrode, 0.1 M (nC4H9)4N. BF4 room temperature under argon scan rate, 100 mV s" the systems are reversible except in a few cases indicated by qrev (quasi reversible) and irr (irreversible). 

The reversibility of the electron transfer reaction may be tested via this equation, which predicts that a plot of E versus log[(id — i)/i] results in a straight line with the slope 0.0591/nV (at T = 298 K) for a reversible redox system. Slopes smaller than 0.059l/nV are observed when the electrode process is quasi-reversible or irreversible. In the latter case, E and i are related through Eq. (79) [238,241]. 

M LiOH, but below this value the Np(VI)/Np(V) couple tends toward a system with reduced electrochemical reversibility. Voltammetric behavior in NaOH solutions is very similar to the voltammograms in LiOH, with a shift in potential for the Np(VI)/Np(V) couple to = 0.106(6) V versus SHE in 3 M NaOH. In the mixed hydroxo-carbonate solutions (0.8 M NaOH/0.4M Na2CO3 and 1.8 M NaOH/0.1 M Na2CO3) the Np(VII)/Np(VI) becomes chemically irreversible and the Np(VI)/Np(V) couple is quasi-reversible. This behavior is... 

An easily assessable and well-researched model system—the glassy carbon electrode—is frequently used for studies of heterogeneous electron transfer with quasi-reversible and irreversible kinetics (34). Moreover, carbon particles can be spray-coated on electrode surfaces to modify its properties, and carbon fibers have been used as microelectrodes of defined diameter. 

This equation is often used to determine the formal potential of a given redox system with the help of cyclic voltammetry. However, the assumption that mid-peak potential is equal to formal potential holds only for a reversible electrode reaction. The diagnostic criteria and characteristics of cyclic voltammetric responses for solution systems undergoing reversible, quasi-reversible, or irreversible heterogeneous electron-transfer process are discussed, for example in Ref [9c]. An electro-chemically reversible process implies that the anodic to cathodic peak current ratio, lpa/- pc equal to 1 and fipc — pa is 2.218RT/nF, which at 298 K is equal to 57/n mV and is independent of the scan rate. For a diffusion-controlled reduction process, Ip should be proportional to the square root of the scan rate v, according to the Randles-Sevcik equation [10] ... 

Fig. 1.3.5 Quasi-reversible and irreversible behavior, (a) Current-potential curves and (b) log j — E plots (Tafel plots) for a redox system at different angular velocities of a rotating disc electrode ct>r = 50s (i) and Fe = O.OV, jo = O.OlAm, n = 1, = 5 x 10 m s, Dq =...

Table 3 shows these expressions and those obtained for quasi-reversible and irreversible systems. Further details are given in Ref (3). 

In the following discussions, it will be usefiil to introduce the term quasi-static. This term has various meanings as used by various authors, but in this chapter it refers to an irreversible process carried out in a very large number of very small steps. The difference between a quasi-static and a reversible process is that the reversible process refers to a series of stable equilibrium states, while the quasi-static process is a series of metastable equilibrium states. After every step of a reversible process, the system is at stable equilibrium with only two constraints. After every step of a quasi-static process, the system is at a metastable equilibrium and has at least three constraints. This concept and the need for it will become clear by considering some examples. 

This change from reversible, to quasi-reversible and finally irreversible behaviour can readily be seen from a plot of Ip as a function of as shown in Fig. 6.8. Diagnostic tests for a system in the quasi-reversible region are given in Table 6.3. 

For non>Nemstian systems the shape of the cyclic voltammogram changes. For the irreversible case the forward peak ceases to be symmetric, and of course there is no reverse peak. For quasi-reversible reactions there will be a reverse peak but both peaks will be asymmetric and the peak potentials will not be coincident. There is insufficient space here to consider these systems more fully, but further details can be found in the literature [12,13]. 

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