Termination of chain reactions

The relationships of oxidation potential to radical reactivity index Sr and nucleophilic reactivity index Sn illustrated in Figure 4 are very similar to those with antioxidation and antiozonization, where the maximum values were observed at 0.4 and 0.25 volt. Therefore, antioxidation seems to proceed by a radical mechanism in contrast to the nucleophilic type of antiozonization. Indeed, the antioxidation effect of amines toward NR, SBR, BR, and HR is well correlated with radical reactivity as shown in Figures 5-8. The protection of SBR solution by amines from oxidative degradation and the termination of chain reaction in the oxygen-Tetralin system are also shown as functions of Sr in Figures 9 and 10. 

The mechanisms and resulting kinetic equations are shown in Figure 4. Other mechanisms are possible as well as modifications of these—e.g., disproportion termination of chain reactions, and condensation between unlike monomers. The left sides of the equations represent the reactor operator (note that all resulting differential equations are nonlinear because of the second-order propagation and termination reactions). To this is added the complexity of considering separate equations for the thousands of separate species frequently required to define completely commercially useful polymers. Solution by direct application of classical techniques is impractical or impossible in most cases even direct numerical solution is often difficult. Simplifying assumptions or special mathematical techniques must be used (described below in the calculations of MWD). 

The reasons for the appearance of the flash are not yet fully clear it is also unclear why the flash can be supressed by introducing certain additives to the powder (probably catalytic termination of chain reactions). It is certain that muzzle flash is promoted by the high temperature of the combustion gases, the high gas pressure and the high velocity of the gas emerging from the muzzle. 

Chain reactions do not go on forever. The fog may clear and the improved visibility ends the succession of accidents. Neutron-scavenging control rods may be inserted to shut down a nuclear reactor. The chemical reactions which terminate polymer chain reactions are also an important part of the polymerization mechanism. Killing off the reactive intermediate that keeps the chain going is the essence of these termination reactions. Some unusual polymers can be formed without this termination these are called living polymers. 

One characteristic of chain reactions is that frequentiy some initiating process is required. In hydrocarbon oxidations radicals must be introduced and to be self-sustained, some source of radicals must be produced in a chain-branching step. Moreover, new radicals must be suppHed at a rate sufficient to replace those lost by chain termination. In hydrocarbon oxidation, this usually involves the hydroperoxide cycle (eqs. 1—5). 

The left-hand end of the activated monomer is sealed off by the OH terminator, but the right-hand end (with the star) is aggressively reactive and now attacks another ethylene molecule, as we illustrated earlier in Fig. 22.1. The process continues, forming a longer and longer molecule by a sort of chain reaction. The —OH used to start a chain will, of course, terminate one just as effectively, so excess initiator leads to short chains. As the monomer is exhausted the reaction slows down and finally stops. The DP depends not only on the amount of initiator, but on the pressure and temperature as well. 

Reactions (7.2), (7.3) and (7.4) form a series of chain reactions, with reaction (7.3) the rate-determining stage. The chain reaction terminates by the reactions... 

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 inhibition method has found wide usage as a means for determining the rate at which chain radicals are introduced into the system either by an initiator or by illumination. It is, however, open to criticism on the ground that some of the inhibitor may be consumed by primary radicals and, hence, that actual chain radicals will not be differentiated from primary radicals some of which would not initiate chains in the absence of the inhibitor. This possibility is rendered unlikely by the very low concentration of inhibitor (10 to 10 molar). The concentration of monomer is at least 10 times that of the inhibitor, yet the reaction rate constant for addition of the primary radical to monomer may be less than that for combination with inhibitor by only a factor of 10 to 10 Hence most of the primary radicals may be expected to react with monomer even in the presence of inhibitor, the action of the latter being confined principally to the termination of chain radicals of very short length. ... 

Termination of the reaction by radical/radical interaction is unlikely to occur to any significant extent, until the concentration of long-chain alkane has dropped to a very low level. 

Catalyst reacts with peroxyl radicals. So, an increase in the catalyst concentration increases the rate of chain reaction proportional to [catalyst]172 and at the same time it increases the chain termination proportional to the catalyst concentration. Therefore the retardation or cessation of the chain reaction is observed at a high concentration of the catalyst. This is called critical phenomenon. 

Radical polymerizations have three important reaction steps in common chain initiation, chain propagation, and chain termination. For the termination of chain radicals several mechanisms are possible. Since the lifetime of a radical is usually less than 1 s, radicals are continuously generated and terminated. Each propagating radical can add a finite number of monomers between its initiation and termination. If a divinyl monomer is in the monomer mixture, the reaction kinetics changes drastically. In this case, a dead polymer chain may grow again as a macroradical, when its pendant vinyl groups react with radicals, and the size of the macromolecule increases until it extends over the whole available volume. 

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. 

Which t q)e of chain-reaction polymerization is most likely to terminate by coupling ... 

Let us for the moment disregard chain transfer reactions. Radical polymerization then consists of three component reactions initiation, propagation of the polymer chains, and termination of chain growth. The rate of primary radical formation, v, by decomposition of the initiator I, may be written ... 

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, ... 

The termination of chain growth can also occur both in the gas phase and at the polymer surface. In the gas phase, free radicals are lost by reaction with both hydrogen atoms and other free radicals. The kinetics of these processes are given by... 

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. 

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