Scaling and Universality in Polymer Reaction Kinetics

This review highlights recent developments in the theory of reacting polymer solutions and melts, where reactive groups are attached to macromolecules. Reaction kinetics of this type govern the evolution of many polymerizations and have been extensively measured using photophysical techniques. Three related theoretical approaches are described and illustrated with examples: (1) simple scaling arguments, (2) renormalization group methods and (3) the self-consistent method of Wilemski and Fixman. AM three approaches predict that two distinct universality classes of reaction kinetics exist, with different scaling laws for rate constants k: mean field (MF) and diffusion-controlled (DC). Increasing chain length or time drives kinetics to one behavior or the other, depending only on the regime of polymer concentration ϕ. Dilute solutions (good solvents) obey MF kinetics because a pair of reactive groups in close proximity is unlikely to react; the mean number of collisions is very small. This is universally true, independently of the group chemistry. In melts, by contrast, reaction is very likely because many collisions occur and thus kinetics are intrinsically DC. In semi-dilute solutions, as ϕ increases from dilute towards the melt a transition occurs, from MF to DC kinetics. At the transition point k is peaked. A range of experimental studies are discussed and their findings compared with theory.