Kinetics of Diffusion-Controlled Reactions in Polymer Melts

It is shown that in the limit of continuously flexible, Gaussian polymer chains, the first-order rate for end-to-end reactions, kcyc(t), scales as the fundamental reptation time, τᵣₑₚ. At short times t<τᵣₑₚ, kcyc(t)→(0.333τᵣₑₚ)(tτᵣₑₚ)^-1/4, while at long times, kcyc(∞)=0.363τᵣₑₚ. The analysis also gives the exact chain-length-dependent memory and reaction-rate functions in the discrete case of bead-rod chains obeying the earthworm equations of Doi and Edwards.