Reactive Polymer Interfaces: How Reaction Kinetics Depend on Reactivity and Density of Chemical Groups

Abstract

We present a systematic theory of polymer reaction kinetics at an interface separating two immiscible melts, A and B, in each of which a fraction of chains carry reactive end groups. We consider arbitrary values of local group reactivity, Qb, and reactive group densities in either bulk, n A and n B , with the convention nA e nB . At short times reaction kinetics are second order in bulk densities. Initially, kinetics are of simple mean field type, with surface density of reaction product after time t given by R t Qbha 3 tnA nB where h is the interface width and a reactive group size. If Qb exceeds a density-dependent threshold a transition occurs, at a time less than the longest polymer relaxation time U, to second order diffusion-controlled (DC) kinetics with R t xt 4nA nB . Here xt is the rms monomer displacement. Logarithmic corrections arise in marginal cases. This leads to R t t/(ln t) for unentangled chains, while for entangled melts consecutive regimes R t t/(ln t), R t t . At a certain time scale the interface saturates with AB copolymer product and reactions are strongly suppressed. This prevents the onset of the long time first-order DC regime if the reactivity is very small, Qb < Qb † with Qb † 1/N 1/2 (unentangled melts) or Qb † 1/N 3/2 (entangled).