Quasi-reversible processes

The electron transfer Au(R2voltametric measurements 163). The half-wave potentials of the quasi-reversible process depends on the substituent R according to the Taft relation, as was described for Mo, W and Mn 37). The value of p decreases in the series Au > Mn > Mo = W, which indicates that in this sequence the mixing of ligand orbitals into the redox orbital decreases. The dominant ligand character of the unpaired electron MO in Au(R2dtc)2 relative to those in copper and silver compounds is found from Extended Hiickel MO calculations, as will be discussed later on. 

Square planar Ni11 complexes (50a) and (50b) of the quinoxaline-2,3-dithiolate ligand are oxidizable in chemically reversible, electrochemically quasi-reversible processes to yield Ni111 species, also featuring the (dxy)1 configuration.198 Interestingly, the difference in protonation state makes for a 0.20V difference in oxidation potential ((50a) +0.12V (50b) +0.32V vs. SCE), consistent with the less basic S-donors in the thione form. 

The effects of mercury film electrode morphology in the anodic stripping SWV of electrochemically reversible and quasi-reversible processes were investigated experimentally [47-51], Mercury electroplated onto solid electrodes can take the form of either a uniform thin film or an assembly of microdroplets, which depends on the substrate [51 ]. At low sqtrare-wave frequencies the relationship between the net peak crrrrent and the frequency can be described by the theory developed for the thin-film electrode because the diffusion layers at the snrface of microdroplets are overlapped and the mass transfer can be approximated by the planar diffusion model [47,48],... 

As can be observed from these curves, the rate of variation of linear and real diffusion layer thickness with time increases with k°, being maximum for A° > 0.1 cm s 1. which corresponds to the reversible case. From Fig. 3.1a, it can be seen that for reversible processes the surface concentration is independent of time in agreement with Eq. (2.20) (see also Fig. 2.1 in Sect. 2.2.1). However, for non-reversible processes (Fig. 3.1b and c), the time has an important effect on the surface concentration, such that csQ decreases as I increases, with this behavior being more marked for intermediate k° values (quasi-reversible processes). So, for k° = 10 3 cm s 1. the surface concentration decreases by 19 % from t = 0.1 to 0.4 s, whereas for k° = 10 4 cm s 1 it only varies 7 %. It is also worth noting that for the reversible case (Fig. 3.1a), the diffusion control (cf, > 0) has practically been reached at the selected potential. 

These regions have been indicated in Fig. 5.13 for a = 0.5. Matsuda and Ayabe suggest the following ranges for classifying the electrode process [35] Kplane >15, Reversible process 10-3 < Kplane < 15, Quasi-reversible process Kplane < 10 3. Totally irreversible process. The reversible limit is similar to that proposed here, but the totally irreversible one is clearly excessive (see Fig. 5.13). In any case, this criterion has only an approximate character. 

Cyclic Square Wave Voltammetry (CSWV) is very useful in determining the reversibility degree and the charge transfer coefficient of a non-Nemstian electrochemical reaction. In order to prove this, the CSWV curves of a quasi-reversible process with Kplane = 0.03 and different values of a have been plotted in Fig. 7.17. In this figure, we have included the net current for the first and second scans (Fig. 7.17b, d, and f) and also the forward, reverse, and net current of a single scan (first or second, Fig. 7.17a, c, e) to help understand the observed response. 

So, a totally irreversible process could be mistaken for a quasi-reversible one with a 0.5 (Fig. 7.17f). In order to discriminate the reversibility degree of the electrochemical reaction, it is necessary to take into account that for a quasi-reversible process the peak corresponding to more cathodic potentials in the second scan (denoted as RC by [29]) is higher than that located at more anodic ones (denoted as RA by [29]) when a 3> 0.5, whereas the opposite is observed for a fully irreversible electron transfer for any value of a (see also Table insert, Fig. 7.20). 

Blaedel and Engstrom [48] noted that for a quasi-reversible process the current could be simply expressed in terms of the rate constant and mass-transport coefficient. Application of a square wave step in the rotation rate of a RDE (i.e., PRV, see Section 10.4.1.3) resulted in modulation of the diffusion-limited current and hence modulation of the mass-transfer coefficient. By solving the appropriate quadratic equation it was possible to derive a value for the heterogeneous rate constant for the electrochemical cathodic, kf, or anodic, kb, process of interest. Values for the standard heterogeneous rate constant and transfer coefficient were subsequently... 

For a quasi-reversible process, both charge transfer and mass transfer affect the current. The shape of the cyclic voltammogram is a function of k° It mi D (where a = nFv/RT). The peak separation between the anodic and cathodic peaks can give information about k°. 

