Copolymers with first-order Markov sequence distributions

2 Copolymers with first-order Markov sequence distributions 

The vast majority of copolymers described in the literature conform to the terminal model for copolymerisation and therefore exhibit sequence distributions which will in principle conform to first-order Markov statistics. Of 

Bovey and Tiers [20]. These parameters represent the (Bernoullian) probability of generating a meso dyad between a growing chain ending in x and incoming monomer y. Thus, for example, the probability of finding an isotactic MMM triad is simply given by first-order Markov probability of finding any MMM triad multiplied by 

Assuming that (Tam = ma Roman and Valero were able to determine the values of the tacticity parameters for these A/M copolymers from the NMR data = 0.24, = 0.31, (7 = = 0.41). 

Fukuda et al [22] have carried out an extensive study of the kinetics of the S/M copolymer system. They showed that, although copolymer compositions conform to the terminal model, rate constants for propagation are best represented by the penultimate model. There must therefore be some doubt over the assignments of Uebel and Dinan [18] since these were made on the premise of terminal model conformity. 

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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. 

In this work, coupled SEC-NMR analysis has been demonstrated for three samples of alginates. The NMR data have been treated with two-component 1 order Markov statistical models. The first component reflects a mostly G homopolymer, and the second con onent is a MG copolymer with an almost random or alternating sequence distribution. The relevance of the two components to the epimerization reactions has been noted. 

The microstructure of the SAN copolymer with respect to the chain sequence distribution can be found from the first-order hidden Markov model. The HMM architecture is shown in Figures 11.1A and B. The conditional dyad probabilities... 

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