Copolymerization equation depropagation

Studies by many authors, e. q. on copolymerizations of styrene with a-methylstyrene (characterized by low Tc, 334 K), appear to agree with the ideas of Lowry. Some author claim, however, that even copolymerization of this pair can be described by the simple copolymerization equation [221], Johnston and Rudin are of the opionion that the depropagation reaction is not as important in this case because only short sequences of a-methylstyrene are produced. The formation of short blocks is accompanied by relatively high polymerization enthalpy. They are thermodynamically more stable than the homopolymer and have a higher Tc. Only at considerably higher copolymerization temperatures (with the pair styrene—a-methylstyrene > 420 K) does the depropagation effect become important. 

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... 

However, with the exception of copolymerization of the three- and/or four-membered comonomers, the copolymerization of higher rings is expected to be reversible, such that four additional homo- or cross-depropagation reactions must be added (kinetic Equation 1.44). In such a situation, the traditional methods of kinetic analysis must be put on hold , as a numerical solving of the corresponding differential equations is necessary. Moreover, depending on the selectivity of the active centers, any reversible transfer reactions can interfere to various degrees with the copolymerization process. Thus, the kinetically controlled microstructure of the copolymer may differ substantially from that at equilibrium (cf Section 1.2.4). 

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