Kinetic scheme, radical polymerization

From the point of view of elementary reaction steps, free-radical cross-linking polymerization does not differ from linear polymerization of monovinyl compounds and involves initiation, propagation and termination. However, the investigation of mono- and multifunctional monomer pol3merization kinetics up to late in the conversion process shows both common and special features of these processes that do not follow the classical kinetic scheme of polymerization which is satisfactory for the initial state of polymerization. 

Studies in the photoinitiation of polymerization by transition metal chelates probably stem from the original observations of Bamford and Ferrar [33]. These workers have shown that Mn(III) tris-(acety]acetonate) (Mn(a-cac)3) and Mn (III) tris-(l,l,l-trifluoroacetyl acetonate) (Mn(facac)3) can photosensitize the free radical polymerization of MMA and styrene (in bulk and in solution) when irradiated with light of A = 365 at 25°C and also abstract hydrogen atom from hydrocarbon solvents in the absence of monomer. The initiation of polymerization is not dependant on the nature of the monomer and the rate of photodecomposition of Mn(acac)3 exceeds the rate of initiation and the initiation species is the acac radical. The mechanism shown in Scheme (14) is proposed according to the kinetics and spectral observations ... 

The literature on Nitroxide-Mediated Polymerization (NMP) through 2001 was reviewed by Hawker el al. vu 7 More recently the subject has been reviewed by Sluder and Schulte10 and Solomon.109 NMP is also discussed by Fischer110 and Goto and Fukuda" in their reviews of the kinetics of living radical polymerization and is mentioned in most reviews on living radical polymerization. A simplified mechanism of NMP is shown in Scheme 9.17. 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

The following kinetic scheme, usually adopted in free radical polymerization studies, is considered ... 

The accepted kinetic scheme for free radical polymerization reactions (equations 1-M1) has been used as basis for the development of the mathematical equations for the estimation of both, the efficiencies and the rate constants. Induced decomposition reactions (equations 3 and 10) have been Included to generalize the model for initiators such as Benzoyl Peroxide for... 

In conclusion, several examples of free radical polymerizations under phase transfer conditions have been described in the literature since the initial reports in 1981. In all of these cases it is apparent that transfer of an active species from one phase to a second phase is intimately involved in the initiation step of the polymerization. However, it is also clear that these are complex reactions mechanistically, and one general kinetic scheme may not be sufficient to describe them all. The extent of phase transfer and the exact species transferred will depend to a large extent upon the nature of the two phases, upon the... 

P is a partition coefficient for radicals between two parts of the system - template and surrounding medium. The kinetic scheme of template polymerization is more complicated than that for simple radical polymerization. For many systems (monomer-template-solvent) general kinetic equation was applied ... 

Beasley s derivation contains, however, as well as some probably trivial mathematical approximations, certain implicit assumptions that make this conclusion doubtful. He did not present a detailed kinetic scheme for the polymerization reaction, but it is implied by his Eq. (2) that the formation of branches is instantaneous after a new radical site has been produced on the dead polymer. That is, no account is taken of the fact that some growing radicals will be removed from the reactor before the growth of the new branch is completed. The mean time for growth of a branch is 1 /akp(M) and the ratio t of the mean residence time V/q to this time, Le. ... 

Finally, various attempts have been reported to interpret the kinetics of radiation grafting. The study by Mock, and Vanderkooi (123) concerned the mutual radiation grafting of styrene from the vapor phase to ethyl cellulose film at 50° C. The radical flux was determined separately using electron spin resonance. The kinetic scheme rigorously took account of the diffusion controlled nature of the reaction and the appropriate diffusion constants were separately determined (124). The value for the ratio of for the graft polymerization was determined as... 

A kinetic scheme is most easily worked out for the pure polymerization.106 It is useful first to make certain simplifying approximations and definitions. We replace Scheme 6 by Scheme 8, where In is an initiator producing radicals R , M is the monomer, Mn is the growing polymer chain, and M —Mm is combination product and Mn( H) are disproportionation products. If all radicals R produced by the initiator were available to start chains, we could write, from the first two reactions, kinetic Equation 9.40 for rate of change of R-concentration. Because of cage recombination, only some fraction f of the... 

