Polymer Reaction Kinetics at Interfaces

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 $Q$, $k\sim h$ and is independent of molecular weight $N$. For large $Q$, $k\sim \frac{1}{\ln N}$ and $k\sim \frac{1}{N\ln N}$ 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, ${\rho }_s^{\mathrm{crit}}\sim \frac{1}{N^{\frac{1}{2}}}$.