Branching chain mechanism

Chain mechanisms may be classified as linear-chain mechanisms or branched-chain mechanisms. In a linear chain, one chain carrier is produced for each chain carrier reacted in the propagation steps, as in steps (3) and (4) above. In a branched chain, more than one carrier is produced. It is the latter that is involved in one type of explosion (a thermal explosion is the other type). We treat these types of chain mechanisms in turn in the next two sections. 

In a branched-chain mechanism, there are elementary reactions which produce more than one chain carrier for each chain carrier reacted. An example of such an elementary reaction is involved in the hydrogen-oxygen reaction ... 

Note that the SSH cannot be applied to the chain carrier R in this branched-chain mechanism. If it were applied, we would obtain, setting rR.= 0 in equation 7.1-4,... 

In the examples in Sections 7.1 and 7.2.1, explicit analytical expressions for rate laws are obtained from proposed mechanisms (except branched-chain mechanisms), with the aid of the SSH applied to reactive intermediates. In a particular case, a rate law obtained in this way can be used, if the Arrhenius parameters are known, to simulate or model the reaction in a specified reactor context. For example, it can be used to determine the concentration-(residence) time profiles for the various species in a BR or PFR, and hence the product distribution. It may be necessary to use a computer-implemented numerical procedure for integration of the resulting differential equations. The software package E-Z Solve can be used for this purpose. 

The shift of curves, as shown in Fig. 3.9, is unsurprising since the larger fuel molecules and their intermediates tend to break down more readily to form radicals that initiate fast reactions. The shape of the propane curve suggests that branched chain mechanisms are possible for hydrocarbons. One can conclude that the character of the propane mechanism is different from that of the H2—02 reaction when one compares this explosion curve with the H2—02 pressure peninsula. The island in the propane-air curve drops and goes slightly to the left for higher-order paraffins for example, for hexane it occurs at 1 atm. For the reaction of propane with pure oxygen, the curve drops to about 0.5 atm. 

Even though there have been appreciably more studies of CS2, COS is known to exist as an intermediate in CS2 flames. Thus it appears logical to analyze the COS oxidation mechanism first. Both substances show explosion limit curves that indicate that branched-chain mechanisms exist. Most of the reaction studies used flash photolysis hence very little information exists on what the chain-initiating mechanism for thermal conditions would be. 

At 125°C, the results were more complex. In some cases both d>(c-C3Fe) and d>(C2F40) exceeded unity a branched chain mechanism was indicated. However, by suitable manipulation of the data, some rate-constant ratios could also be estimated at this temperature and they are also listed in Tables XIX and XX. 

The reaction of hydrogen with oxygen runs according to a branching chain mechanism ... 

Polyakov and co-workers [5] made an especially detailed study of the influence of the initial pressure and diameter of the vessel on the formation of nitric oxide in an explosion. They came to the conclusion that combustion takes place according to a branching chain mechanism and that the breaking off of the chains in the volume, i.e., the reaction of the active centers with... 

Oxidation of hydrocarbons - mechanism and steady state analysis, 229-232 A stylised branched chain mechanism - a steady state analysis, and kinetic criteria for the explosive region, 246-249... 

A reaction mechanism is a sequence of elementary processes proposed to account for experimental kinetic results. Pure chemical kinetics proposes a classification of various types of mechanism (non-chain mechanisms, straight-chain and branched-chain mechanisms, etc.), establishes relationships between the properties of a global reaction and those of the elementary processes involved in the corresponding mechanism, and provides rules for writing a priori a reaction mechanism from a knowledge of the thermochemical and kinetic characteristics of the... 

Although the features of the movement of the boundaries are not explained fully, the general shape of the three limits can be explained by reasonable hypotheses of mechanisms. The manner in which the reaction is initiated to give the boundary designated by the curve in Fig. 2 suggests, as was implied earlier, that the explosion is in itself a branched chain phenomenon. Thus, one must consider possible branched chain mechanisms to explain the limits. 

