Branching mechanisms

Branching mechanisms involve both consecutive and parallel electron transfers. The most important application of the RRDE in this context has been to the electrochemical reduction of oxygen [175], on which a large amount of research has been done. Different mechanistic models give rise to different expressions linking the rate constants, which can be compared with experimental data as in previous sections, the most important is the variation of (iD / h ) with rotation speed. A summary of different models has recently appeared [176] the conclusion of which is that, at platinum, the model of Damjanovic et al. [177] is correct diagnostic criteria to test the model have been developed. 

The plot of D/iR vs. co 1/2 will, in general, give lines of different positive slopes and different intercepts, depending on the applied potential (which directly affects the ratio k /k 2 and k 3). 

Diagnostic plots for heterogeneous catalytic electrode reactions at the RRDE have many features in common with those for simple parallel reactions [178]. This type of analysis is important in the investigation of the oxygen electrode reaction where non-electrochemical surface processes can occur. 

Around 1980, some branching mechanisms were proposed with the intention of describing the processes occurring in the active, transition, and prepassive ranges of the overall active state, and explaining the different values of the experimental kinetic data obtained by their authors. In addition to this, the supporters of the consecutive electron-transfer concept offered an explanation for the disagreement between the experimental low steady-state Tafel slope and the inductive behavior of the electrode, on the one hand, and the theoretical predictions, on the other, as demonstrated by Plonski since 1969. 

The common concept of these models was the existence of at least one single electron-transfer stage and of special centers on the metal surface which are active in catalyst formation and/or adsorption of 

The electron-transfer reactions proposed to occur in the active range were either consecutive or catalytic ones, or both, and will be indicated in the reaction schemes by solid lines. Dashed lines will indicate to the processes which are supposed to occur in the other range of polarization (which will not be discussed in this chapter). 

In 1981, the following variant of the B. D. D. mechanism, called the branching mechanism, was proposed by Drazic and Vorkapic  

Furthermore, the authors predict that for annealed iron, at lower current densities there is a low 0 and a Tafel slope of 40 mV dec while at higher current densities there is an increase to 120 mV dec They also include the possible appearance of a limiting reaction current when the rate of the step A2 cannot be increased further with increase of potential due to the subsequent chemical desorption B or becoming rate-control- 

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Both polymers are linear with a flexible chain backbone and are thus both thermoplastic. Both the structures shown Figure 19.4) are regular and since there is no question of tacticity arising both polymers are capable of crystallisation. In the case of both materials polymerisation conditions may lead to structures which slightly impede crystallisation with the polyethylenes this is due to a branching mechanism, whilst with the polyacetals this may be due to copolymerisation. 

Hinshelwood suggested the chain branching mechanism for reaction H2 + 02 C. Hinshelwood [50]... 

Tin(II) was found to be oxidized by dioxygen via the chain branching mechanism [156-162]. The oxidation rate is v = k[02]2 in organic solvents and v = [Sn(II)]1/2[02]1/2 in aqueous solutions. The reaction, under certain conditions, has an induction period. Free radical acceptors retard this reaction. The following kinetic scheme was proposed for tin(II) oxidation by dioxygen. 

J.M. Romo-Herrera, B.G. Sumpter, D.A. Cuiien, H. Terrones, E. Cruz-Siiva, D.J. Smith, V. Meunier, M. Terrones, An atomistic branching mechanism for carbon nanotubes Suifure as the triggering agent, Angew. Chem. Int. Ed., vol. 47, pp. 2948-2953, 2008. 

It has been suggested [18] that the greater tendency for long-chain hydrocarbons to knock as compared to smaller and branched chain molecules may be a result of this internal, isomerization branching mechanism. 

Structure characterization, degree of branching Mechanical properties... 

It is generally agreed that alkenyl hydroperoxides are primary products in the liquid-phase oxidation of olefins. Kamneva and Panfilova (8) believe the dimeric and trimeric dialkyl peroxides they obtained from the oxidation of cyclohexene at 35° to 40° to be secondary products resulting from cyclohexene hydroperoxide. But Van Sickle and co-workers (20) report that, The abstraction/addition ratio is nearly independent of temperature in oxidation of isobutylene and cycloheptene and of solvent changes in oxidations of cyclopentene, tetramethylethylene, and cyclooctene. They interpret these results to support a branching mechanism which gives rise to alkenyl hydroperoxide and polymeric dialkyl peroxide, both as primary oxidation products. This interpretation has been well accepted (7, 13). Brill s (4) and our results show that acyclic alkenyl hydroperoxides decompose extensively at temperatures above 100°C. to complicate the reaction kinetics and mechanistic interpretations. A simplified reaction scheme is outlined below. 

At Van Sickle s conditions of low temperatures and low conversions, branching routes A and B appear to be dominant since there is little alkenyl hydroperoxide decomposition. In our work above 100°C., the branching routes are supported by the nearly linear initial portions at low conversions for alkenyl hydroperoxide and polymeric dialkyl peroxide curves (see Figures 2, 3, and 4). The polymeric dialkyl peroxides formed under our reaction conditions include those formed by the branching mechanism postulated by Van Sickle (routes A and B) and those formed by the reaction of the alkenoxy and hydroxy radicals from alkenyl hydroperoxide thermal decomposition reacting further and alternately with olefin and oxygen (step C). The importance and kinetic fit of the sequential route A to C appears to increase with temperature and extent of olefin conversion owing to the extensive thermal decomposition of the alkenyl hydroperoxides above 100°C. 

The oxidation of methane (as well as other hydrocarbons) proceeds via a chain branching mechanism. Each of the stages of the chain branding mechanism initiation, propagation termination, may be affected to a different degree by relatively slight changes in ambient conditions under which oxidation takes place. 

Scheme 9.18 Kinetic isotope effects in a branching mechanism.

This type of reaction is often called the branched mechanism and corresponds to many real systems such as, for example, the electroreduction of oxygen. At platinum electrodes, a mechanism that explains the experimental data is17... 

Between the lines neither of the previously mentioned branching mechanisms is very effective and consequently rates in the lower part of the region are low. Further into this intermediate chemistry regime the reactions of HO2 can lead to branching ... 

The XH can be the parent hydrocarbon but is more usually an intermediate oxidation product with weaker C—H bonds, such as an aldehyde or alkene. Even so, the abstraction reaction has a large activation energy, as does the hydrogen peroxide decomposition (which is also pressure dependent), so that the branching mechanism tends to be of greater importance towards the higher temperature and pressure part of the region. 

An alternative explanation of prompt NO proposed by several investigators is as follows it is known that the combustion reactions proceed by a chain-branching mechanism involving the rapid buildup of such species as H, OH, and O to high levels, in some cases considerably above the values predicted by assuming equilibration of the reactions ... 

Most of the surface was found covered by a thick coke film (ca. 2 nm to 6 tun) in the form of individual clusters, which fiised into a "flower" type pattern (agglomerates). Note the clear domain boundaries around each carbon "flower pattern. Regarding the shape of the observed carbon features it could be concluded that during formation, carbon coke clusters possess some kind of limited mobility. These coke deposits possibly grow by spreading over the catalysts surface via a branching mechanism. Fig. 4e shows an AFM image recorded at the... 

Fig. 16 Typical short-chain branching mechanisms for ethylene homopolymerization (A) formation of a butyl branch (B) formation of paired ethyl branches. (From Ref.. )...

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