The CE Mechanism

FIGURE 2.8. CE reaction scheme in cyclic voltammetry. Kinetic zone diagram showing the competition between diffusion and preceding reaction as a function of the equilibrium constant, K, and the dimensionless kinetic parameter, X [equation (2.1)]. The boundaries between the zones are based on an uncertainty of 5% at 25°C on peak of plateau currents. 

COUPLING OF ELECTRODE ELECTRON TRANSFERS WITH CHEMICAL REACTIONS 

Further increase in 2 restores reversibility progressively. The wave eventually becomes a full one-electron reversible wave, with, however, a negatively displaced peak potential corresponding to a new standard potential which corresponds to the standard potential of the C/B couple  

More generally, in the DE zone, the standard potential may be defined as 

Once the equilibrium constant has been derived from the peak current in zone KO or from the peak potential in zone DE [Equation (2.16)], the rate constants may be obtained from equation (2.15) in zone KP. If all these zones are not experimentally accessible, K, k+, and may be derived from the peak current and potential by a simple two-parameter fitting. 

Experimentally, the initial solution contains the species P and Ox at equilibrium concentrations. During the reductive sweep. Ox is reduced to Red, and P starts to convert to Ox according to the chemical kinetic rate constants. If the experiment is started with initial concentration of the species Red only, the oxidative CV is an EC mechanism. 

The cyclic voltammetric response for this system (with the electrode reaction reversible, a CE, mechanism) is determined by X, and (k +k 2)/v. The limiting cases of the CE mechanism are (1) the chemical step is fast and at equilibrium, and (2) the forward chemical reaction is slow with respect to the time scale of the experiment. In case 1, the CV has an p determined by the E9 and Xgq. In case 2, the cyclic voltammogram will be reversible and will reflect only ° and the initial concentration of species Ox. 

Let us examine the transition from case I to case 2, which can be effected by a change in scan rate. As the scan rate is increased, the kinetics of the chemical reaction are apparent the cathodic peak/.yv decreases because Ox does not maintain equilibrium concentrations on the time scale of the experiment. The cathodic peak potential also shifts negative relative to the peak in case 1. At large scan rates, the reversible case 2 is achieved. 

A quantitative study of the equilibrium and kinetics of an C / C-type mechanism was recently reported by Lee et al. This study utilized a combination of potential step and cyclic voltammetric experiments in an examination of the reduction of the nitronium ion and the reverse process, the oxidation of nitrogen dioxide. 

This is our first encounter with the use of simulation to analyze CV results. Through the theory of simulation (Chapters 4-6), a cyclic voltammetric or potential step response can be calculated for any electrochemical mechanism, given the parameters that describe the experiment (scan rate, scan range, electrode area) and the mechanism (reduction potentials, electrode kinetics, chemical reaction kinetics, and diffusion coefficients of all chemical species). The unknown parameters of the electrochemical mechanism can be varied until a simulation is obtained that closely resembles the experimental result. 

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For the CE mechanism equations for k and id have been derived20 that for ik contains the term m2/3<2/3, which means that, as is approximately... 

In the CE mechanism (Scheme 2.2), a first-order (or pseudo-first-order) homogeneous reaction precedes the electron transfer step. In the case where the initial electron transfer is fast enough not to interfere kinetically, the electrochemical response is a function of two parameters the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic... 

The electrode reaction (2.46) is followed by a first-order homogeneous chemical reaction (2.47), in which the product of the electrode reaction O is converted to a final electroinactive product Y. By analogy with the CE mechanism, the chemical step can proceed as ... 

Electroreduction of Cd(II)-nitrilotriace-tic acid and Cd(II)-aspartic acid systems was studied on DME using SWV [73]. The CE mechanism in which the chemical reaction precedes a reversible electron transfer was established. Also, the rate constants of dissociation of the complexes were determined. Esteban and coworkers also studied the cadmium complexes with nitrilotriacetic acid [74, 75] and fulvic acid [76]. The complexation reaction of cadmium by glycine was investigated by different electrochemical methods using HMDE and mercury microelectrode [77, 78]. 

The three limiting cases clearly show up in a plot of — r1/2 vs. —as an example, the result for the CE mechanism has been reproduced in Fig. 37. 

The convective-diffusion equations and boundary conditions for z = °° will be exactly the same as for the CE mechanism. However, at z — 0 we have... 

In the CE mechanism (or preceding chemical reaction) the electroactive species is generated from an electroinactive species by a chemical reaction ... 

Contrarily to the CE mechanism, in this case the current-potential curve is more affected by the chemical reaction the higher the rate and the equilibrium constants / and Keq = 1 /K. 