The first two reactions give sigmoid ur-time curves that are well expressed by the Prout-Tompkins equation. These are believed to involve a branching-chain mechanism. The third process is fitted by the contracting volume equation, possibly due to decomposition through ion-pair evaporation. The thermal stabihty of N02CJ04 is decreased [42] by the incorporation of impurities which increase the mnnber of cation vacancies, whereas the creation of anion vacancies has the opposite effect. 

Isothermal (593 to 693 K) ar-time curves for the decomposition of lanthanum oxalate [81] were sigmoid but asymmetrical with the decay period being the more pronounced. The Prout-Tompkins equation applied in two linear regions with , = 132 kJ mol. A branching chain mechanism was proposed during which channels fi om the surface penetrate the crystals as reaction proceeds. The predominant initial product was carbon monoxide, which disproportionated to yield carbon dioxide, and the residual solid contained carbonate and finely divided carbon. 

The branching chain mechanism has some general features. The rate constants of reactions 1-6 ofR- and ROO- radicals are high and their concentrations quickly reach stationary values. At sufficiently high dioxygen concentration [ROO-] IR.) and the termination proceeds only by reaction 6. For the steady-state conditions... 

Contribution of Ions in the Subthreshoid Piasma Ignition of Hydrogen. Analyze the non-branching chain mechanism (11-25), (11-27), (11-28), (11-29) of the plasma-stimulated quasi-catalytic low-temperature oxidation of H2. Why does the conventional gas-phase oxidation of hydrogen have a threshold nature (explosion/no explosion see Section 11.2.3), whereas the quasi-catalytic chain mechanism (11-25), (11-27), (11-28), (11-29) is able to occur in a wide range of pressures and temperatures without any specific thresholds ... 

The Semenov equation is widely used and reproduces experimental measurements well for a variety of rather slow flames, but it does not predict the observed dependence of flame velocity on pressure. It is also inadequate for fast flames, such as those dominated by a branched-chain mechanism involving hydrogen atoms. These flames are much faster than the hydrocarbon flame to which the Semonov equation was originally applied, and have lower overall energies of activation. The... 

Analysis of the kinetics suggests that under non-isothermal conditions, the reaction mechanism differs from that during isothermal reduction and, accordingly to Delmon [316], can be interpreted as a branched chain growth. Assuming that the branched chain mechanism is valid in this case only, an approximation of reaction kinetics can be represented as follows ... 

The chemical interaction of hydrocarbons with oxygen occurs in two regions. At 200-—500 K a slow oxidation obeying the degenerate branching mechanism occurs. At higher temperatures the combustion proceeding by the usual branched chain mechanism and characteristic of common hot hydrocarbon flames predominates. 

A completely different cause of explosion is found in reactions which proceed by a branched-chain mechanism. Here more than one atom of intermediate is produced in the chain propagation scheme for each atom that reacts. The result, if chain carrier is produced faster in the initiation and propagation steps than it is consumed in termination steps, is a rapid increase in the concentration of chain carriers. As a consequence the reaction velocity accelerates rapidly and explosions can occur. The best-known mechanism of this type is the fission reaction in an atomic bomb. Chemical examples abound and include the reactions of oxygen with hydrogen, phosphorous, carbon monoxide, etc. Heating is an after effect of explosion, not the cause. 

The simplest branched-chain mechanism requires initiation, branching, and termination steps. If we assume a first-order chain termination step, such as reaction of the chain carrier R at the walls of the container, and let. .. indicate any reactant or product other than chain carrier, the mechanism is... 

Fickett, Jacobson, and Schott have used the characteristic method to investigate ideal gas detonations with a rate function approximating reactions dominated by a branching chain mechanism resulting in an induction period followed by the main strongly exothermic reaction. They observed pulsating detonations similar to those described above for first-order Arrhenius kinetics. 

Heating polycaprolactam (PCL) at comparatively low temperatures (about 100 °C) in air causes the formation of peroxides which act as branching agents, leading to thermal oxidation via a degenerate branched chain mechanism. Peroxide compounds are not found in PCL at higher temperatures. 

Consequently, at the initial stage, the process develops according to the branched-chain mechanism, with an exponential growth of the concentration of radicals and, hence, the reaction rate. 

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