Polymer Reaction Kinetics at Interfaces

Abstract

We study polymer reaction kinetics at interfaces. The interface of width $h$ increments the effective dimensionality by 1: Rate constants $k$ obey scaling laws as for 4-dimensional bulk reaction problems. For groups with small reactivity $Q$, $k\ensuremath{\sim}h$ and is independent of molecular weight $N$. For large $Q$, $k\ensuremath{\sim}\frac{1}{\mathrm{ln}N}$ and $k\ensuremath{\sim}\frac{1}{N\mathrm{ln}N}$ for unentangled and entangled polymers, respectively, with weak $h$ dependence. Consistent with recent experiments, we find $k$ is exponentially suppressed when copolymer product attains surface densities above a critical level, ${\ensuremath{\rho}}_{s}^{\mathrm{crit}}\ensuremath{\sim}\frac{1}{{N}^{\frac{1}{2}}}$.