Bernoullian model mechanisms

When the polymerization mechanism is known, peak intensities in the spectra of polymers with different monomer compositions can be compared with calculated intensities based on various polymerization models [e.g., first order Bernoullian (B) or first order Markovian model]. For example, if polymerization mechanism of a vinyl monomer fits a Bernoullian model, then the fractions of triads will be given by ... 

Corradini suggested a novel mechanism for syndiospecific chain-end control reactions in which the olefin migratory-insertion was assumed with 2,1-regiospecificity and in which the configuration of the last inserted monomer unit determines the configuration of the active sites in a subsequent rapid isomerization step. The satistical equations for this mechanism are equivalent to those for the chain-end control, Bernoullian model. 

As reported in section II.E, the two main mechanisms of stereocontrol in 1-olefin polymerization arise from the chirality of the catalytic site enantiomor-phic site control) and from the chirality of the last methine in the polymer chain (chain-end control). Two statistical models, based on these basic mechanisms, have been developed and used by different authors and are known as the enantiomorphic site modeP and the Bernoullian modeB ... 

Other propagation models are also possible. An example is an adaptation [48,55,65] of the Coleman-Fox [66] mechanism in which the polymerisation is considered to take place at two active sites, each with a different Bernoullian propagation probability (see chapter 2). 

Several examples of NMR studies of copolymers that exhibit Bernoullian sequence distributions but arise from non-Bernoullian mechanisms have been reported. Komoroski and Schockcor [11], for example, have characterised a range of commercial vinyl chloride (VC)/vinylidene chloride (VDC) copolymers using carbon-13 NMR spectroscopy. Although these polymers were prepared to high conversion, the monomer feed was continuously adjusted to maintain a constant comonomer composition. Full triad sequence distributions were determined for each sample. These were then compared with distributions calculated using Bernoullian and first-order Markov statistics the better match was observed with the former. Independent studies on the variation of copolymer composition with feed composition have indicated that the VDC/VC system exhibits terminal model behaviour, with reactivity ratios = 3.2 and = 0.3 [12]. As the product of these reactivity ratios is close to unity, sequence distributions that are approximately Bernoullian are expected. 

NMR m and r dyad analysis of syndiotactic polystyrenes prepared with MAO activated CpTiCb or Cp TiCl3 systems was in agreement with the Bernoullian symmetric statistical model for stereoselective propagation. The polymer microstracture is a long sequence of syndiotactic dyads with only isolated m defects and no consecutive isotactic dyads (Figure 14.17), which is consistent with a chain-end control mechanism directed by the configuration of the tertiary carbon of the last inserted styrene unit (unlike 1,3-asymmetric induction). Thus, the syndiotactic preference exerted by the chain end arises from the phenyl-phenyl repulsive interaction between the last inserted... 

Reaction stereoregulation mechanisms have been reduced to mathematical, kinetic models in several cases. A one-parameter Bernoullian statistical model accounts for the NMR methyl pentad intensities of both syndiotactic and isotactic polypropylenes obtained at subambient temperatures with homogeneous, achiral catalyst precursors. The polypropylenes have. ..rrrrrmrrrrr... and. ..mmmmmrmmmmm... microstructures respectively. The m and r deffects are consistent with the chain-end configurations being responsible for stereoregulation. Two additional models of the chain-end control type are the first- and the... 

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