Bemoullian model stereochemistry

The Bemoullian model (also referred to as the zero-order Markov model) assumes that only the last monomer unit in the propagating chain end is important in determining polymer stereochemistry. Polymer stereochemistry is not affected by the penultimate unit or units... 

Having established that a particular polymerization follows Bemoullian or first-order Markov or catalyst site control behavior tells us about the mechanism by which polymer stereochemistry is determined. The Bemoullian model describes those polymerizations in which the chain end determines stereochemistry, due to interactions between either the last two units in the chain or the last unit in the chain and the entering monomer. This corresponds to the generally accepted mechanism for polymerizations proceeding in a nonco-ordinated manner to give mostly atactic polymer—ionic polymerizations in polar solvents and free-radical polymerizations. Highly isoselective and syndioselective polymerizations follow the catalyst site control model as expected. Some syndioselective polymerizations follow Markov behavior, which is indicative of a more complex form of chain end control. 

The polymer stereosequence distributions obtained by NMR analysis are often analyzed by statistical propagation models to gain insight into the propagation mechanism [Bovey, 1972, 1982 Doi, 1979a,b, 1982 Ewen, 1984 Farina, 1987 Inoue et al., 1984 Le Borgne et al., 1988 Randall, 1977 Resconi et al., 2000 Shelden et al., 1965, 1969]. Propagation models exist for both catalyst (initiator) site control (also referred to as enantiomorphic site control) and polymer chain end control. The Bemoullian and Markov models describe polymerizations where stereochemistry is determined by polymer chain end control. The catalyst site control model describes polymerizations where stereochemistry is determined by the initiator. 

You can now test the models. So far we have only talked about Bemoullian statistics, where the stereochemistry of the addition of a monomer does not depend upon the configuration at the end of the chain. Just to make sure you understand, from NMR triad information—i.e., (mm), (mr) and (rr) data—we can readily calculate the conditional probabilities P(r/m), P(m/m), P(m/r) and P(r/r) as shown in Equations 7-32. Bemouillian statistics are followed if Equations 7-33 are obeyed. 

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See also in sourсe #XX -- [ ]

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