Propagation steps reaction

It is instructive to sketch this reaction as in Figure 10-1. The chain is fed by initiation reactions that create CHs and terminated by reactions that destroy CHy- to form C2H6. However, the major processes by which the reaction proceeds are the two propagation steps that alternately create and destroy the two chain-propagating radicals CH3 and CHsCOv Thus we have the notion of a chain of reactions, which is a kinetic chain of propagation reaction steps that feed reactants into the chain and spit out stable products. This is a kinetic chain reaction, which is different from the polymerization chain of reactions, which we wiU introduce in the next chapter (although those reactions form both kinetic and polymer chains). 

We call this type of reaction autocatalytic because the initiation step generates the catalyst [CH3-], which is necessary to make the overall process proceed, and the concentration of the catalyst molecule is not changed by the propagation reaction steps. It is called autocatalytic because the reaction itself generates the catalyst that promotes the reaction. Note also that the overall rate is enhanced by large fcj and inhibited by large Jit even though and ki are much smaller than kp. 

Each primary polymer radical (P ) can add a monomer molecule to produce a dimer (P ) and then a trimer (P ), and so on. This series of successive additions of monomer molecules to a polymer chain is called chain propagation. The propagation reaction step is very fast and almost as soon as a radical is initiated it can lead to the formation of very high molecular weight polymer. 

Bromine formed in this step then reacts with an allyl radical to continue the chain propagation reactions (Step 3). 

At some point in the polymerization, the chain of propagating reaction steps are terminated by annihilation of the reactive center at the end of the chain. This annihilation occurs by one or more mechanisms depending largely on the type of reactive center (radical, cation, or anion), nature of the monomer, and the overall chemical environment and conditions of reaction. Two common methods of termination are combination and disproportionation. The polymerization may also involve chain transfer. In this process, the propagating chain is terminated and a new reactive species is produced. 

The polymerization mechanism continues to include initiation, termination, and propagation steps. This time, however, there are four distinctly different propagation reactions ... 

If the initiation reaction is much faster than the propagation reaction, then all chains start to grow at the same time. Because there is no inherent termination step, the statistical distribution of chain lengths is very narrow. The average molecular weight is calculated from the mole ratio of monomer-to-initiator sites. Chain termination is usually accompHshed by adding proton donors, eg, water or alcohols, or electrophiles such as carbon dioxide. 

Model based on the variation of the number of active" coordination sites at the catalyst surface. The growth of tubules during the decomposition of acetylene can be explained in three steps, which are the decomposition of acetylene, the initiation reaction and the propagation reaction. This is illustrated in Fig. 14 by the model of a (5,5) tubule growing on a catalyst particle ... 

Also, the rates of the propagation steps are equal to one another (see Problem 8-4). This observation is no surprise The rates of all the steps are the same in any ordinary reaction sequence to which the steady-state approximation applies, since each is governed by the same rate-controlling step. The form of the rate law for chain reactions is greatly influenced by the initiation and termination reactions. But the chemistry that converts reactant to product, and is presumably the matter of greatest importance, resides in the propagation reactions. Sensitivity to trace impurities, deliberate or adventitious, is one signal that a chain mechanism is operative. 

The decomposition of acetaldehyde has Eq. (8-6) as the rate-controlling step, this being the one (aside from initiation and termination) whose rate constant appears in the rate law. In the sequence of reactions (8-20)—(8-23), the same reasoning leads us to conclude that the reaction between ROO and RM, Eq. (8-22), is rate-controlling. Interestingly, when Cu2+ is added as an inhibitor, rate control switches to the other propagating reaction, that between R and O2, in Eq. (8-21). The reason, of course, is that Cu2+ greatly lowers [R ] by virtue of the new termination step of reaction (8-30). 

The propagation reactions of the growing cationic chain end with the monomer ethene have already been discussed in part 4.3. The reaction enthalpies of the corresponding propagation steps show different tendencies for the gas phase and solution, when the cationic chain end is lengthened. However, as the monomer is increased in size and the cationic chain end remains the same, then the tendencies for the gas phase and solution correspond to each other. This is an indication that the solvent influence on the cationic propagation reaction is determined by the nature of the cations in question and their solvation. 

The explanation for autoacceleration is as follows. As polymerisation proceeds there is an increase in the viscosity of the reaction mixture which reduces the mobility of the reacting species. Growing polymer molecules are more affected by this than either the molecules of monomer or the fragments arising from decomposition of the initiator. Hence termination reactions slow down and eventually stop, while initiation and propagation reactions still continue. Such a decrease in the rate of the termination steps thus leads to the observed increase in the overall rate of polymerisation. 

These propagation reactions are circular. They consume a methane radical but also generate one. There is no net consumption of free radicals, so a single initiation reaction can cause an indefinite number of propagation reactions, each one of which does consume an acetaldehyde molecule. Ignoring any accumulation of methane radicals, the overall stoichiometry is given by the net sum of the propagation steps ... 

