Bernoullian model copolymers

Note the 2 1 relationships for the triad ratios, (BAA- -AAB)/ABA and (ABB-hBBA)/BAB, which is a characteristic of Bernoullian or zero-order Markovian distributions. The calculated and observed distributions for the original model copolymer chain are given in Table 1. 

The triad distribution for the model copolymer chain is close to a random distribution but it is does not fit perfectly. The experimental error encountered in measuring triad distributions leads to the conclusion that an observed distribution is random if it is within 0.005 to 0.01 of the calculated Bernoullian distribution. 

A general purpose program has been developed for the analysis of NMR spectra of polymers. A database contains the peak assignments, stereosequence names for homopolymers or monomer sequence names for copolymers, and intensities are analyzed automatically in terms of Bernoullian or Markov statistical propagation models. A calculated spectrum is compared with the experimental spectrum until optimized probabilities, for addition of the next polymer unit, that are associated with the statistical model are produced. 

Carbon-13 nuclear magnetic resonance was used to determine the molecular structure of four copolymers of vinyl chloride and vinylidene chloride. The spectra were used to determine both monomer composition and sequence distribution. Good agreement was found between the chlorine analysis determined from wet analysis and the chlorine analysis determined by the C nmr method. The number average sequence length for vinylidene chloride measured from the spectra fit first order Markovian statistics rather than Bernoullian. The chemical shifts in these copolymers as well as their changes in areas as a function of monomer composition enable these copolymers to serve as model... 

The triad distribution in the copolymer was found to be bernoullian and is accounted for by a one-parameter model therefore, chain end control of the stereochemistry was assumed [80]. For the systems based on bipyridine, no influence of the counter-ion on the stereochemistry of the produced copolymers was found however, the catalytic activity was highest with the weakest coordinating anion [81]. Bis-chelated complexes of 2,2 -bipyridine or 1,10-phenanthroline [ Pd(N-N)2 X2 ] were efficient catalyst precursors, particularly when used in 2,2,2-tri-fluoroethanol as the solvent [82] under these conditions stabilization of the catalytic system by an oxidant is unnecessary, and very high molecular weights were obtained [83]. 

The correctness of each model for a given copolymer system can be tested and confirmed by experimental observation. In general, when Bernoullian statistics do not describe the sequence distribution, Markovian statistics do. 

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. 

Statistics of Copolymer Chains. A triad distribution is capable of giving even more microstructural information after comparing an experimental distribution to a calculated distribution having specifically defined chain statistics (3,6,15,16). The calculated statistical distributions can be random or some higher level of a so-called Markovian chain. These models are constructed on the premise of a conditional probability of finding any particular unit or sequence in a copolymer chain. In a perfectly random statistical model, there are no previous conditions required for one unit to follow any other particular unit. These types of statistical models are called Bernoullian or zero-order Markovian. For these statistical models, only mole fraction information is required to determine what the corresponding triad distribution would look like for a perfectly random copolymer, that is. 

San Roman and co-workers [161] studied the microstructure and stereochemical configuration of methacrylonitrile (N), methyl methacrylate (M), copolymers prepared by free-radical polymerisation at 60 C on the basis of the classical terminal copolymerisation model and with the assumption of Bernoullian statistics for the... 

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