Statistical analysis of copolymer sequence distribution

As an extension to this type of sequence information, it has become common practice to check for conformity of the observed sequence distribution to an appropriate statistical model. The rationale for this is that, as well as providing a more complete description of copolymer microstructure, conformity to a particular model can impart important information concerning the mechanism of polymer propagation. In addition, in favourable cases, the relative reactivities of the comonomers can also be established. The more traditional methods for assessing comonomer reactivities are significantly more laborious than NMR methods and often relatively crude. 

Some polymer systems of both academic and commercial interest are derived from chemical modification of preformed polymers. For example, poly (vinyl alcohol) is prepared by hydrolysis of poly (vinyl acetate) because vinyl alcohol monomer does not exist. NMR spectroscopy again plays an important role in characterising such materials. In cases where chemical modification is incomplete, these systems fall into the category of copolymers comprising modified and unmodified monomer repeat units. Statistical analyses of the 

The purpose of this chapter, therefore, is to describe the basic concepts of the statistical analysis of copolymer sequence distribution. The necessary relationships between various comonomer sequence abundances are introduced, along with simple statistical models based on monomer addition probabilities. The relationships between the statistical models and propagation models based on reactivity ratios are discussed. The use of these models is then illustrated by means of selected examples. Techniques for extracting sequence information from in situ NMR measurements are also described. Finally, the statistical analysis of chemically modified polymers is introduced with examples. 

The development of statistical analyses of polymers was pioneered by Bovey [1,2] and Price [3] and has also been discussed in detail by Randall [4]. Here, the intention is to discuss only the principal elements of copolymer statistics required for the analysis of the various sequence abundances observed using NMR spectroscopy. For the full derivation of copolymer statistics, the interested reader is referred to the original work of these authors. It should also be noted that most of what follows is limited to A/B copolymer systems. Whilst it is relatively straightforward to extend the analysis to copolymers containing more than two comonomers, the number of equations required to define the system increases dramatically. Furthermore, for such systems, it proves increasingly difficult to assign their NMR spectra in the detail required for complete analysis. 

1 Copolymer number-average sequence lengths and necessary relationships 

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