Propagation reactions, diffusion controlled

Beyond Interval II, the second maximal polymerization rate can be attributed to the gel effect. The bimolecular termination reaction becomes diffusion-controlled in the latex particles and the average number of free radicals per particle increases signihcantly in the latter stage of polymerization, thereby leading to an acceleration of the free radical polymerization. The rate of polymerization then decreases continuously toward the end of polymerization due to the depletion of monomer and/or the diffusion-controlled propagation reaction in the reaction loci. 

C olvents have different effects on polymerization processes. In radical polymerizations, their viscosity influences the diffusion-controlled bimolecular reactions of two radicals, such as the recombination of the initiator radicals (efficiency) or the deactivation of the radical chain ends (termination reaction). These phenomena are treated in the first section. In anionic polymerization processes, the different polarities of the solvents cause a more or less strong solvation of the counter ion. Depending on this effect, the carbanion exists in three different forms with very different propagation constants. These effects are treated in the second section. The final section shows that the kinetics of the... 

For health, safety, and environmental reasons, significant efforts have been made to reduce the residual monomer content in commercial latexes. Some of the techniques are already being apphed industrially, whereas others are still being developed. In general, the available methods for the reduction of residual monomer are based on two different concepts. The first of these aims at further conversion of the monomer by increasing the diffusion-controlled propagation rate of the polymerization reaction, while the second involves removal of the residual monomer. 

The notion of diffusion-controlled termination reaction was first proposed by Schulz in 1956 [4] (Figure 4.3). Several investigators have shown experimentally that when reaction diffusion is controlling the termination mechanism, the termination kinetic constant becomes proportional to the propagation frequency, as shown below [5-8J ... 

Figure 4.3. Illustration of the diffusion-controlled termination reaction. In (a), the radicals are physically separated in space and are unable to terminate. In (b), the radicals have moved closer together by propagating through monomeric or pendent double bonds. The propagation reaction is a means for physical movement of the radical.

In the older literature one can encounter quite a number of papers suggesting that bimolecular termination is not chain-length dependent e.g. 36, 66, 68, 139-143] Experimental evidence, however, has disproved these suggestions and numerous papers have proven termination to be chain-length dependent. The evidence takes several forms and has been obtained employing different experimental approaches, which can roughly be divided in three classes (i) termination studies of free-radical polymerizations, (ii) termination studies of non-propagating species and (iii) diffusion-controlled mimic reactions. 

Termination. The conversion of peroxy and alkyl radicals to nonradical species terminates the propagation reactions, thus decreasing the kinetic chain length. Termination reactions (eqs. 7 and 8) are significant when the oxygen concentration is very low, as in polymers with thick cross-sections where the oxidation rate is controlled by the diffusion of oxygen, or in a closed extmder. The combination of alkyl radicals (eq. 7) leads to cross-linking, which causes an undesirable increase in melt viscosity. 

Kinetic studies have shown that the enolate and phosphorus nucleophiles all react at about the same rate. This suggests that the only step directly involving the nucleophile (step 2 of the propagation sequence) occurs at essentially the diffusion-controlled rate so that there is little selectivity among the individual nucleophiles. The synthetic potential of the reaction lies in the fact that other substituents which activate the halide to substitution are not required in this reaction, in contrast to aromatic nucleophilic substitution which proceeds by an addition-elimination mechanism (see Seetion 10.5). 

Before any chemistry can take place the radical centers of the propagating species must conic into appropriate proximity and it is now generally accepted that the self-reaction of propagating radicals- is a diffusion-controlled process. For this reason there is no single rate constant for termination in radical polymerization. The average rate constant usually quoted is a composite term that depends on the nature of the medium and the chain lengths of the two propagating species. Diffusion mechanisms and other factors that affect the absolute rate constants for termination are discussed in Section 5.2.1.4. 

Termination by self-reaction of propagating radicals is a diffusion-controlled process even at very low conversion.1 The evidence for this includes the following ... 

More complex models for diffusion-controlled termination in copolymerization have appeared.1 tM7j Russo and Munari171 still assumed a terminal model for propagation but introduced a penultimate model to describe termination. There are ten termination reactions to consider (Scheme 7.1 1). The model was based on the hypothesis that the type of penultimate unit defined the segmental motion of the chain ends and their rate of diffusion. 

The remaining problem in the model development is to estimate the decrease in kp as a function of conversion. As the reaction proceeds beyond the point of chain entanglement, a critical conversion is reached where the propagation reaction becomes diffusion controlled and kp begins to fall with further increase in polymer concentration. At the critical conversion, one may write... 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

The % Conversion at Stall Time Vs the Rate of Polymerization. In a normal free radical polymerization, the rate of polymerization stalls at certain time when the mobility of molecules, including those of propagating radicals, decrease to a certain level. After that, the rate of polymerization diminishes and it becomes a diffusion controlled reaction. Table VI lists some representative % of conversion at the stall time for randomly selected HEMA-based monomer mixes with different initiators at different concentration(s). They indicated that faster polymerization rate led to higher conversion of... 

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