Copolymerization equation penultimate models

It has been argued that for a majority of copolymerizations, composition data can be adequately predicted by the terminal model copolymer composition equation (eqs. 5-9). However, in that composition data are not particularly good for model discrimination, any conclusion regarding the widespread applicability of the implicit penultimate model on this basis is premature. 

The terminal and penultimate models then correspond to first- and second-order Markovian statistics, respectively. But you don t actually have to know this, in the sense that we can just proceed using common sense. For example, the probability of finding the sequence ABABA in a system obeying first-order Markovian statistics (i.e., copolymerization where the terminal model applies) is given in Equations 6-31. 

To summarize, we know firstly from simple model-testing studies spanning the last 20 years that for almost all systems tested, the terminal model can be fitted to (kp) or composition data for a copolymerization system, but not both simultaneously. Secondly, more recent experimental and theoretical studies have demonstrated that the assiunption of the implicit penultimate model— that the penultimate imit affects radical reactivity but not selectivity—cannot be justified. Therefore, on the basis of existing evidence, the explicit penultimate model should replace the terminal model as the basis of free-radical copolymerization propagation kinetics, and hence the failure of the terminal model kp) equation must be taken as a failure of the terminal model and hence of the terminal model composition equation. This means that the terminal model composition equation is not physically valid for the majority of systems to which it has been apphed. 

Penultimate Group Effects Copolymerization Model. This model represents an extension of the Mayo-Lewis model in which the next to last or penultimate group is assumed to affect the reaction rate. Under this assumption the eight reactions represented by the following equations are of importance ( ) ... 

Even though the discussion has been mainly on homopolymerization, the same polymerization mechanism steps are valid for copolymerization with coordination catalysts. In this case, for a given catalyst/cocatalyst system, propagation and transfer rates depend not only on the type of coordinating monomer, but also on the type of the last monomer attached to the living polymer chain. It is easy to understand why the last monomer in the chain will affect the behavior of the incoming monomer as the reacting monomer coordinates with the active site, it has to be inserted into the carbon-metal bond and will interact with the last (and, less likely, next-to-last or penultimate) monomer unit inserted into the chain. This is called the terminal model for copolymerization and is also commonly used to describe free-radical copolymerization. In the next section it will be seen that, with a proper transformation, not only the same mechanism, but also the same polymerization kinetic equations for homopolymerization can be used directly to describe copolymerization. 

The basic kinetic equations for chain addition copolymerization are given in Table I for three termination models geometric mean (GM), phi factor (PF) and penultimate effect (PE). It Is important to note the symmetry in form created by confining the effect of choice of termination model to a single factorable function H. 

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