These kinetic results have led to a variety of interpretations. Magat and associates have proposed kinetic schemes based on the idea that a steady state does not exist and that only small (primary) radicals can terminate polymer chains (52, 93). Bamford and Jenkins have criticized this concept of emulsion-type polymerization (77). They point out that if the source of initiation were removed no more small radicals would be formed and polymerization should continue indefinitely. They cite a photosensitized reaction at 60° in which the light was shut off at about 15% conversion, whereupon the rate fell to one-half of its original value in 60 seconds. Bamford and Jenkins point also to evidence from the fast reaction that argues against emphasis on termination between polymer radicals and small radicals. 

The above example gives us an idea of the difficulties in stating a rigorous kinetic model for the free-radical polymerization of formulations containing polyfunctional monomers. An example of efforts to introduce a mechanistic analysis for this kind of reaction, is the case of (meth)acrylate polymerizations, where Bowman and Peppas (1991) coupled free-volume derived expressions for diffusion-controlled kp and kt values to expressions describing the time-dependent evolution of the free volume. Further work expanded this initial analysis to take into account different possible elemental steps of the kinetic scheme (Anseth and Bowman, 1992/93 Kurdikar and Peppas, 1994 Scott and Peppas, 1999). The analysis of these mechanistic models is beyond our scope. Instead, one example of models that capture the main concepts of a rigorous description, but include phenomenological equations to account for the variation of specific rate constants with conversion, will be discussed. 

Radiation-Induced Polymerization. Polymerization induced by irradiation is initiated by free radicals and by ionic species. On very pure vinyl monomers, D. J. Metz demonstrated that ionic polymerization can become the dominating process. In Chapter 12 he postulates a kinetic scheme starting with the formation of ions, followed by a propagation step via carbonium ions and chain transfer to the vinyl monomer. C. Schneider studied the polymerization of styrene and a-methylstyrene by pulse radiolysis in aqueous medium and found results similar to those obtained in conventional free-radical polymerization. She attributes this to a growing polymeric benzyl type radical which is formed partially through electron capture by the styrene molecule, followed by rapid protonation in the side chain and partially by the addition of H and OH to the double vinyl bond. A. S. Chawla and L. E. St. Pierre report on the solid state polymerization of hexamethylcyclotrisiloxane by high energy radiation of the monomer crystals. 

The former theory suggests that the reactivity of the polymeric radical is determined by the type of both ultimate and penultimate units. In this case the kinetic scheme of propagation reaction can be presented as follows [25] ... 

If an overall conclusion could be made, it might be considered that the counterradicals vary considerably (Scheme 3). They can either be stable (e.g., nitroxyls, arylazooxyls), semi persistent (e.g., from thiourams) and also metallic (e.g., acetoacetato metals). In addition, if these radicals either terminate or transfer, non-living (or inactive) species will be produced. But, in order to preserve the living character, the radicals must propagate and in specific cases (e.g., iodine transfer polymerization or degenerative transfer) active species will be obtained. The more that one of these latter steps is favored, the more living is the tendency of the radical polymerization, with a very high kinetic control of this reaction. 

The solution for specific cases is greatly simplified when one of the reactions (87) or (88) is much slower than the other and thus controls the initiation rate. [In radical polymerizations, this is usually reaction (87).] We know, of course, that reaction (87) can be reversible, that R° can decay by secondary decomposition to R j (the reactivity of which generally differs from that of R°), and both reactions can only be a part of a much more complicated set of interactions, especially in ionic and coordination polymerizations. An exact kinetic analysis must be based on a proved scheme with identified intermediate transition states and products, and a knowledge of the rate constants and of the rates of various initiation stages. Such a complete and complex analysis does not yet exist. 

The kinetic scheme with constant reaction of the polymer/monomer droplet increases fairly quickly with conversion, and the mobility of the polymer chains rapidly falls below the mobility of the monomer. The reduced diffusion of live polymer chains in the droplet will reduce the rate of termination of polymerization. The associated increase in the number of radicals will cause a rapid increase in the polymerization rate. This phenomenon is well known as the Trommsdorf or gel effect [8,9]. The gel effect causes a growth of the polymer chain length and widening of the molecular weight distribution (Figure 9.5). 

The kinetic scheme that has been developed in this chapter provides a very useful framework for the organization of experimental results and for the systematic modification of polymerization conditions when the polymer properties or reaction are not entirely satisfactory. Most practical free-radical polymerizations will deviate to a greater or lesser extent from the standard relations outlined, however, either because the reaction conditions are not entirely as postulated here or because some of the assumptions that undcriy the kinetic scheme are not valid. This section is a review of the principal causes and results of such deviations. 

