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Elementary Rate Laws of Diffusion-Limited Species in the A+T→T Reaction in Low Dimension

Published online by Cambridge University Press:  15 February 2011

Rod Schoonover  and
Raoul Kopelman
Rod Schoonover
Affiliation:
Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109
Raoul Kopelman
Affiliation:
Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109
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Abstract

Through computer simulation we look at the elementary reaction rate laws of the trapping reaction A+T→T reaction on a one-dimensional lattice. In particular, we calculate the heterogeneity exponent h of the integrated reaction rate law. However, as the reaction probability p is varied, the heterogeneity exponent becomes a function of time. We find a bifurcation of asymptotic values of h: 1/2 for reactions where p ≤ 1.0 and 0 where p=0. In addition, the usual constraints of the trapping problem have been relaxed, and we look at systems where the A's move and the T remains immobile and the reverse case, where the T moves and the A's sit.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 290: Symposium N – Dynamics in Small Confining Systems , 1992 , 255
Copyright
Copyright © Materials Research Society 1993

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References

1. Anacker, L.W. and Kopelman, R., Phys. Rev. Lett. 58 (1987) 289.Google Scholar
2. Kuzovkov, V. and Kotomin, E., Rep. Prog. Phys. 51 (1988) 1479.Google Scholar
3. Argyrakis, P. and Kopelman, R., Phys. Rev. A 45, 5814 (1992).Google Scholar
4. Meakin, P. and Stanley, H.E.,J. Phys. A 17, L173 (1984).Google Scholar
5. Havlin, S. and Ben-Avraham, D., Adv. Phys. 36, 695 (1987).Google Scholar
6. Ovchinnikov, A.A. and Zeldovich, Y.B., Chem. Phys. 28 (1978) 215.Google Scholar
7. Smoluchowski, M.v., Z Phys. Chem. 92 (1917) 129.Google Scholar
8. Rate Processes on Fractals: Theory, Simulation and Experiments, Kopelman, R., J. Stat. Phys. 42, 185 (1986).Google Scholar
9. Toussaint, D. and Wilczek, F., J. Chem. Phys. 78, 2642 (1983).Google Scholar
10. Kopelman, R., Science 241, 1620 (1988).Google Scholar
11. Schoonover, R., Ben-Avraham, D., Havlin, S., Kopelman, R. and Weiss, G., Physica A 171, 232 (1991).Google Scholar
12. Moore, John W. and Pearson, Ralph G., Kinetics and Mechanism(John Wiley & Sons, New York, 1981), p. 93.Google Scholar
13. Weiss, G., Kopelman, R. and Havlin, S., Phyvs. Rev. A 39, 466 (1989).Google Scholar