Interfacial Reactions: Mixed Order Kinetics and Segregation Effects

We study A-B reaction kinetics at a fixed interface separating A and B bulks. Initially, the number of reactions ${\cal R}_t \sim t n_A^\infty n_B^\infty$ is 2nd order in the far-field densities $n_A^\infty,n_B^\infty$. First order kinetics, governed by diffusion from the dilute bulk, onset at long times: ${\cal R}_t\approx x_t n_A^\infty$ where $x_t\sim t^{1/z}$ is the rms molecular displacement. Below a critical dimension, $d<d_c=z-1$, mean field theory is invalid: a new regime appears, ${\cal R}_t\sim x_t^{d+1} n_A^\infty n_B^\infty$, and long time A-B segregation (similar to bulk $A+B\gt\emptyset$) leads to anomalous decay of interfacial densities. Numerical simulations for $z=2$ support the theory.