# Reaction Kinetics in Polymer Melts

Source: [Reaction Kinetics in Polymer Melts](<https://www.sota2.com/research/paper/68fa248e2c2a3760193a5c0e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T02:58:37.529Z

Authors: Ben O'Shaughnessy, Dimitrios Vavylonis (2) \_\_INSTITUTION\_2\_\_ Dept. Chemical Engineering, Columbia University, (2) Dept. Physics, Columbia University)

Published: 1998-05-26T08:13:21.000Z

## Abstract

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, de Gennes, and Friedman and O'Shaughnessy, to arbitrary initial reactive group density $n\_0$ and local chemical reactivity $Q$. Simple mean field (MF) kinetics apply at short times, $k \\sim Q$. For high $Q$, a transition occurs to diffusion-controlled (DC) kinetics with $k \\approx x\_t^3/t$ (where $x\_t$ is rms monomer displacement in time $t$) leading to a density decay $n\_t \\approx n\_0 - n\_0^2 x\_t^3$. If $n\_0$ exceeds the chain overlap threshold, this behavior is followed by a regime where $n\_t \\approx 1/x\_t^3$ during which $k$ has the same power law dependence in time, $k \\approx x\_t^3/t$, but possibly different numerical coefficient. For unentangled melts this gives $n\_t \\sim t^{-3/4}$ while for entangled cases one or more of the successive regimes $n\_t \\sim t^{-3/4}$, $t^{-3/8}$ and $t^{-3/4}$ may be realized depending on the magnitudes of $Q$ and $n\_0$. Kinetics at times longer than the longest polymer relaxation time $\\tau$ are always MF. If a DC regime has developed before $\\tau$ then the long time rate constant is $k \\approx R^3/\\tau$ where $R$ is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9805331>)

[PDF](<https://arxiv.org/pdf/cond-mat/9805331.pdf>)