Scalings of A + B Reaction Kinetics due to Anisotropic Confinements


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 \(\alpha = \frac{\beta }{{a - b}}\), 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.

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  1. [1]

    A. A. Ovchinnikov and Y. G. Zeldovich, Chem. Phys. B 28 215 (1978).

    CAS  Google Scholar 

  2. [2]

    K. Kang, R. Redner, Phys. Rev. Lett. 52 955 (1984).

    CAS  Article  Google Scholar 

  3. [3]

    L. W. Anacker and R. Kopelman, Phys. Rev. Lett. 58 289 (1987).

    CAS  Article  Google Scholar 

  4. [4]

    K. Lindenberg, B. J. West, and R. Kopelman, Phys. Rev. Lett. 60 1777 (1988).

    CAS  Article  Google Scholar 

  5. [5]

    A. Lin, R. Kopelman, and P. Argyrakis, Phys. Rev. E. 53 1502 (1996).

    CAS  Article  Google Scholar 

  6. [6]

    A. L. Lin, R. Kopelman and P. Argyrakis, J. Phys. Chem. A 101 802 (1997).

    CAS  Article  Google Scholar 

  7. [7]

    J. Li, Phys. Rev. E. 55 6646 (1997).

    CAS  Article  Google Scholar 

  8. [8]

    R. Kopelman, A. L. Lin, and P. Argyrakis, Phys. Lett. A 232 34 (1997).

    CAS  Article  Google Scholar 

  9. [9]

    A. L. Lin, R. Kopelman, and P. Argyrakis, Phys. Rev. E 56 6204 (1997).

    CAS  Article  Google Scholar 

  10. [10]

    D. Linde and A.Mezhlumian, Phys. Rev. D 49 1783 (1994).

    CAS  Article  Google Scholar 

  11. [11]

    J. Ahn, R. Kopelman, and P. Argyrakis, J. Chem. Phys. 110 xxxx (1999).

  12. [12]

    K. Lindenberg, P. Argyrakis, and R. Kopelman, in Fluctuations and Order: the New Synthesis, M. Millonas, ed. Springer, Berlin 1996, p. 171.

  13. [13]

    K. Lindenberg, P. Argyrakis, and R. Kopelman, J. Phys. Chem. 98 3389 (1994).

    CAS  Article  Google Scholar 

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Correspondence to Panos Argyrakis.

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Argyrakis, P., Ahn, J., Lin, A. et al. Scalings of A + B Reaction Kinetics due to Anisotropic Confinements. MRS Online Proceedings Library 543, 339–344 (1998).

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