Compartmentalization of radicals

Compartmentalization of radicals into polymer particles may yield a unique MWD for the linear chains, as discussed in Sect. 3.1, except when the dominant chain termination mode is the chain transfer reaction. Branched polymer molecules are assemblies of linear polymer chains (called primary chains), and compartmentalization effects on the primary chain length distribution must be properly accounted for. 

The compartmentalization of radicals may produce another important effect when large-sized branched polymer molecules are formed by chain transfer to polymer plus combination termination. As clarified in Sect. 4.1, when the n value is small, the frequency of bimolecular termination reactions between large polymer radicals drops significantly compared to models that do not account for compartmentalization of radicals. From this fact, it is easy to see that the size of branched polymer molecule is smaller than that calculated without considering compartmentalization effects [281]. 

The dependence of the maximal Rp on [KPS] is quite similar for both the MMA mini-emulsion polymerization with HD (x=0.4) and the conventional emulsion polymerization (x=0.39) but different on [SDS] (y=0.16,ME) and (y= 0.24, CE) [ 108]. The reaction orders x and y are a complex function of the radical entry (particle nucleation) and the extent of compartmentalization of radicals. The radical entry or particle nucleation increases Rp. Np increases with increasing [KPS] and the degree of increase is more pronounced for the MMA emulsion polymerization (Np°c[KPS]x, x =0.28) as compared with that for the MMA mini-emulsion polymerization (x =0.11) (Table 1). The radical entry events are restricted due to the close-packed droplet surface layer, but the pseudo-bulk ki-... 

In an emulsion polymerization system, radicals are distributed among the polymer particles. The size of these particles is so small that there are only a small number of radicals per particle, as an average less than one radical per particle in many cases of practical interest. The compartmentalization of radicals among the particles is the most distinctive kinetic... 

The kinetic behavior in each segregated entity can be different in view of die random nature of exit and entry phenomena and the nanometer scale of these identities, that is, a deviation from bulk kinetics ( one big droplet ) is to be expected. Hence, for emulsion polymerization, it is crucial to track the number of low-abundant (radical) species per segregated entity, as compartmentalization of radical species may influence the overall kinetics and thus the development of the polymer microstructure. If u radical types are present, this implies the calculation of the number of segregated entities characterized by u indices, with each index reflecting the discrete presence of one radical type. 

One consequence of the compartmentalization of radicals in the particles is that the overall concentration of radicals in the system is much greater than in solution and bulk polymerization, and hence the polymerization rate is higher. 

In emulsion polymerization with relatively small latex particles (< 100 nm diameter), a zero-one system is considered to more accurately describe the situation. In a zero-one system, the rate of radical termination within a latex particle is fast relative to the rate of radical entry. Or, in other words, termination is not rate-determining. Consequently, the entry of a radical into a particle, which already contains a free radical, will cause immediate termination. Therefore, under the zero-one system, the latex particles can be easily split into two groups those with zero free radicals and those containing exactly one free radical. The rate of termination, however, for the entire process is reduced due to the compartmentalization of radicals. That is, while the radicals remain in separate particles, they cannot terminate without at least one transferring phase. This naturally takes time and thus corresponds to a higher rate of propagation compared to similar bulk systems (this is one of the many attractions of emulsion polymerization). Furthermore, in a zero-one system, the following assumptions are made ... 

In bacteria and plants, the individual enzymes of the fatty acid synthase system are separate, and the acyl radicals are found in combination with a protein called the acyl carrier protein (ACP). However, in yeast, mammals, and birds, the synthase system is a multienzyme polypeptide complex that incorporates ACP, which takes over the role of CoA. It contains the vitamin pantothenic acid in the form of 4 -phosphopan-tetheine (Figure 45-18). The use of one multienzyme functional unit has the advantages of achieving the effect of compartmentalization of the process within the cell without the erection of permeability barriers, and synthesis of all enzymes in the complex is coordinated since it is encoded by a single gene. 

Ito s group [83] reported the micellar polymerization mechanism was operative during the radical polymerization of PEO macromonomers in cyclohexane and water under similar reaction conditions. The reaction medium has an important effect on the polymerization behavior of macromonomers. Cyclohexane was chosen as a nonpolar type of solvent. The polymerization was found to be independent of the lengths of p-alkyl group (R) and the PEO chain in benzene. On the other hand, the rate of polymerization in cyclohexane increased with increasing number of EO units. This may be attributed to the formation of aggregates (micelles) and/or compartmentalization of reaction loci,i.e., polymerization in distinct aggregates (polymer particles). The C12-(EO)14-MA macromonomer polymerized faster in bulk than in benzene but far slower than in water. 

Theory of Compartmentalized Free-Radical Polymerization Reactions... 

In heterogeneous, compartmentalized biological systems, it is important to appreciate the site at which radicals are generated. This knowledge is essential to an understanding of mechanisms of radical production and its subsequent metabolism. Reactive radicals generated in the aqueous phase are unlikely... 

