Propagating radicals per reaction

The theory of compartmentalised free-radical polymerisation reactions of the type considered in this paper is of interest primarily because it is believed that most of the polymer which is formed in the course of an emulsion polymerisation reaction is formed by way of reactions of this type. The objective of the theory is to calculate the relative proportions of the reaction loci which at any instant contain 0, 1, 2,. .., r,. .. propagating radicals, and also such properties of the locus population distribution as the average number of propagating radicals per reaction locus, and the variance of the distribution of locus populations. 

It is then a straightforward matter to write down an expression for the overall rate of polymerisation in the reaction system, once an expression has been obtained for the average number of propagating radicals per reaction locus. 

The average number of propagating radicals per reaction locus can be found from... 

The number of reaction loci is assumed not to vary with time. No nucleation of new reaction loci occurs as polymerization proceeds, and the number of loci is not reduced by processes such as particle agglomeration. The monomer is assumed to he only sparingly soluble in the external phase (a typical examide is styrene as monomer and water as the external phase), and thus polymerization is assumed to occur exclusively within the reaction loci and not within the external phase. The monomer is assumed to be present in sufficient quantity throughout the reaction to ensure that monomer droplets are present as a separate phase, and the rate of transfer of monomer to the reaction loci from the droplets is assumed to be rapid relative to the rate of consumption of moncuner in the loci by polymerization. The monomer concentration within the reaction loci is then taken to be constant throughout the reaction. This assumption is important if an attempt is made to relate the overall rate of polymerization to the average number of propagating radicals per reaction locus. The assumption will therefore be examined in further detail below. 

In this set of equations, n is the number of reaction loci per arbitrary volume of reaction system which contain i propagating radicals, cr is the average rate of entry of radicals into a single reaction locus, xr is the volume of the reaction locus, A. is the rate coefficient for the mutual termination of radicals, and k is a composite constant which quantifies the rate at which radicals are lost from reaction loci by first-order processes. For convenience we put kju s x ... 

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... 

The most widely used antioxidants are free radical scavengers that remove reactive radicals formed in the initiation and propagation steps of autoxidation. A number of natural or synthetic phenols can compete, even at low concentrations, with lipid molecules as hydrogen donors to hydroperoxy and alkoxy radicals, producing hydroperoxides and alcohols and an unreactive radical. (3-carotene reacts with per-oxy radicals, producing a less-reactive radical. These stabilized radicals do not initiate or propagate the chain reaction. 

The number of particles present The average number of radicals per particle The rate constant of the propagation reaction The monomer concentration in the particles... 

In addition, short-chain branches of C5 and C7 are seen at levels of 1 per 1000 carbon atoms, compared with a maximum of 15 n-butyl branches. This also arises from a backbiting reaction of the propagating radical and the resultant intramolecular chain transfer, and the relative amounts of the branches of various lengths may vary depending on the conditions of synthesis. 

Chain-transfer reactions to monomers and chain-transfer agents lead to the formation of small and mobile radicals that can exit the polymer particle. Radical desorption leads to a decrease in the average number of radicals per particle. Equation (10), where is the rate coefficient for radical exit [Eq. (11)] [25], gives the rate of radical exit from a population of particles with an average number of radicals per particle n. In Eq. (11), X is an overall mass-transfer rate coefficient, y/rj the ratio between the rate of generation of small radicals by chain transfer and the rate of consumption of these radicals (mostly by propagation), m the partition coefficient of the small radicals between the polymer particles and the aqueous phase, [M] the concentration of monomer in the aqueous phase, km, the termination rate constant in the aqueous phase, and [R] the concentration of radicals in the aqueous phase. 

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