|73. Litvinenko, G. I.; Müller, A.H.E.: General Kinetic Analysis and Comparison of Molecular Weight Distributions for Various Mechanisms of Activity Exchange in Living Polymerizations, Macromolecules 30, 1253 (1997)|
The molecular weight distributions in many living (e.g. anionic, group transfer, cationic, and radical) polymerizations strongly depend on the dynamics of various equilibria between chain ends of different reactivity. A very important special case is equilibria between active and dormant centers. Various mechanisms including uni- and bimolecular isomerization (or activation/deactivation), aggregation, and direct bimolecular activity exchange ("degenerative transfer") are discussed and compared. For all these mechanisms (and for both fast and slow monomer addition), the averages of the molecular weight distribution and the polydispersity index (DPI), w/n, are derived in a unified way. Their dependencies on three universal parameters are analyzed: (i) on the reactivity ratio of the two species, = k'p/k*p, (ii) on the fraction of the more active species, = P*/I0, which is determined by the initial concentrations of reagents, and (iii) on a generalized exchange rate parameter, , which quantifies the rate of exchange relative to that of propagation. The dependence of on the initial concentrations of reagents is defined by the mechanism of exchange and can be used as a mechanistic criterion to distinguish between various possible mechanisms. For the typical case > 1, the PDI decreases with monomer conversion, which is a common observation in many living polymerizations where 10 100 was determined. At full conversion, a simple relation, w/n 1 + /, is valid, where depends on and . For the common case where one species is dormant this simplifies further to w/n 1 + 1/. Generally, the molecular weight distribution is narrower if monomer is added slowly.