The present section analyzes the above concepts in detail. There are many different mathematical methods for analyzing molecular weight distributions. The method of moments is particularly easy when applied to a living pol5mer polymerization. Equation (13.30) shows the propagation reaction, each step of which consumes one monomer molecule. Assume equal reactivity. Then for a batch polymerization. 

Chain polymerization involves three steps. To start the reaction, a catalyst that can generate an active site, such as a free radical (R ), is used. In the initiation step, the radical adds to the double bond, and the radical site is moved to the end carbon. This new radical reacts with another molecule to give a larger radical, and the propagation reaction is imderway. Usually, the number of monomers in the chain is greater than 1000. In the above formulae. 

Cobalt porphyrin complexes are involved in the chain transfer catalysis of the free-radical polymerization of acrylates. Chain transfer catalysis occurs by abstraction of a hydrogen atom from a grow ing polymer radical, in this case by Co(Por) to form Co(Por)H. The hydrogen atom is then transferred to a new monomer, which then initiates a new propagating polymer chain. The reaction steps are shown in Eqs. 12 (where R is the polymer chain. X is CN), (13), and (14)." ... 

If the initiation and termination steps are excluded because the chain is long, the sum of the propagation reactions gives the stoichiometric relationship (A). 

If the chains are long, the composition of the copolymer and the arrangement oi units along the chain are determined almost entirely by the relative rates of the various chain propagation reactions. On the other hand, the rate of polymerization depends not only on the rates of these propagation steps but also on the rates of the termination reactions. Copolymer composition has received far more attention than has the rate of copolymerization. The present section will be confined to consideration of the composition of copolymers formed by a free radical mechanism. 

The rate of copolymerization in a binary system depends not only on the rates of the four propagation steps but also on the rates of initiation and termination reactions. To simplify matters the rate of initiation may be made independent of the monomer composition by choosing an initiator which releases primary radicals that combine efficiently with either monomer. The spontaneous decomposition rate of the initiator should be substantially independent of the reaction medium, as otherwise the rate of initiation may vary with the monomer composition. 2-Azo-bis-isobutyronitrile meets these requirements satisfactorily. The rate Ri of initiation of chain radicals of both types Ml and M2 is then fixed and equal to 2//Cd[7], or twice the rate of decomposition of the initiator I if the efficiency / is equal to unity (see Chap. IV). The relative proportion of the two types of chain radicals created at the initiation step is of no real importance, for they wall be converted one into the other by the two cross-propagation reactions of the set (1). Melville, Noble, and Watson presented the first complete theory of copolymerization suitable for handling the problem of the rate. The theory was reduced to a more concise form by Walling, whose procedure is followed here. 

This reaction undergoes conversion in one sequence of consecutive elementary reaction steps and so only one propagating front is formed in a spatially distributed system [68]. Depending on the initial ratio of reactants, iodine as colored and iodide as uncolored product, or both, are formed [145]. 

The apparent lack of dependence of the propagation reaction on the surface area of the sodium suggests that the reaction of a chlorine ended chain with sodium is probably fast and not the rate determining step. The rate determining process is probably the reaction of the sodium ended chain with the dichloride. This latter reaction is presumably not on the sodium surface because of the lack of dependence on the surface area. This is supported by the observation that if the sodium is allowed to settle part way through the reaction most of the polymer appears to be in the solution and not absorbed on the sodium surface via the longlived active chain ends. 

This particular mechanism assumes that Rx and Ri are different radicals and that the latter do not participate in the propagation reactions. In the more general case the radical R can participate in propagation reactions analogous to reactions (2) and (3). These propagation steps consist of a bimolecular hydrogen abstraction reaction followed by a unimolecular decomposition reaction. 

In order for the overall rate expression to be 3/2 order in reactant for a first-order initiation process, the chain terminating step must involve a second-order reaction between two of the radicals responsible for the second-order propagation reactions. In terms of our generalized Rice-Herzfeld mechanistic equations, this means that reaction (4a) is the dominant chain breaking process. One may proceed as above to show that the mechanism leads to a 3/2 order rate expression. 

A sequence of elementary steps of radical reaction leading to the regeneration of the original radical is called the chain cycle, whereas the particular reaction steps are the events of chain propagation. 

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. 

If the step is only equilibrium controlled, a lumped analysis of both fluid and solid phase is possible and the corresponding nonlinear wavefront analysis is straight forward too. Analysis of propagation speed data yield information about the relevant equilibrium sorption mechanism (7). The different form of the transients when a reaction step has been stimulated, is discussed in the Appendix. 

The propagation steps are very fast because of the reactivity of the free radicals. In contrast to the initiation reaction, the propagation reaction much lower activation energy and, therefore, Rp, the rate of... 

---