The MWD function and moments are derived for a "living" polymerization process which proceeds via active and "dormant" species and where the activity is directly exchanged between these chain ends in a bimolecular reaction ("degenerative transfer"). Such a mechanism is believed to be applicable to many "living" polymerizations (e.g., anionic, group transfer, cationic, and radical). For constant monomer concentration (slow addition of monomer or low conversion), the polydispersity index, PJPn, depends on the ratio of molar concentrations of monomer and initiator, = M/Io, the degree of polymerization, Pn, and the ratio of rate constants of exchange and propagation, ß = keJkv. In a limiting case (ß > 1 and Pn » 1), Pw/Pn ~1 + 2 /(ß ). The molecular weight distributions are always narrower than those obtained for a batch process, where monomer concentration decreases during polymerization.

The kinetics of cationic polymerization is studied theoretically in accordance with a three-state mechanism which consists of two successive equilibria:  the ionization/ion collapse equilibrium between covalent species and ion pairs, and the subsequent dissociation/association equilibrium between ion pairs and free ions. The number- and weight-average degrees of polymerization and the polydispersity index (PDI), P̄ w/P̄ n, are derived. The molecular weight distribution of the polymer generated from this mechanism is generally broader than that of polymers formed via a two-state mechanism, i.e. with only one equilibrium either between covalent species and ion pairs or between covalent species and free ions. Under this general mechanism, the exchange rate parameter, β, is more complicated than that of two-state mechanisms and is a combination of the corresponding exchange rate parameters for these two mechanisms. The molecular weight distribution becomes narrower if dissociation is reduced by adding common counterions to the reaction system. Excess common ions lead to a two-state polymerization with covalent species and ion pairs only. On the other hand, if dissociation is very strong, the PDI is predominantly given by the rate of the ionization/ion collapse equilibrium unless the dissociation/association equilibrium is very much slower than the former one.

This work deals with the kinetics of polymerization processes with chain transfer to monomer and reversible formation of dormant species. Such a mechanism is typical for cationic polymerization in the presence of Lewis acids as co-initiators. The expressions of number- and weight-average degrees of polymerization and polydispersity index are derived rigorously for a mechanism with free ions as the active species, but it is also applied to other mechanisms, e.g., ion pairs as active species. Plots of polydispersity index versus monomer conversion can be easily computed on a PC computer even though the expressions for the weight-average degree of polymerization and the concentration of residual initiator consist of confluent hypergeometric functions. Numerical calculations show that the polydispersity index of the resulting polymer approaches M w/M n = 2 with increasing rate constant of chain transfer. Addition of common ions led to narrower molecular weight distributions. For the polymerization of indene with the cumyl chloride/titanium tetrachloride initiating system in methylene chloride, the calculated results of number-average degree of polymerization are in agreement with the experimental data reported in the literature.

In this work, ring opening insertion polymerization (ROIP) of ε‐caprolactone (ε‐CL) using a series of hydrogen phosphonates (H‐phosphonates) as initiators was investigated. The ROIP occurred by a coordination‐insertion mechanism containing two steps. First, the carbonyl carbon was attacked by the phosphorus atom of the H‐phosphonate tautomerization (a phosphine‐like structure) and the acyl‐oxygen bond was broken. An intermediate was formed by the coordination of the former carbonyl carbon and acyl‐oxygen of ε‐CL to phosphorus atom. Then the phosphorus‐alkoxide of H‐phosphonate was cleavaged to form acyl‐alkoxide bond. Poly(ε‐caprolactone) (PCL)‐inserted H‐phosphonates (PCL‐HPs), which was not only the product of the occurred ROIP but also the initiator for the next ROIP, were produced. After 60 min of microwave irradiation (510 W), PCL with a number‐average molar mass of 7800 g/mol and monomer conversion over 92% was obtained. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6214–6222, 2009

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