Criteria for livingness and control in nitroxide-mediated and related radical polymerizations

In nitroxide mediated radical polymerizations large living and controlled polymer fractions at high conversions require equilibrium constants of the polymeric alkoxyamine dissociation-coupling cycle K =k(d)/k(c) that are smaller than K-max = k(p)[I](0)/21n(10)k(t). Perfect livingness is reached if K K-max/100. These conditions imply minimum monomer conversion times. Small polydispersity indices at moderate to large conversions result if k(d)k(c). is close to or above a limit k(d)k(c)(perf) = 9(k(p)/21n(10))(3)[M](0)(2)/[I](0)k(t). The limits depend on the propagation and termination constants (k(p), k(t)), that is, on the monomer, and on the initiator concentration [I](0). Five cases with different time evolutions of conversion, livingness and molecular weight distribution are distinguished. They explain the course of reported polymerizations. Effects of initially present persistent radicals, self- and external initiation and reaction temperature are discussed. Further, the criteria are translated to apply also to atom transfer radical polymerizations.