Kinetics of Diffusion-Controlled Reactions in Polymer Melts

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Abstract
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)−14, 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.

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