Propagation Branched chains

The molecular structure of low density polyethylene is principally governed by the reaction conditions used in its production. To optimize the yield and properties of the final resin it is necessary to balance the various reactions involved with initiation, propagation, branching, chain transfer, and termination. The principal control variables are the reaction temperature and pressure. The type of initiator employed is of importance only with respect to its decomposition rate and overall concentration. The concentration and efficiency of chain transfer agents are secondary variables, which are not always employed. 

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 ... 

One of the most dramatic examples of a solvent effect on propagation taken from the early literature is for vinyl acetate polymerization.78,79 Kamachi el al.n reported a ca. 80-fold reduction in kp (30aC) on shifting from ethyl acetate to benzonilrile solvent (Table 8.1). Effects on polymer structure were also reported. Hatada ef a m conducted a H NMR study on the structure of the PVAc formed in various solvents. They found that PVAc (M n 20000) produced in ethyl acetate solvent has 0.7 branches/chain while that formed in aromatic solvents is essentially unbranched. 

Chain reactions begin with the initiation of a reactive intermediate that propagates the chain and concludes with termination when radicals combine. Branching chain reactions can be explosively fast. 

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

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

Both of these reactions involve the production of two active centers where there was only one before. When reactions of this type occur to a significant extent, the total number of active centers present in the system can increase very rapidly, since a multiplication effect sets in as the chains propagate. The growth of chain carriers in a branched chain reaction is pictured below. 

Chain reactions can lead to thermal explosions when the energy liberated by the reaction cannot be transferred to the surroundings at a sufficiently fast rate. An explosion may also occur when chain branching processes cause a rapid increase in the number of chains being propagated. This section treats the branched chain reactions that can lead to nonthermal explosions and the physical phenomena that are responsible for both branched chain and thermal explosions. 

Chain mechanisms may be classified as linear-chain mechanisms or branched-chain mechanisms. In a linear chain, one chain carrier is produced for each chain carrier reacted in the propagation steps, as in steps (3) and (4) above. In a branched chain, more than one carrier is produced. It is the latter that is involved in one type of explosion (a thermal explosion is the other type). We treat these types of chain mechanisms in turn in the next two sections. 

The reaction temperature is above the critical temperature of ethylene so that the ethylene is in gas phase. High pressures are needed for propagation reaction. Only about 6-25 per cent of ethylene is polymerised. Rest of monomer is recycled. Extensive chain transfer reactions takes place during polymerisation to yield a branched chain polyethylene. In addition to long branches, it also contains a large number of short branches of upto 5 carbon atoms produced by intra-molecular chain transfer reactions. A typical molecule of Low density polyethylene contains a short branch for about every 50 carbon atoms and one or two long branches per molecule. 

The hydrogen-chlorine chain reaction has proved to be one of the most controversial systems yet studied. After thirty years of investigation Bodenstein43 was able to say in 1931 that every worker on the photochemical synthesis of HC1 had produced his own mechanism even as late as 1940 little positive information had been obtained. However, the accumulated techniques and experience had firmly established the importance of atom chain reactions. The mechanism of photo-initiation and propagation is the same as for the hydrogen bromide photosynthesis, a non-branching chain reaction... 

In (b) and (c), it can be seen that from each H atoms, two radicals O and H are produced which propagate the chain. Thus, a branching of chain occurs. When reactions proceed to some extent, the amount of free radicals would be very large and an explosion would occur. The free radicals may also be destroyed mainly by collision with the walls. 

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. 

It would seem that the concept of ignition temperature as a basic kinetic characteristic of a mixture, and a crucial one in the propagation of the flame as well, is revived in the theory developed by Semenov of branching chain... 

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. 

In contrast, in a branched chain, as one radical is destroyed more than one radical is produced, so that there is a net increase in the number of radicals as a result of propagation. 

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

This mechanism includes all the features necessary to describe a branched chain reaction. For simplicity, the initiation and second propagation steps are taken to be in... 

Results of the numerical experiments are given in Fig. 29. We believe they represent all the peculiarities of the Barelko et al. dynamic experiment. The observed activation energy for the propagation of active centres found from the plotted dependence tjx = f(T) at a fixed T2(TX > T+, T2 < T ) [158] amounts to 100-150 kcal mol 1 (Fig. 30). This value is close to that of the heat of sublimation for platinum. This correlation has been treated as an additional argument in favour of the branched-chain model. But our numerical experiment based on model (2)-(3) provides the same plotted dependence... 

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. 

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