Propagation and Chain Branching

Propagation and chain branching both maintain the number of radicals generated by the initiation steps, but affect the polymerization kinetics differently. Propagation increases the 

Propagation steps lead to the incorporation of additional monomers to the polymer at the growing end of the chain. We make the assumption that the rate of addition is constant, regardless of the chain length, because the reaction itself is the same. This is the same assumption we made for the overall polymerization process in step gro vth polymerization. The reaction can be represented as shown in Eq. 4.10. 

As discussed previously, we are able to infer the order of each of the reactants from the mechanisms presented in Chapter 2. In this case, the process by which monomers add to the reactive group is bimolecular, making the order of each of the reactants equal to one. 

The kinetic description of chain branching is complex, because the probability of a chain branching event depends on many things that we cannot simplify for the model we are developing. Suffice it to say that chain branching slows down the polymerization process. This is because any reaction occurring between chains does not incorporate the free monomer, leading to a reduced rate of monomer consumption. 

Termination results in the removal of the activated species from the reaction. It involves the bimolecular reaction between the MA and a specific reactive species, D. Depending on the type of polymerization reaction, the reactive species may be a radical or an ion acceptor. The reaction, then, can be defined as Eq. 4.12. 

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Promotion occurs because these reactions provide an extra mode of chain propagation and chain branching. Reactions 1, 2, and 3 would constitute promoting steps when their activation energies are lower than those of the corresponding reactions ... 

Below are some examples of chain-propagating and chain-branching systems. These examples are used to illustrate the different stages of a gas-phase reaction and to introduce the steady-state and partial equilibrium assumptions as tools for analysis. 

Reaction (3.1) is the initiation step, where M is a reactant molecule forming a radical R. Reaction (3.2) is a particular representation of a collection of propagation steps and chain branching to the extent that the overall chain branching ratio can be represented as a. M is another reactant molecule and a has any value greater than 1. Reaction (3.3) is a particular chain propagating step forming a product R It will be shown in later discussions of the hydrocarbon-air... 

In addition to the propagation and termination steps shown, various chain-transfer and chain-branching reactions may occur, which lead to a highly branched structure. Such alternative reactions are diminished, and a more strictly linear product is obtained, by the polymerization of 1-alkyl- or l-beuzenesulfbnyl-ariridmee, 1... 

Comparison of conjugated and usual dehydrogenation results indicates the desirability of the oxidation method. Each consecutive reaction described by the chain non-branched scheme represents a combination of initiation, propagation and chain termination stages. 

The steam pyrolysis of LPG follows the same pathway of that for ethane, namely by a complex branching chain free radical mechanism. This can be divided into initiation, chain propagation and chain termination reactions. This gives rise to a large number of intermediates and products. As with ethane, products of higher carbon number than the feed are formed. 

The agent responsible for autocatalytic behavior need not be the product of the reaction, it can be an intermediate. Low-temperature oxidation of methane provides an example [59,85], The key free radical turns out to be CH3-, produced from methane by initiation and giving rise to other free radicals. The propagation mechanism with six interlocking steps and chain branching is such that build-up of CH3- accelerates the rate (see Figure 9.4, previous page). 

Propagation Reactions of LOOM Mono- vs. Bimoiecuiar LOOM Decomposition and Chain Branching... 

As may be deduced from the discussions undertaken in Chapter 3, the most damaging reactions within the autoxidation cycle posited for polymers are initiation and chain branching, and propagation. These are also the reactions where it may be possible to utilise specific chemical compounds to interfere with the processes involved. 

Similar schemes of propagation or chain branching have been reviewed elsewhere [12]. In addition to the volatile pyrolysis products there remains the charred carbonaceous solid residue, which continues to burn by glowing and so continues to generate heat. 

Further let us impose restrictions on the control variables kj, and k . the rate constants of chain propagation and degenerate branching, respectively... 

The extent of chain branching in a particular polymer depends on the relative rates of the chain-propagating and chain-transfer steps. If radical addition is very fast compared with hydrogen abstraction, the polymer will be mainly linear. On the other hand, if the chain-transfer rate were, for example, one-tenth of the addition rate, we might expect an average of one branch for every ten linearly linked monomers. 

The main characteristic of chain-growth reactions is that the polymerization takes place in three distinct steps chain initiation, chain propagation, and chain termination. Macromolecules with high molar masses are formed at low conversion. Small molecules, such as H2O, are not eliminated in this process. Side reactions may occur, e.g. chain transfer to polymers, which result in branched macromolecules. 

The free radical reaction may be accelerated and propagated via chain branching or homolytical fission of hydroperoxides formed to generate more free radicals (equations (11.4), (11.5)). Free radicals formed can initiate or promote fatty acid oxidation at a faster rate. Thus, once initiated, the free radical reaction is self-sustaining and capable of oxidizing large amounts of lipids. On the other hand, the free radical chain reaction may be terminated by antioxidants (AH) such as vitamin E (tocopherols) that competitively react with a peroxy radical and remove a free radical from the system (equation (11.6)). Also, the chain reaction may be terminated by self-quenching or pol)rmerization of free radicals to form non-radical dimers, trimers and polymers (equation (11.7)). 

As formulated for general radical-based degradation pathways, this process can be regarded as proceeding in three distinct steps chain initiation, chain propagation including chain branching, and chain termirration (Scheme 3). ... 

Chemical Interaction. Halogens and some phosphoms flame retardants act by chemical interaction. The flame retardant dissociates into radical species that compete with chain propagating and branching steps in the combustion process. 

Ethylene oxide is a coproduct, probably formed by the reaction of ethylene and HOO (124—126). Chain branching also occurs through further oxidation of ethylene hydroxyl radicals are the main chain centers of propagation (127). 

Intermolecular chain transfer reactions may occur between two propagating polymer chains and result in the termination of one of the chains. Alternatively, these reactions take place by an intramolecular reaction by the coiling of a long chain. Intramolecular chain transfer normally results in short branches ... 

The microstrueture of PVC has been the subject of numerous studies (Sections 4.3.1.2 and 6.2.6.3).214 Starnes el n/.l6S determined the long chain branch points by NMR studies on PE formed by Bu,SnlI reduction of PVC. They concluded that the probable mechanism for the formation of these branches involved transfer to polymer that occurred by hydrogen abstraction of a backbone methine by the propagating radical (Scheme 6.32),... 

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