Radical polymerization reactions, compartmentalized

Theory of Compartmentalized Free-Radical Polymerization Reactions... 

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. 

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... 

This chapter has been concerned exclusively with predictions for the distribution of locus populations within a compartmentalized free-radical polymerization reaction system. Other matters of considerable interest are the distribution of polymer molecular weights which the polymerization reaction produces, and the distribution of sizes of the reaction loci at the end of the reaction. A significant literature concerning both these aspects is beginning to develop, but because of the complexity of the subject and limited space, only a brief summary of the various contributions can be given here. 

Birtwistle and Blackley (in press) have recently applied the locus-population generating function approach to the problem of the evolution of the locus-size distribution in compartmentalized free-radical polymerization reactions. They have introduced a generalized locus-population generating function Sl (, r,r), defined as... 

Interval II Particle Growth in the Presence of Monomer Droplets.—Birtwistle, Blackley, and Jeffers have now published the full version of their theory for the decay of a compartmentalized free-radical polymerization reaction following the cessation of the generation of new radicals within the external phase. Separate treatments are necessary for the cases where radicals can and cannot be lost from reaction loci by first-order processes. In addition to completely general results. 

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. 

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. 

A similar compartmentalization resulted in a successful one-pot process for the combination of ATRP and eROP, i.e., in a one-pot, two-step procedure (17). For this process CL, t-butyl methacrylate (t-BMA), Novozym 435 and 2 were heated to 60 °C to initiate the eROP and obtain the PCL block end-capped with 2. After 120 min. CuBr/dNbipy was added in order to activate the ATRP and thus the block copolymer formation. Figure 4 shows that during the first step of the consecutive process, i.e. the eROP, CL conversion reached 95 % while only negligible conversion of t-BMA was detected. Only upon addition of the ATRP catalyst, the radical polymerization started and reached ca. 43 % conversion within 180 min (300 min. total). Both reaction kinetics are comparable with the kinetics observed from the homopolymerization under similar conditions, suggesting that both reactions run undisturbed by each other (Figure 4). A clear... 

In this section, the concept of compartmentalization is illustrated by assuming the presence of one segregated entity, which for simplicity is referred to as a polymer particle. Macroscale effects are also neglected for simplicity. The number of polymer particles Np is taken to be constant, as well as the partiele diameter dp and particle volume Vp. A distinction is made between the calculation of the polymerization rate and the CLD characteristics as a function of polymerization time, on the one hand, and a free radical polymerization (HIP) and CRP (NMP) reaction scheme on the other hand. 

Compartmentalized Free-radical Polymerization.—Considerable interest has been shown in recent years in the solution of the differential difference equations which are obtained when the theory of Smith and Ewart is applied to reaction systems which contain a fixed number of reaction loci, but in which a steady state for the various locus populations has yet to be established. An example of such a reaction system would be a seeded emulsion polymerization system within whose external phase new radicals suddenly begin to be generated, and which does not contain sufficient surfactant to permit the nucleation of new particles. The theory which has been developed is concerned with the question of the nature of the approach to the steady-state distribution of locus populations, and with what might be learned from accurate measurements made during the approach to the steady state. 

The fundamental difficulty in constructing a theory for the MWD in emulsion polymers is to account for the compartmentalized nature of the system- In the commouly occurring situation where particles contain only a few free radicals at any given time, it is obviously incorrect to consider that each latex particle behaves like a mini-bulk reaction vessel, and so the conventional methods used for bulk polymerizations are inapplicable. Nevertheless, some assumptions which introduce only minor errors may often be made. The most important such assumptions is that the evaluation of the MWD may be separated from that of the PSD. In other words, provided that the MWD being produced at any given moment is the same as would be formed in an equivalent set of monodispersed latex particle systems [as expressed in Eq. (27) below], then the MWD evolved in a system that is polydispersed in size may be computed trivially. Formally, this is expressed as follows. Let S(M,a,t) be the MWD formed in a monodisperse system of size o at time f here M is the molecular weight variable. In a polydisperse system with PSD n([Pg.115]

We will consider the MWD in two simple cases. The first is when chain transfer is sufficiently rapid to ensure that all other chain-stopping events can be ignored. In such a situation, whereas the compartmentalized nature of the reaction may affect the rate of initiation of new chains, it will not affect the lifetime distributions of the chains once they are formed. The MWD may then be found from the bulk formulas, provided only that the average number of free radicals per particle, is known. Such an approach has been used by Friis et al. (1974) to calculate the MWD evolved in a vinyl acetate emukion polymerization. These authors included in addition the mechanisms of terminal bond polymerization and of transfer to polymer (both of which cause broadening). The formulas required for the in corporation of these mechanisms could be taken from bulk theory. 

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 model for the reaction system will be considered in detail in Section II. However, it is convenient to note here that, in principle, the free radicals that initiate the polymerization may be generated cither within the external phase (external initiation) or within the reaction loci themselves (internal initiation). Whereas very brief reference will be made at the conclusion of this chapter to reaction systems of the latter type, the concern here will be almost exclusively with reaction systems of the former type. Insofar as the initiating radicals are generated exclusively within the external phase (and therefore have to be by some means acquired by the loci by absorption from the external phase), we have a farther important distinction between homogeneous and compartmentalized reactions. In the latter case, the processes that lead to the generation of the initiatit radicals are physically isolated from the propagation, termination, and transfer reactions. One minor consequence of this is that transfer-to-initiator reactions may be virtually eliminated in the latter case. 

This problem was first treated in detail by Haward (1949). He considered the case of a bulk polymerization that has been compartmentalized by subdividing the reaction system into a large number of separate droplets, each of volume v. Radicals are generated exclusively within the droplets and always in pairs. An example would be the polymerizatiim of styrene in emulsified droplets dispersed in water initiated the thermal decomposition of an oil-soluble initiator which partitions almost exclusively within the monomer droplets. In the model considered by Haward, radicals are unable to exit from the droplets into the external phase. The only radical-loss process is in fact bimolecular mutual termination. It therefore follows that all the droplets must always contain an even number (including zero) of propagating radicals, and that the state of radical occupancy will change in increments of 2. The conclusion reached by Haward is that in this case the effect of compartmentalization is to reduce the overall rate of polymerization per unit volume of disperse phase. The f ysical reason for this is that, as the volume of the droplets is reduced, so are the opportunities for a radical to escape from the others—and hence to avoid mutual... 

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