Propagation of chain reactions

To inhibit the propagation of chain reactions by elimination of atomic oxygen and active radicals by... 

It is reasonable to assume that the probability of the chain breaking, P, varies in the gas phase in proportion with the pressure. Indeed, the propagation of chain reactions with or without branching are due to bimolecular colhsions whereas breaking reactions are due to trimolecular collisions. As the nmnber of double collisions varies proportionally to the squared value of the pressme and the number of triple collisions to the cubic value of the pressure, the probability of termination must ultimately vary as the ratio of the cube over the square of the pressure, which is in proportion to the pressure ... 

The mechanism of these reactions places addition polymerizations in the kinetic category of chain reactions, with either free radicals or ionic groups responsible for propagating the chain reaction. 

The degree of polymerization is controlled by the rate of addition of the initiator. Reaction in the presence of an initiator proceeds in two steps. First, the rate-determining decomposition of initiator to free radicals. Secondly, the addition of a monomer unit to form a chain radical, the propagation step (Fig. 2) (9). Such regeneration of the radical is characteristic of chain reactions. Some of the mote common initiators and their half-life values are Hsted in Table 3 (10). 

The step in which the reactive intermediate, in this case A-, is generated is called the initiation step. In the next four equations in the example above, a sequence of two reactions is repeated this is the propagation phase. Chain reactions are characterized by a chain length, which is the number of propagation steps that take place per initiation step. Finally, there are termination steps, which include any reactions that destroy one of the reactive intermediates necessary for the propagation of the chain. Clearly, the greater the frequency of termination steps, the lower the chain length will be. 

The overall rate of a chain process is determined by the rates of initiation, propagation, and termination reactions. Analysis of the kinetics of chain reactions normally depends on application of the steady-state approximation (see Section 4.2) to the radical intermediates. Such intermediates are highly reactive, and their concentrations are low and nearly constant throughout the course of the reaction ... 

The presence of oxygen can modify the course of a fiee-radical chain reaction if a radical intermediate is diverted by reaction with molecular oxygen. The oxygen molecule, with its two unpaired electrons, is extremely reactive toward most free-radical intermediates. The product which is formed is a reactive peroxyl radical, which can propagate a chain reaction leading to oxygen-containing products. 

The two nuclei on the right side are just two of the many possible products of the fission process. Since more than one neutron is released in each process, the fission reaction is a self-propagating, or chain reaction. Neutrons released by one fission event may induce other fissions. When fission reactions are run under controlled conditions in a nuclear reactor, the energy released by... 

Some of the most conclusive studies of the mechanisms of chain reactions come from experiments in which some of the propagating steps have been independently measured directly. This measurement can sometimes be done by the use of flash photolysis and pulse radiolysis (Chapter 11). Such determinations can verify the occurrence of a certain reaction in the sequence and provide its rate constant. 

The values of the rate constants of the chain propagation in chain reactions of ROOH decomposition are collected in Table 4.23. 

When the rate of initiation is very low the important moment of chain reaction becomes the kinetics of the establishment of the stationary concentration of free radicals. This time is comparable with the lifetime of the radical that reaction limits the chain propagation. The... 

In chain reactions, the inhibitor 7n interacts with free radical P and makes it unavailable for the propagation of chain, thus providing an extra termination step... 

To iterate water vapour and air are pressurised by the compression stroke, partial electrolysis occurs, partial H2 ignition occurs, causing heat, which changes some of the vapour to steam, which elevates pressure, which increases temperature, which forms more steam, which continues to propagate in chain reaction during (perhaps the first 10% of) the power stroke. Is it true that s1r9 s HP output cannot be explained thus - especially in view of the unprecedented application water in a 4-stroke cycle ... 

A kinetic chain reaction usually consists of at least three steps (1) initiation, (2) propagation, and (3) termination. The initiator may be an anion, a cation, a free radical, or a coordination catalyst. Although coordination catalysts are the most important commercially, the ionic initiators will be discussed first in an attempt to simplify the discussion of chain-reaction polymerization. 

Another characteristic of chain reactions is that they generate minorproducts (C2H6 and CHO ) as well as the major products (CO and CH4). The major products are made by the propagation steps and the minor products by the initiation and termination steps. In fact, the ratio of CH4 to C2H gives the ratio of rp to r, ... 

Figure 10-7 Sketch of chain reaction in H2 + O2 H2O. This is a highly simplified set of the reactions shown in the table, which indicate the dominant chain reaction steps in forming water from three chain-propagating radical species H, 0, and OH.

Assuming perfect living polymerization in which all polymer chains are induced to initiate the simultaneous propagation of chains without any termination and chain transfer reactions, in such idealized scenarios, the number-average molecular weight, Mn, can be estimated using... 

The kinetics of template polymerization depends, in the first place, on the type of polyreaction involved in polymer formation. The polycondensation process description is based on the Flory s assumptions which lead to a simple (in most cases of the second order), classic equation. The kinetics of addition polymerization is based on a well known scheme, in which classical rate equations are applied to the elementary processes (initiation, propagation, and termination), according to the general concept of chain reactions. 

On the mechanism of explosive reaction. An attempt to apply the theory of chain reactions to certain phenomena observed in expls) 12)K.K.Andreev Yu.Khariton, TransFarad Soc 31, No 168 (1935) (On the mechanism of propagation of reactions by chain) 13)C.N.Hurshelwood, ZAngewChem 49, 370... 

CA 42, 5229(1948)(Theory of propagation of flame. States conditions in an expl chem reaction necesssry for propagation of the flame at a const rate. Calcs this rate for a definite relationship between diffusion and heat conductance. Evaluates the effect of chain reactions on the propagation of the flame) 4) B. Karlovitz, JChemPhys 19, 541-46(1951) Sc CA 45, 9341 (1951)(Theory of turbulent flames) 5) G. Klein, Phil-TransRoySocLondon 249, 389—415 (1957)... 

There is no reason why a combination of mechanisms should not operate in particular examples, e. g. the Linde-mann mechanism followed hy quite short chains. Moreover the results to be described in Chapter VI show that the ease of propagation of chains varies very much with pressure, so that it would be possible to have a normal reaction at higher pressures reinforced by chains at low pressures, or between certain limits of pressure. 

Weigert and Kellermann obtained direct evidence of the propagation of chains in mixtures of hydrogen and chlorine. By photographic methods they were able to show that when the mixture was illuminated momentarily the chemical change, as rendered visible by the changes in refractive index caused by the heat of reaction, did not... 

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