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

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, nA ∞ and nB , 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 ≈ QbhatnAnB 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 τ, to second order diffusion-controlled (DC) kinetics with R t ≈ xtnAnB. 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 ∼ t1/2 and R t ∼ t/(ln t) exist. Which regimes are realized depends on Qb and nB . At long times, a transition occurs to first-order DC kinetics. The reaction rate, R t ≈ xtnA, is determined by the more dilute A side, where a density depletion hole of size xt develops at the interface. For high reactive chain densities on the B side (nB R3 > 1 where R is polymer coil size), and for Qb sufficiently large, these kinetics onset before τ. Then R t ∼ t1/4 for unentangled melts, while for entangled cases consecutive regimes R t ∼ t1/4, R t ∼ t1/8, and R t ∼ t1/4 arise, some or all of which may be realized depending on Qb and nB . The final first-order regime is always governed by center of gravity diffusion, R t ∼ t1/2. 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/N1/2 (unentangled melts) or Qb ∼ 1/N3/2 (entangled).