In situ methods and simulation techniques

In a number of the examples discussed in the preceding section, comonomer reactivity ratios were used to predict sequence distributions. A number of procedures exist for deriving reactivity ratios based on copolymer/comonomer composition data. Recently, a new method for determining reactivity ratios, based on in situ NMR measurements has been derived. This method is described. In addition, some of the mathematical techniques available to calculate sequence distributions using reactivity ratios are mentioned briefly, since their use can impinge on a number of the NMR studies of sequence distributions. 

The Mayo-Lewis equation [8] describing terminal model binary copolymerisation was given in section 2.2.3 and is also given below  

The terms A and B represent the number of moles of the two comonomers in the feed at any given instant, and and are the comonomer reactivity ratios defined earlier. The differential dA/dB is sometimes termed the instantaneous copolymer composition since it represents the composition of polymer chains forming at any instant. A variety of methods have been developed to determine the reactivity ratios. Most of these methods are based on the assumption that for conversions up to approximately 5%, the ratio of the two monomers in the feed does not change appreciably. Thus, equation (2.24) can be rewritten as 

A new method has recently been devised for determining comonomer reactivity ratios [45], following a suggestion by Maitland that proton NMR spectroscopy can be used as a convenient monitor of free-radical copolymerisation reactions performed in situ in an NMR tube [46]. From the 

For convenience, a modified form of the differential equation derived by Skeist [47] was used in this method  

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