Kinetic conditions for living and controlled free radical polymerizations mediated by reversible combination of transient propagating and persistent radicals: The ideal mechanism

A full kinetic analysis is presented for living polymerizations controlled by the reversible combination of growing propagating and persistent radicals. Analytical equations are derived for the concentrations of the radicals, the dormant and unreactive polymer chains, the monomer, the number-average degree of polymerization, and the polydispersity. In the absence of side reactions, these specify optimum ranges of rate constants of the dissociation and combination to ensure, for specific monomers, formation of products with preset molecular weights, predictable small fractions of unreactive polymer, and low polydispersities in predictable conversion times. The theoretical conclusions agree with experimental findings for alkoxyamine initiators. Consideration of borderline cases shows that a living and controlled radical polymerization can degenerate to give living polymers with no apparent control of molecular weight and polydispersity or can produce mainly unreactive polymers with regulated molecular weight and small polydispersity. The chain-length and viscosity dependence of the self-termination constant does not change the overall mechanism but does affect the polymerization rate.