Current density, coupled

The device model describes transport in the organic device by the time-dependent continuity equation, with a drift-diffusion form for the current density, coupled to Poisson s equation. To be specific, consider single-carrier structures with holes as the dominant carrier type. In this case,... 

At higher current densities, the primary electron transfer rate is usually no longer limiting instead, limitations arise tluough the slow transport of reactants from the solution to the electrode surface or, conversely, the slow transport of the product away from the electrode (diffusion overpotential) or tluough the inability of chemical reactions coupled to the electron transfer step to keep pace (reaction overpotential). 

Cathodic protection of different materials in installations of dissimilar metals is only possible if the protection potential ranges of the individual materials overlap. Section 2.4 gives information on the protection potential ranges of various systems. If there is no overlapping, then insulating couplings must be installed. This is also appropriate and even necessary if the protection current densities are very different. 

The reaction rate per unit area i. For a corroding metal the partial anodic and cathodic current densities cannot be determined directly by means of an ammeter unless the anodic and cathodic areas can be separated physically, e.g. as in a bimetallic couple. If the metal is polarised a net current 4 for cathodic polarisation, and for anodic polarisation, will be obtained and can be measured by means of an ammeter. 

The exchange current density for common redox couples (at room temperature) can range from 10-6 pAcm-2 to A cm"2. Equation (1-24) can be written in terms of the exchange current to give the Butler-Volmer equation ... 

Kolbe electrolysis is a powerful method of generating radicals for synthetic applications. These radicals can combine to symmetrical dimers (chap 4), to unsymmetrical coupling products (chap 5), or can be added to double bonds (chap 6) (Eq. 1, path a). The reaction is performed in the laboratory and in the technical scale. Depending on the reaction conditions (electrode material, pH of the electrolyte, current density, additives) and structural parameters of the carboxylates, the intermediate radical can be further oxidized to a carbocation (Eq. 1, path b). The cation can rearrange, undergo fragmentation and subsequently solvolyse or eliminate to products. This path is frequently called non-Kolbe electrolysis. In this way radical and carbenium-ion derived products can be obtained from a wide variety of carboxylic acids. 

To some degree the ratio of additive monomer to additive dimer can be infiuenced by the current density. High current densities favor the formation of additive monomers, low ones these of additive dimers (Table 8, Nos. 4, 5). This result can be rationalized according to Eq. 9 At high current densities, which corresponds to a high radical concentration in front of the electrode, the olefin can trap only part of the Kolbe radicals formed. This leads to a preferred coupling to the Kolbe dimer and a combination of the Kolbe radical with the primary adduct to the additive monomer. At low current densities the majority of the Kolbe radicals are scavenged by the olefin, which leads to a preferential formation of the additive dimer. 

In an ideal case the electroactive mediator is attached in a monolayer coverage to a flat surface. The immobilized redox couple shows a significantly different electrochemical behaviour in comparison with that transported to the electrode by diffusion from the electrolyte. For instance, the reversible charge transfer reaction of an immobilized mediator is characterized by a symmetrical cyclic voltammogram ( pc - Epa = 0 jpa = —jpc= /p ) depicted in Fig. 5.31. The peak current density, p, is directly proportional to the potential sweep rate, v ... 

The charge propagates in the film by electron hopping between the polymer Red/Ox couples. This is controlled by the electrode potential only in a close proximity of the electrode in more distant sites, the charge transport is driven by a concentration gradient of reduced or oxidized mediators. The observed faradaic current density, jF, is a superposition of... 

As an example we may consider the Kolbe reaction, the oxidation of carboxylic acid and carboxylates of the form R-COOH or R-COO- to form coupled hydrocarbon products of the form R2. Investigation of this reaction in aqueous and non-aqueous solvents has revealed that the processes taking place are very complex indeed. In general, the product R2 is only formed at high current densities on smooth electrodes. At lower current densities, alkenes and non-dimeric products such as R-H are found, and, especially in alkaline solutions, the product R-OH can be formed in good... 

The flux of CQ1 at the surface must be related to the current, since it is the passage of the current that leads to the flux of components of the redox couple. We need to be careful here since there are subtleties of sign but for an increase in positive current density, SJ, there will be an increase in positive flux of CQ. The change in flux of Cc at the surface (x = 0) is given by Fick s first law as... 

Pletcher and associates [155, 159, 160] have studied the electrochemical reduction of alkyl bromides in the presence of a wide variety of macrocyclic Ni(II) complexes. Depending on the substrate, the mediator, and the reaction conditions, mixtures of the dimer and the disproportionation products of the alkyl radical intermediate were formed (cf. Section 18.4.1). The same group [161] reported that traces of metal ions (e.g., Cu2+) in the catholyte improved the current density and selectivity for several cathodic processes, and thus the conversion of trichloroacetic acid to chloroacetic acid. Electrochemical reductive coupling of organic halides was accompanied several times by hydrodehalogena-tion, especially when Ni complexes were used as mediators. In many of the reactions examined, dehalogenation of the substrate predominated over coupling [162-165]. 

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