Intermolecular Reactions in Dilute Polymer Solutions: Nonexistence of Diffusion-Controlled Limit

Using scaling and renormalization group methods, we show that intermolecular-irreversible-reaction kinetics in polymeric liquids belong to either of two universality classes depending on concentration and solvent quality. Dilute-solution kinetics obey mean-field theory for good solvents, even for highly reactive groups: there is no “diffusion-controlled” (DC) limit. Reaction rates k thus scale as equilibrium contact probabilities; for interior groups k is related to the statistics of 3-arm and 4-arm star molecules. Unentangled melts, by contrast, exhibit intrinsically DC kinetics, whilst theta-solvents are marginal. For reacting polymers of unequal lengths, k is dominated by the smallest chain in all cases.