The assumption that k, is independent of the sizes of the radicals involved in the termination reaction is not true. Tlie standard kinetic scheme has been developed to this point by making use of this assumption, however, because the presentation is simpler and more readily comprehended and because the errors involved are not large in most commercial free-radical polymerizations. 

Deviations resulting from the diffusion control of termination at low conversions of monomer to polymer are the relatively weak effects discussed in the preceding subsection. By contrast, changes in reaction rate resulting from hindered diffusion at high conversions are very important in most radical polymerizations. Figure 6-3 shows rate curves for the polymerization of methyl methacrylate in benzene at 50°C [17]. At monomer concentrations less than about 40 wt % in this case, the rate is approximately as anticipated from the standard kinetic scheme described in this chapter. Rp decreases gradually as the reaction proceeds and the concentrations of monomer and initiator are depicted. 

The kinetic schemes described in this chapter apply to free-radical polymerizations in bulk monomer, solution, or in suspension. Suspension polymerizations ([Section 10.4.2.(iii)]) involve the reactions of monomers which are dispersed in droplets in water. These monomer droplets contain the initiator, and polymerization is a water-cooled bulk reaction in effect. Emulsion systems also contain water, monomer and initiator, but the kinetics of emulsion polymerizations are different from those of the processes listed above. Chapter 8 describes emulsion polymerizations. 

The free-radical kinetics described in Chapter 6 hold for homogeneous systems. They will prevail in well-stirred bulk or solution polymerizations or in suspension polymerizations if the polymer is soluble in its monomer. Polystyrene suspension polymerization is an important commercial example of this reaction type. Suspension polymerizations of vinyl ehloride and of acrylonitrile are described by somewhat different kinetic schemes because the polymers precipitate in these cases. Emulsion polymerizations aie controlled by still different reaetion parameters because the growing macroradicals are isolated in small volume elements and because the free radieals which initiate the polymerization process are generated in the aqueous phase. The emulsion process is now used to make large tonnages of styrene-butadiene rubber (SBR), latex paints and adhesives, PVC paste polymers, and other produets. 

The inclusion of a primary radical termination process in radical polymerization schema usually leads to kinetic equations which cannot be reduced to a straightforward expression for the orders of reaction with respect to initiator and monomer concentration (48). It is interesting to note therdbre that, using only the normal approximations, such an expt ion can be derived from the above scheme which predicts that the polymerization will be half-or r in initiator and light intensity and first-order in monomer concentration, despite the participation of primary radical termination. Straightforward solution of the kinetics is made possiUe by the following assumptions, implicit in the scheme ... 

In the present ehapter we consider the inter- or intramolecular photoinduced electron transfer phenomenon. We mainly focus on photoinduced electron transfer processes that lead to the photoinitiation of polymerization, and on processes initiated by photoredueed or photooxidized excited states. We concentrate especially on a description of the kinetic schemes, a description of the reactions that follow the primary proeess of eleetron transfer, and the characteristics of intermediates formed after electron transfer. Understanding the complexity of the processes of photo-initiated polymerization requires a thorough analysis of the examples illustrating the meehanistie aspects of the formation of free radicals with the ability to start polymerization. 

A limited number of attempts have been made to set up a general mechanistic scheme describing cationic systems in terms of fundamental reactions, in a similar manner to that used in free radical polymerizations, and to derive generally applicable kinetic equations [3—4]. Because of the individuality of each cationic system, however, this approach has met with little success, and there has been a greater tendency towards treating each polymerization in isolation for detailed kinetic analysis. It is possible, however, to postulate at least token schemes which can be used as a guide. After the pre-initiation equilibria, polymerization can be considered in terms of classical initiation, propagation, transfer and termination reactions, i.e. for vinyl monomers... 

Rates of radiation induced polymerizations are normally determined by dilatometric [85] or gravimetric [84] experiments. Some of the first quantitative results from cyclopentadiene [86] and a-methylstyrene [87] were obtained by competitive kinetic methods, based on the retarding effect of ammonia and amines. This approach tends to yield maximum values for Rp. More recently, however, a procedure combining stationary state kinetic and conductance measurements has been described [88, 89], and further refined [85]. Because the ions generated by 7-ray irradiation have a transient existence, the kinetic treatment leads to expressions which are very similar to those derived for homogeneous free radical polymerizations [90]. A simplified version of the kinetic scheme is as follows ... 

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