Electrochemical wave

Ca waves in systems [ike Xenopus laevis oocytes and pancreatic (3 cells fall into this category Electrochemical waves in cardiac and nerve tissue have this origin and the appearance and/or breakup of spiral wave patterns in excitable media are believed to be responsible for various types of arrhythmias in the heart [39, 40]. Figure C3.6.9 shows an excitable spiral wave in dog epicardial muscle [41]. 

Figure C3.6.9 Spiral electrochemical wave in dog epicardial muscle visualized using a voltage-sensitive dye. Reproduced by pennission from Pertsov and Jalife [41].

Dloxygen reduction electrocatalysis by metal macrocycles adsorbed on or bound to electrodes has been an Important area of Investigation (23 ) and has achieved a substantial molecular sophistication in terms of structured design of the macrocyclic catalysts (2A). Since there have been few other electrochemical studies of polymeric porphyrin films, we elected to inspect the dloxygen electrocatalytic efficacy of films of electropolymerized cobalt tetraphenylporphyrins. All the films exhibited some activity, to differing extents, with films of the cobalt tetra(o-aminophenylporphyrin) being the most active (2-4). Curiously, this compound, both as a monomer In solution and as an electropolymerized film, also exhibited two electrochemical waves... 

The evolution of a new set of electrochemical waves (as opposed to the gradual shifting of the redox couple) on addition of guest species may be due to a number of factors. If the complex formed has a particularly high stability constant and has a redox potential which is markedly different from that of the free ligand, a new set of waves may be observed. However, if the decomplexation kinetics of the complex formed is particularly slow on the electrochemical time scale then, as the potential is scanned between the vertex points during a cyclic voltammetric experiment, the solution complexed species will be stable over this time period and the two sets of waves will correspond to free ligand and complex. Therefore care should be taken to determine the cause of the evolution of a new set of electrochemical waves and... 

As the concentration of electrolyte is lowered to a range equal to or less than the concentration of TCNQ, the first wave remains near its original height, but the second wave decreases in amplitude relative to the first (Fig. 12.7). The behavior of the first electrochemical wave is that expected for the reduction of a neutral, since the limiting current for such a process should be independent of migration. However, to explain the behavior of the limiting current of the second wave, the chemical processes in the diffusion layer must be considered. 

Lateral macrobicycles are dissymmetric by design thus, monoelectronic reduction of the Cu(ll) ion bound to the [12]-N2S2 macrocyclic subunit in the bis-Cu(ll) cryptate 45, gives a mixed valence Cu(i)-Cu(ll) complex [4.6]. Macrotricycle 46 forms a dinuclear Cu(ll) cryptate that acts as a dielectronic receptor and exchanges two electrons in a single electrochemical wave [4.7]. Complexes of type 47 combine a redox centre and a Lewis acid centre for the potential activation of a bound substrate [4.8]. 

Returning now to the comproportionation equilibrium, it is interesting to notice that for large systems (2 mm co) the comproportionation constant tends towards a statistical limit of 4 (see below). Then a single electrochemical wave is observed, a fact which has frequently dissuaded researchers from further studies on such binu-clear complexes. However, even in this apparently unfavorable case, the proportion of mixed-valence species at half-oxidation (reduction) is, according to Eq. (3), a comfortable 50 %, nevertheless allowing a meaningful correction. 

As stated above, electrochemical wave splitting in itself cannot be actually considered as a manifestation of wire-like properties. However, some spectacular or intriguing examples deserve to be quoted. 

For very long systems, all effects decrease with distance except the statistical factor ( ). Thus when the metal-metal distance is large enough, should approach 4 as a lower limit. Then the electrochemical wave shape becomes indistinguishable from the case of a complex undergoing a single electron transfer, apart from the fact that the coneentration has doubled. 

In the converse situation, three limiting cases may be observed. In the first case the electron transfer is intrinsically slow. The RDS of the overall process is then the forward electron transfer, and the redox system is said to be slow and chemically irreversible. The electrochemical wave is then observed at potentials sufficiently different from E° for n(E — E°) 0 (Sec. III.C.3). The two other situations are encountered when is large... 

