Linear copolymers monomer reactivity ratio

Various methods have been used to obtain monomer reactivity ratios from the copolymer composition data. The most often used method involves a rearrangement of the copolymer composition equation into a form linear in the monomer reactivity ratios. Mayo and Lewis [1944] rearranged Eq. 6-12 to... 

Trying to completely avoid the technically unpleasant process of chloromethylation, Negre et al. [48, 49] prepared a linear styrene copolymer with p-vinylbenzyl chloride and then subjected the product to self-crosslinking. Alternatively to the earlier-mentioned crosslinking of linear polystyrene with MCDE, this procedure results in local inhomogeneity of crosslinks distribution, because of the uneven distribution of the two comonomers along the initial chain (the monomer reactivity ratios of vinylbenzyl chloride and styrene are 1.41 and 0.71, respectively). Nevertheless, vinylbenzyl chloride became a popular comonomer for styrene and DVB in the preparation of beaded hypercrosslinked products [50-52]. 

There is a large body of published monomer reactivity ratios summarized in reference 5. Values are typically determined from a series of low conversion experiments in which copolymer composition Fp is measured (e.g., by NMR) as a function of monomer composition, and ri and T2 estimated from fitting the data set according to Equation 3.35. The estimation is best accomplished by non-linear techniques, and a statistical analysis... 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

Another important recent contribution is the provision of a good measurement of the precision of estimated reactivity ratios. The calculation of independent standard deviations for each reactivity ratio obtained by linear least squares fitting to linear forms of the differential copolymer equations is invalid, because the two reactivity ratios are not statistically independent. Information about the precision of reactivity ratios that are determined jointly is properly conveyed by specification of joint confidence limits within which the true values can be assumed to coexist. This is represented as a closed curve in a plot of r and r2- Standard statistical techniques for such computations are impossible or too cumbersome for application to binary copolymerization data in the usual absence of estimates of reliability of the values of monomer feed and copolymer composition data. Both the nonlinear least squares and the EVM calculations provide computer-assisted estimates of such joint confidence loops [15]. 

There are several cases where NMR spectroscopy has been used to investigate copolymers which deviate from the terminal model for copolymerisation (see also chapter 3). For example, Hill and co-workers [23, 24] have examined sequence distributions in a number of low conversion styrene/acrylonitrile (S/A) copolymers using carbon-13 NMR spectroscopy. Previous studies on this copolymer system, based on examination of the variation of copolymer composition with monomer feed ratio, indicated significant deviation from the terminal model. In order to explain this deviation, propagation conforming to the penultimate (second-order Markov) and antepenultimate (third-order Markov) models had been proposed [25-27]. Others had invoked the complex participation model as the cause of deviation [28]. From their own copolymer/comonomer composition data. Hill et al [23] obtained best-fit reactivity ratios for the terminal, penultimate, and the complex participation models using non-linear methods. After application of the statistical F-test, they rejected the terminal model as an inadequate description of the data in comparison to the other two models. However, they were unable to discriminate between the penultimate and complex participation models. Attention was therefore turned to the sequence distribution of the polymer. 

The main purpose of the workers was to establish the usefulness of controlled-potential electrochemical methodology for the production of the electroinitiated chain copolymers. As expected, they found an increase in the monomer reactivities (mi and m2) with increasing potential, and a change in their relative ratio in the copolymer, but there was not a linear dependence either with or without ultrasound. 

Brar and Sunita [58] described a method for the analysis of acrylonitrile-butyl acrylate (A/B) copolymers of different monomer compositions. Copolymer compositions were determined by elemental analyses and comonomers reactivity ratios were determined using a non-linear least squares errors-in-variables model. Terminal and penultimate reactivity ratios were calculated using the observed distribution determined from C( H)-NMR spectra. The triad sequence distribution was used to calculate diad concentrations, conditional probability parameters, number-average sequence lengths and block character of the copolymers. The observed triad sequence concentrations determined from C( H)-NMR spectra agreed well with those calculated from reactivity ratios. 

Ito and Yamashita [7 , 75] have shown that Eqs. (11) —(13) can be condensed and simplified to obtain Eqs. (14) and (15), where is the reactivity ratio for the methacrylate monomer in the copolymerization system and where X is the ratio of styrene to methacrylate monomer in the copolymerization system used to prepare the copolymer studied. These equations are useful only for low conversion copolymers, but they can be integrated to predict resonance patterns for high conversion copolymers [75]. According to these equations, plots of 1/(1—Pa ) or 1 -h 2Pa/Pb vs. X should be linear and superimposable. We will term such plots I —Y plots. They can of course be used to evaluate a and... 

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