STATISTICAL MODELS OF PROPAGATION in .NET

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STATISTICAL MODELS OF PROPAGATION
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Catalyst (Initiator) Site Control
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Isoselective polymerization by traditional Ziegler Natta, metallocene, and other initiators is described by the catalyst (initiator) site control model. The initiator has enantiomeric propagation sites, R and S sites, at which propagation occurs through the re and si faces of monomer (R and S monomer, respectively, if the monomer is optically active). The model is described in terms of the single parameter s [Doi, 1979a,b, 1982; Farina, 1987; Inoue et al., 1984; Le Borgne et al., 1988; Shelden et al., 1965, 1969]. Parameter s is the probability of an R or re monomer unit adding at the R site; s is also the probability of an S or si monomer unit adding at the S site. The dyad fractions are given by
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The triad fractions are given by
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The tetrad fractions are given by
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mmm 2s4 4s3 6s2 4s 1 mmr mrr 4s4 8s3 6s2 2s mrm rmr rrr 2s 4s 2s
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The pentad fractions are given by
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Syndioselective polymerization by a Cs metallocene such as Me2 C(Cp)(Flu)ZrCl2 proceeds by catalyst site control. A statistical model for syndioselective catalyst site control has been described in terms of the parameter r [Resconi et al., 2000]. Parameter r is the probability of a monomer with a given enantioface inserting at one site of the initiator; r is also the probability of the monomer with the opposite enantioface inserting at the other site of the initiator. The pentad fractions are given by
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STEREOCHEMISTRY OF POLYMERIZATION
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Application of Propagation Statistics
Experimentally obtained sequence distributions in a particular polymerization are used to determine whether the polymerization follows the Bernoullian, Markov, or catalyst site control models. The general approach is to t data on the dyad, triad, and higher sequence fractions to the appropriate equations for the different models. One needs to recognize the difference between tting and testing of data. Fitting of data involves calculating the value(s) of the appropriate probability term(s) from the sequence distributions. Testing involves determining that the sequence data are consistent or inconsistent with a particular model. All the models can be tted but not tested with dyad data. The Bernoullian and catalyst site control models require triad data as a minimum for testing; the rst-order Markov model requires tetrad data. The appropriate level of sequence data tests a model by showing the consistency or inconsistency of the Pm values (Bernoullian model) or Pmr and Prm values ( rst-order Markov), or s (or r) values (catalyst site control models). There are alternate criteria for testing the different models [Bovey, 1972; Chujo, 1967; Inoue et al., 1971, 1984]. The Bernoullian model requires
4 mm rr mr 2
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The term on the left is extremely sensitive, and this criterion should be used only with suf ciently accurate triad data. This is especially important if the polymer is very highly isotactic or syndiotactic, that is, with very small value of either (rr) or (mm). The term 4(mm)(rr)/ (mr)2 is considerably larger than one for the Markov and catalyst site control models. The rst-order Markov model requires
4 mmm rmr mmr 2 1 and 4 mrm rrr mrr 2 1 8-106
while the catalyst site control models have the criteria
2 rr 4 1 1 and 1 1 mr mr 2 rr rr 8-107
Having established that a particular polymerization follows Bernoullian or rst-order Markov or catalyst site control behavior tells us about the mechanism by which polymer stereochemistry is determined. The Bernoullian 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 noncoordinated 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. More sophisticated experimental and theoretical analysis of isoselective polymerizations have been performed by using a two-site model for propagation [Inoue et al., 1984; Wu et al., 1990]. The polymer product is fractionated into the highly isotactic, insoluble and atactic,