General Kinetic Analysis and Comparison of Molecular Weight Distributions for Various Mechanisms of Activity Exchange in Living Polymerizations

Abstract

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), P̄ w/P̄ n, are derived in a unified way. Their dependencies on three universal parameters are analyzed: (i) on the reactivity ratio of the two species, λ = k‘p/k*p, (ii) on the fraction of the more active species, α = P*/I 0, which is determined by the initial concentrations of reagents, and (iii) on a generalized exchange rate parameter, β, which quantifies the rate of exchange relative to that of propagation. The dependence of β 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 β > 1, the PDI decreases with monomer conversion, which is a common observation in many living polymerizations where 10 ≤ β ≤ 100 was determined. At full conversion, a simple relation, P̄ w/P̄ n ≈ 1 + ϑ/β, is valid, where ϑ depends on α and λ. For the common case where one species is dormant this simplifies further to P̄ w/P̄ n ≈ 1 + 1/β. Generally, the molecular weight distribution is narrower if monomer is added slowly.

“Green” Atom Transfer Radical Polymerization: From Process Design to Preparation of Well-Defined Environmentally Friendly Polymeric Materials

“…The polymer polydispersity index (PDI), which reflects the polymerization control, is given by an equation originally derived for the case of living ionic polymerization. 287,288 The dependence was later 289 modified to describe the somewhat simpler case of controlled/living radical polymerization, and it was finally generalized for all polymerizations involving exchange reactions: 290 The amount of deactivator in ICAR ATRP depends upon the value of K ATRP according to eq 12.…”

Anionic polymerization of methyl methacrylate using tetrakis[tris(dimethylamino)phosphoranylidenamino] phosphonium (P5+) as counterion in tetrahydrofuran

“…The nature of the counterion, their interaction with carbonyl groups as well as the association of ion pairs play a significant role in synthesizing well-defined poly(meth)acrylates 1,2) . The intramolecular solvation of the metal cation by the carbonyl group during propagation facilitates termination by an intramolecular Claisen condensation ("back-biting") 3,4) and slow equilibria between aggregated and nonaggregated ion pairs lead to broad molecular weight distributions 2,5) . Several new strategies have been used to circumvent the problem of termination and aggregation.…”

On the Origins of Nitroxide Mediated Polymerization (NMP) and Reversible Addition–Fragmentation Chain Transfer (RAFT)

“…RAFT process) the C tr of the transfer agent should be greater than two. [97] However, it has been shown that this limitation can be overcome by the use of a monomer feed polymerization process to reduce the rate of propagation and thereby produce narrow polydispersity polymers from a less active CTA. [68,98] The effect of various Z groups on the chain transfer activity of RAFT agents was discussed in a recent report.…”