The influence of the chemical kinetics is analyzed in Fig. 4.31 where ADDPV curves are plotted for different values of the dimensionless rate constant %2(= (k + ki)zi). For comparison, the curve corresponding to a simple, reversible charge transfer process (Er) of species C + B for the CE mechanism and of species A for the EC one has also been plotted (dashed line in Fig. 4.31a, b). As can be observed, the behavior of ADDPV curves with is very different depending on the reaction scheme. For the CE mechanism with K = (1 /Kepeak current increases and the peak potential shifts toward more negative values as the kinetics is faster, that is, as xi increases. For very fast chemical reactions, the ADDPV signal is equivalent to that of a reversible E mechanism (Er) with... 

The relative magnitude of the peaks of the ADDPV curve is also very informative about the electrode process [55, 81, 82]. It can be observed that for the CE mechanism it is fulfilled that/ lane < / ll ll ine whereas for the EC one / i"L > / I I "L. This behavior contrasts with the case of the first-order catalytic mechanism and with the reversible E mechanism for which the value of the peak currents is equal (/ lane = / lane ). Therefore, this simple criterion allows us to discriminate between these mechanisms. 

The chemical kinetics (j2), has no effect on the symmetry of the peaks in the case of the irreversible EC mechanism (K = 0) under kinetic steady-state conditions. On the other hand, for the CE mechanism the /J ane/I/Plane I value does depend on xi and it tends to /Plane — 1 in the limiting case of very fast chemical reactions (see Fig. 4.31a). 

A most advanced kinetic study was carried out by Senda and coworkers [166], who investigated the transfer of Na across the water-nitrobenzene interface in the presence of dibenzo-18-crown-6. This ligand is known to form a stable 1 1 complex with the transferred ion. It was shown that the ac impedance technique makes it possible to distinguish between three basic mechanisms, which can be described as (1) transfer of the ion followed by its complexation in the organic phase (the EC mechanism) (2) complexation of the ion in the aqueous phase followed by transfer of the complex ion (the CE mechanism) or (3) complexation of the ion at the interface with simultaneous transfer of the ioti from the aqueous to the organic phase (the E mechanism). For the system studied, the E mechanism described by Eq. (58) has turned out to be most probable. The apparent rate constant of the assisted ion transfer... 

The theory for linear-scan voltammetry (LSV) and cyclic voltammetry (CV) for the CE mechanism uses a terminology in which ... 

You have probably noticed that the CE mechanism actually does not include a chromatographic distribution mechanism. Consequently, it is as readily applicable to macromolecules as to smaller ones. Hence, it is valuable for the separation of large biomolecules. Chemical modification of the sihca wall or addition of detergents to the background electrolyte is often required to eliminate wall adsorption of proteins. 

As with LSV or CV, the mass-transfer equations for the various species must be changed to take account of loss or production of material because of the coupled reactions. Thus for the CE mechanism [(12.3.1) and (12.3.2)] at the RDE, (9.3.13) becomes... 

From the analysis of polarograms for the transfer of procaine in Case 2, Senda et al. concluded that the transfer of procaine is described by the CE mechanism, that is, the transfer of the protonated form of procaine with the preceding protonation reaction in W. The major contribution to was found to be proton donation from the acid form of a buffer component, AH, employed. The values of = kf/[AH] at pH 8.0 are given in Table 1 for three different buffers. In this example, the reaction-layer thickness is much thinner, of the order of 10 cm, than the diffusion-layer thickness, which ensures the applicability of the concept of the reaction layer [22]. 

Fleischmann, M. and Pons, S. (1988) The behaviour of microdisc and microring electrodes. Mass transport to the disc in the unsteady state. The effects of coupled chemical reactions. The CE mechanism. Journal of Electroanalytical Chemistry, 250, 285. 

The simulation analysis resulted in the following parameters for the CE mechanism (in acetonitrile) ... 

Fig. 8 Experimental DNP enhancement profiles for the SE and the CE mechanisms showing the positions of positive and negative enhancement and their dependence on the microwave irradiation frequency (or, rather the magnetic field for a given microwave frequency) as well as on the electron and nuclear Larmor frequencies coos and too/, respectively, (a) A tj/pical SE enhancement profile obtained with 40 mM trityl. (b) A typical CE enhancement profile obtained with 10 mM TOTAPOL (20 mM electrons). The EPR spectrum of each radical is shown on top. The lines connecting the data points are to guide the eye. Reprinted with permission from [206]. Copyright 2012, American Institute of Physics...

The cathodic limit observed in an ionic liquid is generally due to the reduction of the ammonium cations [114,115]. Such a reduction proceeds by the CE mechanism first, the deprotonation of ammonium cation occurred (Eq. 7.5), followed by the reduction of the proton (Eq. 7.6). For the anodic limit, the ammonium could, in this case, be oxidized in the presence of oxygen. 

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