Tacticity chain statistics

With simple homopolymers this is sufficient for the purpose, but with copolymers, including stereocopolymers which arise in any monomer %quence where tactic placements are possible, the chain statistics cannot be developed by operation with U alone. Here, the copolymer sequence, even if stereoisomeric, has to be generated using Monte Cario methods and a generator matrix G. The final result of such calculations provides a dipole moment ratio o/(nm) (where n is the number of skeletal bonds carrying dipole moments m) or (wdiere z is the degree... 

An excellent way to treat such data is to use reaction probability models.(1,2) In the NMR analysis of tacticity, it is frequently possible to distinguish whether the configuration is chain-end controlled or catalytic-site controlled during polymerization. Various statistical models have been proposed. The chain-end controlled models include Bemoullian (B), and first- and second-order Markovian (Ml and M2) statistics.(1) The simplest catalytic-site controlled model is the enantiomorphic site (E) model.(3) The relationship between the chain-end and catalytic-site controlled models and possible hybrid models have been delineated in a recent article.(4)... 

Zambelli et al. reported on the mechanism of styrene polymerization [36]. They showed that the main chain of the syndiotactic polymer has a statistically trans-trans conformation. It was established then the double-bond opening mechanism in the syndiospecific polymerization of styrene involves a cis opening. The details in the control of the monomer coordination for this polymerization mechanism were examined by Newman and Malanga using detailed, 3C NMR. It was shown through the analysis of tacticity error (rmrr) that the tacticity in the polymer is chain-end controlled and that the last monomer added directs the orientation and coordination of the incoming monomer unit prior to insertion [37]. 

Two matrices that describe conformations that alternate in sequence are used to specify conformation in tactic vinyl polymers. Tacticity introduces asymmetric elements into the chain. One convention used in specifying chain asymmetry consists of distinguishing between right handed chains termed d and left handed or 1 chains. This convention, admittedly arbitrary, is borrowed from the field of optical activity. For a tactic polymer with a threefold potential (Figure 2.13), the statistical weight matrix for a d placement between neighboring bonds is... 

The use of statistical models to interpret (and to rationalize) NMR tacticity and sequence data is well established (97,98). In this volume the enantiomorphic-site model has been used by Segre et al. in their studies of polypropylene at high fields (55). A two-site model has been en loyed by Shimozawa et al. to observe the effects of internal donors m propylene polymerization (56). Other models for polyolefins have been reported in the literature, e.g., the multi-site model (99), the dual catalytic-site/chain-end model (100), the perturbed model (101), the consecutive two-site model (102), the four-component model (103), and the chain end model (104). 

By determining which statistical model is followed in a polymerization, such as Bemoullian, or Markov, or other, it should be possible to understand better the mechanism of steric control. Thus the Bernoulli model describes those reactions in which the chain ends determine the steric arrangement. These are polymerizations that are carried out under conditions that yield mostly atactic polymers. The high isotactic sequences follow the enantiomorphic site model and the high syndio-tactic ones usually follow the Markov models. 

Abe et ah have studied the conformational characteristics of a series of poly[oxy(-l-alkylethylenes)]. In the first paper a comparison of the statistical weights of various conformations in poly(propylene oxide), deduced from the solution properties of isotactic and atactic chains, were compared with conformational weights derived from a potential-energy surface, and an anomeric effect identified with a discrepancy between the two. Flexible side-chains influence the main chain in a manner which is expressible in the statistical weight matrices. The dimensions of these chains are strongly influenced by their tacticity. Polymer chains containing both sulphur and oxygen heteroatoms have received the attention of... 

Informations on the distribution of both configurational units in the chain could be obtained from C NMR study. Both methine and methyl carbons are stereosensitive but show complex patterns with several peaks. In the me thine pattern the upfield peak located at 45.8 ppm is well separated and increases with the optical activity. It was assigned to isotactic triads of configurational units of the type -RR-RR-RR-. Using a Bemouillian statistics a tentative correlation between optical activity and tacticity was established and the distribution in different triads, i.e. enantiomeric composition, evaluated. It was concluded that polymers with -RR-/-SS- ratios up to 10 are obtained. 

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