Chain reactions polymerization rates

When dealing with catalysis it is best, however, to classify polymerization reactions according to the mechanism of chain propagation (2). One may distinguish in this way between chain-reaction polymerization and step-reaction (stepwise) polymerization. The essential features of these classes are shown in Table I (15). The diflFerences between the two types of polymerization are also evident from equations of rate (Rp) and average degree of polymerization (DP). For a free-radical polymerization of vinyl compounds (an example of a chain reaction), Rp and DP are functions of monomer and catalyst concentration (Equations 9 and 10) ... 

The kinetics of chain-reaction polymerization is illustrated in Fig. 3.28 for a free radical process. Analogous equations, except for termination, can be written for ionic polymerizations. Coordination reactions are more difficult to describe since they may involve solid surfaces, adsorption, and desorption. Even the crystallization of the macromolecule after polymerization may be able to influence the reaction kinetics. The rate expressions, as given in Appendix 7, Fig. A7.1, are easily written under the assumption that the chemical equations represent the actual reaction path. Most important is to derive an equation for the kinetic chain length, v, which is equal to the ratio of propagation to termination-reaction rates. This equation permits computation of the molar mass distribution (see also Sect. 1.3). The concentration of the active species is very small and usually not known. First one must, thus, ehminate [M ] from the rate expression, as shown in the figure. The boxed equation is the important equation for v. 

Step-growth polymerization processes are much slower than chain-reaction processes. Because they also typically have higher activation enthalpies, heating is often required to attain satisfactory rates of polymerization. Finally, step-growth polymers generally have lower average molar masses than polymers formed by chain-reaction polymerization. 

In this chapter, different mechanisms of chain-reaction polymerization have been discussed in detail. Based on the mechanism involved, expressions for the rate of polymerization, molecular-weight disiributiorr, average chain lengths, and the polydispersity index can be derived. 

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. 

Azobisnittiles are efficient sources of free radicals for vinyl polymerizations and chain reactions, eg, chlorinations (see Initiators). These compounds decompose in a variety of solvents at nearly first-order rates to give free radicals with no evidence of induced chain decomposition. They can be used in bulk, solution, and suspension polymerizations, and because no oxygenated residues are produced, they are suitable for use in pigmented or dyed systems that may be susceptible to oxidative degradation. 

The degree of polymerization is controlled by the rate of addition of the initiator. Reaction in the presence of an initiator proceeds in two steps. First, the rate-determining decomposition of initiator to free radicals. Secondly, the addition of a monomer unit to form a chain radical, the propagation step (Fig. 2) (9). Such regeneration of the radical is characteristic of chain reactions. Some of the mote common initiators and their half-life values are Hsted in Table 3 (10). 

The main industrial use of alkyl peroxyesters is in the initiation of free-radical chain reactions, primarily for vinyl monomer polymerizations. Decomposition of unsymmetrical diperoxyesters, in which the two peroxyester functions decompose at different rates, results in the formation of polymers of enhanced molecular weights, presumably due to chain extension by sequential initiation (204). 

Lipases have also been used as initiators for the polymerization of lactones such as /3-bu tyro lac tone, <5-valerolactone, e-caprolactone, and macrolides.341,352-357 In this case, the key step is the reaction of lactone with die serine residue at the catalytically active site to form an acyl-enzyme hydroxy-terminated activated intermediate. This intermediate then reacts with the terminal hydroxyl group of a n-mer chain to produce an (n + i)-mer.325,355,358,359 Enzymatic lactone polymerization follows a conventional Michaelis-Menten enzymatic kinetics353 and presents a controlled character, without termination and chain transfer,355 although more or less controlled factors, such as water content of the enzyme, may affect polymerization rate and the nature of endgroups.360... 

Peaking and Non-isothermal Polymerizations. Biesenberger a (3) have studied the theory of "thermal ignition" applied to chain addition polymerization and worked out computational and experimental cases for batch styrene polymerization with various catalysts. They define thermal ignition as the condition where the reaction temperature increases rapidly with time and the rate of increase in temperature also increases with time (concave upward curve). Their theory, computations, and experiments were for well stirred batch reactors with constant heat transfer coefficients. Their work is of interest for understanding the boundaries of stability for abnormal situations like catalyst mischarge or control malfunctions. In practice, however, the criterion for stability in low conversion... 

Our treatment of chain reactions has been confined to relatively simple situations where the number of participating species and their possible reactions have been sharply bounded. Most free-radical reactions of industrial importance involve many more species. The set of possible reactions is unbounded in polymerizations, and it is perhaps bounded but very large in processes such as naptha cracking and combustion. Perhaps the elementary reactions can be postulated, but the rate constants are generally unknown. The quasi-steady hypothesis provides a functional form for the rate equations that can be used to fit experimental data. 

In solution polymerization, monomers mix and react while dissolved in a suitable solvent or a liquid monomer under high pressure (as in the case of the manufacture of polypropylene). The solvent dilutes the monomers which helps control the polymerization rate through concentration effects. The solvent also acts as a heat sink and heat transfer agent which helps cool the locale in which polymerization occurs. A drawback to solution processes is that the solvent can sometimes be incorporated into the growing chain if it participates in a chain transfer reaction. Polymer engineers optimize the solvent to avoid this effect. An example of a polymer made via solution polymerization is poly(tetrafluoroethylene), which is better knoivn by its trade name Teflon . This commonly used commercial polymer utilizes water as the solvent during the polymerization process,... 

A final example of homogeneous catalysis is the use of metallocene catalyst systems in chain growth polymerization processes. The metallocene, which consists of a metal ion sandtviched between two unsaturated ring systems, is activated by a cocatalyst. The activated catalyst complexes with the monomer thereby reducing the reaction s energy of activation. This increases the rate of the reaction by up to three orders of magnitude. 

To determine the rate behavior of chain growth polymerization reactions, we rely on standard chemical techniques. We can choose to follow the change in concentration of the reactive groups, such as the carboxylic acid or amine groups above, with spectroscopic or wet lab techniques. We may also choose to monitor the average molecular weight of the sample as a function of time. From these data it is possible to calculate the reaction rate, the rate constant, and the order of the reacting species. 

The polymerization rates of styrene and acrylonitrile monomer are not equal. If we were to initiate polymerization in an equimolar solution of the two monomers, the styrene monomer would initially be depleted at a faster rate than the acrylonitrile. Thus, the copolymer molecules initially produced would contain a higher concentration of styrene than acrylonitrile. As the reaction progressed, the styrene would be depleted from the solution and the comonomer ratio in the copolymer would gradually shift towards a higher acrylonitrile content. The final product would consist of polymer chains with a range of comonomer compositions, not all... 

Successful application of radical polymerization requires the appropriate choice of the specific initiator to achieve the desired initiation rate at the desired reaction temperature and the realization that higher polymerization rates achieved by increasing the initiation rate (either by increasing [I] or kmolecular weights. Higher radical concentrations result in more propagating chains but each propagates for a shorter time. 

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