Free radical addition polymerization kinetics

Example 1.4-6 Free Radical Addition Polymerization Kinetics 

Many olefinic addition polymerization reactions, such as that of ethylene or styrene polymerization, occur by free radical mechanisms. The initiation step can be activate thermally or by bond breaking additives such as peroxides. The general reaction scheme is  

There are several possibilities for initiation, as mentioned above second order in monomer (thermal), first order in each monomer and initiator catalyst, f, or first order in 1. For the latter, the initiation rate of formation of radicals is given by. 

This expression for the overall polymerization rate is found to be generally true for such practical examples of free radical addition polymerization as polyethylene, and others. 

Even further useful relations can be found by use of the above methods. Consider the case of reactions in the presence of chain transfer substances as treated by Alfrey in Rutgers [38] and Boudart [5]. This means a chemical species, S, that reacts with any active chain, P , to form an inactive chain but an active species. S  

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Kinetics. Monomer can be converted into polymer by any chemical reaction which creates a new covalent bond. Most of this review will concern polymerization of vinyl monomers by free radical addition polymerization. However, some attention will be given to cationic polymerization of epoxy functional materials. No extensive review of polymerization processes and kinetics will be given here, but some of the fundamental notions will be described. For reviews, see (4a-d). 

Tihe theory of free-radical addition polymerization, described in numer-ous publications (2, 3, 4, 17, 21), makes it clear that radical chain-growth reactions of polymers are regulated by statistical laws. Because of their statistical character the products from these reactions must be heterodisperse. The ranges extend from a single unit upward, depending upon kinetic details of the reactions. 

Generalized methods of initiating the polymerization of these monomers have recently been reviewed in detail [9], and were also mentioned briefly earlier in this Chapter. As with vinyl monomers initiation can be efficient and rapid, with the production of a fixed number of active centres. Propagation appears to be much slower, however, and rates of polymerization are comparable to those in free radical addition polymerizations. Techniques such as dilatometry, spectrophotometry etc. are therefore convenient for kinetic investigation of this type of cationic reaction. 

The specificity of the reaction mechanism to the chemistry of the initiator, co-initiator and monomer as well as to the termination mechanism means that a totally general kinetic scheme as has been possible for free-radical addition polymerization is inappropriate. However, the general principles of the steady-state approximation to the reactive intermediate may still be applied (with some limitations) to obtain the rate of polymerization and the kinetic chain length for this living polymerization. Using a simplified set of reactions (Allcock and Lampe, 1981) for a system consisting of the initiator, I, and co-initiator, RX, added to the monomer, M, the following elementary reactions and their rates may be... 

Since emulsion polymerization is a free-radical addition polymerization, all the kinetic events, namely, initiation, propagation, termination and transfer reactions which have already been described in Chapter 1, are applicable to describe the overall rate of the polymerization and molar mass development of the latex polymer. However, the heterogeneous nature of the polymerization adds some complications due to partitioning of the various ingredients between the phases ... 

The classical kinetic scheme for free-radical addition polymerization neglects one other possible form of termination, primary-radical termination (PRT), in which a growing chain is killed by reaction with a free-radical R- from initiator decomposition ... 

In order to simplify the kinetic scheme a steady-state approximation has to be made. It is assumed that under steady-state conditions the net rate of production of radicals is zero. This means that in unit time the number of radicals produced by the initiation process must equal the number destroyed during the termination process. If this were not so and the total number of radicals increased during the reaction, the temperature would rise rapidly and there could even be an explosion since the propagation reactions are normally exothermic. In practice it is found that the steady-state assumption is usually valid for all but the first few seconds of most free radical addition polymerization reactions. 

The degree of polymerization of the polymer molecules produced during free radical addition polymerization can be calculated from the kinetic chain length F which is simply the number of times monomer molecules add on to the initiator radical during its life-time. It is given by... 

In free radical addition polymerization the distribution of molar mass depends upon the mechanism of termination. The simplest case to consider is when the mechanism is through disproportionation and is equal to the kinetic chain length v. In this case the chain grows and terminates at the length to which it had grown. At this point it is necessary to define a new... 

It is often found that there can be serious deviations from steady-state kinetics during free radical addition polymerization especially towards the end of reactions using pure monomers or concentrated solutions. This can be most readily demonstrated by looking at the simplified equation for the rate of polymerization... 

Figure 4. Operation of a plug-flow tubular addition polymerization reactor of fixed size using a specified free-radical initiator (initiator kinetic parameters Ea = 32,921 Kcal/mol In k/ = 26,492 In sec f = 0,5 10 ppm initiation, 1,0 mol %...

The inherent driving force of the partition of reactants between phases has a strong impact on both the kinetics and the product properties, especially if the polymerization mechanism has strict stoichiometric requirements. This is the main reason why heterophase polymerizations via step-growth mechanisms frequently face serious problems. Similar issues may be valid for some radical polymerization techniques where active reactants (e.g., control agents) must partition equally between aU particles. The most common type of polymerization mechanism applied in the production of emulsion polymers is free-radical addition, and this will form the focus of the present chapter. 

The kinetics of the free radical emulsion polymerization of a-meth-ylene-y-valerolactone has been investigated (58). Stable polymer latices could be prepared. A homogeneous nucleation is the dominant path for particle formation. Also, the miniemulsion copolymerization with styrene as comonomer has been investigated. Both the reversible addition-fragmentation chain transfer (RAFT) miniemulsion polymerization and the RAFT bulk polymerization are weU controlled and copolymers with a narrow polydispersity are formed. 

Propagation. Since chain polymerization kinetics are usually followed for free radically photoinitiated polymerizations, the propagation mechanism involves the addition of monomer to the growing polymer chain ... 

In the second chapter (Preparation of polymer-based nanomaterials), we summarize and discuss the literature data concerning of polymer and polymer particle preparations. This includes the description of mechanism of the radical polymerization of unsaturated monomers by which polymer (latexes) dispersions are generated. The mechanism of polymer particles (latexes) formation is both a science and an art. A science is expressed by the kinetic processes of the free radical-initiated polymerization of unsaturated monomers in the multiphase systems. It is an art in that way that the recipes containing monomer, water, emulsifier, initiator and additives give rise to the polymer particles with the different shapes, sizes and composition. The spherical shape of polymer particles and the uniformity of their size distribution are reviewed. The reaction mechanisms of polymer particle preparation in the micellar systems such as emulsion, miniemulsion and microemulsion polymerizations are described. The short section on radical polymerization mechanism is included. Furthermore, the formation of larger sized monodisperse polymer particles by the dispersion polymerization is reviewed as well as the assembling phenomena of polymer nanoparticles. 

Cationic polymerization is often rapid and heterogeneous and this tends to make the formulation of a general kinetic scheme somewhat difficult. However, it is possible to produce a kinetic scheme similar to that for free-radical addition (Section 2.2.5), but care must be taken in applying the scheme to any particular system. 

The mechanism of these reactions places addition polymerizations in the kinetic category of chain reactions, with either free radicals or ionic groups responsible for propagating the chain reaction. 

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. 

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

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