# Interfacial Reactions: Mixed Order Kinetics and Segregation Effects

Source: [Interfacial Reactions: Mixed Order Kinetics and Segregation Effects](<https://www.sota2.com/research/paper/68fa24952c2a3760193a6232>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:20:15.324Z

Authors: Ben O'Shaughnessy, Dimitrios Vavylonis (2) \_\_INSTITUTION\_2\_\_ Dept. Chemical Engineering, Columbia Univ, (2) Dept. Physics, Columbia Univ)

Published: 1998-04-08T02:54:04.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9804091>)

[PDF](<https://arxiv.org/pdf/cond-mat/9804091.pdf>)