J-mer radicals

Since we are considering an emulsion polymerization system where tbe particle contains at most one radical, the rate of decrease in the number of active particles containing a j-mer radical equals the desorption rate of jf-mer radicals from the particles. Thus, applying Eq. (3 we have... 

The first term on the right-hand side of Eq, (44) represents the desorption rate of a j-mer radical and the last term expresses the absoiption rate ofj-mer radicals from the water phase into the particles containing no /-met radicals. Rewriting Eq, (44) we get... 

The second term on tbe right-hand side of Eq. (47) usually represents tbe absorption rate of j-mer radical from the water phase into tbe active particles that already contain a radical, and hence rq>resents tbe rate of increase in the number of particles containing two radicals, one of which is a j-mer radical. However, this term must be changed from positive to negative because it expresses tbe rate of decrease in the number of active particles when instantaneous termination in tbe particles is assumed. Thus, using Eq. (43), Eq. (47) can be rewritten as... 

In order for the rate coefficients kf and f ., defined by Eqs, (49) and (SO), to be predicted it is necessary to know how K j and K j are expressed in terms of the chemical and physical properties involved in the desorption and reabsoiption processes. First of all, let us consider the mass-transfer coefficient for a j-mer radical in the individual diffusion films. There is a large number of published stndies concerning the mass-transfer cocSicient in an external diffusion film around a spherical particle. One of these is the following semitheoretical equation proposed by Ranz and Marshall (1952)... 

This form predicts that k approaches zero when either k or k approaches zero. Considering that the beginning of the gel effect is the result of translational diffusion controlled termination (1), it is reasonable to assume that k may become very small if the translational diffusivity of the i-mer approaches zero. However, if i-mer radicals whose k = 0 are mixed with j-mer radicals whose k i 0, it must be realized that there can be termination due to the mobility of the j-mer. Equation (3) would predict no reaction and on this basis the authors do not accept the geometric mixing rule as having general applicability. 

J. HE CHEMICAL STRUCTURE of the homopolymers consists of an exact repetition of the chemical structure of the mer unit. The chemical bonds are mostly primary covalent ones, mainly C—C and C—H, but include also C—O, C—N, and so forth. There appear also various isomers, double bonds (imsaturation), tertiary or quaternary carbons, ring-like structures, and others. There are also secondary bonds, albeit weaker than the primary ones. One typical isomer, foimd in polymers, is based on the presence of "head-to-tail" bonds as compared to "head-to-head" or "tail-to-tail" bonds. This is illustrated by the vinyl group, with the substitute radical —X. 

The origin of the factor 2 in equation 3.12 lies in the fact that 2 identical radicals disappear simultaneously from the reaction mixture, where the factor 2 in equation 3.13 is a permutation factor. This latter factor arises as an /-mer can encounter ay-mer or the other way around, ay -mer encountering an /-mer. The advantage of this notation is the termination rate coefficient now only relates to the rate of diffusion and not to stoichiometric (or other) factors. In other words, if i equals j, then the rate coefficient k / and kl - are identical, which would not be the case if the above notation would not be used. 

Suginome, H. and Wang, J.B., Intramolecular P,y-addition of allylic alkoxyl radicals. A new general synthesis of a-iodoepoxides by photolysis of allylic alcohol hypoiodites in the presence of mer-cury(II) oxide, iodine and pyridine in benzene, /. Chem. Soc., Chem. Commun., 1629,1990. Suginome, H., Isayama, S., Maeda, N., Furusaki, A., and Katayama, C., Photo-induced transformations. 57. The formation of bridged oxabicycHc compounds by intramolecular radical addition of oxyl radicals generated from some A-homo-4a-cholesten-3-ol hypoiodites, /. Chem. Soc., Perkin Trans. 1, 2963,1981. 

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