Reaction Kinetics in Polymer Melts
نویسندگان
چکیده
We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [1], de Gennes [2], and Friedman and O’Shaughnessy [3], to arbitrary initial reactive group density n0 and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, k ∼ Q. For high Q, a transition occurs to diffusioncontrolled (DC) kinetics with k ≈ xt/t (where xt is rms monomer displacement in time t) leading to a density decay nt ≈ n0 − n 2 0x 3 t . If n0 is above the chain overlap threshold, this regime is followed by nt ≈ 1/x 3 t during which k has the same power law dependence, k ≈ xt/t, but presumably different numerical coefficient. For unentangled melts this leads to nt ∼ t −3/4 while for entangled cases successive regimes nt ∼ t , t and t may occur depending on Q, n0. Kinetics at times longer than the longest polymer relaxation time τ are always MF. If a DC regime has developed before τ then the long time rate constant is k ≈ R/τ where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. PACS numbers: 82.35.+t, 05.40.+j, 05.70.Ln
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