From this description it is seen that, depending on the exact degree of competition between the four rates in Scheme 7, the electrochemical wave is observed in potential ranges that may be positive or negative to E°, as summarized in Table 4. Without a quantitative treatment of the pertinent electrochemical data, it is almost impossible to decide the position of E° vis-a-vis the potential location E, where the wave is observed. This is an important caveat to remember when using potential data, such as peak potentials or half-wave potentials, instead of E° values. The experimental difficulty is even more severe in practice. Indeed, when one considers a series of related chemicals, there are great chances that E°, k°, and k vary uniformly with respect to each other because they relate intimately to the orbital energy and characteristics of the acquired (LUMO) or lost... 

Table 4 Nature and Location of the Electrochemical Wave Observed for an EC Sequence as a Function of the Mass Transfer Rate...

HOMO) electron [16,29]. Thus, the potential at which the electrochemical wave is observed may correlate with E , since it depends on the three figures. Such a case is presented in Fig. 17 for the series of akylbenzenes [29] already mentioned in this chapter, in which the peak potentials of the chemically irreversible voltammograms (at 0.1 Vs ) correlate with E° with a slope close to unity. 

Any characteristic potential pertaining to a given electrochemical wave Half-wave potential... 

Chemical and electrochemical oxidation of these [Pt Me2(a-diimine)] species in MeCN was later studied in more detail in the Tdset group (38). Irreversible electrochemical waves were again observed, and bulk electrolysis revealed consumption of 1.1-1.6 FmoP indicative of a le oxidation process. (Electro)chemical bulk oxidation leads to only marginal formation of methane or ethane, and almost quantitative formation of the species [Pt Me3(a-diimine)(NCMe)] and [Pt Me(a-diimine)(NCMe)] in a 1 1 ratio. It was proposed that the short-lived [Pt Me2(a-diimine)] " " decomposes via a bimolecular methyl transfer from one platinum to another. This explains the product distribution and the lack of products derived from free alkyl radicals. This could either involve a reaction between two [Pt °Me2(a-diimine)] + intermediates or a reaction of [Pt° Me2(a-diimine)] + with the starting material [Pt Me2 (a-diimine)]. 

Winfree A T 1987 When Time Breaks Down The Three Dimensional Dynamics of Electrochemical Waves and Cardiac Arrythmias (Princeton, NJ Princeton University Press)... 

The apparent character of many-electron processes, and thus the experimental possibility to observe the one-electron electrochemical steps, depends on the stabilities of the LVls, either thermodynamically or kinetically defined. A process should appear as raie-stage many-electron one at low stabilities of LVls and will split into sequential reactions at higher stabilities. The intermediate region exists where the overall process is represented by one distorted electrochemical wave in an electrochemical curve. Thus, the discussion on one- or many-electron electrochemical steps is becoming of quantitative rather than qualitative nature. 

One can see that, in the general case, the equations of voltammetric curves cannot be reduced to the simple functions of (2.9) or (2.10) type. Also it is clear that, if K 0, these dependencies are not the equations of electrochemical waves having neither anode P —> oc) nor cathode (F 0) constant limit current. It should be only noted that the curves represented by Eq. (2.42) or equation system (2.42) and... 

Hence, the equation of -function type (2.10) describes the polarographic current-potential wave of a many-electron electrochemical process with depolarization. For example, it was established [2] that this kind of equation provides good approximation for the electrochemical wave of reduction of Si(IV) on a platinum electrode in KCl-KF-K2SiF6 melt (Fig. 2.6). 

There is another characteristic value of the stability where the apparent process splits into a series of sequential one-electron steps. Between these thresholds, a rather wide range of stability lies where a process manifests itself as an electrochemical wave with specific distortions. 

Nevertheless, certain conclusions may be drawn from even a brief perusal of this work. These include the necessity of positively identifying electrochemical waves by methods such as the standard addition technique. Moreover, there is a clear need to control the sulfur partial pressure over melts. Lastly, more attention must be given to the role of solvent and solute cation composition, since many of the apparent disagreements in the literature have arisen because authors have employed different alkali and alkaline earth sulfides. 

In this model, e is the ratio of the time scales associated with the reactive dynamics of the two variables u and v, while D and are their diffusion coefficients. The parameters a and p characterize the local reactive dynamics. The FHN model was originally constructed as a simple scheme for describing electrochemical wave propagation in excitable nerve or cardiac tissue. The variable u corresponds to the potential while v represents ion currents in the nerve tissue. It has since been used extensively as a generic model that describes so-called excitable behavior of chemically reacting systems. In fact, as we shall show later in this chapter, it is possible to write a chemical reaction scheme whose rate law is of FUN form. ... 

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