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Scalings of A + B Reaction Kinetics due to Anisotropic Confinements

Published online by Cambridge University Press:  10 February 2011

Panos Argyrakis ,
Jaewook Ahn ,
Anna Lin  and
Raoul Kopelman
Panos Argyrakis
Affiliation:
Departments of Chemistry and Physics, University of Michigan, Ann Arbor, MI 48109-1055 Department of Physics, University of Thessaloniki, 54006 Thessaloniki, Greece
Jaewook Ahn
Affiliation:
Departments of Chemistry and Physics, University of Michigan, Ann Arbor, MI 48109-1055
Anna Lin
Affiliation:
Departments of Chemistry and Physics, University of Michigan, Ann Arbor, MI 48109-1055
Raoul Kopelman
Affiliation:
Departments of Chemistry and Physics, University of Michigan, Ann Arbor, MI 48109-1055
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Abstract

We report on the diffusion-limited A + B reaction in highly anisotropic spaces. In addition to the highly non-classical behavior of the density of reactants predicted for isotropic spaces, we observe a dimensional crossover in A + B → 0 reactions due to the geometrical compactness of the tubular 2- and 3-dimensional spaces (baguettelike structures). For slabs, we find the crossover time Tc. = Wα, which scales as , where a, b and β are given by the earlier and the late time inverse density scalings of ρ− 1 ˜-, ta and ρ−1 - tbWβ, respectively. We also obtain a critical width W, below which the chemical reaction progresses without traversing a 2- or 3-dimensional Ovchinnikov-Zeldovich reaction regime. We find that there exist different hierarchies of dimensionally forced crossovers, depending on the initial conditions and geometric restrictions. Kinetic phase diagrams are employed and exponents are given for the A + B elementary reactions in various euclidean geometries. Monte-Carlo simulations illustrate some of the kinetic hierarchies.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 543: Symposium W – Dynamics in Small Confining Systems IV , 1998 , 339
Copyright
Copyright © Materials Research Society 1999

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