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Reaction-Diffusion Model for the A + A → O Reaction

Published online by Cambridge University Press:  15 February 2011

Katja Lindenberg,
Raoul Kopelman and
Panos Argyrakis
Katja Lindenberg
Affiliation:
Department of Chemistry and Biochemistry and Institute for Nonlinear Science, University of California at San Diego. La Jolla, CA 92093–0340
Raoul Kopelman
Affiliation:
Departments of Chemistry and Physics, The University of Michigan, Ann Arbor, MI 48109
Panos Argyrakis
Affiliation:
Department of Chemistry, The University of Michigan, Ann Arbor, MI 48109 and Department of Physics, University of Thessaloniki, GR-54006 Thessaloniki, Greece
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Abstract

We formulate an approach to the A + A → products reaction based on a reaction-diffusion model. We construct the first equations in a moment hierarchy whose first two members are the global density of A particles and the pair correlation function. We terminate the hierarchy by relating the three-particle correlation function to two-particle correlation functions and thereby obtain a set of coupled equations that turns out to be linear and hence analytically tractable.

This approach leads naturally to the proportionality of the rate of the reaction to the pair correlation function evaluated at r=a, where a is the diameter of the reacting particles. It also confirms the relation between anomalous kinetics and the deviation of the pair correlation function from that associated with a random distribution of particles.

Numerical simulations in one and two dimensions that support our theory are presented in a companion paper in this session.

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Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 366: Symposium N – Dynamics in Small Confining Systems , 1994, 377
Copyright
Copyright © Materials Research Society 1995

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