Chain growth

A chain carrier is formed from the reaction of the free radical and a monomer unit chain propagation then proceeds rapidly by addition to produce a linear polymer. 

The average life time of the growing chain is short, bnt a chain of over 1000 iniits can be produced in 10 to 10 s. Bamford and Dewar have estimated that the thermal polymerization of styrene at 373 K leads to chains of x = 1650 in approximately 1.24 s, i.e., a monomer adds on once in every 0.75 ms. 

Chain-growth polymerization does not produce a leaving group. Rather, it results from the coupling of reactive centers (often free radicals or ions) adding monomer units. Polyethylene is an example of a chain-growth polymer, where the propagation step is 

In this system conversion affects polymer properties. We typically cannot go to high conversion because of molecular weight or heat removal constraints (if adiabatic). There may also be a large increase in viscosity that affects the heat removal, agitation, and processability of the polymer solution. Here conditions dictate the kind of molecular weight distribution. The polymer is often affected by impurities and chain transfer agents that determine the amount of branching and termination. 

For an adiabatic reactor, we may be able to control temperature and conversion using the initiator feed flow (Fig. 4.38). Incomplete conversion introduces recycle streams for the monomer. Because of the effect of chain transfer agents, we often must be able to measure the feed compositions to the reactor. Further, we must know what the chain transfer agents do if they are dominant variables to have any chance of controlling the molecular weight. So our control will only be as good as our correlations or models. Hence in polymer reactors we often have to use what is basically steady-state control on the setpoints of the dominant variables to achieve many of the control objectives that de- 

Here we have dealt with the control of chemical reactors. We covered some of the fundamentals about kinetics, reactor types, reactor models, and open-loop behavior. In particular we have shown that reactors with recycle or backmixing can exhibit multiple steady states, some of which are unstable. Nonlinearities in reactor systems also frequently give rise to open-loop parametric sensitivity. 

Most importantly, we introduced the ideas of dominance, effective degrees of freedom, and partial control for chemical reactors. In essence, dominant variables are controlled by manipulators with a fast response and the setpoints are adjusted to achieve the economic objectives. These notions are useful in this context, but they can be utilized more widely for other unit operations. 

This is a fairly reasonable way to describe man-made amorphous polymers, which had not been given time to anneal. For polymers that form very quickly, a quick Monte Carlo search on addition can insert an amount of nonoptimal randomness, as is expected in the physical system. 

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Chain growth algorithms that build up the chain one unit at a time with some randomness in the way units are added. This process can be repeated to yield multiple conformations. 

The presence of monomers with two functional groups of the same kind limits chain growth and decreases the molecular weight. 

In the next group of chapters we shall discuss condensation or step-growth polymers and polymerizations in Chap. 5, addition or chain-growth polymers and polymerizations in Chap. 6, and copolymers and stereoregular polymers in Chap. 7. It should not be inferred from this that these are the only classes of polymers and polymerization reactions. Topics such as ring-opening polymeri-... 

We shall have considerably more to say about this type of kinetic analysis when we discuss chain-growth polymerizations in Chap. 6. 

Our primary purpose in this section is to point out some of the similarities and differences between step-growth and chain-growth polymerizations. In so doing we shall also have the opportunity to indicate some of the different types of chain-growth polymerization systems. 

Chain-Growth and Step-Growth Polymerizations Some Comparisons... 

Step-growth polymerizations can be schematically represented by one of the individual reaction steps VA + B V —> Vab V with the realization that the species so connected can be any molecules containing A and B groups. Chain-growth polymerization, by contrast, requires at least three distinctly different kinds of reactions to describe the mechanism. These three types of reactions will be discussed in the following sections in considerable detail. For now our purpose is to introduce some vocabulary rather than develop any of these beyond mere definitions. The principal steps in the chain growth mechanism are the following ... 

Elsewhere in this chapter we shall see that other reactions-notably, chain transfer and chain inhibition-also need to be considered to give a more fully developed picture of chain-growth polymerization, but we shall omit these for the time being. Much of the argumentation of this chapter is based on the kinetics of these three mechanistic steps. We shall describe the rates of the three general kinds of reactions by the notation Rj, Rp, and R for initiation, propagation, and termination, respectively. 

An important application of photochemical initiation is in the determination of the rate constants which appear in the overall analysis of the chain-growth mechanism. Although we shall take up the details of this method in Sec. 6.6, it is worthwhile to develop Eq. (6.7) somewhat further at this point. It is not possible to give a detailed treatment of light absorption here. Instead, we summarize some pertinent relationships and refer the reader who desires more information to textbooks of physical or analytical chemistry. The following results will be useful ... 

Photoinitiation is not as important as thermal initiation in the overall picture of free-radical chain-growth polymerization. The foregoing discussion reveals, however, that the contrast between the two modes of initiation does provide insight into and confirmation of various aspects of addition polymerization. The most important application of photoinitiated polymerization is in providing a third experimental relationship among the kinetic parameters of the chain mechanism. We shall consider this in the next section. 

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