Markov model stereochemistry

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. 

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... 

The first-order markov model describes a polymerization where the penultimate unit is important in determining subsequent stereochemistry. Meso and racemic dyads can each react in two ways ... 

A second-order Markov model has also been described to show the effect on stereochemistry of the monomer unit behind the penultimate unit [Bovey, 1972],... 

Syndiotactic propagation of propylene is know to be catalyzed by homogeneous vanadium catalyst (1 ). In the polypropylene samples prepared with the homogeneous catalysts, the relative population of iso-, hetero- and syndiotactic triads is in accordance with that predicted from the first order Markov model (25, 26). There is no chiral structure around the homogeneous vanadium species. The stereochemistry of the entering monomer is controlled by the chirality of the growing chain end, in contrast with the isotactic propagation. 

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. 

Analyses of polymers to determine stereosequence distributions and understand the propagation mechanism can be carried out with NMR spectroscopy aided by statistical propagation models. 75 detailed discussion of the subject is beyond this book. The following is a brief explanation of the concepts. The Bernoulli, Markov, and Colman-Fox, models describe propagation reactions with chain end control over monomer placement. The Bernoulli model assumes that the last monomer unit in the propagating chain end determines the stereochemistry of the polymer. No consideration is given to the penultimate unit or other units further back. In such an event, two modes... 

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