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 R(t) approximately tn(infinity)(A)n(infinity)(B) is second order in the far-field densities n(infinity)(A), n(infinity)(B). First order kinetics, governed by diffusion from the dilute bulk, onset at long times: R(t) approximately x(t)n(infinity)(A), where x(t) approximately 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, R(t) approximately x(d+1)(t)n(infinity)(A)n(infinity)(B), and long time A-B segregation (similar to bulk A+B-->0) leads to anomalous decay of interfacial densities. Numerical simulations for z = 2 support the theory.
O'Shaughnessy
B
Department of Chemical Engineering, Columbia University, New York, New York 10027, USA.
Vavylonis
D