Copolymerization depropagation model

In contrast to the kinetic approach, deviations from the terminal model have also been treated from a thermodynamic viewpoint [Kruger et al., 1987 Lowry, 1960 Palmer et al., 2000, 2001]. Altered copolymer compositions in certain copolymerizations are accounted for in this treatment in terms of the tendency of one of the monomers (M2) to depropagate. An essential difference between the kinetic and thermodynamic treatments is that the latter implies that the copolymer composition can vary with the concentrations of the monomers. If the concentration of monomer M2 falls below its equilibrium value [M]c at the particular reaction temperature, terminal M2 units will be prone to depropagate. The result would be a... 

The ability to determine which copolymerization model best describes the behavior of a particular comonomer pair depends on the quality of the experimental data. There are many reports in the literature where different workers conclude that a different model describes the same comonomer pair. This occurs when the accuracy and precision of the composition data are insufficient to easily discriminate between the different models or composition data are not obtained over a wide range of experimental conditions (feed composition, monomer concentration, temperature). There are comonomer pairs where the behavior is not sufficiently extreme in terms of depropagation or complex participation or penultimate effect such that even with the best composition data it may not be possible to conclude that only one model fits the composition data [Hill et al., 1985 Moad et al., 1989]. 

A typical example showing that we are able to build macromolecules at will is given by C. P. Pinazzi and co-workers in the first chapter of the second section, Chapter 27. They report how model polyenes can be built and how they react. In Chapter 28 K. F. O Driscoll illustrates the limitations in polymerization. For every vinyl monomer, a ceiling temperature exists, above which depropagation exceeds polymerization. If two vinyl monomers are copolymerized at a temperature at which one depropa-gates, the polymer formed will have an unusual composition and sequence distribution. 

Ivin and Spensley (10) tested the Lowry Case II model and equations for the anionic copolymerization of vinyl mesitylene (Mi) with a-methyl-styrene at 0°C. by varying the total concentration of the two monomers while keeping their mole ratio constant. As pointed out above, theory predicts a dependence on absolute monomer concentration when depropagation occurs. Table I summarizes some of Ivin and Spensley s data. 

Yamashita et al. [157] have derived a copolymer composition equation that includes the depropj ation reaction such as might be expected in the cationic copolymerization of BCMO and THF. They consider two models. For the first one it is assumed that monomer M2 adds reversibly to both active chain ends mf and m and that depropagation by detachment of an M1 unit is neglected. The elementary reactions are then... 

It is clear from the above discussion that any physically realistic model for free-radical copolymerization kinetics should be based on the penultimate model and, depending on the system, should also incorporate various types of solvent effects and/or depropagation. The resulting model would not only be very complex, but would also contain numerous characteristic constants (ie, reactivity ratios, equilibrium constants). This poses a major problem as such parameters are difficult to... 

Scheme 1 A simplified scheme of an equilibrium binary RO copolymerization. Only the dyad model of propagation and depropagation reactions, reversible cyclizations, and segmental exchange reactions are shown. Equilibrium constants of the corresponding reactions (denoted with the capital letter /Cwith subscripts) are equal to the ratios of the corresponding rate constants. D, E, F, V, W, and Z denote copolymer units A and/or B.

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