I-mer radicals

Part of these radicals will escape from the particles before growing (s + I)-mer radicals and that fraction is given by... 

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. 

Applying the steady-state approximation, the rate equation for propagating i-mer radicals may be written ... 

An important step in the thermal degradation of many polymers such as PMMA involves depropagation. Here the polymer molecule or radical fragment rapidly unzips in such a way that produces mainly a monomer. This process may be modeled simply by a rapid reaction where an z-mer is converted to an (i - l)-mer plus a monomer P —> P x + Px. In reality, this is a gross oversimplification of the process and a more sophisticated model will be discussed subsequently and also later in the chapter in relation to the thermal degradation of PMMA. 

The term bare has been chosen here to define carbenium ions or radical cations which are formed without the corresponding anion. The difference in reactivity between these ecies and the free ions present in cationic systems involving fully dissociated entities such as carbenium ion salts, resides of course in the absence of all interactions involving the anion, namely ion pairing, coll se to give a covalent bond, etc. Most techniques available for the production of bare cations involve the expulsion of an electron from amono-mer molecule, i.e. ph3 cally-induced initiation. The present chapter deals with these techniques and their major contributions to the understanding of the chemistry and properties of active species in cationic polymerisation. 

There is a chance for copolymerizatirai if the two compment monomers can be h( nopdymeiized by the same type of mechanism, i.e., caticmic, aniraiic, radical, oxonium ion, ete. Both isobutylene and -pinene are highly reactive catimic mraio-mers and as such can readily be polymerized by the same caticmic initiator systems, eg., AICI3, BF3, etc. to hi polymers. 

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. 

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