From mean field to diffusion-controlled kinetics: Concentration-induced transition in reacting polymer solutions

We study irreversible interpolymeric reaction rates k in polymer solutions as a function of concentration φ. At high dilution, kinetics obey mean field theory, and screening of excluded-volume repulsions as φ increases results in a growth, k∼${\mathrm{\phi }}^{3\mathit{g}/4\mathrm{}}$, where g is the monomer contact exponent. Screening effects cause a transition to diffusion-controlled kinetics at a value ${\mathrm{\phi }}^{\mathrm{*}\mathrm{*}}$, beyond which (for entangled solutions) k decreases as k∼${\mathrm{\phi }}^{\mathrm{-}(5/8+\gamma )}$, γ being the entanglement exponent. Thus k is peaked at ${\mathrm{\phi }}^{\mathrm{*}\mathrm{*}}$ which, in agreement with experiment, is distinct from the overlap threshold.