Propagation steps Markov model

The first-order Markov model In the first-over Markov model, the probability of monomer addition depends upon the identity of the preceding monomer unit. Hence, for an A/B copolymer, there are four possible propagation steps defined by four monomer addition probabilities ... 

First-order Markov processes are therefore defined by two independent addition probabilities. Although the propagation steps shown above depict free radical polymerisation, the statistical models are equally applicable to other types of chain growth as found, for example, in ionic and Ziegler-Natta polymers (see section 2.3.4). 

Other models sometimes invoked include two-component models based on combinations of the models discussed above [5] and the complex participation model [6]. Examples of the use of these are given in section 2.3. The complex participation model is a modification of the first-order Markov model to take account of the formation of A-B comonomer complexes which compete with monomer during polymerisation. Thus, four propagation steps in addition to those shown for the first-order Markov model are required to describe addition of A-B and B-A complexes (i.e. it can add either way round) to the two types of growing chain and (either A or B). The monomer and comonomer complex addition probabilities are then related to the equilibrium constant for complex formation. As might be expected, this model has been applied particularly to systems that show a marked tendency towards alternation of their comonomers [7]. A probabilistic description of the complex participation model has been given by Cais et al [6]. 

These propagation steps are entirely analogous to those given for the first-order Markov model, except that addition probabilities have been replaced by rate constants. Mayo and Lewis derived the following differential equation to describe terminal model copolymerisation [8] ... 

The stereochemical sequences of the prevailingly syndiotactic polymers follow a perturbed first order Markov model (a strictly first order Markov model should be expected from the propagation step [22]) (20). The secondary (or Markownikow)regiospecificity of the step [22] turns primary across ethylene units with contemporary decrease of the syndiotactic content. Syndiotactic control is therefore lost whenever the last unit is achiral. 

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