Conversion copolymerization

The instantaneous composition of a copolymer X formed at a monomer mixture composition x coincides, provided the ideal model is applicable, with stationary vector ji of matrix Q with the elements (8). The mathematical apparatus of the theory of Markov chains permits immediately one to wright out of the expression for the probability of any sequence P Uk in macromolecules formed at given x. This provides an exhaustive solution to the problem of sequence distribution for copolymers synthesized at initial conversions p l when the monomer mixture composition x has had no time to deviate noticeably from its initial value x°. As for the high-conversion copolymerization products they evidently represent a mixture of Markovian copolymers prepared at different times, i.e. under different concentrations of monomers in the reaction system. Consequently, in order to calculate the probability of a certain sequence Uk, it is necessary to average its instantaneous value P Uk over all conversions p preceding the conversion p up to which the synthesis was conducted. 

Some other anomalies, falling well outside the boundaries of traditional theories, have been experimentally found by Semchikov, Smirnova et al. (see [44-47] and references cited therein) who examined bulk low-conversion copolymerization of about thirty pairs constituted of the commonly encountered vinyl monomers. These anomalies can be listed as follows ... 

It is easy to notice a certain formal resemblance between this expression and the expression (11) for the composition inhomogeneity of the products of high-conversion copolymerization describable by the ideal model. In both expressions angular brackets denote the operation of averaging the bracketed quantity... 

At low-conversion copolymerization in classical systems, the composition of macromolecules X whose value enters in expression (Eq. 69) does not depend on their length l, and thus the weight composition distribution / ( ) (Eq. 1) equals 5(f -X°) where X° = jt(x°). Hence, according to the theory, copolymers prepared in classical systems will be in asymptotic limit (/) -> oo monodisperse in composition. In the next approximation in small parameter 1/(1), where (/) denotes the average chemical size of macromolecules, the weight composition distribution will have a finite width. However, its dispersion specified by formula (Eq. 13) upon the replacement in it of l by (l) will be substantially less than the dispersion of distribution (Eq. 69)... 

The reactivity ratios may be evaluated by performing a series of low-conversion copolymerizations at different, monomer-feed ratios, isolating the copolymer, and determining its composition. A number of mathematical analyses have been proposed in order to provide, from the experimental data, correct values for the two unknown reactivity ratios. There is some difference of opinion as to the best method for obtaining values having quantifiable errors.84,64" However, several of... 

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... 

A method for calculating apparent reactivity ratios based on run number theory has been applied to "starved-feed" styrene/ ethyl acrylate systems. The reactivity ratios found are in agreement with those determined from solution polymerization data. The further confirmation of the observed agreement between reactivity ratios determined at low conversions and those determined by run number theory in "starved-feed" high conversion copolymerization requires the analysis of other comonomer pairs. 

At present, the kinetic parameters for prediction of copolymerization rates are scanty, except for a few low conversion copolymerizations of styrene and some acrylic comonomers. Engineering models of high conversion eopolymerizations are, however, overdetermined, in the sense that the number of input parameters (kinetie rate constants, activation energies, enthalpies of polymerization, and soon)... 

Finally, it should be noted that the above discussion refers to low-conversion copolymerizations, for which composition drift is not significant. For conversion-dependent data, the appropriate integrated composition equation should instead be fitted to the data using an error-in-variables procedure (71) to deal with the statistical uncertainties in the multiple independent variables. 

PVDF polymer is used in copolymers with TrFE in certain range of its molar ratio. This procedure will increase crystallinity ratio of the polymer up to 90%. Therefore such copolymers exhibit much stronger piezoelectric activity. The most interesting molar ratio range is 60-80% of PVDF. In that range the thickness electromechanical coupling factor kt reaches its maximum value k is a measure for the electromechanical energy conversion). Copolymerized TrFE units decrease the Curie temperature of the polymer (e.g. c = 80°C for P(60%VDF/40%TrFE) polymer). 

Copolymerizations with less hindered monomers such as acrylates, NVF, or vinyl acetate were faster and went easily to high conversion. Copolymerizations in methanol to partial conversions indicate reactivity ratios similar to those of NVF, with slightly faster conversion of either acrylates or NVF and slightly slower conversions of vinyl esters than the Michael adduct comonomers (Figure 2). 

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