Interfacial Reactions: Mixed Order Kinetics and Segregation Effects

Abstract

We study A-B reaction kinetics at a fixed interface separating A and B bulks. Initially, the number of reactions ${\mathcal{R}}_t\sim t{n}_A^{\infty }{n}_B^{\infty }$ 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: ${\mathcal{R}}_t\approx x_t{n}_A^{\infty }$ 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, ${\mathcal{R}}_t\sim x_t^{d+1}{n}_A^{\infty }{n}_B^{\infty }$, and long time A-B segregation (similar to bulk $A+B>\varnothing$) leads to anomalous decay of interfacial densities. Numerical simulations for $z=2$ support the theory.

11 pages, 2 figures (uses fund.sty). Numerical simulation results added, minor changes. Submitted to Phys. Rev. Lett

References in corpus (4)

• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0
• Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

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