Obviously, therefore there must be an intermediate case in which the kinetics of both the forward and reverse electron-transfer processes have to be taken account of. Such systems are described as being quasi-reversible and as would be expected, the scan rate can have a considerable effect on the nature of the cyclic voltammetry. At sufficiently slow scan rates, quasi-reversible processes appear to be fully reversible. However, as the scan rate is increased, the kinetics of the electron transfer are not fast enough to maintain (Nernstian) equilibrium. In the scan-rate region when the process is quasi-reversible, the following observations are made. 

The separation of the forward and reverse peaks (A p) is larger than the value of 56/n mV associated with a reversible process at 25°C. Importantly, A p increases with increasing scan rate and the value of the standard rate constant for the electron-transfer process, ko, may be calculated from the separation of the peaks in a quasi-reversible process (Bard and Faulkner, 1980), provided voltammograms are corrected for solution resistance effects (see below). 

The oxidation of iron(II) clathrochelates to iron(III) complexes is a quasi-reversible process with Eirz from 775 to 580 mV for clathrochelate dimethylglyoximates, from 850 to 570 mV for nioxime compounds, from 1 250 to 1 040 mV for glyoximates, and from 940 to 760 mV for a-benzyldioxime complexes. In the dioxime series Nx > Dm > Bd > Gm, the Eyz values becomes higher. 

The oxidation of encapsulated ruthenium(II) ion to ruthenium(III) ion is a quasi-reversible process with Em from 1 430 to 1 140 mV. As on additional parameter, the cathodic and anodic current ratio (IpJIpa) obtained from voltammetric data was used to determine the relative stability of the resulting ruthenium (III) complexes. It was shown that the stability of these complexes increases with lengthening of the linear chain of alkoxy-groups and decreases with an increase in their volumes [77, 329]. 

The auraferraborane clusters of System 7 show a marked dependence on the identity of the MPhj ligand. The As complex is easier to reduce than the corresponding P complex and the reduction product is more stable (tj/j 0.1 s for the As complex, and tj/2 0.01 s for the P complex ). The major difference, however, is found for the oxidations while the P complex shows two well-defined electrochemically and chemically quasi-reversible processes in CV, the As complex only gives one well-defined oxidation peak at a potential ca 0.3 V higher than F ,i for the P complex (i.e. close to F ,2 for the P complex). A difference of ca 0.3 V in the redox potential upon a change from PPhj to AsPhj seems very unlikely based on the other data in Table 18, and the explanation of the observation is probably that a small pre-peak in the CV of the As complex (at a potential close to F ,i for the P complex) is in fact the first oxidation of the As complex. The unexpected small size may be due to a reorganization process prior to electron transfer, which is much slower for the As than for the P complex. 

Feedback theory has been the basis for most quantitative SECM applications reported to date. Historically, the first theoretical treatment of the feedback response was the finite-element simulation of a diffusion-controlled process by Kwak and Bard (1), but we will start from a more general formulation for a quasi-reversible process under non-steady-state conditions and then consider some important special cases. 

The decrease in the rate constant with increasing cTEA+,w/cTEA+.o ratio may allow probing faster IT reactions with no complications associated with slow diffusion in the bottom phase. One should also notice that, unlike previously studied ET processes at the ITIES, the rate of the reverse reaction cannot be neglected. The difference is that in the former experiments no ET equilibrium existed at the interface because only one (reduced) form of redox species was initially present in each liquid phase (15,25). In contrast, reaction (29) is initially at equilibrium and has to be treated as a quasi-reversible process (56c). Probing kinetics of IT reactions at a nonpolarizable ITIES under steady-state conditions should be as advantageous as analogous ET measurements (25). The theory required for probing simple IT reactions with the pipet tips has not been published to date. ... 

There is another aspect of sequestering that ean be illuminated by the calculation of the entropy differences. Highly configured distributions of reaction centers can often be decomposed into a number of disjoint (geometrically uncoupled) subsystems. The question is If, for eaeh of the subsystems comprising the overall assembly, one calculates the statistical entropy associated with an irreversible (or quasi-reversible) process, is the entropy S for the composite system a simple additive function of the entropies [5, 5y,...] calculated for the individual subsystems That is, is... 

Reversible process Irreversible process Quasi-reversible process... 

Fig. 6.27) is consistent with the theory of Matsuda and Ayabe [14]. We can observe three regions reversible process—scan rates lower than 0.1 V s (area 1), irreversible—scan rates higher than 0.5 V s (area 2) and quasi-reversible— process in between (area 3). 

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