Implicit in the form of Equation 13.4 are the assumptions that AA, AB and BB are the only products, that they are always obtained 1 2 1 ratios of from out-of-cage combinations, and that exclusive formation of AB signihes complete in-cage reaction of the radical pairs. The limitations of Equation 13.4, particularly when applied to the evaluation of the cage factor in constrained or microphase-compartmentalized media, have been discussed recently. In symmetrically substituted compounds where the geminate radicals produced upon lysis have the same structures, the addition of radical scavengers or time-resolved detection of the radicals is needed for the estimation of FoAB-... 

Considerations of radical compartmentalization and higher polymer concentration effects are not sufficient to describe the processes that build branched polymer molecules in emulsion polymerization, and the effects of limited space must be properly taken into account [266-269]. 

It is important to note that, even in this present limiting case of a transfer-dominated system, the chain-stoppage mechanism can be changed by compartmentalization. Thus, the MWD formed in the polymerization of styrene appears to be transfer-dominated in some emulsion systems (Piirma et al., 1975) but to be combination dominated in bulk or solution (George, 1967). This difference occurs because, in serene emulsion systems, the rate of radical entry into a particle is slow, and most particles usually contain either zero or one free radical. In the state one particles (Section I,B), the growing free radical has time to undergo several transfer reactions before a further entry causes radical annihilation. 

The primary objective of the theory of compartmentalized free-radical polymerization reactions is to predict from the physicochemical parameters of e reaction system the nature of the locus population distribution. By this latter term is meant collectively the proportions of the total population of reaction loci which at any instant contain 0, l,2,...,i,... propagating radicals. The theory is concerned with the prediction of these actual populations and also with such characteristics of the locus population distribution as the average number of propagating radicals per reaction locus and the variance of the distribution of locus populations. 

Apart from intrinsic interest, the theoiy of compartmentalized free-radical polymerization reactions is of importance primarily because it is believed that most of the polymer which is form in the course of an emulsion polymerization reaction is formed via reactions of this type. The general sl pe of the conversion-time curve for many emulsion polymerization reactions suggests (see Fig. I) that the reaction occurs in three more-or-less distinct stages or intervals. The first of these, the so-called Interval I, is interpreted as the stage of polymerization in which the discrete reaction loci are formed. In the second and third stages—Intervals II and III—the polymerization is believed to occur essentially by compartmentalized free-radical polymerization within the loci which were formed during Interval I. 

The theory also has relevance to the so-called seeded " emulsion polymerization reactioas- In these reactions, polymerization is initial in the presence of a seed latex under conditions such that new particles are unlikely to form. The loci for the compartmentalized free-radical polymerization that occurs are therefore provided principally by the particles of the initial seed latex. Such reactions are of interest for the preparation of latices whose particles have, for instance, a core-shell" structure. They are also of great interest for investigating the fondamentals of compartmentalized free-radical polymerization processes. In this latter connection it is important to note that, in principle, measurements of conversion as a function of time during nonsteady-state polymerizations in seeded systems offer the possibility of access to certain fundamental properties of reaction systems not otherwise available. As in the case of free-radical polymerization reactions that occur in homogeneous media, investigation of the reaction during the nonsteady state can provide information of a fundamental nature not available through measurements made on the same reaction system in the steady state. 

A related matter concerns the physical mechanism by which radicals (primary or oligomeric) are acquired by the reaction loci. One possibility, first proposed by Garden (1968) and subsequently developed by Fitch and Tsai (1971), is that capture occurs by a collision mechanism. In this case, the rate of capture is proportional to, inter alia, the surface area of the particle. Thus, if the size of the reaction locus in a compartmentalized free-radical polymerization varies, then a should be proportional to r, where r is the radius of the locus. A second possibility (Fitch, I973) is that capture occurs by a diffusion mechanism. In this case, the rate of capture is approximatdy proportional to r rather than to r. A fairly extensive literature now exists concerning this matter (see, e.g., Ugelstad and Hansen, 1976, 1978. 1979a, b). The consensus of present opinion seems to favor the diffusion theory rather than the collision theory. The nature of the capture mechanism is not. however, relevant to the theory discussed in this chapter. It is merely necessary to note that both mechanisms predict that the rate of capture will depend on the size of the reaction locus constancy of a therefore implies that the size of the locus does not change much as a consequence of polymerization. 

Since most of the monomer in a compartmentalized free-radical polymerization reaction is consumed in the propagation reaction, it is customary to write the overall rate of polymerization as... 

The fundamental equations that govern the behavior of a compartmentalized free-radical polymerization reaction in which the radicals are generated exclusively in the external phase are most readily derived by considering the rates of the various processes by which loci containing exactly i propageting radicals are formed and destroyed. These processes are illustrated in Fig. 2 as transitions between various states of radical occupancy of the loci, each state of occupancy being defined as the number of... 

Kinetics of Compartmentalized Free-Radical Polyinerization Reactions 171... 

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