Chain reactions with branching

The development of studies along this line entered a new phase after N. N. Semenov formulated the theory of chain reactions with branches [3], and especially after the creation of the theory of degenerate explosions [4]. 

The equality/= g is the critical condition for the transition of the system fk>m one state to another. Thus, the chain reaction with branching occurs as a self-accelerating process only when active centers enter into branching acts more rapidly than into termination acts. 

Figure 12.10. Example of a chain reaction with branching...

Semenov put forward the concept of slow hydrocarbon oxidation as the chain reaction with degenerate branching N. N. Semenov [49]... 

As already noted (see Chapter 4), autoxidation is a degenerate branching chain reaction with a positive feedback via hydroperoxide the oxidation of RH produces ROOH that acts as an initiator of oxidation. The characteristic features of inhibited autoxidation, which are primarily due to this feedback, are the following [18,21,23,26,31-33] ... 

We again note that the thesis of the decisive role of the chemical reaction in the zone of highest temperatures, which lies at the basis of the combustion theory developed here, remains fully applicable to chain reactions with both branching and non-branching chains. It is precisely this fact which has allowed us to successfully apply the general laws of the theory of combustion to interesting, non-artificial, and practically important systems. 

However, we know that the kinetic characteristics on which the flame velocity depends differ from the factors which determine the conditions of self-ignition in particular, self-ignition is relatively hindered, while flame propagation is eased in the case of an autocatalytic reaction or a reaction with branching chains. 

Question. In a branched chain reaction with a = 2, there is a consequent build-up of radicals with each cycle of branched chain propagation ... 

Equation (8) undoubtedly is identical to corresponding Semenov s equation which describes kinetics of N active sites in branched chain reaction with quadratic law of chain termination and zero order of initiation [5], However the essence of processes is different. 

The thermodynamic basis of the calculation of the maximum possible work potential or chemical exergy of reversible and irreversible chemical reactions is explained and discussed. Combustion is asserted to be fundamentally irreversible. It is a nonequilibrium uncontrollable chain reaction with hot branches, in a cool milieu, and a limited work output proportional to Carnot efficiency x calorific value (Barclay, 2002). 

Perhaps the most striking feature of chain reactions is that some of them can result in detonation. If the propagation mechanism includes a step or steps that produce more chain carriers than they consume, the reaction is self-accelerating. This is called chain branching. The result may be an event much more violent than a thermal explosion, in which self-acceleration stems from temperature increase owing to the inability of heat transfer to keep up with the heat production of the reaction. The detonation of a nuclear bomb can be viewed as a chain reaction with neutrons as carriers and with chain branching. 

These observations all point clearly to the occurrence of a branched chain reaction with chain breaking at the vessel surface. The expression for the rate of a chain reaction is shown by the formal treatments of Semenov and Hinshelwood to have the general form... 

Lewis and Feitknecht found that HBr reacted rapidly with O3 at room temperature. Above a critical pressure (20-30 torr for equimolar mixtures) explosion occurs, as is typical of a branched-chain reaction with wall termination. 

We have also revealed that europium-catalyzed decomposition of DO results in quantum chain reactions with energetic branching. Complex formation between Eu(fod)3 and DO (or Ad=0) plays an important role in this process since it... 

In summary, we have reported a new class of intense chemiluminescent reactions (in liquid and solid phase) with uranium participation We have shown that decomposition of adamantylidenadamantane-l,2-dioxetane (DO), catalyzed by Eu(FOD)3, results in a quantum chain reactions with energetic branching We have revealed that Eu(III) ion in excited state forms more stable complex with organic ligands then that in ground state, which is a strong evidence for participation of the f-electrons in chemical bonding. 

Kazakov VP, Voloshin AI, Ostakhov SS. Quantum chain reactions with energetic branching catalytic decomposition of dioxetanes. Kinet Catal 1999 40 180-93. 

The polymerase chain reaction (PCR), branched-DNA analyses, and related techniques are highly sensitive methods to quantify both viral RNA and provi-ral DNA. Proviral DNA is a measure of the number of cells infected, whereas viral RNA reflects production of virions. As with the measurement of viral products, one cannot easily determine whether the nucleic acids measured represent infectious viruses. A number of commercially available technologies, exist for the measurement of HIV nucleic acids, since this methodology is now the standard of care for AIDS patients. Laboratories performing their own quantitative analyses have generally used a modification of the quantitative competitive (QC)-PCR (66). 

The conditions above are necessary, but not sufficient. For example, an exothermic, nonisothermal reaction is stable unless the temperature is so high that its heat generation (with exponential temperature dependence) exceeds the heat loss to the environment or a cooling coil (with linear temperature dependence). A chain reaction with chain branching is stable unless the radical population is so large that acceleration by chain branching (with exponential dependence on the radical population) outruns termination (with quadratic dependence). 

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