Quasi-reversible systems

Quasi-reversible charge transfer differs from the Nernstian case in that Co (0, f)/CR (0, t) is not dictated by the Nernst equation and depends both on the rates of the forward and reverse charge transfer reactions. The flux of O at the surface, where f = F/RT, is given by [15] 

Numerical methods were used to obtain solutions for LSV [15] and CV [26]. The current is given by 

Peak potential separations (AEp) for CV of quasi-reversible charge transfer have been numerically evaluated as a function of a normalized rate constant p defined by the equation [26] 

This relationship is useful in the study of heterogeneous charge transfer kinetics, which is discussed in a subsequent section. 

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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 quasi-reversible systems (with 10 1 > k" > 10 5 cm s1) 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 = nFv/RT). As k"/s/naD increases, the process approaches the reversible case. For small values of k°/+JnaD (i.e., at very fast i>) the system exhibits an irreversible behavior. Overall, the voltaimnograms of a quasi-reversible system are more drawn-out and exhibit a larger separation in peak potentials compared to those of a reversible system (Figure 2-5, curve B). 

Suimnarize the different features of the cyclic voltammogramic response for reversible and quasi-reversible systems. 

For quasi-reversible systems the limiting current is controlled by both mass transport and charge transfer ... 

Quasi-reversible systems, 32 Quaternary ammonium salts, 153 Quinliydrone electrode, 151... 

This means that Ei lies about midway on the SV wave between Ev and Epl2 at the high, i.e. positive, side, as we have already mentioned in connection with Fig. 3.64. However, in practice and on the basis of the above arguments (1)—(3), the position of E, will deviate from this more or less theoretical approximation where the sphericity term of eqn. 3.80 has been neglected. Further, with incompletely reversible redox couples, e.g. for quasi-reversible systems (cf., pp. 125-126), there will of course be more deviations, but at any rate the linear relationship between ip and C appears to remain. 

In practice, the majority of redox reactions behave more like a quasi-reversible system. It is also common that a reaction that behaves reversibly at low scan rate becomes irreversible at high scan rate passing through a quasi-reversible region. 

The key parameters from a CV measurement include the wave shape, the peak potential(s), pa and pc, and, more importantly, their dependence on the scan rate. For reversible and many quasi-reversible systems, the average of pa and equals or closely approximates EV2. Forjudging the reversibility of an electrode reduction like reaction (A.l) at 25°C, the useful criteria are ... 

The equations for reversible and quasi-reversible systems are given in Table 11.1. The table shows, as mentioned in Section 11.4, that the phase angle is lower the slower the electrode reaction. 

Generally, the ratio of the peak currents 1 /Fp is equal to one for a quasi-reversible system. 

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... 

In this manner, it is possible to measure Eq with a precision of a few mV or better. Although Eq might be determined more easily and with a similar precision for a reversible system by the CV technique, the OTTLE/Nernst experiment is very useful for the study of quasi-reversible systems. The presence of slow heterogeneous kinetics means that the equilibrium is attained relatively slowly upon changing the potential, but this presents no problem as long as the redox pair is kinetically stable. The technique has therefore been used in the measurement of Eq and n for a large number of inorganic salts and enzymes [70, 82]. 

Principles Reversible or Quasi-Reversible Systems. Electrolysis by the OTTLSET involves a very small solution volume, and the equilibrium state is quickly achieved at a fixed applied potential. The ratio of ([O]/ [RDsurface the electrode surface is determined by... 

For a quasi-reversible system with a small reaction rate, a longer equilibrium time is needed for each change in the applied potential, but the thermodynamic parameters can be determined in the same way. 

The procedure employed assumes that the heterogeneous charge transfer process is quasi-reversible on the a.c. time scale and reversible (nernstian) on the d.c. time scale (quasi-reversible systems on the d.c. time scale normally are not selected for assay work). Under these conditions, the faradaic rate law may be written as... 

If the dc process is not fully reversible, the surface concentrations of the electroactive species are different at a given dc potential for forward and reverse scans, that is, for quasi-reversible systems a displacement of the peaks for forward and reverse scan can be observed. This displacement can be used to derive kinetic parameters of the electrode reaction. For... 

When defining the overall current-potential curve in general cases, which are sometimes called mixed control or quasi-reversible systems, first one needs to write the equation for the current, based on general rate laws involving the interfacial concentrations ... 

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. 

Fig. 32. Calculated faradaic fundamental-harmonic AC polarograms of the reversible and quasi-reversible systems. 1, a reversible system, 2 and 3, systems characterized by the standard rate constant k° (ms ) (2), 10 (3), 10 , the electron transfer coefficient af = 0.5. Adapted according to [78]. The shifts of Ep of curves 2 and 3 with respect to curve 1 are neglected.

Fig. 34. Calculated faradaic second-harmonic AC polarogram. 1, a reversible system, 2, quasi-reversible system of k = 10"" ms" (dashed line). Adapted according to [78].

The quasi-reversible systems were treated first in [111]. The current appearing in these processes obeys a relation similar to the Eqs. (78) and (84) ... 

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... 

Table 6.3 - Diagnostic tests for quasi-reversible systems...

Fig. 8.18 - Calculated a.c. polarograms for quasi-reversible systems, showing decreasing peak height with decreasing exchange current at fixed frequency (2000s ), A p = 5 mV. Exchange current densities shown in Acm. Reproduced with permission from D. E. Smith, Electroanal Chem., 1 (1966), 1.

In case of quasi-reversible systems, the cyclic voltammograms show considerably different behavior from their reversible counterparts. Figure 3 shows the voltammogram for a quasi-reversible reaction for different values of the reduction and oxidation rate constants. 

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